Search results for "FACTORIZATION"

On Pietsch measures for summing operators and dominated polynomials

2012

We relate the injectivity of the canonical map from $C(B_{E'})$ to $L_p(\mu)$, where $\mu$ is a regular Borel probability measure on the closed unit ball $B_{E'}$ of the dual $E'$ of a Banach space $E$ endowed with the weak* topology, to the existence of injective $p$-summing linear operators/$p$-dominated homogeneous polynomials defined on $E$ having $\mu$ as a Pietsch measure. As an application we fill the gap in the proofs of some results of concerning Pietsch-type factorization of dominated polynomials.

Multi-domain Feature of Event-Related Potential Extracted by Nonnegative Tensor Factorization: 5 vs. 14 Electrodes EEG Data

2012

As nonnegative tensor factorization (NTF) is particularly useful for the problem of underdetermined linear transform model, we performed NTF on the EEG data recorded from 14 electrodes to extract the multi-domain feature of N170 which is a visual event-related potential (ERP), as well as 5 typical electrodes in occipital-temporal sites for N170 and in frontal-central sites for vertex positive potential (VPP) which is the counterpart of N170, respectively. We found that the multi-domain feature of N170 from 5 electrodes was very similar to that from 14 electrodes and more discriminative for different groups of participants than that of VPP from 5 electrodes. Hence, we conclude that when the …

Localized potentials in electrical impedance tomography

2008

In this work we study localized electric potentials that have an arbitrarily high energy on some given subset of a domain and low energy on another. We show that such potentials exist for general L ∞ -conductivities in almost arbitrarily shaped subregions of a domain, as long as these regions are connected to the boundary and a unique continuation principle is satisfied. From this we deduce a simple, but new, theoretical identifiability result for the famous Calderon problem with partial data. We also show how to con- struct such potentials numerically and use a connection with the factorization method to derive a new non-iterative algorithm for the detection of inclusions in electrical imp…

Exploratory multiblock data: do they lead to the same results?

2022

Integrable Systems and Factorization Problems

2002

The present lectures were prepared for the Faro International Summer School on Factorization and Integrable Systems in September 2000. They were intended for participants with the background in Analysis and Operator Theory but without special knowledge of Geometry and Lie Groups. In order to make the main ideas reasonably clear, I tried to use only matrix algebras such as $\frak{gl}(n)$ and its natural subalgebras; Lie groups used are either GL(n) and its subgroups, or loop groups consisting of matrix-valued functions on the circle (possibly admitting an extension to parts of the Riemann sphere). I hope this makes the environment sufficiently easy to live in for an analyst. The main goal is…

Non-negative matrix factorization Vs. FastICA on mismatch negativity of children

2009

In this presentation two event-related potentials, mismatch negativity (MMN) and P3a, are extracted from EEG by non-negative matrix factorization (NMF) simultaneously. Typically MMN recordings show a mixture of MMN, P3a, and responses to repeated standard stimuli. NMF may release the source independence assumption and data length limitations required by Fast independent component analysis (FastICA). Thus, in theory NMF could reach better separation of the responses. In the current experiment MMN was elicited by auditory duration deviations in 102 children. NMF was performed on the time-frequency representation of the raw data to estimate sources. Support to Absence Ratio (SAR) of the MMN co…

Visual Cortex Performs a Sort of Non-linear ICA

2010

Here, the standard V1 cortex model optimized to reproduce image distortion psychophysics is shown to have nice statistical properties, e.g. approximate factorization of the PDF of natural images. These results confirm the efficient encoding hypothesis that aims to explain the organization of biological sensors by information theory arguments.

Stoïlow’s theorem revisited

2020

Stoilow's theorem from 1928 states that a continuous, open, and light map between surfaces is a discrete map with a discrete branch set. This result implies that such maps between orientable surfaces are locally modeled by power maps z -> z(k) and admit a holomorphic factorization. The purpose of this expository article is to give a proof of this classical theorem having readers in mind that are interested in continuous, open and discrete maps. (C) 2019 Elsevier GmbH. All rights reserved. Peer reviewed

A Side-by-Side Single Sex Age-Structured Human Population Dynamic Model: Exact Solution and Model Validation

2008

A side-by-side single sex age-structured population dynamic model is presented in this paper. The model consists of two coupled von Foerster-McKendrick-type quasi-linear partial differential equations, two initial conditions, and two boundary conditions. The state variables of the model are male and female population densities. The solutions of these partial differential equations provide explicit time and age dependence of the variables. The initial conditions define the male and female population densities at the initial time, while the boundary conditions compute the male and female births at zero-age by using fertility rates. The assumptions of the nontime-dependence of the death and fe…

The Large Hadron–Electron Collider at the HL-LHC

2021

The Large Hadron-Electron Collider (LHeC) is designed to move the field of deep inelastic scattering (DIS) to the energy and intensity frontier of particle physics. Exploiting energy-recovery technology, it collides a novel, intense electron beam with a proton or ion beam from the High-Luminosity Large Hadron Collider (HL-LHC). The accelerator and interaction region are designed for concurrent electron-proton and proton-proton operations. This report represents an update to the LHeC's conceptual design report (CDR), published in 2012. It comprises new results on the parton structure of the proton and heavier nuclei, QCD dynamics, and electroweak and top-quark physics. It is shown how the LH…