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Published work

108 published item(s)

preprint2026arXiv

StampFormer: A Physics-Guided Material-Geometry-Coupled Multimodal Model for Rapid Prediction of Physical Fields in Sheet Metal Stamping

Traditional sheet metal forming relies on time-consuming and expensive Finite Element Analysis (FEA) for design validation, a process that significantly prolongs design cycles. While surrogate models offer faster iteration, current approaches have limitations: scalar-based methods cannot capture comprehensive field-based FEA results, while existing image-based models often ignore the critical role of material properties by focusing solely on geometry. To address this gap, we develop a physics-guided deep learning framework, namely StampFormer, which simultaneously uses component geometry and material stress-strain responses to predict FEA outcomes. The StampFormer framework uses three core components to process data. A Material-Augmented Geometric Network (MAGN) first fuses geometric and material data. This information is then integrated at various levels by a Hierarchical Material Embedding Injection Unit (HMEIU) before being processed by the primary network backbone, an adapted Swin-UNet. We evaluated our model on the stamping of a crossmember panel with two simulation datasets for steel and aluminium panels, and results demonstrate that StampFormer provides high-fidelity predictions of critical physical fields - including thinning, major strain, minor strain, plastic strain, and displacement - in under a second. Compared with ground truth FEA, our model achieved an average relative error of less than 8.5% on the four 2D fields and a mean squared error of less than 1.2 mm2 for the 3D displacement field. In summary, we introduce a practical and efficient framework that integrates multimodal information, namely geometry and material properties, to provide fast and accurate predictions, enabling designers to perform real-time manufacturability assessments.

preprint2024arXiv

Advanced Unstructured Data Processing for ESG Reports: A Methodology for Structured Transformation and Enhanced Analysis

In the evolving field of corporate sustainability, analyzing unstructured Environmental, Social, and Governance (ESG) reports is a complex challenge due to their varied formats and intricate content. This study introduces an innovative methodology utilizing the "Unstructured Core Library", specifically tailored to address these challenges by transforming ESG reports into structured, analyzable formats. Our approach significantly advances the existing research by offering high-precision text cleaning, adept identification and extraction of text from images, and standardization of tables within these reports. Emphasizing its capability to handle diverse data types, including text, images, and tables, the method adeptly manages the nuances of differing page layouts and report styles across industries. This research marks a substantial contribution to the fields of industrial ecology and corporate sustainability assessment, paving the way for the application of advanced NLP technologies and large language models in the analysis of corporate governance and sustainability. Our code is available at https://github.com/linancn/TianGong-AI-Unstructure.git.

preprint2024arXiv

The Mood of the Sunlight: Visualization of the Sunlight Data for Public Art

The application of data visualization in public art attracts increasing attention. In this paper, we present the design and implementation of a visualization method for sunlight data collected over a long period of time with an industrial camera. The proposed method makes use of the saturation and value information of collected sunlight image data in Hue Saturation Value color model to show the variation of the mood of the sunlight. Specifically, we create visual patterns with a rotating planet gear, which has an intuitively consistent geometric meaning with HSV color model and the planetary motion. Due to the variation of the sunlight data over time, the generated visual pattern presents a periodic variation that corresponds to the changing mood of the sunlight. Furthermore, we also use the sunlight data to generate music as another form of data representation. Two public artworks have been created with the above visualization and auralization methods and displayed on an exhibition held at China Resources Tower, Shenzhen, China. This work is a typical practice of creating public installations with data visualization technology, giving a glimpse into the many ways science and art intersect.

preprint2022arXiv

Classifying Galaxy Morphologies with Few-Shot Learning

The taxonomy of galaxy morphology is critical in astrophysics as the morphological properties are powerful tracers of galaxy evolution. With the upcoming Large-scale Imaging Surveys, billions of galaxy images challenge astronomers to accomplish the classification task by applying traditional methods or human inspection. Consequently, machine learning, in particular supervised deep learning, has been widely employed to classify galaxy morphologies recently due to its exceptional automation, efficiency, and accuracy. However, supervised deep learning requires extensive training sets, which causes considerable workloads; also, the results are strongly dependent on the characteristics of training sets, which leads to biased outcomes potentially. In this study, we attempt Few-shot Learning to bypass the two issues. Our research adopts the dataset from Galaxy Zoo Challenge Project on Kaggle, and we divide it into five categories according to the corresponding truth table. By classifying the above dataset utilizing few-shot learning based on Siamese Networks and supervised deep learning based on AlexNet, VGG_16, and ResNet_50 trained with different volumes of training sets separately, we find that few-shot learning achieves the highest accuracy in most cases, and the most significant improvement is $21\%$ compared to AlexNet when the training sets contain 1000 images. In addition, to guarantee the accuracy is no less than 90\%, few-shot learning needs $\sim$6300 images for training, while ResNet_50 requires 13000 images. Considering the advantages stated above, foreseeably, few-shot learning is suitable for the taxonomy of galaxy morphology and even for identifying rare astrophysical objects, despite limited training sets consisting of observational data only.

preprint2022arXiv

Detection of Strongly Lensed Arcs in Galaxy Clusters with Transformers

Strong lensing in galaxy clusters probes properties of dense cores of dark matter halos in mass, studies the distant universe at flux levels and spatial resolutions otherwise unavailable, and constrains cosmological models independently. The next-generation large scale sky imaging surveys are expected to discover thousands of cluster-scale strong lenses, which would lead to unprecedented opportunities for applying cluster-scale strong lenses to solve astrophysical and cosmological problems. However, the large dataset challenges astronomers to identify and extract strong lensing signals, particularly strongly lensed arcs, because of their complexity and variety. Hence, we propose a framework to detect cluster-scale strongly lensed arcs, which contains a transformer-based detection algorithm and an image simulation algorithm. We embed prior information of strongly lensed arcs at cluster-scale into the training data through simulation and then train the detection algorithm with simulated images. We use the trained transformer to detect strongly lensed arcs from simulated and real data. Results show that our approach could achieve 99.63 % accuracy rate, 90.32 % recall rate, 85.37 % precision rate and 0.23 % false positive rate in detection of strongly lensed arcs from simulated images and could detect almost all strongly lensed arcs in real observation images. Besides, with an interpretation method, we have shown that our method could identify important information embedded in simulated data. Next step, to test the reliability and usability of our approach, we will apply it to available observations (e.g., DESI Legacy Imaging Surveys) and simulated data of upcoming large-scale sky surveys, such as the Euclid and the CSST.

preprint2022arXiv

Development of a deep learning platform for optimising sheet stamping geometries subject to manufacturing constraints

The latest sheet stamping processes enable efficient manufacturing of complex shape structural components that have high stiffness to weight ratios, but these processes can introduce defects. To assist component design for stamping processes, this paper presents a novel deep-learning-based platform for optimising 3D component geometries. The platform adopts a non-parametric modelling approach that is capable of optimising arbitrary geometries from multiple geometric parameterisation schema. This approach features the interaction of two neural networks: 1) a geometry generator and 2) a manufacturing performance evaluator. The generator predicts continuous 3D signed distance fields (SDFs) for geometries of different classes, and each SDF is conditioned on a latent vector. The zero-level-set of each SDF implicitly represents a generated geometry. Novel training strategies for the generator are introduced and include a new loss function which is tailored for sheet stamping applications. These strategies enable the differentiable generation of high quality, large scale component geometries with tight local features for the first time. The evaluator maps a 2D projection of these generated geometries to their post-stamping physical (e.g., strain) distributions. Manufacturing constraints are imposed based on these distributions and are used to formulate a novel objective function for optimisation. A new gradient-based optimisation technique is employed to iteratively update the latent vectors, and therefore geometries, to minimise this objective function and thus meet the manufacturing constraints. Case studies based on optimising box geometries subject to a sheet thinning constraint for a hot stamping process are presented and discussed. The results show that expressive geometric changes are achievable, and that these changes are driven by stamping performance.

preprint2022arXiv

Displacement calibration of optical tweezers with absolute gravitational acceleration

In recent years, levitated particles of optical traps in vacuum have shown enormous potential in precision sensor development and searching for new physics. The accuracy of the calibration relating the detected signal to absolute displacement of the trapped particle is a critical factor for absolute measurement performance. In this paper, we suggest and experimentally demonstrate a novel calibration method for optical tweezers based on free-falling particles in vacuum, where the gravitational acceleration is introduced as an absolute reference. Our work provides a calibration protocol with great certainty and traceability, which is significant in improving the accuracy of precision sensing based on optically levitated particles.

preprint2022arXiv

Distributed Deep Learning Inference Acceleration using Seamless Collaboration in Edge Computing

This paper studies inference acceleration using distributed convolutional neural networks (CNNs) in collaborative edge computing. To ensure inference accuracy in inference task partitioning, we consider the receptive-field when performing segment-based partitioning. To maximize the parallelization between the communication and computing processes, thereby minimizing the total inference time of an inference task, we design a novel task collaboration scheme in which the overlapping zone of the sub-tasks on secondary edge servers (ESs) is executed on the host ES, named as HALP. We further extend HALP to the scenario of multiple tasks. Experimental results show that HALP can accelerate CNN inference in VGG-16 by 1.7-2.0x for a single task and 1.7-1.8x for 4 tasks per batch on GTX 1080TI and JETSON AGX Xavier, which outperforms the state-of-the-art work MoDNN. Moreover, we evaluate the service reliability under time-variant channel, which shows that HALP is an effective solution to ensure high service reliability with strict service deadline.

preprint2022arXiv

Identifying outliers in astronomical images with unsupervised machine learning

Astronomical outliers, such as unusual, rare or unknown types of astronomical objects or phenomena, constantly lead to the discovery of genuinely unforeseen knowledge in astronomy. More unpredictable outliers will be uncovered in principle with the increment of the coverage and quality of upcoming survey data. However, it is a severe challenge to mine rare and unexpected targets from enormous data with human inspection due to a significant workload. Supervised learning is also unsuitable for this purpose since designing proper training sets for unanticipated signals is unworkable. Motivated by these challenges, we adopt unsupervised machine learning approaches to identify outliers in the data of galaxy images to explore the paths for detecting astronomical outliers. For comparison, we construct three methods, which are built upon the k-nearest neighbors (KNN), Convolutional Auto-Encoder (CAE)+ KNN, and CAE + KNN + Attention Mechanism (attCAE KNN) separately. Testing sets are created based on the Galaxy Zoo image data published online to evaluate the performance of the above methods. Results show that attCAE KNN achieves the best recall (78%), which is 53% higher than the classical KNN method and 22% higher than CAE+KNN. The efficiency of attCAE KNN (10 minutes) is also superior to KNN (4 hours) and equal to CAE+KNN(10 minutes) for accomplishing the same task. Thus, we believe it is feasible to detect astronomical outliers in the data of galaxy images in an unsupervised manner. Next, we will apply attCAE KNN to available survey datasets to assess its applicability and reliability.

preprint2022arXiv

Illumination-Invariant Active Camera Relocalization for Fine-Grained Change Detection in the Wild

Active camera relocalization (ACR) is a new problem in computer vision that significantly reduces the false alarm caused by image distortions due to camera pose misalignment in fine-grained change detection (FGCD). Despite the fruitful achievements that ACR can support, it still remains a challenging problem caused by the unstable results of relative pose estimation, especially for outdoor scenes, where the lighting condition is out of control, i.e., the twice observations may have highly varied illuminations. This paper studies an illumination-invariant active camera relocalization method, it improves both in relative pose estimation and scale estimation. We use plane segments as an intermediate representation to facilitate feature matching, thus further boosting pose estimation robustness and reliability under lighting variances. Moreover, we construct a linear system to obtain the absolute scale in each ACR iteration by minimizing the image warping error, thus, significantly reduce the time consume of ACR process, it is nearly $1.6$ times faster than the state-of-the-art ACR strategy. Our work greatly expands the feasibility of real-world fine-grained change monitoring tasks for cultural heritages. Extensive experiments tests and real-world applications verify the effectiveness and robustness of the proposed pose estimation method using for ACR tasks.

preprint2022arXiv

Improved proof-by-contraction method and relative homologous entropy inequalities

The celebrated holographic entanglement entropy triggered investigations on the connections between quantum information theory and quantum gravity. An important achievement is that we have gained more insights into the quantum states. It allows us to diagnose whether a given quantum state is a holographic state, a state whose bulk dual admits semiclassical geometrical description. The effective tool of this kind of diagnosis is holographic entropy cone (HEC), an entropy space bounded by holographic entropy inequalities allowed by the theory. To fix the HEC and to prove a given holographic entropy inequality, a proof-by-contraction technique has been developed. This method heavily depends on a contraction map $f$, which is very difficult to construct especially for more-region ($n\geq 4$) cases. In this work, we develop a general and effective rule to rule out most of the cases such that $f$ can be obtained in a relatively simple way. In addition, we extend the whole framework to relative homologous entropy, a generalization of holographic entanglement entropy that is suitable for characterizing the entanglement of mixed states.

preprint2022arXiv

Mass Testing and Characterization of 20-inch PMTs for JUNO

Main goal of the JUNO experiment is to determine the neutrino mass ordering using a 20kt liquid-scintillator detector. Its key feature is an excellent energy resolution of at least 3 % at 1 MeV, for which its instruments need to meet a certain quality and thus have to be fully characterized. More than 20,000 20-inch PMTs have been received and assessed by JUNO after a detailed testing program which began in 2017 and elapsed for about four years. Based on this mass characterization and a set of specific requirements, a good quality of all accepted PMTs could be ascertained. This paper presents the performed testing procedure with the designed testing systems as well as the statistical characteristics of all 20-inch PMTs intended to be used in the JUNO experiment, covering more than fifteen performance parameters including the photocathode uniformity. This constitutes the largest sample of 20-inch PMTs ever produced and studied in detail to date, i.e. 15,000 of the newly developed 20-inch MCP-PMTs from Northern Night Vision Technology Co. (NNVT) and 5,000 of dynode PMTs from Hamamatsu Photonics K. K.(HPK).

preprint2022arXiv

Neural Program Synthesis with Query

Aiming to find a program satisfying the user intent given input-output examples, program synthesis has attracted increasing interest in the area of machine learning. Despite the promising performance of existing methods, most of their success comes from the privileged information of well-designed input-output examples. However, providing such input-output examples is unrealistic because it requires the users to have the ability to describe the underlying program with a few input-output examples under the training distribution. In this work, we propose a query-based framework that trains a query neural network to generate informative input-output examples automatically and interactively from a large query space. The quality of the query depends on the amount of the mutual information between the query and the corresponding program, which can guide the optimization of the query framework. To estimate the mutual information more accurately, we introduce the functional space (F-space) which models the relevance between the input-output examples and the programs in a differentiable way. We evaluate the effectiveness and generalization of the proposed query-based framework on the Karel task and the list processing task. Experimental results show that the query-based framework can generate informative input-output examples which achieve and even outperform well-designed input-output examples.

preprint2022arXiv

On the dual relation in the Hawking--Page phase transition of the black holes in a cavity

The Hawking--Page phase transitions of the $d$-dimensional Schwarzschild and charged black holes are explored in a cavity. The phase transition temperature $T_{\rm HP}$, the minimum black hole temperature $T_0$, and the Gibbs free energy $G$ are systematically calculated. A dual relation for the Schwarzschild black holes in the anti-de Sitter space, $T_{\rm HP}(d)=T_0(d+1)$, is found to be also approximately valid in the cavity case to a high precision, and this relation can be further generalized to the charged black holes in a suitable form. Our work reveals the universal properties of the black holes in different extended phase spaces and motivates further studies on their thermodynamic behaviors that are sensitive to specific boundary conditions, like the terminal points in the $G$--$T$ curves.

preprint2022arXiv

On value distribution of certain delay-differential polynomials

Given an entire function $f$ of finite order $ρ$, let $L(z,f)=\sum_{j=0}^{m}b_{j}(z)f^{(k_{j})}(z+c_{j})$ be a linear delay-differential polynomial of $f$ with small coefficients in the sense of $O(r^{λ+\varepsilon})+S(r,f)$, $λ<ρ$. Provided $α$, $β$ be similar small functions, we consider the zero distribution of $L(z,f)-αf^{n}-β$ for $n\geq 3$ and $n=2$, respectively. Our results are improvements and complements of Chen(Abstract Appl. Anal., 2011, 2011: ID239853, 1--9), and Laine (J. Math. Anal. Appl. 2019, 469(2): 808--826.), etc.

preprint2022arXiv

Restarted randomized surrounding methods for solving large linear equations

A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the randomized row selection rule and the expectation convergence rate is also addressed. Numerical experiments further demonstrate that the proposed algorithms are efficient and outperform the existing method for over-determined and under-determined linear equation, as well as in the application of image processing.

preprint2022arXiv

Robust Action Governor for Uncertain Piecewise Affine Systems with Non-convex Constraints and Safe Reinforcement Learning

The action governor is an add-on scheme to a nominal control loop that monitors and adjusts the control actions to enforce safety specifications expressed as pointwise-in-time state and control constraints. In this paper, we introduce the Robust Action Governor (RAG) for systems the dynamics of which can be represented using discrete-time Piecewise Affine (PWA) models with both parametric and additive uncertainties and subject to non-convex constraints. We develop the theoretical properties and computational approaches for the RAG. After that, we introduce the use of the RAG for realizing safe Reinforcement Learning (RL), i.e., ensuring all-time constraint satisfaction during online RL exploration-and-exploitation process. This development enables safe real-time evolution of the control policy and adaptation to changes in the operating environment and system parameters (due to aging, damage, etc.). We illustrate the effectiveness of the RAG in constraint enforcement and safe RL using the RAG by considering their applications to a soft-landing problem of a mass-spring-damper system.

preprint2022arXiv

Survey on Evolutionary Deep Learning: Principles, Algorithms, Applications and Open Issues

Over recent years, there has been a rapid development of deep learning (DL) in both industry and academia fields. However, finding the optimal hyperparameters of a DL model often needs high computational cost and human expertise. To mitigate the above issue, evolutionary computation (EC) as a powerful heuristic search approach has shown significant merits in the automated design of DL models, so-called evolutionary deep learning (EDL). This paper aims to analyze EDL from the perspective of automated machine learning (AutoML). Specifically, we firstly illuminate EDL from machine learning and EC and regard EDL as an optimization problem. According to the DL pipeline, we systematically introduce EDL methods ranging from feature engineering, model generation, to model deployment with a new taxonomy (i.e., what and how to evolve/optimize), and focus on the discussions of solution representation and search paradigm in handling the optimization problem by EC. Finally, key applications, open issues and potentially promising lines of future research are suggested. This survey has reviewed recent developments of EDL and offers insightful guidelines for the development of EDL.

preprint2022arXiv

The Quasar Candidates Catalogs of DESI Legacy Imaging Survey Data Release 9

Quasars can be used to measure baryon acoustic oscillations at high redshift, which are considered as direct tracers of the most distant large-scale structures in the Universe. It is fundamental to select quasars from observations before implementing the above research. This work focuses on creating a catalog of quasar candidates based on photometric data to provide primary priors for further object classification with spectroscopic data in the future, such as The Dark Energy Spectroscopic Instrument (DESI) Survey. We adopt a machine learning algorithm (Random Forest, RF) for quasar identification. The training set includes $651,073$ positives and $1,227,172$ negatives, in which the photometric information are from DESI Legacy Imaging Surveys (DESI-LIS) \& Wide-field Infrared Survey Explore (WISE), and the labels are from a database of spectroscopically confirmed quasars based on Sloan Digital Sky Survey (SDSS) and the Set of Identifications \& Measurements and Bibliography for Astronomical Data (SIMBAD). The trained RF model is applied to point-like sources in DESI-LIS Data Release 9. To quantify the classifier's performance, we also inject a testing set into the to-be-applied data. Eventually, we obtained $1,953,932$ Grade-A quasar candidates and $22,486, 884$ Grade-B quasar candidates out of $425,540,269$ sources ($\sim 5.7\%$). The catalog covers $\sim 99\%$ of quasars in the to-be-applied data by evaluating the completeness of the classification on the testing set. The statistical properties of the candidates agree with that given by the method of color-cut selection. Our catalog can intensely decrease the workload for confirming quasars with the upcoming DESI data by eliminating enormous non-quasars but remaining high completeness. All data in this paper is publicly available online.

preprint2021arXiv

Auto-identification of unphysical source reconstructions in strong gravitational lens modelling

With the advent of next-generation surveys and the expectation of discovering huge numbers of strong gravitational lens systems, much effort is being invested into developing automated procedures for handling the data. The several orders of magnitude increase in the number of strong galaxy-galaxy lens systems is an insurmountable challenge for traditional modelling techniques. Whilst machine learning techniques have dramatically improved the efficiency of lens modelling, parametric modelling of the lens mass profile remains an important tool for dealing with complex lensing systems. In particular, source reconstruction methods are necessary to cope with the irregular structure of high-redshift sources. In this paper, we consider a Convolutional Neural Network (CNN) that analyses the outputs of semi-analytic methods which parametrically model the lens mass and linearly reconstruct the source surface brightness distribution. We show the unphysical source reconstructions that arise as a result of incorrectly initialised lens models can be effectively caught by our CNN. Furthermore, the CNN predictions can be used to automatically re-initialise the parametric lens model, avoiding unphysical source reconstructions. The CNN, trained on reconstructions of lensed Sérsic sources, accurately classifies source reconstructions of the same type with a precision $P > 0.99$ and recall $R > 0.99$. The same CNN, without re-training, achieves $P=0.89$ and $R=0.89$ when classifying source reconstructions of more complex lensed HUDF sources. Using the CNN predictions to re-initialise the lens modelling procedure, we achieve a 69 per cent decrease in the occurrence of unphysical source reconstructions. This combined CNN and parametric modelling approach can greatly improve the automation of lens modelling.

preprint2021arXiv

Beating humans in a penny-matching game by leveraging cognitive hierarchy theory and Bayesian learning

It is a long-standing goal of artificial intelligence (AI) to be superior to human beings in decision making. Games are suitable for testing AI capabilities of making good decisions in non-numerical tasks. In this paper, we develop a new AI algorithm to play the penny-matching game considered in Shannon's "mind-reading machine" (1953) against human players. In particular, we exploit cognitive hierarchy theory and Bayesian learning techniques to continually evolve a model for predicting human player decisions, and let the AI player make decisions according to the model predictions to pursue the best chance of winning. Experimental results show that our AI algorithm beats 27 out of 30 volunteer human players.

preprint2021arXiv

Coordinated Receding-Horizon Control of Battery Electric Vehicle Speed and Gearshift Using Relaxed Mixed Integer Nonlinear Programming

In this paper, we propose an approach to coordinated receding-horizon control of vehicle speed and transmission gearshift for automated battery electric vehicles (BEVs) to achieve improved energy efficiency. The introduction of multi-speed transmissions in BEVs creates an opportunity to manipulate the operating point of electric motors under given vehicle speed and acceleration command, thus providing the potential to further improve the energy efficiency. However, co-optimization of vehicle speed and transmission gearshift leads to a mixed integer nonlinear program (MINLP), solving which can be computationally very challenging. In this paper, we propose a novel continuous relaxation technique to treat such MINLPs that makes it possible to compute solutions with conventional nonlinear programming solvers. After analyzing its theoretical properties, we use it to solve the optimization problem involved in coordinated receding-horizon control of BEV speed and gearshift. Through simulation studies, we show that co-optimizing vehicle speed and transmission gearshift can achieve considerably greater energy efficiency than optimizing them sequentially, and the proposed relaxation technique can reduce the online computational cost to a level that is comparable to the time available for real-time implementation.

preprint2021arXiv

Damage accumulation during high temperature fatigue of Ti/SiC$_f$ metal matrix composites under different stress amplitudes

The damage mechanisms and load redistribution of high strength TC17 titanium alloy/unidirectional SiC fibre composite (fibre diameter = 100 $μ$m) under high temperature (350 °C) fatigue cycling have been investigated in situ using synchrotron X-ray computed tomography (CT) and X-ray diffraction (XRD) for high cycle fatigue (HCF) under different stress amplitudes. The three-dimensional morphology of the crack and fibre fractures has been mapped by CT. During stable growth, matrix cracking dominates with the crack deflecting (by 50-100 $μ$m in height) when bypassing bridging fibres. A small number of bridging fibres have fractured close to the matrix crack plane especially under relatively high stress amplitude cycling. Loading to the peak stress led to rapid crack growth accompanied by a burst of fibre fractures. Many of the fibre fractures occurred 50-300 $μ$m from the matrix crack plane during rapid growth, in contrast to that in the stable growth stage, leading to extensive fibre pull-out on the fracture surface. The changes in fibre loading, interfacial stress, and the extent of fibre-matrix debonding in the vicinity of the crack have been mapped for the fatigue cycle and after the rapid growth by high spatial resolution XRD. The fibre/matrix interfacial sliding extends up to 600 $μ$m (in the stable growth zone) or 700 $μ$m (in the rapid growth zone) either side of the crack plane. The direction of interfacial shear stress reverses with the loading cycle, with the maximum frictional sliding stress reaching ~55 MPa in both the stable growth and rapid growth regimes.

preprint2021arXiv

Hawking--Page phase transitions in four-dimensional Einstein--Gauss--Bonnet gravity

The Hawking-Page (HP) phase transitions of the anti-de Sitter black holes in the extended phase space are studied in a novel four-dimensional Einstein-Gauss-Bonnet (4EGB) gravity, which is proposed by rescaling the Gauss--Bonnet (GB) coupling constant $α\toα/(d-4)$ in $d$ dimensions and redefining the four-dimensional gravity in the limit $d \to 4$. The GB term shows nontrivial contributions to both black hole mass and entropy simultaneously, and decreases the HP phase transition temperature $T_{\rm HP}$. Moreover, the HP phase transitions can happen only within a range of pressure in the 4EGB gravity. For the charged black holes, $T_{\rm HP}$ also decreases with the electric potential in the grand canonical ensemble. A general discussion of the HP phase transitions in the Einstein, GB, and 4EGB gravities is also presented.

preprint2021arXiv

JUNO Physics and Detector

The Jiangmen Underground Neutrino Observatory (JUNO) is a 20 kton LS detector at 700-m underground. An excellent energy resolution and a large fiducial volume offer exciting opportunities for addressing many important topics in neutrino and astro-particle physics. With 6 years of data, the neutrino mass ordering can be determined at 3-4 sigma and three oscillation parameters can be measured to a precision of 0.6% or better by detecting reactor antineutrinos. With 10 years of data, DSNB could be observed at 3-sigma; a lower limit of the proton lifetime of 8.34e33 years (90% C.L.) can be set by searching for p->nu_bar K^+; detection of solar neutrinos would shed new light on the solar metallicity problem and examine the vacuum-matter transition region. A core-collapse supernova at 10 kpc would lead to ~5000 IBD and ~2000 (300) all-flavor neutrino-proton (electron) scattering events. Geo-neutrinos can be detected with a rate of ~400 events/year. We also summarize the final design of the JUNO detector and the key R&D achievements. All 20-inch PMTs have been tested. The average photon detection efficiency is 28.9% for the 15,000 MCP PMTs and 28.1% for the 5,000 dynode PMTs, higher than the JUNO requirement of 27%. Together with the >20 m attenuation length of LS, we expect a yield of 1345 p.e. per MeV and an effective energy resolution of 3.02%/\sqrt{E (MeV)}$ in simulations. The underwater electronics is designed to have a loss rate <0.5% in 6 years. With degassing membranes and a micro-bubble system, the radon concentration in the 35-kton water pool could be lowered to <10 mBq/m^3. Acrylic panels of radiopurity <0.5 ppt U/Th are produced. The 20-kton LS will be purified onsite. Singles in the fiducial volume can be controlled to ~10 Hz. The JUNO experiment also features a double calorimeter system with 25,600 3-inch PMTs, a LS testing facility OSIRIS, and a near detector TAO.

preprint2021arXiv

Kinematics and star formation toward W33: a central hub as a hub--filament system

We performed a large-scale mapping observation toward the W33 complex and its surroundings, covering an area of $1.3^\circ \times 1.0^\circ$ , in $^{12}$CO (1-0), $^{13}$CO (1-0), and C$^{18}$O (1-0) lines from the Purple Mountain Observatory (PMO). We found a new hub--filament system ranging from 30 to 38.5 \kms located at the W33 complex. Three supercritical filaments are directly converging into the central hub W33. Velocity gradients are detected along the filaments and the accretion rates are in order of $\rm 10^{-3}\,M_\odot\, yr^{-1}$. The central hub W33 has a total mass of $\rm\sim 1.8\times10^5\,M_\odot$, accounting for $\sim 60\%$ of the mass of the hub--filament system. This indicates that the central hub is the mass reservoir of the hub-filament system. Furthermore, 49 ATLASGAL clumps are associated with the hub--filament system. We find $57\%$ of the clumps to be situated in the central hub W33 and clustered at the intersections between the filaments and the W33 complex. Moreover, the distribution of Class I young stellar objects (YSOs) forms a structure resembling the hub--filament system and peaks at where the clumps group; it seems to suggest that the mechanisms of clump formation and star formation in this region are correlated. Gas flows along the filaments are likely to feed the materials into the intersections and lead to the clustering and formation of the clumps in the hub--filament system W33. The star formation in the intersections between the filaments and the W33 complex might be triggered by the motion of gas converging into the intersections.

preprint2021arXiv

Optimization of graded filleted lattice structures subject to yield and buckling constraints

To reduce the stress concentration and ensure the structural safety for lattice structure designs, in this paper, a new optimization framework is developed for the optimal design of graded lattice structures, innovatively integrating fillet designs as well as yield and elastic buckling constraints. Both strut and fillet radii are defined as design variables. Homogenization method is employed to characterize the effective elastic constants and yield stresses of the lattice metamaterials. Metamaterial models are developed to represent the relationships between the metamaterial effective properties and lattice geometric variables. A yield constraint, based on the modified Hills yield criterion, is developed as a function of relative strut radii and fillet parameters. An elastic buckling constraint, based on the Euler buckling formula and the Johnson formula, is developed as a function of relative strut radii. Both yield and buckling constraints are integrated into an optimization problem formulation; a new optimization framework is proposed and a case study of minimizing the compliance of a Messerschmitt-Bolkow-Blohm beam is conducted. The yield and buckling constraints guarantee the safety of the optimized beams composed of BCC and PC lattices. Reductions in compliance and stress concentration are achieved by the optimized MBB beams.

preprint2021arXiv

Some results on transcendental entire solutions of certain nonlinear differential-difference equations

In this paper, we study the transcendental entire solutions for the nonlinear differential-difference equations of the forms: $f^{2}(z)+\widetildeω f(z)f'(z)+q(z)e^{Q(z)}f(z+c)=u(z)e^{v(z)}$, and $f^{n}(z)+ωf^{n-1}(z)f'(z)+q(z)e^{Q(z)}f(z+c)=p_{1}e^{λ_{1} z}+p_{2}e^{λ_{2} z}, \quad n\geq 3,$ where $ω$ is a constant, $\widetildeω, c, λ_{1}, λ_{2}, p_{1}, p_{2}$ are non-zero constants, $q, Q, u, v$ are polynomials such that $Q,v$ are not constants and $q,u\not\equiv0$. Our results are improvements and complements of some previous results.

preprint2021arXiv

The LSST DESC DC2 Simulated Sky Survey

We describe the simulated sky survey underlying the second data challenge (DC2) carried out in preparation for analysis of the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) by the LSST Dark Energy Science Collaboration (LSST DESC). Significant connections across multiple science domains will be a hallmark of LSST; the DC2 program represents a unique modeling effort that stresses this interconnectivity in a way that has not been attempted before. This effort encompasses a full end-to-end approach: starting from a large N-body simulation, through setting up LSST-like observations including realistic cadences, through image simulations, and finally processing with Rubin's LSST Science Pipelines. This last step ensures that we generate data products resembling those to be delivered by the Rubin Observatory as closely as is currently possible. The simulated DC2 sky survey covers six optical bands in a wide-fast-deep (WFD) area of approximately 300 deg^2 as well as a deep drilling field (DDF) of approximately 1 deg^2. We simulate 5 years of the planned 10-year survey. The DC2 sky survey has multiple purposes. First, the LSST DESC working groups can use the dataset to develop a range of DESC analysis pipelines to prepare for the advent of actual data. Second, it serves as a realistic testbed for the image processing software under development for LSST by the Rubin Observatory. In particular, simulated data provide a controlled way to investigate certain image-level systematic effects. Finally, the DC2 sky survey enables the exploration of new scientific ideas in both static and time-domain cosmology.

preprint2020arXiv

A Game Theoretic Approach for Parking Spot Search with Limited Parking Lot Information

We propose a game theoretic approach to address the problem of searching for available parking spots in a parking lot and picking the ``optimal'' one to park. The approach exploits limited information provided by the parking lot, i.e., its layout and the current number of cars in it. Considering the fact that such information is or can be easily made available for many structured parking lots, the proposed approach can be applicable without requiring major updates to existing parking facilities. For large parking lots, a sampling-based strategy is integrated with the proposed approach to overcome the associated computational challenge. The proposed approach is compared against a state-of-the-art heuristic-based parking spot search strategy in the literature through simulation studies and demonstrates its advantage in terms of achieving lower cost function values.

preprint2020arXiv

A Neural Architecture Search based Framework for Liquid State Machine Design

Liquid State Machine (LSM), also known as the recurrent version of Spiking Neural Networks (SNN), has attracted great research interests thanks to its high computational power, biological plausibility from the brain, simple structure and low training complexity. By exploring the design space in network architectures and parameters, recent works have demonstrated great potential for improving the accuracy of LSM model with low complexity. However, these works are based on manually-defined network architectures or predefined parameters. Considering the diversity and uniqueness of brain structure, the design of LSM model should be explored in the largest search space possible. In this paper, we propose a Neural Architecture Search (NAS) based framework to explore both architecture and parameter design space for automatic dataset-oriented LSM model. To handle the exponentially-increased design space, we adopt a three-step search for LSM, including multi-liquid architecture search, variation on the number of neurons and parameters search such as percentage connectivity and excitatory neuron ratio within each liquid. Besides, we propose to use Simulated Annealing (SA) algorithm to implement the three-step heuristic search. Three datasets, including image dataset of MNIST and NMNIST and speech dataset of FSDD, are used to test the effectiveness of our proposed framework. Simulation results show that our proposed framework can produce the dataset-oriented optimal LSM models with high accuracy and low complexity. The best classification accuracy on the three datasets is 93.2%, 92.5% and 84% respectively with only 1000 spiking neurons, and the network connections can be averagely reduced by 61.4% compared with a single LSM. Moreover, we find that the total quantity of neurons in optimal LSM models on three datasets can be further reduced by 20% with only about 0.5% accuracy loss.

preprint2020arXiv

Action Governor for Discrete-Time Linear Systems with Non-Convex Constraints

This paper introduces an add-on, supervisory scheme, referred to as Action Governor (AG), for discrete-time linear systems to enforce exclusion-zone avoidance requirements. It does so by monitoring, and minimally modifying when necessary, the nominal control signal to a constraint-admissible one. The AG operates based on set-theoretic techniques and online optimization. This paper establishes its theoretical foundation, discusses its computational realization, and uses two simulation examples to illustrate its effectiveness.

preprint2020arXiv

Domain Priori Knowledge based Integrated Solution Design for Internet of Services

Various types of services, such as web APIs, IoT services, O2O services, and many others, have flooded on the Internet. Interconnections among these services have resulted in a new phenomenon called "Internet of Services" (IoS). By IoS,people don't need to request multiple services by themselves to fulfill their daily requirements, but it is an IoS platform that is responsible for constructing integrated solutions for them. Since user requirements (URs) are usually coarse-grained and transboundary, IoS platforms have to integrate services from multiple domains to fulfill the requirements. Considering there are too many available services in IoS, a big challenge is how to look for a tradeoff between the construction efficiency and the precision of final solutions. For this challenge, we introduce a framework and a platform for transboundary user requirement oriented solution design in IoS. The main idea is to make use of domain priori knowledge derived from the commonness and similarities among massive historical URs and among historical integrated service solutions(ISSs). Priori knowledge is classified into three types: requirement patterns (RPs), service patterns (SPs), and probabilistic matching matrix (PMM) between RPs and SPs. A UR is modeled in the form of an intention tree (ITree) along with a set of constraints on intention nodes, and then optimal RPs are selected to cover the I-Tree as much as possible. By taking advantage of the PMM, a set of SPs are filtered out and composed together to form the final ISS. Finally, the design of a platform supporting the above process is introduced.

preprint2020arXiv

End-to-End Learnable Geometric Vision by Backpropagating PnP Optimization

Deep networks excel in learning patterns from large amounts of data. On the other hand, many geometric vision tasks are specified as optimization problems. To seamlessly combine deep learning and geometric vision, it is vital to perform learning and geometric optimization end-to-end. Towards this aim, we present BPnP, a novel network module that backpropagates gradients through a Perspective-n-Points (PnP) solver to guide parameter updates of a neural network. Based on implicit differentiation, we show that the gradients of a "self-contained" PnP solver can be derived accurately and efficiently, as if the optimizer block were a differentiable function. We validate BPnP by incorporating it in a deep model that can learn camera intrinsics, camera extrinsics (poses) and 3D structure from training datasets. Further, we develop an end-to-end trainable pipeline for object pose estimation, which achieves greater accuracy by combining feature-based heatmap losses with 2D-3D reprojection errors. Since our approach can be extended to other optimization problems, our work helps to pave the way to perform learnable geometric vision in a principled manner. Our PyTorch implementation of BPnP is available on http://github.com/BoChenYS/BPnP.

preprint2020arXiv

Estimation of genomic characteristics by analyzing k-mer frequency in de novo genome projects

Background: With the fast development of next generation sequencing technologies, increasing numbers of genomes are being de novo sequenced and assembled. However, most are in fragmental and incomplete draft status, and thus it is often difficult to know the accurate genome size and repeat content. Furthermore, many genomes are highly repetitive or heterozygous, posing problems to current assemblers utilizing short reads. Therefore, it is necessary to develop efficient assembly-independent methods for accurate estimation of these genomic characteristics. Results: Here we present a framework for modeling the distribution of k-mer frequency from sequencing data and estimating the genomic characteristics such as genome size, repeat structure and heterozygous rate. By introducing novel techniques of k-mer individuals, float precision estimation, and proper treatment of sequencing error and coverage bias, the estimation accuracy of our method is significantly improved over existing methods. We also studied how the various genomic and sequencing characteristics affect the estimation accuracy using simulated sequencing data, and discussed the limitations on applying our method to real sequencing data. Conclusion: Based on this research, we show that the k-mer frequency analysis can be used as a general and assembly-independent method for estimating genomic characteristics, which can improve our understanding of a species genome, help design the sequencing strategy of genome projects, and guide the development of assembly algorithms. The programs developed in this research are written using C/C++, and freely accessible at Github URL (https://github.com/fanagislab/GCE) or BGI ftp ( ftp://ftp.genomics.org.cn/pub/gce).

preprint2020arXiv

Feasibility and physics potential of detecting $^8$B solar neutrinos at JUNO

The Jiangmen Underground Neutrino Observatory~(JUNO) features a 20~kt multi-purpose underground liquid scintillator sphere as its main detector. Some of JUNO's features make it an excellent experiment for $^8$B solar neutrino measurements, such as its low-energy threshold, its high energy resolution compared to water Cherenkov detectors, and its much large target mass compared to previous liquid scintillator detectors. In this paper we present a comprehensive assessment of JUNO's potential for detecting $^8$B solar neutrinos via the neutrino-electron elastic scattering process. A reduced 2~MeV threshold on the recoil electron energy is found to be achievable assuming the intrinsic radioactive background $^{238}$U and $^{232}$Th in the liquid scintillator can be controlled to 10$^{-17}$~g/g. With ten years of data taking, about 60,000 signal and 30,000 background events are expected. This large sample will enable an examination of the distortion of the recoil electron spectrum that is dominated by the neutrino flavor transformation in the dense solar matter, which will shed new light on the tension between the measured electron spectra and the predictions of the standard three-flavor neutrino oscillation framework. If $Δm^{2}_{21}=4.8\times10^{-5}~(7.5\times10^{-5})$~eV$^{2}$, JUNO can provide evidence of neutrino oscillation in the Earth at the about 3$σ$~(2$σ$) level by measuring the non-zero signal rate variation with respect to the solar zenith angle. Moveover, JUNO can simultaneously measure $Δm^2_{21}$ using $^8$B solar neutrinos to a precision of 20\% or better depending on the central value and to sub-percent precision using reactor antineutrinos. A comparison of these two measurements from the same detector will help elucidate the current tension between the value of $Δm^2_{21}$ reported by solar neutrino experiments and the KamLAND experiment.

preprint2020arXiv

Game-theoretic Modeling of Traffic in Unsignalized Intersection Network for Autonomous Vehicle Control Verification and Validation

For a foreseeable future, autonomous vehicles (AVs) will operate in traffic together with human-driven vehicles. Their planning and control systems need extensive testing, including early-stage testing in simulations where the interactions among autonomous/human-driven vehicles are represented. Motivated by the need for such simulation tools, we propose a game-theoretic approach to modeling vehicle interactions, in particular, for urban traffic environments with unsignalized intersections. We develop traffic models with heterogeneous (in terms of their driving styles) and interactive vehicles based on our proposed approach, and use them for virtual testing, evaluation, and calibration of AV control systems. For illustration, we consider two AV control approaches, analyze their characteristics and performance based on the simulation results with our developed traffic models, and optimize the parameters of one of them.

preprint2020arXiv

Gluing of multiple Alexandrov spaces

In this paper we discuss the sufficient and necessary conditions for multiple Alexandrov spaces being glued to an Alexandrov space. We propose a Gluing Conjecture, which says that the finite gluing of Alexandrov spaces is an Alexandrov space, if and only if the gluing is by path isometry along the boundaries and the tangent cones are glued to Alexandrov spaces. This generalizes Petrunin's Gluing Theorem. Under the assumptions of the Gluing Conjecture, we classify the $2$-point gluing over $(n-1,ε)$-regular points as local separable gluing and the gluing near un-glued $(n-1,ε)$-regular points as local involutional gluing. We also prove that the Gluing Conjecture is true if the complement of $(n-1,ε)$-regular points is discrete in the glued boundary. In particular, this implies the general Gluing Conjecture as well as a new Gluing Theorem in dimension 2.

preprint2020arXiv

Identifying Strong Lenses with Unsupervised Machine Learning using Convolutional Autoencoder

In this paper we develop a new unsupervised machine learning technique comprised of a feature extractor, a convolutional autoencoder (CAE), and a clustering algorithm consisting of a Bayesian Gaussian mixture model (BGM). We apply this technique to visual band space-based simulated imaging data from the Euclid Space Telescope using data from the Strong Gravitational Lenses Finding Challenge. Our technique promisingly captures a variety of lensing features such as Einstein rings with different radii, distorted arc structures, etc, without using predefined labels. After the clustering process, we obtain several classification clusters separated by different visual features which are seen in the images. Our method successfully picks up $\sim$63\ percent of lensing images from all lenses in the training set. With the assumed probability proposed in this study, this technique reaches an accuracy of $77.25\pm 0.48$\% in binary classification using the training set. Additionally, our unsupervised clustering process can be used as the preliminary classification for future surveys of lenses to efficiently select targets and to speed up the labelling process. As the starting point of the astronomical application using this technique, we not only explore the application to gravitationally lensed systems, but also discuss the limitations and potential future uses of this technique.

preprint2020arXiv

Maximizing Cumulative User Engagement in Sequential Recommendation: An Online Optimization Perspective

To maximize cumulative user engagement (e.g. cumulative clicks) in sequential recommendation, it is often needed to tradeoff two potentially conflicting objectives, that is, pursuing higher immediate user engagement (e.g., click-through rate) and encouraging user browsing (i.e., more items exposured). Existing works often study these two tasks separately, thus tend to result in sub-optimal results. In this paper, we study this problem from an online optimization perspective, and propose a flexible and practical framework to explicitly tradeoff longer user browsing length and high immediate user engagement. Specifically, by considering items as actions, user's requests as states and user leaving as an absorbing state, we formulate each user's behavior as a personalized Markov decision process (MDP), and the problem of maximizing cumulative user engagement is reduced to a stochastic shortest path (SSP) problem. Meanwhile, with immediate user engagement and quit probability estimation, it is shown that the SSP problem can be efficiently solved via dynamic programming. Experiments on real-world datasets demonstrate the effectiveness of the proposed approach. Moreover, this approach is deployed at a large E-commerce platform, achieved over 7% improvement of cumulative clicks.

preprint2020arXiv

Off-road Autonomous Vehicles Traversability Analysis and Trajectory Planning Based on Deep Inverse Reinforcement Learning

Terrain traversability analysis is a fundamental issue to achieve the autonomy of a robot at off-road environments. Geometry-based and appearance-based methods have been studied in decades, while behavior-based methods exploiting learning from demonstration (LfD) are new trends. Behavior-based methods learn cost functions that guide trajectory planning in compliance with experts' demonstrations, which can be more scalable to various scenes and driving behaviors. This research proposes a method of off-road traversability analysis and trajectory planning using Deep Maximum Entropy Inverse Reinforcement Learning. To incorporate vehicle's kinematics while solving the problem of exponential increase of state-space complexity, two convolutional neural networks, i.e., RL ConvNet and Svf ConvNet, are developed to encode kinematics into convolution kernels and achieve efficient forward reinforcement learning. We conduct experiments in off-road environments. Scene maps are generated using 3D LiDAR data, and expert demonstrations are either the vehicle's real driving trajectories at the scene or synthesized ones to represent specific behaviors such as crossing negative obstacles. Different cost functions of traversability analysis are learned and tested at various scenes of capability in guiding the trajectory planning of different behaviors. We also demonstrate the performance and computation efficiency of the proposed method.

preprint2020arXiv

On algebraic differential equations concerning the Riemann-zeta function and the Euler-gamma function

In this paper, we prove that $ζ$ is not a solution of any non-trivial algebraic differential equation whose coefficients are polynomials in $Γ, Γ^{(n)}, Γ^{(l)}$ over the ring of polynomials in $\mathbb{C}$, $l>n\geq 1$ are positive integers. We extended the result that $ζ$ does not satisfy any non-trivial algebraic differential equation whose coefficients are polynomials in $Γ, Γ', Γ''$ over the field of complex numbers, which is proved by Li and Ye[7].

preprint2020arXiv

Optimising Automatic Morphological Classification of Galaxies with Machine Learning and Deep Learning using Dark Energy Survey Imaging

There are several supervised machine learning methods used for the application of automated morphological classification of galaxies; however, there has not yet been a clear comparison of these different methods using imaging data, or a investigation for maximising their effectiveness. We carry out a comparison between several common machine learning methods for galaxy classification (Convolutional Neural Network (CNN), K-nearest neighbour, Logistic Regression, Support Vector Machine, Random Forest, and Neural Networks) by using Dark Energy Survey (DES) data combined with visual classifications from the Galaxy Zoo 1 project (GZ1). Our goal is to determine the optimal machine learning methods when using imaging data for galaxy classification. We show that CNN is the most successful method of these ten methods in our study. Using a sample of $\sim$2,800 galaxies with visual classification from GZ1, we reach an accuracy of $\sim$0.99 for the morphological classification of Ellipticals and Spirals. The further investigation of the galaxies that have a different ML and visual classification but with high predicted probabilities in our CNN usually reveals an the incorrect classification provided by GZ1. We further find the galaxies having a low probability of being either spirals or ellipticals are visually Lenticulars (S0), demonstrating that supervised learning is able to rediscover that this class of galaxy is distinct from both Es and Spirals. We confirm that $\sim$2.5\% galaxies are misclassified by GZ1 in our study. After correcting these galaxies' labels, we improve our CNN performance to an average accuracy of over 0.99 (accuracy of 0.994 is our best result).

preprint2020arXiv

ReADS: A Rectified Attentional Double Supervised Network for Scene Text Recognition

In recent years, scene text recognition is always regarded as a sequence-to-sequence problem. Connectionist Temporal Classification (CTC) and Attentional sequence recognition (Attn) are two very prevailing approaches to tackle this problem while they may fail in some scenarios respectively. CTC concentrates more on every individual character but is weak in text semantic dependency modeling. Attn based methods have better context semantic modeling ability while tends to overfit on limited training data. In this paper, we elaborately design a Rectified Attentional Double Supervised Network (ReADS) for general scene text recognition. To overcome the weakness of CTC and Attn, both of them are applied in our method but with different modules in two supervised branches which can make a complementary to each other. Moreover, effective spatial and channel attention mechanisms are introduced to eliminate background noise and extract valid foreground information. Finally, a simple rectified network is implemented to rectify irregular text. The ReADS can be trained end-to-end and only word-level annotations are required. Extensive experiments on various benchmarks verify the effectiveness of ReADS which achieves state-of-the-art performance.

preprint2020arXiv

TAO Conceptual Design Report: A Precision Measurement of the Reactor Antineutrino Spectrum with Sub-percent Energy Resolution

The Taishan Antineutrino Observatory (TAO, also known as JUNO-TAO) is a satellite experiment of the Jiangmen Underground Neutrino Observatory (JUNO). A ton-level liquid scintillator detector will be placed at about 30 m from a core of the Taishan Nuclear Power Plant. The reactor antineutrino spectrum will be measured with sub-percent energy resolution, to provide a reference spectrum for future reactor neutrino experiments, and to provide a benchmark measurement to test nuclear databases. A spherical acrylic vessel containing 2.8 ton gadolinium-doped liquid scintillator will be viewed by 10 m^2 Silicon Photomultipliers (SiPMs) of >50% photon detection efficiency with almost full coverage. The photoelectron yield is about 4500 per MeV, an order higher than any existing large-scale liquid scintillator detectors. The detector operates at -50 degree C to lower the dark noise of SiPMs to an acceptable level. The detector will measure about 2000 reactor antineutrinos per day, and is designed to be well shielded from cosmogenic backgrounds and ambient radioactivities to have about 10% background-to-signal ratio. The experiment is expected to start operation in 2022.

preprint2020arXiv

The Hawking-Page phase transitions in the extended phase space in the Gauss-Bonnet gravity

In this paper, the Hawking-Page phase transitions between the black holes and thermal anti-de Sitter (AdS) space are studied with the Gauss-Bonnet term in the extended phase space, in which the varying cosmological constant plays the role of an effective thermodynamic pressure. The Gauss-Bonnet term exhibits its effects via introducing the corrections to the black hole entropy and Gibbs free energy. The global phase structures, especially the phase transition temperature $T_{\rm HP}$ and the Gibbs free energy $G$, are systematically investigated, first for the Schwarzschild-AdS black holes and then for the charged and rotating AdS black holes in the grand canonical ensembles, with both analytical and numerical methods. It is found that there are terminal points in the coexistence lines, and $T_{\rm HP}$ decreases at large electric potentials and angular velocities and also decreases with the Gauss-Bonnet coupling constant $α$.

preprint2020arXiv

Three results on transcendental meromorphic solutions of certain nonlinear differential equations

In this paper, we study the transcendental meromorphic solutions for the nonlinear differential equations: $f^{n}+P(f)=R(z)e^{α(z)}$ and $f^{n}+P_{*}(f)=p_{1}(z)e^{α_{1}(z)}+p_{2}(z)e^{α_{2}(z)}$ in the complex plane, where $P(f)$ and $P_{*}(f)$ are differential polynomials in $f$ of degree $n-1$ with coefficients being small functions and rational functions respectively, $R$ is a non-vanishing small function of $f$, $α$ is a nonconstant entire function, $p_{1}, p_{2}$ are non-vanishing rational functions, and $α_{1}, α_{2}$ are nonconstant polynomials. Particularly, we consider the solutions of the second equation when $p_{1}, p_{2}$ are nonzero constants, and $°α_{1}=°α_{2}=1$. Our results are improvements and complements of Liao (Complex Var. Elliptic Equ. 2015, 60(6): 748--756), and Rong-Xu (Mathematics 2019, 7, 539), etc., which partially answer a question proposed by Li (J. Math. Anal. Appl. 2011, 375: 310--319).

preprint2019arXiv

CosmoDC2: A Synthetic Sky Catalog for Dark Energy Science with LSST

This paper introduces cosmoDC2, a large synthetic galaxy catalog designed to support precision dark energy science with the Large Synoptic Survey Telescope (LSST). CosmoDC2 is the starting point for the second data challenge (DC2) carried out by the LSST Dark Energy Science Collaboration (LSST DESC). The catalog is based on a trillion-particle, 4.225 Gpc^3 box cosmological N-body simulation, the `Outer Rim' run. It covers 440 deg^2 of sky area to a redshift of z=3 and is complete to a magnitude depth of 28 in the r-band. Each galaxy is characterized by a multitude of properties including stellar mass, morphology, spectral energy distributions, broadband filter magnitudes, host halo information and weak lensing shear. The size and complexity of cosmoDC2 requires an efficient catalog generation methodology; our approach is based on a new hybrid technique that combines data-driven empirical approaches with semi-analytic galaxy modeling. A wide range of observation-based validation tests has been implemented to ensure that cosmoDC2 enables the science goals of the planned LSST DESC DC2 analyses. This paper also represents the official release of the cosmoDC2 data set, including an efficient reader that facilitates interaction with the data.

preprint2016arXiv

A comprehensive investigation on the slowing down of cosmic acceleration

Shafieloo ea al. firstly proposed the possibility that the current cosmic acceleration (CA) is slowing down. However, this is rather counterintuitive because a slowing down CA cannot be accommodated in most mainstream cosmological models. In this work, by exploring the evolutionary trajectories of dark energy equation of state $w(z)$ and deceleration parameter $q(z)$, we present a comprehensive investigation on the slowing down of CA from both the theoretical and the observational sides. For the theoretical side, we study the impact of different $w(z)$ by using six parametrization models, and then discuss the effects of spatial curvature. For the observational side, we investigate the effects of different type Ia supernovae (SNe Ia), different baryon acoustic oscillation (BAO), and different cosmic microwave background (CMB) data, respectively. We find that (1) The evolution of CA are insensitive to the specific form of $w(z)$; in contrast, a non-flat Universe more favors a slowing down CA than a flat Universe. (2) SNLS3 SNe Ia datasets favor a slowing down CA at 1$σ$ confidence level, while JLA SNe Ia samples prefer an eternal CA; in contrast, the effects of different BAO data are negligible. (3) Compared with CMB distance prior data, full CMB data more favor a slowing down CA. (4) Due to the low significance, the slowing down of CA is still a theoretical possibility that cannot be confirmed by the current observations.

preprint2016arXiv

Difference analogue of Cartan's Second Main Theorem for slowly moving periodic targets

We extend the difference analogue of Cartan's second main theorem for the case of slowly moving periodic hyperplanes, and introduce two different natural ways to find a difference analogue of the truncated second main theorem. As applications, we obtain a new Picard type theorem and difference analogues of the deficiency relation for holomorphic curves.

preprint2016arXiv

Explorations of two empirical formulae for fermion masses

Two empirical formulae for the lepton and quark masses (i.e. Kartavtsev's extended Koide formulae), $K_l=(\sum_l m_l)/(\sum_l\sqrt{m_l})^2=2/3$ and $K_q=(\sum_q m_q)/(\sum_q\sqrt{m_q})^2=2/3$, are explored in this paper. For the lepton sector, we show that $K_l=2/3$, only if the uncertainty of the tauon mass is relaxed to about $2σ$ confidence level, and the neutrino masses can consequently be extracted with the current experimental data. For the quark sector, the extended Koide formula should only be applied to the running quark masses, and $K_q$ is found to be rather insensitive to the renormalization effects in a large range of energy scales from GeV to $10^{12}$ GeV. However, $K_q$ is always slightly larger than $2/3$, but the discrepancy is merely about $5\%$.

preprint2016arXiv

Fisher-symmetric informationally complete measurements for pure states

We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that injectively represent pure quantum states in the neighborhood of a fiducial pure state. The measurement is locally informationally complete---i.e., it uniquely determines these parameters, as opposed to distinguishing two arbitrary quantum states---and it is maximal in the sense of a multi-parameter quantum Cramer-Rao bound. For a $d$-dimensional quantum system, requiring only local informational completeness allows us to reduce the number of outcomes of the measurement from a minimum close to but below $4d-3$, for the usual notion of global pure-state informational completeness, to $2d-1$.

preprint2016arXiv

Game-Theoretic Modeling of Driver and Vehicle Interactions for Verification and Validation of Autonomous Vehicle Control Systems

Autonomous driving has been the subject of increased interest in recent years both in industry and in academia. Serious efforts are being pursued to address legal, technical and logistical problems and make autonomous cars a viable option for everyday transportation. One significant challenge is the time and effort required for the verification and validation of the decision and control algorithms employed in these vehicles to ensure a safe and comfortable driving experience. Hundreds of thousands of miles of driving tests are required to achieve a well calibrated control system that is capable of operating an autonomous vehicle in an uncertain traffic environment where multiple interactions between vehicles and drivers simultaneously occur. Traffic simulators where these interactions can be modeled and represented with reasonable fidelity can help decrease the time and effort necessary for the development of the autonomous driving control algorithms by providing a venue where acceptable initial control calibrations can be achieved quickly and safely before actual road tests. In this paper, we present a game theoretic traffic model that can be used to 1) test and compare various autonomous vehicle decision and control systems and 2) calibrate the parameters of an existing control system. We demonstrate two example case studies, where, in the first case, we test and quantitatively compare two autonomous vehicle control systems in terms of their safety and performance, and, in the second case, we optimize the parameters of an autonomous vehicle control system, utilizing the proposed traffic model and simulation environment.

preprint2016arXiv

Impacts of different SNLS3 light-curve fitters on cosmological consequences of interacting dark energy models

We explore the cosmological consequences of interacting dark energy (IDE) models using the SNLS3 supernova samples. In particular, we focus on the impacts of different SNLS3 light-curve fitters (LCF) (corresponding to "SALT2", "SiFTO", and "Combined" sample). Firstly, making use of the three SNLS3 data sets, as well as the Planck distance priors data and the galaxy clustering data, we constrain the parameter spaces of three IDE models. Then, we study the cosmic evolutions of Hubble parameter $H(z)$, deceleration diagram $q(z)$, statefinder hierarchy $S^{(1)}_3(z)$ and $S^{(1)}_4(z)$, and check whether or not these dark energy diagnosis can distinguish the differences among the results of different SNLS3 LCF. At last, we perform high redshift cosmic age test using three old high redshift objects (OHRO), and explore the fate of the Universe. We find that, the impacts of different SNLS3 LCF are rather small, and can not be distinguished by using $H(z)$, $q(z)$, $S^{(1)}_3(z)$, $S^{(1)}_4(z)$, and the age data of OHRO. In addition, we infer, from the current observations, how far we are from a cosmic doomsday in the worst case, and find that the "Combined" sample always gives the largest 2$σ$ lower limit of the time interval between "big rip" and today, while the results given by the "SALT2" and the "SiFTO" sample are close to each other. These conclusions are insensitive to a specific form of dark sector interaction. Our method can be used to distinguish the differences among various cosmological observations.

preprint2016arXiv

More Evidence for the Redshift Dependence of Color from the JLA Supernova Sample Using Redshift Tomography

In this work, by applying the redshift tomography method to Joint Light-curve Analysis (JLA) supernova sample, we explore the possible redshift-dependence of stretch-luminosity parameter $α$ and color-luminosity parameter $β$. The basic idea is to divide the JLA sample into different redshift bins, assuming that $α$ and $β$ are piecewise constants. Then, by constraining the $Λ$CDM model, we check the consistency of cosmology-fit results given by the SN sample of each redshift bin. We also adopt the same technique to explore the possible evolution of $β$ in various subsamples of JLA. Using the full JLA data, we find that $α$ is always consistent with a constant. In contrast, at high redshift $β$ has a significant trend of decreasing, at $\sim 3.5σ$ confidence level (CL). Moreover, we find that low-$z$ subsample favors a constant $β$; in contrast, SDSS and SNLS subsamples favor a decreasing $β$ at 2$σ$ and $3.3σ$ CL, respectively. Besides, by using a binned parameterization of $β$, we study the impacts of $β$'s evolution on parameter estimation. We find that compared with a constant $β$, a varying $β$ yields a larger best-fit value of fractional matter density $Ω_{m0}$, which slightly deviates from the best-fit result given by other cosmological observations. However, for both the varying $β$ and the constant $β$ cases, the $1σ$ regions of $Ω_{m0}$ are still consistent with the result given by other observations.

preprint2016arXiv

Order-Chain Polytopes

Given two families $X$ and $Y$ of integral polytopes with nice combinatorial and algebraic properties, a natural way to generate new class of polytopes is to take the intersection $\mathcal{P}=\mathcal{P}_1\cap\mathcal{P}_2$, where $\mathcal{P}_1\in X$, $\mathcal{P}_2\in Y$. Two basic questions then arise: 1) when $\mathcal{P}$ is integral and 2) whether $\mathcal{P}$ inherits the "old type" from $\mathcal{P}_1, \mathcal{P}_2$ or has a "new type", that is, whether $\mathcal{P}$ is unimodularly equivalent to some polytope in $X\cup Y$ or not. In this paper, we focus on the families of order polytopes and chain polytopes and create a new class of polytopes following the above framework, which are named order-chain polytopes. In the study on their volumes, we discover a natural relation with Ehrenborg and Mahajan's results on maximizing descent statistics.

preprint2016arXiv

PICS: Simulations of Strong Gravitational Lensing in Galaxy Clusters

Gravitational lensing has become one of the most powerful tools available for investigating the 'dark side' of the universe. Cosmological strong gravitational lensing, in particular, probes the properties of the dense cores of dark matter halos over decades in mass and offers the opportunity to study the distant universe at flux levels and spatial resolutions otherwise unavailable. Studies of strongly-lensed variable sources offer yet further scientific opportunities. One of the challenges in realizing the potential of strong lensing is to understand the statistical context of both the individual systems that receive extensive follow-up study, as well as that of the larger samples of strong lenses that are now emerging from survey efforts. Motivated by these challenges, we have developed an image-simulation pipeline, PICS (Pipeline for Images of Cosmological Strong lensing) to generate realistic strong gravitational lensing signals from group and cluster scale lenses. PICS uses a low-noise and unbiased density estimator based on (resampled) Delaunay Tessellations to calculate the density field; lensed images are produced by ray-tracing images of actual galaxies from deep Hubble Space Telescope observations. Other galaxies, similarly sampled, are added to fill in the light cone. The pipeline further adds cluster-member galaxies and foreground stars into the lensed images. The entire image ensemble is then observed using a realistic point spread function which includes appropriate detector artifacts for bright stars. Noise is further added, including such non-Gaussian elements as noise window-paning from mosaiced observations, residual bad pixels, and cosmic rays. The aim is to produced simulated images that appear identical - to the eye (expert or otherwise) - to real observations in various imaging surveys.

preprint2016arXiv

The Gini Coefficient as a Morphological Measurement of Strongly Lensed Galaxies in the Image Plane

Characterization of the morphology of strongly lensed galaxies is challenging because images of such galaxies are typically highly distorted. Lens modeling and source plane reconstruction is one approach that can provide reasonably undistorted images from which morphological measurements can be made, although at the expense of a highly spatially variable telescope PSF when mapped back to the source plane. Unfortunately, modeling the lensing mass is a time and resource intensive process, and in many cases there are too few constraints to precisely model the lensing mass. If, however, useful morphological measurements could be made in the image plane rather than the source plane, it would bypass this issue and obviate the need for a source reconstruction process for some applications. We examine the use of the Gini coefficient as one such measurement. Because it depends on the cumulative distribution of the light of a galaxy, but not the relative spatial positions, the fact that surface brightness is conserved by lensing means that the Gini coefficient may be well-preserved by strong gravitational lensing. Through simulations, we test the extent to which the Gini coefficient is conserved, including by effects due to PSF convolution and pixelization, to determine whether it is invariant enough under lensing to be used as a measurement of galaxy morphology that can be made in the image plane.

preprint2016arXiv

The numbers of edges of the order polytope and the chain poyltope of a finite partially ordered set

Let $P$ be an arbitrary finite partially ordered set. It will be proved that the number of edges of the order polytope ${\mathcal O}(P)$ is equal to that of the chain polytope ${\mathcal C}(P)$. Furthermore, it will be shown that the degree sequence of the finite simple graph which is the $1$-skeleton of ${\mathcal O}(P)$ is equal to that of ${\mathcal C}(P)$ if and only if ${\mathcal O}(P)$ and ${\mathcal C}(P)$ are unimodularly equivalent.

preprint2015arXiv

Age-Specific Mortality and Fertility Rates for Probabilistic Population Projections

The United Nations released official probabilistic population projections (PPP) for all countries for the first time in July 2014. These were obtained by projecting the period total fertility rate (TFR) and life expectancy at birth ($e_0$) using Bayesian hierarchical models, yielding a large set of future trajectories of TFR and $e_0$ for all countries and future time periods to 2100, sampled from their joint predictive distribution. Each trajectory was then converted to age-specific mortality and fertility rates, and population was projected using the cohort-component method. This yielded a large set of trajectories of future age- and sex-specific population counts and vital rates for all countries. In this paper we describe the methodology used for deriving the age-specific mortality and fertility rates in the 2014 PPP, we identify limitations of these methods, and we propose several methodological improvements to overcome them. The methods presented in this paper are implemented in the publicly available bayesPop R package.

preprint2015arXiv

An Exploration of the Black Hole Entropy via the Weyl Tensor

The Weyl tensor is the trace-free part of the Riemann tensor. Therefore, it is independent of the energy-momentum tensor and is thus not linked to the dynamics of gravitational fields. In this paper, we explore its possible thermodynamical property (i.e. its relationship with the black hole entropy). For a Schwarzschild black hole, the Weyl scalar invariant, $C_{μνλρ}C^{μνλρ}$, is proportional to its Bekenstein--Hawking entropy. This observation inspires us to interpret $C_{μνλρ}C^{μνλρ}$ as the entropy density of the gravitational fields of black holes. A dimensional analysis indicates that this interpretation is only valid in 5-dimensional space-time. We calculate the volume integrals of $C_{μνλρ}C^{μνλρ}$ for the 5-dimensional Schwarzschild and Schwarzschild--anti-de Sitter black holes, and find that these integrals indeed lead to the correct entropy formulae, only up to some coefficients.

preprint2015arXiv

Cooperative Communication Using Network Coding

We consider a cognitive radio network scenario where a primary transmitter and a secondary transmitter, respectively, communicate a message to their respective primary receiver and secondary receiver over a packet-based wireless link, using a joint automatic-repeat-request (ARQ) error control scheme. The secondary transmitter assists in the retransmission of the primary message, which improves the primary performance, and is granted limited access to the transmission resources. Conventional ARQ, as well as two network-coding schemes are investigated for application in the retransmission phase; namely the static network-coding (SNC) scheme and the adaptive network-coding (ANC) scheme. For each scheme we analyze the transmission process by investigating the distribution of the number of transmission attempts and approximate it by normal distributions. Considering both the cases of an adaptive frame size and a truncated frame size, we derive analytical results on packet throughput and infer that the ANC scheme outperforms the SNC scheme.

preprint2015arXiv

Holographic Dark Energy with Cosmological Constant

Inspired by the multiverse scenario, we study a heterotic dark energy model in which there are two parts, the first being the cosmological constant and the second being the holographic dark energy, thus this model is named the $Λ$HDE model. By studying the $Λ$HDE model theoretically, we find that the parameters $d$ and $Ω_{hde}$ are divided into a few domains in which the fate of the universe is quite different. We investigate dynamical behaviors of this model, and especially the future evolution of the universe. We perform fitting analysis on the cosmological parameters in the $Λ$HDE model by using the recent observational data. We find the model yields $χ^2_{\rm min}=426.27$ when constrained by $\rm Planck+SNLS3+BAO+HST$, comparable to the results of the HDE model (428.20) and the concordant $Λ$CDM model (431.35). At 68.3\% CL, we obtain $-0.07<Ω_{\Lambda0}<0.68$ and correspondingly $0.04<Ω_{hde0}<0.79$, implying at present there is considerable degeneracy between the holographic dark energy and cosmological constant components in the $Λ$HDE model.

preprint2015arXiv

Kullback-Leibler entropy and Penrose conjecture in the Lemaitre-Tolman-Bondi model

Our universe hosts various large-scale structures from voids to galaxy clusters, so it would be interesting to find some simple and reasonable measure to describe the inhomogeneities in the universe. We explore two different methods for this purpose: the Kullback-Leibler entropy and the Weyl curvature tensor. These two quantities characterize the deviation of the actual distribution of matter from the unperturbed background. We calculate these two measures in the spherically symmetric Lemaitre-Tolman-Bondi model in the dust universe. Both exact and perturbative calculations are presented, and we observe that these two measures are in proportion up to second order.

preprint2015arXiv

Lipschitz-Volume rigidity in Alexandrov geometry

We prove a Lipschitz-Volume rigidity theorem in Alexandrov geometry, that is, if a 1-Lipschitz map $f\colon X=\amalg X_\ell\to Y$ between Alexandrov spaces preserves volume, then it is a path isometry and an isometry when restricted to the interior of $X$. We furthermore characterize the metric structure on $Y$ with respect to $X$ when $f$ is also onto. This implies the converse of Petrunin's Gluing Theorem: if a gluing of two Alexandrov spaces via a bijection between their boundaries produces an Alexandrov space, then the bijection must be an isometry.

preprint2015arXiv

Logic BIST: State-of-the-Art and Open Problems

Many believe that in-field hardware faults are too rare in practice to justify the need for Logic Built-In Self-Test (LBIST) in a design. Until now, LBIST was primarily used in safety-critical applications. However, this may change soon. First, even if costly methods like burn-in are applied, it is no longer possible to get rid of all latent defects in devices at leading-edge technology. Second, demands for high reliability spread to consumer electronics as smartphones replace our wallets and IDs. However, today many ASIC vendors are reluctant to use LBIST. In this paper, we describe the needs for successful deployment of LBIST in the industrial practice and discuss how these needs can be addressed. Our work is hoped to attract a wider attention to this important research topic.

preprint2015arXiv

On dimensions of tangent cones in limit spaces with lower Ricci curvature bounds

We show that if $X$ is a limit of $n$-dimensional Riemannian manifolds with Ricci curvature bounded below and $γ$ is a limit geodesic in $X$ then along the interior of $γ$ same scale measure metric tangent cones $T_{γ(t)}X$ are Hölder continuous with respect to measured Gromov-Hausdorff topology and have the same dimension in the sense of Colding-Naber.

preprint2015arXiv

The Gini Coefficient as a Tool for Image Family Idenitification in Strong Lensing Systems with Multiple Images

The sample of cosmological strong lensing systems has been steadily growing in recent years and with the advent of the next generation of space-based survey telescopes, the sample will reach into the thousands. The accuracy of strong lens models relies on robust identification of multiple image families of lensed galaxies. For the most massive lenses, often more than one background galaxy is magnified and multiply-imaged, and even in the cases of only a single lensed source, identification of counter images is not always robust. Recently, we have shown that the Gini coefficient in space-telescope-quality imaging is a measurement of galaxy morphology that is relatively well-preserved by strong gravitational lensing. Here, we investigate its usefulness as a diagnostic for the purposes of image family identification and show that it can remove some of the degeneracies encountered when using color as the sole diagnostic, and can do so without the need for additional observations since whenever a color is available, two Gini coefficients are as well.

preprint2015arXiv

Transductive Optimization of Top k Precision

Consider a binary classification problem in which the learner is given a labeled training set, an unlabeled test set, and is restricted to choosing exactly $k$ test points to output as positive predictions. Problems of this kind---{\it transductive precision@$k$}---arise in information retrieval, digital advertising, and reserve design for endangered species. Previous methods separate the training of the model from its use in scoring the test points. This paper introduces a new approach, Transductive Top K (TTK), that seeks to minimize the hinge loss over all training instances under the constraint that exactly $k$ test instances are predicted as positive. The paper presents two optimization methods for this challenging problem. Experiments and analysis confirm the importance of incorporating the knowledge of $k$ into the learning process. Experimental evaluations of the TTK approach show that the performance of TTK matches or exceeds existing state-of-the-art methods on 7 UCI datasets and 3 reserve design problem instances.

preprint2014arXiv

Baryon Asymmetries in the Natural Inflation Model

A variation of Affleck-Dine mechanism was proposed to generate the observed baryon asymmetry in [1], in which the inflaton was assumed to be a complex scalar field with a weakly broken $U(1)$ symmetry, and the baryon asymmetry generation was easily unified with the stage of inflation and reheating. We adapt this mechanism to natural inflation scenarios and compare the results with those in chaotic inflation models. We compute the net particle number obtained at the end of inflation and transform it into net baryon number after reheatings. We observed that in natural inflation models, the desired baryon-to-photon ratio can be achieved equally well as in chaotic models.

preprint2014arXiv

Capturing "attrition intensifying" structural traits from didactic interaction sequences of MOOC learners

This work is an attempt to discover hidden structural configurations in learning activity sequences of students in Massive Open Online Courses (MOOCs). Leveraging combined representations of video clickstream interactions and forum activities, we seek to fundamentally understand traits that are predictive of decreasing engagement over time. Grounded in the interdisciplinary field of network science, we follow a graph based approach to successfully extract indicators of active and passive MOOC participation that reflect persistence and regularity in the overall interaction footprint. Using these rich educational semantics, we focus on the problem of predicting student attrition, one of the major highlights of MOOC literature in the recent years. Our results indicate an improvement over a baseline ngram based approach in capturing "attrition intensifying" features from the learning activities that MOOC learners engage in. Implications for some compelling future research are discussed.

preprint2014arXiv

Cutting convex polytopes by hyperplanes

Cutting a polytope is a very natural way to produce new classes of interesting polytopes. Moreover, it has been very enlightening to explore which algebraic and combinatorial properties of the orignial polytope are hereditary to its subpolytopes obtained by a cut. In this work, we put our attention to all the seperating hyperplanes for some given polytope (integral and convex) and study the existence and classification of such hyperplanes. We prove the exitence of seperating hyperplanes for the order and chain polytopes for any finite posets that are not a single chain; prove there are no such hyperplanes for any Birkhoff polytopes. Moreover, we give a complete seperating hyperplane classification for the unit cube and its subpolytopes obtained by one cut, together with some partial classification results for order and chain polytopes.

preprint2014arXiv

Decomposable edge polytopes of finite graphs

Edge polytopes is a class of interesting polytope with rich algebraic and combinatorial properties, which was introduced by Ohsugi and Hibi. In this papar, we follow a previous study on cutting edge polytopes by Hibi, Li and Zhang. Instead of focusing on the algeraic properties of the subpolytopes as the previous study, in this paper, we take a closer look on the graphs whose edge polytopes are decomposable. In particular, we answer two important questions raised in the previous study about 1) the relationship between type I and type II decomposable graphs and 2) description of decomposable graphs.

preprint2014arXiv

Top Rank Optimization in Linear Time

Bipartite ranking aims to learn a real-valued ranking function that orders positive instances before negative instances. Recent efforts of bipartite ranking are focused on optimizing ranking accuracy at the top of the ranked list. Most existing approaches are either to optimize task specific metrics or to extend the ranking loss by emphasizing more on the error associated with the top ranked instances, leading to a high computational cost that is super-linear in the number of training instances. We propose a highly efficient approach, titled TopPush, for optimizing accuracy at the top that has computational complexity linear in the number of training instances. We present a novel analysis that bounds the generalization error for the top ranked instances for the proposed approach. Empirical study shows that the proposed approach is highly competitive to the state-of-the-art approaches and is 10-100 times faster.

preprint2014arXiv

Your click decides your fate: Inferring Information Processing and Attrition Behavior from MOOC Video Clickstream Interactions

In this work, we explore video lecture interaction in Massive Open Online Courses (MOOCs), which is central to student learning experience on these educational platforms. As a research contribution, we operationalize video lecture clickstreams of students into cognitively plausible higher level behaviors, and construct a quantitative information processing index, which can aid instructors to better understand MOOC hurdles and reason about unsatisfactory learning outcomes. Our results illustrate how such a metric inspired by cognitive psychology can help answer critical questions regarding students' engagement, their future click interactions and participation trajectories that lead to in-video & course dropouts. Implications for research and practice are discussed

preprint2013arXiv

An Algorithm for Constructing a Smallest Register with Non-Linear Update Generating a Given Binary Sequence

Registers with Non-Linear Update (RNLUs) are a generalization of Non-Linear Feedback Shift Registers (NLFSRs) in which both, feedback and feedforward, connections are allowed and no chain connection between the stages is required. In this paper, a new algorithm for constructing RNLUs generating a given binary sequence is presented. Expected size of RNLUs constructed by the presented algorithm is proved to be O(n/log(n/p)), where n is the sequence length and p is the degree of parallelization. This is asymptotically smaller than the expected size of RNLUs constructed by previous algorithms and the expected size of LFSRs and NLFSRs generating the same sequence. The presented algorithm can potentially be useful for many applications, including testing, wireless communications, and cryptography.

preprint2013arXiv

Apollonian Equilateral Triangles

Given an equilateral triangle with $a$ the square of its side length and a point in its plane with $b$, $c$, $d$ the squares of the distances from the point to the vertices of the triangle, it can be computed that $a$, $b$, $c$, $d$ satisfy $3(a^2+b^2+c^2+d^2)=(a+b+c+d)^2$. This paper derives properties of quadruples of nonnegative integers $(a,\, b,\, c,\, d)$, called triangle quadruples, satisfying this equation. It is easy to verify that the operation generating $(a,\, b,\, c,\, a+b+c-d)$ from $(a,\, b,\, c,\, d)$ preserves this feature and that it and analogous ones for the other elements can be represented by four matrices. We examine in detail the triangle group, the group with these operations as generators, and completely classify the orbits of quadruples with respect to the triangle group action. We also compute the number of triangle quadruples generated after a certain number of operations and approximate the number of quadruples bounded by characteristics such as the maximal element. Finally, we prove that the triangle group is a hyperbolic Coxeter group and derive information about the elements of triangle quadruples by invoking Lie groups. We also generalize the problem to higher dimensions.

preprint2013arXiv

Bounding geometry of loops in Alexandrov spaces

For a path in a compact finite dimensional Alexandrov space $X$ with curv $\ge κ$, the two basic geometric invariants are the length and the turning angle (which measures the closeness from being a geodesic). We show that the sum of the two invariants of any loop is bounded from below in terms of $κ$, the dimension, diameter and Hausdorff measure of $X$. This generalizes a basic estimate of Cheeger on the length of a closed geodesic in closed Riemannian manifold ([Ch], [GP1,2]). To see that the above result also generalizes and improves an analogous of the Cheeger type estimate in Alexandrov geometry in [BGP], we show that for a class of subsets of $X$, the $n$-dimensional Hausdorff measure and rough volume are proportional by a constant depending on $n=\dim(X)$.

preprint2013arXiv

Embedding of Deterministic Test Data for In-Field Testing

This paper presents a new feedback shift register-based method for embedding deterministic test patterns on-chip suitable for complementing conventional BIST techniques for in-field testing. Our experimental results on 8 real designs show that the presented approach outperforms the bit-flipping approach by 24.7% on average. We also show that it is possible to exploit the uneven distribution of don't care bits in test patterns in order to reduce the area required for storing deterministic test patterns more than 3 times with less than 2% fault coverage drop.

preprint2013arXiv

Flashcard games

We study a certain family of discrete dynamical processes introduced by Novikoff, Kleinberg and Strogatz that we call flashcard games. We prove a number of results on the evolution of these games, an in particular we settle a conjecture of NKS on the frequency with which a given card appears. We introduce a number of generalizations and variations that we believe are of interest, and provide a large number of open questions and problems.

preprint2013arXiv

Reexamination of inflation in noncommutative space-time after Planck results

An inflationary model in the framework of noncommutative space-time may generate a nontrivial running of the scalar spectral index, but usually induces a large tensor-to-scalar ratio simultaneously. With the latest observational data from the Planck mission, we reexamine the inflationary scenarios in a noncommutative space-time. We find that either the running of the spectral index is tiny compared with the recent observational result, or the tensor-to-scalar ratio is too large to allow a sufficient number of $e$-folds. As examples, we show that the chaotic and power-law inflation models with the noncommutative effects are not favored by the current Planck data.

preprint2012arXiv

A canonical expansion of the product of two Stanley symmetric functions

We study the problem of expanding the product of two Stanley symmetric functions $F_w\cdot F_u$ into Stanley symmetric functions in some natural way. Our approach is to consider a Stanley symmetric function as a stabilized Schubert polynomial $F_{w}=\lim_{n\to \infty}\mathfrak{S}_{1^{n}\times w}$, and study the behavior of the expansion of $\s_{1^n\times w}\cdot\s_{1^n\times u}$ into Schubert polynomials, as $n$ increases. We prove that this expansion stabilizes and thus we get a natural expansion for the product of two Stanley symmetric functions. In the case when one permutation is Grassmannian, we have a better understanding of this stability. We then study some other related stable properties, which provides a second proof of the main result.

preprint2012arXiv

A Multi-Criteria Framework with Voxel-Dependent Parameters for Radiotherapy Treatment Plan Optimization

In a treatment plan optimization problem for radiotherapy, a clinically acceptable plan is usually generated by an optimization process with weighting factors or reference doses adjusted for organs. Recent discoveries indicate that adjusting parameters associated with each voxel may lead to better plan quality. However, it is still unclear regarding the mathematical reasons behind it. To answer questions related to this problem, we establish in this work a new mathematical framework equipped with two theorems. The new framework clarifies the different consequences of adjusting organ-dependent and voxel-dependent parameters for the treatment plan optimization of radiation therapy, as well as the different effects of adjusting weighting factors versus reference doses in the optimization process. The main discoveries are threefold: 1) While in the organ-based model the selection of the objective function has an impact on the quality of the optimized plans, this is no longer an issue for the voxel-based model since the entire Pareto surface could be generated regardless the specific form of the objective function as long as it satisfies certain mathematical conditions; 2) A larger Pareto surface is explored by adjusting voxel-dependent parameters than by adjusting organ-dependent parameters, possibly allowing for the generation of plans with better trade-offs among different clinical objectives; 3) Adjusting voxel weighting factors is preferred to adjusting the voxel reference doses since the Pareto optimality can be maintained.

preprint2012arXiv

An Eulerian permutation statistic and generalizations

Recently, the second author studied an Eulerian statistic (called cover) in the context of convex polytopes, and proved an equal joint distribution of (cover,des) with (des,exc). In this paper, we present several direct bijective proofs that cover is Eulerian, and examine its generalizations and their Mahonian partners. We also present a quasi-symmetric function proof (suggested by Michelle Wachs) of the above equal joint distribution.

preprint2012arXiv

Efficient Optimization of Performance Measures by Classifier Adaptation

In practical applications, machine learning algorithms are often needed to learn classifiers that optimize domain specific performance measures. Previously, the research has focused on learning the needed classifier in isolation, yet learning nonlinear classifier for nonlinear and nonsmooth performance measures is still hard. In this paper, rather than learning the needed classifier by optimizing specific performance measure directly, we circumvent this problem by proposing a novel two-step approach called as CAPO, namely to first train nonlinear auxiliary classifiers with existing learning methods, and then to adapt auxiliary classifiers for specific performance measures. In the first step, auxiliary classifiers can be obtained efficiently by taking off-the-shelf learning algorithms. For the second step, we show that the classifier adaptation problem can be reduced to a quadratic program problem, which is similar to linear SVMperf and can be efficiently solved. By exploiting nonlinear auxiliary classifiers, CAPO can generate nonlinear classifier which optimizes a large variety of performance measures including all the performance measure based on the contingency table and AUC, whilst keeping high computational efficiency. Empirical studies show that CAPO is effective and of high computational efficiency, and even it is more efficient than linear SVMperf.

preprint2012arXiv

Ehrhart $h^*$-vectors of hypersimplices

We consider the Ehrhart $h^*$-vector for the hypersimplex. It is well-known that the sum of the $h_i^*$ is the normalized volume which equals an Eulerian numbers. The main result is a proof of a conjecture by R. Stanley which gives an interpretation of the $h^*_i$ coefficients in terms of descents and excedances. Our proof is geometric using a careful book-keeping of a shelling of a unimodular triangulation. We generalize this result to other closely related polytopes.

preprint2012arXiv

Relative information entropy and Weyl curvature of the inhomogeneous Universe

Penrose conjectured a connection between entropy and Weyl curvature of the Universe. This is plausible, as the almost homogeneous and isotropic Universe at the onset of structure formation has negligible Weyl curvature, which then grows (relative to the Ricci curvature) due to the formation of large-scale structure and thus reminds us of the second law of thermodynamics. We study two scalar measures to quantify the deviations from a homogeneous and isotropic space-time, the relative information entropy and a Weyl tensor invariant, and show their relation to the averaging problem. We calculate these two quantities up to second order in standard cosmological perturbation theory and find that they are correlated and can be linked via the kinematic backreaction of a spatially averaged universe model.

preprint2012arXiv

Separating hyperplanes of edge polytopes

Let $G$ be a finite connected simple graph with $d$ vertices and let $\Pc_G \subset \RR^d$ be the edge polytope of $G$. We call $\Pc_G$ \emph{decomposable} if $\Pc_G$ decomposes into integral polytopes $\Pc_{G^+}$ and $\Pc_{G^-}$ via a hyperplane. In this paper, we explore various aspects of decomposition of $\Pc_G$: we give an algorithm deciding the decomposability of $\Pc_G$, we prove that $\Pc_G$ is normal if and only if both $\Pc_{G^+}$ and $\Pc_{G^-}$ are normal, and we also study how a condition on the toric ideal of $\Pc_G$ (namely, the ideal being generated by quadratic binomials) behaves under decomposition.

preprint2012arXiv

Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems

In this paper, we generalize the algorithm described by Rump and Graillat, as well as our previous work on certifying breadth-one singular solutions of polynomial systems, to compute verified and narrow error bounds such that a slightly perturbed system is guaranteed to possess an isolated singular solution within the computed bounds. Our new verification method is based on deflation techniques using smoothing parameters. We demonstrate the performance of the algorithm for systems with singular solutions of multiplicity up to hundreds.

preprint2012arXiv

Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems: Case of Breadth One

In this paper we describe how to improve the performance of the symbolic-numeric method in (Li and Zhi,2009, 2011) for computing the multiplicity structure and refining approximate isolated singular solutions in the breadth one case. By introducing a parameterized and deflated system with smoothing parameters, we generalize the algorithm in (Rump and Graillat, 2009) to compute verified error bounds such that a slightly perturbed polynomial system is guaranteed to have a breadth-one multiple root within the computed bounds.

preprint2011arXiv

AIG Rewriting Using 5-Input Cuts

Rewriting is a common approach to logic optimization based on local transformations. Most commercially available logic synthesis tools include a rewriting engine that may be used multiple times on the same netlist during optimization. This paper presents an And-Inverter graph based rewriting algorithm using 5-input cuts. The best circuits are pre-computed for a subset of NPN classes of 5-variable functions. Cut enumeration and Boolean matching are used to identify replacement candidates. The presented approach is expected to complement existing rewriting approaches which are usually based on 4-input cuts. The experimental results show that, by adding the new rewriting algorithm to ABC synthesis tool, we can further reduce the area of heavily optimized large circuits by 5.57% on average.

preprint2011arXiv

Computing Isolated Singular Solutions of Polynomial Systems: Case of Breadth One

We present a symbolic-numeric method to refine an approximate isolated singular solution $\hat{\mathbf{x}}=(\hat{x}_{1}, ..., \hat{x}_{n})$ of a polynomial system $F=\{f_1, ..., f_n\}$ when the Jacobian matrix of $F$ evaluated at $\hat{\mathbf{x}}$ has corank one approximately. Our new approach is based on the regularized Newton iteration and the computation of approximate Max Noether conditions satisfied at the approximate singular solution. The size of matrices involved in our algorithm is bounded by $n \times n$. The algorithm converges quadratically if $\hat{\xx}$ is close to the isolated exact singular solution.

preprint2011arXiv

Effects of supermassive binary black holes on gravitational lenses

Recent observations indicate that many if not all galaxies host massive central black holes (BHs). In this paper we explore the influence of supermassive binary black holes (SMBBHs) on their actions as gravitational lenses. When lenses are modelled as singular isothermal ellipsoids, binary black holes change the critical curves and caustics differently as a function of distance. Each black hole can in principle create at least one additional image, which, if observed, provides evidence of black holes. By studying how SMBBHs affect the cumulative distribution of magnification for images created by black holes, we find that the cross section for at least one such additional image to have a magnification larger than $10^{-5}$ is comparable to the cross section for producing multiple-images in singular isothermal lenses. Such additional images may be detectable with high-resolution and large dynamic range maps of multiply-imaged systems from future facilities, such as the SKA. The probability of detecting at least one image (two images) with magnification above $10^{-3}$ is $\sim 0.2 \fBH$ ($\sim 0.05 \fBH$) in a multiply-imaged lens system, where $\fBH$ is the fraction of galaxies housing binary black holes. We also study the effects of SMBBHs on the core images when galaxies have shallower central density profiles (modelled as non-singular isothermal ellipsoids). We find that the cross section of the usually faint core images is further suppressed by SMBBHs. Thus their presence should also be taken into account when one constrains the core radius from the lack of central images in gravitational lenses.

preprint2011arXiv

Hermite normal forms and $δ$-vector

Let $δ(\Pc) = (δ_0, δ_1,..., δ_d)$ be the $δ$-vector of an integral polytope $\Pc \subset \RR^N$ of dimension $d$. Following the previous work of characterizing the $δ$-vectors with $\sum_{i=0}^d δ_i \leq 3$, the possible $δ$-vectors with $\sum_{i=0}^d δ_i = 4$ will be classified. And each possible $δ$-vectors can be obtained by simplices. We get this result by studying the problem of classifying the possible integral simplices with a given $δ$-vector $(δ_0, δ_1,..., δ_d)$, where $\sum_{i=0}^d δ_i \leq 4$, by means of Hermite normal forms of square matrices.

preprint2011arXiv

Relatively maximum volume rigidity in Alexandrov geometry

Given a compact Alexadrov $n$-space $Z$ with curvature curv $\ge κ$, and let $f: Z\to X$ be a distance non-increasing onto map to another Alexandrov $n$-space with curv $\ge κ$. The relative volume rigidity conjecture says that if $X$ achieves the relative maximal volume i.e. $vol(Z)=vol(X)$, then $X$ is isometric to $Z/\sim$, where $z, z'\in\partial Z$ and $z\sim z'$ if only if $f(z)=f(z')$. We will partially verify this conjecture, and give a classification for compact Alexandrov $n$-spaces with relatively maximal volume. We will also give an elementary proof for a pointed version of Bishop-Gromov relative volume comparison with rigidity in Alexandrov geometry.

preprint2010arXiv

Generalized Ehrhart polynomials

Let $P$ be a polytope with rational vertices. A classical theorem of Ehrhart states that the number of lattice points in the dilations $P(n) = nP$ is a quasi-polynomial in $n$. We generalize this theorem by allowing the vertices of P(n) to be arbitrary rational functions in $n$. In this case we prove that the number of lattice points in P(n) is a quasi-polynomial for $n$ sufficiently large. Our work was motivated by a conjecture of Ehrhart on the number of solutions to parametrized linear Diophantine equations whose coefficients are polynomials in $n$, and we explain how these two problems are related.

preprint2010arXiv

Relative information entropy of an inhomogeneous universe

In the context of averaging an inhomogeneous cosmological model, we propose a natural measure identical to the Kullback-Leibler relative information entropy, which expresses the distinguishability of the local inhomogeneous density field from its spatial average on arbitrary compact domains. This measure is expected to be an increasing function in time and thus to play a significant role in studying gravitational entropy. To verify this conjecture, we explore the time evolution of the measure using the linear perturbation theory of a spatially flat FLRW model and a spherically symmetric nonlinear solution. We discuss the generality and conditions for the time-increasing nature of the measure, and also the connection to the backreaction effect caused by inhomogeneities.

preprint2005arXiv

Relations between quark and lepton mixing angles and matrices

We discuss the relations between the mixing angles and the mixing matrices of quarks and leptons. With Raidal's numerical relations, we parametrize the lepton mixing (PMNS) matrix with the parameters of the quark mixing (CKM) matrix, and calculate the products of $V_{\mathrm{CKM}}U_{\mathrm{PMNS}}$ and $U_{\mathrm{PMNS}}V_{\mathrm{CKM}}$. Also, under the conjectures $V_{\mathrm{CKM}}U_{\mathrm{PMNS}}=U_{\mathrm{bimax}}$ or $U_{\mathrm{PMNS}}V_{\mathrm{CKM}}=U_{\mathrm{bimax}}$, we get the PMNS matrix naturally, and test Raidal's relations in these two different versions. The similarities and the differences between the different versions are discussed in detail.

preprint2005arXiv

Unified Parametrization of Quark and Lepton Mixing Matrices

We present a unified parametrization of quark and lepton mixing matrices. By using some simple relations between the mixing angles of quarks and leptons, i.e., the quark-lepton complementarity, we parametrize the lepton mixing matrix with the Wolfenstein parameters $λ$ and $A$ of the quark mixing matrix. It is shown that the Wolfenstein parameter $λ$ can measure both the deviation of the quark mixing matrix from the unit matrix, and the deviation of the lepton mixing matrix from the exactly bimaximal mixing pattern.

preprint2004arXiv

A New Parametrization of the Neutrino Mixing Matrix

The neutrino mixing matrix is expanded in powers of a small parameter $λ$, which approximately equals to 0.1. The meaning of every order of the expansion is discussed respectively, and the range of $λ$ is carefully calculated. We also present some applications of this new parametrization, such as to the expression of the Jarlskog parameter $J$, in which the simplicities and advantages of this parametrization are shown.

preprint2004arXiv

Parametrization of Neutrino Mixing Matrix in Tri-bimaximal Mixing Pattern

The neutrino mixing matrix is expanded in powers of a small parameter $λ$ in tri-bimaximal mixing pattern. We also present some applications of this parametrization, such as to the expression of the Jarlskog parameter $J$. Comparing with other parametrizations (such as the parametrization in bimaximal mixing pattern), this parametrization converges more quickly, but is of less symmetry.