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

BENDING THE DOMING EFFECT IN STRUCTURE FROM MOTION RECONSTRUCTIONS THROUGH BUNDLE ADJUSTMENT

Structure from Motion techniques provides low-cost and flexible methods that can be adopted in arial surveying to collect topographic data with accurate results. Nevertheless, the so-called "doming effect", due to unfortunate acquisition conditions or unreliable modeling of radial distortion, has been recognized as a critical issue that disrupts the quality of the attained 3D reconstruction. In this paper we propose a novel method, that works effectively in the presence of a nearly flat soil, to tackle a posteriori the doming effect: an automatic ground detection method is used to capture the doming deformation flawing the reconstruction, which in turn is wrapped to the correct geometry by iteratively enforcing a planarity constraint through a Bundle Adjustment framework. Experiments on real word datasets demonstrate promising results

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

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

The quasi-bi-Hamiltonian formulation of the Lagrange top

Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the possible reductions of the Poisson tensors, the vector field and its Hamiltonian functions on a four-dimensional space. We show that the vector field of the Lagrange top possesses, on the reduced phase space, a quasi-bi-Hamiltonian formulation, which provides a set of separation variables for the corresponding Hamilton-Jacobi equation.Comment: 12 pages, no figures, LaTeX, to appear in J. Phys. A: Math. Gen. (March 2002

Versal deformations of a Dirac type differential operator

If we are given a smooth differential operator in the variable $x\in {\mathbb R}/2\pi {\mathbb Z},$ its normal form, as is well known, is the simplest form obtainable by means of the \mbox{Diff}(S^1)-group action on the space of all such operators. A versal deformation of this operator is a normal form for some parametric infinitesimal family including the operator. Our study is devoted to analysis of versal deformations of a Dirac type differential operator using the theory of induced \mbox{Diff}(S^1)-actions endowed with centrally extended Lie-Poisson brackets. After constructing a general expression for tranversal deformations of a Dirac type differential operator, we interpret it via the Lie-algebraic theory of induced \mbox{Diff}(S^1)-actions on a special Poisson manifold and determine its generic moment mapping. Using a Marsden-Weinstein reduction with respect to certain Casimir generated distributions, we describe a wide class of versally deformed Dirac type differential operators depending on complex parameters

Role of surface structural motifs on the stability and reflectance anisotropy spectra of Sb-rich GaSb(001) reconstructions

The structure of the technologically important-but still mostly unknown-GaSb(001)-c(2 x 6) surface reconstruction is investigated by means of ab initio simulations of reflectance anisotropy spectroscopy (RAS) and total energy calculations. A large number of reconstruction models for the GaSb(001) surface in the Sb-rich coverage regime are considered. The influence of each single surface structural motif on the RAS spectra is studied in detail, as well as their role in the surface stability with regard to application of the electron counting rule (ECR). We interpret the features of the RAS data measured for this reconstruction and suggest a new model for the c(2 x 6) phase. In this model a few Sb atoms in the second layer are randomly substituted by Ga, forming surface antisite defects. When used to fulfill the ECR, this "doping" effect considerably lowers the total energy of the long chain c(2 x 6) reconstruction model, making it competitive with the more stable short-chain (4 x 3) reconstructions. Formation of the surface antisites occurs spontaneously in the presence of dynamical negative charge fluctuations and is favored by the excellent matching between GaSb(001) and metallic Sb and by the natural softness of the Ga-Sb bonds. Calculations of the reflectance anisotropy spectra confirm that this structure is a major component of a largely disordered surface, where motifs of the stable (4 x 3) reconstructions are also present

Detection of Leishmania sp. kDNA in questing Ixodes ricinus (Acari, Ixodidae) from the Emilia-Romagna Region in northeastern Italy

To date, sand flies (Phlebotominae) are the only recognized biological vectors of Leishmania infantum, the causative agent of human visceral leishmaniasis, which is endemic in the Mediterranean basin and also widespread in Central and South America, the Middle East, and Central Asia. Dogs are the main domestic reservoir of zoonotic visceral leishmaniasis, and the role of secondary vectors such as ticks and fleas and particularly Rhipicephalus sanguineus (the brown dog tick) in transmitting L. infantum has been investigated. In the present paper, the presence of Leishmania DNA was investigated in questing Ixodes ricinus ticks collected from 4 rural areas included in three parks of the Emilia-Romagna Region (north-eastern Italy), where active foci of human visceral leishmaniasis have been identified. The analyses were performed on 236 DNA extracts from 7 females, 6 males, 72 nymph pools, and 151 larvae pools. Four samples (1.7%) (i.e., one larva pool, 2 nymph pools, and one adult male) tested positive for Leishmania kDNA. To the best of our knowledge, this is the first report of the presence of Leishmania kDNA in questing I. ricinus ticks collected from a rural environment. This finding in unfed larvae, nymphs, and adult male ticks supports the hypothesis that L. infantum can have both transstadial and transovarial passage in I. ricinus ticks. The potential role of I. ricinus ticks in the sylvatic cycle of leishmaniasis should be further investigated

Evolving always‐critical networks

Living beings share several common features at the molecular level, but there are very few large‐scale “operating principles” which hold for all (or almost all) organisms. However, biology is subject to a deluge of data, and as such, general concepts such as this would be extremely valuable. One interesting candidate is the “criticality” principle, which claims that biological evolution favors those dynamical regimes that are intermediaries between ordered and disordered states (i.e., “at the edge of chaos”). The reasons why this should be the case and experimental evidence are briefly discussed, observing that gene regulatory networks are indeed often found on, or close to, the critical boundaries. Therefore, assuming that criticality provides an edge, it is important to ascertain whether systems that are critical can further evolve while remaining critical. In order to explore the possibility of achieving such “always‐critical” evolution, we resort to simulated evolution, by suitably modifying a genetic algorithm in such a way that the newly‐generated individuals are constrained to be critical. It is then shown that these modified genetic algorithms can actually develop critical gene regulatory networks with two interesting (and quite different) features of biological significance, involving, in one case, the average gene activation values and, in the other case, the response to perturbations. These two cases suggest that it is often possible to evolve networks with interesting properties without losing the advantages of criticality. The evolved networks also show some interesting features which are discussed