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Jie Sun

Jie Sun appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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math.DSnlin.AOnlin.CDcond-mat.stat-mechphysics.soc-phcond-mat.dis-nnInformation Theorymath.ITComputer Visionmath.OCphysics.data-anApplicationsArtificial Intelligencemath.RAPopulations and EvolutionMachine Learningmath-phmath.MPphysics.opticsComputationComputation and Languagecond-mat.mes-hallcond-mat.quant-gaseess.IVeess.SPInformation Retrievalmath.AGmath.CAmath.NANetworking and Internet Architecturenlin.PSNumerical Analysisphysics.comp-phq-fin.MFquant-phQuantitative MethodsRoboticsSocial and Information Networks

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Published work

53 published item(s)

preprint2026arXiv

SOD: Step-wise On-policy Distillation for Small Language Model Agents

Tool-integrated reasoning (TIR) is difficult to scale to small language models due to instability in long-horizon tool interactions and limited model capacity. While reinforcement learning methods like group relative policy optimization provide only sparse outcome-level rewards. Recently, on-policy distillation (OPD) has gained popularity by supplying dense token-level supervision from a teacher on student-generated trajectories. However, our experiments indicate that applying OPD to TIR leads to a critical failure mode: erroneous tool calls tend to cascade across subsequent reasoning steps, progressively amplifying student-teacher divergence and rendering the teacher's token-level supervision increasingly unreliable. To address this, we propose SOD, a step-wise on-policy distillation framework for small language model agents, which adaptively reweights distillation strength at each step based on step-level divergence. Therefore, SOD can attenuate potentially misleading teacher signals in high-divergence regions while preserving dense guidance in well-aligned states. Experiments on challenging math, science, and code benchmarks show that SOD achieves up to 20.86% improvement over the second-best baseline. Notably, our 0.6B student achieves 26.13% on AIME 2025, demonstrating effective transfer of agentic reasoning to lightweight models. Our code is available at https://github.com/YoungZ365/SOD.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Credible Remote Sensing Scene Classification Using Evidential Fusion on Aerial-Ground Dual-view Images

Due to their ability to offer more comprehensive information than data from a single view, multi-view (multi-source, multi-modal, multi-perspective, etc.) data are being used more frequently in remote sensing tasks. However, as the number of views grows, the issue of data quality becomes more apparent, limiting the potential benefits of multi-view data. Although recent deep neural network (DNN) based models can learn the weight of data adaptively, a lack of research on explicitly quantifying the data quality of each view when fusing them renders these models inexplicable, performing unsatisfactorily and inflexible in downstream remote sensing tasks. To fill this gap, in this paper, evidential deep learning is introduced to the task of aerial-ground dual-view remote sensing scene classification to model the credibility of each view. Specifically, the theory of evidence is used to calculate an uncertainty value which describes the decision-making risk of each view. Based on this uncertainty, a novel decision-level fusion strategy is proposed to ensure that the view with lower risk obtains more weight, making the classification more credible. On two well-known, publicly available datasets of aerial-ground dual-view remote sensing images, the proposed approach achieves state-of-the-art results, demonstrating its effectiveness. The code and datasets of this article are available at the following address: https://github.com/gaopiaoliang/Evidential.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

AD-GAN: End-to-end Unsupervised Nuclei Segmentation with Aligned Disentangling Training

We consider unsupervised cell nuclei segmentation in this paper. Exploiting the recently-proposed unpaired image-to-image translation between cell nuclei images and randomly synthetic masks, existing approaches, e.g., CycleGAN, have achieved encouraging results. However, these methods usually take a two-stage pipeline and fail to learn end-to-end in cell nuclei images. More seriously, they could lead to the lossy transformation problem, i.e., the content inconsistency between the original images and the corresponding segmentation output. To address these limitations, we propose a novel end-to-end unsupervised framework called Aligned Disentangling Generative Adversarial Network (AD-GAN). Distinctively, AD-GAN introduces representation disentanglement to separate content representation (the underling spatial structure) from style representation (the rendering of the structure). With this framework, spatial structure can be preserved explicitly, enabling a significant reduction of macro-level lossy transformation. We also propose a novel training algorithm able to align the disentangled content in the latent space to reduce micro-level lossy transformation. Evaluations on real-world 2D and 3D datasets show that AD-GAN substantially outperforms the other comparison methods and the professional software both quantitatively and qualitatively. Specifically, the proposed AD-GAN leads to significant improvement over the current best unsupervised methods by an average 17.8% relatively (w.r.t. the metric DICE) on four cell nuclei datasets. As an unsupervised method, AD-GAN even performs competitive with the best supervised models, taking a further leap towards end-to-end unsupervised nuclei segmentation.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Mind The Gap: Alleviating Local Imbalance for Unsupervised Cross-Modality Medical Image Segmentation

Unsupervised cross-modality medical image adaptation aims to alleviate the severe domain gap between different imaging modalities without using the target domain label. A key in this campaign relies upon aligning the distributions of source and target domain. One common attempt is to enforce the global alignment between two domains, which, however, ignores the fatal local-imbalance domain gap problem, i.e., some local features with larger domain gap are harder to transfer. Recently, some methods conduct alignment focusing on local regions to improve the efficiency of model learning. While this operation may cause a deficiency of critical information from contexts. To tackle this limitation, we propose a novel strategy to alleviate the domain gap imbalance considering the characteristics of medical images, namely Global-Local Union Alignment. Specifically, a feature-disentanglement style-transfer module first synthesizes the target-like source-content images to reduce the global domain gap. Then, a local feature mask is integrated to reduce the 'inter-gap' for local features by prioritizing those discriminative features with larger domain gap. This combination of global and local alignment can precisely localize the crucial regions in segmentation target while preserving the overall semantic consistency. We conduct a series of experiments with two cross-modality adaptation tasks, i,e. cardiac substructure and abdominal multi-organ segmentation. Experimental results indicate that our method achieves state-of-the-art performance in both tasks.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

On the Opportunity of Causal Learning in Recommendation Systems: Foundation, Estimation, Prediction and Challenges

Recently, recommender system (RS) based on causal inference has gained much attention in the industrial community, as well as the states of the art performance in many prediction and debiasing tasks. Nevertheless, a unified causal analysis framework has not been established yet. Many causal-based prediction and debiasing studies rarely discuss the causal interpretation of various biases and the rationality of the corresponding causal assumptions. In this paper, we first provide a formal causal analysis framework to survey and unify the existing causal-inspired recommendation methods, which can accommodate different scenarios in RS. Then we propose a new taxonomy and give formal causal definitions of various biases in RS from the perspective of violating the assumptions adopted in causal analysis. Finally, we formalize many debiasing and prediction tasks in RS, and summarize the statistical and machine learning-based causal estimation methods, expecting to provide new research opportunities and perspectives to the causal RS community.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Outpainting by Queries

Image outpainting, which is well studied with Convolution Neural Network (CNN) based framework, has recently drawn more attention in computer vision. However, CNNs rely on inherent inductive biases to achieve effective sample learning, which may degrade the performance ceiling. In this paper, motivated by the flexible self-attention mechanism with minimal inductive biases in transformer architecture, we reframe the generalised image outpainting problem as a patch-wise sequence-to-sequence autoregression problem, enabling query-based image outpainting. Specifically, we propose a novel hybrid vision-transformer-based encoder-decoder framework, named \textbf{Query} \textbf{O}utpainting \textbf{TR}ansformer (\textbf{QueryOTR}), for extrapolating visual context all-side around a given image. Patch-wise mode's global modeling capacity allows us to extrapolate images from the attention mechanism's query standpoint. A novel Query Expansion Module (QEM) is designed to integrate information from the predicted queries based on the encoder's output, hence accelerating the convergence of the pure transformer even with a relatively small dataset. To further enhance connectivity between each patch, the proposed Patch Smoothing Module (PSM) re-allocates and averages the overlapped regions, thus providing seamless predicted images. We experimentally show that QueryOTR could generate visually appealing results smoothly and realistically against the state-of-the-art image outpainting approaches.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Solvability of Multistage Pseudomonotone Stochastic Variational Inequalities

This paper focuses on the solvability of multistage pseudomonotone stochastic variational inequalities (SVIs). On one hand, some known solvability results of pseudomonotone deterministic variational inequalities cannot be directly extended to pseudomonotone SVIs, so we construct the isomorphism between both and then establish theoretical results on the existence, convexity, boundedness and compactness of the solution set for pseudomonotone SVIs via such an isomorphism. On the other hand, the progressive hedging algorithm (PHA) is an important and effective method for solving monotone SVIs, but it cannot be directly used to solve nonmonotone SVIs. We propose some sufficient conditions on the elicitability of pseudomonotone SVIs, which opens the door for applying elicited PHA to solve pseudomonotone SVIs. Numerical results on solving a pseudomonotone two-stage stochastic market optimization problem and randomly generated two stage pseudomonotone linear complementarity problems are presented to show the efficiency of the elicited PHA for solving pseudomonotone SVIs.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Ground-SLAM: Ground Constrained LiDAR SLAM for Structured Multi-Floor Environments

This paper proposes a 3D LiDAR SLAM algorithm named Ground-SLAM, which exploits grounds in structured multi-floor environments to compress the pose drift mainly caused by LiDAR measurement bias. Ground-SLAM is developed based on the well-known pose graph optimization framework. In the front-end, motion estimation is conducted using LiDAR Odometry (LO) with a novel sensor-centric sliding map introduced, which is maintained by filtering out expired features based on the model of error propagation. At each key-frame, the sliding map is recorded as a local map. The ground nearby is extracted and modelled as an infinite planar landmark in the form of Closest Point (CP) parameterization. Then, ground planes observed at different key-frames are associated, and the ground constraints are fused into the pose graph optimization framework to compress the pose drift of LO. Finally, loop-closure detection is carried out, and the residual error is jointly minimized, which could lead to a globally consistent map. Experimental results demonstrate superior performances in the accuracy of the proposed approach.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Bright solitons in a spin-tensor-momentum-coupled Bose-Einstein condensate

Synthetic spin-tensor-momentum coupling has recently been proposed to realize in atomic Bose-Einstein condensates. Here we study bright solitons in Bose-Einstein condensates with spin-tensor-momentum coupling and spin-orbit coupling. The properties and dynamics of spin-tensor-momentum-coupled and spin-orbit-coupled bright solitons are identified to be different. We contribute the difference to the different symmetries.

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preprint2020arXiv

Data-Driven Learning of Boolean Networks and Functions by Optimal Causation Entropy Principle (BoCSE)

Boolean functions and networks are commonly used in the modeling and analysis of complex biological systems, and this paradigm is highly relevant in other important areas in data science and decision making, such as in the medical field and in the finance industry. Automated learning of a Boolean network and Boolean functions, from data, is a challenging task due in part to the large number of unknowns (including both the structure of the network and the functions) to be estimated, for which a brute force approach would be exponentially complex. In this paper we develop a new information theoretic methodology that we show to be significantly more efficient than previous approaches. Building on the recently developed optimal causation entropy principle (oCSE), that we proved can correctly infer networks distinguishing between direct versus indirect connections, we develop here an efficient algorithm that furthermore infers a Boolean network (including both its structure and function) based on data observed from the evolving states at nodes. We call this new inference method, Boolean optimal causation entropy (BoCSE), which we will show that our method is both computationally efficient and also resilient to noise. Furthermore, it allows for selection of a set of features that best explains the process, a statement that can be described as a networked Boolean function reduced order model. We highlight our method to the feature selection in several real-world examples: (1) diagnosis of urinary diseases, (2) Cardiac SPECT diagnosis, (3) informative positions in the game Tic-Tac-Toe, and (4) risk causality analysis of loans in default status. Our proposed method is effective and efficient in all examples.

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preprint2020arXiv

Risk Minimization, Regret Minimization and Progressive Hedging Algorithms

This paper begins with a study on the dual representations of risk and regret measures and their impact on modeling multistage decision making under uncertainty. A relationship between risk envelopes and regret envelopes is established by using the Lagrangian duality theory. Such a relationship opens a door to a decomposition scheme, called progressive hedging, for solving multistage risk minimization and regret minimization problems. In particular, the classical progressive hedging algorithm is modified in order to handle a new class of linkage constraints that arises from reformulations and other applications of risk and regret minimization problems. Numerical results are provided to show the efficiency of the progressive hedging algorithms.

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preprint2020arXiv

RODE-Net: Learning Ordinary Differential Equations with Randomness from Data

Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge. Extracting the governing equations from data with less prior knowledge remains a great challenge. In this paper, we propose a deep neural network, called RODE-Net, to tackle such challenge by fitting a symbolic expression of the differential equation and the distribution of parameters simultaneously. To train the RODE-Net, we first estimate the parameters of the unknown RODE using the symbolic networks \cite{long2019pde} by solving a set of deterministic inverse problems based on the measured data, and use a generative adversarial network (GAN) to estimate the true distribution of the RODE's parameters. Then, we use the trained GAN as a regularization to further improve the estimation of the ODE's parameters. The two steps are operated alternatively. Numerical results show that the proposed RODE-Net can well estimate the distribution of model parameters using simulated data and can make reliable predictions. It is worth noting that, GAN serves as a data driven regularization in RODE-Net and is more effective than the $\ell_1$ based regularization that is often used in system identifications.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

How Entropic Regression Beats the Outliers Problem in Nonlinear System Identification

In this work, we developed a nonlinear System Identification (SID) method that we called Entropic Regression. Our method adopts an information-theoretic measure for the data-driven discovery of the underlying dynamics. Our method shows robustness toward noise and outliers and it outperforms many of the current state-of-the-art methods. Moreover, the method of Entropic Regression overcomes many of the major limitations of the current methods such as sloppy parameters, diverse scale, and SID in high dimensional systems such as complex networks. The use of information-theoretic measures in entropic regression poses unique advantages, due to the Asymptotic Equipartition Property (AEP) of probability distributions, that outliers and other low-occurrence events are conveniently and intrinsically de-emphasized as not-typical, by definition. We provide a numerical comparison with the current state-of-the-art methods in sparse regression, and we apply the methods to different chaotic systems such as the Lorenz System, the Kuramoto-Sivashinsky equations, and the Double Well Potential.

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preprint2019arXiv

Synchronization of Network-Coupled Oscillators with Uncertain Dynamics

Synchronization of network-coupled dynamical units is important to a variety of natural and engineered processes including circadian rhythms, cardiac function, neural processing, and power grids. Despite this ubiquity, it remains poorly understood how complex network structures and heterogeneous local dynamics combine to either promote or inhibit synchronization. Moreover, for most real-world applications it is impossible to obtain the exact specifications of the system, and there is a lack of theory for how uncertainty affects synchronization. We address this open problem by studying the Synchrony Alignment Function (SAF), which is an objective measure for the synchronization properties of a network of heterogeneous oscillators with given natural frequencies. We extend the SAF framework to analyze network-coupled oscillators with heterogeneous natural frequencies that are drawn as a multivariate random vector. Using probability theory for quadratic forms, we obtain expressions for the expectation and variance of the SAF for given network structures. We conclude with numerical experiments that illustrate how the incorporation of uncertainty yields a more robust theoretical framework for enhancing synchronization, and we provide new perspectives for why synchronization is generically promoted by network properties including degree-frequency correlations, link directedness, and link weight delocalization.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

A robust optimal control problem with moment constraints on distribution: theoretical analysis and an algorithm

We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as the worst-case expectation over a set of possible distributions of the uncertain parameter. This ambiguity set of distributions is, in turn, defined by the first two moments of the random variables involved. The optimal control is found by minimizing the worst-case expectation over all possible distributions in this set. If the distributions are discrete, the stochastic min-max optimal control problem can be converted into a convensional optimal control problem via duality, which is then approximated as a finite-dimensional optimization problem via the control parametrization. We derive necessary conditions of optimality and propose an algorithm to solve the approximation optimization problem. The results of discrete probability distribution are then extended to the case with one dimensional continuous stochastic variable by applying the control parametrization methodology on the continuous stochastic variable, and the convergence results are derived. A numerical example is present to illustrate the potential application of the proposed model and the effectiveness of the algorithm.

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preprint2016arXiv

Collective frequency variation in network synchronization and reverse PageRank

A wide range of natural and engineered phenomena rely on large networks of interacting units to reach a dynamical consensus state where the system collectively operates. Here we study the dynamics of self-organizing systems and show that for generic directed networks the collective frequency of the ensemble is {\it not} the same as the mean of the individuals' natural frequencies. Specifically, we show that the collective frequency equals a weighted average of the natural frequencies, where the weights are given by an out-flow centrality measure that is equivalent to a reverse PageRank centrality. Our findings uncover an intricate dependence of the collective frequency on both the structural directedness and dynamical heterogeneity of the network, and also reveal an unexplored connection between synchronization and PageRank, which opens the possibility of applying PageRank optimization to synchronization. Finally, we demonstrate the presence of collective frequency variation in real-world networks by considering the UK and Scandinavian power grids.

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preprint2016arXiv

Commutators of multilinear Calderón-Zygmund operators with kernels of Dini's type and applications

Let $T$ be a multilinear Calderón-Zygmund operator of type $ω$ with $ω(t)$ being nondecreasing and satisfying a kind of Dini's type condition. Let $T_{Π\vec{b}}$ be the iterated commutators of $T$ with $BMO$ functions. The weighted strong and weak $L(\log{L})$-type endpoint estimates for $T_{Π\vec{b}}$ with multiple weights are established. Some boundedness properties on weighted variable exponent Lebesgue spaces are also obtained. As applications, multiple weighted estimates for iterated commutators of paraproducts and bilinear pseudo-differential operators with mild regularity are given.

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preprint2016arXiv

Inference of Causal Information Flow in Collective Animal Behavior

Understanding and even defining what constitutes animal interactions remains a challenging problem. Correlational tools may be inappropriate for detecting communication between a set of many agents exhibiting nonlinear behavior. A different approach is to define coordinated motions in terms of an information theoretic channel of direct causal information flow. In this work, we consider time series data obtained by an experimental protocol of optical tracking of the insect species Chironomus riparius. The data constitute reconstructed 3-D spatial trajectories of the insects' flight trajectories and kinematics. We present an application of the optimal causation entropy (oCSE) principle to identify direct causal relationships or information channels among the insects. The collection of channels inferred by oCSE describes a network of information flow within the swarm. We find that information channels with a long spatial range are more common than expected under the assumption that causal information flows should be spatially localized. The tools developed herein are general and applicable to the inference and study of intercommunication networks in a wide variety of natural settings.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Information theoretical noninvasive damage detection in bridge structures

Damage detection of mechanical structures such as bridges is an important research problem in civil engineering. Using spatially distributed sensor time series data collected from a recent experiment on a local bridge in upper state New York, we study noninvasive damage detection using information-theoretical methods. Several findings are in order. First, the time series data, which represent accelerations measured at the sensors, more closely follow Laplace distribution than normal distribution, allowing us to develop parameter estimators for various information-theoretic measures such as entropy and mutual information. Secondly, as damage is introduced by the removal of bolts of the first diaphragm connection, the interaction between spatially nearby sensors as measured by mutual information become weaker, suggesting that the bridge is "loosened". Finally, using a proposed oMII procedure to prune away indirect interactions, we found that the primary direction of interaction or influence aligns with the traffic direction on the bridge even after damaging the bridge.

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preprint2016arXiv

Master Stability Islands for Amplitude Death in Networks of Delay-Coupled Oscillators

This paper presents a master stability function (MSF) approach for analyzing the stability of amplitude death (AD) in networks of delay-coupled oscillators. Unlike the familiar MSFs for instantaneously coupled networks, which typically have a single input encoding for the effects of the eigenvalues of the network Laplacian matrix, for delay-coupled networks we show that such MSFs generally require two additional inputs: the time delay and the coupling strength. To utilize the MSF for predicting the stability of AD of arbitrary networks for a chosen nonlinear system (node dynamics) and coupling function, we introduce the concept of master stability islands (MSIs), which are two-dimensional stability islands of the delay-coupling space together with a third dimension ("altitude") encoding for eigenvalues that result in stable AD. We compute the MSFs and show the corresponding MSIs for several common chaotic systems including the Rossler, the Lorenz, and Chen's system, and found that it is generally possible to achieve AD and that a nonzero time delay is necessary for the stabilization of the AD states.

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preprint2016arXiv

Optimal synchronization of directed complex networks

We study optimal synchronization of networks of coupled phase oscillators. We extend previous theory for optimizing the synchronization properties of undirected networks to the important case of directed networks. We derive a generalized synchrony alignment function that encodes the interplay between network structure and the oscillators' natural frequencies and serves as an objective measure for the network's degree of synchronization. Using the generalized synchrony alignment function, we show that a network's synchronization properties can be systematically optimized. This framework also allows us to study the properties of synchrony-optimized networks, and in particular, investigate the role of directed network properties such as nodal in- and out-degrees. For instance, we find that in optimally rewired networks the heterogeneity of the in-degree distribution roughly matches the heterogeneity of the natural frequency distribution, but no such relationship emerges for out-degrees. We also observe that a network's synchronization properties are promoted by a strong correlation between the nodal in-degrees and the natural frequencies of oscillators, whereas the relationship between the nodal out-degrees and the natural frequencies has comparatively little effect. This result is supported by our theory, which indicates that synchronization is promoted by a strong alignment of the natural frequencies with the left singular vectors corresponding to the largest singular values of the Laplacian matrix.

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preprint2015arXiv

Broadband Linear-Dichroic Photodetector in a Black Phosphorus Vertical p-n Junction

The ability to detect light over a broad spectral range is central for practical optoelectronic applications, and has been successfully demonstrated with photodetectors of two-dimensional layered crystals such as graphene and MoS2. However, polarization sensitivity within such a photodetector remains elusive. Here we demonstrate a linear-dichroic broadband photodetector with layered black phosphorus transistors, using the strong intrinsic linear dichroism arising from the in-plane optical anisotropy with respect to the atom-buckled direction, which is polarization sensitive over a broad bandwidth from 400 nm to 3750 nm. Especially, a perpendicular build-in electric field induced by gating in black phosphorus transistors can spatially separate the photo-generated electrons and holes in the channel, effectively reducing their recombination rate, and thus enhancing the efficiency and performance for linear dichroism photodetection. This provides new functionality using anisotropic layered black phosphorus, thereby enabling novel optical and optoelectronic device applications.

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preprint2015arXiv

Causal Network Inference by Optimal Causation Entropy

The broad abundance of time series data, which is in sharp contrast to limited knowledge of the underlying network dynamic processes that produce such observations, calls for a rigorous and efficient method of causal network inference. Here we develop mathematical theory of causation entropy, an information-theoretic statistic designed for model-free causality inference. For stationary Markov processes, we prove that for a given node in the network, its causal parents forms the minimal set of nodes that maximizes causation entropy, a result we refer to as the optimal causation entropy principle. Furthermore, this principle guides us to develop computational and data efficient algorithms for causal network inference based on a two-step discovery and removal algorithm for time series data for a network-couple dynamical system. Validation in terms of analytical and numerical results for Gaussian processes on large random networks highlight that inference by our algorithm outperforms previous leading methods including conditioned Granger causality and transfer entropy. Interestingly, our numerical results suggest that the number of samples required for accurate inference depends strongly on network characteristics such as the density of links and information diffusion rate and not necessarily on the number of nodes.

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preprint2015arXiv

Causation entropy from symbolic representations of dynamical systems

Identification of causal structures and quantification of direct information flows in complex systems is a challenging yet important task, with practical applications in many fields. Data generated by dynamical processes or large-scale systems are often symbolized, either because of the finite resolution of the measurement apparatus, or because of the need of statistical estimation. By algorithmic application of causation entropy, we investigated the effects of symbolization on important concepts such as Markov order and causal structure of the tent map. We uncovered that these quantities depend nonmontonically and, most of all, sensitively on the choice of symbolization. Indeed, we show that Markov order and causal structure do not necessarily converge to their original analog counterparts as the resolution of the partitioning becomes finer.

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preprint2015arXiv

Causation Entropy Identifies Indirect Influences, Dominance of Neighbors and Anticipatory Couplings

Inference of causality is central in nonlinear time series analysis and science in general. A popular approach to infer causality between two processes is to measure the information flow between them in terms of transfer entropy. Using dynamics of coupled oscillator networks, we show that although transfer entropy can successfully detect information flow in two processes, it often results in erroneous identification of network connections under the presence of indirect interactions, dominance of neighbors, or anticipatory couplings. Such effects are found to be profound for time-dependent networks. To overcome these limitations, we develop a measure called causation entropy and show that its application can lead to reliable identification of true couplings.

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preprint2015arXiv

Detecting structural breaks in seasonal time series by regularized optimization

Real-world systems are often complex, dynamic, and nonlinear. Understanding the dynamics of a system from its observed time series is key to the prediction and control of the system's behavior. While most existing techniques tacitly assume some form of stationarity or continuity, abrupt changes, which are often due to external disturbances or sudden changes in the intrinsic dynamics, are common in time series. Structural breaks, which are time points at which the statistical patterns of a time series change, pose considerable challenges to data analysis. Without identification of such break points, the same dynamic rule would be applied to the whole period of observation, whereas false identification of structural breaks may lead to overfitting. In this paper, we cast the problem of decomposing a time series into its trend and seasonal components as an optimization problem. This problem is ill-posed due to the arbitrariness in the number of parameters. To overcome this difficulty, we propose the addition of a penalty function (i.e., a regularization term) that accounts for the number of parameters. Our approach simultaneously identifies seasonality and trend without the need of iterations, and allows the reliable detection of structural breaks. The method is applied to recorded data on fish populations and sea surface temperature, where it detects structural breaks that would have been neglected otherwise. This suggests that our method can lead to a general approach for the monitoring, prediction, and prevention of structural changes in real systems.

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preprint2015arXiv

Editorial Comment on the Special Issue of "Information in Dynamical Systems and Complex Systems"

This special issue collects contributions from the participants of the "Information in Dynamical Systems and Complex Systems" workshop, which cover a wide range of important problems and new approaches that lie in the intersection of information theory and dynamical systems. The contributions include theoretical characterization and understanding of the different types of information flow and causality in general stochastic processes, inference and identification of coupling structure and parameters of system dynamics, rigorous coarse-grain modeling of network dynamical systems, and exact statistical testing of fundamental information-theoretic quantities such as the mutual information. The collective efforts reported herein reflect a modern perspective of the intimate connection between dynamical systems and information flow, leading to the promise of better understanding and modeling of natural complex systems and better/optimal design of engineering systems.

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preprint2015arXiv

Erosion of synchronization in networks of coupled oscillators

We report erosion of synchronization in networks of coupled phase oscillators, a phenomenon where perfect phase synchronization is unattainable in steady-state, even in the limit of infinite coupling. An analysis reveals that the total erosion is separable into the product of terms characterizing coupling frustration and structural heterogeneity, both of which amplify erosion. The latter, however, can differ significantly from degree heterogeneity. Finally, we show that erosion is marked by the reorganization of oscillators according to their node degrees rather than their natural frequencies.

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preprint2015arXiv

Erosion of synchronization: Coupling heterogeneity and network structure

We study the dynamics of network-coupled phase oscillators in the presence of coupling frustration. It was recently demonstrated that in heterogeneous network topologies, the presence of coupling frustration causes perfect phase synchronization to become unattainable even in the limit of infinite coupling strength. Here, we consider the important case of heterogeneous coupling functions and extend previous results by deriving analytical predictions for the total erosion of synchronization. Our analytical results are given in terms of basic quantities related to the network structure and coupling frustration. In addition to fully heterogeneous coupling, where each individual interaction is allowed to be distinct, we also consider partially heterogeneous coupling and homogeneous coupling in which the coupling functions are either unique to each oscillator or identical for all network interactions, respectively. We demonstrate the validity of our theory with numerical simulations of multiple network models, and highlight the interesting effects that various coupling choices and network models have on the total erosion of synchronization. Finally, we consider some special network structures with well-known spectral properties, which allows us to derive further analytical results.

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preprint2015arXiv

Growing Networks with Super-Joiners

We study the Krapivsky-Redner (KR) network growth model but where new nodes can connect to any number of existing nodes, $m$, picked from a power-law distribution $p(m)\sim m^{-α}$. Each of the $m$ new connections is still carried out as in the KR model with probability redirection $r$ (corresponding to degree exponent $γ_{\rm KR}=1+1/r$, in the original KR model). The possibility to connect to any number of nodes resembles a more realistic type of growth in several settings, such as social networks, routers networks, and networks of citations. Here we focus on the in-, out-, and total-degree distributions and on the potential tension between the degree exponent $α$, characterizing new connections (outgoing links), and the degree exponent $γ_{\rm KR}(r)$ dictated by the redirection mechanism.

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preprint2015arXiv

Regularity underlies erratic population abundances in marine ecosystems

The abundance of a species' population in an ecosystem is rarely stationary, often exhibiting large fluctuations over time. Using historical data on marine species, we show that the year-to-year fluctuations of population growth rate obey a well-defined double-exponential (Laplace) distribution. This striking regularity allows us to devise a stochastic model despite seemingly irregular variations in population abundances. The model identifies the effect of reduced growth at low population density as a key factor missed in current approaches of population variability analysis and without which extinction risks are severely underestimated. The model also allows us to separate the effect of demographic stochasticity and show that single-species growth rates are dominantly determined by stochasticity common to all species. This dominance---and the implications it has for interspecies correlations, including co-extinctions---emphasizes the need of ecosystem-level management approaches to reduce the extinction risk of the individual species themselves.

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preprint2014arXiv

Chip-Scale Continuously Tunable Optical Orbital Angular Momentum Generator

Light carrying orbital angular momentum (OAM) has potential to impact a wide variety of applications ranging from optical communications to quantum information and optical forces for the excitation and manipulation of atoms, molecules, and micro-particles. The unique advantage of utilizing OAM in these applications relies, to a large extent, on the use of multiple different OAM states. Therefore, it is desirable to have a device that is able to gen- erate light with freely adjustable OAM states in an integrated form for large- scale integration. We propose and demonstrate a compact silicon photonic integrated circuit to generate a free-space optical beam with OAM state con- tinuously tuned from a single electrical input signal, realizing both integer and non-integer OAM states. The compactness and flexibility of the device and its compatibility with complementary metal-oxide-semiconductor (CMOS) pro- cessing hold promise for integration with other silicon photonic components for wide-ranging applications.

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preprint2014arXiv

Identifying Coupling Structure in Complex Systems through the Optimal Causation Entropy Principle

Inferring the coupling structure of complex systems from time series data in general by means of statistical and information-theoretic techniques is a challenging problem in applied science. The reliability of statistical inferences requires the construction of suitable information-theoretic measures that take into account both direct and indirect influences, manifest in the form of information flows, between the components within the system. In this work, we present an application of the optimal causation entropy (oCSE) principle to identify the coupling structure of a synthetic biological system, the repressilator. Specifically, when the system reaches an equilibrium state, we use a stochastic perturbation approach to extract time series data that approximate a linear stochastic process. Then, we present and jointly apply the aggregative discovery and progressive removal algorithms based on the oCSE principle to infer the coupling structure of the system from the measured data. Finally, we show that the success rate of our coupling inferences not only improves with the amount of available data, but it also increases with a higher frequency of sampling and is especially immune to false positives.

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preprint2014arXiv

Optimal synchronization of complex networks

We study optimal synchronization in networks of heterogeneous phase oscillators. Our main result is the derivation of a synchrony alignment function that encodes the interplay between network structure and oscillators' frequencies and can be readily optimized. We highlight its utility in two general problems: constrained frequency allocation and network design. In general, we find that synchronization is promoted by strong alignments between frequencies and the dominant Laplacian eigenvectors, as well as a matching between the heterogeneity of frequencies and network structure.

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preprint2014arXiv

Spatially distributed social complex networks

We propose a bare-bones stochastic model that takes into account both the geographical distribution of people within a country and their complex network of connections. The model, which is designed to give rise to a scale-free network of social connections and to visually resemble the geographical spread seen in satellite pictures of the Earth at night, gives rise to a power-law distribution for the ranking of cities by population size (but for the largest cities) and reflects the notion that highly connected individuals tend to live in highly populated areas. It also yields some interesting insights regarding Gibrat's law for the rates of city growth (by population size), in partial support of the findings in a recent analysis of real data [Rozenfeld et al., Proc. Natl. Acad. Sci. U.S.A. 105, 18702 (2008)]. The model produces a nontrivial relation between city population and city population density and a superlinear relationship between social connectivity and city population, both of which seem quite in line with real data.

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preprint2014arXiv

Spectral Operators of Matrices

The class of matrix optimization problems (MOPs) has been recognized in recent years to be a powerful tool by researchers far beyond the optimization community to model many important applications involving structured low rank matrices. This trend can be credited to some extent to the exciting developments in the emerging field of compressed sensing. The Löwner operator, which generates a matrix valued function by applying a single-variable function to each of the singular values of a matrix, has played an important role for a long time in solving matrix optimization problems. However, the classical theory developed for Löwner operators has become inadequate in these recent applications. The main objective of this paper is to provide some necessary theoretical foundations for designing numerical methods for solving the MOP. This goal is achieved by introducing and conducting a thorough study on a new class of matrix valued functions, coined as spectral operators of matrices. Several fundamental properties of spectral operators, including the well-definedness, continuity, directional differentiability, Fréchet-differentiability, locally Lipschitzian continuity, $ρ$-order B(ouligand)-differentiability ($0<ρ\leq 1$), $ρ$-order G-semismooth ($0<ρ\leq 1$) and the characterization of Clarke's generalized Jacobian, are systematically studied.

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preprint2013arXiv

A one femtojoule athermal silicon modulator

Silicon photonics has emerged as the leading candidate for implementing ultralow power wavelength division multiplexed communication networks in high-performance computers, yet current components (lasers, modulators, filters, and detectors) consume too much power for the femtojouleclass links that will ultimately be required. Here, we propose, demonstrate, and characterize the first modulator to achieve simultaneous high-speed (25-Gb/s), low voltage (0.5VPP) and efficient 1-fJ/bit error-free operation while maintaining athermal operation. Both the low energy and athermal operation were enabled by a record free-carrier accumulation/depletion response obtained in a vertical p-n junction device that at 250-pm/V (30-GHz/V) is up to ten times larger than prior demonstrations. Over a 7.5°C temperature range, the massive electro-optic response was used to compensate for thermal drift without increasing energy consumption and over a 10°C temperature range, increasing energy consumption by only 2-fJ/bit. The results represent a new paradigm in modulator development, one where thermal compensation is achieved electro-optically.

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preprint2013arXiv

Controllability transition and nonlocality in network control

A common goal in the control of a large network is to minimize the number of driver nodes or control inputs. Yet, the physical determination of control signals and the properties of the resulting control trajectories remain widely under-explored. Here we show that: (i) numerical control fails in practice even for linear systems if the controllability Gramian is ill-conditioned, which occurs frequently even when existing controllability criteria are satisfied unambiguously; (ii) the control trajectories are generally nonlocal in the phase space, and their lengths are strongly anti-correlated with the numerical success rate and number of control inputs; (iii) numerical success rate increases abruptly from zero to nearly one as the number of control inputs is increased, a transformation we term numerical controllability transition. This reveals a trade-off between nonlocality of the control trajectory in the phase space and nonlocality of the control inputs in the network itself. The failure of numerical control cannot be overcome in general by merely increasing numerical precision---successful control requires instead increasing the number of control inputs beyond the numerical controllability transition.

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preprint2013arXiv

On models of nonlinear evolution paths in adiabatic quantum algorithms

In this paper, we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state. If the overlap between the initial state and final state of the quantum system is not equal to zero, both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity". But when the initial state has a zero overlap with the solution state in the problem, the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time. However, inspired by a related reference, a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model-an increase in energy. Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above. These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.

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preprint2012arXiv

Effects of degree-frequency correlations on network synchronization: universality and full phase-locking

We introduce a model to study the effect of degree-frequency correlations on synchronization in networks of coupled oscillators. Analyzing this model, we find several remarkable characteristics. We find a stationary synchronized state that is (i) universal, i.e., the degree of synchrony, as measured by a global order parameter, is independent of network topology, and (ii) fully phase-locked, i.e., all oscillators become simultaneously phase-locked despite having different natural frequencies. This state separates qualitatively different behaviors for two other classes of correlations where, respectively, slow and fast oscillators can remain unsynchronized. We close by presenting analysis of the dynamics under arbitrary degree-frequency correlations.

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preprint2011arXiv

A Mathematical Model for the Dynamics and Synchronization of Cows

We formulate a mathematical model for daily activities of a cow (eating, lying down, and standing) in terms of a piecewise affine dynamical system. We analyze the properties of this bovine dynamical system representing the single animal and develop an exact integrative form as a discrete-time mapping. We then couple multiple cow "oscillators" together to study synchrony and cooperation in cattle herds. We comment on the relevant biology and discuss extensions of our model. With this abstract approach, we not only investigate equations with interesting dynamics but also develop interesting biological predictions. In particular, our model illustrates that it is possible for cows to synchronize \emph{less} when the coupling is increased.

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preprint2011arXiv

Comment on "Controllability of Complex Networks with Nonlinear Dynamics"

The recent paper by W.-X. Wang, Y.-C. Lai, J. Ren, B. Li & C. Grebogi [arXiv:1107.2177v1] proposed a method for the control of complex networks with nonlinear dynamics based on linearizing the system around a finite number of local desired states. The authors purport that any bidirectional network with one-dimensional intrinsic node dynamics can be fully controlled by a single driver node, which can be any node in the network, regardless of the network topology. According to this result, a network with an arbitrarily large number of nodes (a million, a billion, or even more) could be controlled by a single node. Here we show, however, that this result is specious and that it does not hold true even for networks with only two nodes. We demonstrate that the erroneous results are a consequence of a fundamental flaw in the proposed method, namely, that reaching a local desired state using the proposed linearization procedure generally requires a nonlocal trajectory, which grossly violates the linear approximation. Their further conclusion that network systems with nonlinear dynamics are more controllable than those with linear dynamics is a known fact presented as novel based on a flawed argument. A central problem underlying the authors' argument is that their formulation is entirely based on the number of driver nodes required to reach a desired state---even when this number is one, keeping the system at that desired state generally requires directly controlling all nodes in the network. When this is taken into account, the conclusion that nonlinear dynamics can facilitate network control was already anticipated in S.P. Cornelius, W.L. Kath & A.E. Motter [arXiv:1105.3726v1], which is not referenced in their paper. If one insists on using the authors' formulation, then, in contradiction to their claim, nonlinear systems would never be more controllable than linear ones because...

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preprint2011arXiv

Robustness of Optimal Synchronization in Real Networks

Experimental studies of synchronization properties on networks with controlled connection topology can provide powerful insights into the physics of complex networks. Here, we report experimental results on the influence of connection topology on synchronization in fiber-optic networks of chaotic optoelectronic oscillators. We find that the recently predicted non-monotonic, cusp-like synchronization landscape manifests itself in the rate of convergence to the synchronous state. We also observe that networks with the same number of nodes, same number of links, and identical eigenvalues of the coupling matrix can exhibit fundamentally different approaches to synchronization. This previously unnoticed difference is determined by the degeneracy of associated eigenvectors in the presence of noise and mismatches encountered in real-world conditions.

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preprint2010arXiv

Approximating Spectral Impact of Structural Perturbations in Large Networks

Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as synchronization and cascading processes on networks. Here we develop a theory for estimating the change of the largest eigenvalue of the adjacency matrix or the extreme eigenvalues of the graph Laplacian when small but arbitrary set of links are added or removed from the network. We demonstrate the effectiveness of our approximation schemes using both real and artificial networks, showing in particular that we can accurately obtain the spectral ranking of small subgraphs. We also propose a local iterative scheme which computes the relative ranking of a subgraph using only the connectivity information of its neighbors within a few links. Our results may not only contribute to our theoretical understanding of dynamical processes on networks, but also lead to practical applications in ranking subgraphs of real complex networks.

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preprint2010arXiv

Cyclotomic Temperley-Lieb algebra of type D and its representation theory

We define a new class of algebras, cyclotomic Temperley-Lieb algebras of type D, in a diagrammatic way, which is a generalization of Temperley-Lieb algebras of type D. We prove that the cyclotomic Temperley-Lieb algebras of type D are cellular. In fact, an explicit cellular basis is given by means of combinatorial methods. After determining all the irreducible representations of these algebras, we give a necessary and sufficient condition for a cyclotomic Temperley-Lieb algebra of type D to be quasi-hereditary.

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preprint2010arXiv

Greedy Connectivity of Geographically Embedded Graphs

We introduce a measure of {\em greedy connectivity} for geographical networks (graphs embedded in space) and where the search for connecting paths relies only on local information, such as a node's location and that of its neighbors. Constraints of this type are common in everyday life applications. Greedy connectivity accounts also for imperfect transmission across established links and is larger the higher the proportion of nodes that can be reached from other nodes with a high probability. Greedy connectivity can be used as a criterion for optimal network design.

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preprint2010arXiv

Judging Model Reduction of Chaotic Systems via Optimal Shadowing Criteria

A common goal in the study of high dimensional and complex system is to model the system by a low order representation. In this letter we propose a general approach for assessing the quality of a reduced order model for high dimensional chaotic systems. The key of this approach is the use of optimal shadowing, combined with dimensionality reduction techniques. Rather than quantify the quality of a model based on the quality of predictions, which can be irrelevant for chaotic systems since even excellent models can do poorly, we suggest that a good model should allow shadowing by modeled data for long times; this principle leads directly to an optimal shadowing criterion of model reduction. This approach overcomes the usual difficulties encountered by traditional methods which either compare systems of the same size by normed-distance in the functional space, or measure how close an orbit generated by a model is to the observed data. Examples include interval arithmetic computations to validate the optimal shadowing.

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preprint2009arXiv

Asymptotic behavior of the Kleinberg model

We study Kleinberg navigation (the search of a target in a d-dimensional lattice, where each site is connected to one other random site at distance r, with probability proportional to r^{-a}) by means of an exact master equation for the process. We show that the asymptotic scaling behavior for the delivery time T to a target at distance L scales as (ln L)^2 when a=d, and otherwise as L^x, with x=(d-a)/(d+1-a) for a<d, x=a-d for d<a<d+1, and x=1 for a>d+1. These values of x exceed the rigorous lower-bounds established by Kleinberg. We also address the situation where there is a finite probability for the message to get lost along its way and find short delivery times (conditioned upon arrival) for a wide range of a's.

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preprint2008arXiv

Synchronization Stability of Coupled Near-Identical Oscillator Network

We derive variational equations to analyze the stability of synchronization for coupled near-identical oscillators. To study the effect of parameter mismatch on the stability in a general fashion, we define master stability equations and associated master stability functions, which are independent of the network structure. In particular, we present several examples of coupled near-identical Lorenz systems configured in small networks (a ring graph and sequence networks) with a fixed parameter mismatch and a large Barabasi-Albert scale-free network with random parameter mismatch. We find that several different network architectures permit similar results despite various mismatch patterns.

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preprint2007arXiv

Graph Compression -- Save Information by Exploiting Redundancy

In this paper we raise the question of how to compress sparse graphs. By introducing the idea of redundancy, we find a way to measure the overlap of neighbors between nodes in networks. We exploit symmetry and information by making use of the overlap in neighbors and analyzing how information is reduced by shrinking the network and using the specific data structure we created, we generalize the problem of compression as an optimization problem on the possible choices of orbits. To find a reasonably good solution to this problem we use a greedy algorithm to determine the orbit of symmetry identifications, to achieve compression. Some example implementations of our algorithm are illustrated and analyzed.

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