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It is commonly known that the dephasing in open quantum systems is due to the establishment of bipartite correlations with ambient environments, which are typically difficult to be fully characterized. Recently, a new approach of average over disordered Hamiltonian ensemble is developed and shown to be capable of describing the nonclassicality of incoherent dynamics based on inferring the nonclassical nature of the correlations. Here we further extend the approach of Hamiltonian ensemble in the canonical form to the realm of structural disorder. Under the variable separation of the probability distribution within the Hamiltonian ensemble, the geometrical structure is easily visualized and can be characterized according to the degree of symmetry. We demonstrate four degrees and investigate the effects of different types of symmetry breaking on the incoherent dynamics. We show that these effects are easily understood from the emergences of additional terms in the master equations, leading to rather general master equations and, consequently, going beyond the previous frameworks of pure dephasing or isotropic depolarization., Comment: 15 pages, 7 figures

We consider a general statistical inference model of finite-rank tensor products. For any interaction structure and any order of tensor products, we identify the limit free energy of the model in terms of a variational formula. Our approach consists of showing first that the limit free energy must be the viscosity solution to a certain Hamilton-Jacobi equation., Comment: 24 pages, final version

We prove that if ${(P_x)}_{x\in \mathscr X}$ is a family of probability measures which satisfy the log-Sobolev inequality and whose pairwise chi-squared divergences are uniformly bounded, and $\mu$ is any mixing distribution on $\mathscr X$, then the mixture $\int P_x \, \mathrm{d} \mu(x)$ satisfies a log-Sobolev inequality. In various settings of interest, the resulting log-Sobolev constant is dimension-free. In particular, our result implies a conjecture of Zimmermann and Bardet et al. that Gaussian convolutions of measures with bounded support enjoy dimension-free log-Sobolev inequalities., Comment: 16 pages

Current-induced spin-orbit torques (SOTs) are of interest for fast and energy-efficient manipulation of magnetic order in spintronic devices. To be deterministic, however, switching of perpendicularly magnetized materials by SOT requires a mechanism for in-plane symmetry breaking. Existing methods to do so involve the application of an in-plane bias magnetic field, or incorporation of in-plane structural asymmetry in the device, both of which can be difficult to implement in practical applications. Here, we reported bias-field-free SOT switching in a single perpendicular CoTb layer with an engineered vertical composition gradient. The vertical structural inversion asymmetry induces strong intrinsic SOTs and a gradient-driven Dzyaloshinskii-Moriya interaction (g-DMI), which breaks the in-plane symmetry during the switching process. Micromagnetic simulations are in agreement with experimental results, and elucidate the role of g-DMI in the deterministic switching. This bias-field-free switching scheme for perpendicular ferrimagnets with g-DMI provides a strategy for efficient and compact SOT device design., Comment: 27 pages, 5 figures

We develop a dynamical approach to infinite volume directed polymer measures in random environments. We define polymer dynamics in 1+1 dimension as a stochastic gradient flow on polymers pinned at the origin, for energy involving quadratic nearest neighbor interaction and local interaction with random environment. We prove existence and uniqueness of the solution, continuity of the flow, the order-preserving property with respect to the coordinatewise partial order, and the invariance of the asymptotic slope. We establish ordering by noise which means that if two initial conditions have distinct slopes, then the associated solutions eventually get ordered coordinatewise. This, along with the shear-invariance property and existing results on static infinite volume polymer measures, allows to prove that for a fixed asymptotic slope and almost every realization of the environment, the polymer dynamics has a unique invariant distribution given by a unique infinite volume polymer measure, and, moreover, One Force -- One Solution principle holds. We also prove that every polymer measure is concentrated on paths with well-defined asymptotic slopes and give an estimate on deviations from straight lines., Comment: 49 pages

A pointed convex cone naturally induces a partial order, and further a notion of nondecreasingness for functions. We consider extended real-valued functions defined on the cone. Monotone conjugates for these functions can be defined in an analogous way to the standard convex conjugate. The only difference is that the supremum is taken over the cone instead of the entire space. We give sufficient conditions for the cone under which the corresponding Fenchel-Moreau biconjugation identity holds for proper, convex, lower semicontinuous, and nondecreasing functions defined on the cone. In addition, we show that these conditions are satisfied by a class of cones known as perfect cones., Comment: 18 pages; generalized the main result; changed "self-dual cones" in the title to "convex cones"

We study the high-dimensional limit of the free energy associated with the inference problem of finite-rank matrix tensor products. In general, we bound the limit from above by the unique solution to a certain Hamilton-Jacobi equation. Under additional assumptions on the nonlinearity in the equation which is determined explicitly by the model, we identify the limit with the solution. Two notions of solutions, weak solutions and viscosity solutions, are considered, each of which has its own advantages and requires different treatments. For concreteness, we apply our results to a model with i.i.d. entries and symmetric interactions. In particular, for the first order and even order tensor products, we identify the limit and obtain estimates on convergence rates; for other odd orders, upper bounds are obtained., Comment: 44 pages

With the rise of deep learning methods, person Re-Identification (ReID) performance has been improved tremendously in many public datasets. However, most public ReID datasets are collected in a short time window in which persons' appearance rarely changes. In real-world applications such as in a shopping mall, the same person's clothing may change, and different persons may wearing similar clothes. All these cases can result in an inconsistent ReID performance, revealing a critical problem that current ReID models heavily rely on person's apparels. Therefore, it is critical to learn an apparel-invariant person representation under cases like cloth changing or several persons wearing similar clothes. In this work, we tackle this problem from the viewpoint of invariant feature representation learning. The main contributions of this work are as follows. (1) We propose the semi-supervised Apparel-invariant Feature Learning (AIFL) framework to learn an apparel-invariant pedestrian representation using images of the same person wearing different clothes. (2) To obtain images of the same person wearing different clothes, we propose an unsupervised apparel-simulation GAN (AS-GAN) to synthesize cloth changing images according to the target cloth embedding. It's worth noting that the images used in ReID tasks were cropped from real-world low-quality CCTV videos, making it more challenging to synthesize cloth changing images. We conduct extensive experiments on several datasets comparing with several baselines. Experimental results demonstrate that our proposal can improve the ReID performance of the baseline models., Comment: 10 pages

We study the high-dimensional limit of the free energy associated with the inference problem of a rank-one nonsymmetric matrix. The matrix is expressed as the outer product of two vectors, not necessarily independent. The distributions of the two vectors are only assumed to have scaled bounded supports. We bound the difference between the free energy and the solution to a suitable Hamilton-Jacobi equation in terms of two much simpler quantities: concentration rate of this free energy, and the convergence rate of a simpler free energy in a decoupled system. To demonstrate the versatility of this approach, we apply our result to the i.i.d. case and the spherical case. By plugging in estimates of the two simpler quantities, we identify the limits and obtain convergence rates.

Spatio-temporal sequence forecasting is one of the fundamental tasks in spatio-temporal data mining. It facilitates many real world applications such as precipitation nowcasting, citywide crowd flow prediction and air pollution forecasting. Recently, a few Seq2Seq based approaches have been proposed, but one of the drawbacks of Seq2Seq models is that, small errors can accumulate quickly along the generated sequence at the inference stage due to the different distributions of training and inference phase. That is because Seq2Seq models minimise single step errors only during training, however the entire sequence has to be generated during the inference phase which generates a discrepancy between training and inference. In this work, we propose a novel curriculum learning based strategy named Temporal Progressive Growing Sampling to effectively bridge the gap between training and inference for spatio-temporal sequence forecasting, by transforming the training process from a fully-supervised manner which utilises all available previous ground-truth values to a less-supervised manner which replaces some of the ground-truth context with generated predictions. To do that we sample the target sequence from midway outputs from intermediate models trained with bigger timescales through a carefully designed decaying strategy. Experimental results demonstrate that our proposed method better models long term dependencies and outperforms baseline approaches on two competitive datasets., Comment: ECAI 2020 Accepted, preprint

We investigate contraction of the Wasserstein distances on $\mathbb{R}^d$ under Gaussian smoothing. It is well known that the heat semigroup is exponentially contractive with respect to the Wasserstein distances on manifolds of positive curvature; however, on flat Euclidean space---where the heat semigroup corresponds to smoothing the measures by Gaussian convolution---the situation is more subtle. We prove precise asymptotics for the $2$-Wasserstein distance under the action of the Euclidean heat semigroup, and show that, in contrast to the positively curved case, the contraction rate is always polynomial, with exponent depending on the moment sequences of the measures. We establish similar results for the $p$-Wasserstein distances for $p \neq 2$ as well as the $\chi^2$ divergence, relative entropy, and total variation distance. Together, these results establish the central role of moment matching arguments in the analysis of measures smoothed by Gaussian convolution., Comment: 24 pages

A graph is Hamiltonian if it contains a cycle which visits every vertex of the graph exactly once. In this paper, we consider the problem of Hamiltonicity of a graph $G_n$, which will be called the prime difference graph of order $n$, with vertex set $\{1,2,\cdots, n\}$ and edge set $\{uv: |u-v|$ is a prime number$\}$. A recent result, conjectured by Sun and later proved by Chen, asserts that $G_n$ is Hamiltonian for $n\geq 5$. This paper extends their result in three directions. First, we prove that for any two integers $a$ and $b$ with $1\leq a

Visual cryptography encrypts the secret image into $n$ shares (transparency) so that only stacking a qualified number of shares can recover the secret image by the human visual system while no information can be revealed without a large enough number of shares. This paper investigates the $(k,n)$-threshold Visual Secret Sharing (VSS) model, where one can decrypt the original image by stacking at least $k$ shares and get nothing with less than $k$ shares. There are two main approaches in the literature: codebook-based schemes and random-grid-based schemes; the former is the case of this paper. In general, given any positive integers $k$ and $n$, it is not easy to design a valid scheme for the $(k,n)$-threshold VSS model. In this paper, we propose a simple strategy to construct an efficient scheme for the $(k,n)$-threshold VSS model for any positive integers $2\leq k\leq n$. The crucial idea is to establish a seemingly unrelated connection between the $(k,n)$-threshold VSS scheme and a mathematical structure -- the generalized Pascal's triangle. This paper improves and extends previous results in four aspects: Our construction offers a unified viewpoint and covers several known results; The resulting scheme has a progressive-viewing property that means the more shares being stacked together the clearer the secret image would be revealed. The proposed scheme can be constructed explicitly and efficiently based on the generalized Pascal's triangle without a computer. Performance of the proposed scheme is comparable with known results., Comment: 16 pages