Incidences Between Planes Over Finite Fields

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With the advent of data science, the analysis of network or graph data has become a very timely research problem. A variety of recent works have been proposed to generalize neural networks to graphs, either from a spectral graph theory or a spatial perspec ...

In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer

n\ge 3

, we define

e(n)

to be the minimum positive integer such that an ...

This article proposes a new clock-dependent gain-scheduled dynamic output feedback controller for delayed linear parameter varying systems with piecewise constant parameters. The proposed controller guarantees Script capital L2-performance. By employing a ...

We cast the problem of source localization on graphs as the simultaneous problem of sparse recovery and diffusion ker- nel learning. An l1 regularization term enforces the sparsity constraint while we recover the sources of diffusion from a single snapshot ...

We first consider the additive Brownian motion process (X(s(1), s(2)), (s(1), s(2)) is an element of R-2) defined by X(s(1), s(2)) = Z(1)(s(1)) - Z2(s2), where Z(1) and Z(2) are two independent (two-sided) Brownian motions. We show that with probability 1, ...

We consider rank-1 lattices for integration and reconstruction of functions with series expansion supported on a finite index set. We explore the connection between the periodic Fourier space and the non-periodic cosine space and Chebyshev space, via tent ...

We propose a new framework for the analysis of low- rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the classical low-rank S ...

Classical Serre-Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the base of its universal deformation with a Frobenius lifting and canonical multipl ...

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We construct reduced order models for two classes of globally coupled multi-component oscillatory systems, selected as prototype models that exhibit synchronization. These are the Kuramoto model, considered both in its original formulation and with a suita ...

A double-normal pair of a finite set S of points that spans R-d is a pair of points {p, q} from S such that S lies in the closed strip bounded by the hyperplanes through p and q perpendicular to pq. A double-normal pair {p, q} is strict if S \ {p,q} lies i ...

It is possible to construct Levy white noises as generalized random processes in the sense of Gel'fand and Vilenkin, or as an independently scattered random measures introduced by Rajput and Rosinski. In this article, we unify those two approaches by exten ...

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Suppose that the vertices of a graph G are colored with two colors in an unknown way. The color that occurs on more than half of the vertices is called the majority color (if it exists), and any vertex of this color is called a majority vertex. We study th ...

Non-adaptive group testing involves grouping arbitrary subsets of

n

items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to identify at most

d

d ...

This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) when A is subject to low-rank modifications. It extends our previous work in this context on polynomial Krylov methods, for which we present a simplified conve ...

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely the spectral deco ...

Non-adaptive group testing involves grouping arbitrary subsets of

n

items into different pools and identifying defective items based on tests obtained for each pool. Motivated by applications in network tomography, sensor networks and infection propagati ...

Let G = (V, E) be a graph with n vertices and m >= 4n edges drawn in the plane. The celebrated Crossing Lemma states that G has at least Omega(m(3)/n(2)) pairs of crossing edges; or equivalently, there is an edge that crosses Omega(m(2)/n(2)) other edges. ...

In graph coarsening, one aims to produce a coarse graph of reduced size while preserving important graph properties. However, as there is no consensus on which specific graph properties should be preserved by coarse graphs, measuring the differences betwee ...

Incidences Between Planes Over Finite Fields

Chat with Graph Search

iPool--Information-Based Pooling in Hierarchical Graph Neural Networks

On some algebraic and extremal problems in discrete geometry

L2 output feedback control of delayed linear parameter varying systems with piecewise constant parameters: A clock-dependent L-K approach

Source Localization on Graphs via l1 Recovery and Spectral Graph Theory

Hausdorff dimension of the boundary of bubbles of additive Brownian motion and of the Brownian sheet

Function Integration, Reconstruction And Approximation Using Rank-1 Lattices

Multilinear Low-Rank Tensors on Graphs & Applications

Serre-Tate theory for Calabi-Yau varieties

Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering

Modeling synchronization in globally coupled oscillatory systems using model order reduction

Double-Normal Pairs In Space

The domain of definition of the Levy white noise

Group testing for connected communities

Adaptive majority problems for restricted query graphs and for weighted sets

Graph-Constrained Group Testing

Low-Rank Updates Of Matrix Functions Ii: Rational Krylov Methods

Wavelets on graphs via spectral graph theory

Graph-Constrained Group Testing

A bipartite strengthening of the Crossing Lemma

Graph Coarsening with Preserved Spectral Properties