A multi-parametric programming approach for constrained dynamic programming problems

In this work, we present a new algorithm for solving complex multi-stage optimization problems involving hard constraints and uncertainties, based on dynamic and multi-parametric programming techniques. Each echelon of the dynamic programming procedure, typically employed in the context of multi-stage optimization models, is interpreted as a multi-parametric optimization problem, with the present states and future decision variables being the parameters, while the present decisions the corresponding optimization variables. This reformulation significantly reduces the dimension of the original problem, essentially to a set of lower dimensional multi-parametric programs, which are sequentially solved. Furthermore, the use of sensitivity analysis circumvents non-convexities that naturally arise in constrained dynamic programming problems. The potential application of the proposed novel framework to robust constrained optimal control is highlighted.     

A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform

Fourier transform is applied to remove the time-dependent variable in the diffusion equation. Under non-harmonic initial conditions this gives rise to a non-homogeneous Helmholtz equation, which is solved by the method of fundamental solutions and the method of particular solutions. The particular solution of Helmholtz equation is available as shown in [4, 15]. The approximate solution in frequency domain is then inverted numerically using the inverse Fourier transform algorithm. Complex frequencies are used in order to avoid aliasing phenomena and to allow the computation of the static response. Two numerical examples are given to illustrate the effectiveness of the proposed approach for solving 2-D diffusion equations.     

Minimizing the Entropy Penalty for Ligand Binding: Lessons from the Molecular Recognition of the Histo Blood‐Group Antigens by Human Galectin‐3

Ligand conformational entropy plays an important role in carbohydrate recognition events. Glycans are characterized by intrinsic flexibility around the glycosidic linkages, thus in most cases, loss of conformational entropy of the sugar upon complex formation strongly affects the entropy of the binding process. By employing a multidisciplinary approach combining structural, conformational, binding energy, and kinetic information, we investigated the role of conformational entropy in the recognition of the histo blood‐group antigens A and B by human galectin‐3, a lectin of biomedical interest. We show that these rigid natural antigens are pre‐organized ligands for hGal‐3, and that restriction of the conformational flexibility by the branched fucose (Fuc) residue modulates the thermodynamics and kinetics of the binding process. These results highlight the importance of glycan flexibility and provide inspiration for the design of high‐affinity ligands as antagonists for lectins.     

DFT study on electronic properties of single- and double-shell icosahedral fullerenes

Multi-shell fullerenes are widely studied for their interesting properties although comparative studies on single- and multi-shell structures remain scarce. In this work, important electronic features of single- and double-shell icosahedral fullerenes as a function of their sizes were calculated in the framework of the density functional theory. Fully optimized structures were used to get the gap between the highest occupied molecular and the lowest unoccupied molecular orbital (H-L gap), electronegativity, softness and density of the electronic states. This work shows that the H-L gap of the single-shell fullerenes decreases nonlinearly as the nanoparticles size increases, whereas for the double-shell fullerenes an opposite trend is obtained. A decrease of the H-L gap is found going from single- to double-shell fullerenes with similar external sizes, up to a diameter of 3.13 nm. The electron density of states revealed that isolated peaks give way to more dense electronic states for nanoparticles with diameters above 2 nm.     

One-pot synthesis of 1-exo-alkylidene-2,3-anhydro furanoses: convenient precursors for exo-glycals and functionalized C-glycals

1-exo-Methylene-2,3-anhydro furanoses, obtained from C-glycals in a one-pot, three step operation can be readily transformed into functionalized C-glycals by palladium-catalyzed nucleophilic addition.     

On folded coverings of quasi-manifolds with boundary

LetM andN be quasi-manifolds possibly with boundary, we call afolded-covering p: N→M to a non-degenerate simplicial map, such thatp: N/p ^?1(?M)→M/?M is a branched covering. The purpose of this paper will be to classify the folded coverings of a given quasi-manifold by using the representations of a particular group on permutation groups, similar to the monodromy representations for coverings and in such a way that includes these ones a particular case. We shall apply our result to the theory of orbifolds to obtain a presentation (alternative to the one in [H-Q]) of the fundamental group for an orbifold defined on a quasi-manifold.     

Efficiency and robustness in ant networks of galleries

Recent theoretical and empirical studies have focused on the topology of large networks of communication/interactions in biological, social and technological systems. Most of them have been studied in the scope of the small-world and scale-free networks theory. Here we analyze the characteristics of ant networks of galleries produced in a 2-D experimental setup. These networks are neither small-worlds nor scale-free networks and belong to a particular class of network, i.e. embedded planar graphs emerging from a distributed growth mechanism. We compare the networks of galleries with both minimal spanning trees and greedy triangulations. We show that the networks of galleries have a path system efficiency and robustness to disconnections closer to the one observed in triangulated networks though their cost is closer to the one of a tree. These networks may have been prevented to evolve toward the classes of small-world and scale-free networks because of the strong spatial constraints under which they grow, but they may share with many real networks a similar trend to result from a balance of constraints leading them to achieve both path system efficiency and robustness at low cost.Received: 16 July 2004, Published online: 26 November 2004PACS: 89.75.Fb Structures and organization in complex systems - 89.75.Hc Networks and genealogical trees - 87.23.Ge Dynamics of social systems     

Ribonucleotide activation by enzyme ribonucleotide reductase: understanding the role of the enzyme

This article focuses on the first step of the catalytic mechanism for the reduction of ribonucleotides catalyzed by the enzyme Ribonucleotide Reductase (RNR). This corresponds to the activation of the substrate. In this work a large model of the active site region involving 130 atoms was used instead of the minimal gas phase models used in previous works. The ONIOM method was employed to deal with such a large system. The results gave additional information, which previous small models could not provide, allowing a much clearer evaluation of the role of the enzyme in this step. Enzyme-substrate interaction energies, specific transition state stabilization, and substrate steric strain energies were obtained. It was concluded that the transition state is stabilized in 4.0 kcal/mol by specific enzyme-substrate interactions. However, this stabilization is cancelled by the cost in conformational energy for the enzyme to adopt the transition state geometry; the overall result is that the enzyme machinery does not lead to a rate enhancement in this step. It was also found that the substrate binds to the active site with almost no steric strain, emphasizing the complementarity and specificity of the RNR active site for nucleotide binding. The main role of the enzyme at the very beginning of the catalytic cycle was concluded to be to impose stereospecifity upon substrate activation and to protect the enzyme radical from the solvent, rather than to be an reaction rate enhancement.     

Identification of synthetic precursors of amphetamine-like drugs using Raman spectroscopy and ab initio calculations: beta-Methyl-beta-nitrostyrene derivatives

The present work reports a vibrational spectroscopic study of several beta-methyl-beta-nitrostyrene derivatives, which are important intermediates in the synthesis of illicit amphetamine-like drugs, such as 3,4-methylenedioxymethamphetamine (MDMA), 3,4-methylenedioxyamphetamine (MDA), p-methoxyamphetamine (PMA) and 4-methylthioamphetamine (4-MTA). A complete conformational analysis of 3,4-methylenedioxy-beta-methyl-beta-nitrostyrene (3,4-MD-MeNS), 4-methoxy-beta-methyl-beta-nitrostyrene (4-MeO-MeNS), 4-methylthio-beta-methyl-beta-nitrostyrene (4-MeS-MeNS), was carried out by Raman spectroscopy coupled to ab initio MO calculations--both complete geometry optimisation and harmonic frequency calculation. The Raman spectra show characteristic features of these precursors, which allow their ready differentiation and identification. It was verified that the conformational behaviour of these systems is mainly determined by the stabilising effect of pi-electron delocalisation.