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Jie Lin

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

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Computer VisionMachine Learningcond-mat.softInformation Retrievalastro-ph.HEcond-mat.stat-mechCryptography and Securitymath.NTquant-phcond-mat.str-elmath.RAcond-mat.dis-nnphysics.chem-phApplicationsArtificial Intelligenceastro-ph.IMastro-ph.SRBiological PhysicsComputation and Languagecond-mat.mes-hallcond-mat.mtrl-scicond-mat.quant-gascond-mat.supr-coneess.ASeess.IVeess.SPmath.OCmath.RTMultimediaNeural and Evolutionary Computingphysics.app-phPopulations and EvolutionSound

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Published work

48 published item(s)

preprint2026arXiv

A Highly Magnetic Ultra Massive White Dwarf with a 23-minute Rotation Period

We present a physical characterization of TMTS J00063798+3104160 (J0006), a rapidly rotating,ultra-massive white dwarf (WD) identified in high-cadence light curves from the Tsinghua University-Ma Huateng Telescope for Survey (TMTS). A coherent 23-minute periodicity is detected in TMTS, TESS, and ZTF photometry. A time series of low-resolution spectra with the Keck-I 10 m telescope reveals broad, shallow hydrogen absorption features indicative of an extreme magnetic field and shows no evidence for radial-velocity variations. Atmospheric modeling yields a magnetic field strength of $\sim$ 250 MG, while Gaia astrometry and photometry imply a mass of 1.06 $\pm$ 0.01 M$_{\odot}$. A significant infrared excess is detected in the WISE W1 band and is well fitted by a 550 K blackbody, likely arising from residual material of a merger. We interpret the 23-minute photometric modulation as the rotation period of an isolated, massive WD formed likely through the merger of a double WD binary. With one of the shortest rotation periods known among candidate merger remnants and with constraints from a deep Einstein Probe X-ray nondetection, J0006 provides a rare and important observational window into the poorly explored intermediate stages of post-merger evolution.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Preferences Order, Ratings Anchor: From Fused Expert Aesthetic Ground Truth to Self-Distillation

Pairwise preferences and pointwise ratings are the two dominant annotation protocols in image aesthetic assessment (IAA), yet existing benchmarks adopt only one, leaving their complementarity unmeasured under controlled conditions. We introduce PPaint, a matched dual-protocol benchmark in which 15 domain experts, 5 per category, annotate 150 Chinese paintings under both protocols across five aesthetic dimensions, collecting 45,900 pairwise expert judgments through a locally dense preference design alongside the matched ratings. The matched design reveals complementary strengths: preferences yield more consistent ordinal rankings, while ratings anchor the absolute score scale. Fusing both signals via two independent preference-to-score methods yields a fused expert ground truth on which the two constructions converge to nearly identical scores. The same preference-to-score principle extends to label-free VLM training. PSDistill converts VLM pairwise judgments into calibrated pseudo-scores via an Elo reference pool, and trains the same VLM with confidence-weighted ranking optimization to produce a single-pass aesthetic scorer. Trained on a single painting category, the distilled Qwen3-VL-8B improves mean SRCC from 0.504 to 0.709 across all three categories, outperforming all open-source baselines including the dedicated aesthetic model ArtiMuse and matching closed-source Gemini-3.1-Pro within 0.04 SRCC at single-pass inference cost, with cross-domain transfer further validated on APDDv2. We will release the full PPaint dataset and training code.

0 citations0 reviewsNo code linkedOpen access
preprint2025arXiv

Constraining the Properties of GRB Accreting Magnetar with $R/I$ Evolutionary Effects Using \emph{Swift}/XRT Data

A newly born millisecond magnetar has been proposed as one possible central engine of some long gamma-ray bursts (LGRBs) with X-ray plateau. In this work, we used a universal correlation between initial spin period ($P_0$) and surface magnetic field ($B_p$) of newborn magnetar based on an LGRB sample in \cite{Lan2025} to explore the propeller properties of accreting magnetars with $R/I$ evolutionary effects. We found that $B_p-P_0$ relation is approximately consistent with $B_p\propto P_{\rm eq}^{7/6}$. Here $P_{\rm eq}$ is equilibrium spin period in magnetic propeller model. The $B_p-P_0$ relation indicates that $P_0$ may not be true initial spin period of newborn magnetar but had reached an equilibrium spin period via fallback accretion in propeller model. The magnetar accretion rate in our LGRBs is in range of $\dot{M}\sim10^{-5}-10^{-2} M_{\odot} \rm s^{-1}$ by incorporating $R/I$ evolutionary effects and using the transition relation between gravitational mass $M_g$ and baryonic mass $M_b$ in different equations of state. Such accretion rates ensure that the accreting magnetars in our sample survive until reaching the equilibrium spin period, and the accretion rate is one order of magnitude lower compared to the statistical results in \cite{Stratta2018} and \cite{Linweili2020}, which used constant $R/I/M_g$ scenario. We suggested that adopting a constant $R/I/M_g$ scenario for modeling propeller regime in accreting magnetar results in a higher mass accretion rate, which may impair our understanding of the physical nature and its surroundings of accreting magnetar, and low-metallicity progenitors can provide enough material to satisfy the accretion requirements of newborn accreting magnetar in LGRBs.

0 citations0 reviewsNo code linkedOpen access
preprint2025arXiv

TTC: Transformer-based TDE Classifier for the Wide Field Survey Telescope (WFST)

We propose the Transformer-based Tidal disruption events (TDE) Classifier (\texttt{TTC}), specifically designed to operate effectively with both real-time alert streams and archival data of the Wide Field Survey Telescope (WFST). It aims to minimize the reliance on external catalogs and find TDE candidates from pure light curves, which is more suitable for finding TDEs in faint and distant galaxies. \texttt{TTC} consists of two key modules that can work independently: (1) A light curve parametric fitting module and (2) a Transformer (\texttt{Mgformer})-based classification network. The training of the latter module and evaluation for each module utilize a light curve dataset of 7413 spectroscopically classified transients from the Zwicky Transient Facility (ZTF). The \texttt{Mgformer}-based module is superior in performance and flexibility. Its representative recall and precision values are 0.79 and 0.76, respectively, and can be modified by adjusting the threshold. It can also efficiently find TDE candidates within 30 days from the first detection. For comparison, the parametric fitting module yields values of 0.72 and 0.40, respectively, while it is $>$10 times faster in average speed. Hence, the setup of modules allows a trade-off between performance and time, as well as precision and recall. \texttt{TTC} has successfully picked out all spectroscopically identified TDEs among ZTF transients in a real-time classification test, and selected $\sim$20 TDE candidates in the deep field survey data of WFST. The discovery rate will greatly increase once the differential database for the wide field survey is ready.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Point Discriminative Learning for Data-efficient 3D Point Cloud Analysis

3D point cloud analysis has drawn a lot of research attention due to its wide applications. However, collecting massive labelled 3D point cloud data is both time-consuming and labor-intensive. This calls for data-efficient learning methods. In this work we propose PointDisc, a point discriminative learning method to leverage self-supervisions for data-efficient 3D point cloud classification and segmentation. PointDisc imposes a novel point discrimination loss on the middle and global level features produced by the backbone network. This point discrimination loss enforces learned features to be consistent with points belonging to the corresponding local shape region and inconsistent with randomly sampled noisy points. We conduct extensive experiments on 3D object classification, 3D semantic and part segmentation, showing the benefits of PointDisc for data-efficient learning. Detailed analysis demonstrate that PointDisc learns unsupervised features that well capture local and global geometry.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

FFConv: Fast Factorized Convolutional Neural Network Inference on Encrypted Data

Homomorphic Encryption (HE), allowing computations on encrypted data (ciphertext) without decrypting it first, enables secure but prohibitively slow Convolutional Neural Network (CNN) inference for privacy-preserving applications in clouds. To reduce the inference latency, one approach is to pack multiple messages into a single ciphertext in order to reduce the number of ciphertexts and support massive parallelism of Homomorphic Multiply-Accumulate (HMA) operations between ciphertexts. Despite the faster HECNN inference, the mainstream packing schemes Dense Packing (DensePack) and Convolution Packing (ConvPack) introduce expensive rotation overhead, which prolongs the inference latency of HECNN for deeper and wider CNN architectures. In this paper, we propose a low-rank factorization method named FFConv dedicated to efficient ciphertext packing for reducing both the rotation overhead and HMA operations. FFConv approximates a d x d convolution layer with low-rank factorized convolutions, in which a d x d low-rank convolution with fewer channels is followed by a 1 x 1 convolution to restore the channels. The d x d low-rank convolution with DensePack leads to significantly reduced rotation operations, while the rotation overhead of 1 x 1 convolution with ConvPack is close to zero. To our knowledge, FFConv is the first work that is capable of reducing the rotation overhead incurred by DensePack and ConvPack simultaneously, without introducing additional special blocks into the HECNN inference pipeline. Compared to prior art LoLa and Falcon, our method reduces the inference latency by up to 88% and 21%, respectively, with comparable accuracy on MNIST and CIFAR-10.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Hybrid Multimodal Feature Extraction, Mining and Fusion for Sentiment Analysis

In this paper, we present our solutions for the Multimodal Sentiment Analysis Challenge (MuSe) 2022, which includes MuSe-Humor, MuSe-Reaction and MuSe-Stress Sub-challenges. The MuSe 2022 focuses on humor detection, emotional reactions and multimodal emotional stress utilizing different modalities and data sets. In our work, different kinds of multimodal features are extracted, including acoustic, visual, text and biological features. These features are fused by TEMMA and GRU with self-attention mechanism frameworks. In this paper, 1) several new audio features, facial expression features and paragraph-level text embeddings are extracted for accuracy improvement. 2) we substantially improve the accuracy and reliability of multimodal sentiment prediction by mining and blending the multimodal features. 3) effective data augmentation strategies are applied in model training to alleviate the problem of sample imbalance and prevent the model from learning biased subject characters. For the MuSe-Humor sub-challenge, our model obtains the AUC score of 0.8932. For the MuSe-Reaction sub-challenge, the Pearson's Correlations Coefficient of our approach on the test set is 0.3879, which outperforms all other participants. For the MuSe-Stress sub-challenge, our approach outperforms the baseline in both arousal and valence on the test dataset, reaching a final combined result of 0.5151.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Improving the Robustness and Generalization of Deep Neural Network with Confidence Threshold Reduction

Deep neural networks are easily attacked by imperceptible perturbation. Presently, adversarial training (AT) is the most effective method to enhance the robustness of the model against adversarial examples. However, because adversarial training solved a min-max value problem, in comparison with natural training, the robustness and generalization are contradictory, i.e., the robustness improvement of the model will decrease the generalization of the model. To address this issue, in this paper, a new concept, namely confidence threshold (CT), is introduced and the reducing of the confidence threshold, known as confidence threshold reduction (CTR), is proven to improve both the generalization and robustness of the model. Specifically, to reduce the CT for natural training (i.e., for natural training with CTR), we propose a mask-guided divergence loss function (MDL) consisting of a cross-entropy loss term and an orthogonal term. The empirical and theoretical analysis demonstrates that the MDL loss improves the robustness and generalization of the model simultaneously for natural training. However, the model robustness improvement of natural training with CTR is not comparable to that of adversarial training. Therefore, for adversarial training, we propose a standard deviation loss function (STD), which minimizes the difference in the probabilities of the wrong categories, to reduce the CT by being integrated into the loss function of adversarial training. The empirical and theoretical analysis demonstrates that the STD based loss function can further improve the robustness of the adversarially trained model on basis of guaranteeing the changeless or slight improvement of the natural accuracy.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Long-tailed Recognition by Learning from Latent Categories

In this work, we address the challenging task of long-tailed image recognition. Previous long-tailed recognition methods commonly focus on the data augmentation or re-balancing strategy of the tail classes to give more attention to tail classes during the model training. However, due to the limited training images for tail classes, the diversity of tail class images is still restricted, which results in poor feature representations. In this work, we hypothesize that common latent features among the head and tail classes can be used to give better feature representation. Motivated by this, we introduce a Latent Categories based long-tail Recognition (LCReg) method. Specifically, we propose to learn a set of class-agnostic latent features shared among the head and tail classes. Then, we implicitly enrich the training sample diversity via applying semantic data augmentation to the latent features. Extensive experiments on five long-tailed image recognition datasets demonstrate that our proposed LCReg is able to significantly outperform previous methods and achieve state-of-the-art results.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

OPQ: Compressing Deep Neural Networks with One-shot Pruning-Quantization

As Deep Neural Networks (DNNs) usually are overparameterized and have millions of weight parameters, it is challenging to deploy these large DNN models on resource-constrained hardware platforms, e.g., smartphones. Numerous network compression methods such as pruning and quantization are proposed to reduce the model size significantly, of which the key is to find suitable compression allocation (e.g., pruning sparsity and quantization codebook) of each layer. Existing solutions obtain the compression allocation in an iterative/manual fashion while finetuning the compressed model, thus suffering from the efficiency issue. Different from the prior art, we propose a novel One-shot Pruning-Quantization (OPQ) in this paper, which analytically solves the compression allocation with pre-trained weight parameters only. During finetuning, the compression module is fixed and only weight parameters are updated. To our knowledge, OPQ is the first work that reveals pre-trained model is sufficient for solving pruning and quantization simultaneously, without any complex iterative/manual optimization at the finetuning stage. Furthermore, we propose a unified channel-wise quantization method that enforces all channels of each layer to share a common codebook, which leads to low bit-rate allocation without introducing extra overhead brought by traditional channel-wise quantization. Comprehensive experiments on ImageNet with AlexNet/MobileNet-V1/ResNet-50 show that our method improves accuracy and training efficiency while obtains significantly higher compression rates compared to the state-of-the-art.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Robust Interior Point Method for Quantum Key Distribution Rate Computation

Security proof methods for quantum key distribution, QKD, that are based on the numerical key rate calculation problem, are powerful in principle. However, the practicality of the methods are limited by computational resources and the efficiency and accuracy of the underlying algorithms for convex optimization. We derive a stable reformulation of the convex nonlinear semidefinite programming, SDP, model for the key rate calculation problems. We use this to develop an efficient, accurate algorithm. The stable reformulation is based on novel forms of facial reduction, FR, for both the linear constraints and nonlinear quantum relative entropy objective function. This allows for a Gauss-Newton type interior-point approach that avoids the need for perturbations to obtain strict feasibility, a technique currently used in the literature. The result is high accuracy solutions with theoretically proven lower bounds for the original QKD from the FR stable reformulation. This provides novel contributions for FR for general SDP. We report on empirical results that dramatically improve on speed and accuracy, as well as solving previously intractable problems.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

A*HAR: A New Benchmark towards Semi-supervised learning for Class-imbalanced Human Activity Recognition

Despite the vast literature on Human Activity Recognition (HAR) with wearable inertial sensor data, it is perhaps surprising that there are few studies investigating semisupervised learning for HAR, particularly in a challenging scenario with class imbalance problem. In this work, we present a new benchmark, called A*HAR, towards semisupervised learning for class-imbalanced HAR. We evaluate state-of-the-art semi-supervised learning method on A*HAR, by combining Mean Teacher and Convolutional Neural Network. Interestingly, we find that Mean Teacher boosts the overall performance when training the classifier with fewer labelled samples and a large amount of unlabeled samples, but the classifier falls short in handling unbalanced activities. These findings lead to an interesting open problem, i.e., development of semi-supervised HAR algorithms that are class-imbalance aware without any prior knowledge on the class distribution for unlabeled samples. The dataset and benchmark evaluation are released at https://github.com/I2RDL2/ASTAR-HAR for future research.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Anisotropic thermal characterisation of large-format lithium-ion pouch cells

Temperature strongly impacts battery performance, safety and durability, but modelling heat transfer requires accurately measured thermal properties. Herein we propose new approaches to characterise the heat capacity and anisotropic thermal-conductivity components for lithium-ion pouch cells. Heat capacity was estimated by applying Newton's law of cooling to an insulated container within which the cell was submerged in warmed dielectric fluid. Thermal conductivity was quantified by heating one side of the cell and measuring the opposing temperature distribution with infra-red thermography, then inverse modelling with the anisotropic heat equation. Experiments were performed on commercial 20 Ah lithium iron phosphate (LFP) pouch cells. At 100% state-of-charge (SOC), the heat capacity of a 489 g, 224 mL pouch cell was 541 J/K. The through-plane and in-plane thermal conductivities were respectively 0.52 and 26.6 W/(mK). Capturing anisotropies in conductivity is important for accurate thermal simulations. State-of-charge dependence was also probed by testing at 50% SOC: the heat capacity dropped by 6% and thermal conductivity did not significantly change.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Blockchain Aided Privacy-Preserving Outsourcing Algorithms of Bilinear Pairings for Internet of Things Devices

Bilinear pairing is a fundamental operation that is widely used in cryptographic algorithms (e.g., identity-based cryptographic algorithms) to secure IoT applications. Nonetheless, the time complexity of bilinear pairing is $O(n^3)$, making it a very time-consuming operation, especially for resource-constrained IoT devices. Secure outsourcing of bilinear pairing has been studied in recent years to enable computationally weak devices to securely outsource the bilinear pairing to untrustworthy cloud servers. However, the state-of-art algorithms often require to pre-compute and store some values, which results in storage burden for devices. In the Internet of Things, devices are generally with very limited storage capacity. Thus, the existing algorithms do not fit the IoT well. In this paper, we propose a secure outsourcing algorithm of bilinear pairings, which does not require pre-computations. In the proposed algorithm, the outsourcer side's efficiency is significantly improved compared with executing the original bilinear pairing operation. At the same time, the privacy of the input and output is ensured. Also, we apply the Ethereum blockchain in our outsourcing algorithm to enable fair payments, which ensures that the cloud server gets paid only when he correctly accomplished the outsourced work. The theoretical analysis and experimental results show that the proposed algorithm is efficient and secure.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Multiscale coupling of surface temperature with solid diffusion in large lithium-ion pouch cells

Untangling the relationship between reactions, mass transfer, and temperature within lithium-ion batteries enables control approaches that mitigate thermal hot spots and slow degradation. Here, we develop an efficient physics-based pouch-cell model to simulate lock-in thermography experiments, which synchronously record the applied current, cell voltage, and surface-temperature distribution. Prior modelling efforts have been confounded by experimental temperature profiles whose characteristics suggest anisotropic heat conduction. Accounting for a multiscale coupling between heat flow and solid-state diffusion rationalizes this surface-temperature nonuniformity. We extend an earlier streamlined model based on the popular Doyle--Fuller--Newman theory, augmented by a local heat balance. The reduced-order model is exploited to parametrize and simulate commercial 20 Ah lithium iron phosphate (LFP) cells at currents up to 80 A. This work highlights how microscopic intercalation processes produce distinctive macroscopic heat signatures in large-format cells, as well as how heat signatures can be exploited to fingerprint material properties.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Privacy-Preserving Cloud-Aided Broad Learning System

With the rapid development of artificial intelligence and the advent of the 5G era, deep learning has received extensive attention from researchers. Broad Learning System (BLS) is a new deep learning model proposed recently, which shows its effectiveness in many fields, such as image recognition and fault detection. However, the training process still requires vast computations, and therefore cannot be accomplished by some resource-constrained devices. To solve this problem, the resource-constrained device can outsource the BLS algorithm to cloud servers. Nevertheless, some security challenges also follow with the use of cloud computing, including the privacy of the data and the correctness of returned results. In this paper, we propose a secure, efficient, and verifiable outsourcing algorithm for BLS. This algorithm not only improves the efficiency of the algorithm on the client but also ensures that the clients sensitive information is not leaked to the cloud server. In addition, in our algorithm, the client can verify the correctness of returned results with a probability of almost 1. Finally, we analyze the security and efficiency of our algorithm in theory and prove our algorithms feasibility through experiments.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Security proof of practical quantum key distribution with detection-efficiency mismatch

Quantum key distribution (QKD) protocols with threshold detectors are driving high-performance QKD demonstrations. The corresponding security proofs usually assume that all physical detectors have the same detection efficiency. However, the efficiencies of the detectors used in practice might show a mismatch depending on the manufacturing and setup of these detectors. A mismatch can also be induced as the different spatial-temporal modes of an incoming signal might couple differently to a detector. Here we develop a method that allows to provide security proofs without the usual assumption. Our method can take the detection-efficiency mismatch into account without having to restrict the attack strategy of the adversary. Especially, we do not rely on any photon-number cut-off of incoming signals such that our security proof is directly applicable to practical situations. We illustrate our method for a receiver that is designed for polarization encoding and is sensitive to a number of spatial-temporal modes. In our detector model, the absence of quantum interference between any pair of spatial-temporal modes is assumed. For a QKD protocol with this detector model, we can perform a security proof with characterized efficiency mismatch and without photon-number cut-off assumption. Our method also shows that in the absence of efficiency mismatch in our detector model, the key rate increases if the loss due to detection inefficiency is assumed to be outside of the adversary's control, as compared to the view where for a security proof this loss is attributed to the action of the adversary.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Deeply Activated Salient Region for Instance Search

The performance of instance search depends heavily on the ability to locate and describe a wide variety of object instances in a video/image collection. Due to the lack of proper mechanism in locating instances and deriving feature representation, instance search is generally only effective for retrieving instances of known object categories. In this paper, a simple but effective instance-level feature representation is presented. Different from other approaches, the issues in class-agnostic instance localization and distinctive feature representation are considered. The former is achieved by detecting salient instance regions from an image by a layer-wise back-propagation process. The back-propagation starts from the last convolution layer of a pre-trained CNN that is originally used for classification. The back-propagation proceeds layer-by-layer until it reaches the input layer. This allows the salient instance regions in the input image from both known and unknown categories to be activated. Each activated salient region covers the full or more usually a major range of an instance. The distinctive feature representation is produced by average-pooling on the feature map of certain layer with the detected instance region. Experiments show that such kind of feature representation demonstrates considerably better performance over most of the existing approaches. In addition, we show that the proposed feature descriptor is also suitable for content-based image search.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

From single-cell variability to population growth

Single-cell experiments have revealed cell-to-cell variability in generation times and growth rates for genetically identical cells. Theoretical models relating the fluctuating generation times of single cells to the population growth rate are usually based on the assumption that the generation times of mother and daughter cells are uncorrelated. This assumption, however, is inconsistent with the exponential growth of cell volume in time observed for many cell types. Here we develop a more general and biologically relevant model in which cells grow exponentially and generation times are correlated in a manner which controls cell size. In addition to the fluctuating generation times, we also allow the single-cell growth rates to fluctuate and account for their correlations across the lineage tree. Surprisingly, we find that the population growth rate only depends on the distribution of single-cell growth rates and their correlations.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

GRB 111209A/SN 2011kl: Collapse of a supramassive magnetar with r-mode oscillation and fall-back accretion onto a newborn black hole

Ultra-long-duration gamma-ray burst GRB 111209A was found to be associated with a very luminous supernovae (SNe) SN 2011kl. The physics of GRB 111209A/SN 2011kl has been extensively studied in the literures, but does not settle down yet. By investigating in detail the characteristics of the X-ray light curve of GRB 111209A, coupled with the temporal and spectral features observed in SN 2011kl, we argue that a short-living supramassive magnetar can be responsible for the initial shallow X-ray emission. Then the electromagnetic extraction of spin energy from a black hole results in the steeply declining X-ray flux when the magnetar collapses into a black hole (BH). A fraction of the envelope materials falls back and activates the accretion onto the newborn BH, which produces the X-ray rebrightening bump at late times. During this process, a centrifugally driven baryon-rich quasi-isotropic Blandford \& Payne outflow from the revived accretion disk deposits its kinetic energy on the SN ejecta, which powers luminous SN 2011kl. Finally, we place a limitation on the magnetar's physical parameters based on the observations.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Role-Wise Data Augmentation for Knowledge Distillation

Knowledge Distillation (KD) is a common method for transferring the ``knowledge'' learned by one machine learning model (the \textit{teacher}) into another model (the \textit{student}), where typically, the teacher has a greater capacity (e.g., more parameters or higher bit-widths). To our knowledge, existing methods overlook the fact that although the student absorbs extra knowledge from the teacher, both models share the same input data -- and this data is the only medium by which the teacher's knowledge can be demonstrated. Due to the difference in model capacities, the student may not benefit fully from the same data points on which the teacher is trained. On the other hand, a human teacher may demonstrate a piece of knowledge with individualized examples adapted to a particular student, for instance, in terms of her cultural background and interests. Inspired by this behavior, we design data augmentation agents with distinct roles to facilitate knowledge distillation. Our data augmentation agents generate distinct training data for the teacher and student, respectively. We find empirically that specially tailored data points enable the teacher's knowledge to be demonstrated more effectively to the student. We compare our approach with existing KD methods on training popular neural architectures and demonstrate that role-wise data augmentation improves the effectiveness of KD over strong prior approaches. The code for reproducing our results can be found at https://github.com/bigaidream-projects/role-kd

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Towards the AlexNet Moment for Homomorphic Encryption: HCNN, theFirst Homomorphic CNN on Encrypted Data with GPUs

Deep Learning as a Service (DLaaS) stands as a promising solution for cloud-based inference applications. In this setting, the cloud has a pre-learned model whereas the user has samples on which she wants to run the model. The biggest concern with DLaaS is user privacy if the input samples are sensitive data. We provide here an efficient privacy-preserving system by employing high-end technologies such as Fully Homomorphic Encryption (FHE), Convolutional Neural Networks (CNNs) and Graphics Processing Units (GPUs). FHE, with its widely-known feature of computing on encrypted data, empowers a wide range of privacy-concerned applications. This comes at high cost as it requires enormous computing power. In this paper, we show how to accelerate the performance of running CNNs on encrypted data with GPUs. We evaluated two CNNs to classify homomorphically the MNIST and CIFAR-10 datasets. Our solution achieved a sufficient security level (> 80 bit) and reasonable classification accuracy (99%) and (77.55%) for MNIST and CIFAR-10, respectively. In terms of latency, we could classify an image in 5.16 seconds and 304.43 seconds for MNIST and CIFAR-10, respectively. Our system can also classify a batch of images (> 8,000) without extra overhead.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

A search for short-term hard X-ray bursts in the direction of the repeating FRB 121102

The nature of fast radio bursts (FRBs), which occurs on millisecond time scales in the radio band, has not been well-understood. Among their unknown observational properties are their broadband spectra and persistent and transient multi-wavelength counterparts. Well-localized FRBs provide us the opportunity to address these issues in archival observations. We have performed searches for 15-150 keV hard X-ray bursts on time scales as short as millisecond in the direction of the repeating FRB 121102 (with a spacial resolution of a few arcminutes) in the archival Swift/BAT data during the period between October 2016 and September 2017. We have found no significant (5 $σ$) hard X-ray bursts in the direction of the repeating FRB. We have derived an upper limit of the hard X-ray (15--150 keV) flux of any X-ray bursts on 1 ms time scale of around $1.01 \times 10^{-7}$erg cm$^{-2}$s$^{-1}$, if assuming a photo-index of 2 for potential X-ray flares in X-ray band. A plausible scenario for the repeating FRB as being associated with \emph{magnetar giant flare} is still far below the upper limit.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Asymptotic security analysis of discrete-modulated continuous-variable quantum key distribution

Continuous-variable quantum key distribution (CV QKD) protocols with discrete modulation are interesting due to their experimental simplicity and their great potential for massive deployment in the quantum-secured networks, but their security analysis is less advanced than that of Gaussian modulation schemes. In this work, we apply a numerical method to analyze the security of discrete-modulation protocols against collective attacks in the asymptotic limit, paving the way for a full security proof with finite-size effects. While our method is general for discrete-modulation schemes, we focus on two variants of the CV QKD protocol with quaternary modulation. Interestingly, thanks to the tightness of our proof method, we show that this protocol is capable of achieving much higher key rates over significantly longer distances with experimentally feasible parameters compared with previous security proofs of binary and ternary modulation schemes and also yielding key rates comparable to Gaussian modulation schemes. Furthermore, as our security analysis method is versatile, it allows us to evaluate variations of the discrete-modulated protocols, including direct and reverse reconciliation, and postselection strategies. In particular, we demonstrate that postselection of data in combination with reverse reconciliation can improve the key rates.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Quantum-enhanced least-square support vector machine: simplified quantum algorithm and sparse solutions

Quantum algorithms can enhance machine learning in different aspects. Here, we study quantum-enhanced least-square support vector machine (LS-SVM). Firstly, a novel quantum algorithm that uses continuous variable to assist matrix inversion is introduced to simplify the algorithm for quantum LS-SVM, while retaining exponential speed-up. Secondly, we propose a hybrid quantum-classical version for sparse solutions of LS-SVM. By encoding a large dataset into a quantum state, a much smaller transformed dataset can be extracted using quantum matrix toolbox, which is further processed in classical SVM. We also incorporate kernel methods into the above quantum algorithms, which uses both exponential growth Hilbert space of qubits and infinite dimensionality of continuous variable for quantum feature maps. The quantum LS-SVM exploits quantum properties to explore important themes for SVM such as sparsity and kernel methods, and stresses its quantum advantages ranging from speed-up to the potential capacity to solve classically difficult machine learning tasks.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Egocentric Activity Recognition with Multimodal Fisher Vector

With the increasing availability of wearable devices, research on egocentric activity recognition has received much attention recently. In this paper, we build a Multimodal Egocentric Activity dataset which includes egocentric videos and sensor data of 20 fine-grained and diverse activity categories. We present a novel strategy to extract temporal trajectory-like features from sensor data. We propose to apply the Fisher Kernel framework to fuse video and temporal enhanced sensor features. Experiment results show that with careful design of feature extraction and fusion algorithm, sensor data can enhance information-rich video data. We make publicly available the Multimodal Egocentric Activity dataset to facilitate future research.

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preprint2016arXiv

Evidence for marginal stability in emulsions

We report the first measurements of the effect of pressure on vibrational modes in emulsions, which serve as a model for soft frictionless spheres at zero temperature. As a function of the applied pressure, we find that the density of states D(omega) exhibits a low-frequency cutoff omega*, which scales linearly with the number of extra contacts per particle dz. Moreover, for omega<omega*, D(omega)~ omega^2/omega*^2; a quadratic behavior whose prefactor is larger than what is expected from Debye theory. This surprising result agrees with recent theoretical findings. Finally, the degree of localization of the softest low frequency modes increases with compression, as shown by the participation ratio as well as their spatial configurations. Overall, our observations show that emulsions are marginally stable and display non-plane-wave modes up to vanishing frequencies.

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preprint2016arXiv

Galois equivariance of critical values of $L$-functions for unitary groups

The goal of this paper is to provide a refinement of a formula proved by the first author which expresses some critical values of automorphic $L$-functions on unitary groups as Petersson norms of automorphic forms. Here we provide a Galois equivariant version of the formula. We also give some applications to special values of automorphic representations of $\GL_{n}\times\GL_{1}$. We show that our results are compatible with Deligne's conjecture.

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preprint2016arXiv

Group Invariant Deep Representations for Image Instance Retrieval

Most image instance retrieval pipelines are based on comparison of vectors known as global image descriptors between a query image and the database images. Due to their success in large scale image classification, representations extracted from Convolutional Neural Networks (CNN) are quickly gaining ground on Fisher Vectors (FVs) as state-of-the-art global descriptors for image instance retrieval. While CNN-based descriptors are generally remarked for good retrieval performance at lower bitrates, they nevertheless present a number of drawbacks including the lack of robustness to common object transformations such as rotations compared with their interest point based FV counterparts. In this paper, we propose a method for computing invariant global descriptors from CNNs. Our method implements a recently proposed mathematical theory for invariance in a sensory cortex modeled as a feedforward neural network. The resulting global descriptors can be made invariant to multiple arbitrary transformation groups while retaining good discriminativeness. Based on a thorough empirical evaluation using several publicly available datasets, we show that our method is able to significantly and consistently improve retrieval results every time a new type of invariance is incorporated. We also show that our method which has few parameters is not prone to overfitting: improvements generalize well across datasets with different properties with regard to invariances. Finally, we show that our descriptors are able to compare favourably to other state-of-the-art compact descriptors in similar bitranges, exceeding the highest retrieval results reported in the literature on some datasets. A dedicated dimensionality reduction step --quantization or hashing-- may be able to further improve the competitiveness of the descriptors.

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preprint2016arXiv

Nested Invariance Pooling and RBM Hashing for Image Instance Retrieval

The goal of this work is the computation of very compact binary hashes for image instance retrieval. Our approach has two novel contributions. The first one is Nested Invariance Pooling (NIP), a method inspired from i-theory, a mathematical theory for computing group invariant transformations with feed-forward neural networks. NIP is able to produce compact and well-performing descriptors with visual representations extracted from convolutional neural networks. We specifically incorporate scale, translation and rotation invariances but the scheme can be extended to any arbitrary sets of transformations. We also show that using moments of increasing order throughout nesting is important. The NIP descriptors are then hashed to the target code size (32-256 bits) with a Restricted Boltzmann Machine with a novel batch-level regularization scheme specifically designed for the purpose of hashing (RBMH). A thorough empirical evaluation with state-of-the-art shows that the results obtained both with the NIP descriptors and the NIP+RBMH hashes are consistently outstanding across a wide range of datasets.

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preprint2016arXiv

Period relations and special values of Rankin-Selberg $L$-functions

This is a survey of recent work on values of Rankin-Selberg $L$-functions of pairs of cohomological automorphic representations that are {\it critical} in Deligne's sense. The base field is assumed to be a CM field. Deligne's conjecture is stated in the language of motives over $\QQ$, and express the critical values, up to rational factors, as determinants of certain periods of algebraic differentials on a projective algebraic variety over homology classes. The results that can be proved by automorphic methods express certain critical values as (twisted) period integrals of automorphic forms. Using Langlands functoriality between cohomological automorphic representations of unitary groups, which can be identified with the de Rham cohomology of Shimura varieties, and cohomological automorphic representations of $GL(n)$, the automorphic periods can be interpreted as motivic periods. We report on recent results of the two authors, of the first-named author with Grobner, and of Guerberoff.

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preprint2016arXiv

Scaling Description of Non-Local Rheology

Non-locality is crucial to understand the plastic flow of an amorphous material, and has been successfully described by the fluidity, along with a cooperativity length scale ξ. We demonstrate, by applying the scaling hypothesis to the yielding transition, that non-local effects in non-uniform stress configurations can be explained within the framework of critical phenomena. From the scaling description, scaling relations between different exponents are derived, and collapses of strain rate profiles are made both in shear driven and pressure driven flow. We find that the cooperative length in non-local flow is governed by the same correlation length in finite dimensional homogeneous flow, excluding the mean field exponents. We also show that non-locality also affects the finite size scaling of the yield stress, especially the large finite size effects observed in pressure driven flow. Our theoretical results are nicely verified by the elasto-plastic model, and experimental data.

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preprint2015arXiv

A Practical Guide to CNNs and Fisher Vectors for Image Instance Retrieval

With deep learning becoming the dominant approach in computer vision, the use of representations extracted from Convolutional Neural Nets (CNNs) is quickly gaining ground on Fisher Vectors (FVs) as favoured state-of-the-art global image descriptors for image instance retrieval. While the good performance of CNNs for image classification are unambiguously recognised, which of the two has the upper hand in the image retrieval context is not entirely clear yet. In this work, we propose a comprehensive study that systematically evaluates FVs and CNNs for image retrieval. The first part compares the performances of FVs and CNNs on multiple publicly available data sets. We investigate a number of details specific to each method. For FVs, we compare sparse descriptors based on interest point detectors with dense single-scale and multi-scale variants. For CNNs, we focus on understanding the impact of depth, architecture and training data on retrieval results. Our study shows that no descriptor is systematically better than the other and that performance gains can usually be obtained by using both types together. The second part of the study focuses on the impact of geometrical transformations such as rotations and scale changes. FVs based on interest point detectors are intrinsically resilient to such transformations while CNNs do not have a built-in mechanism to ensure such invariance. We show that performance of CNNs can quickly degrade in presence of rotations while they are far less affected by changes in scale. We then propose a number of ways to incorporate the required invariances in the CNN pipeline. Overall, our work is intended as a reference guide offering practically useful and simply implementable guidelines to anyone looking for state-of-the-art global descriptors best suited to their specific image instance retrieval problem.

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preprint2015arXiv

Co-Regularized Deep Representations for Video Summarization

Compact keyframe-based video summaries are a popular way of generating viewership on video sharing platforms. Yet, creating relevant and compelling summaries for arbitrarily long videos with a small number of keyframes is a challenging task. We propose a comprehensive keyframe-based summarization framework combining deep convolutional neural networks and restricted Boltzmann machines. An original co-regularization scheme is used to discover meaningful subject-scene associations. The resulting multimodal representations are then used to select highly-relevant keyframes. A comprehensive user study is conducted comparing our proposed method to a variety of schemes, including the summarization currently in use by one of the most popular video sharing websites. The results show that our method consistently outperforms the baseline schemes for any given amount of keyframes both in terms of attractiveness and informativeness. The lead is even more significant for smaller summaries.

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preprint2015arXiv

Criticality in the approach to failure in amorphous solids

Failure of amorphous solids is fundamental to various phenomena, including landslides and earthquakes. Recent experiments indicate that highly plastic regions form elongated structures that are especially apparent near the maximal shear stress $Σ_{\max}$ where failure occurs. This observation suggested that $Σ_{\max}$ acts as a critical point where the length scale of those structures diverges, possibly causing macroscopic transient shear bands. Here we argue instead that the entire solid phase ($Σ<Σ_{\max}$) is critical, that plasticity always involves system-spanning events, and that their magnitude diverges at $Σ_{\max}$ independently of the presence of shear bands. We relate the statistics and fractal properties of these rearrangements to an exponent $θ$ that captures the stability of the material, which is observed to vary continuously with stress, and we confirm our predictions in elastoplastic models.

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preprint2015arXiv

DeepHash: Getting Regularization, Depth and Fine-Tuning Right

This work focuses on representing very high-dimensional global image descriptors using very compact 64-1024 bit binary hashes for instance retrieval. We propose DeepHash: a hashing scheme based on deep networks. Key to making DeepHash work at extremely low bitrates are three important considerations -- regularization, depth and fine-tuning -- each requiring solutions specific to the hashing problem. In-depth evaluation shows that our scheme consistently outperforms state-of-the-art methods across all data sets for both Fisher Vectors and Deep Convolutional Neural Network features, by up to 20 percent over other schemes. The retrieval performance with 256-bit hashes is close to that of the uncompressed floating point features -- a remarkable 512 times compression.

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preprint2015arXiv

One-parameter formal deformations of Hom-Lie-Yamaguti algebras

This paper studies one-parameter formal deformations of Hom-Lie-Yamaguti algebras. The first, second and third cohomology groups on Hom-Lie-Yamaguti algebras extending ones on Lie-Yamaguti algebras are provided. It is proved that first and second cohomology groups are suitable to the deformation theory involving infinitesimals, equivalent deformations and rigidity. However, the third cohomology group is not suitable for the obstructions.

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preprint2015arXiv

Period relations for automorphic induction and applications, I

Let $K$ be a quadratic imaginary field. Let $Π$ (resp. $Π'$) be a regular algebraic cuspidal representation of $GL_{n}(K)$ (resp. $GL_{n-1}(K)$) which is moreover cohomological and conjugate self-dual. In \cite{harris97}, M. Harris has defined automorphic periods of such a representation. These periods are automorphic analogues of motivic periods. In this paper, we show that automorphic periods are functorial in the case where $Π$ is a cyclic automorphic induction of a Hecke character $χ$ over a CM field. More precisely, we prove relations between automorphic periods of $Π$ and those of $χ$. As a corollary, we refine the formula given by H. Grobner and M. Harris of critical values for the Rankin-Selberg $L$-function $L(s,Π\times Π')$ in terms of automorphic periods. This completes the proof of an automorphic version of Deligne's conjecture in certain cases.

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preprint2015arXiv

Special values of automorphic $L$-functions for $GL_{n}\times GL_{n'}$ over CM fields, factorization and functoriality of arithmetic automorphic periods

Michael HARRIS defined the arithmetic automorphic periods for certain cuspidal representations of $GL_{n}$ over quadratic imaginary fields in his Crelle paper 1997. He also showed that critical values of automorphic L-functions for $GL_{n}\times GL_{1}$ can be interpreted in terms of these arithmetic automorphic periods. In the thesis, we generalize his results in two ways. Firstly, the arithmetic automorphic periods have been defined over general CM fields. We also prove that these periods factorize as products of local periods over infinity places. Secondly, we show that critical values of automorphic $L$ functions for $GL_{n}\times GL_{n'}$ can be interpreted in terms of these automorphic periods in many situations. Consequently we show that the automorphic periods are functorial for automorphic induction and cyclic base change. We also define certain motivic periods if the motive is restricted from a CM field to the field of rational numbers. We can calculate Deligne's period for tensor product of two such motives. We see directly that our automorphic results are compatible with Deligne's conjecture for motives.

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preprint2015arXiv

Tiny Descriptors for Image Retrieval with Unsupervised Triplet Hashing

A typical image retrieval pipeline starts with the comparison of global descriptors from a large database to find a short list of candidate matches. A good image descriptor is key to the retrieval pipeline and should reconcile two contradictory requirements: providing recall rates as high as possible and being as compact as possible for fast matching. Following the recent successes of Deep Convolutional Neural Networks (DCNN) for large scale image classification, descriptors extracted from DCNNs are increasingly used in place of the traditional hand crafted descriptors such as Fisher Vectors (FV) with better retrieval performances. Nevertheless, the dimensionality of a typical DCNN descriptor --extracted either from the visual feature pyramid or the fully-connected layers-- remains quite high at several thousands of scalar values. In this paper, we propose Unsupervised Triplet Hashing (UTH), a fully unsupervised method to compute extremely compact binary hashes --in the 32-256 bits range-- from high-dimensional global descriptors. UTH consists of two successive deep learning steps. First, Stacked Restricted Boltzmann Machines (SRBM), a type of unsupervised deep neural nets, are used to learn binary embedding functions able to bring the descriptor size down to the desired bitrate. SRBMs are typically able to ensure a very high compression rate at the expense of loosing some desirable metric properties of the original DCNN descriptor space. Then, triplet networks, a rank learning scheme based on weight sharing nets is used to fine-tune the binary embedding functions to retain as much as possible of the useful metric properties of the original space. A thorough empirical evaluation conducted on multiple publicly available dataset using DCNN descriptors shows that our method is able to significantly outperform state-of-the-art unsupervised schemes in the target bit range.

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preprint2014arXiv

Scaling description of the yielding transition in soft amorphous solids at zero temperature

Yield stress materials flow if a sufficiently large shear stress is ap- plied. Although such materials are ubiquitous and relevant for indus- try, there is no accepted microscopic description of how they yield, even in the simplest situations where temperature is negligible and where flow inhomogeneities such as shear bands or fractures are ab- sent. Here we propose a scaling description of the yielding transition in amorphous solids made of soft particles at zero temperature. Our description makes a connection between the Herschel-Bulkley expo- nent characterizing the singularity of the flow curve near the yield stress Σc, the extension and duration of the avalanches of plasticity observed at threshold, and the density P(x) of soft spots, or shear transformation zones, as a function of the stress increment x be- yond which they yield. We argue that the critical exponents of the yielding transition can be expressed in terms of three independent exponents θ, df and z, characterizing respectively the density of soft spots, the fractal dimension of the avalanches, and their duration. Our description shares some similarity with the depinning transition that occurs when an elastic manifold is driven through a random potential, but also presents some striking differences. We test our arguments in an elasto-plastic model, an automaton model similar to those used in depinning, but with a different interaction kernel, and find satisfying agreement with our predictions both in two and three dimensions.

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preprint2013arXiv

On the density of shear transformation zones in amorphous solids

We study the stability of amorphous solids, focusing on the distribution P(x) of the local stress increase x that would lead to an instability. We argue that this distribution is singular P(x)x^θ, where the exponent θ is non-zero if the elastic interaction between rearranging regions is non-monotonic, and increases with the interaction range. For a class of finite dimensional models we show that stability implies a lower bound on θ, which is found to lie near saturation. For quadrupolar interactions these models yield θ ~ 0.6 for d=2 and θ~ 0.4 in d=3 where d is the spatial dimension, accurately capturing previously unresolved observations in atomistic models, both in quasi-static flow and after a fast quench.

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preprint2013arXiv

Systems of quotients of Lie triple systems

In this paper, we introduce the notion of system of quotients of Lie triple systems and investigate some properties which can be lifted from a Lie triple system to its systems of quotients. We relate the notion of Lie triple system of Martindale-like quotients with respect to a filter of ideals and the notion of system of quotients, and prove that the system of quotients of a Lie triple system is equivalent to the algebra of quotients of a Lie algebra in some sense, and these allow us to construct the maximal system of quotients for nondegenerate Lie triple systems.

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preprint2012arXiv

Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid

We study inelastic decay of bosonic excitations in a Luttinger liquid. In a model with linear excitation spectrum the decay rate diverges. We show that this difficulty is resolved when the interaction between constituent particles is strong, and the excitation spectrum is nonlinear. Although at low energies the nonlinearity is weak, it regularizes the divergence in the decay rate. We develop a theoretical description of the approach of the system to thermal equilibrium. The typical relaxation rate scales as the fifth power of temperature.

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preprint2010arXiv

Lifshitz transition in two-dimensional spin-density wave models

We argue that both pocket-disappearing and neck-disrupting types of Lifshitz transitions can be realized in two-dimensional spin-density wave models for underdoped cuprates, and study both types of transitions with impurity scattering treated in the self-consistent Born approximation. We first solve for the electron self-energy from the self-consistent equation, and then study the low-temperature electrical conductivity and thermopower. Close to the Lifshitz transition, the thermopower is strongly enhanced. For the pocket-disappearing type, it has a sharp peak, while for the neck-disrupting type, it changes sign at the transition, with its absolute value peaked on both sides of the transition. We discuss possible applications to underdoped cuprates.

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preprint2010arXiv

Lifshitz Transition in Underdoped Cuprates

Recent studies show that quantum oscillations thought to be associated with a density wave reconstructed Fermi surface disappear at a critical value of the doping for YBa2Cu3O6+y, and the cyclotron mass diverges as the critical value is approached from the high doping side. We argue that the phenomenon is due to a Lifshitz transition where the pockets giving rise to the quantum oscillations connect to form an open (quasi-1d) Fermi surface. The estimated critical doping is close to that found by experiment, and the theory predicts a logarithmic divergence of the cyclotron mass with a coefficient comparable to that observed in experiment.

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preprint2010arXiv

Optical and Hall conductivities of a thermally disordered two-dimensional spin-density wave: two-particle response in the pseudogap regime of electron-doped high-$T_c$ superconductors

We calculate the longitudinal ($σ_{xx}$) and Hall ($σ_{xy}$) optical conductivities for two-dimensional metals with thermally disordered antiferromagnetism using a generalization of an approximation introduced by Lee, Rice and Anderson for the self energy. The conductivities are calculated from the Kubo formula, with current vertex function treated in a conserving approximation satisfying the Ward identity. In order to obtain a finite DC limit, we introduce phenomenologically impurity scattering, with relaxation time $τ$. $σ_{xx}(Ω)$ satisfies the $f$-sum rule. For the infinitely peaked spin correlation function, $χ(\mathbf{q})\propto δ(\mathbf{q}-\mathbf{Q})$, we recover the expressions for the conductivities in the mean-field theory of the ordered state. When the spin correlation length $ξ$ is large but finite, both $σ_{xx}$ and $σ_{xy}$ show behaviors characteristic of the state with long-range order. The calculation runs into difficulty for $Ω\lesssim 1/τ$. The difficulties are traced to an inaccurate treatment of the very low energy density of states within the Lee-Rice-Anderson approximation. The results for $σ_{xx}(Ω)$ and $σ_{xy}(Ω)$ are qualitatively consistent with data on electron-doped cuprates when $Ω>1/τ$.

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