Exact operator solution of the Calogero-Sutherland model

The wave functions of the Calogero-Sutherland model are known to be expressible in terms of Jack polynomials. A formula which allows to obtain the wave functions of the excited states by acting with a string of creation operators on the wave function of the ground state is presented and derived. The creation operators that enter in this formula of Rodrigues-type for the Jack polynomials involve Dunkl operators.Comment: 35 pages, LaTeX2e with amslate

A lecture on the Calogero-Sutherland models

In these lectures, I review some recent results on the Calogero-Sutherland model and the Haldane Shastry-chain. The list of topics I cover are the following: 1) The Calogero-Sutherland Hamiltonian and fractional statistics. The form factor of the density operator. 2) The Dunkl operators and their relations with monodromy matrices, Yangians and affine-Hecke algebras. 3) The Haldane-Shastry chain in connection with the Calogero-Sutherland Hamiltonian at a specific coupling constant.Comment: (2 references added, small modifications

Gag-Protease Sequence Evolution Following Protease Inhibitor Monotherapy Treatment Failure in HIV-1 Viruses Circulating in East Africa.

Around 2.5 million HIV-infected individuals failing first-line therapy qualify for boosted protease inhibitor (bPI)-based second-line therapy globally. Major resistance mutations are rarely present at treatment failure in patients receiving bPI and the determinants of failure in these patients remain unknown. There is evidence that Gag can impact PI susceptibility. Here, we have sequenced Gag-Protease before and following failure in 23 patients in the SARA trial infected with subtypes A, C, and D viruses. Before bPI, significant variation in Protease and Gag was observed at positions previously associated with PI exposure and resistance including Gag mutations L449P, S451N, and L453P and Protease K20I and L63P. Following PI failure, previously described mutations in Protease and Gag were observed, including those at the cleavage sites such as R361K and P453L. However, the emergence of clear genetic determinants of therapy failure across patients was not observed. Larger Gag sequence datasets will be required to comprehensively identify mutational correlates of bPI failure across subtypes

Regulation of phosphorylase kinase by low concentrations of Ca ions upon muscle contraction: the connection between metabolism and muscle contraction and the connection between muscle physiology and Ca-dependent signal transduction

It had long been one of the crucial questions in muscle physiology how glycogenolysis is regulated in connection with muscle contraction, when we found the answer to this question in the last half of the 1960s. By that time, the two principal currents of muscle physiology, namely, the metabolic flow starting from glycogen and the mechanisms of muscle contraction, had already been clarified at the molecular level thanks to our senior researchers. Thus, the final question we had to answer was how to connect these two currents. We found that low concentrations of Ca ions (10−7–10−4 M) released from the sarcoplasmic reticulum for the regulation of muscle contraction simultaneously reversibly activate phosphorylase kinase, the enzyme regulating glycogenolysis. Moreover, we found that adenosine 3′,5′-monophosphate (cyclic AMP), which is already known to activate muscle phosphorylase kinase, is not effective in the absence of such concentrations of Ca ions. Thus, cyclic AMP is not effective by itself alone and only modifies the activation process in the presence of Ca ions (at that time, cyclic AMP-dependent protein kinase had not yet been identified). After a while, it turned out that our works have not only provided the solution to the above problem on muscle physiology, but have also been considered as the first report of Ca-dependent protein phosphorylation, which is one of the central problems in current cell biology. Phosphorylase kinase is the first protein kinase to phosphorylate a protein resulting in the change in the function of the phosphorylated protein, as shown by Krebs and Fischer. Our works further showed that this protein kinase is regulated in a Ca-dependent manner. Accordingly, our works introduced the concept of low concentrations of Ca ions, which were first identified as the regulatory substance of muscle contraction, to the vast field of Ca biology including signal transduction

The chemical enrichment of the ICM from hydrodynamical simulations

The study of the metal enrichment of the intra-cluster and inter-galactic media (ICM and IGM) represents a direct means to reconstruct the past history of star formation, the role of feedback processes and the gas-dynamical processes which determine the evolution of the cosmic baryons. In this paper we review the approaches that have been followed so far to model the enrichment of the ICM in a cosmological context. While our presentation will be focused on the role played by hydrodynamical simulations, we will also discuss other approaches based on semi-analytical models of galaxy formation, also critically discussing pros and cons of the different methods. We will first review the concept of the model of chemical evolution to be implemented in any chemo-dynamical description. We will emphasise how the predictions of this model critically depend on the choice of the stellar initial mass function, on the stellar life-times and on the stellar yields. We will then overview the comparisons presented so far between X-ray observations of the ICM enrichment and model predictions. We will show how the most recent chemo-dynamical models are able to capture the basic features of the observed metal content of the ICM and its evolution. We will conclude by highlighting the open questions in this study and the direction of improvements for cosmological chemo-dynamical models of the next generation.Comment: 25 pages, 11 figures, accepted for publication in Space Science Reviews, special issue "Clusters of galaxies: beyond the thermal view", Editor J.S. Kaastra, Chapter 18; work done by an international team at the International Space Science Institute (ISSI), Bern, organised by J.S. Kaastra, A.M. Bykov, S. Schindler & J.A.M. Bleeke

What Physical Processes Drive the Interstellar Medium in the Local Bubble?

Recent 3D high-resolution simulations of the interstellar medium in a star form- ing galaxy like the Milky Way show that supernova explosions are the main driver of the structure and evolution of the gas. Its physical state is largely controlled by turbulence due to the high Reynolds numbers of the average flows. For a constant supernova rate a dynam- ical equilibrium is established within 200 Myr of simulation as a consequence of the setup of a galactic fountain. The resulting interstellar medium reveals a typical density/pressure pattern, i.e. distribution of so-called gas phases, on scales of 500–700 pc, with interstellar bubbles being a common phenomenon just like the Local Bubble and the Loop I superbub- ble, which are assumed to be interacting. However, modeling the Local Bubble is special, because it is driven by a moving group, passing through its volume, as it is inferred from the analysis of Hipparcos data. A detailed analysis reveals that between 14 and 19 super- novae have exploded during the last 15 Myr. The age of the Local Bubble is derived from comparison with HI and UV absorption line data to be 14.5±0.7 Myr. We further predict the 0.4merging of the two bubbles in about 3 Myr from now, when the interaction shell starts to fragment. The Local Cloud and its companion HI clouds are the consequence of a dynamical instability in the interaction shell between the Local and the Loop I bubble

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Localization of the human Chromosome 5q genes Gabra-1, Gabrg-2, Il-4, Il-5 , and Irf-1 on mouse Chromosome 11

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46991/1/335_2004_Article_BF00350629.pd

Dust in Supernovae and Supernova Remnants II: Processing and survival

Observations have recently shown that supernovae are efficient dust factories, as predicted for a long time by theoretical models. The rapid evolution of their stellar progenitors combined with their efficiency in precipitating refractory elements from the gas phase into dust grains make supernovae the major potential suppliers of dust in the early Universe, where more conventional sources like Asymptotic Giant Branch (AGB) stars did not have time to evolve. However, dust yields inferred from observations of young supernovae or derived from models do not reflect the net amount of supernova-condensed dust able to be expelled from the remnants and reach the interstellar medium. The cavity where the dust is formed and initially resides is crossed by the high velocity reverse shock which is generated by the pressure of the circumstellar material shocked by the expanding supernova blast wave. Depending on grain composition and initial size, processing by the reverse shock may lead to substantial dust erosion and even complete destruction. The goal of this review is to present the state of the art about processing and survival of dust inside supernova remnants, in terms of theoretical modelling and comparison to observations