Classical analogue of the statistical operator

We advance the notion of a classical density matrix, as a classical analogue of the quantum mechanical statistical operator, and investigate its main properties. In the case of composite systems a partial trace-like operation performed upon the global classical density matrix leads to a marginal density matrix describing a subsystem. In the case of dynamically independent subsystems (that is, non-interacting subsystems) this marginal density matrix evolves locally, its behavior being completely determined by the local phase-space flow associated with the subsystem under consideration. However, and in contrast with the case of ordinary marginal probability densities, the marginal classical density matrix contains information concerning the statistical correlations between a subsystem and the rest of the system.     

A note on the Stefanescu conjecture

We prove the existence of a magnetic field created by a planar configuration of piecewise rectilinear wires having no analytic first integral. This is a counterexample to the Stefanescu conjecture (Rev Roum Phys 31:701–721, 1986) in the analytic setting.     

The Zakai Equation of Nonlinear Filtering for Jump-Diffusion Observations: Existence and Uniqueness

In this paper we study a nonlinear filtering problem for a general Markovian partially observed system (X,Y), whose dynamics is modeled by correlated jump-diffusions having common jump times. At any time t∈[0,T], the σ-algebra $\mathcal{F}^{Y}_{t}:= \sigma\{ Y_{s}: s\leq t\}$ provides all the available information about the signal X _t . The central goal of stochastic filtering is to characterize the filter, π _t , which is the conditional distribution of X _t , given the observed data $\mathcal{F}^{Y}_{t}$ . In Ceci and Colaneri (Adv. Appl. Probab. 44(3):678–701, 2012) it is proved that π is the unique probability measure-valued process satisfying a nonlinear stochastic equation, the so-called Kushner-Stratonovich equation (in short KS equation). In this paper the aim is to improve the hypotheses to obtain the KS equation and describe the filter π in terms of the unnormalized filter ?, which is solution of a linear stochastic differential equation, the so-called Zakai equation. We prove the equivalence between strong uniqueness of the solution of the KS equation and strong uniqueness of the solution of the Zakai one and, as a consequence, we deduce pathwise uniqueness of the solution of the Zakai equation by applying the Filtered Martingale Problem approach (Kurtz and Ocone in Ann. Probab. 16:80–107, 1988; Ceci and Colaneri in Adv. Appl. Probab. 44(3):678–701, 2012). To conclude, we discuss some particular models.     

A condition of indecomposability for Butler \mathrm B (n)-groups

We give a manageable sufficient condition for indecomposability of Butler \(\mathrm B (n)\) -groups, allowing the easy construction of a big family of indecomposable torsionfree Abelian groups of finite rank.     

Biosprayed spleen cells integrate and function in mouse models

Bio-electrospraying (BES) and aerodynamically assisted bio-jetting (AABJ), two non-contact direct cell handling approaches, have recently undergone rigorous scientific testing to assess whether cells retain chemical, physical and more importantly biological functions similarly to their unmanipulated counterparts. Previous in vitro validation of these two approaches has shown that they are inert for the direct handling and distributing of cells with great accuracy. In the present investigation we aim to validate, in vivo, that the spray techniques do not functionally or phenotypically alter splenic cells. By taking advantage of an adoptive transfer mouse model we demonstrated that the in vivo behaviour of treated cells is indistinguishable from unmanipulated cells following adoptive transfer into C57/BL6 mice. Indeed, sprayed cells survived and proliferated in response to antigen activation to similar levels observed in unmanipulated cells. In addition, in vivo sprayed cells displayed identical migratory characteristics to those observed in unmanipulated cells. Thus, demonstrating the inertness of these biosprays. Hence these biotechniques hold great potential for use in the development of three-dimensional cultures, tracking and monitoring cell-interactions and in vitro modelling of disease-states and therapeutics.