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We investigate the problem of synthesizing optimal control policies for Markov decision processes (MDPs) with both qualitative and quantitative objectives. Specifically, our goal is to achieve a given linear temporal logic (LTL) task with…
Regularization of control policies using entropy can be instrumental in adjusting predictability of real-world systems. Applications benefiting from such approaches range from, e.g., cybersecurity, which aims at maximal unpredictability, to…
In this work, we investigate the relation between the concept of ``information rate'', an information geometric method for measuring the speed of the time evolution of the statistical states of a stochastic process, and stochastic…
We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by…
This paper studies birth and death processes in interactive random environments where the birth and death rates and the dynamics of the state of the environment are dependent on each other. Two models of a random environment are considered:…
Many systems across the sciences evolve through a combination of multiplicative growth and diffusive transport. In the presence of disorder, these systems tend to form localized structures which alternate between long periods of relative…
We consider a general honest homogeneous continuous-time Markov process with restarts. The process is forced to restart from a given distribution at time moments generated by an independent Poisson process. The motivation to study such…
The well-posedness of a multi-population dynamical system with an entropy regularization and its convergence to a suitable mean-field approximation are proved, under a general set of assumptions. Under further assumptions on the evolution…
Finding the entropy rate of Hidden Markov Processes is an active research topic, of both theoretical and practical importance. A recently used approach is studying the asymptotic behavior of the entropy rate in various regimes. In this…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics.…
Is evolution always gradual or can it make leaps? We examine a mathematical model of an evolutionary process on a fitness landscape and obtain analytic solutions for the probability of multi-mutation leaps, that is, several mutations…
New entropy measures have been recently introduced for the quantification of the complexity of networks. Most of these entropy measures apply to static networks or to dynamical processes defined on static complex networks. In this paper we…
Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…
Boolean network models of strongly connected modules are capable of capturing the high regulatory complexity of many biological gene regulatory circuits. We study numerically the previously introduced basin entropy, a parameter for the…
Entropy production plays a fundamental role in the study of non-equilibrium systems by offering a quantitative handle on the degree of time-reversal symmetry breaking. It depends crucially on the degree of freedom considered as well as on…
We show how concepts from statistical physics, such as order parameter, thermodynamic limit, and quantum phase transition, translate into biological concepts in mutation-selection models for sequence evolution and can be used there. The…
A measure called Physical Complexity is established and calculated for a population of sequences, based on statistical physics, automata theory, and information theory. It is a measure of the quantity of information in an organism's genome.…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
Using results from neurobiology on perceptual decision making and value-based decision making, the problem of decision making between lotteries is reformulated in an abstract space where uncertain prospects are mapped to corresponding…