Influence of memory in deterministic walks in random media: Analytical calculation within a mean-field approximation

Consider a random medium consisting of N points randomly distributed so that there is no correlation among the distances separating them. This is the random link model, which is the high dimensionality limit (mean-field approximation) for the Euclidean random point structure. In the random link model, at discrete time steps, a walker moves to the nearest point, which has not been visited in the last mu steps (memory), producing a deterministic partially self-avoiding walk (the tourist walk). We have analytically obtained the distribution of the number n of points explored by the walker with memory mu=2, as well as the transient and period joint distribution. This result enables us to explain the abrupt change in the exploratory behavior between the cases mu=1 (memoryless walker, driven by extreme value statistics) and mu=2 (walker with memory, driven by combinatorial statistics). In the mu=1 case, the mean newly visited points in the thermodynamic limit (N >> 1) is just < n >=e=2.72... while in the mu=2 case, the mean number < n > of visited points grows proportionally to N(1/2). Also, this result allows us to establish an equivalence between the random link model with mu=2 and random map (uncorrelated back and forth distances) with mu=0 and the abrupt change between the probabilities for null transient time and subsequent ones.

Systematic investigation of a family of gradient-dependent functionals for solids

Eleven density functionals are compared with regard to their performance for the lattice constants of solids. We consider standard functionals, such as the local-density approximation and the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA), as well as variations of PBE GGA, such as PBEsol and similar functionals, PBE-type functionals employing a tighter Lieb-Oxford bound, and combinations thereof. On a test set of 60 solids, we perform a system-by-system analysis for selected functionals and a full statistical analysis for all of them. The impact of restoring the gradient expansion and of tightening the Lieb-Oxford bound is discussed, and confronted with previous results obtained from other codes, functionals or test sets. No functional is uniformly good for all investigated systems, but surprisingly, and pleasingly, the simplest possible modifications to PBE turn out to have the most beneficial effect on its performance. The atomization energy of molecules was also considered and on a testing set of six molecules, we found that the PBE functional is clearly the best, the others leading to strong overbinding.

Gradient-dependent density functionals of the Perdew-Burke-Ernzerhof type for atoms, molecules, and solids

One of the standard generalized-gradient approximations (GGAs) in use in modern electronic-structure theory [Perdew-Burke-Ernzerhof (PBE) GGA] and a recently proposed modification designed specifically for solids (PBEsol) are identified as particular members of a family of functionals taking their parameters from different properties of homogeneous or inhomogeneous electron liquids. Three further members of this family are constructed and tested, together with the original PBE and PBEsol, for atoms, molecules, and solids. We find that PBE, in spite of its popularity in solid-state physics and quantum chemistry, is not always the best performing member of the family and that PBEsol, in spite of having been constructed specifically for solids, is not the best for solids. The performance of GGAs for finite systems is found to sensitively depend on the choice of constraints stemming from infinite systems. Guidelines both for users and for developers of density functionals emerge from this work.

Approximation to density functional theory for the calculation of band gaps of semiconductors

The local-density approximation (LDA) together with the half occupation (transitionstate) is notoriously successful in the calculation of atomic ionization potentials. When it comes to extended systems, such as a semiconductor infinite system, it has been very difficult to find a way to half ionize because the hole tends to be infinitely extended (a Bloch wave). The answer to this problem lies in the LDA formalism itself. One proves that the half occupation is equivalent to introducing the hole self-energy (electrostatic and exchange correlation) into the Schrodinger equation. The argument then becomes simple: The eigenvalue minus the self-energy has to be minimized because the atom has a minimal energy. Then one simply proves that the hole is localized, not infinitely extended, because it must have maximal self-energy. Then one also arrives at an equation similar to the self- interaction correction equation, but corrected for the removal of just 1/2 electron. Applied to the calculation of band gaps and effective masses, we use the self- energy calculated in atoms and attain a precision similar to that of GW, but with the great advantage that it requires no more computational effort than standard LDA.

Nonuniversal behavior for aperiodic interactions within a mean-field approximation

We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta. For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.

Guidance for the implementation of best practice for the care of patients with tuberculosis

The first two chapters of Best practice for the care of patients with tuberculosis: a guide for low-income countries include an introduction and guidance regarding implementation of best practice. The background to how the guide was developed is significant, as it was developed in collaboration with nurses and other health workers working in the most challenging settings. It therefore provides realistic and practical guidance for best practice where patient loads are large and resources are stretched. Guidance regarding standard setting and clinical audit is an important part of enabling people to recognise the strengths that already exist in their practice and approach those areas that require change in a systematic and practical way. The guide itself consists of a series of standards covering different aspects of patient care, from the moment they seek health care with symptoms to their diagnosis to early stages of treatment, directly observed treatment, the continuation phase and transfer of treatment. There are also standards relating specifically to HIV testing and the care of patients co-infected with tuberculosis and HIV. The standards themselves will appear in full in the subsequent chapters of this series.

A STUDY OF PENALTY FORMULATIONS USED IN THE NUMERICAL APPROXIMATION OF A RADIALLY SYMMETRIC ELASTICITY PROBLEM

We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.

Discrete approximation to the global spectrum of the tangent operator for flow past a circular cylinder

This paper deals with the calculation of the discrete approximation to the full spectrum for the tangent operator for the stability problem of the symmetric flow past a circular cylinder. It is also concerned with the localization of the Hopf bifurcation in laminar flow past a cylinder, when the stationary solution loses stability and often becomes periodic in time. The main problem is to determine the critical Reynolds number for which a pair of eigenvalues crosses the imaginary axis. We thus present a divergence-free method, based on a decoupling of the vector of velocities in the saddle-point system from the vector of pressures, allowing the computation of eigenvalues, from which we can deduce the fundamental frequency of the time-periodic solution. The calculation showed that stability is lost through a symmetry-breaking Hopf bifurcation and that the critical Reynolds number is in agreement with the value presented in reported computations. (c) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

The choice of the best among the shortest routes in transparent optical networks

This work introduces the problem of the best choice among M combinations of the shortest paths for dynamic provisioning of lightpaths in all-optical networks. To solve this problem in an optimized way (shortest path and load balance), a new fixed routing algorithm, named Best among the Shortest Routes (BSR), is proposed. The BSR`s performance is compared in terms of blocking probability and network utilization with Dijkstra`s shortest path algorithm and others algorithms proposed in the literature. The evaluated scenarios include several representative topologies for all-optical networking and different wavelength conversion architectures. For all studied scenarios, BSR achieved superior performance. (C) 2010 Elsevier B.V. All rights reserved.

On the convergence of successive Galerkin approximation for nonlinear output feedback H(infinity) control

Although the formulation of the nonlinear theory of H(infinity) control has been well developed, solving the Hamilton-Jacobi-Isaacs equation remains a challenge and is the major bottleneck for practical application of the theory. Several numerical methods have been proposed for its solution. In this paper, results on convergence and stability for a successive Galerkin approximation approach for nonlinear H(infinity) control via output feedback are presented. An example is presented illustrating the application of the algorithm.

Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a sufficient condition, based only on some positive semi-definite and kernel restrictions on some matrices, under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution fir the GCARE. We also present a solution for the discounted and long run average cost problems when the performance criterion is assumed be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables. The paper is concluded with a numerical example for pension fund with regime switching.

Molecular modeling and QSAR studies of a set of indole and benzimidazole derivatives as H(4) receptor antagonists

Histamine is an important biogenic amine, which acts with a group of four G-protein coupled receptors (GPCRs), namely H(1) to H(4) (H(1)R - H(4)R) receptors. The actions of histamine at H(4)R are related to immunological and inflammatory processes, particularly in pathophysiology of asthma, and H(4)R ligands having antagonistic properties could be helpful as antiinflammatory agents. In this work, molecular modeling and QSAR studies of a set of 30 compounds, indole and benzimidazole derivatives, as H(4)R antagonists were performed. The QSAR models were built and optimized using a genetic algorithm function and partial least squares regression (WOLF 5.5 program). The best QSAR model constructed with training set (N = 25) presented the following statistical measures: r (2) = 0.76, q (2) = 0.62, LOF = 0.15, and LSE = 0.07, and was validated using the LNO and y-randomization techniques. Four of five compounds of test set were well predicted by the selected QSAR model, which presented an external prediction power of 80%. These findings can be quite useful to aid the designing of new anti-H(4) compounds with improved biological response.

Evaluation of the enthalpy of formation, proton affinity, and gas-phase basicity of gamma-butyrolactone and 2-pyrrolidinone by isodesmic reactions

The knowledge of thermochemical parameters such as the enthalpy of formation, gas-phase basicity, and proton affinity may be the key to understanding molecular reactivity. The obtention of these thermochemical parameters by theoretical chemical models may be advantageous when experimental measurements are difficult to accomplish. The development of ab initio composite models represents a major advance in the obtention of these thermochemical parameters,. but these methods do not always lead to accurate values. Aiming at achieving a comparison between the ab initio models and the hybrid models based on the density functional theory (DFT), we have studied gamma-butyrolactone and 2-pyrrolidinone with a goal of obtaining high-quality thermochemical parameters using the composite chemical models G2, G2MP2, MP2, G3, CBS-Q, CBS-4, and CBS-QB3; the DFT methods B3LYP, B3P86, PW91PW91, mPW1PW, and B98; and the basis sets 6-31G(d), 6-31+G(d), 6-31G(d,p), 6-31+G(d,p), 6-31++G(d,p), 6-311G(d), 6-311+G(d), 6-311G(d,p), 6-311+G(d,p), 6-311++G(d,p), aug-cc-pVDZ, and aug-cc-pVTZ. Values obtained for the enthalpies of formation, proton affinity, and gas-phase basicity of the two target molecules were compared to the experimental data reported in the literature. The best results were achieved with the use of DFT models, and the B3LYP method led to the most accurate data.

Expectation Propagation with Factorizing Distributions: A Gaussian Approximation and Performance Results for Simple Models

We discuss the expectation propagation (EP) algorithm for approximate Bayesian inference using a factorizing posterior approximation. For neural network models, we use a central limit theorem argument to make EP tractable when the number of parameters is large. For two types of models, we show that EP can achieve optimal generalization performance when data are drawn from a simple distribution.

Which is the best technique for hepatic venous reconstruction in pediatric living-donor liver transplantation? Experience from a single center

Background/purpose: The introduction of the piggyback technique for reconstruction of the liver outflow in reduced-size liver transplants for pediatric patients has increased the incidence of hepatic venous outflow block (HVOB). Here, we proposed a new technique for hepatic venous reconstruction in pediatric living-donor liver transplantation. Methods: Three techniques were used: direct anastomosis of the orifice of the donor hepatic veins and the orifice of the recipient hepatic veins (group 1); triangular anastomosis after creating a wide triangular orifice in the recipient inferior vena cava at the confluence of all the hepatic veins (group 2); and a new technique, which is a wide longitudinal anastomosis performed at the anterior wall of the inferior vena cava (group 3). Results: In groups 1 and 2, the incidences of HVOB were 27.7% and 5.7%, respectively. In group 3, no patient presented HVOB (P = .001). No difference was noted between groups 2 and 3. Conclusions: Hepatic venous reconstruction in pediatric living-donor liver transplantation must be preferentially performed by using a wide longitudinal incision at the anterior wall of the recipient inferior vena cava. As an alternative technique, triangulation of the recipient inferior vena cava, including the orifices of the 3 hepatic veins, may be used. Published by Elsevier Inc.