Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter H > 1/2. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann¿Stieltjes integral.

Criteria for hitting probabilities with applications to systems of stochastic wave equations

We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these results to a system of stochastic wave equations in spatial dimension k >- 1 driven by a d-dimensional spatially homogeneous additive Gaussian noise that is white in time and colored in space.

Stochastic differential equations with random coefficients

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of the Stratonovich integral.

Large deviations for stochastic Volterra equations

This paper is devoted to prove a large-deviation principle for solutions to multidimensional stochastic Volterra equations.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Pom1 regulates the assembly of Cdr2-Mid1 cortical nodes for robust spatial control of cytokinesis.

Proper division plane positioning is essential to achieve faithful DNA segregation and to control daughter cell size, positioning, or fate within tissues. In Schizosaccharomyces pombe, division plane positioning is controlled positively by export of the division plane positioning factor Mid1/anillin from the nucleus and negatively by the Pom1/DYRK (dual-specificity tyrosine-regulated kinase) gradients emanating from cell tips. Pom1 restricts to the cell middle cortical cytokinetic ring precursor nodes organized by the SAD-like kinase Cdr2 and Mid1/anillin through an unknown mechanism. In this study, we show that Pom1 modulates Cdr2 association with membranes by phosphorylation of a basic region cooperating with the lipid-binding KA-1 domain. Pom1 also inhibits Cdr2 interaction with Mid1, reducing its clustering ability, possibly by down-regulation of Cdr2 kinase activity. We propose that the dual regulation exerted by Pom1 on Cdr2 prevents Cdr2 assembly into stable nodes in the cell tip region where Pom1 concentration is high, which ensures proper positioning of cytokinetic ring precursors at the cell geometrical center and robust and accurate division plane positioning.

Predicting the deleterious effects of mutation load in fragmented populations.

Human-induced habitat fragmentation constitutes a major threat to biodiversity. Both genetic and demographic factors combine to drive small and isolated populations into extinction vortices. Nevertheless, the deleterious effects of inbreeding and drift load may depend on population structure, migration patterns, and mating systems and are difficult to predict in the absence of crossing experiments. We performed stochastic individual-based simulations aimed at predicting the effects of deleterious mutations on population fitness (offspring viability and median time to extinction) under a variety of settings (landscape configurations, migration models, and mating systems) on the basis of easy-to-collect demographic and genetic information. Pooling all simulations, a large part (70%) of variance in offspring viability was explained by a combination of genetic structure (F(ST)) and within-deme heterozygosity (H(S)). A similar part of variance in median time to extinction was explained by a combination of local population size (N) and heterozygosity (H(S)). In both cases the predictive power increased above 80% when information on mating systems was available. These results provide robust predictive models to evaluate the viability prospects of fragmented populations.

Stochastic models and numerical algorithms for a class of regulatory gene networks.

Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.

Immunization with HIV Gag targeted to dendritic cells followed by recombinant New York vaccinia virus induces robust T-cell immunity in nonhuman primates.

Protein vaccines, if rendered immunogenic, would facilitate vaccine development against HIV and other pathogens. We compared in nonhuman primates (NHPs) immune responses to HIV Gag p24 within 3G9 antibody to DEC205 ("DEC-HIV Gag p24"), an uptake receptor on dendritic cells, to nontargeted protein, with or without poly ICLC, a synthetic double stranded RNA, as adjuvant. Priming s.c. with 60 μg of both HIV Gag p24 vaccines elicited potent CD4(+) T cells secreting IL-2, IFN-γ, and TNF-α, which also proliferated. The responses increased with each of three immunizations and recognized multiple Gag peptides. DEC-HIV Gag p24 showed better cross-priming for CD8(+) T cells, whereas the avidity of anti-Gag antibodies was ∼10-fold higher with nontargeted Gag 24 protein. For both protein vaccines, poly ICLC was essential for T- and B-cell immunity. To determine whether adaptive responses could be further enhanced, animals were boosted with New York vaccinia virus (NYVAC)-HIV Gag/Pol/Nef. Gag-specific CD4(+) and CD8(+) T-cell responses increased markedly after priming with both protein vaccines and poly ICLC. These data reveal qualitative differences in antibody and T-cell responses to DEC-HIV Gag p24 and Gag p24 protein and show that prime boost with protein and adjuvant followed by NYVAC elicits potent cellular immunity.

Out-of-sample forecast tests robust to the choice of window size

This paper proposes new methodologies for evaluating out-of-sample forecastingperformance that are robust to the choice of the estimation window size. The methodologies involve evaluating the predictive ability of forecasting models over a wide rangeof window sizes. We show that the tests proposed in the literature may lack the powerto detect predictive ability and might be subject to data snooping across differentwindow sizes if used repeatedly. An empirical application shows the usefulness of themethodologies for evaluating exchange rate models' forecasting ability.

On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management

The choice network revenue management (RM) model incorporates customer purchase behavioras customers purchasing products with certain probabilities that are a function of the offeredassortment of products, and is the appropriate model for airline and hotel network revenuemanagement, dynamic sales of bundles, and dynamic assortment optimization. The underlyingstochastic dynamic program is intractable and even its certainty-equivalence approximation, inthe form of a linear program called Choice Deterministic Linear Program (CDLP) is difficultto solve in most cases. The separation problem for CDLP is NP-complete for MNL with justtwo segments when their consideration sets overlap; the affine approximation of the dynamicprogram is NP-complete for even a single-segment MNL. This is in contrast to the independentclass(perfect-segmentation) case where even the piecewise-linear approximation has been shownto be tractable. In this paper we investigate the piecewise-linear approximation for network RMunder a general discrete-choice model of demand. We show that the gap between the CDLP andthe piecewise-linear bounds is within a factor of at most 2. We then show that the piecewiselinearapproximation is polynomially-time solvable for a fixed consideration set size, bringing itinto the realm of tractability for small consideration sets; small consideration sets are a reasonablemodeling tradeoff in many practical applications. Our solution relies on showing that forany discrete-choice model the separation problem for the linear program of the piecewise-linearapproximation can be solved exactly by a Lagrangian relaxation. We give modeling extensionsand show by numerical experiments the improvements from using piecewise-linear approximationfunctions.

Fast Approximation of Nonlinearities for improving inversion algorithms of PNL mixtures and Wiener systems

This paper proposes a very fast method for blindly approximating a nonlinear mapping which transforms a sum of random variables. The estimation is surprisingly good even when the basic assumption is not satisfied.We use the method for providing a good initialization for inverting post-nonlinear mixtures and Wiener systems. Experiments show that the algorithm speed is strongly improved and the asymptotic performance is preserved with a very low extra computational cost.