Rotation Invariance and Directional Sensitivity: Spherical Harmonics versus Radiomics Features

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Scale-Invariant Models of Gravity and Particle Physics and their Cosmological Implications

Currently, the best theoretical description of fundamental matter and its gravitational interaction is given by the Standard Model (SM) of particle physics and Einstein's theory of General Relativity (GR). These theories contain a number of seemingly unrel ...

EPFL2011

A New Method to Explore Conformal Field Theories in Any Dimension

Alessandro Vichi

The thesis represents an investigation into Conformal Field Theories (CFT's) in arbitrary dimensions. We propose an innovative method to extract informations about CFT's in a quantitative way. Studying the crossing symmetry of the four point function of sc ...

EPFL2011

Bounds in 4D conformal field theories with global symmetry

Riccardo Rattazzi, Alessandro Vichi

We explore the constraining power of OPE associativity in 4D conformal field theory with a continuous global symmetry group. We give a general analysis of crossing symmetry constraints in the 4-point function , where phi is ...

2011

Fractional Brownian Vector Fields

Michaël Unser, Pouya Dehghani Tafti

This work puts forward an extended definition of vector fractional Brownian motion (fBm) using a distribution theoretic formulation in the spirit of Gel′fand and Vilenkin's stochastic analysis. We introduce random vector fields that share the statistical i ...

SIAM2010

Wavelet Steerability and the Higher-Order Riesz Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our main goal in this paper is to set the foundations of a general continuous-domain framework for designing steerable, reversible signal transformations (a.k.a. frames) in multiple dimensions (d ≥ 2). To that end, we introduce a self-reversible, Nth-order ...

Institute of Electrical and Electronics Engineers2010

Maximal symmetrization and reduction of fields: Application to wave functions in solid-state nanostructures

Marc-André Dupertuis, Sascha Dalessi

A general formalism for the maximal symmetrization and reduction of fields (MSRFs) is proposed and applied to wave functions in solid-state nanostructures. Its primary target is to provide an essential tool for the study and analysis of the electronic and ...

2010

Wavelets on the two-sphere and other conic sections

Pierre Vandergheynst

We review the construction of the continuous wavelet transform (CWT) on the two-sphere by two methods, the group-theoretical approach and the geometrical method based on conformal invariance. Then we discuss the discretization of the spherical CWT, obtaini ...

2007

Variational reconstruction of scalar and vector images from non-uniform samples

Muthuvel Arigovindan

We address the problem of reconstructing scalar and vector functions from non-uniform data. The reconstruction problem is formulated as a minimization problem where the cost is a weighted sum of two terms. The first data term is the quadratic measure of go ...

EPFL2005

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