Explicit solution of the quantum three-body Calogero-Sutherland model

Quantum integrable systems generalizing Calogero-Sutherland systems were introduced by Olshanetsky and Perelomov (1977). Recently, it was proved that for systems with trigonometric potential, the series in the product of two wave functions is a deformation of the Clebsch-Gordan series. This yields recursion relations for the wave functions of those systems. In this note, this approach is used to compute the explicit expressions for the three-body Calogero-Sutherland wave functions, which are the Jack polynomials. We conjecture that similar results are also valid for the more general two-parameters deformation introduced by Macdonald.Comment: 10 page

On Poincare and logarithmic Sobolev inequalities for a class of singular Gibbs measures

This note, mostly expository, is devoted to Poincar{\'e} and log-Sobolev inequalities for a class of Boltzmann-Gibbs measures with singular interaction. Such measures allow to model one-dimensional particles with confinement and singular pair interaction. The functional inequalities come from convexity. We prove and characterize optimality in the case of quadratic confinement via a factorization of the measure. This optimality phenomenon holds for all beta Hermite ensembles including the Gaussian unitary ensemble, a famous exactly solvable model of random matrix theory. We further explore exact solvability by reviewing the relation to Dyson-Ornstein-Uhlenbeck diffusion dynamics admitting the Hermite-Lassalle orthogonal polynomials as a complete set of eigenfunctions. We also discuss the consequence of the log-Sobolev inequality in terms of concentration of measure for Lipschitz functions such as maxima and linear statistics.Comment: Minor improvements. To appear in Geometric Aspects of Functional Analysis -- Israel Seminar (GAFA) 2017-2019", Lecture Notes in Mathematics 225

Evidence for Two Modes of Synergistic Induction of Apoptosis by Mapatumumab and Oxaliplatin in Combination with Hyperthermia in Human Colon Cancer Cells

Colorectal cancer is the third leading cause of cancer-related mortality in the world-- the main cause of death from colorectal cancer is hepatic metastases, which can be treated with isolated hepatic perfusion (IHP). Searching for the most clinically relevant approaches for treating colorectal metastatic disease by isolated hepatic perfusion (IHP), we developed the application of oxaliplatin concomitantly with hyperthermia and humanized death receptor 4 (DR4) antibody mapatumumab (Mapa), and investigated the molecular mechanisms of this multimodality treatment in human colon cancer cell lines CX-1 and HCT116 as well as human colon cancer stem cells Tu-12, Tu-21 and Tu-22. We showed here, in this study, that the synergistic effect of the multimodality treatment-induced apoptosis was caspase dependent and activated death signaling via both the extrinsic apoptotic pathway and the intrinsic pathway. Death signaling was activated by c-Jun N-terminal kinase (JNK) signaling which led to Bcl-xL phosphorylation at serine 62, decreasing the anti-apoptotic activity of Bcl-xL, which contributed to the intrinsic pathway. The downregulation of cellular FLICE inhibitory protein long isoform (c-FLIPL) in the extrinsic pathway was accomplished through ubiquitination at lysine residue (K) 195 and protein synthesis inhibition. Overexpression of c-FLIPL mutant (K195R) and Bcl-xL mutant (S62A) completely abrogated the synergistic effect. The successful outcome of this study supports the application of multimodality strategy to patients with colorectal hepatic metastases who fail to respond to standard chemoradiotherapy that predominantly targets the mitochondrial apoptotic pathway. © 2013 Song et al

On supersymmetric quantum mechanics

This paper constitutes a review on N=2 fractional supersymmetric Quantum Mechanics of order k. The presentation is based on the introduction of a generalized Weyl-Heisenberg algebra W_k. It is shown how a general Hamiltonian can be associated with the algebra W_k. This general Hamiltonian covers various supersymmetrical versions of dynamical systems (Morse system, Poschl-Teller system, fractional supersymmetric oscillator of order k, etc.). The case of ordinary supersymmetric Quantum Mechanics corresponds to k=2. A connection between fractional supersymmetric Quantum Mechanics and ordinary supersymmetric Quantum Mechanics is briefly described. A realization of the algebra W_k, of the N=2 supercharges and of the corresponding Hamiltonian is given in terms of deformed-bosons and k-fermions as well as in terms of differential operators.Comment: Review paper (31 pages) to be published in: Fundamental World of Quantum Chemistry, A Tribute to the Memory of Per-Olov Lowdin, Volume 3, E. Brandas and E.S. Kryachko (Eds.), Springer-Verlag, Berlin, 200

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

Nonlinear Supersymmetry as a Hidden Symmetry

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The Einstein-Vlasov System/Kinetic Theory

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein--Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein--Vlasov system. Since then many theorems on global properties of solutions to this system have been established.Comment: Published version http://www.livingreviews.org/lrr-2011-

Alzheimer's disease: new diagnostic and therapeutic tools

On March 19, 2008 a Symposium on Pathophysiology of Ageing and Age-Related diseases was held in Palermo, Italy. Here, the lectures of M. Racchi on History and future perspectives of Alzheimer Biomarkers and of G. Scapagnini on Cellular Stress Response and Brain Ageing are summarized. Alzheimer's disease (AD) is a heterogeneous and progressive neurodegenerative disease, which in Western society mainly accounts for clinica dementia. AD prevention is an important goal of ongoing research. Two objectives must be accomplished to make prevention feasible: i) individuals at high risk of AD need to be identified before the earliest symptoms become evident, by which time extensive neurodegeneration has already occurred and intervention to prevent the disease is likely to be less successful and ii) safe and effective interventions need to be developed that lead to a decrease in expression of this pathology. On the whole, data here reviewed strongly suggest that the measurement of conformationally altered p53 in blood cells has a high ability to discriminate AD cases from normal ageing, Parkinson's disease and other dementias. On the other hand, available data on the involvement of curcumin in restoring cellular homeostasis and rebalancing redox equilibrium, suggest that curcumin might be a useful adjunct in the treatment of neurodegenerative illnesses characterized by inflammation, such as AD

Automatic evaluation of body-related words among young women: an experimental study

Background: Sociocultural models of body image disturbance have linked the development of body dissatisfaction and eating disorders to exposure to media messages depicting the unrealistically slender female physique. Previous research has demonstrated that exposure to images depicting the thin female ideal has negative effects on some females’ levels of body dissatisfaction. Much of this research, however, has utilised relatively long stimulus exposure times; thereby focusing on effortful and conscious processing of body-related stimuli. Relatively little is known about the nature of females’ affective responses to the textual components of body-related stimuli, especially when these stimuli are only briefly encountered. The primary aim of the current research was to determine whether young women automatically evaluate body-related words and whether these responses are associated with body image concerns, including self-reported levels of appearance schematicity, thin internalisation, body dissatisfaction, and dietary restraint. Methods: An affective priming task was used to investigate whether females automatically evaluate body-related words, and whether this is associated with self-reported body image concerns. In a within-participants experimental design, the valence congruence of the prime and target pairs was manipulated. Participants selected body words as primes in Experiment 1 (N = 27), while normatively selected body words were primes in Experiment 2 (N = 50). Each prime was presented briefly, followed by a target word which participants judged as “good” or “bad”. The dependent variable was response latency to the target. Results: Automatic evaluation was evident: responding to congruent pairs was faster than responding to incongruent pairs. Body image concerns were unrelated to automaticity. Conclusions: The findings suggest that brief encounters with body words are likely to prompt automatic evaluation in all young women, and that this process proceeds unintentionally and efficiently, without conscious guidance. The potential implications for higher order, conscious information processing is discussed