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

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

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

Compositional inhomogeneities as a source of indirect combustion noise

The generation of indirect combustion noise by compositional inhomogeneities is examined theoretically. For this, the compact nozzle theory of~\cite{MARBLE_CANDEL_JSV1977} is extended to a multi-component gas mixture, and the chemical potential function is introduced as an additional acoustic source mechanism. Transfer functions for subcritical and supercritical nozzle flows are derived and the contribution of compositional noise is compared to entropy noise and direct noise by considering an idealized nozzle downstream of the combustor exit. It is shown that compositional noise is dependent on the local mixture composition and can exceed entropy noise for fuel-lean conditions and supercritical nozzle flows. This suggests that the compositional indirect noise requires potential consideration with the implementation of low-emission combustors.Financial support through NASA with award number NNX15AV04A and the Ford–Stanford Alliance project no. C2015-0590 is gratefully acknowledged.This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2016.39

Influence of infection on the distribution patterns of NIH-Chronic Prostatitis Symptom Index scores in patients with chronic prostatitis/chronic pelvic pain syndrome (CP/CPPS)

Chronic prostatitis/chronic pelvic pain syndrome (CP/CPPS) is a complex condition for which the etiological determinants are still poorly defined. To better characterize the diagnostic and therapeutic profile of patients, an algorithm known as UPOINT was created, addressing six major phenotypic domains of CP/CPPS, specifically the urinary (U), psycho-social (P), organ-specific (O), infection (I), neurological/systemic (N) and muscular tenderness (T) domains. An additional sexual dysfunction domain may be included in the UPOINT(S) system. The impact of the infection domain on the severity of CP/CPPS symptoms is a controversial issue, due to the contradictory results of different trials. The aim of the present retrospective study was to further analyze the extent to which a positive infection domain of UPOINTS may modify the pattern of CP/CPPS symptom scores, assessed with the National Institutes of Health-Chronic Prostatitis Symptom Index (NIH-CPSI). In a cohort of 935 patients that was divided on the basis of the presence or absence of prostatic infection, more severe clinical symptoms were shown by the patients with infection (median NIH total score: 24 versus 20 points in uninfected patients; P<0.001). Moreover, NIH-CPSI score distribution curves were shifted towards more severe symptoms in patients with a positive infection domain. Division of the patients into the six most prominent phenotypic clusters of UPOINTS revealed that the 'prostate infection-related sexual dysfunction' cluster, including the highest proportion of patients with evidence of infection (80%), scored the highest number of NIH-CPSI points among all the clusters. To assess the influence of the infection domain on the severity of patients' symptoms, all subjects with evidence of infection were withdrawn from the 'prostate infection-related sexual dysfunction' cluster. This modified cluster showed symptom scores significantly less severe than the original cluster, and the CPSI values became comparable to the scores of the five other clusters, which were virtually devoid of patients with evidence of infection. These results suggest that the presence of pathogens in the prostate gland may significantly affect the clinical presentation of patients affected by CP/CPPS, and that the infection domain may be a determinant of the severity of CP/CPPS symptoms in clusters of patients phenotyped with the UPOINTS system. This evidence may convey considerable therapeutic implications

A Novel Hierarchy of Integrable Lattices

In the framework of the reduction technique for Poisson-Nijenhuis structures, we derive a new hierarchy of integrable lattice, whose continuum limit is the AKNS hierarchy. In contrast with other differential-difference versions of the AKNS system, our hierarchy is endowed with a canonical Poisson structure and, moreover, it admits a vector generalisation. We also solve the associated spectral problem and explicity contruct action-angle variables through the r-matrix approach.Comment: Latex fil

Laryngeal lymphoma : the high and low grades of rare lymphoma involvement sites

The larynx is an extremely rare site of involvement by lymphomatous disease.We present two cases of isolated laryngeal high-grade and another low-grade lymphoma, together with a literature review of laryngeal lymphoma management.peer-reviewe

On the integrability of stationary and restricted flows of the KdV hierarchy.

A bi--Hamiltonian formulation for stationary flows of the KdV hierarchy is derived in an extended phase space. A map between stationary flows and restricted flows is constructed: in a case it connects an integrable Henon--Heiles system and the Garnier system. Moreover a new integrability scheme for Hamiltonian systems is proposed, holding in the standard phase space.Comment: 25 pages, AMS-LATEX 2.09, no figures, to be published in J. Phys. A: Math. Gen.

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