Related papers: Sufficient conditions for memory kernel master equ…
Valuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notion of solution. Typical examples are satisfying…
We study the problem of extending a positive-definite operator-valued kernel, defined on words of a fixed finite length from a free semigroup, to a global kernel defined on all words. We show that if the initial kernel satisfies a natural…
We point to the connection between a recently introduced class of non-Markovian master equations and the general structure of quantum collisional models. The basic construction relies on three basic ingredients: a collection of time…
We use a graph to define a new stability condition for algebraic moduli spaces of rational curves. We characterize when the tropical compactification of the moduli space agrees with the theory of geometric tropicalization. The…
The constraints imposed by the initial system-environment correlation can lead to nonpositive Dynamical maps. We find the conditions for positivity and complete positivity of such dynamical maps by using the concept of an assignment map.…
Markovian master equations are a ubiquitous tool in the study of open quantum systems, but deriving them from first principles involves a series of compromises. On the one hand, the Redfield equation is valid for fast environments (whose…
We formalize constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We provide conditions for a "natural" family of constraint-based structure-learning algorithms that…
Semi-Markov processes generalize Markov processes by adding temporal memory effects as expressed by a semi-Markov kernel. We recall the path weight for a semi-Markov trajectory and the fact that thermodynamic consistency in equilibrium…
In this paper a general approach for the perfect simulation of a stationary process with at most countable state space is outlined. The process is specified through a kernel, prescribing the probability of each state conditional to the…
We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…
Memory effects in the dynamics of open systems have been the subject of significant interest in the last decades. The methods involved in quantifying this effect, however, are often difficult to compute and may lack analytical insight. With…
Coupling between quantum and classical systems is consistent, provided the evolution is linear in the state space, preserves the split of systems into quantum and classical degrees of freedom, and preserves probabilities. The evolution law…
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…
This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating…
In this work, we derive a deterministic master equation to model a general, possibly non-Markovian, feedback. The master equation describes a system with a general evolution and measurement operation, with feedback being applied in terms of…
In the paper a set of necessary and sufficient conditions for \textit{v-}sufficiency (equiv. \textit{sv-}sufficiency) of jets of map-germs $f:(\mathbb{R}^{n},0)\to (\mathbb{R}^{m},0)$ is proved which generalize both the Kuiper-Kuo and the…
This tutorial describes recently developed general optimality conditions for Markov Decision Processes that have significant applications to inventory control. In particular, these conditions imply the validity of optimality equations and…
Two kinds of maps that describe evolution of states of a subsystem coming from dynamics described by a unitary operator for a larger system, maps defined for fixed mean values and maps defined for fixed correlations, are found to be quite…
We explore the asymptotic convergence and nonasymptotic maximal inequalities of supermartingales and backward submartingales in the space of positive semidefinite matrices. These are natural matrix analogs of scalar nonnegative…
It is common, when dealing with quantum processes involving a subsystem of a much larger composite closed system, to treat them as effectively memory-less (Markovian). While open systems theory tells us that non-Markovian processes should…