In the last lecture we got familiar with the concept of discrete-time Markov chains and Hidden Markov Models (HMMs). A Markov chain is a discrete random process that abides by the Markov property, that the probability of the next state depends only on the current state and not the past. The Markov chain models how a state changes from step to step using transition probabilities. Therefore, a Ma...

We study a natural Wasserstein gradient flow on manifolds of probability distributions with discrete sample spaces. We derive the Riemannian structure for the probability simplex from the dynamical formulation of the Wasserstein distance on a weighted graph. We pull back the geometric structure to the parameter space of any given probability model, which allows us to define a natural gradient f...

Backward Monte Carlo methods for solving the Boltzmann equation are investigated. A stable estimator is proposed since a previously published estimator was found to be numerically instable. The principle of detailed balance, which is obeyed by state transitions of a physical system and ensures existence of a stable equilibrium solution, is violated by the transition probability of the unstable ...

This study investigates strategies in reasoning about mental states of others, a process that requires theory of mind. It is a first step in studying the cognitive basis of such reasoning, as strategies affect tradeoffs between cognitive resources. Participants were presented with a two-player game that required reasoning about the mental states of the opponent. Game theory literature discerns ...

An important approach to game theory is to examine the consequences of beliefs that rational agents may have about each other. This paper considers respect for public preferences. Consider an agent A who believes that B strictly prefers an option a to an option b. Then A respects B’s preference if A considers the choice of a “infinitely more likely” than the choice of B; equivalently, if A assi...

Cytoplasmic dynein exhibits a directional processive movement on microtubule filaments and is known to move in steps of varying length based on the number of ATP molecules bound to it and the load that it carries. It is experimentally observed that dynein takes occasional backward steps and the frequency of such backward steps increases as the load approaches the stall force. Using a stochastic...

We consider probabilistic timed automata of [13], an extension of the timed automata model of [2] with discrete probability distributions. In contrast to timed automata, which model real-time systems purely in terms of nondeterminism, our model allows to express the likelihood of the system making certain transitions, and is thus appropriate for modelling fault-tolerance and probabilistic failu...

This article investigates the model evaluation problem for stochastic Boolean control networks (SBCNs). First, an algebraic expression of SBCN is obtained based on semitensor product method, and a straightforward approach then proposed to compute probability that given observed output sequence produced by considered model. Second, two recursive algorithms, namely forward backward are designed r...