Search results for "mes"

Computing the Trace

2001

So far we have been interested in the general expression for the WKB-propagation function. Now we turn our attention to the trace of that propagator, since we want to exhibit the energy eigenvalues of a given potential. From earlier discussions we know that the energy levels of a given Hamiltonian are provided by the poles of the Green’s function:

ChemInform Abstract: Magnetic Exchange Between Metal Ions with Unquenched Orbital Angular Momenta: Basic Concepts and Relevance to Molecular Magnetism

2010

This review article is a first attempt to give a systematic and comprehensive description (in the framework of the unified theoretical approach) of the exchange interactions in polynuclear systems based on orbitally degenerate metal ions in the context of their relevance to the modern molecular magnetism. Interest in these systems is related to the fundamental problems of magnetism and at the same time steered by a number of impressive potential applications of molecular magnets, like high-density memory storage units, nanoscale qubits, spintronics and photoswitchable devices. In the presence of orbital degeneracy, the conventional spin Hamiltonian (Heisenberg–Dirac–van Vleck model) becomes…

A comparison between two feature selection algorithms

2017

This article provides a comparison of two feature selection algorithms, Information Gain Thresholding and Koller and Sahami's algorithm in the context of text document classification on the Reuters Corpus Volume 1 dataset. The algorithms were evaluated by testing the performance of classifiers trained on the features they select from a given dataset. Results show that Koller and Sahami's algorithm consistently outperforms Information Gain Thresholding by capturing interactions between features and avoiding redundancy among features, although it achieves its gains through increased complexity and longer running time.

Errors Generated by Uncertain Data

2014

In this chapter, we study effects caused by incompletely known data. In practice, the data are never known exactly, therefore the results generated by a mathematical model also have a limited accuracy. Then, the whole subject of error analysis should be treated in a different manner, and accuracy of numerical solutions should be considered within a framework of a more complicated scheme, which includes such notions as maximal and minimal distances to the solution set and its radius.

Applications in Mathematical Physics

2009

It turns out that pip-space methods have many applications in physics, although they are seldom mentioned as such. To draw on a literary analogy, like Moliere’s Monsieur Jourdain speaking in prose without knowing so, many authors have been using pip-space language without realizing it. In particular, chains or lattices of Hilbert spaces are quite common in many fields of mathematical physics. Some of these applications will be discussed at length in this chapter. To mention a few examples: quantum mechanics, in particular singular interactions (Section 7.1.3), scattering theory (Section 7.2), quantum field theory (Section 7.3), representations of Lie groups (Section 7.4), etc.

Theoretical Study of the Electronic Spectrum of trans-Stilbene

1997

The electronic spectrum of trans-stilbene in the energy range up to 6 eV has been studied using multiconfigurational second-order perturbation theory (CASPT2). The study includes a geometry determination of the ground state. In all, 12 singlet and one triplet excited states were studied. The calculated spectrum makes it possible to assign the valence excited singlet states corresponding to the three bands observed in the low-energy region of the one-photon absorption spectrum. The most intense feature of the calculated spectrum corresponds to the 11Ag → 21Bu transition at 4.07 eV. The weakly allowed 11Bu state was found 0.3 eV below 21Bu. Transition to the 31Ag state, computed at 4.95 eV, i…

Formulas for the thermodynamic properties of dense nitrogen.

1969

Phonons in MoSe2/WSe2 van der Waals heterobilayer

2021

We report first-principles calculations of the structural and vibrational properties of the synthesized two-dimensional van der Waals heterostructures formed by single-layers dichalcogenides MoSe2 and WSe2. We show that, when combining these systems in a periodic two-dimensional heterostructures, the intrinsic phonon characteristics of the free-standing constituents are to a large extent preserved but, furthermore, exhibit shear and breathing phonon modes that are not present in the individual building blocks. These peculiar modes depend strongly on the weak vdW forces and has a great contibution to the thermal properties of the layered materials. Besides these features, the departure of fl…

Computing variations of entropy and redundancy under nonlinear mappings not preserving the signal dimension: quantifying the efficiency of V1 cortex

2021

In computational neuroscience, the Efficient Coding Hypothesis argues that the neural organization comes from the optimization of information-theoretic goals [Barlow Proc.Nat.Phys.Lab.59]. A way to confirm this requires the analysis of the statistical performance of biological systems that have not been statistically optimized [Renart et al. Science10, Malo&Laparra Neur.Comp.10, Foster JOSA18, Gomez-Villa&Malo J.Neurophysiol.19]. However, when analyzing the information-theoretic performance, cortical magnification in the retina-cortex pathway poses a theoretical problem. Cortical magnification stands for the increase the signal dimensionality [Cowey&Rolls Exp. Brain Res.74]. Conventional mo…

General Theory: Topological Aspects

2009

In Chapter 1, we have analyzed the structure of pip-spaces from the algebraic point of view only, (i.e., the compatibility relation). Here we will discuss primarily the topological structure given by the partial inner product itself. The aim is to tighten the definitions so as to eliminate as many pathologies as possible. The picture that emerges is reassuringly simple: Only two types of pip-spaces seem sufficiently regular to have any practical use, namely lattices of Hilbert spaces (LHS) or Banach spaces (LBS), that we have introduced briefly in the Introduction. Our standard reference on locally convex topological vector spaces (LCS) will be the textbook of Kothe [Kot69]. In addition, fo…