Related papers: Modeling the Monty Hall Decision Problem with Reac…
We present a stochastic lattice theory describing the kinetic behavior of trapping reactions $A + B \to B$, in which both the $A$ and $B$ particles perform an independent stochastic motion on a regular hypercubic lattice. Upon an encounter…
The Prisoners' Dilemma is perhaps the most famous model in the field of game theory. Consequently, it is natural to investigate its quantum version when one considers to apply quantum strategies to game theory. There are two main results in…
Exploiting the information provided by the molecular noise of a biological process has proven to be valuable in extracting knowledge about the underlying kinetic parameters and sources of variability from single cell measurements. However,…
We model stochastic choice as environment-dependent switching among a small library of deterministic decision rules. A Random Rule Model generates menu-level choice probabilities via named, interpretable rules weighted by observable menu…
Learning performance can show non-monotonic behavior. That is, more data does not necessarily lead to better models, even on average. We propose three algorithms that take a supervised learning model and make it perform more monotone. We…
We study a decision-maker's problem of finding optimal monetary incentive schemes for retention when faced with agents whose participation decisions (stochastically) depend on the incentive they receive. Our focus is on policies constrained…
This thesis considers sequential decision problems, where the loss/reward incurred by selecting an action may not be inferred from observed feedback. A major part of this thesis focuses on the unsupervised sequential selection problem,…
The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by widely disparate time scales. As a result,…
In this paper we model the problem of learning preferences of a population as an active learning problem. We propose an algorithm can adaptively choose pairs of items to show to users coming from a heterogeneous population, and use the…
The basic Monty Hall problem is explored to introduce into the fundamental concepts of the game theory and to give a complete Bayesian and a (noncooperative) game-theoretic analysis of the situation. Simple combinatorial arguments are used…
We generalize the rejection-free event-chain Monte Carlo algorithm from many particle systems with pairwise interactions to systems with arbitrary three- or many-particle interactions. We introduce generalized lifting probabilities between…
It is increasingly realized that taking stochastic effects into account is important in order to study biological cells. However, the corresponding mathematical formulation, the chemical master equation (CME), suffers from the curse of…
A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow only two strategies: to cooperate (C) or to defect (D) unconditionally. The players updated in a random sequence have a…
The slow microstructural evolution of materials often plays a key role in determining material properties. When the unit steps of the evolution process are slow, direct simulation approaches such as molecular dynamics become prohibitive and…
We present a detailed study of prisoner's dilemma game with stochastic modifications on a two-dimensional lattice, in presence of evolutionary dynamics. By very nature of the rules, the cooperators have incentive to cheat and the fear to…
This paper is concerned with the dynamical properties of deterministically modeled chemical reaction systems with mass-action kinetics. Such models are ubiquitously found in chemistry, population biology, and the burgeoning field of systems…
Traditional chemical kinetics may be inappropriate to describe chemical reactions in micro-domains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a…
We present a detailed kinetic model for the Polymerase Chain Reaction, and model the probability of replication in terms of the physical parameters of the problem. Applying the theory of branching processes, we show the existance of a new…
We study the emergency of mutual cooperation in evolutionary prisoner's dilemma games when the players are located on a square lattice. The players can choose one of the three strategies: cooperation (C), defection (D) or "tit for tat" (T),…
We address the following dynamic version of the school choice question: a city, named City, admits students in two temporally-separated rounds, denoted $\mathcal{R}_1$ and $\mathcal{R}_2$. In round $\mathcal{R}_1$, the capacity of each…