Related papers: Outliers, Dynamics, and the Independence Postulate
Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by these developments, we study stationary multivariate…
We obtain higher order necessary conditions for a minimum of a Mayer optimal control problem connected with a nonlinear, control-affine system, where the controls range on an m-dimensional Euclidean space. Since the allowed velocities are…
The paper starts with the proposal that the cause of the apparent insolubility of the free-will problem are several popular but strongly metaphysical notions and hypotheses. To reduce the metaphysics, some ideas are borrowed from physics. A…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
Dissipative processes in physics are usually associated with non-unitary actions. However, the important resource of entanglement is not invariant under general unitary transformations, and is thus susceptible to unitary "dissipation". In…
Existence and non-existence results are established for quasilinear elliptic problems with nonlinear boundary conditions and lack of compactness. The proofs combine variational methods with the geometrical feature, due to the competition…
It is shown that the phenomenon of irreversibility in many-body and few-body systems can be explained and described within the framework of the concept of direct (not instantaneous) interaction of particles without using probabilistic…
The probability distribution function for an out of equilibrium system may sometimes be approximated by a physically motivated "trial" distribution. A particularly interesting case is when a driven system (e.g., active matter) is…
In all existing quantum walk models, the assumption about a pre-existing fixed background causal structure is always made and has been taken for granted. Nevertheless, in this work we will get rid of this tacit assumption especially by…
The concept of complementarity in combination with a non-Boolean calculus of propositions refers to a pivotal feature of quantum systems which has long been regarded as a key to their distinction from classical systems. But a non-Boolean…
A common assumption in causal inference from observational data is that there is no hidden confounding. Yet it is, in general, impossible to verify this assumption from a single dataset. Under the assumption of independent causal mechanisms…
Entropy is the distinguishing and most important concept of our efforts to understand and regularize our observations of a very large class of natural phenomena, and yet, it is one of the most contentious concepts of physics. In this…
We investigate the notion of independence, which is at the basis of many, seemingly unrelated, properties of logic like Rational Monotony in non-monotonic logics, and interpolation theorems.
We consider infinite particle system on the positive half-line moving independently of each other. When a particle hits the boundary it immediately disappears, and the boundary moves to the right on some fixed quantity (particle size). We…
We analyze the quantum dynamics of a non-relativistic particle moving in a bounded domain of physical space, when the boundary conditions are rapidly changed. In general, this yields new boundary conditions, via a dynamical composition law…
Perfect adaptation in a dynamical system is the phenomenon that one or more variables have an initial transient response to a persistent change in an external stimulus but revert to their original value as the system converges to…
We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although…
We show that two-dimensional billiard systems are Turing complete, in the sense that the halting of any Turing machine with a given input is equivalent to a certain bounded trajectory in this system entering a specified open set. Billiards…
The continuous limit of large systems of particles of finite size on the line is described. The particles are assumed to move freely and stick under collision, to form compound particles whose mass and size is the sum of the masses and…
Incremental stability properties are considered for certain systems of forced, nonlinear differential equations with a particular positivity structure. An incremental stability estimate is derived for pairs of input/state/output…