ϵ-Optimal and Optimal Controls for the Stochastic Linear-Quadratic Problem

We study the stochastic regulator problem in Hilbert spaces for systems governed by linear stochastic differential equations with retarded controls and with state and control dependent noise. We use integral Riccati equations and no reference to a Riccati differential equation or to the Ito formula is made.     

A search for sonoluminescence in vivo in the human cheek

In a previous experiment, sonoluminescence was observed in aerated water, especially at the pressure antinodes in the standing-wave field of a physiotherapeutic ultrasound device (Therasonic 1030). Mammalian cells in vitro showed growth inhibition when placed at the pressure antinodes but not at adjacent pressure nodes. In the light of these results, we looked for sonoluminescence in vivo when a similar standing-wave field was set up. To detect luminescence, a light guide was held against the inner surface of the human cheek. This would channel any luminescence photons to a cooled, red-sensitive photomultiplier which would quantify the light. Direct insonation of the cheek produced no detectable luminescence. Similarly when a water bag was placed against the outer surface of the cheek, and the latter was insonated through the bag, no luminescence was detected. Sonoluminescence from the water bag was, however, detected when the bag was placed against the inner surface of the cheek, showing that absorption of sound by the cheek tissue was not preventing cavitation. Further analysis showed that if cavitation had been occurring in the cheek without detection using the system employed, then the resulting sonoluminescence would have to be at most 0.025 times as intense as that produced by an equivalent volume of aerated water.     

Hamiltonian Hopf Bifurcation with Symmetry

In this paper we study the appearance of branches of relative periodic orbits in Hamiltonian Hopf bifurcation processes in the presence of compact symmetry groups that do not generically exist in the dissipative framework. The theoretical study is illustrated with several examples.     

Scaffold topologies. 1. Exhaustive enumeration up to eight rings

Mapping the chemical space of small organic molecules is approached from a theoretical graph theory viewpoint, in an effort to begin the systematic exploration of molecular topologies. We present an algorithm for exhaustive generation of scaffold topologies with up to eight rings and an efficient comparison method for graphs within this class. This method uses the return index, a topological invariant derived from the adjacency matrix of the graph. Furthermore, we describe an algorithm that verifies the adequacy of the comparison method. Applications of this method for chemical space exploration in the context of drug discovery are discussed. The key result is a unique characterization of scaffold topologies, which may lead to more efficient ways to query large chemical databases.     

Nonequilibrium spin dynamics in a trapped fermi gas with effective spin-orbit interactions

We consider a trapped atomic system in the presence of spatially varying laser fields. The laser-atom interaction generates a pseudospin degree of freedom (referred to simply as spin) and leads to an effective spin-orbit coupling for the fermions in the trap. Reflections of the fermions from the trap boundaries provide a physical mechanism for effective momentum relaxation and nontrivial spin dynamics due to the emergent spin-orbit coupling. We explicitly consider evolution of an initially spin-polarized Fermi gas in a two-dimensional harmonic trap and derive nonequilibrium behavior of the spin polarization. It shows periodic echoes with a frequency equal to the harmonic trapping frequency. Perturbations, such as an asymmetry of the trap, lead to the suppression of the spin echo amplitudes. We discuss a possible experimental setup to observe spin dynamics and provide numerical estimates of relevant parameters.     

Investigation of single-molecule kinetics mediated by weak hydrogen bonds within a biological nanopore

The study of factors essential for protein-peptide interactions and protein pore-mediated peptide transport are of particular relevance in biology. Wild-type α-hemolysin was adopted as a "nanoreactor" in which perturbations of the current through a protein containing a lumen-residing, aryl-capped antimicrobial peptide were seen for the first time and studied at the single-molecule level. Energy and steric considerations hint that Met-aryl interactions between aromatic residues placed at a peptide's extremities and any of the methionines lining the α-hemolysin constriction region may be the primary cause of peptide stabilization within the lumen and may be particularly important to the peptide-α-hemolysin interaction.     

Synthesis, structural and spectral studies of Cu(II) and V(IV) complexes of a novel Schiff base derived from pyridoxal. Antimicrobial activity

A novel Schiff base, N-(4-amino-2,3-dimethyl-1-phenyl-3-pyrazolin-5-one)pyridoxaldimine (HL·HCl), was prepared and structurally characterized on the basis of elemental analyses, ¹H and ¹³C NMR, and IR spectral data. The synthesis and characterization of several Cu(II) (1-6) and V(IV) (7) complexes with N-(4-amino-2,3-dimethyl-1-phenyl-3-pyrazolin-5-one)pyridoxaldimine are reported. The composition and structures of the copper(II) and vanadium(IV) complexes were proposed based on elemental analyses, molar conductance, magnetic susceptibility measurements, IR, electronic and EPR spectroscopy. In addition, the structures of the ligand and the complex [CuL(H₂O)₂]NO₃·2.25H₂O (1) have been determined by single-crystal X-ray diffraction, showing that the Cu(II) center has a distorted square-pyramidal geometry. The ligand and the complexes were also tested for their in vitro antibacterial activity.