Classical results from spectral theory of stationary linear kinetic equations are applied to efficiently approximate two physically relevant weakly nonlinear kinetic models: a model of chemotaxis involving a biased velocity-redistribution integral term, and a Vlasov-Fokker-Planck (VFP) system. Both are coupled to an attractive elliptic equation producing corresponding mean-field potentials.

Vaccination is the most successful and cost-effective method to prevent infectious diseases. However, many vaccine antigens have poor in vivo immunogenic potential and need adjuvants to enhance immune response. The application of systems biology to immunity and vaccinology has yielded crucial insights about how vaccines and adjuvants work. We have previously characterized two safe and powerful delivery systems derived from non-pathogenic prokaryotic organisms: E2 and fd filamentous bacteriophage systems.

Within the framework of general relativity, we investigate the tidal acceleration of astrophysical jets relative to the central collapsed configuration ("Kerr source"). To simplify matters, we neglect electromagnetic forces throughout; however, these must be included in a complete analysis. The rest frame of the Kerr source is locally defined via the set of hypothetical static observers in the spacetime exterior to the source.

Volterra Integral Equations (VIEs) arise in many problems of real life, as, for example, feedback control theory, population dynamics and fluid dynamics. A reliable numerical simulation of these phenomena requires a careful analysis of the long time behavior of the numerical solution. Here we develop a numerical stability theory for Direct Quadrature (DQ) methods which applies to a quite general and representative class of problems. We obtain stability results under some conditions on the stepsize and, in particular cases, unconditional stability for DQ methods of whatever order.

We estimate the error of Gauss-Jacobi quadrature rule applied to a function f, which is supposed locally absolutely continuous in some Besov type spaces, or of bounded variation on [-1,1]. In the first case the error bound concerns the weighted main part phi-modulus of smoothness of f introduced by Z. Ditzian and V. Totik, while in the second case we deal with a Stieltjes integral with respect to f.

Comparison results for solutions to the Dirichlet problems for a class of nonlinear, anisotropic parabolic equations are established. These results are obtained through a semidiscretization method in time after providing estimates for solutions to anisotropic elliptic problems with zero-order terms.

Hypomorphic mutations in DNA-methyltransferase DNMT3B cause majority of the rare disorder Immunodeficiency, Centromere instability and Facial anomalies syndrome cases (ICF1). By unspecified mechanisms, mutant-DNMT3B interferes with lymphoid-specific pathways resulting in immune response defects. Interestingly, recent findings report that DNMT3B shapes intragenic CpG-methylation of highly-transcribed genes. However, how the DNMT3B-dependent epigenetic network modulates transcription and whether ICF1-specific mutations impair this process remains unknown.