A Gentle (without Chopping) Approach to the Full Kostant-Toda Lattice

In this paper we propose a new algorithm for obtaining the rational integrals of the full Kostant-Toda lattice. This new approach is based on a reduction of a bi-Hamiltonian system on gl(n,R). This system was obtained by reducing the space of maps from Z_n to GL(n,R) endowed with a structure of a pair of Lie-algebroids.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Separation of Coupled Systems of Schrodinger Equations by Darboux transformations

Darboux transformations in one independent variable have found numerous applications in various field of mathematics and physics. In this paper we show that the extension of these transformations to two dimensions can be used to decouple systems of Schrodinger equations and provide explicit representation for three classes of such systems. We show also that there is an elegant relationship between these transformations and analytic complex matrix functions.Comment: 14 page

Self-assembly of multi-component fluorescent molecular logic gates in micelles

A recent strategy for developing supramolecular logic gates in water is based on combinations of molecules via self-assembly with surfactants, which eliminates the need for time-consuming synthesis. The self-assembly of surfactants and lumophores and receptors can result in interesting properties providing cooperative e ffects useful for molecular information processing and other potential applications such as drug delivery systems. This article highlights some of the recent advancements in supramolecular information processing using microheterogeneous media including micelles in aqueous solution.peer-reviewe

Low-frequency local field potentials and spikes in primary visual cortex convey independent visual information

Local field potentials (LFPs) reflect subthreshold integrative processes that complement spike train measures. However, little is yet known about the differences between how LFPs and spikes encode rich naturalistic sensory stimuli. We addressed this question by recording LFPs and spikes from the primary visual cortex of anesthetized macaques while presenting a color movie.Wethen determined how the power of LFPs and spikes at different frequencies represents the visual features in the movie.Wefound that the most informative LFP frequency ranges were 1– 8 and 60 –100 Hz. LFPs in the range of 12– 40 Hz carried little information about the stimulus, and may primarily reflect neuromodulatory inputs. Spike power was informative only at frequencies <12 Hz. We further quantified “signal correlations” (correlations in the trial-averaged power response to different stimuli) and “noise correlations” (trial-by-trial correlations in the fluctuations around the average) of LFPs and spikes recorded from the same electrode. We found positive signal correlation between high-gamma LFPs (60 –100 Hz) and spikes, as well as strong positive signal correlation within high-gamma LFPs, suggesting that high-gamma LFPs and spikes are generated within the same network. LFPs<24 Hz shared strong positive noise correlations, indicating that they are influenced by a common source, such as a diffuse neuromodulatory input. LFPs<40 Hz showed very little signal and noise correlations with LFPs>40Hzand with spikes, suggesting that low-frequency LFPs reflect neural processes that in natural conditions are fully decoupled from those giving rise to spikes and to high-gamma LFPs

A robust adaptive algebraic multigrid linear solver for structural mechanics

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated with lower order functions, like stress or deformation fields. Such task represents the most time-consuming kernel in commercial simulators; thus, it is of significant interest the development of robust and efficient linear solvers for such applications. In this context, direct solvers, which are based on LU factorization techniques, are often used due to their robustness and easy setup; however, they can reach only superlinear complexity, in the best case, thus, have limited applicability depending on the problem size. On the other hand, iterative solvers based on algebraic multigrid (AMG) preconditioners can reach up to linear complexity for sufficiently regular problems but do not always converge and require more knowledge from the user for an efficient setup. In this work, we present an adaptive AMG method specifically designed to improve its usability and efficiency in the solution of structural problems. We show numerical results for several practical applications with millions of unknowns and compare our method with two state-of-the-art linear solvers proving its efficiency and robustness.Comment: 50 pages, 16 figures, submitted to CMAM

Applications of Information Theory to Analysis of Neural Data

Information theory is a practical and theoretical framework developed for the study of communication over noisy channels. Its probabilistic basis and capacity to relate statistical structure to function make it ideally suited for studying information flow in the nervous system. It has a number of useful properties: it is a general measure sensitive to any relationship, not only linear effects; it has meaningful units which in many cases allow direct comparison between different experiments; and it can be used to study how much information can be gained by observing neural responses in single trials, rather than in averages over multiple trials. A variety of information theoretic quantities are commonly used in neuroscience - (see entry "Definitions of Information-Theoretic Quantities"). In this entry we review some applications of information theory in neuroscience to study encoding of information in both single neurons and neuronal populations.Comment: 8 pages, 2 figure

Generalized Lenard Chains, Separation of Variables and Superintegrability

We show that the notion of generalized Lenard chains naturally allows formulation of the theory of multi-separable and superintegrable systems in the context of bi-Hamiltonian geometry. We prove that the existence of generalized Lenard chains generated by a Hamiltonian function defined on a four-dimensional \omega N manifold guarantees the separation of variables. As an application, we construct such chains for the H\'enon-Heiles systems and for the classical Smorodinsky-Winternitz systems. New bi-Hamiltonian structures for the Kepler potential are found.Comment: 14 pages Revte

Littoral land use competition at Xemxija a touristic area in the Maltese Islands

The Maltese Islands are a group of central Mediterranean islands lying 93 km from the southern Sicilian coast and 352 km north of Tripoli on the coast of the North African mainland. The basic spatial and demographic data for the three inhabited islands making up the archipelago show marked differences with Malta having 246,000 people and Gozo 29,000 (Census, 1995). It has long been recognised that the economic areas that the Maltese Islands should principally promote are tourism and manufacturing. Following the phasing out of the British Military presence (1958-1979) and the granting of independence in 1964 investment in tourism started to gain ground. Figures 1 and 2 give a graphical account of the development of tourism over a seventeen year period. Essentially, it has been a success story especially with the multiplier effects that were generated as a result.peer-reviewe

Quasi-BiHamiltonian Systems and Separability

Two quasi--biHamiltonian systems with three and four degrees of freedom are presented. These systems are shown to be separable in terms of Nijenhuis coordinates. Moreover the most general Pfaffian quasi-biHamiltonian system with an arbitrary number of degrees of freedom is constructed (in terms of Nijenhuis coordinates) and its separability is proved.Comment: 10 pages, AMS-LaTeX 1.1, to appear in J. Phys. A: Math. Gen. (May 1997

Electronic structure of self-assembled InAs/InP quantum dots: A Comparison with self-assembled InAs/GaAs quantum dots

We investigate the electronic structure of the InAs/InP quantum dots using an atomistic pseudopotential method and compare them to those of the InAs/GaAs QDs. We show that even though the InAs/InP and InAs/GaAs dots have the same dot material, their electronic structure differ significantly in certain aspects, especially for holes: (i) The hole levels have a much larger energy spacing in the InAs/InP dots than in the InAs/GaAs dots of corresponding size. (ii) Furthermore, in contrast with the InAs/GaAs dots, where the sizeable hole $p$, $d$ intra-shell level splitting smashes the energy level shell structure, the InAs/InP QDs have a well defined energy level shell structure with small $p$, $d$ level splitting, for holes. (iii) The fundamental exciton energies of the InAs/InP dots are calculated to be around 0.8 eV ($\sim$ 1.55 $\mu$m), about 200 meV lower than those of typical InAs/GaAs QDs, mainly due to the smaller lattice mismatch in the InAs/InP dots. (iii) The widths of the exciton $P$ shell and $D$ shell are much narrower in the InAs/InP dots than in the InAs/GaAs dots. (iv) The InAs/GaAs and InAs/InP dots have a reversed light polarization anisotropy along the [100] and [1$\bar{1}$0] directions