Related papers: Modeling the Monty Hall Decision Problem with Reac…

Tasks where the set of possible actions depend discontinuously on the state pose a significant challenge for current reinforcement learning algorithms. For example, a locked door must be first unlocked, and then the handle turned before the…

We consider a generalization of the classical 100 Prisoner problem and its variant, involving empty boxes, whereby winning probabilities for a team depend on the number of attempts, as well as on the number of winners. We call this the…

The problem of retrosynthetic planning can be framed as one player game, in which the chemist (or a computer program) works backwards from a molecular target to simpler starting materials though a series of choices regarding which reactions…

Here, we present the quantum version of a very famous statistical decision problem, whose classical version is counter-intuitive to many. The Monty Hall game can be phrased as a two person game between Alice and Bob. In their pioneering…

We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction…

When a model makes a consequential decision, e.g., denying someone a loan, it needs to additionally generate actionable, realistic feedback on what the person can do to favorably change the decision. We cast this problem through the lens of…

For two molecules to react they first have to meet. Yet, reaction times are rarely on par with the first-passage times that govern such molecular encounters. A prime reason for this discrepancy is stochastic transitions between reactive and…

When people pursue rewards in stochastic environments, they often match their choice frequencies to the observed target frequencies, even when this policy is demonstrably sub-optimal. We used a ``hide and seek'' task to evaluate this…

This paper studies the decision making problem with Funnel Structure. Funnel structure, a well-known concept in the marketing field, occurs in those systems where the decision maker interacts with the environment in a layered manner…

We consider chemical reaction networks taken with mass action kinetics. The steady states of such a system are solutions to a system of polynomial equations. Even for small systems the task of finding the solutions is daunting. We develop…

In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response.…

Engineering molecular systems that exhibit complex behavior requires the design of kinetic barriers. For example, an effective catalytic pathway must have a large barrier when the catalyst is absent. While programming such energy barriers…

The probability distribution describing the state of a Stochastic Reaction Network evolves according to the Chemical Master Equation (CME). It is common to estimated its solution using Monte Carlo methods such as the Stochastic Simulation…

The system-level dynamics of multivalent biomolecular interactions can be simulated using a rule-based kinetic Monte Carlo method in which a rejection sampling strategy is used to generate reaction events. This method becomes inefficient…

Incentives are more likely to elicit desired outcomes when they are designed based on accurate models of agents' strategic behavior. A growing literature, however, suggests that people do not quite behave like standard economic agents in a…

Chemical reaction network theory is a powerful framework to describe and analyze chemical systems. While much about the concentration profile in an equilibrium state can be determined in terms of the graph structure, the overall reaction's…

The induced kinetic differential equation of a reaction network endowed with mass action type kinetics is a system of polynomial differential equations. The problem studied here is: Given a polynomial differential equation, is it possible…

Learning to adapt and make real-time informed decisions in a dynamic and complex environment is a challenging problem. Monopoly is a popular strategic board game that requires players to make multiple decisions during the game.…

In the first part of this paper we give a short review of the hierarchy of stochastic models, related to physical chemistry. In the basement of this hierarchy there are two models --- stochastic chemical kinetics and the Kac model for…

Understanding cooperative behavior in biological and social systems constitutes a scientific challenge, being the object of intense research over the past decades. Many mechanisms have been proposed to explain the presence and persistence…