arXiv subjects
Publications and source records attributed to Dong Yao.
For matrices drawn from the standard Gaussian orthogonal ensemble (GOE) and Gaussian unitary ensemble (GUE), we prove that the normalized zero counting measure of the permanental characteristic polynomial $Per(zI_N-H_N)$ converges almost surely to the standard Wigner semicircle law on $[-2,2]$, rotated by $\pi/2$ onto the imaginary axis. This proves the conjecture proposed by Fyodorov in \cite{Fyodorov2006}.
In this paper, we study the smallest gaps between successive zeros of nondegenerate smooth stationary centered Gaussian processes on the real line with the assumption that the covariance kernel $\kappa(x)$ and its derivatives decay to 0 as $|x|\to\infty$. We prove that, after rescaling, the smallest gaps converge to a Poisson point process with a specific rate. Moreover, the positions where these smallest gaps occur tend to a uniform distribution. Consequently, we can derive the limiting density for the $k$-th smallest gap.
In this article, we study the smallest distances between the zeros of Gaussian analytic functions over compact Riemann surfaces. Our main result is that, after appropriate rescaling, the point process of the smallest distances converge to a Poisson point process with a universal rate. Furthermore, the locations where these smallest distances occur tend to follow a uniform measure with respect to the volume form. As a consequence, the limiting density of the $k$-th rescaled smallest distance is proportional to $x^{4k-1}e^{-x^4}$ for any $k\geq 1$. Analogous results hold for the classical Gaussian Entire Functions.
Consider an SI process on a graph $G$ where each S--I connection becomes I--I at rate $\lambda$. Here S and I stand for ``susceptible'' and ``infected'' respectively. The evoSI model is a modification of the SI model in which S--I edges are broken at rate $\rho$ and the ``S'' connects to a randomly chosen vertex. It is proven in Durrett and Yao [2022, Electron. J. Probab.] that, for the supercritical evoSI process on the configuration model, there exists a quantity $\Delta$ depending on the first three moments of the degree distribution such that the sign of $\Delta$ governs the continuity of the phase transition of the final epidemic size near the critical infection rate $\lambda_c$. In this paper, we consider the critical evoSI model on the configuration model, i.e., $\lambda=\lambda_c$. We show that, if $\Delta>0$, then the probability of a major outbreak starting from a single infected individual is $Cn^{-1/3}(1+o(1))$ for some explicit constant $C>0$, where $n$ is the size of the graph. On the contrary, if $\Delta<0$, then this probability is $o(n^{-1/3})$. The case $\Delta<0$ is reminiscent of the critical {\ER} graphs, where the probability for the size of the largest component to be of order $n$ decays exponentially in $n$.
In the standard SIR model on a graph, infected vertices infect their neighbors at rate $\alpha$ and recover at rate $\mu$. We consider a two-type SIR process where each individual in the graph can be infected with two types of diseases, $A$ and $B$. Moreover, the two diseases interact in a cooperative way so that an individual that has been infected with one type of disease can acquire the other at a higher rate. We prove that if the underlying graph is a Galton-Watson tree and initially the root is infected with both $A$ and $B$, while all others are susceptible, then the two-type SIR model has the same critical value for the survival probability as the classic single-type model.
We consider the Plancherel-Rotach type asymptotics of the biorthogonal polynomials associated to the biorthogonal ensemble with the joint probability density function \begin{equation*} \frac{1}{C} \prod_{1 \leq i < j \leq n} (λ_j -λ_i)(f(λ_j) - f(λ_i)) \prod^n_{j = 1} W^{(n)}_α(λ_j) dλ_j, \end{equation*} where \begin{align*} f(x) = {}& \sinh^2(\sqrt{x}), & W^{(n)}_α(x) = {}& x^α h(x) e^{-nV(x)}. \end{align*} In the special case that the potential function $V$ is linear, this biorthogonal ensemble arises in the quantum transport theory of disordered wires. We analyze the asymptotic problem via $2$-component vector-valued Riemann-Hilbert problems, and solve it under the one-cut regular with a hard edge condition. We use the asymptotics of biorthogonal polynomials to establish sine universality for the correlation kernel in the bulk, and provide a central limit theorem with a specific variance for holomorphic linear statistics. As an application of our theories, we establish the Ohm's law (1.12) and universal conductance fluctuation (1.13) for the disordered wire model, thereby rigorously confirming predictions from experimental physics [Washburn-Webb86].
Copper-based chalcopyrite semiconductors have attracted sustained interest owing to their promising thermoelectric (TE) performance, yet the microscopic origins of their TE behavior remain incompletely understood. Here, we systematically investigate the TE properties of Cu$MX_2$ ($M=$ Al, Ga, and In; $X=$ S, Se, and Te) using first-principles calculations. For $p$-type doping, the calculated electrical conductivities ($σ$), hole mobilities ($μ$), Seebeck coefficients ($S$), and power factors (PFs) of CuGaTe$_2$ and CuInTe$_2$ show excellent agreement with experimental data. At fixed temperature and hole concentration, as $X$ varies from S to Te, the hole mobility increases markedly due to progressively weaker polar--optical--phonon scattering, reflecting the reduced ionic contribution to the dielectric response in compounds with heavier chalcogens. Combined with smaller transport effective masses, Cu$M$Te$_2$ compounds therefore exhibit high $σ$ and large PFs. Across the Cu$MX_2$ family, the anomalously lower $κ_{\mathrm{L}}$ of Cu$M$Se$_2$ relative to Cu$M$Te$_2$ arises primarily from enhanced three-phonon scattering at low-frequency region. For a given $M$, Cu$M$S$_2$ displays the steepest temperature-induced decrease in $κ_{\mathrm{L}}$ and attains a smaller $κ_{\mathrm{L}}$ than Cu$M$Se$_2$ and Cu$M$Te$_2$ at 800~K. Given the low band degeneracy and comparatively modest hole mobilities of Cu$MX_2$ compounds, the most effective routes to further improve their TE performance are to enhance $σ$ and reduce $κ_{\mathrm{L}}$ through doping.
In the standard SIR model, infected vertices infect their neighbors at rate $λ$ independently across each edge. They also recover at rate $γ$. In this work we consider the SIR-$ω$ model where the graph structure itself co-evolves with the SIR dynamics. Specifically, $S-I$ connections are broken at rate $ω$. Then, with probability $α$, $S$ rewires this edge to another uniformly chosen vertex; and with probability $1-α$, this edge is simply dropped. When $α=1$ the SIR-$ω$ model becomes the evoSIR model. Jiang et al. proved in \cite{DOMath} that the probability of an outbreak in the evoSIR model converges to 0 as $λ$ approaches the critical infection rate $λ_c$. On the other hand, numerical experiments in \cite{DOMath} revealed that, as $λ\to λ_c$, (conditionally on an outbreak) the fraction of infected vertices may not converge to 0, which is referred to as a discontinuous phase transition. In \cite{BB} Ball and Britton give two (non-matching) conditions for continuous and discontinuous phase transitions for the fraction of infected vertices in the SIR-$ω$ model. In this work, we obtain a necessary and sufficient condition for the emergence of a discontinuous phase transition of the final epidemic size of the SIR-$ω$ model on \ER\, graphs, thus closing the gap between these two conditions.
We study random waves on smooth, compact, Riemannian manifolds under the spherical ensemble. Our first main result shows that there is a positive universal limit for the critical radius of a specific deterministic embedding, defined via the eigenfunctions of the Laplace-Beltrami operator, of such manifolds into higher dimensional Euclidean spaces. This result enables the application of Weyl's tube formula to derive the tail probabilities for the suprema of random waves. Consequently, the estimate for the expectation of the Euler characteristic of the excursion set follows directly.
Data from observational studies (OSs) is widely available and readily obtainable yet frequently contains confounding biases. On the other hand, data derived from randomized controlled trials (RCTs) helps to reduce these biases; however, it is expensive to gather, resulting in a tiny size of randomized data. For this reason, effectively fusing observational data and randomized data to better estimate heterogeneous treatment effects (HTEs) has gained increasing attention. However, existing methods for integrating observational data with randomized data must require \textit{complete} observational data, meaning that both treated subjects and untreated subjects must be included in OSs. This prerequisite confines the applicability of such methods to very specific situations, given that including all subjects, whether treated or untreated, in observational studies is not consistently achievable. In our paper, we propose a resilient approach to \textbf{C}ombine \textbf{I}ncomplete \textbf{O}bservational data and randomized data for HTE estimation, which we abbreviate as \textbf{CIO}. The CIO is capable of estimating HTEs efficiently regardless of the completeness of the observational data, be it full or partial. Concretely, a confounding bias function is first derived using the pseudo-experimental group from OSs, in conjunction with the pseudo-control group from RCTs, via an effect estimation procedure. This function is subsequently utilized as a corrective residual to rectify the observed outcomes of observational data during the HTE estimation by combining the available observational data and the all randomized data. To validate our approach, we have conducted experiments on a synthetic dataset and two semi-synthetic datasets.
In this paper, we study the smallest gaps for the Gaussian symplectic ensemble (GSE). We prove that the rescaled smallest gaps and their locations converge to a Poisson point process with an explicit rate. The approach provides an alternative proof for the GOE case and complements the results in \cite{FTW}. By combining the main results from \cite{BB, FTW, FW2}, the study of the smallest gaps for the classical random matrix ensembles C$β$E and G$β$E for $β= 1, 2,$ and $4$ is now complete.
Recent research in self-supervised contrastive learning of music representations has demonstrated remarkable results across diverse downstream tasks. However, a prevailing trend in existing methods involves representing equally-sized music clips in either waveform or spectrogram formats, often overlooking the intrinsic part-whole hierarchies within music. In our quest to comprehend the bottom-up structure of music, we introduce MART, a hierarchical music representation learning approach that facilitates feature interactions among cropped music clips while considering their part-whole hierarchies. Specifically, we propose a hierarchical part-whole transformer to capture the structural relationships between music clips in a part-whole hierarchy. Furthermore, a hierarchical contrastive learning objective is crafted to align part-whole music representations at adjacent levels, progressively establishing a multi-hierarchy representation space. The effectiveness of our music representation learning from part-whole hierarchies has been empirically validated across multiple downstream tasks, including music classification and cover song identification.
Sentence semantic matching is a research hotspot in natural language processing, which is considerably significant in various key scenarios, such as community question answering, searching, chatbot, and recommendation. Since most of the advanced models directly model the semantic relevance among words between two sentences while neglecting the \textit{keywords} and \textit{intents} concepts of them, DC-Match is proposed to disentangle keywords from intents and utilizes them to optimize the matching performance. Although DC-Match is a simple yet effective method for semantic matching, it highly depends on the external NER techniques to identify the keywords of sentences, which limits the performance of semantic matching for minor languages since satisfactory NER tools are usually hard to obtain. In this paper, we propose to generally and flexibly resolve the text into multi concepts for multilingual semantic matching to liberate the model from the reliance on NER models. To this end, we devise a \underline{M}ulti-\underline{C}oncept \underline{P}arsed \underline{S}emantic \underline{M}atching framework based on the pre-trained language models, abbreviated as \textbf{MCP-SM}, to extract various concepts and infuse them into the classification tokens. We conduct comprehensive experiments on English datasets QQP and MRPC, and Chinese dataset Medical-SM. Besides, we experiment on Arabic datasets MQ2Q and XNLI, the outstanding performance further prove MCP-SM's applicability in low-resource languages.
Effectively representing users lie at the core of modern recommender systems. Since users' interests naturally exhibit multiple aspects, it is of increasing interest to develop multi-interest frameworks for recommendation, rather than represent each user with an overall embedding. Despite their effectiveness, existing methods solely exploit the encoder (the forward flow) to represent multiple aspects of interests. However, without explicit regularization, the interest embeddings may not be distinct from each other nor semantically reflect representative historical items. Towards this end, we propose the Re4 framework, which leverages the backward flow to reexamine each interest embedding. Specifically, Re4 encapsulates three backward flows, i.e., 1) Re-contrast, which drives each interest embedding to be distinct from other interests using contrastive learning; 2) Re-attend, which ensures the interest-item correlation estimation in the forward flow to be consistent with the criterion used in final recommendation; and 3) Re-construct, which ensures that each interest embedding can semantically reflect the information of representative items that relate to the corresponding interest. We demonstrate the novel forward-backward multi-interest paradigm on ComiRec, and perform extensive experiments on three real-world datasets. Empirical studies validate that Re4 helps to learn learning distinct and effective multi-interest representations.
In this paper, we study the extremal process of the maxima of all the largest eigenvalues of principal minors of the classical Gaussian orthogonal ensemble (GOE). We prove that the fluctuation of the maxima is given by the Gumbel distribution in the limit. We also derive the limiting joint distribution of the maxima and the corresponding eigenvector, which implies that these two random variables are asymptotically independent.
The evoSIR model is a modification of the usual SIR process on a graph $G$ in which $S-I$ connections are broken at rate $ρ$ and the $S$ connects to a randomly chosen vertex. The evoSI model is the same as evoSIR but recovery is impossible. In \cite{DOMath} the critical value for evoSIR was computed and simulations showed that when $G$ is an Erd\H os-Rényi graph with mean degree 5, the system has a discontinuous phase transition, i.e., as the infection rate $λ$ decreases to $λ_c$, the fraction of individuals infected during the epidemic does not converge to 0. In this paper we study evoSI dynamics on graphs generated by the configuration model. We show that there is a quantity $Δ$ determined by the first three moments of the degree distribution, so that the phase transition is discontinuous if $Δ>0$ and continuous if $Δ<0$.
Microscale imaging of mesoscale bulk materials under dynamic compression is important for understanding their properties. In this work, we study the effects of the depth of field (DoF) and field of view (FoV) of the optical lens and extract the scattered light of the region to be imaged within the bulk polycrystalline material based on the objective Bragg coherent diffraction imaging. We describe how the DoF and FoV quantitatively limit the diffraction volume, where the DoF and FoV limit the scattering region parallel and perpendicular to the direction of the light source respectively. We demonstrate this scheme by simulating the separate imaging of a submicron-sized crack region within a few μm-sized Si bulk material, and obtain a high imaging quality. This scheme enables imaging of selected regions within bulk polycrystalline materials with the resolution up to the order of 10 nm.
There is a rapidly-growing research interest in engaging users with multi-modal data for accurate user modeling on recommender systems. Existing multimedia recommenders have achieved substantial improvements by incorporating various modalities and devising delicate modules. However, when users decide to interact with items, most of them do not fully read the content of all modalities. We refer to modalities that directly cause users' behaviors as point-of-interests, which are important aspects to capture users' interests. In contrast, modalities that do not cause users' behaviors are potential noises and might mislead the learning of a recommendation model. Not surprisingly, little research in the literature has been devoted to denoising such potential noises due to the inaccessibility of users' explicit feedback on their point-of-interests. To bridge the gap, we propose a weakly-supervised framework based on contrastive learning for denoising multi-modal recommenders (dubbed Demure). In a weakly-supervised manner, Demure circumvents the requirement of users' explicit feedback and identifies the noises by analyzing the modalities of all interacted items from a given user.