Negative Fukui functions: new insights based on electronegativity equalization

The occurrence of negative values for Fukui functions was studied through the electronegativity equalization method. Using algebraic relations between Fukui functions and different other conceptual DFT quantities on the one hand and the hardness matrix on the other hand, expressions were obtained for Fukui functions for several archetypical small molecules. Based on EEM calculations for large molecular sets, no negative Fukui functions were found

A comparative analysis of two methods for the calculation of electric-field-induced perturbations to molecular vibration

Two common methods of accounting for electric-field-induced perturbations to molecular vibration are analyzed and compared. The first method is based on a perturbation-theoretic treatment and the second on a finite-field treatment. The relationship between the two, which is not immediately apparent, is made by developing an algebraic formalism for the latter. Some of the higher-order terms in this development are documented here for the first time. As well as considering vibrational dipole polarizabilities and hyperpolarizabilities, we also make mention of the vibrational Stark effec

Capacity-approaching rate function for layered multiantenna architectures

The simultaneous use of multiple transmit and receive antennas can unleash very large capacity increases in rich multipath environments. Although such capacities can be approached by layered multi-antenna architectures with per-antenna rate control, the need for short-term feedback arises as a potential impediment, in particular as the number of antennas—and thus the number of rates to be controlled—increases. What we show, however, is that the need for short-term feedback in fact vanishes as the number of antennas and/or the diversity order increases. Specifically, the rate supported by each transmit antenna becomes deterministic and a sole function of the signal-to-noise, the ratio of transmit and receive antennas, and the decoding order, all of which are either fixed or slowly varying. More generally, we illustrate -through this specific derivation— the relevance of some established random CDMA results to the single-user multi-antenna problem.

On fast-decodable space-time block codes

We focus on full-rate, fast-decodable space–time block codes (STBCs) for 2 x 2 and 4 x 2 multiple-input multiple-output (MIMO) transmission. We first derive conditions and design criteria for reduced-complexity maximum-likelihood (ML) decodable 2 x 2 STBCs, and we apply them to two families of codes that were recently discovered. Next, we derive a novel reduced-complexity 4 x 2 STBC, and show that it outperforms all previously known codes with certain constellations.

On high-rate full-diversity 2x2 space-time codes with low-complexity optimum detection

The 2×2 MIMO profiles included in Mobile WiMAX specifications are Alamouti’s space-time code (STC) fortransmit diversity and spatial multiplexing (SM). The former hasfull diversity and the latter has full rate, but neither of them hasboth of these desired features. An alternative 2×2 STC, which is both full rate and full diversity, is the Golden code. It is the best known 2×2 STC, but it has a high decoding complexity. Recently, the attention was turned to the decoder complexity, this issue wasincluded in the STC design criteria, and different STCs wereproposed. In this paper, we first present a full-rate full-diversity2×2 STC design leading to substantially lower complexity ofthe optimum detector compared to the Golden code with only a slight performance loss. We provide the general optimized form of this STC and show that this scheme achieves the diversitymultiplexing frontier for square QAM signal constellations. Then, we present a variant of the proposed STC, which provides a further decrease in the detection complexity with a rate reduction of 25% and show that this provides an interesting trade-off between the Alamouti scheme and SM.

Low-density parity-check codes for nonergodic block-fading channels

We design powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel. We first study the case of maximum-likelihood decoding, and show that the design criterion is rather straightforward. Since optimal constructions for maximum-likelihood decoding do not performwell under iterative decoding, we introduce a new family of full-diversity LDPC codes that exhibit near-outage-limit performance under iterative decoding for all block-lengths. This family competes favorably with multiplexed parallel turbo codes for nonergodic channels.

Full diversity product codes for block erasure and block fading channels

We show how to build full-diversity product codes under both iterative encoding and decoding over non-ergodic channels, in presence of block erasure and block fading. The concept of a rootcheck or a root subcode is introduced by generalizing the same principle recently invented for low-density parity-check codes. We also describe some channel related graphical properties of the new family of product codes, a familyreferred to as root product codes.

Silver space-time trellis-coded modulation

Silver Code (SilC) was originally discovered in [1–4] for 2×2 multiple-input multiple-output (MIMO) transmission. It has non-vanishing minimum determinant 1/7, slightly lower than Golden code, but is fast-decodable, i.e., it allows reduced-complexity maximum likelihood decoding [5–7]. In this paper, we present a multidimensional trellis-coded modulation scheme for MIMO systems [11] based on set partitioning of the Silver Code, named Silver Space-Time Trellis Coded Modulation (SST-TCM). This lattice set partitioning is designed specifically to increase the minimum determinant. The branches of the outer trellis code are labeled with these partitions. Viterbi algorithm is applied for trellis decoding, while the branch metrics are computed by using a sphere-decoding algorithm. It is shown that the proposed SST-TCM performs very closely to the Golden Space-Time Trellis Coded Modulation (GST-TCM) scheme, yetwith a much reduced decoding complexity thanks to its fast-decoding property.

A total order in [0,1] defined through a 'next' operator

A `next' operator, s, is built on the set R1=(0,1]-{ 1-1/e} defining a partial order that, with the help of the axiom of choice, can be extended to a total order in R1. Besides, the orbits {sn(a)}nare all dense in R1 and are constituted by elements of the samearithmetical character: if a is an algebraic irrational of degreek all the elements in a's orbit are algebraic of degree k; if a istranscendental, all are transcendental. Moreover, the asymptoticdistribution function of the sequence formed by the elements in anyof the half-orbits is a continuous, strictly increasing, singularfunction very similar to the well-known Minkowski's ?(×) function.

Fermat's treatise on quadrature: A new reading

The Treatise on Quadrature of Fermat (c. 1659), besides containing the first known proof of the computation of the area under a higher parabola, R x+m/n dx, or under a higher hyperbola, R x-m/n dx with the appropriate limits of integration in each case , has a second part which was not understood by Fermat s contemporaries. This second part of the Treatise is obscure and difficult to read and even the great Huygens described it as'published with many mistakes and it is so obscure (with proofs redolent of error) that I have been unable to make any sense of it'. Far from the confusion that Huygens attributes to it, in this paper we try to prove that Fermat, in writing the Treatise, had a very clear goal in mind and he managed to attain it by means of a simple and original method. Fermat reduced the quadrature of a great number of algebraic curves to the quadrature of known curves: the higher parabolas and hyperbolas of the first part of the paper. Others, he reduced to the quadrature of the circle. We shall see how the clever use of two procedures, quite novel at the time: the change of variables and a particular case of the formulaof integration by parts, provide Fermat with the necessary tools to square very easily curves as well-known as the folium of Descartes, the cissoid of Diocles or the witch of Agnesi.

Teoremas de isomorfía en grupos diedros

En este art\'\ı culo discutimos los resultados principalesalcanzados en mi trabajo de grado, el cual fue dirigido por elprofesor Jairo Charris Casta\~neda. La discusi\'on la limitaremos alos llamados $(p, q)$ grupos, en particular a los grupos diedros.

Unified formalism for non-autonomous mechanical systems

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defind by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincare-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

Performance evaluation of MPEG-4 Video encoder on Adres

Actualment un típic embedded system (ex. telèfon mòbil) requereix alta qualitat per portar a terme tasques com codificar/descodificar a temps real; han de consumir poc energia per funcionar hores o dies utilitzant bateries lleugeres; han de ser el suficientment flexibles per integrar múltiples aplicacions i estàndards en un sol aparell; han de ser dissenyats i verificats en un període de temps curt tot i l’augment de la complexitat. Els dissenyadors lluiten contra aquestes adversitats, que demanen noves innovacions en arquitectures i metodologies de disseny. Coarse-grained reconfigurable architectures (CGRAs) estan emergent com a candidats potencials per superar totes aquestes dificultats. Diferents tipus d’arquitectures han estat presentades en els últims anys. L’alta granularitat redueix molt el retard, l’àrea, el consum i el temps de configuració comparant amb les FPGAs. D’altra banda, en comparació amb els tradicionals processadors coarse-grained programables, els alts recursos computacionals els permet d’assolir un alt nivell de paral•lelisme i eficiència. No obstant, els CGRAs existents no estant sent aplicats principalment per les grans dificultats en la programació per arquitectures complexes. ADRES és una nova CGRA dissenyada per I’Interuniversity Micro-Electronics Center (IMEC). Combina un processador very-long instruction word (VLIW) i un coarse-grained array per tenir dues opcions diferents en un mateix dispositiu físic. Entre els seus avantatges destaquen l’alta qualitat, poca redundància en les comunicacions i la facilitat de programació. Finalment ADRES és un patró enlloc d’una arquitectura concreta. Amb l’ajuda del compilador DRESC (Dynamically Reconfigurable Embedded System Compile), és possible trobar millors arquitectures o arquitectures específiques segons l’aplicació. Aquest treball presenta la implementació d’un codificador MPEG-4 per l’ADRES. Mostra l’evolució del codi per obtenir una bona implementació per una arquitectura donada. També es presenten les característiques principals d’ADRES i el seu compilador (DRESC). Els objectius són de reduir al màxim el nombre de cicles (temps) per implementar el codificador de MPEG-4 i veure les diferents dificultats de treballar en l’entorn ADRES. Els resultats mostren que els cícles es redueixen en un 67% comparant el codi inicial i final en el mode VLIW i un 84% comparant el codi inicial en VLIW i el final en mode CGA.

Macaulay style formulas for sparse resultants

We present formulas for computing the resultant of sparse polyno- mials as a quotient of two determinants, the denominator being a minor of the numerator. These formulas extend the original formulation given by Macaulay for homogeneous polynomials.