828 research outputs found
Molecular Mechanism of the pH-Dependent Calcium Affinity in Langerin
The C-type lectin receptor langerin plays a vital role in the mammalian defense against invading pathogens. Its function hinges on the affinity to its co-factor Ca2+ which in turn is regulated by the pH. We studied the structural consequences of pro-tonating the allosteric pH-sensor histidine H294 by molecular dynamics simulations (total simulation time: about 120 μs) and Markov models. We discovered a mechanism in which the signal that the pH has dropped is transferred to the Ca2+-binding site without transferring the initial proton. Instead, protonation of H294 unlocks a conformation in which a protonated lysine side-chain forms a hydrogen bond with a Ca2+-coordinating aspartic acid. This destabilizes Ca2+ in the binding pocket, which we probed by steered molecular dynamics. After Ca2+-release, the proton is likely transferred to the aspartic acid and stabilized by a dyad with a nearby glutamic acid, triggering a conformational transition and thus preventing Ca2+-rebinding
Level density of a Fermi gas: average growth and fluctuations
We compute the level density of a two--component Fermi gas as a function of
the number of particles, angular momentum and excitation energy. The result
includes smooth low--energy corrections to the leading Bethe term (connected to
a generalization of the partition problem and Hardy--Ramanujan formula) plus
oscillatory corrections that describe shell effects. When applied to nuclear
level densities, the theory provides a unified formulation valid from
low--lying states up to levels entering the continuum. The comparison with
experimental data from neutron resonances gives excellent results.Comment: 4 pages, 1 figur
Зміна роздільної здатності зображень на основі власних векторів матриць-операторів індукованих з піксельних наборів
The method of problem solving increase resolution image sets provided that the
dimension of the set. The method is to build a matrix operator and find its
eigenvectors. Using sets of eigenvectors and matrix color images developed a practical set of algorithm changes the resolution
Fermi-Dirac statistics and the number theory
We relate the Fermi-Dirac statistics of an ideal Fermi gas in a harmonic trap
to partitions of given integers into distinct parts, studied in number theory.
Using methods of quantum statistical physics we derive analytic expressions for
cumulants of the probability distribution of the number of different
partitions.Comment: 7pages, 2 figures, epl.cls, revised versio
Finsler Conformal Lichnerowicz-Obata conjecture
We prove the Finsler analog of the conformal Lichnerowicz-Obata conjecture
showing that a complete and essential conformal vector field on a
non-Riemannian Finsler manifold is a homothetic vector field of a Minkowski
metric.Comment: 13 pages, 2 figures; the new version has only minor changes with
respect to v1, and is the version that will be published in Annales de
L'Institut Fourie
The type numbers of closed geodesics
A short survey on the type numbers of closed geodesics, on applications of
the Morse theory to proving the existence of closed geodesics and on the recent
progress in applying variational methods to the periodic problem for Finsler
and magnetic geodesicsComment: 29 pages, an appendix to the Russian translation of "The calculus of
variations in the large" by M. Mors
Spherical Casimir energies and Dedekind sums
Casimir energies on space-times having general lens spaces as their spatial
sections are shown to be given in terms of generalised Dedekind sums related to
Zagier's. These are evaluated explicitly in certain cases as functions of the
order of the lens space. An easily implemented recursion approach is used.Comment: 18 pages, 2 figures, v2:typos corrected, inessential equation in
Discussion altered. v3:typos corrected, 1 reference and comments added.
v4:typos corrected. Ancillary results added in an appendi
Special Functions Related to Dedekind Type DC-Sums and their Applications
In this paper we construct trigonometric functions of the sum T_{p}(h,k),
which is called Dedekind type DC-(Dahee and Changhee) sums. We establish
analytic properties of this sum. We find trigonometric representations of this
sum. We prove reciprocity theorem of this sums. Furthermore, we obtain
relations between the Clausen functions, Polylogarithm function, Hurwitz zeta
function, generalized Lambert series (G-series), Hardy-Berndt sums and the sum
T_{p}(h,k). We also give some applications related to these sums and functions
Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems
We report the results of certain integrations of quantum-theoretic interest,
relying, in this regard, upon recently developed parameterizations of Boya et
al of the n x n density matrices, in terms of squared components of the unit
(n-1)-sphere and the n x n unitary matrices. Firstly, we express the normalized
volume elements of the Bures (minimal monotone) metric for n = 2 and 3,
obtaining thereby "Bures prior probability distributions" over the two- and
three-state systems. Then, as an essential first step in extending these
results to n > 3, we determine that the "Hall normalization constant" (C_{n})
for the marginal Bures prior probability distribution over the
(n-1)-dimensional simplex of the n eigenvalues of the n x n density matrices
is, for n = 4, equal to 71680/pi^2. Since we also find that C_{3} = 35/pi, it
follows that C_{4} is simply equal to 2^{11} C_{3}/pi. (C_{2} itself is known
to equal 2/pi.) The constant C_{5} is also found. It too is associated with a
remarkably simple decompositon, involving the product of the eight consecutive
prime numbers from 2 to 23.
We also preliminarily investigate several cases, n > 5, with the use of
quasi-Monte Carlo integration. We hope that the various analyses reported will
prove useful in deriving a general formula (which evidence suggests will
involve the Bernoulli numbers) for the Hall normalization constant for
arbitrary n. This would have diverse applications, including quantum inference
and universal quantum coding.Comment: 14 pages, LaTeX, 6 postscript figures. Revised version to appear in
J. Phys. A. We make a few slight changes from the previous version, but also
add a subsection (III G) in which several variations of the basic problem are
newly studied. Rather strong evidence is adduced that the Hall constants are
related to partial sums of denominators of the even-indexed Bernoulli
numbers, although a general formula is still lackin
A natural Finsler--Laplace operator
We give a new definition of a Laplace operator for Finsler metric as an
average with regard to an angle measure of the second directional derivatives.
This definition uses a dynamical approach due to Foulon that does not require
the use of connections nor local coordinates. We show using 1-parameter
families of Katok--Ziller metrics that this Finsler--Laplace operator admits
explicit representations and computations of spectral data.Comment: 25 pages, v2: minor modifications, changed the introductio
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