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Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems

Fabrizio Minganti

Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- (PT-) and anti-PT-symmetric physics have gained ever-growing interest, due to the existence of non-Hermitian sp ...

AMER PHYSICAL SOC2023

Strictly Real Fundamental Theorem Of Algebra Using Polynomial Interlacing

Soham Basu

Without resorting to complex numbers or any advanced topological arguments, we show that any real polynomial of degree greater than two always has a real quadratic polynomial factor, which is equivalent to the fundamental theorem of algebra. The proof uses ...

CAMBRIDGE UNIV PRESS2021

Hyperbolicity as an obstruction to smoothability for one-dimensional actions

Yash Lodha

Ghys and Sergiescu proved in the 1980s that Thompson's group T, and hence F, admits actions by C-infinity diffeomorphisms of the circle. They proved that the standard actions of these groups are topologically conjugate to a group of C-infinity diffeomorphi ...

GEOMETRY & TOPOLOGY PUBLICATIONS2019

Four-Variable Expanders Over The Prime Fields

Adrian Claudiu Valculescu, Van Thang Pham, Seyed Hossein Nassajianmojarrad

Let F-p be a prime field of order p > 2, and let A be a set in F-p with very small size in terms of p. In this note, we show that the number of distinct cubic distances determined by points in A x A satisfies vertical bar(A - A)(3) + (A - A)(3 vertical bar ...

AMER MATHEMATICAL SOC2018

A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary

Robert Gerhard Jérôme Luce

A nonnegative matrix factorization (NMF) can be computed efficiently under the separability assumption, which asserts that all the columns of the given input data matrix belong to the cone generated by a (small) subset of them. The provably most robust met ...

Ieee-Inst Electrical Electronics Engineers Inc2018

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We analyze the accuracy of the discrete least-squares approximation of a function

u

in multivariate polynomial spaces

P_\Lambda:=span\{y\mapsto y^\nu \,: \, \nu\in \Lambda\}

with

\Lambda\subset N_0^d

over the domain

\Gamma:=[-1,1]^d

, based on the s ...

2017

On some algebraic and extremal problems in discrete geometry

Seyed Hossein Nassajianmojarrad

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 ...

EPFL2017

Decoding of Self-paced Lower-Limb Movement Intention: A Case Study on the Influence Factors

José del Rocio Millán Ruiz, Ricardo Andres Chavarriaga Lozano, Dong Liu

Brain-machine interfaces (BMIs) have been applied as new rehabilitation tools for motor disabled individuals. Active involvement of cerebral activity has been shown to enhance neuroplasticity and thus to restore mobility. Various studies have focused on th ...

Frontiers Research Foundation2017

Invariant forms on irreducible modules of simple algebraic groups

Mikko Tapani Korhonen

Let G be a simple linear algebraic group over an algebraically dosed field K of characteristic p >= 0 and let V be an irreducible rational G-module with highest weight A. When is self-dual, a basic question to ask is whether V has a non-degenerate G-invari ...

Elsevier2017

Inhomogeneous minima of mixed signature lattices

Eva Bayer Fluckiger, Martino Borello, Peter Simon Jossen

We establish an explicit upper bound for the Euclidean minimum of a number field which depends, in a precise manner, only on its discriminant and the number of real and complex embeddings. Such bounds were shown to exist by Davenport and Swinnerton-Dyer ([ ...

Academic Press Inc Elsevier Science2016

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