arXiv subjects

Yanjun Li

Publications and source records attributed to Yanjun Li.

At least 55 records · Page 3Linked to original sources

arXiv2021

Constructing new APN functions through relative trace functions

In 2020, Budaghyan, Helleseth and Kaleyski [IEEE TIT 66(11): 7081-7087, 2020] considered an infinite family of quadrinomials over $\mathbb{F}_{2^{n}}$ of the form $x^3+a(x^{2^s+1})^{2^k}+bx^{3\cdot 2^m}+c(x^{2^{s+m}+2^m})^{2^k}$, where $n=2m$ with $m$ odd. They proved that such kind of quadrinomials can provide new almost perfect nonlinear (APN) functions when $\gcd(3,m)=1$, $ k=0 $, and $(s,a,b,c)=(m-2,ω, ω^2,1)$ or $((m-2)^{-1}~{\rm mod}~n,ω, ω^2,1)$ in which $ω\in\mathbb{F}_4\setminus \mathbb{F}_2$. By taking $a=ω$ and $b=c=ω^2$, we observe that such kind of quadrinomials can be rewritten as $a {\rm Tr}^{n}_{m}(bx^3)+a^q{\rm Tr}^{n}_{m}(cx^{2^s+1})$, where $q=2^m$ and $ {\rm Tr}^n_{m}(x)=x+x^{2^m} $ for $ n=2m$. Inspired by the quadrinomials and our observation, in this paper we study a class of functions with the form $f(x)=a{\rm Tr}^{n}_{m}(F(x))+a^q{\rm Tr}^{n}_{m}(G(x))$ and determine the APN-ness of this new kind of functions, where $a \in \mathbb{F}_{2^n} $ such that $ a+a^q\neq 0$, and both $F$ and $G$ are quadratic functions over $\mathbb{F}_{2^n}$. We first obtain a characterization of the conditions for $f(x)$ such that $f(x) $ is an APN function. With the help of this characterization, we obtain an infinite family of APN functions for $ n=2m $ with $m$ being an odd positive integer: $ f(x)=a{\rm Tr}^{n}_{m}(bx^3)+a^q{\rm Tr}^{n}_{m}(b^3x^9) $, where $ a\in \mathbb{F}_{2^n}$ such that $ a+a^q\neq 0 $ and $ b $ is a non-cube in $ \mathbb{F}_{2^n} $.

cs.IT↗

arXiv2021

Joint Dimensionality Reduction for Separable Embedding Estimation

Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method that learns linear embeddings jointly for two feature vectors representing data of different modalities or data from distinct types of entities. We also propose an efficient feature selection method that complements, and can be applied prior to, our joint dimensionality reduction method. Assuming that there exist true linear embeddings for these features, our analysis of the error in the learned linear embeddings provides theoretical guarantees that the dimensionality reduction method accurately estimates the true embeddings when certain technical conditions are satisfied and the number of samples is sufficiently large. The derived sample complexity results are echoed by numerical experiments. We apply the proposed dimensionality reduction method to gene-disease association, and predict unknown associations using kernel regression on the dimension-reduced feature vectors. Our approach compares favorably against other dimensionality reduction methods, and against a state-of-the-art method of bilinear regression for predicting gene-disease associations.

cs.LG↗

arXiv2020

PRI-VAE: Principle-of-Relevant-Information Variational Autoencoders

Although substantial efforts have been made to learn disentangled representations under the variational autoencoder (VAE) framework, the fundamental properties to the dynamics of learning of most VAE models still remain unknown and under-investigated. In this work, we first propose a novel learning objective, termed the principle-of-relevant-information variational autoencoder (PRI-VAE), to learn disentangled representations. We then present an information-theoretic perspective to analyze existing VAE models by inspecting the evolution of some critical information-theoretic quantities across training epochs. Our observations unveil some fundamental properties associated with VAEs. Empirical results also demonstrate the effectiveness of PRI-VAE on four benchmark data sets.

cs.LG↗

arXiv2020

Application of Deep Interpolation Network for Clustering of Physiologic Time Series

Background: During the early stages of hospital admission, clinicians must use limited information to make diagnostic and treatment decisions as patient acuity evolves. However, it is common that the time series vital sign information from patients to be both sparse and irregularly collected, which poses a significant challenge for machine / deep learning techniques to analyze and facilitate the clinicians to improve the human health outcome. To deal with this problem, We propose a novel deep interpolation network to extract latent representations from sparse and irregularly sampled time-series vital signs measured within six hours of hospital admission. Methods: We created a single-center longitudinal dataset of electronic health record data for all (n=75,762) adult patient admissions to a tertiary care center lasting six hours or longer, using 55% of the dataset for training, 23% for validation, and 22% for testing. All raw time series within six hours of hospital admission were extracted for six vital signs (systolic blood pressure, diastolic blood pressure, heart rate, temperature, blood oxygen saturation, and respiratory rate). A deep interpolation network is proposed to learn from such irregular and sparse multivariate time series data to extract the fixed low-dimensional latent patterns. We use k-means clustering algorithm to clusters the patient admissions resulting into 7 clusters. Findings: Training, validation, and testing cohorts had similar age (55-57 years), sex (55% female), and admission vital signs. Seven distinct clusters were identified. M Interpretation: In a heterogeneous cohort of hospitalized patients, a deep interpolation network extracted representations from vital sign data measured within six hours of hospital admission. This approach may have important implications for clinical decision-support under time constraints and uncertainty.

cs.LG↗

arXiv2020

A Set-Theoretic Study of the Relationships of Image Models and Priors for Restoration Problems

Image prior modeling is the key issue in image recovery, computational imaging, compresses sensing, and other inverse problems. Recent algorithms combining multiple effective priors such as the sparse or low-rank models, have demonstrated superior performance in various applications. However, the relationships among the popular image models are unclear, and no theory in general is available to demonstrate their connections. In this paper, we present a theoretical analysis on the image models, to bridge the gap between applications and image prior understanding, including sparsity, group-wise sparsity, joint sparsity, and low-rankness, etc. We systematically study how effective each image model is for image restoration. Furthermore, we relate the denoising performance improvement by combining multiple models, to the image model relationships. Extensive experiments are conducted to compare the denoising results which are consistent with our analysis. On top of the model-based methods, we quantitatively demonstrate the image properties that are inexplicitly exploited by deep learning method, of which can further boost the denoising performance by combining with its complementary image models.

eess.IV↗

arXiv2019

DeepAtom: A Framework for Protein-Ligand Binding Affinity Prediction

The cornerstone of computational drug design is the calculation of binding affinity between two biological counterparts, especially a chemical compound, i.e., a ligand, and a protein. Predicting the strength of protein-ligand binding with reasonable accuracy is critical for drug discovery. In this paper, we propose a data-driven framework named DeepAtom to accurately predict the protein-ligand binding affinity. With 3D Convolutional Neural Network (3D-CNN) architecture, DeepAtom could automatically extract binding related atomic interaction patterns from the voxelized complex structure. Compared with the other CNN based approaches, our light-weight model design effectively improves the model representational capacity, even with the limited available training data. With validation experiments on the PDBbind v.2016 benchmark and the independent Astex Diverse Set, we demonstrate that the less feature engineering dependent DeepAtom approach consistently outperforms the other state-of-the-art scoring methods. We also compile and propose a new benchmark dataset to further improve the model performances. With the new dataset as training input, DeepAtom achieves Pearson's R=0.83 and RMSE=1.23 pK units on the PDBbind v.2016 core set. The promising results demonstrate that DeepAtom models can be potentially adopted in computational drug development protocols such as molecular docking and virtual screening.

q-bio.BM↗

arXiv2019

Algorithmic Design and Implementation of Unobtrusive Multistatic Serial LiDAR Image

To fully understand interactions between marine hydrokinetic (MHK) equipment and marine animals, a fast and effective monitoring system is required to capture relevant information whenever underwater animals appear. A new automated underwater imaging system composed of LiDAR (Light Detection and Ranging) imaging hardware and a scene understanding software module named Unobtrusive Multistatic Serial LiDAR Imager (UMSLI) to supervise the presence of animals near turbines. UMSLI integrates the front end LiDAR hardware and a series of software modules to achieve image preprocessing, detection, tracking, segmentation and classification in a hierarchical manner.

eess.IV↗

arXiv2019

On constructions and properties of $(n,m)$-functions with maximal number of bent components

For any positive integers $n=2k$ and $m$ such that $m\geq k$, in this paper we show the maximal number of bent components of any $(n,m)$-functions is equal to $2^{m}-2^{m-k}$, and for those attaining the equality, their algebraic degree is at most $k$. It is easily seen that all $(n,m)$-functions of the form $G(x)=(F(x),0)$ with $F(x)$ being any vectorial bent $(n,k)$-function, have the maximum number of bent components. Those simple functions $G$ are called trivial in this paper. We show that for a power $(n,n)$-function, it has such large number of bent components if and only if it is trivial under a mild condition. We also consider the $(n,n)$-function of the form $F^{i}(x)=x^{2^{i}}h({\rm Tr}^{n}_{e}(x))$, where $h: \mathbb{F}_{2^{e}} \rightarrow \mathbb{F}_{2^{e}}$, and show that $F^{i}$ has such large number if and only if $e=k$, and $h$ is a permutation over $\mathbb{F}_{2^{k}}$. It proves that all the previously known nontrivial such functions are subclasses of the functions $F^{i}$. Based on the Maiorana-McFarland class, we present constructions of large numbers of $(n,m)$-functions with maximal number of bent components for any integer $m$ in bivariate representation. We also determine the differential spectrum and Walsh spectrum of the constructed functions. It is found that our constructions can also provide new plateaued vectorial functions.

cs.IT↗

arXiv2019

Constructing vectorial bent functions via second-order derivatives

Let $n$ be an even positive integer, and $m<n$ be one of its positive divisors. In this paper, inspired by a nice work of Tang et al. on constructing large classes of bent functions from known bent functions [27, IEEE TIT, 63(10): 6149-6157, 2017], we consider the construction of vectorial bent and vectorial plateaued $(n,m)$-functions of the form $H(x)=G(x)+g(x)$, where $G(x)$ is a vectorial bent $(n,m)$-function, and $g(x)$ is a Boolean function over $\mathbb{F}_{2^{n}}$. We find an efficient generic method to construct vectorial bent and vectorial plateaued functions of this form by establishing a link between the condition on the second-order derivatives and the key condition given by [27]. This allows us to provide (at least) three new infinite families of vectorial bent functions with high algebraic degrees. New vectorial plateaued $(n,m+t)$-functions are also obtained ($t\geq 0$ depending on $n$ can be taken as a very large number), two classes of which have the maximal number of bent components.

cs.IT↗

arXiv2019

Multichannel Sparse Blind Deconvolution on the Sphere

Multichannel blind deconvolution is the problem of recovering an unknown signal $f$ and multiple unknown channels $x_i$ from their circular convolution $y_i=x_i \circledast f$ ($i=1,2,\dots,N$). We consider the case where the $x_i$'s are sparse, and convolution with $f$ is invertible. Our nonconvex optimization formulation solves for a filter $h$ on the unit sphere that produces sparse output $y_i\circledast h$. Under some technical assumptions, we show that all local minima of the objective function correspond to the inverse filter of $f$ up to an inherent sign and shift ambiguity, and all saddle points have strictly negative curvatures. This geometric structure allows successful recovery of $f$ and $x_i$ using a simple manifold gradient descent (MGD) algorithm. Our theoretical findings are complemented by numerical experiments, which demonstrate superior performance of the proposed approach over the previous methods.

cs.IT↗

arXiv2019

Thermodynamics of charged accelerating AdS black holes and holographic heat engines

Using a reasonable choice in normalizing the timelike Killing vector, we investigate the thermodynamic properties of charged accelerating Anti-de Sitter (AdS) black holes. We find that the expression of the thermodynamic mass in the first law of thermodynamics displays an inextricably intertwining behavior with the charge due to the unusual asymptotic structure of the accelerating black holes. Meanwhile, the thermodynamic length as a potential conjugate to the varying cosmic string tension is introduced and analyzed in detail, and the possible phase behavior of the charged accelerating black holes is also discussed in a standard thermodynamic analysis. Furthermore, we also investigate the properties of holographic heat engines with charged accelerating AdS black holes as the working substance in a benchmarking scheme. We find that the efficiencies of the black hole heat engines can be influenced by both the size of the benchmark circular cycle and the cosmic string tension. More interestingly, the existence of charge may significantly increase the efficiencies of the black hole heat engines and make them be more sensitive to a varying cosmic string tension. A cross-comparison of the efficiencies of different black hole heat engines suggests that the acceleration also increases the efficiency and renders it more sensitive as the charge varies.

hep-th↗

arXiv2019

Comfort-Centered Design of a Lightweight and Backdrivable Knee Exoskeleton

This paper presents design principles for comfort-centered wearable robots and their application in a lightweight and backdrivable knee exoskeleton. The mitigation of discomfort is treated as mechanical design and control issues and three solutions are proposed in this paper: 1) a new wearable structure optimizes the strap attachment configuration and suit layout to ameliorate excessive shear forces of conventional wearable structure design; 2) rolling knee joint and double-hinge mechanisms reduce the misalignment in the sagittal and frontal plane, without increasing the mechanical complexity and inertia, respectively; 3) a low impedance mechanical transmission reduces the reflected inertia and damping of the actuator to human, thus the exoskeleton is highly-backdrivable. Kinematic simulations demonstrate that misalignment between the robot joint and knee joint can be reduced by 74% at maximum knee flexion. In experiments, the exoskeleton in the unpowered mode exhibits 1.03 Nm root mean square (RMS) low resistive torque. The torque control experiments demonstrate 0.31 Nm RMS torque tracking error in three human subjects.

cs.RO↗

arXiv2018

FoldingZero: Protein Folding from Scratch in Hydrophobic-Polar Model

De novo protein structure prediction from amino acid sequence is one of the most challenging problems in computational biology. As one of the extensively explored mathematical models for protein folding, Hydrophobic-Polar (HP) model enables thorough investigation of protein structure formation and evolution. Although HP model discretizes the conformational space and simplifies the folding energy function, it has been proven to be an NP-complete problem. In this paper, we propose a novel protein folding framework FoldingZero, self-folding a de novo protein 2D HP structure from scratch based on deep reinforcement learning. FoldingZero features the coupled approach of a two-head (policy and value heads) deep convolutional neural network (HPNet) and a regularized Upper Confidence Bounds for Trees (R-UCT). It is trained solely by a reinforcement learning algorithm, which improves HPNet and R-UCT iteratively through iterative policy optimization. Without any supervision and domain knowledge, FoldingZero not only achieves comparable results, but also learns the latent folding knowledge to stabilize the structure. Without exponential computation, FoldingZero shows promising potential to be adopted for real-world protein properties prediction.

cs.LG↗

arXiv2018

The Power of Complementary Regularizers: Image Recovery via Transform Learning and Low-Rank Modeling

Recent works on adaptive sparse and on low-rank signal modeling have demonstrated their usefulness in various image / video processing applications. Patch-based methods exploit local patch sparsity, whereas other works apply low-rankness of grouped patches to exploit image non-local structures. However, using either approach alone usually limits performance in image reconstruction or recovery applications. In this work, we propose a simultaneous sparsity and low-rank model, dubbed STROLLR, to better represent natural images. In order to fully utilize both the local and non-local image properties, we develop an image restoration framework using a transform learning scheme with joint low-rank regularization. The approach owes some of its computational efficiency and good performance to the use of transform learning for adaptive sparse representation rather than the popular synthesis dictionary learning algorithms, which involve approximation of NP-hard sparse coding and expensive learning steps. We demonstrate the proposed framework in various applications to image denoising, inpainting, and compressed sensing based magnetic resonance imaging. Results show promising performance compared to state-of-the-art competing methods.

cs.CV↗

arXiv2018

Accelerating AdS black holes as the holographic heat engines in a benchmarking scheme

We investigate the properties of holographic heat engines with an uncharged accelerating non-rotating AdS black hole as the working substance in a benchmarking scheme. We find that the efficiencies of the black hole heat engines can be influenced by both the size of the benchmark circular cycle and the cosmic string tension as a thermodynamic variable. In general, the efficiency can be increased by enlarging the cycle, but is still constrained by a universal bound $2π/(π+4)$ as expected. A cross-comparison of the efficiencies of the accelerating black hole heat engines and Schwarzschild-AdS black hole heat engines suggests that the acceleration also increases the efficiency although the amount of increase is not remarkable.

hep-th↗

arXiv2017

Optimal Sample Complexity for Stable Matrix Recovery

Tremendous efforts have been made to study the theoretical and algorithmic aspects of sparse recovery and low-rank matrix recovery. This paper fills a theoretical gap in matrix recovery: the optimal sample complexity for stable recovery without constants or log factors. We treat sparsity, low-rankness, and potentially other parsimonious structures within the same framework: constraint sets that have small covering numbers or Minkowski dimensions. We consider three types of random measurement matrices (unstructured, rank-1, and symmetric rank-1 matrices), following probability distributions that satisfy some mild conditions. In all these cases, we prove a fundamental result -- the recovery of matrices with parsimonious structures, using an optimal (or near optimal) number of measurements, is stable with high probability.

cs.IT↗

arXiv2017

Optimal Sample Complexity for Stable Matrix Recovery

cs.IT↗

arXiv2017

Blind Gain and Phase Calibration via Sparse Spectral Methods

Blind gain and phase calibration (BGPC) is a bilinear inverse problem involving the determination of unknown gains and phases of the sensing system, and the unknown signal, jointly. BGPC arises in numerous applications, e.g., blind albedo estimation in inverse rendering, synthetic aperture radar autofocus, and sensor array auto-calibration. In some cases, sparse structure in the unknown signal alleviates the ill-posedness of BGPC. Recently there has been renewed interest in solutions to BGPC with careful analysis of error bounds. In this paper, we formulate BGPC as an eigenvalue/eigenvector problem, and propose to solve it via power iteration, or in the sparsity or joint sparsity case, via truncated power iteration. Under certain assumptions, the unknown gains, phases, and the unknown signal can be recovered simultaneously. Numerical experiments show that power iteration algorithms work not only in the regime predicted by our main results, but also in regimes where theoretical analysis is limited. We also show that our power iteration algorithms for BGPC compare favorably with competing algorithms in adversarial conditions, e.g., with noisy measurement or with a bad initial estimate.

cs.IT↗