Self-Similar Random Processes and Infinite-Dimensional Configuration Spaces

We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary representations of the diffeomorphism group, which are important to nonrelativistic quantum statistical physics and to the quantum theory of extended objects in d-dimensional Euclidean space. Special attention is given to measurable structure and topology underlying measures on generalized configuration spaces obtained from self-similar random processes (both for d = 1 and d > 1), which describe infinite point configurations having accumulation points

Unconstrained Astrometric Orbits for Hipparcos Stars with Stochastic Solutions

A considerable number of astrometric binaries whose positions on the sky do not obey the standard model of mean position, parallax and linear proper motion, were observed by the Hipparcos satellite. Some of them remain non-discovered, and their observational data have not been properly processed with the more adequate astrometric model that includes nonlinear orbital motion. We develop an automated algorithm based on "genetic optimization", to solve the orbital fitting problem with no prior information about the orbital elements is available (from, e.g., spectroscopic data or radial velocity monitoring). We test this method on Hipparcos stars with known orbital solutions in the catalog, and further apply it to stars with stochastic solutions, which may be unresolved binaries. At a confidence level of 99%, orbital fits are obtained for 65 stars, most of which have not been known as binary. A few of the new probable binaries with A-type primaries with periods 444-2015 d are chemically peculiar stars, including Ap and \lambda Boo type. The anomalous spectra of these stars are explained as admixture of the light from the unresolved, sufficiently bright and massive companions. We estimate the apparent orbits of four stars which have been identified as members of the 300 Myr-old UMa kinematic group. Another four new nearby binaries may include low-mass M-type or brown dwarf companions. Similar astrometric models and algorithms can be used for binary stars and planet hosts observed by SIM PlanetQuest and Gaia

On the virial coefficients of nonabelian anyons

We study a system of nonabelian anyons in the lowest Landau level of a strong magnetic field. Using diagrammatic techniques, we prove that the virial coefficients do not depend on the statistics parameter. This is true for all representations of all nonabelian groups for the statistics of the particles and relies solely on the fact that the effective statistical interaction is a traceless operator.Comment: 9 pages, 3 eps figure

Inactivation of cloned Na channels expressed in Xenopus oocytes

This study investigates the inactivation properties of Na channels expressed in Xenopus oocytes from two rat IIA Na channel cDNA clones differing by a single amino acid residue. Although the two cDNAs encode Na channels with substantially different activation properties (Auld, V. J., A. L. Goldin, D. S. Krafte, J. Marshall, J. M. Dunn, W. A. Catterall, H. A. Lester, N. Davidson, and R. J. Dunn. 1988. Neuron. 1:449-461), their inactivation properties resemble each other strongly but differ markedly from channels induced by poly(A+) rat brain RNA. Rat IIA currents inactivate more slowly, recover from inactivation more slowly, and display a steady-state voltage dependence that is shifted to more positive potentials. The macroscopic inactivation process for poly(A+) Na channels is defined by a single exponential time course; that for rat IIA channels displays two exponential components. At the single-channel level these differences in inactivation occur because rat IIA channels reopen several times during a depolarizing pulse; poly(A+) channels do not. Repetitive stimulation (greater than 1 Hz) produces a marked decrement in the rat IIA peak current and changes the waveform of the currents. When low molecular weight RNA is coinjected with rat IIA RNA, these inactivation properties are restored to those that characterize poly(A+) channels. Slow inactivation is similar for rat IIA and poly(A+) channels, however. The data suggest that activation and inactivation involve at least partially distinct regions of the channel protein

Voltage-gated sodium channels (NaV) in GtoPdb v.2021.3

Sodium channels are voltage-gated sodium-selective ion channels present in the membrane of most excitable cells. Sodium channels comprise of one pore-forming α subunit, which may be associated with either one or two β subunits [177]. α-Subunits consist of four homologous domains (I-IV), each containing six transmembrane segments (S1-S6) and a pore-forming loop. The positively charged fourth transmembrane segment (S4) acts as a voltage sensor and is involved in channel gating. The crystal structure of the bacterial NavAb channel has revealed a number of novel structural features compared to earlier potassium channel structures including a short selectivity filter with ion selectivity determined by interactions with glutamate side chains [274]. Interestingly, the pore region is penetrated by fatty acyl chains that extend into the central cavity which may allow the entry of small, hydrophobic pore-blocking drugs [274]. Auxiliary β1, β2, β3 and β4 subunits consist of a large extracellular N-terminal domain, a single transmembrane segment and a shorter cytoplasmic domain.The nomenclature for sodium channels was proposed by Goldin et al., (2000) [144] and approved by the NC-IUPHAR Subcommittee on sodium channels (Catterall et al., 2005, [52])

Voltage-gated sodium channels (version 2019.4) in the IUPHAR/BPS Guide to Pharmacology Database

Sodium channels are voltage-gated sodium-selective ion channels present in the membrane of most excitable cells. Sodium channels comprise of one pore-forming α subunit, which may be associated with either one or two β subunits [176]. α-Subunits consist of four homologous domains (I–IV), each containing six transmembrane segments (S1–S6) and a pore-forming loop. The positively charged fourth transmembrane segment (S4) acts as a voltage sensor and is involved in channel gating. The crystal structure of the bacterial NavAb channel has revealed a number of novel structural features compared to earlier potassium channel structures including a short selectivity filter with ion selectivity determined by interactions with glutamate side chains [268]. Interestingly, the pore region is penetrated by fatty acyl chains that extend into the central cavity which may allow the entry of small, hydrophobic pore-blocking drugs [268]. Auxiliary β1, β2, β3 and β4 subunits consist of a large extracellular N-terminal domain, a single transmembrane segment and a shorter cytoplasmic domain.The nomenclature for sodium channels was proposed by Goldin et al., (2000) [143] and approved by the NC-IUPHAR Subcommittee on sodium channels (Catterall et al., 2005, [51])

Voltage-gated sodium channels (NaV) in GtoPdb v.2023.1

Sodium channels are voltage-gated sodium-selective ion channels present in the membrane of most excitable cells. Sodium channels comprise of one pore-forming α subunit, which may be associated with either one or two β subunits [179]. α-Subunits consist of four homologous domains (I-IV), each containing six transmembrane segments (S1-S6) and a pore-forming loop. The positively charged fourth transmembrane segment (S4) acts as a voltage sensor and is involved in channel gating. The crystal structure of the bacterial NavAb channel has revealed a number of novel structural features compared to earlier potassium channel structures including a short selectivity filter with ion selectivity determined by interactions with glutamate side chains [278]. Interestingly, the pore region is penetrated by fatty acyl chains that extend into the central cavity which may allow the entry of small, hydrophobic pore-blocking drugs [278]. Auxiliary β1, β2, β3 and β4 subunits consist of a large extracellular N-terminal domain, a single transmembrane segment and a shorter cytoplasmic domain.The nomenclature for sodium channels was proposed by Goldin et al., (2000) [146] and approved by the NC-IUPHAR Subcommittee on sodium channels (Catterall et al., 2005, [53])

Oscillatory instabilities in d.c. biased quantum dots

We consider a `quantum dot' in the Coulomb blockade regime, subject to an arbitrarily large source-drain voltage V. When V is small, quantum dots with odd electron occupation display the Kondo effect, giving rise to enhanced conductance. Here we investigate the regime where V is increased beyond the Kondo temperature and the Kondo resonance splits into two components. It is shown that interference between them results in spontaneous oscillations of the current through the dot. The theory predicts the appearance of ``Shapiro steps'' in the current-voltage characteristics of an irradiated quantum dot; these would constitute an experimental signature of the predicted effect.Comment: Four pages with embedded figure