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This paper analyzes a (1, $\lambda$)-Evolution Strategy, a randomized comparison-based adaptive search algorithm, optimizing a linear function with a linear constraint. The algorithm uses resampling to handle the constraint. Two cases are…
With the increasing ubiquity of safety-critical autonomous systems operating in uncertain environments, there is a need for mathematical methods for formal verification of stochastic models. Towards formally verifying properties of…
Macroscopic dynamical descriptions of complex physical systems are crucial for understanding and controlling material behavior. With the growing availability of data and compute, machine learning has become a promising alternative to…
Time-homogeneous Markov chains are often used as disease progression models in studies of cost-effectiveness and optimal decision-making. Maximum likelihood estimation of these models can be challenging when data are collected at a time…
The limits of molecular dynamics (MD) simulations of macromolecules are steadily pushed forward by the relentless developments of computer architectures and algorithms. This explosion in the number and extent (in size and time) of MD…
If the state space of a homogeneous continuous-time Markov chain is too large, making inferences - here limited to determining marginal or limit expectations - becomes computationally infeasible. Fortunately, the state space of such a chain…
In multi-state life insurance, an adequate balance between analytic tractability, computational efficiency, and statistical flexibility is of great importance. This might explain the popularity of Markov chain modelling, where matrix…
Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…
Despite their widespread utility across domains, basic network models face fundamental limitations when applied to complex biological systems, particularly in neuroscience. This paper critically examines these limitations and explores…
Stochastic models of biochemical reaction networks are widely used to capture intrinsic noise in cellular systems. The typical formulation of these models are based on Markov processes for which there is extensive research on efficient…
In this work we address the analysis of discrete-time models of structured metapopulations subject to environmental stochasticity. Previous works on these models made use of the fact that migrations between the patches can be considered…
The ability to interpret machine learning models has become increasingly important now that machine learning is used to inform consequential decisions. We propose an approach called model extraction for interpreting complex, blackbox…
Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…
Under a markovian evolutionary process, the expected number of substitutions per site (also called branch length) that have occurred when a sequence has evolved from another according to a transition matrix $P$ can be approximated by…
In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed inter-event times have…
1. Temporal trends in species distributions are necessary for monitoring changes in biodiversity, which aids policymakers and conservationists in making informed decisions. Dynamic species distribution models are often fitted to ecological…
Four chapters of the synthesis represent four major areas of my research interests: 1) data analysis in molecular biology, 2) mathematical modeling of biological networks, 3) genome evolution, and 4) cancer systems biology. The first…
Many systems are partially stochastic in nature. We have derived data driven approaches for extracting stochastic state machines (Markov models) directly from observed data. This chapter provides an overview of our approach with numerous…
In networking applications, one often wishes to obtain estimates about the number of objects at different parts of the network (e.g., the number of cars at an intersection of a road network or the number of packets expected to reach a node…
Population structure can have a significant effect on evolution. For some systems with sufficient symmetry, analytic results can be derived within the mathematical framework of evolutionary graph theory which relate to the outcome of the…