Practical algorithms for a family of waterfilling solutions

Many engineering problems that can be formulatedas constrained optimization problems result in solutionsgiven by a waterfilling structure; the classical example is thecapacity-achieving solution for a frequency-selective channel.For simple waterfilling solutions with a single waterlevel and asingle constraint (typically, a power constraint), some algorithmshave been proposed in the literature to compute the solutionsnumerically. However, some other optimization problems result insignificantly more complicated waterfilling solutions that includemultiple waterlevels and multiple constraints. For such cases, itmay still be possible to obtain practical algorithms to evaluate thesolutions numerically but only after a painstaking inspection ofthe specific waterfilling structure. In addition, a unified view ofthe different types of waterfilling solutions and the correspondingpractical algorithms is missing.The purpose of this paper is twofold. On the one hand, itoverviews the waterfilling results existing in the literature from aunified viewpoint. On the other hand, it bridges the gap betweena wide family of waterfilling solutions and their efficient implementationin practice; to be more precise, it provides a practicalalgorithm to evaluate numerically a general waterfilling solution,which includes the currently existing waterfilling solutions andothers that may possibly appear in future problems.

Reconstruction of the join time-delay Doppler-scale reflectivity density in the wide-band regime. A frame theory based approach

The inverse scattering problem concerning the determination of the joint time-delayDoppler-scale reflectivity density characterizing continuous target environments is addressed by recourse to the generalized frame theory. A reconstruction formula,involving the echoes of a frame of outgoing signals and its corresponding reciprocalframe, is developed. A ‘‘realistic’’ situation with respect to the transmission ofa finite number of signals is further considered. In such a case, our reconstruction formula is shown to yield the orthogonal projection of the reflectivity density onto a subspace generated by the transmitted signals.

Blind channel estimation and data detection using hidden Markov models theory

In this correspondence, we propose applying the hiddenMarkov models (HMM) theory to the problem of blind channel estimationand data detection. The Baum–Welch (BW) algorithm, which is able toestimate all the parameters of the model, is enriched by introducingsome linear constraints emerging from a linear FIR hypothesis on thechannel. Additionally, a version of the algorithm that is suitable for timevaryingchannels is also presented. Performance is analyzed in a GSMenvironment using standard test channels and is found to be close to thatobtained with a nonblind receiver.

Scheduling an European basketball competition. An application of graph theory

The object of this project is to schedule a ctitious European basketball competition with many teams situated a long distances. The schedule must be fair, feasible and economical, which means that the total distance trav- eled by every team must be the minimal possible. First, we de ne the sport competition terminology and study di erent competition systems, focusing on the NBA and the Euroleague systems. Then we de ne concepts of graph theory and spherical distance that will be needed. Next we propose a com- petition system, explaining where will be allocated the teams and how will be the scheduling. Then there is a description of the programs that have been implemented, and, nally, the complete schedule is displayed, and some possible improvements are mentioned.

A Theory of Representative Behavior in the Dictator Game

In this paper we present a model of representative behavior in the dictator game. Individuals have simultaneous and non-contradictory preferences over monetary payoffs, altruistic actions and equity concerns. We require that these behaviors must be aggregated and founded in principles of representativeness and empathy. The model results match closely the observed mean split and replicate other empirical regularities (for instance, higher stakes reduce the willingness to give). In addition, we connect representative behavior with an allocation rule built on psychological and behavioral arguments. An approach consistently neglected in this literature. Key words: Dictator Game, Behavioral Allocation Rules, Altruism, Equity Concerns, Empathy, Self-interest JEL classification: C91, D03, D63, D74.

On the origin of the inertia: the modified Newtonian dynamics theory

The sameness between the inertial mass and the gravitational mass is an assumption and not a consequence of the equivalent principle is shown. In the context of the Sciama’s inertia theory, the sameness between the inertial mass and the gravitational mass is discussed and a certain condition which must be experimentally satisfied is given. The inertial force proposed by Sciama, in a simple case, is derived from the Assis’ inertia theory based in the introduction of a Weber type force. The origin of the inertial force is totally justified taking into account that the Weber force is, in fact, an approximation of a simple retarded potential, see [18, 19]. The way how the inertial forces are also derived from some solutions of the general relativistic equations is presented. We wonder if the theory of inertia of Assis is included in the framework of the General Relativity. In the context of the inertia developed in the present paper we establish the relation between the constant acceleration a0 , that appears in the classical Modified Newtonian Dynamics (M0ND) theory, with the Hubble constant H0 , i.e. a0 ≈ cH0 .

Teaching fundamentals of computing theory: a constructivist approach

A Fundamentals of Computing Theory course involves different topics that are core to the Computer Science curricula and whose level of abstraction makes them difficult both to teach and to learn. Such difficulty stems from the complexity of the abstract notions involved and the required mathematical background. Surveys conducted among our students showed that many of them were applying some theoretical concepts mechanically rather than developing significant learning. This paper shows a number of didactic strategies that we introduced in the Fundamentals of Computing Theory curricula to cope with the above problem. The proposed strategies were based on a stronger use of technology and a constructivist approach. The final goal was to promote more significant learning of the course topics.

String theory dualities and supergravity divergences

We demonstrate how duality invariance of the low energy expansion of the four-supergraviton amplitude in type II string theory determines the precise coefficients of multiloop logarithmic ultraviolet divergences of maximal supergravity in various dimensions. This is illustrated by the explicit moduli-dependence of terms of the form ¿2k R4, with k ¿ 3, in the effective action. Furthermore, we show that in the supergravity limit the perturbative contributions are swamped by an accumulation of non-perturbative effects of zero-action instantons.

Application of Information Statistical Theory to the Description of the Effect of Heat Conduction on the Chemical Reaction Rate in Gases

The effect of the heat flux on the rate of chemical reaction in dilute gases is shown to be important for reactions characterized by high activation energies and in the presence of very large temperature gradients. This effect, obtained from the second-order terms in the distribution function (similar to those obtained in the Burnett approximation to the solution of the Boltzmann equation), is derived on the basis of information theory. It is shown that the analytical results describing the effect are simpler if the kinetic definition for the nonequilibrium temperature is introduced than if the thermodynamic definition is introduced. The numerical results are nearly the same for both definitions

Loanword Phonology, Lexical Exceptions, Morphologically Driven Underapplication, and the Nature of Positionally Biased Constraints

In this paper we provide a formal account for underapplication of vowel reduction to schwa in Majorcan Catalan loanwords and learned words. On the basis of the comparison of these data with those concerning productive derivation and verbal inflection, which show analogous patterns, in this paper we also explore the existing and not yet acknowledged correlation between those processes that exhibit a particular behaviour in the loanword phonology with respect to the native phonology of the language, those processes that show lexical exceptions and those processes that underapply due to morphological reasons. In light of the analysis of the very same data and taking into account the aforementioned correlation, we show how there might exist a natural diachronic relation between two kinds of Optimality Theory constraints which are commonly used but, in principle, mutually exclusive: positional faithfulness and contextual markedness constraints. Overall, phonological productivity is proven to be crucial in three respects: first, as a context of the grammar, given that «underapplication» is systematically found in what we call the productive phonology of the dialect (including loanwords, learned words, productive derivation and verbal inflection); second, as a trigger or blocker of processes, in that the productivity or the lack of productivity of a specific process or constraint in the language is what explains whether it is challenged or not in any of the depicted situations, and, third, as a guiding principle which can explain the transition from the historical to the synchronic phonology of a linguistic variety.

Friedman's Excess energy and the McMillan-Mayer theory of solutions:Thermodynamics

In his version of the theory of multicomponent systems, Friedman used the analogy which exists between the virial expansion for the osmotic pressure obtained from the McMillan-Mayer (MM) theory of solutions in the grand canonical ensemble and the virial expansion for the pressure of a real gas. For the calculation of the thermodynamic properties of the solution, Friedman proposed a definition for the"excess free energy" that is a reminder of the ancient idea for the"osmotic work". However, the precise meaning to be attached to his free energy is, within other reasons, not well defined because in osmotic equilibrium the solution is not a closed system and for a given process the total amount of solvent in the solution varies. In this paper, an analysis based on thermodynamics is presented in order to obtain the exact and precise definition for Friedman"s excess free energy and its use in the comparison with the experimental data.

Thomas-Fermi theory for atomic nuclei revisited

The recently developed semiclassical variational Wigner-Kirkwood (VWK) approach is applied to finite nuclei using external potentials and self-consistent mean fields derived from Skyrme inter-actions and from relativistic mean field theory. VWK consist s of the Thomas-Fermi part plus a pure, perturbative h 2 correction. In external potentials, VWK passes through the average of the quantal values of the accumulated level density and total en energy as a function of the Fermi energy. However, there is a problem of overbinding when the energy per particle is displayed as a function of the particle number. The situation is analyzed comparing spherical and deformed harmonic oscillator potentials. In the self-consistent case, we show for Skyrme forces that VWK binding energies are very close to those obtained from extended Thomas-Fermi functionals of h 4 order, pointing to the rapid convergence of the VWK theory. This satisfying result, however, does not cure the overbinding problem, i.e., the semiclassical energies show more binding than they should. This feature is more pronounced in the case of Skyrme forces than with the relativistic mean field approach. However, even in the latter case the shell correction energy for e.g.208 Pb turns out to be only ∼ −6 MeV what is about a factor two or three off the generally accepted value. As an adhoc remedy, increasing the kinetic energy by 2.5%, leads to shell correction energies well acceptable throughout the periodic table. The general importance of the present studies for other finite Fermi systems, self-bound or in external potentials, is pointed out.

Nuclear surface properties in relativistic effective field theory

We perform Hartree calculations of symmetric and asymmetric semi-infinite nuclear matter in the framework of relativistic models based on effective hadronic field theories as recently proposed in the literature. In addition to the conventional cubic and quartic scalar self-interactions, the extended models incorporate a quartic vector self-interaction, scalar-vector non-linearities and tensor couplings of the vector mesons. We investigate the implications of these terms on nuclear surface properties such as the surface energy coefficient, surface thickness, surface stiffness coefficient, neutron skin thickness and the spin-orbit force.