We study the so-called signed discrete Choquet integral (also called non-monotonic discrete Choquet integral) regarded as the Lovász extension of a pseudo-Boolean function which vanishes at the origin. We present axiomatizations of this generalized Choquet integral, given in terms of certain functional equations, as well as by necessary and sufficient conditions which reveal desirable propertie...

We model the logarithm of the price (log-price) of a financial asset as a random variable obtained by projecting an operator stable random vector with a scaling index matrix E onto a non-random vector. The scaling index E models prices of the individual financial assets (stocks, mutual funds, etc.). We find the functional form of the characteristic function of real powers of the price returns a...

Introduction: The main idea of Compressed Sensing is to exploit the fact that there is some structure and redundancy in most signals of interest. Clearly, the more we known about the signal and the more the information we encode into the signal processing algorithm, the better performance we can achieve. In this paper, we propose an adaptive compressed MRI sensing scheme that combined wavelet e...

Deviations from the Friedmann-Robertson-Walker (FRW) cosmological model in the form of density inhomogeneities induce observational effects on the light propagating through these fluctuations. Using a rigorously parametrized metricwhose pseudo-Newtonian potential is related to (possibly nonlinear) density inhomogeneities through a relativistic Green function, the behavior of radiation propagati...

In this paper, we characterize multiresolution analysis(MRA) Parseval frame multiwavelets in L^2(R^d) with matrix dilations of the form (D f )(x) = sqrt{2}f (Ax), where A is an arbitrary expanding dtimes d matrix with integer coefficients, such that |detA| =2. We study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of MRA tight frame multiwa...

A function f : {−1, 1} → R is called pseudo-Boolean. It is wellknown that each pseudo-Boolean function f can be written as f(x) =

The aim of this paper is to completely classify all aggregation functions based on the notion of arity gap. We first establish explicit descriptions of the arity gap of the Lovász extensions of pseudo-Boolean functions and, in particular, of the Choquet integrals. Then we consider the wider class of order-preserving functions between arbitrary, possibly different, posets, and show that similar ...

Computation of headmodel and sourcemodel from the subject's MRI scan is an essential step for source localization of magnetoencephalography (MEG) (or EEG) sensor signals. In the absence of a real MRI scan, pseudo MRI (i.e., associated headmodel and sourcemodel) is often approximated from an available standard MRI template or pool of MRI scans considering the subject's digitized head surface. In...