Publication

Quadratic Sieving

Publications associées (25)

Simulating supercontinua from mixed and cascaded nonlinearities

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Nonlinear optical frequency conversion is of fundamental importance in photonics and underpins countless of its applications: Sum- and difference-frequency generation in media with quadratic nonlinearity permits reaching otherwise inaccessible wavelength r ...

AIP Publishing2023

Byzantine consensus is Θ(n^2): the Dolev-Reischuk bound is tight even in partial synchrony!

Rachid Guerraoui, Seth Gilbert, Vincent Gramoli, Manuel José Ribeiro Vidigueira, Jovan Komatovic, Pierre Philippe Civit

The Dolev-Reischuk bound says that any deterministic Byzantine consensus protocol has (at least) quadratic (in the number of processes) communication complexity in the worst case: given a system with n processes and at most f < n/3 failures, any solution t ...

2023

Hierarchy of quasisymmetries and degeneracies in the CoSi family of chiral crystal materials

Yi-Chiang Sun, Philip Johannes Walter Moll, Chunyu Guo

In materials, certain approximated symmetry operations can exist in a lower-order approximation of the effective model but are good enough to influence the physical responses of the system, and these approximated symmetries were recently dubbed "quasisymme ...

AMER PHYSICAL SOC2023

A finiteness result for p-adic families of Bianchi modular forms

Vlad Serban

We study p-adic families of cohomological automorphic forms for GL(2) over imaginary quadratic fields and prove that families interpolating a Zariski-dense set of classical cuspidal automorphic forms only occur under very restrictive conditions. We show ho ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

The double exponential runtime is tight for 2-stage stochastic ILPs

Kim-Manuel Klein, Klaus Jansen, Alexandra Anna Lassota

We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called 2-stage stochastic. A 2-stage stochastic ILP is an integer program of the form min{c(T)x vertical bar Ax = ...

SPRINGER HEIDELBERG2022

The fourth moment of individual Dirichlet L-functions on the critical line

Berke Topacogullari

We prove an asymptotic formula for the second moment of a product of two Dirichlet L-functions on the critical line, which has a power saving in the error term and which is uniform with respect to the involved Dirichlet characters. As special cases we give ...

2021

Relax and Recover: Guaranteed Range-Only Continuous Localization

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Range-only localization has applications as diverse as underwater navigation, drone tracking and indoor localization. While the theoretical foundations of lateration---range-only localization for static points---are well understood, there is a lack of unde ...

2020

Petersson inner products of weight-one modular forms

Maryna Viazovska

In this paper we study the regularized Petersson product between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight-one modular form with integral Fourier coefficients. In [18], we proved that ...

2019

Efficient Verifiable Delay Functions

Benjamin Pierre Charles Wesolowski

We construct a verifiable delay function (VDF). A VDF is a function whose evaluation requires running a given number of sequential steps, yet the result can be efficiently verified. They have applications in decentralised systems, such as the generation of ...

SPRINGER INTERNATIONAL PUBLISHING AG2019

Residual-based a posteriori error estimation for contact problems approximated by Nitsche's method

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We introduce a residual-based a posteriori error estimator for contact problems in two- and three-dimensional linear elasticity, discretized with linear and quadratic finite elements and Nitsche’s method. Efficiency and reliability of the estimator are pro ...

2018

Statistical physics approaches to subnetwork dynamics in biochemical systems

Barbara Bravi

We apply a Gaussian variational approximation to model reduction in large biochemical networks of unary and binary reactions. We focus on a small subset of variables (subnetwork) of interest, e.g. because they are accessible experimentally, embedded in a l ...

Iop Publishing Ltd2017

Bilinear forms with Kloosterman sums and applications

Philippe Michel

We prove nontrivial bounds for general bilinear forms in hyper-Kloosterman sums when the sizes of both variables may be below the range controlled by Fourier-analytic methods (Polya-Vinogradov range). We then derive applications to the second moment of cus ...

Annal Mathematics2017

A feasible-side globally convergent modifier-adaptation scheme

Dominique Bonvin, Alejandro Gabriel Marchetti, Timm Faulwasser

In the context of static real-time optimization (RTO) of uncertain plants, the standard modifier-adaptation scheme consists in adding first-order correction terms to the cost and constraint functions of a model based optimization problem. If the algorithm ...

Elsevier Sci Ltd2017

Enumeration of reversible functions and its application to circuit complexity

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We review combinational results to enumerate and classify reversible functions and investigate the application to circuit complexity. In particularly, we consider the effect of negating and permuting input and output variables and the effect of applying li ...

Springer2016

Quadratic variance swap models

Loriano Mancini, Damir Filipovic

We introduce a novel class of term structure models for variance swaps. The multivariate state process is characterized by a quadratic diffusion function. The variance swap curve is quadratic in the state variable and available in closed form, greatly faci ...

Elsevier2016

Computational Aspects of Jacobians of Hyperelliptic Curves

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Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest ...

EPFL2016

Shimura Curves and Special Values of p-adic L-functions

Ernest Hunter Brooks

We construct "generalized Heegner cycles" on a variety fibered over a Shimura curve, defined over a number field. We show that their images under the p-adic Abel-Jacobi map coincide with the values (outside the range of interpolation) of a p-adic L-functio ...

Oxford University Press2015

Producing absorption mode Fourier transform ion cyclotron resonance mass spectra with non-quadratic phase correction functions

Yury Tsybin, Konstantin Zhurov, Anton Kozhinov, Konstantin Nagornov

RATIONALE: Previously described methods for producing absorption mode Fourier transform ion cyclotron resonance (FTICR) mass spectra have all relied on the phase correction function being quadratic. This assumption has been found to be invalid for some ins ...

Wiley-Blackwell2015

A twisted Motohashi formula and Weyl-subconvexity for -functions of weight two cusp forms

Ian Nicholas Petrow

We derive a Motohashi-type formula for the cubic moment of central values of -functions of level cusp forms twisted by quadratic characters of conductor , previously studied by Conrey and Iwaniec and Young. Corollaries of this formula include Weyl-subconve ...

Springer Verlag2015

Sums Of Squares In Algebraic Function Fields Over A Complete Discretely Valued Field

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A recently found local-global principle for quadratic forms over function fields of curves over a complete discretely valued field is applied to the study of quadratic forms, sums of squares, and related field invariants. ...

Pacific Journal Mathematics2014