Publications related to Dimension of an algebraic variety

Reduced representations of complexes, signals, and multifiltrations

The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...

EPFL2022

Bootstrapping mixed correlators in N=4 super Yang-Mills

Andrea Manenti, Alessandro Vichi

We perform a numerical bootstrap study of the mixed correlator system containing the half-BPS operators of dimension two and three in N = 4 Super Yang-Mills. This setup improves on previous works in the literature that only considered single correlators of ...

Springer Nature2021

On the Volume of the John-Lowner Ellipsoid

Grigory Ivanov

We find an optimal upper bound on the volume of the John ellipsoid of a k-dimensional section of the n-dimensional cube, and an optimal lower bound on the volume of the Lowner ellipsoid of a projection of the n-dimensional cross-polytope onto a k-dimension ...

SPRINGER2020

Polarization dependence of angle-resolved photoemission with submicron spatial resolution reveals emerging one-dimensionality of electrons in NbSe3

Marco Grioni, Helmuth Berger, Emmanouil Frantzeskakis, Miguel Angel Valbuena

In materials with nearly commensurate band filling the electron liquid may spontaneously separate into components with distinct properties, yielding complex intra- and interunit cell ordering patterns and a reduced dimensionality. Polarization-dependent an ...

AMER PHYSICAL SOC2019

Exact diagonalization of SU( N ) Heisenberg and Affleck-Kennedy-Lieb-Tasaki chains using the full SU( N ) symmetry

Frédéric Mila, Pierre Marcel Nataf, Kianna Wan

We present a method for the exact diagonalization of the SU(N) Heisenberg interaction Hamiltonian using Young tableaus to work directly in each irreducible representation of the global SU(N) group. This generalized scheme is applicable to chains consisting ...

2017

Combinatorial presentation of multidimensional persistent homology

Martina Scolamiero

A multifiltration is a functor indexed by Nr that maps any morphism to a monomorphism. The goal of this paper is to describe in an explicit and combinatorial way the natural Nr-graded R[x(1),...x(r)]-module structure on the homology of a multifiltration of ...

Elsevier2017

Estimation of Phase and Its Higher Order Derivatives from a Single Complex Interferogram

Pramod Rastogi, Rishikesh Dilip Kulkarni

This paper reports a method for the simultaneous estimation of unwrapped phase and higher order phase derivatives from a single phase fringe pattern recorded in an optical interferometric setup, thereby overcoming substantial barriers to achieving such mea ...

2016

Algebraic Cryptanalysis of Deterministic Symmetric Encryption

Petr Susil

Deterministic symmetric encryption is widely used in many cryptographic applications. The security of deterministic block and stream ciphers is evaluated using cryptanalysis. Cryptanalysis is divided into two main categories: statistical cryptanalysis and ...

EPFL2015

Rigorous optimization recipes for sparse and low rank inverse problems with applications in data sciences

Anastasios Kyrillidis

Many natural and man-made signals can be described as having a few degrees of freedom relative to their size due to natural parameterizations or constraints; examples include bandlimited signals, collections of signals observed from multiple viewpoints in ...

EPFL2014

Phage display libraries of differently sized bicyclic peptides

Christian Heinis, Inmaculada Rentero Rebollo, Alessandro Angelini

Phage selections with combinatorial libraries of uniformly sized bicyclic peptides have recently yielded potent and selective binders of several protein targets. In this work we varied in a combinatorial fashion the ring sizes of bicyclic peptides in phage ...

Royal Soc Chemistry2013

Chow-Witt groups and Grothendieck-Witt groups of regular schemes

Jean Fasel

Let A be a noetherian commutative Z[1/2]-algebra of Krull dimension d and let P be a projective A-module of rank d. We use derived Grothendieck-Witt groups and Euler classes to detect some obstructions for P to split off a free factor of rank one. If d

2009

Quotient method for controlling the acrobot

Dominique Bonvin, Philippe Müllhaupt

This paper describes a two-sweep control design method to stabilize the acrobot, an input-afﬁne under-actuated system, at the upper equilibrium point. In the forward sweep, the system is successively reduced, one dimension at a time, until a two-dimensiona ...

2009

Groebner Basis Methods for Multichannel Sampling with Unknown Offsets

Martin Vetterli, Luciano Sbaiz, Patrick Vandewalle

In multichannel sampling, several sets of sub-Nyquist sampled signal values are acquired. The offsets between the sets are unknown, and have to be resolved, just like the parameters of the signal itself. This problem is nonlinear in the offsets, but linear ...

Elsevier2008

Growth-interruption-induced low-density InAs quantum dots on GaAs

Blandine Alloing

We investigate the use of growth interruption to obtain low-density InAs quantum dots (QDs) on GaAs. The process was realized by Ostwald-type ripening of a thin InAs layer. It was found that the optical properties of the QDs as a function of growth interru ...

American Institute of Physics2008

Signal Reconstruction from Multiple Unregistered Sets of Samples using Groebner Bases

Martin Vetterli, Luciano Sbaiz, Patrick Vandewalle

We present a new method for signal reconstruction from multiple sets of samples with unknown offsets. We rewrite the reconstruction problem as a set of polynomial equations in the unknown signal parameters and the offsets between the sets of samples. Then, ...

2006