Publications related to Degree of a field extension

A NEW PROOF OF THE ERDOS-KAC CENTRAL LIMIT THEOREM

In this paper we use the Riemann zeta distribution to give a new proof of the Erdos-Kac Central Limit Theorem. That is, if zeta(s) = Sigma(n >= 1) (1)(s)(n) , s > 1, then we consider the random variable X-s with P(X-s = n) = (1) (zeta) ( ...

Amer Mathematical Soc2023

L'aménagement du territoire comme espace public : quelques questions de démocratie locale posées par l’extension de l’École hôtelière dans le périurbain lausannois

Vincent Kaufmann, Luca Giovanni Pattaroni, Mischa-Sébastien Piraud

Based on a field survey on the conflicts regarding the extension of the Ecole Hôtelière de Lausanne, this text discusses the production of public space. These controversies make possible an understanding of the production process of peri-urban space in ter ...

2022

On the commutativity of flows of rough vector fields

Maria Colombo, Riccardo Tione

In the class of Sobolev vector fields in R-n of bounded divergence, for which the theory of DiPerna and Lions provides a well defined notion of flow, we characterize the vector fields whose flow commutes in terms of the Lie bracket and of a regularity cond ...

ELSEVIER2022

On arithmetic progressions in symmetric sets in finite field model

Jan Hazla

We consider two problems regarding arithmetic progressions in symmetric sets in the finite field (product space) model. ...

ELECTRONIC JOURNAL OF COMBINATORICS2020

Depth of field extension through polarization aberrations

Alessandro Grosso

This paper focuses on depth of field (DOF) extension through polarization aberrations. The addition of polarizing elements into an optical system allows to exploit the polarization of the incoming light as an additional degree of freedom in the optical sys ...

SPIE-INT SOC OPTICAL ENGINEERING2019

A Functional Framework For Ultrasound Imaging

Paul Hurley, Matthieu Martin Jean-André Simeoni

Delay-And-Sum (DAS), the state-of-art in ultrasound imaging, is known to be sub-optimal, resulting in low resolution and contrast. Most proposed improvements involve ad-hoc re-weighting, or hit computational bottlenecks given real-time requirements. This p ...

IEEE2018

Arithmetic and geometric structures in cryptography

Benjamin Pierre Charles Wesolowski

We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...

EPFL2018

A Szemeredi-Trotter type theorem, sum-product estimates in finite quasifields, and related results

Van Thang Pham

We prove a Szemeredi-Trotter type theorem and a sum product estimate in the setting of finite quasifields. These estimates generalize results of the fourth author, of Garaev, and of Vu. We generalize results of Gyarmati and Sarkozy on the solvability of th ...

Academic Press Inc Elsevier Science2017

Omnidirectional bats, point-to-plane distances, and the price of uniqueness

Martin Vetterli, Ivan Dokmanic, Miranda Krekovic

We study simultaneous localization and mapping with a device that uses reflections to measure its distance from walls. Such a device can be realized acoustically with a synchronized collocated source and receiver; it behaves like a bat with no capacity for ...

Ieee2017

Incidences between points and generalized spheres over finite fields and related problems

Van Thang Pham

Let F-q be a finite field of q elements, where q is a large odd prime power and Q = a(1)x(1)(c1) + ..... + a(d)x(d)(cd) is an element of F-q[x(1) ,...,x(d)], where 2

Walter De Gruyter Gmbh2017

Elliptic curves over a finite field and the trace formula

Ian Nicholas Petrow

We prove formulas for power moments for point counts of elliptic curves over a finite field k such that the groups of k-points of the curves contain a chosen subgroup. These formulas express the moments in terms of traces of Hecke operators for certain con ...

Wiley2017

Isogeny graphs of ordinary abelian varieties

Dimitar Petkov Jetchev, Benjamin Pierre Charles Wesolowski, Ernest Hunter Brooks

Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse gr ...

Springer Heidelberg2017

Multiple-field based code generator and decoder for communications systems

Mohammad Amin Shokrollahi, Lorenz Minder

A method of encoding data for transmission from a source to a destination over a communications channel is provided. The method operates on an ordered set of input symbols and includes generating a plurality of redundant symbols from the input symbols base ...

2016

Fibre Products of Supersingular Curves and the Enumeration of Irreducible Polynomials with Prescribed Coefficients

Robert Granger

For any positive integers

n\geq 3, r\geq 1

we present formulae for the number of irreducible polynomials of degree

n

over the finite field

\mathbb{F}_{2^r}

where the coefficients of

x^{n-1}

,

x^{n-2}

and

x^{n-3}

are zero. Our proofs involve coun ...

Elsevier2016

Special Reductive Groups Over An Arbitrary Field

Mathieu Huruguen

A linear algebraic group G defined over a field k is called special if every G-torsor over every field extension of k is trivial. In 1958 Grothendieck classified special groups in the case where the base field is algebraically closed. In this paper we desc ...

Springer Birkhauser2016

Motivic Classes of Nakajima Quiver Varieties

Dimitri Stelio Wyss

We prove that Hausel’s formula for the number of rational points of a Nakajima quiver variety over a finite field also holds in a suitable localization of the Grothendieck ring of varieties. In order to generalize the arithmetic harmonic analysis in his pr ...

2016

A Model of Synaptic Reconsolidation

Wulfram Gerstner, Tilo Schwalger, Lorric Ziegler, David Barak Kastner

Reconsolidation of memories has mostly been studied at the behavioral and molecular level. Here, we put forward a simple extension of existing computational models of synaptic consolidation to capture hippocampal slice experiments that have been interprete ...

Frontiers Research Foundation2016

Structure Tensor Total Variation

Michaël Unser, Stamatios Lefkimmiatis

We introduce a novel generic energy functional that we employ to solve inverse imaging problems within a variational framework. The proposed regularization family, termed as structure tensor total variation (STV), penalizes the eigenvalues of the structure ...

SIAM2015

Lower bounds for Pythagoras numbers of function fields

David Maximilian Grimm

We show that the transcendence degree of a real function field over an arbitrary real base field is a strict lower bound for its Pythagoras number and a weak lower bound for all its higher Pythagoras numbers. ...

European Mathematical Soc2015

Multiphoton microscopy in brain imaging

Graham Knott, Bohumil Maco, Ludovico Silvestri

Brain imaging is becoming an important field in the frame of the neurophotonics in correlations with other medical ones in neuroscience studying functional and morphological aspects. In this presentation an overview on multi photon imaging of the brain wil ...

Spie-Int Soc Optical Engineering2015