Spherical Hall algebra of Spec (Z)

We study an arithmetic analog of the Hall algebra of a curve, when the curve is replaced by the spectrum of the integers compactified at infinity. The role of vector bundles is played by lattices with quadratic forms. This algebra H consists of automorphic forms with respect to GL_n(Z), n>0, with multiplication given by the parabolic pseudo-Eisenstein series map. We concentrate on the subalgebra SH in H generated by functions on the Arakelov Picard group of Spec(Z). We identify H with a Feigin-Odesskii type shuffle algebra, with the function defining the shuffle algebra expressed through the Riemann zeta function. As an application we study relations in H. Quadratic relations express the functional equation for the Eisenstein-Maass series. We show that the space of additional cubic relations (lying an an appropriate completion of H and considered modulo rescaling), is identified with the space spanned by nontrivial zeroes of the zeta function

Phase diagram of two-lane driven diffusive systems

We consider a large class of two-lane driven diffusive systems in contact with reservoirs at their boundaries and develop a stability analysis as a method to derive the phase diagrams of such systems. We illustrate the method by deriving phase diagrams for the asymmetric exclusion process coupled to various second lanes: a diffusive lane; an asymmetric exclusion process with advection in the same direction as the first lane, and an asymmetric exclusion process with advection in the opposite direction. The competing currents on the two lanes naturally lead to a very rich phenomenology and we find a variety of phase diagrams. It is shown that the stability analysis is equivalent to an `extremal current principle' for the total current in the two lanes. We also point to classes of models where both the stability analysis and the extremal current principle fail

Spontaneous symmetry breaking in a two-lane model for bidirectional overtaking traffic

First we consider a unidirectional flux \omega_bar of vehicles each of which is characterized by its `natural' velocity v drawn from a distribution P(v). The traffic flow is modeled as a collection of straight `world lines' in the time-space plane, with overtaking events represented by a fixed queuing time tau imposed on the overtaking vehicle. This geometrical model exhibits platoon formation and allows, among many other things, for the calculation of the effective average velocity w=\phi(v) of a vehicle of natural velocity v. Secondly, we extend the model to two opposite lanes, A and B. We argue that the queuing time \tau in one lane is determined by the traffic density in the opposite lane. On the basis of reasonable additional assumptions we establish a set of equations that couple the two lanes and can be solved numerically. It appears that above a critical value \omega_bar_c of the control parameter \omega_bar the symmetry between the lanes is spontaneously broken: there is a slow lane where long platoons form behind the slowest vehicles, and a fast lane where overtaking is easy due to the wide spacing between the platoons in the opposite direction. A variant of the model is studied in which the spatial vehicle density \rho_bar rather than the flux \omega_bar is the control parameter. Unequal fluxes \omega_bar_A and \omega_bar_B in the two lanes are also considered. The symmetry breaking phenomenon exhibited by this model, even though no doubt hard to observe in pure form in real-life traffic, nevertheless indicates a tendency of such traffic.Comment: 50 pages, 16 figures; extra references adde

Spontaneous pulsing states in an active particle system

International audienc

Eigenfunctions of GL(N,\RR) Toda chain: The Mellin-Barnes representation

The recurrent relations between the eigenfunctions for GL(N,\RR) and GL(N-1,\RR) quantum Toda chains is derived. As a corollary, the Mellin-Barnes integral representation for the eigenfunctions of a quantum open Toda chain is constructed for the $N$-particle case.Comment: Latex+amssymb.sty, 7 pages; corrected some typos published in Pis'ma v ZhETF (2000), vol. 71, 338-34

The validation of pharmacogenetics for the identification of Fabry patients to be treated with migalastat

PURPOSE: Fabry disease is an X-linked lysosomal storage disorder caused by mutations in the α-galactosidase A gene. Migalastat, a pharmacological chaperone, binds to specific mutant forms of α-galactosidase A to restore lysosomal activity. METHODS: A pharmacogenetic assay was used to identify the α-galactosidase A mutant forms amenable to migalastat. Six hundred Fabry disease-causing mutations were expressed in HEK-293 (HEK) cells; increases in α-galactosidase A activity were measured by a good laboratory practice (GLP)-validated assay (GLP HEK/Migalastat Amenability Assay). The predictive value of the assay was assessed based on pharmacodynamic responses to migalastat in phase II and III clinical studies. RESULTS: Comparison of the GLP HEK assay results in in vivo white blood cell α-galactosidase A responses to migalastat in male patients showed high sensitivity, specificity, and positive and negative predictive values (≥0.875). GLP HEK assay results were also predictive of decreases in kidney globotriaosylceramide in males and plasma globotriaosylsphingosine in males and females. The clinical study subset of amenable mutations (n = 51) was representative of all 268 amenable mutations identified by the GLP HEK assay. CONCLUSION: The GLP HEK assay is a clinically validated method of identifying male and female Fabry patients for treatment with migalastat

Heat and moisture exchangers (HMEs) and heated humidifiers (HHs) in adult critically ill patients: a systematic review, meta-analysis and meta-regression of randomized controlled trials

The aims of this systematic review and meta-analysis of randomized controlled trials are to evaluate the effects of active heated humidifiers (HHs) and moisture exchangers (HMEs) in preventing artificial airway occlusion and pneumonia, and on mortality in adult critically ill patients. In addition, we planned to perform a meta-regression analysis to evaluate the relationship between the incidence of artificial airway occlusion, pneumonia and mortality and clinical features of adult critically ill patients