Survival of a diffusing particle in an expanding cage

We consider a Brownian particle, with diffusion constant D, moving inside an expanding d-dimensional sphere whose surface is an absorbing boundary for the particle. The sphere has initial radius L_0 and expands at a constant rate c. We calculate the joint probability density, p(r,t|r_0), that the particle survives until time t, and is at a distance r from the centre of the sphere, given that it started at a distance r_0 from the centre.Comment: 5 page

Définition du « mot » et de la « phrase »

Les définitions de la phrase proposées par Hermann Paul et Wilhelm Wundt ignorent le fait que nous savons tous faire la différence entre un mot, un groupe de mots et une phrase. Après avoir rappelé que les quatre constituants obligés de tout acte de langage dans un contexte social sont : (i) le locuteur, (ii) l’auditeur, (iii) ce dont il est parlé, (iv) les signes verbaux utilisés, alias les « mots », le mot est défini comme « un signe-son articulé dont la fonction est de dénoter quelque chose dont il est parlé », et la phrase « un signe-son articulé dont la fonction est de représenter l’intentionnalité du locuteur face à l’auditeur », et le sens de la phrase, « ce que le locuteur a l’intention de faire comprendre à l’auditeur ». Le compte rendu d’un article de Karl Bühler (1918) offre la première présentation en anglais de l’organon.The definitions of the sentence proposed by Hermann Paul and William Wundt fail to take into account that we all know instinctively the difference between a word and a sentence. It must not be forgotten that the 4 obligatory constituents of all speech acts in a social context are (i) the speaker, (ii) the hearer , (iii) the thing spoken of (iv) the verbal symbols or words used. The word is then defined as “an articulate sound-symbol in its aspect of denoting something which is spoken about” and a sentence “an articulate sound-symbol in its aspect of embodying some volitional attitude of the speaker towards the listener”. In a postscript Karl Bühler’s organon is presented as a viable model

Modeling the Insulin-Like Growth Factor System in Articular Cartilage

IGF signaling is involved in cell proliferation, differentiation and apoptosis in a wide range of tissues, both normal and diseased, and so IGF-IR has been the focus of intense interest as a promising drug target. In this computational study on cartilage, we focus on two questions: (i) what are the key factors influencing IGF-IR complex formation, and (ii) how might cells regulate IGF-IR complex formation? We develop a reaction-diffusion computational model of the IGF system involving twenty three parameters. A series of parametric and sensitivity studies are used to identify the key factors influencing IGF signaling. From the model we predict the free IGF and IGF-IR complex concentrations throughout the tissue. We estimate the degradation half-lives of free IGF-I and IGFBPs in normal cartilage to be 20 and 100 mins respectively, and conclude that regulation of the IGF half-life, either directly or indirectly via extracellular matrix IGF-BP protease concentrations, are two critical factors governing the IGF-IR complex formation in the cartilage. Further we find that cellular regulation of IGF-II production, the IGF-IIR concentration and its clearance rate, all significantly influence IGF signaling. It is likely that negative feedback processes via regulation of these factors tune IGF signaling within a tissue, which may help explain the recent failures of single target drug therapies aimed at modifying IGF signaling.National Health and Medical Research Council (Australia) (APP1051455

Intrinsic noise and discrete-time processes

A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For finite populations an approximate Gaussian scheme is devised to describe the stochastic fluctuations in the non-chaotic regime. More generally, the stochastic dynamics can be captured using a stochastic difference equation, derived through an approximation to the Markov chain. The scheme is demonstrated using the logistic map as a case study.Comment: Modified version accepted for publication in Phys. Rev. E Rapid Communications. New figures adde

Reduction of a metapopulation genetic model to an effective one island model

We explore a model of metapopulation genetics which is based on a more ecologically motivated approach than is frequently used in population genetics. The size of the population is regulated by competition between individuals, rather than by artificially imposing a fixed population size. The increased complexity of the model is managed by employing techniques often used in the physical sciences, namely exploiting time-scale separation to eliminate fast variables and then constructing an effective model from the slow modes. Remarkably, an initial model with 2$\mathcal{D}$ variables, where $\mathcal{D}$ is the number of islands in the metapopulation, can be reduced to a model with a single variable. We analyze this effective model and show that the predictions for the probability of fixation of the alleles and the mean time to fixation agree well with those found from numerical simulations of the original model.Comment: 16 pages, 4 figures. Supplementary material: 22 pages, 3 figure

Vicious Walkers in a Potential

We consider N vicious walkers moving in one dimension in a one-body potential v(x). Using the backward Fokker-Planck equation we derive exact results for the asymptotic form of the survival probability Q(x,t) of vicious walkers initially located at (x_1,...,x_N) = x, when v(x) is an arbitrary attractive potential. Explicit results are given for a square-well potential with absorbing or reflecting boundary conditions at the walls, and for a harmonic potential with an absorbing or reflecting boundary at the origin and the walkers starting on the positive half line. By mapping the problem of N vicious walkers in zero potential onto the harmonic potential problem, we rederive the results of Fisher [J. Stat. Phys. 34, 667 (1984)] and Krattenthaler et al. [J. Phys. A 33}, 8835 (2000)] respectively for vicious walkers on an infinite line and on a semi-infinite line with an absorbing wall at the origin. This mapping also gives a new result for vicious walkers on a semi-infinite line with a reflecting boundary at the origin: Q(x,t) \sim t^{-N(N-1)/2}.Comment: 5 page