Related papers: Discrete Mixed Quantization
We adapt modulus of continuity estimates to the study of spectra of combinatorial graph Laplacians, as well as the Dirichlet spectra of certain weighted Laplacians. The latter case is equivalent to stoquastic Hamiltonians and is of current…
This paper investigates asymptotic properties of multifractal products of random fields. The obtained limit theorems provide sufficient conditions for the convergence of cumulative fields in the spaces $L_q.$ New results on the rate of…
Using the Davenport-Heilbronn circle method, we show that for almost all additive Diophantine inequalities of degree $k$ in more than $2k$ variables the expected asymptotic formula for the density of solutions holds true. This appears to be…
Real-world optimization problems are generally not just black-box problems, but also involve mixed types of inputs in which discrete and continuous variables coexist. Such mixed-space optimization possesses the primary challenge of modeling…
We introduce a principled method for the signed clustering problem, where the goal is to partition a graph whose edge weights take both positive and negative values, such that edges within the same cluster are mostly positive, while edges…
Vector bundle cohomology represents a key ingredient for string phenomenology, being associated with the massless spectrum arising in string compactifications on smooth compact manifolds. Although standard algorithmic techniques exist for…
In the present paper we develop a framework in which questions of quantum ergodicity for operators acting on sections of hermitian vector bundles over Riemannian manifolds can be studied. We are particularly interested in the case of…
The Immersed Boundary Method (IBM) is a popular numerical approach to impose boundary conditions without relying on body-fitted grids, thus reducing the costly effort of mesh generation. To obtain enhanced accuracy, IBM can be combined with…
Learning the right graph representation from noisy, multi-source data has garnered significant interest in recent years. A central tenet of this problem is relational learning. Here the objective is to incorporate the partial information…
We survey some recent progress in the theory of vector bundles on algebraic varieties and related questions in algebraic K-theory.
We consider two independent Erd\H{o}s-R\'enyi random graphs, with possibly different parameters, and study two isomorphism problems, a graph embedding problem and a common subgraph problem. Under certain conditions on the graph parameters…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
Classification of high dimensional data finds wide-ranging applications. In many of these applications equipping the resulting classification with a measure of uncertainty may be as important as the classification itself. In this paper we…
We study the general problem of mixing for ab-initio quantum-mechanical problems. Guided by general mathematical principles and the underlying physics, we propose a multisecant form of Broydens second method for solving the self-consistent…
Anomalies are those deviating from the norm. Unsupervised anomaly detection often translates to identifying low density regions. Major problems arise when data is high-dimensional and mixed of discrete and continuous attributes. We propose…
Given the adjacency matrix of an undirected graph, we define a coupling of the spectral measures at the vertices, whose moments count the rooted closed paths in the graph. The resulting joint spectral measure verifies numerous interesting…
We extend the spectral method for proving limit theorems to random non-uniformly expanding dynamical systems. This yields the CLT and moderate deviations principles (MDP). We show that as the amount of non-uniformity decreases the CLT rates…
This work establishes the well-posedness and a priori error analysis for the mixed FEEC-type finite element approximation of the three-dimensional vector Laplace boundary value problem subject to the Dirichlet boundary condition. The…
Bach et al. [1] recently presented an algorithm for constructing confluent drawings, by leveraging power graph decomposition to generate an auxiliary routing graph. We identify two issues with their method which we call the node split and…
In this paper we address distributed learning problems over peer-to-peer networks. In particular, we focus on the challenges of quantized communications, asynchrony, and stochastic gradients that arise in this set-up. We first discuss how…