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1.
The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual. 相似文献
2.
Interactions of Pt‐ttpy with G‐Quadruplexes Originating from Promoter Region of the c‐myc Gene Deciphered by NMR and Gel Electrophoresis Analysis
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Denis Kudryavtsev Anastasia Isaeva Daria Barkova Ekaterina Spirova Renata Mukhutdinova Igor Kasheverov Victor Tsetlin 《Molecules (Basel, Switzerland)》2021,26(5)
Slow-channel congenital myasthenic syndromes (SCCMSs) are rare genetic diseases caused by mutations in muscle nicotinic acetylcholine receptor (nAChR) subunits. Most of the known SCCMS-associated mutations localize at the transmembrane region near the ion pore. Only two SCCMS point mutations are at the extracellular domains near the acetylcholine binding site, α1(G153S) being one of them. In this work, a combination of molecular dynamics, targeted mutagenesis, fluorescent Ca2+ imaging and patch-clamp electrophysiology has been applied to G153S mutant muscle nAChR to investigate the role of hydrogen bonds formed by Ser 153 with C-loop residues near the acetylcholine-binding site. Introduction of L199T mutation to the C-loop in the vicinity of Ser 153 changed hydrogen bonds distribution, decreased acetylcholine potency (EC50 2607 vs. 146 nM) of the double mutant and decay kinetics of acetylcholine-evoked cytoplasmic Ca2+ rise (τ 14.2 ± 0.3 vs. 34.0 ± 0.4 s). These results shed light on molecular mechanisms of nAChR activation-desensitization and on the involvement of such mechanisms in channelopathy genesis. 相似文献
5.
Peter Imkeller 《Probability Theory and Related Fields》1996,106(1):105-135
Summary. The analytic treatment of problems related to the asymptotic behaviour of random dynamical systems generated by stochastic
differential equations suffers from the presence of non-adapted random invariant measures. Semimartingale theory becomes accessible
if the underlying Wiener filtration is enlarged by the information carried by the orthogonal projectors on the Oseledets spaces
of the (linearized) system.
We study the corresponding problem of preservation of the semimartingale property and the validity of a priori inequalities
between the norms of stochastic integrals in the enlarged filtration and norms of their quadratic variations in case the random
element F enlarging the filtration is real valued and possesses an absolutely continuous law. Applying the tools of Malliavin’s calculus,
we give smoothness conditions on F under which the semimartingale property is preserved and a priori martingale inequalities are valid.
Received: 12 April 1995 / In revised form: 7 March 1996 相似文献
6.
Summary In the analysis of discretization methods for stiff intial value problems, stability questions have received most part of the attention in the past.B-stability and the equivalent criterion algebraic stability are well known concepts for Runge-Kutta methods applied to dissipative problems. However, for the derivation ofB-convergence results — error bounds which are not affected by stiffness — it is not sufficient in many cases to requireB-stability alone. In this paper, necessary and sufficient conditions forB-convergence are determined.This paper was written while J. Schneid was visiting the Centre for Mathematics and Computer Science with an Erwin-Schrödinger stipend from the Fonds zur Förderung der wissenschaftlichen Forschung 相似文献
7.
Summary We present an approximation method of a space-homogeneous transport equation which we prove is convergent. The method is very promising for numerical computation. Comparison of a numerical computation with an exact solution is given for the Master equation. 相似文献
8.
Peter Dräxler 《Journal of Pure and Applied Algebra》2002,169(1):33-42
We show that the cleaving functors introduced in [Bautista et al., Invent. Math. 81 (1985) 217] as a tool for proving infinite representation type of finite-dimensional algebras can also be used to establish controlled wildness. The main application is that an algebra is controlled wild if there is an indecomposable projective module with a Loewy factor having a homogeneous direct summand which is of length at least 3. As a second application we derive Han's covering criterion. 相似文献
9.
In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimators and S-estimator through theoretical and simulation studies. The theory is illustrated by an example. 相似文献
10.
Michel Weber 《Transactions of the American Mathematical Society》2006,358(2):911-936
We apply a majorizing measure theorem of Talagrand to obtain uniform bounds for sums of random variables satisfying increment conditions of the type considered in Gál-Koksma Theorems. We give some applications.