Publications related to Quadric

Extractable Witness Encryption for the Homogeneous Linear Equations Problem

Witness encryption is a cryptographic primitive which encrypts a message under an instance of an NP language and decrypts the ciphertext using a witness associated with that instance. In the current state of the art, most of the witness encryption construc ...

Springer2023

Landscape and training regimes in deep learning

Matthieu Wyart, Mario Geiger, Leonardo Petrini

Deep learning algorithms are responsible for a technological revolution in a variety oftasks including image recognition or Go playing. Yet, why they work is not understood.Ultimately, they manage to classify data lying in high dimension – a feat generical ...

2021

A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation

Charles Stuart

In an open, bounded subset Omega of R-N such that 0 is an element of Omega we consider the nonlinear eigenvalue problem -Sigma(N)(i,j,=1) partial derivative(i){A(ij)(x)partial derivative(j)u} + V(x)u + n(x,del u)+ g(x, u) = lambda u in Omega integral(Omega ...

2020

The uniform symbolic topology property for diagonally F-regular algebras

Javier Alonso Carvajal Rojas

Let k be a field of positive characteristic. Building on the work of the second named author, we define a new class of k-algebras, called diagonally F-regular algebras, for which the so-called Uniform. Symbolic Topology Property (USTP) holds effectively. W ...

2020

MATHICSE Technical Report : Analytical and numerical study of a modified cell problem for the numerical homogenization of multiscale random fields

Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni

A central question in numerical homogenization of partial differential equations with multiscale coefficients is the accurate computation of effective quantities, such as the homogenized coefficients. Computing homogenized coefficients requires solving loc ...

EPFL2020

Imaging from Echoes: On Inverse Problems in Ultrasound

Adrien Georges Jean Besson

Ultrasound (US) imaging is currently living a revolution. On the one hand, ultrafast US imaging, a novel way of acquiring and producing US images, has paved the way to several advanced imaging modes, e.g. shear-wave elastography, ultrafast Doppler imaging ...

EPFL2019

Two-step phase demodulation algorithm based on quadratic phase parameter estimation using state space analysis

Pramod Rastogi, Rishikesh Dilip Kulkarni

We propose a noise robust two-step phase shifting algorithm for the evaluation of random and unknown phase step. In this algorithm, the phase within a small size two-dimensional window around a user selected pixel in an interferogram is approximated as a q ...

2018

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

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

Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries

Alfio Quarteroni, Gianluigi Rozza, Laura Iapichino

The aim of this work is to solve parametrized partial differential equations in computational domains represented by networks of repetitive geometries by combining reduced basis and domain decomposition techniques. The main idea behind this approach is to ...

Elsevier2016

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Extractable Witness Encryption for the Homogeneous Linear Equations Problem

Landscape and training regimes in deep learning

A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation

The uniform symbolic topology property for diagonally F-regular algebras

MATHICSE Technical Report : Analytical and numerical study of a modified cell problem for the numerical homogenization of multiscale random fields

Imaging from Echoes: On Inverse Problems in Ultrasound

Two-step phase demodulation algorithm based on quadratic phase parameter estimation using state space analysis

On some algebraic and extremal problems in discrete geometry

Invariant forms on irreducible modules of simple algebraic groups

Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries

Invariant forms on irreducible modules of simple algebraic groups

Landscape and training regimes in deep learning

Extractable Witness Encryption for the Homogeneous Linear Equations Problem

On some algebraic and extremal problems in discrete geometry

Imaging from Echoes: On Inverse Problems in Ultrasound

A critically degenerate elliptic Dirichlet problem, spectral theory and bifurcation

Two-step phase demodulation algorithm based on quadratic phase parameter estimation using state space analysis

MATHICSE Technical Report : Analytical and numerical study of a modified cell problem for the numerical homogenization of multiscale random fields

Reduced basis method and domain decomposition for elliptic problems in networks and complex parametrized geometries

The uniform symbolic topology property for diagonally F-regular algebras