Contact and voter processes on the infinite percolation cluster as models of host-symbiont interactions

We introduce spatially explicit stochastic processes to model multispecies host-symbiont interactions. The host environment is static, modeled by the infinite percolation cluster of site percolation. Symbionts evolve on the infinite cluster through contact or voter type interactions, where each host may be infected by a colony of symbionts. In the presence of a single symbiont species, the condition for invasion as a function of the density of the habitat of hosts and the maximal size of the colonies is investigated in details. In the presence of multiple symbiont species, it is proved that the community of symbionts clusters in two dimensions whereas symbiont species may coexist in higher dimensions.Comment: Published in at http://dx.doi.org/10.1214/10-AAP734 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Survival, extinction and approximation of discrete-time branching random walks

We consider a general discrete-time branching random walk on a countable set X. We relate local, strong local and global survival with suitable inequalities involving the first-moment matrix M of the process. In particular we prove that, while the local behavior is characterized by M, the global behavior cannot be completely described in terms of properties involving M alone. Moreover we show that locally surviving branching random walks can be approximated by sequences of spatially confined and stochastically dominated branching random walks which eventually survive locally if the (possibly finite) state space is large enough. An analogous result can be achieved by approximating a branching random walk by a sequence of multitype contact processes and allowing a sufficiently large number of particles per site. We compare these results with the ones obtained in the continuous-time case and we give some examples and counterexamples.Comment: 32 pages, a few misprints have been correcte

Some results and problems for anisotropic random walks on the plane

This is an expository paper on the asymptotic results concerning path behaviour of the anisotropic random walk on the two-dimensional square lattice Z^2. In recent years Mikl\'os and the authors of the present paper investigated the properties of this random walk concerning strong approximations, local times and range. We give a survey of these results together with some further problems.Comment: 20 page

Characterization of the critical values of branching random walks on weighted graphs through infinite-type branching processes

We study the branching random walk on weighted graphs; site-breeding and edge-breeding branching random walks on graphs are seen as particular cases. We describe the strong critical value in terms of a geometrical parameter of the graph. We characterize the weak critical value and relate it to another geometrical parameter. We prove that, at the strong critical value, the process dies out locally almost surely; while, at the weak critical value, global survival and global extinction are both possible.Comment: 14 pages, corrected some typos and minor mistake

Survival of branching random walks in random environment

We study survival of nearest-neighbour branching random walks in random environment (BRWRE) on ${\mathbb Z}$. A priori there are three different regimes of survival: global survival, local survival, and strong local survival. We show that local and strong local survival regimes coincide for BRWRE and that they can be characterized with the spectral radius of the first moment matrix of the process. These results are generalizations of the classification of BRWRE in recurrent and transient regimes. Our main result is a characterization of global survival that is given in terms of Lyapunov exponents of an infinite product of i.i.d. $2\times 2$ random matrices.Comment: 17 pages; to appear in Journal of Theoretical Probabilit

New value from food and industrial wastes - bioaccumulation of omega-3 fatty acids from an oleaginous microbial biomass paired with a brewery by-product using black soldier fly (Hermetia illucens) larvae.

Research on bioconversion based on insects is intensifying as it addresses the problem of reducing and reusing food and industrial waste. To reach this goal, we need to find more means of pairing waste to insects. With this goal, brewers\u2019 spent grains (BSG) - a food waste of the brewing industry - paired with the oleaginous biomass of the thraustochytrid Schizochytrium limacinum cultivated on crude glycerol - a major waste of biodiesel production - were successfully used to grow Hermetia illucens larvae. Combining BSG and S. limacinum in the diet in an attempt to design the lipid profile of H. illucens larvae to contain a higher percentage of omega-3 fatty acids is novel. Insect larvae were grown on three different substrates: i) standard diet for Diptera (SD), ii) BSG, and iii) BSG + 10% S. limacinum biomass. The larvae and substrates were analyzed for fatty acid composition and larval growth was measured until 25% of insects reached the prepupal stage. Our data showed that including omega-3-rich S. limacinum biomass in the BSG substrate promoted an increase in larval weight compared to larvae fed on SD or BSG substrates. Furthermore, it was possible, albeit in a limited way, to incorporate omega-3 fatty acids, principally docosahexaenoic acid (DHA) from BSG + S. limacinum substrate containing 20% of DHA into the larval fat (7% DHA). However, H. illucens with this level of DHA may not be suitable if the aim is to get larvae with high omega-3 lipids to feed carnivorous fish

Random walks on graphs: ideas, techniques and results

Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and new ideas have been introduced, which can be fruitfully extended to different areas and disciplines. Here we aim at giving a brief but comprehensive perspective of these progresses, with a particular emphasis on physical aspects.Comment: LateX file, 34 pages, 13 jpeg figures, Topical Revie

Random walks on combs

We develop techniques to obtain rigorous bounds on the behaviour of random walks on combs. Using these bounds we calculate exactly the spectral dimension of random combs with infinite teeth at random positions or teeth with random but finite length. We also calculate exactly the spectral dimension of some fixed non-translationally invariant combs. We relate the spectral dimension to the critical exponent of the mass of the two-point function for random walks on random combs, and compute mean displacements as a function of walk duration. We prove that the mean first passage time is generally infinite for combs with anomalous spectral dimension.Comment: 42 pages, 4 figure

RISC-mediated control of selected chromatin regulators stabilizes ground state pluripotency of mouse embryonic stem cells.

BACKGROUND: Embryonic stem cells are intrinsically unstable and differentiate spontaneously if they are not shielded from external stimuli. Although the nature of such instability is still controversial, growing evidence suggests that protein translation control may play a crucial role. RESULTS: We performed an integrated analysis of RNA and proteins at the transition between naïve embryonic stem cells and cells primed to differentiate. During this transition, mRNAs coding for chromatin regulators are specifically released from translational inhibition mediated by RNA-induced silencing complex (RISC). This suggests that, prior to differentiation, the propensity of embryonic stem cells to change their epigenetic status is hampered by RNA interference. The expression of these chromatin regulators is reinstated following acute inactivation of RISC and it correlates with loss of stemness markers and activation of early cell differentiation markers in treated embryonic stem cells. CONCLUSIONS: We propose that RISC-mediated inhibition of specific sets of chromatin regulators is a primary mechanism for preserving embryonic stem cell pluripotency while inhibiting the onset of embryonic developmental programs.This work was funded by: FIRB RBAP10L8TY (MIUR), Fondazione Roma and PAINCAGE FP7 Collaborative Project number 603191 (RB,MD); Flagship Project InterOmics PB.05 and MIUR-PRIN-2012 (FC); Wellcome Trust Core Grant reference 092096 and Cancer Research UK Grant Reference C6946/A14492 (LP); CRUK-Cambridge Institute Core Grant reference C14303/A17197 (DB)