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This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random…
Once failure is irreversible, continuation payoffs cannot be meaningfully aggregated across strategies that differ in their survival properties. Standard scalar evaluation sidesteps this by arbitrarily completing payoffs beyond termination,…
A nonlinear cyclic system with delay and the overall negative feedback is considered. The characteristic equation of the linearized system is studied in detail. Sufficient conditions for the oscillation of all solutions and for the…
The fact that several important effects in multiparticle dynamics, on which QCD has not yet satisfactory predictions, have been interpreted in terms of the validity of negative binomial (Pascal) regularity and related clan properties at the…
Cardinal functions provide valuable insight into the topological properties of spaces, helping to analyze and compare spaces in terms of their covering, convergence and separation properties. This paper focuses on investigating cardinal…
It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the…
Statistical properties of evolving random graphs are analyzed using kinetic theory. Treating the linking process dynamically, structural characteristics such as links, paths, cycles, and components are obtained analytically using the rate…
Combinatorial Game Theory has also been called `additive game theory', whenever the analysis involves sums of independent game components. Such {\em disjunctive sums} invoke comparison between games, which allows abstract values to be…
In this article, we present the properties of the C-parameter which is one of event shape variables. We obtain the coupling constants both in the perturbative and in the non-perturbative part of the QCD theory. To achieve this we fit the…
We discuss partial specifications in first-order logic FO and also in a Turing-complete extension of FO. We compare the compositional and game-theoretic approaches to the systems.
This paper conducts sensitivity analysis of random constraint and variational systems related to stochastic optimization and variational inequalities. We establish efficient conditions for well-posedness, in the sense of robust Lipschitzian…
We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…
The goal of these lectures is to explain speaker's results on uniqueness properties of spherical varieties. By a uniqueness property we mean the following. Consider some special class of spherical varieties. Define some combinatorial…
The Minority Game framework was recently generalized to account for the possibility that agents adapt not only through strategy selection but also by diversifying their response according to the kind of dynamical regime, or the risk, they…
Discrete signatures are invariants computed from time series corresponding to the discretised version of the signature of paths. We study the algebraic varieties arising from their images, the discrete signature varieties. We introduce them…
We propose and axiomatize the categorical thinking model (CTM) in which the framing of the decision problem affects how agents categorize alternatives, that in turn affects their evaluation of it. Prominent models of salience, status quo…
We study weak approximation on rationally connected varieties under an assumption of strong approximation for a "simple" variety or under Schinzel's hypothesis. We also get some unconditional results.
This work investigates the intersection property of conditional independence. It states that for random variables $A,B,C$ and $X$ we have that $X$ independent of $A$ given $B,C$ and $X$ independent of $B$ given $A,C$ implies $X$ independent…
We discuss the computational complexity and feasibility properties of scenario based techniques for uncertain optimization programs. We consider different solution alternatives ranging from the standard scenario approach to recursive…
Characterizations of paracompact finite $C$-spaces via continuous selections are given. We apply these results to obtain some properties of finite $C$-spaces. Factorization theorems and a completion theorem for finite $C$- spaces are also…