arXiv subjects

Lin Chen

Publications and source records attributed to Lin Chen.

At least 361 records · Page 20Linked to original sources

arXiv2021

A novel reversible data hiding in encrypted images based on polynomial arithmetic

Reversible data hiding in encrypted images is an effective technology for data hiding and protecting image privacy. Although there are many high-capacity methods have been presented in recent year, most of them need a pre-processing phase to reserve room in the original image before encryption. It may be unpractical, because the image provider has to analyze the content of the image and accomplish additional operations. In this paper, we propose a new robust vacate room after encryption schema based on polynomial arithmetic, which achieves a high embedding capacity with the perfect recovery of the original image. An efficient symmetric encryption method is applied to protect the privacy of the original image. One polynomial is generated by the encryption key and a group of the encrypted pixel, and the secret data is mapped into another polynomial. Through the arithmetic of these two polynomials, we can extract secret data and recover origin image, separately. Experimental results demonstrate that our solution has a stable and good performance on various images (include rough texture image). Compared with some typical methods, the proposed method can get better decrypted image quality with a large embedding capacity.

cs.CR↗

arXiv2021

An Extension of the Kazhdan-Lusztig Equivalence

We prove a tamely ramified version of the Kazhdan-Lusztig equivalence using factorization algebras. More precisely, we establish an equivalence between the DG category of Iwahori-integrable affine Lie algebra representations and the DG category of representations of the "mixed" quantum group. This confirms a conjecture by D. Gaitsgory in arXiv:1810.09054 [math.RT].

math.RT↗

arXiv2021

Portfolio optimization with idiosyncratic and systemic risks for financial networks

In this study, we propose a new multi-objective portfolio optimization with idiosyncratic and systemic risks for financial networks. The two risks are measured by the idiosyncratic variance and the network clustering coefficient derived from the asset correlation networks, respectively. We construct three types of financial networks in which nodes indicate assets and edges are based on three correlation measures. Starting from the multi-objective model, we formulate and solve the asset allocation problem. We find that the optimal portfolios obtained through the multi-objective with networked approach have a significant over-performance in terms of return measures in an out-of-sample framework. This is further supported by the less drawdown during the periods of the stock market fluctuating downward. According to analyzing different datasets, we also show that improvements made to portfolio strategies are robust.

q-fin.PM↗

arXiv2021

FPT Algorithms for a Special Block-structured Integer Program with Applications in Scheduling

We consider integer programs whose constraint matrix has a special block structure: $\min\{f(x):H_{com}x=b, l\le x\le u,x\in\mathbb{Z}^{t_B+nt_A}\}$, where the objective function $f$ is separable convex and the constraint matrix $H_ {com}$ is composed of small submatrices $A_i,B,C,D_i$ such that the first row is $(C,D_1,D_2,\ldots,D_n)$, the first column is $(C,B,B,\ldots,B)^{\top}$, the main diagonal is $(C,A_1,A_2,\ldots,A_n)$, and the rest entries are 0. Furthermore, $\text{rank}(B)$=1. We study fixed parameter tractable (FPT) algorithms by taking as parameters the number of rows and columns of small submatrices, together with the largest absolute value over their entries. We call the IP (almost) combinatorial 4-block n-fold IP. It generalizes the generalized n-fold IP and is a special case of the generalized 4-block n-fold IP. The existence of FPT algorithms for the generalized 4-block n-fold IP is a major open problem, which motivates us to study special cases of the generalized 4-block n-fold IP to find structural insights. We show the $\ell_{\infty}$-norm of Graver basis elements of combinatorial 4-block n-fold IP is $Ω(n)$. There is some FPT-value $λ$ such that for any nonzero element $g\in\{x: H_{com} x= 0\}$, $λg$ can always be decomposed into Graver basis elements in the same orthant whose $\ell_{\infty}$-norm is FPT-bounded (while g might not admit such a decomposition). Then we can bound the $\ell_{\infty}$-norm of Graver basis elements by $O_{FPT}(n)$ and develop $O_{FPT}({n^4\hat{L}^2})$-time algorithms ($O_{FPT}$ hides a multiplicative FPT-term, and $\hat{L}$ denotes the logarithm of the largest number occurring in the input). As applications, combinatorial 4-block n-fold IP can be used to model some classical problems, including scheduling with rejection and bicriteria scheduling.

math.OC↗

arXiv2021

Strategic COVID-19 vaccine distribution can simultaneously elevate social utility and equity

Balancing social utility and equity in distributing limited vaccines represents a critical policy concern for protecting against the prolonged COVID-19 pandemic. What is the nature of the trade-off between maximizing collective welfare and minimizing disparities between more and less privileged communities? To evaluate vaccination strategies, we propose a novel epidemic model that explicitly accounts for both demographic and mobility differences among communities and their association with heterogeneous COVID-19 risks, then calibrate it with large-scale data. Using this model, we find that social utility and equity can be simultaneously improved when vaccine access is prioritized for the most disadvantaged communities, which holds even when such communities manifest considerable vaccine reluctance. Nevertheless, equity among distinct demographic features are in tension due to their complex correlation in society. We design two behavior-and-demography-aware indices, community risk and societal harm, which capture the risks communities face and those they impose on society from not being vaccinated, to inform the design of comprehensive vaccine distribution strategies. Our study provides a framework for uniting utility and equity-based considerations in vaccine distribution, and sheds light on how to balance multiple ethical values in complex settings for epidemic control.

cs.CY↗

arXiv2021

Multiple Descent: Design Your Own Generalization Curve

This paper explores the generalization loss of linear regression in variably parameterized families of models, both under-parameterized and over-parameterized. We show that the generalization curve can have an arbitrary number of peaks, and moreover, locations of those peaks can be explicitly controlled. Our results highlight the fact that both classical U-shaped generalization curve and the recently observed double descent curve are not intrinsic properties of the model family. Instead, their emergence is due to the interaction between the properties of the data and the inductive biases of learning algorithms.

cs.LG↗

arXiv2021

Encircling exceptional points in a Riemann sphere for efficient asymmetric polarization-locked devices

Dynamically encircling exceptional points (EPs) in two-dimensional Hamiltonian parameter space has enabled intriguing chiral dynamics in which the final state of the system depends on the encircling direction. Here, we show that full Hamiltonian parameter space can be described in a Riemann sphere, and those points on the parameter space boundary with the eigenstates of the system Hamiltonian being convergent, converge to the north vertex. We present that encircling one EP on the Riemann sphere leads to chiral response, and a continuous encircling trajectory passing through the north vertex can realize near-unity asymmetrical transmission. An asymmetric polarization-locked devices are designed by mapping the encircling path onto the L-shaped silicon waveguides. We experimentally demonstrate near 100% asymmetrical polarization conversion efficiency between TE and TM modes with the mode crosstalk below -20 dB at 1550 nm. Our results bring the study of EP-associated dynamics into the realm of highly-efficient asymmetrical polarization conversion and power up new application opportunities for EP physics.

physics.optics↗

arXiv2021

Necessary conditions on effective quantum entanglement catalysts

Quantum catalytic transformations play important roles in the transformation of quantum entangled states under local operations and classical communications (LOCC). The key problems in catalytic transformations are the existence and the bounds on the catalytic states. We present the necessary conditions of catalytic states based on a set of points given by the Schmidt coefficients of the entangled source and target states. The lower bounds on the dimensions of the catalytic states are also investigated. Moreover, we give a detailed protocol of quantum mixed state transformation under entanglement-assisted LOCC.

quant-ph↗

arXiv2021

$H_2$-reducible matrices in six-dimensional mutually unbiased bases

Finding four six-dimensional mutually unbiased bases (MUBs) containing the identity matrix is a long-standing open problem in quantum information. We show that if they exist, then the $H_2$-reducible matrix in the four MUBs has exactly nine $2\times2$ Hadamard submatrices. We apply our result to exclude from the four MUBs some known CHMs, such as symmetric $H_2$-reducible matrix, the Hermitian matrix, Dita family, Bjorck's circulant matrix, and Szollosi family. Our results represent the latest progress on the existence of six-dimensional MUBs.

quant-ph↗

arXiv2021

Adaptive Distillation: Aggregating Knowledge from Multiple Paths for Efficient Distillation

Knowledge Distillation is becoming one of the primary trends among neural network compression algorithms to improve the generalization performance of a smaller student model with guidance from a larger teacher model. This momentous rise in applications of knowledge distillation is accompanied by the introduction of numerous algorithms for distilling the knowledge such as soft targets and hint layers. Despite this advancement in different techniques for distilling the knowledge, the aggregation of different paths for distillation has not been studied comprehensively. This is of particular significance, not only because different paths have different importance, but also due to the fact that some paths might have negative effects on the generalization performance of the student model. Hence, we need to adaptively adjust the importance of each path to maximize the impact of distillation on the student model. In this paper, we explore different approaches for aggregating these different paths and introduce our proposed adaptive approach based on multitask learning methods. We empirically demonstrate the effectiveness of the proposed approach over other baselines on the applications of knowledge distillation in classification, semantic segmentation, and object detection tasks.

cs.CV↗

arXiv2021

Some special complex Hadamard matrices of order six

The complete classification of $6\times 6$ complex Hadamard matrices (CHMs) is a long-standing open problem. In this paper we investigate a series of CHMs, such as the CHMs containing a $2\times 3$ submatrix with rank one, the CHMs containing exactly three distinct elements and all elements of the first row being one, the $H_2$-reducible matrices containing exactly three distinct matrix elements, and the CHMs containing a $3\times 3$ Hadamard submatrix. We characterize all forms of these CHMs. Our results are the latest progress on the complete classification of CHMs.

math-ph↗

arXiv2021

Strong quantum nonlocality from hypercubes

A set of multipartite orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition. Most known constructions of strongly nonlocal orthogonal product set (OPS) are limited to tripartite systems, and they are lack of intuitive structures. In this work, based on the decomposition for the outermost layer of an $n$-dimensional hypercube for $n= 3,4,5$, we successfully construct strongly nonlocal OPSs in any possible three, four and five-partite systems, which answers an open question given by Halder et al. [Phys. Rev. Lett.122, 040403 (2019)] and Yuan et al. [Phys. Rev. A102, 042228 (2020)] for any possible three, four and five-partite systems. Our results build the connection between hypercubes and strongly nonlocal OPSs, and exhibit the phenomenon of strong quantum nonlocality without entanglement in multipartite systems.

quant-ph↗

arXiv2021

Svar: A Tiny C++ Header Brings Unified Interface for Multiple programming Languages

There are numerous types of programming languages developed in the last decades, and most of them provide interface to call C++ or C for high efficiency implementation. The motivation of Svar is to design an efficient, light-weighted and general middle-ware for multiple languages, meanwhile, brings the dynamism features from script language to C++ in a straightforward way. Firstly, a Svar class with JSON like data structure is designed to hold everything exists in C++, including basic values, functions or user defined classes and objects. Secondly, arguments are auto cast to and from Svar efficiently with compile time pointers, references and shared\_ptr detection. Thirdly, classes and functions are binded with string names to support reflection, this means all functions and classes in a shared library can be exported to a Svar object, which also calls a Svar module. The Svar modules can be accessed by different languages and this paper demonstrates how to import and use a Svar module in Python and Node.js. Moreover, the Svar modules or even a python module can also be imported by C++ at runtime, which makes C++ easier to compile and use since headers are not required anymore. We compare the performance of Svar with two state-of-the-art binding tool for Python and Node.js, and the result demonstrates that Svar is efficient, elegant and general. The core of this project is one single tiny modern C++ header with less than 5000 lines code without extra dependency. To help developers using Svar, all the source codes related are public available on http://github.com/zdzhaoyong/Svar, including documentations and benchmarks.

cs.PL↗

arXiv2021

Towards Cross-Granularity Few-Shot Learning: Coarse-to-Fine Pseudo-Labeling with Visual-Semantic Meta-Embedding

Few-shot learning aims at rapidly adapting to novel categories with only a handful of samples at test time, which has been predominantly tackled with the idea of meta-learning. However, meta-learning approaches essentially learn across a variety of few-shot tasks and thus still require large-scale training data with fine-grained supervision to derive a generalized model, thereby involving prohibitive annotation cost. In this paper, we advance the few-shot classification paradigm towards a more challenging scenario, i.e., cross-granularity few-shot classification, where the model observes only coarse labels during training while is expected to perform fine-grained classification during testing. This task largely relieves the annotation cost since fine-grained labeling usually requires strong domain-specific expertise. To bridge the cross-granularity gap, we approximate the fine-grained data distribution by greedy clustering of each coarse-class into pseudo-fine-classes according to the similarity of image embeddings. We then propose a meta-embedder that jointly optimizes the visual- and semantic-discrimination, in both instance-wise and coarse class-wise, to obtain a good feature space for this coarse-to-fine pseudo-labeling process. Extensive experiments and ablation studies are conducted to demonstrate the effectiveness and robustness of our approach on three representative datasets.

cs.CV↗

arXiv2021

Tight running times for minimum $\ell_q$-norm load balancing: beyond exponential dependencies on $1/ε$

We consider a classical scheduling problem on $m$ identical machines. For an arbitrary constant $q>1$, the aim is to assign jobs to machines such that $\sum_{i=1}^m C_i^q$ is minimized, where $C_i$ is the total processing time of jobs assigned to machine $i$. It is well known that this problem is strongly NP-hard. Under mild assumptions, the running time of an $(1+ε)$-approximation algorithm for a strongly NP-hard problem cannot be polynomial on $1/ε$, unless $\text{P}=\text{NP}$. For most problems in the literature, this translates into algorithms with running time at least as large as $2^{Ω(1/\varepsilon)}+n^{O(1)}$. For the natural scheduling problem above, we establish the existence of an algorithm which violates this threshold. More precisely, we design a PTAS that runs in $2^{\tilde{O}(\sqrt{1/ε})}+n^{O(1)}$ time. This result is in sharp contrast to the closely related minimum makespan variant, where an exponential lower bound is known under the exponential time hypothesis (ETH). We complement our result with an essentially matching lower bound on the running time, showing that our algorithm is best-possible under ETH. The lower bound proof exploits new number-theoretical constructions for variants of progression-free sets, which might be of independent interest. Furthermore, we provide a fine-grained characterization on the running time of a PTAS for this problem depending on the relation between $ε$ and the number of machines $m$. More precisely, our lower bound only holds when $m=Θ(\sqrt{1/ε})$. Better algorithms, that go beyond the lower bound, exist for other values of $m$. In particular, there even exists an algorithm with running time polynomial in $1/ε$ if we restrict ourselves to instances with $m=Ω(1/ε\log^21/ε)$.

cs.CC↗

arXiv2021

Feature Cross Search via Submodular Optimization

In this paper, we study feature cross search as a fundamental primitive in feature engineering. The importance of feature cross search especially for the linear model has been known for a while, with well-known textbook examples. In this problem, the goal is to select a small subset of features, combine them to form a new feature (called the crossed feature) by considering their Cartesian product, and find feature crosses to learn an \emph{accurate} model. In particular, we study the problem of maximizing a normalized Area Under the Curve (AUC) of the linear model trained on the crossed feature column. First, we show that it is not possible to provide an $n^{1/\log\log n}$-approximation algorithm for this problem unless the exponential time hypothesis fails. This result also rules out the possibility of solving this problem in polynomial time unless $\mathsf{P}=\mathsf{NP}$. On the positive side, by assuming the \naive\ assumption, we show that there exists a simple greedy $(1-1/e)$-approximation algorithm for this problem. This result is established by relating the AUC to the total variation of the commutator of two probability measures and showing that the total variation of the commutator is monotone and submodular. To show this, we relate the submodularity of this function to the positive semi-definiteness of a corresponding kernel matrix. Then, we use Bochner's theorem to prove the positive semi-definiteness by showing that its inverse Fourier transform is non-negative everywhere. Our techniques and structural results might be of independent interest.

cs.LG↗

arXiv2021

Bending the Bruhat-Tits Tree I:Tensor Network and Emergent Einstein Equations

As an extended companion paper to [1], we elaborate in detail how the tensor network construction of a p-adic CFT encodes geometric information of a dual geometry even as we deform the CFT away from the fixed point by finding a way to assign distances to the tensor network. In fact we demonstrate that a unique (up to normalizations) emergent graph Einstein equation is satisfied by the geometric data encoded in the tensor network, and the graph Einstein tensor automatically recovers the known proposal in the mathematics literature, at least perturbatively order by order in the deformation away from the pure Bruhat-Tits Tree geometry dual to pure CFTs. Once the dust settles, it becomes apparent that the assigned distance indeed corresponds to some Fisher metric between quantum states encoding expectation values of bulk fields in one higher dimension. This is perhaps a first quantitative demonstration that a concrete Einstein equation can be extracted directly from the tensor network, albeit in the simplified setting of the p-adic AdS/CFT.

hep-th↗

arXiv2021

A complete picture of the four-party linear inequalities in terms of the 0-entropy

Multipartite quantum system is complex. Characterizing the relations among the three bipartite reduced density operators $ρ_{AB}$, $ρ_{AC}$ and $ρ_{BC}$ of a tripartite state $ρ_{ABC}$ has been an open problem in quantum information. One of such relations has been reduced by [Cadney et al, LAA. 452, 153, 2014] to a conjectured inequality in terms of matrix rank, namely $r(ρ_{AB}) \cdot r(ρ_{AC})\ge r(ρ_{BC})$ for any $ρ_{ABC}$. It is denoted as open problem $41$ in the website "Open quantum problems-IQOQI Vienna". We prove the inequality, and thus establish a complete picture of the four-party linear inequalities in terms of the $0$-entropy. Our proof is based on the construction of a novel canonical form of bipartite matrices under local equivalence. We apply our result to the marginal problem and the extension of inequalities in the multipartite systems, as well as the condition when the inequality is saturated.

quant-ph↗