Related papers: Describing Function-based Approximations of Biomol…
We describe a mechanism for pronounced biochemical oscillations, relevant to microscopic systems, such as the intracellular environment. This mechanism operates for reaction schemes which, when modeled using deterministic rate equations,…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Using bioimaging technology, biologists have attempted to identify and document analytical interpretations that underlie biological phenomena in biological cells. Theoretical biology aims at distilling those interpretations into knowledge…
With the rise of computers, simulation models have emerged beside the more traditional statistical and mathematical models as a third pillar for ecological analysis. Broadly speaking, a simulation model is an algorithm, typically…
Probabilistic inference provides a language for describing how organisms may learn from and adapt to their environment. The computations needed to implement probabilistic inference often require specific representations, akin to having the…
We present a method for logical specification of the behavior of a system based on the specification of its components and for representing and specifying the effect of a class of communication "signaling pathways" among them. Variations in…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
We address the problem of parameter estimation in models of systems biology from noisy observations. The models we consider are characterized by simultaneous deterministic nonlinear differential equations whose parameters are either taken…
This paper proposes a unique optimization approach for estimating the minimax rational approximation and its application for evaluating matrix functions. Our method enables the extension to generalized rational approximations and has the…
The mathematical models used to capture features of complex, biological systems are typically non-linear, meaning that there are no generally valid simple relationships between their outputs and the data that might be used to validate them.…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…
Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms of biological processes. The mathematical mechanisms…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
The use of approximation is fundamental in computational science. Almost all computational methods adopt approximations in some form in order to obtain a favourable cost/accuracy trade-off and there are usually many approximations that…
Real-world experiments involve batched & delayed feedback, non-stationarity, multiple objectives & constraints, and (often some) personalization. Tailoring adaptive methods to address these challenges on a per-problem basis is infeasible,…
Living systems, from single cells to higher vertebrates, receive a continuous stream of non-stationary inputs that they sense, e.g., via cell surface receptors or sensory organs. Integrating these time-varying, multi-sensory, and often…
Molecular dynamics simulations hold great promise for providing insight into the microscopic behavior of complex molecular systems. However, their effectiveness is often constrained by long timescales associated with rare events. Enhanced…
For the study of complex synthetic and biological molecular systems by computer simulations one is still restricted to simple model systems or to by far too small time scales. To overcome this problem multiscale techniques are being…
The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of Ordinary Differential Equations. Alternative approaches based on formal calculi, often derived from process algebras or term…