We expect that these methods will also apply to similarly give tight polynomial bounds for removal lemmas of linear equations in more variables in vector spaces over Fp. Sets that contain no arithmetic progressions have also been studied over other …

Let $p$ be a fixed prime. A triangle in $\mathbb{F}_p^n$ is an ordered triple $(x,y,z)$ of points satisfying $x+y+z=0$. Let $N=p^n=|\mathbb{F}_p^n|$.…

The author would like to thank the anonymous referee for providing numerous useful comments and suggestions, which helped improve the paper.

In this paper we study certain fundamental and distinguished subsets of weights of an arbitrary highest weight module over a complex semisimple Lie a…

We demonstrate the design, fabrication and characterization of nanobeam cavities with multiple higher order modes. Designs with two high Q modes with…

We want to calculate the monoidal category given by the bimodules of VecZ2. First, let us review the background material of Proposition 3.19 of [14] described in section 3.6, 2.7.

Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf mona…

In this section we show that a globally F-regular type variety is rationally connected.

In this paper, we show that projective globally $F$-regular threefolds, defined over an algebraically closed field of characteristic $p\geq 11$, are …

We investigated an issue encountered when applying Seq2Seq models to conversational response generation. These models tend to generate safe, commonplace responses (e.g., I don’t know) regardless of the input. Our analysis suggests that the issue is …

Sequence-to-sequence neural network models for generation of conversational responses tend to generate safe, commonplace responses (e.g., "I don't kn…

As we have stated, most of the work in the proof is done by Theorem 1.7.

The polynomial Fre\u{\i}man--Ruzsa conjecture is a fundamental open question in additive combinatorics. However, over the integers (or more generally…

The method of exchangeable pairs can also be used to analyze nonlinear matrix-valued functions of random variables. In this section, we explain how to analyze matrix functions that satisfy a self-reproducing property.

This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis r…

We begin by recalling the definition of the 2-Selmer group. If E is an elliptic curve defined over a field K, then E(K)/2E(K) maps into H1(K,E[2]) via the Kummer map. The following diagram commutes for every place v of K, where δ is the Kummer map.

This paper presents a new result concerning the distribution of 2-Selmer ranks in the quadratic twist family of an elliptic curve over an arbitrary n…

We give bounds on the degree of generation and relations of generalized canonical rings of arbitrary $\mathbb{Q}$-divisors on projective spaces of al…

A switched-capacitor matrix multiplier is presented for approximate computing and machine learning applications. The multiply-and-accumulate operatio…

By Theorem 1, Y is a P2π surface. Thus, it is diffeomorphic to either S2 or RP2—see [1, Section 4.3].

A subject of recent interest in inverse problems is whether a corner must diffract fixed frequency waves. We generalize this question somewhat and st…

We have analyzed algorithms for optimization problems that use only random function values—as opposed to gradient computations—to minimize an objective function. The algorithms we present are optimal: their convergence rates cannot be improved (in a…

We consider derivative-free algorithms for stochastic and non-stochastic convex optimization problems that use only function values rather than gradi…

In this work, we introduced a unified convex optimization framework for constructing prediction market mechanisms. We first showed that in this new framework, the pricing mechanism always allows truthful bidding (in a myopic sense) to be an attitude…

Recently, several new pari-mutuel mechanisms have been introduced to organize markets for contingent claims. Hanson introduced a market maker derived…

The proposed taxonomy and the properties shown in Table 1 highlight some surprising characteristics of collective behavior algorithms. The majority of existing mathematical techniques is tailored to either low-level spatially organizing tasks (e.g.,…

In this paper, we review multi-agent collective behavior algorithms in the literature and classify them according to their underlying mathematical st…

Many massive galaxies at the centres of relaxed galaxy clusters and groups have vast reservoirs of cool (~10,000 K) and cold (~100 K) gas. In many lo…

The gravitational redshift due to our own location in the large scale gravitational potential field becomes relevant when using SN data for determination of cosmological parameters to 1% precision. The effect of the gravitational redshift on the bes…

Measurements of cosmological parameters via the distance-redshift relation usually rely on models that assume a homogenous universe. It is commonly p…

In healthcare applications, temporal variables that encode movement, health status and longitudinal patient evolution are often accompanied by rich s…

We consider a one-sided assignment market or exchange network with transferable utility and propose a model for the dynamics of bargaining in such a …

Content caching in wireless networks provides a substantial opportunity to trade off low cost memory storage with energy consumption, yet finding the…

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