arXiv subjects

Yiwei Zhang

Publications and source records attributed to Yiwei Zhang.

At least 73 records · Page 4Linked to original sources

arXiv2024

On shrinking targets for linear expanding and hyperbolic toral endomorphisms

Let $A$ be an invertible $d\times d$ matrix with integer elements. Then $A$ determines a self-map $T$ of the $d$-dimensional torus $\mathbb{T}^d=\mathbb{R}^d/\mathbb{Z}^d$. Given a real number $τ>0$, and a sequence $\{z_n\}$ of points in $\mathbb{T}^d$, let $W_τ$ be the set of points $x\in\mathbb{T}^d$ such that $T^n(x)\in B(z_n,e^{-nτ})$ for infinitely many $n\in\mathbb{N}$. The Hausdorff dimension of $W_τ$ has previously been studied by Hill--Velani and Li--Liao--Velani--Zorin. We provide complete results on the Hausdorff dimension of $W_τ$ for any expanding matrix. For hyperbolic matrices, we compute the dimension of $W_τ$ only when $A$ is a $2 \times 2$ matrix. We give counterexamples to a natural candidate for a dimension formula for general dimension $d$.

math.DS↗

arXiv2024

Coding for Synthesis Defects

Motivated by DNA based data storage system, we investigate the errors that occur when synthesizing DNA strands in parallel, where each strand is appended one nucleotide at a time by the machine according to a template supersequence. If there is a cycle such that the machine fails, then the strands meant to be appended at this cycle will not be appended, and we refer to this as a synthesis defect. In this paper, we present two families of codes correcting synthesis defects, which are t-known-synthesis-defect correcting codes and t-synthesis-defect correcting codes. For the first one, it is assumed that the defective cycles are known, and each of the codeword is a quaternary sequence. We provide constructions for this family of codes for t = 1, 2, with redundancy log 4 and log n+18 log 3, respectively. For the second one, the codeword is a set of M ordered sequences, and we give constructions for t = 1, 2 to show a strategy for constructing this family of codes. Finally, we derive a lower bound on the redundancy for single-known-synthesis-defect correcting codes, which assures that our construction is almost optimal.

cs.IT↗

arXiv2024

Batch Array Codes

Batch codes are a type of codes specifically designed for coded distributed storage systems and private information retrieval protocols. These codes have got much attention in recent years due to their ability to enable efficient and secure storage in distributed systems. In this paper, we study an array code version of the batch codes, which is called the \emph{batch array code} (BAC). Under the setting of BAC, each node stores a bucket containing multiple code symbols and responds with a locally computed linear combination of the symbols in its bucket during the recovery of a requested symbol. We demonstrate that BACs can support the same type of requests as the original batch codes but with reduced redundancy. Specifically, we establish information theoretic lower bounds on the code lengths and provide several code constructions that confirm the tightness of the lower bounds for certain parameter regimes.

cs.IT↗

arXiv2024

On the prevalence of the periodicity of maximizing measures

For a continuous map $T: X\rightarrow X$ on a compact metric space $(X,d)$, we say that a function $f: X \rightarrow \mathbb{R}$ has the property $\mathscr{P}_T$ if its time averages along forward orbits of $T$ are maximized at a periodic orbit. In this paper, we prove that for the one-side full shift of two symbols, the property $\mathscr{P}_T$ is prevalent (in the sense of Hunt--Sauer--Yorke) in spaces of Lipschitz functions with respect to metrics with mildly fast decaying rate on the diameters of cylinder sets. This result is a strengthening of \cite[Theorem~A]{BZ16}, confirms the prediction mentioned in the ICM proceeding contribution of J. Bochi (\cite[Seciton 1]{Boc18}) suggested by experimental evidence, and is another step towards the Hunt--Ott conjectures in the area of ergodic optimization.

math.DS↗

arXiv2023

Pulsating active matter

We reveal that the mechanical pulsation of locally synchronised particles is a generic route to propagate deformation waves. We consider a model of dense repulsive particles whose activity drives periodic change in size of each individual. The dynamics is inspired by biological tissues where cells consume fuel to sustain active deformation. We show that the competition between repulsion and synchronisation triggers an instability which promotes a wealth of dynamical patterns, ranging from spiral waves to defect turbulence. We identify the mechanisms underlying the emergence of patterns, and characterize the corresponding transitions. By coarse-graining the dynamics, we propose a hydrodynamic description of an assembly of pulsating particles, and discuss an analogy with reaction-diffusion systems.

cond-mat.soft↗

arXiv2023

Improved constructions of secondary structure avoidance codes for DNA sequences

In a DNA sequence, we have the celebrated Watson-Crick complement $\overline{T}=A$, $\overline{A}=T$, $\overline{C}=G$, and $\overline{G}=C$. Given an integer $m\ge 2$, a secondary structure in a DNA sequence refers to the existence of two non-overlapping reverse complement consecutive subsequences of length $m$, denoted as $\boldsymbol{x}=(x_1, \dots, x_m)$ and $\boldsymbol{y}=(y_1, \dots, y_m)$, such that $x_i=\overline{y_{m-i+1}}$ for $1\leq i \leq m$. The property of secondary structure avoidance (SSA) forbids a sequence to contain such reverse complement subsequences, and it is a key criterion in the design of single-stranded DNA sequences for DNA computing and storage. In this paper, we improve on a recent result of Nguyen et al., by introducing explicit constructions of secondary structure avoidance codes and analyzing the capacity for any given $m$. In particular, our constructions have optimal rate 1.1679bits/nt and 1.5515bits/nt when $m=2$ and $m=3$, respectively.

cs.IT↗

arXiv2023

SPIDER-WEB generates coding algorithms with superior error tolerance and real-time information retrieval capacity

DNA has been considered a promising medium for storing digital information. As an essential step in the DNA-based data storage workflow, coding algorithms are responsible to implement functions including bit-to-base transcoding, error correction, etc. In previous studies, these functions are normally realized by introducing multiple algorithms. Here, we report a graph-based architecture, named SPIDER-WEB, providing an all-in-one coding solution by generating customized algorithms automatically. SPIDERWEB is able to correct a maximum of 4% edit errors in the DNA sequences including substitution and insertion/deletion (indel), with only 5.5% redundant symbols. Since no DNA sequence pretreatment is required for the correcting and decoding processes, SPIDER-WEB offers the function of real-time information retrieval, which is 305.08 times faster than the speed of single-molecule sequencing techniques. Our retrieval process can improve 2 orders of magnitude faster compared to the conventional one under megabyte-level data and can be scalable to fit exabyte-level data. Therefore, SPIDER-WEB holds the potential to improve the practicability in large-scale data storage applications.

cs.ET↗

arXiv2023

Generative Compression for Face Video: A Hybrid Scheme

As the latest video coding standard, versatile video coding (VVC) has shown its ability in retaining pixel quality. To excavate more compression potential for video conference scenarios under ultra-low bitrate, this paper proposes a bitrate adjustable hybrid compression scheme for face video. This hybrid scheme combines the pixel-level precise recovery capability of traditional coding with the generation capability of deep learning based on abridged information, where Pixel wise Bi-Prediction, Low-Bitrate-FOM and Lossless Keypoint Encoder collaborate to achieve PSNR up to 36.23 dB at a low bitrate of 1.47 KB/s. Without introducing any additional bitrate, our method has a clear advantage over VVC under a completely fair comparative experiment, which proves the effectiveness of our proposed scheme. Moreover, our scheme can adapt to any existing encoder / configuration to deal with different encoding requirements, and the bitrate can be dynamically adjusted according to the network condition.

eess.IV↗

arXiv2023

Gamify Stencil Dwarf on Cloud for Democratizing Scientific Computing

Stencil computation is one of the most important kernels in various scientific computing. Nowadays, most Stencil-driven scientific computing still relies heavily on supercomputers, suffering from expensive access, poor scalability, and duplicated optimizations. This paper proposes Tetris, the first system for high-performance Stencil on heterogeneous CPU+GPU, towards democratizing Stencil-driven scientific computing on Cloud. In Tetris, polymorphic tiling tetrominoes are first proposed to bridge different hardware architectures and various application contexts with a perfect spatial and temporal tessellation automatically. Tetris is contributed by three main components: (1) Underlying hardware characteristics are first captured to achieve a sophisticated Pattern Mapping by register-level tetrominoes; (2) An efficient Locality Enhancer is first presented for data reuse on spatial and temporal dimensions simultaneously by cache/SMEM-level tetrominoes; (3) A novel Concurrent Scheduler is first designed to exploit the full potential of on-cloud memory and computing power by memory-level tetrominoes. Tetris is orthogonal to (and complements) the optimizations or deployments for a wide variety of emerging and legacy scientific computing applications. Results of thermal diffusion simulation demonstrate that the performance is improved by 29.6x, reducing time cost from day to hour, while preserving the original accuracy.

cs.DC↗

arXiv2023

Emergent Bio-Functional Similarities in a Cortical-Spike-Train-Decoding Spiking Neural Network Facilitate Predictions of Neural Computation

Despite its better bio-plausibility, goal-driven spiking neural network (SNN) has not achieved applicable performance for classifying biological spike trains, and showed little bio-functional similarities compared to traditional artificial neural networks. In this study, we proposed the motorSRNN, a recurrent SNN topologically inspired by the neural motor circuit of primates. By employing the motorSRNN in decoding spike trains from the primary motor cortex of monkeys, we achieved a good balance between classification accuracy and energy consumption. The motorSRNN communicated with the input by capturing and cultivating more cosine-tuning, an essential property of neurons in the motor cortex, and maintained its stability during training. Such training-induced cultivation and persistency of cosine-tuning was also observed in our monkeys. Moreover, the motorSRNN produced additional bio-functional similarities at the single-neuron, population, and circuit levels, demonstrating biological authenticity. Thereby, ablation studies on motorSRNN have suggested long-term stable feedback synapses contribute to the training-induced cultivation in the motor cortex. Besides these novel findings and predictions, we offer a new framework for building authentic models of neural computation.

q-bio.NC↗

arXiv2023

Improved constructions of permutation and multi-permutation codes correcting a burst of stable deletions

Permutation codes and multi-permutation codes have been widely considered due to their various applications, especially in flash memory. In this paper, we consider permutation codes and multi-permutation codes against a burst of stable deletions. In particular, we propose a construction of permutation codes correcting a burst stable deletion of length $s$, with redundancy $\log n+ 2\log \log n+O(1)$. Compared to the previous known results, our improvement relies on a different strategy to retrieve the missing symbol on the first row of the array representation of a permutation. We also generalize our constructions for multi-permutations and the variable length burst model. Furthermore, we propose a linear-time encoder with optimal redundancy for single stable deletion correcting permutation codes.

cs.IT↗

arXiv2022

t-Deletion-s-Insertion-Burst Correcting Codes

Motivated by applications in DNA-based storage and communication systems, we study deletion and insertion errors simultaneously in a burst. In particular, we study a type of error named $t$-deletion-$s$-insertion-burst ($(t,s)$-burst for short) which is a generalization of the $(2,1)$-burst error proposed by Schoeny {\it et. al}. Such an error deletes $t$ consecutive symbols and inserts an arbitrary sequence of length $s$ at the same coordinate. We provide a sphere-packing upper bound on the size of binary codes that can correct a $(t,s)$-burst error, showing that the redundancy of such codes is at least $\log n+t-1$. For $t\geq 2s$, an explicit construction of binary $(t,s)$-burst correcting codes with redundancy $\log n+(t-s-1)\log\log n+O(1)$ is given. In particular, we construct a binary $(3,1)$-burst correcting code with redundancy at most $\log n+9$, which is optimal up to a constant.

cs.IT↗

arXiv2022

EvilScreen Attack: Smart TV Hijacking via Multi-channel Remote Control Mimicry

Modern smart TVs often communicate with their remote controls (including those smart phone simulated ones) using multiple wireless channels (e.g., Infrared, Bluetooth, and Wi-Fi). However, this multi-channel remote control communication introduces a new attack surface. An inherent security flaw is that remote controls of most smart TVs are designed to work in a benign environment rather than an adversarial one, and thus wireless communications between a smart TV and its remote controls are not strongly protected. Attackers could leverage such flaw to abuse the remote control communication and compromise smart TV systems. In this paper, we propose EvilScreen, a novel attack that exploits ill-protected remote control communications to access protected resources of a smart TV or even control the screen. EvilScreen exploits a multi-channel remote control mimicry vulnerability present in today smart TVs. Unlike other attacks, which compromise the TV system by exploiting code vulnerabilities or malicious third-party apps, EvilScreen directly reuses commands of different remote controls, combines them together to circumvent deployed authentication and isolation policies, and finally accesses or controls TV resources remotely. We evaluated eight mainstream smart TVs and found that they are all vulnerable to EvilScreen attacks, including a Samsung product adopting the ISO/IEC security specification.

cs.CR↗

arXiv2022

Neuro-Symbolic Learning: Principles and Applications in Ophthalmology

Neural networks have been rapidly expanding in recent years, with novel strategies and applications. However, challenges such as interpretability, explainability, robustness, safety, trust, and sensibility remain unsolved in neural network technologies, despite the fact that they will unavoidably be addressed for critical applications. Attempts have been made to overcome the challenges in neural network computing by representing and embedding domain knowledge in terms of symbolic representations. Thus, the neuro-symbolic learning (NeSyL) notion emerged, which incorporates aspects of symbolic representation and bringing common sense into neural networks (NeSyL). In domains where interpretability, reasoning, and explainability are crucial, such as video and image captioning, question-answering and reasoning, health informatics, and genomics, NeSyL has shown promising outcomes. This review presents a comprehensive survey on the state-of-the-art NeSyL approaches, their principles, advances in machine and deep learning algorithms, applications such as opthalmology, and most importantly, future perspectives of this emerging field.

cs.CV↗

arXiv2022

Coding schemes for locally balanced constraints

Motivated by applications in DNA-based storage, we study explicit encoding and decoding schemes of binary strings satisfying locally balanced constraints, where the $(\ell,δ)$-locally balanced constraint requires that the weight of any consecutive substring of length $\ell$ is between $\frac{\ell}{2}-δ$ and $\frac{\ell}{2}+δ$. In this paper we present coding schemes for the strongly locally balanced constraints and the locally balanced constraints, respectively. Moreover, we introduce an additional result on the linear recurrence formula of the number of binary strings which are $(6,1)$-locally balanced, as a further attempt to both capacity characterization and new coding strategies for locally balanced constraints.

cs.IT↗

arXiv2021

Upper capacity entropy and packing entropy of saturated sets for amenable group actions

Let $(X,G)$ be a $G$-action topological system, where $G$ is a countable infinite discrete amenable group and $X$ a compact metric space. In this paper we study the upper capacity entropy and packing entropy for systems with weaker version of specification. We prove that the upper capacity always carries full entropy while there is a variational principle for packing entropy of saturated sets.

math.DS↗

arXiv2021

Spiking hierarchy in an adaptive exponential integrate-and-fire network synchronization

Neuronal network synchronization has received wide interests. Network connection structure is known to play a key role in its synchronization. In the present manuscript, we study the influence of initial membrane potentials together with network topology on bursting synchronization, in particular the sequential spiking order in stabilized inter bursts. We find a hierarchical phenomenon on spiking order. We grade neurons into different layers: primary neurons are those initiate the spike and lower-layer neurons are then determined via network connections successively. This constructs a directed graph to indicate spiking propagation among different layers of neurons. Neurons in upper layers spike earlier than those in lower layers. More interestingly, we find that among the same layer, neuron spiking order is mainly associated with stimuli they receive from upper layer via network connections; more stimuli leads to earlier spiking. Furthermore, we find that with effectively the same stimuli from upper layer, neurons with less connections spike earlier.

math.DS↗

arXiv2021

Topological structures on saturated sets, optimal orbits and equilibrium states

Pfister and Sullivan proved that if a topological dynamical system $(X,T)$ satisfies almost product property and uniform separation property, then for each nonempty compact %convex subset $K$ of invariant measures, the entropy of saturated set $G_{K}$ satisfies \begin{equation}\label{Bowen's topological entropy} h_{top}^{B}(T,G_{K})=\inf\{h(T,μ):μ\in K\}, \end{equation} where $h_{top}^{B}(T,G_{K})$ is Bowen's topological entropy of $T$ on $G_{K}$, and $h(T,μ)$ is the Kolmogorov-Sinai entropy of $μ$. In this paper, we investigate topological complexity of $G_{K}$ by replacing Bowen's topological entropy with upper capacity entropy and packing entropy and obtain the following formulas: \begin{equation*} h_{top}^{UC}(T,G_{K})=h_{top}(T,X)\ \mathrm{and}\ h_{top}^{P}(T,G_{K})=\sup\{h(T,μ):μ\in K\}, \end{equation*} where $h_{top}^{UC}(T,G_{K})$ is the upper capacity entropy of $T$ on $G_{K}$ and $h_{top}^{P}(T,G_{K})$ is the packing entropy of $T$ on $G_{K}.$ In the proof of these two formulas, uniform separation property is unnecessary.

math.DS↗