Distributed multi-agent optimization with state-dependent communication

We study distributed algorithms for solving global optimization problems in which the objective function is the sum of local objective functions of agents and the constraint set is given by the intersection of local constraint sets of agents. We assume that each agent knows only his own local objective function and constraint set, and exchanges information with the other agents over a randomly varying network topology to update his information state. We assume a state-dependent communication model over this topology: communication is Markovian with respect to the states of the agents and the probability with which the links are available depends on the states of the agents. We study a projected multi-agent subgradient algorithm under state-dependent communication. The state-dependence of the communication introduces significant challenges and couples the study of information exchange with the analysis of subgradient steps and projection errors. We first show that the multi-agent subgradient algorithm when used with a constant stepsize may result in the agent estimates to diverge with probability one. Under some assumptions on the stepsize sequence, we provide convergence rate bounds on a “disagreement metric” between the agent estimates. Our bounds are time-nonhomogeneous in the sense that they depend on the initial starting time. Despite this, we show that agent estimates reach an almost sure consensus and converge to the same optimal solution of the global optimization problem with probability one under different assumptions on the local constraint sets and the stepsize sequence.     

On Taylor series and Kapteyn series of the first and second type

We study the relation between the coefficients of Taylor series and Kapteyn series representing the same function. We compute explicit formulas for expressing one in terms of the other and give examples to illustrate our method.     

Nilmanifolds with a calibrated G2-structure

We introduce obstructions to the existence of a calibrated G₂-structure on a Lie algebra g of dimension seven, not necessarily nilpotent. In particular, we prove that if there is a Lie algebra epimorphism from g to a six-dimensional Lie algebra h with kernel contained in the center of g, then h has a symplectic form. As a consequence, we obtain a classification of the nilpotent Lie algebras that admit a calibrated G₂-structure.     

Dynamical properties of a particle in a wave packet: Scaling invariance and boundary crisis

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is mixed in the sense that there are regular and chaotic regions coexisting. We use a connection with the standard map in order to find the position of the first invariant spanning curve which borders the chaotic sea. We find that the position of the first invariant spanning curve increases as a power of the control parameter with the exponent 2/3. The standard deviation of the kinetic energy of an ensemble of initial conditions obeys a power law as a function of time, and saturates after some crossover. Scaling formalism is used in order to characterise the chaotic region close to the transition from integrability to nonintegrability and a relationship between the power law exponents is derived. The formalism can be applied in many different systems with mixed phase space. Then, dissipation is introduced into the model and therefore the property of area preservation is broken, and consequently attractors are observed. We show that after a small change of the dissipation, the chaotic attractor as well as its basin of attraction are destroyed, thus leading the system to experience a boundary crisis. The transient after the crisis follows a power law with exponent −2.     

Two metals are better than one in the gold catalyzed oxidative heteroarylation of alkenes

We present a detailed study of the mechanism for oxidative heteroarylation, based on DFT calculations and experimental observations. We propose binuclear Au(II)-Au(II) complexes to be key intermediates in the mechanism for gold catalyzed oxidative heteroarylation. The reaction is thought to proceed via a gold redox cycle involving initial oxidation of Au(I) to binuclear Au(II)-Au(II) complexes by Selectfluor, followed by heteroauration and reductive elimination. While it is tempting to invoke a transmetalation/reductive elimination mechanism similar to that proposed for other transition metal complexes, experimental and DFT studies suggest that the key C-C bond forming reaction occurs via a bimolecular reductive elimination process (devoid of transmetalation). In addition, the stereochemistry of the elimination step was determined experimentally to proceed with complete retention. Ligand and halide effects played an important role in the development and optimization of the catalyst; our data provides an explanation for the ligand effects observed experimentally, useful for future catalyst development. Cyclic voltammetry data is presented that supports redox synergy of the Au···Au aurophilic interaction. The monometallic reductive elimination from mononuclear Au(III) complexes is also studied from which we can predict a ~15 kcal/mol advantage for bimetallic reductive elimination.     

Jastrow correlated and quantum Monte Carlo calculations for the low-lying states of the carbon atom

Different computational methods are employed to calculate excitation energies of the carbon atom. Explicitly correlated wave functions have been obtained in a Variational Monte Carlo calculation. Fixed node Diffusion Monte Carlo calculations for the lowest energy excited states of a given symmetry are reported. A systematic and quantitative analysis of the performance of the different schemes in the calculation of the excitation energy of up to 27 excited states of the carbon atom is carried out. The quality of the different methods have been studied in terms of the deviation with respect to the experimental excitation energies. A good agreement with the experimental values has been reached.     

Impregnated ruthenium on magnetite as a recyclable catalyst for the N-alkylation of amines, sulfonamides, sulfinamides, and nitroarenes using alcohols as electrophiles by a hydrogen autotransfer process

Various impregnated metallic salts on magnetite have been prepared, including cobalt, nickel, copper, ruthenium, and palladium salts, as well as a bimetallic palladium-copper derivative. Impregnated ruthenium catalyst is a versatile, inexpensive, and simple system for the selective N-monoalkylation of amino derivatives with poor nucleophilic character, such as aromatic and heteroaromatic amines, sulfonamides, sulfinamides, and nitroarenes, using in all cases alcohols as the initial source of the electrophile, through a hydrogen autotransfer process. In the case of sulfinamides, this is the first time that these amino compounds have been alkylated following this strategy, allowing the use of chiral sulfinamides and secondary alcohols to give the alkylated compound with a diastereomeric ratio of 92:8. In these cases, after alkylation, a simple acid deprotection gave the expected primary amines in good yields. The ruthenium catalyst is quite sensitive, and small modifications of the reaction medium can change the final product. The alkylation of amines using potassium hydroxide renders the N-monoalkylated amines, and the same protocol using sodium hydroxide yields the related imines. The catalyst can be easily removed by a simple magnet and can be reused up to ten times, showing the same activity.     

Highly selective and sensitive chromo-fluorogenic detection of the Tetryl explosive using functional silica nanoparticles

Silica nanoparticles containing polyamines and thiol groups have been used as probes for the selective detection of Tetryl.     

Potent 5-nitrofuran derivatives inhibitors of Trypanosoma cruzi growth: electrochemical, spectroscopic and biological studies

Cyclic voltammetry and electron spin resonance techniques were used in the investigation of several potential antiprotozoal containing thiosemicarbazone and carbamate nitrofurans. In the electrochemical behaviour, a self-protonation process involving the nitro group was observed. The reactivity of the nitro anion radical for these derivatives with glutathione, a biological relevant thiol, was also studied in means of cyclic voltammetry. These studies demonstrated that glutathione could react with radical species from 5-nitrofuryl system. Furthermore, from the voltammetric results, some parameters of biological significance as E(7)(1) (indicative of the biological nitro anion radical formation), and [Formula: see text] (thermodynamic indicator the of oxygen redox cycling) have been calculated. We also evaluated the stability of the nitro anion radical in terms of the dimerization constant (k(d)). The nitrofuran-free radicals from cyclic voltammetry were characterized by electron spin resonance. A clear dependence between both the thiosemicarbazone or carbamate substructure and the length of the linker, furyl- or furylpropenyl-spacer, and the delocalization of the unpaired electron was observed. Through of biological assays we obtained important parameters that account for the selective anti-trypanosomal activity of these derivatives. The trypomastigote viability study showed that all derivatives are as active as in the epimastigote form of the parasite in a doses dependent manner.