In physics, several attempts have been made to apply the concepts and tools of physics to the life sciences. In this context, a thermostatistic framework for active Nambu systems is proposed. The so-called free energy Fokker–Planck equation approach is used to describe stochastic aspects of active Nambu systems. Different thermostatistic settings are considered that are characterized by appropr...

We characterize the geometry of a path in a sub-Riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset A of a metric space is the minimum number of balls of a given radius ε needed to cover A. It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We define the complexity of a path in a subRiemannia...

Heap and data structures represent one of the biggest challenges when applying model checking to the analysis of software programs: in order to verify (unbounded) safety of a program, it is typically necessary to formulate quantified inductive invariants that state properties about an unbounded number of heap locations. Methods like Craig interpolation, which are commonly used to infer invarian...

We introduce an ambidextrous view of stochastic dynamical systems, comparing their forwardtime and reverse-time representations and then integrating them into a single time-symmetric representation. The perspective is useful theoretically, computationally, and conceptually. Mathematically, we prove that the excess entropy—a familiar measure of organization in complex systems—is the mutual infor...

Finite type invariants of knots or links can be defined combinatorially using only link projections in S. In this setting it can be seen that every Jones-type polynomial invariant (quantum invariants) is equivalent to a sequence of finite type invariants. See [B2, BN] and references therein. Although Vassiliev’s original approach to finite type knot invariants ([V]) rests on topological foundat...

A special version of multi–dimensional simple waves given in [G. Boillat, J. Math. Phys. 11, 1482-3 (1970)] and [G.M. Webb, R. Ratkiewicz, M. Brio and G.P. Zank, J. Plasma Phys. 59, 417-460 (1998)] is employed for fully relativistic fluid and plasma flows. Three essential modes: vortex, entropy and sound modes are derived where each of them is different from its nonrelativistic analogue. Vortex...