Related papers: A dynamic p53-mdm2 model with delay kernel
In the genome biology research, regulatory genome modeling is an important topic for many regulatory downstream tasks, such as promoter classification, transaction factor binding sites prediction. The core problem is to model how regulatory…
By integrating heterogeneous functional genomic datasets, we have developed a new framework for detecting combinatorial control of gene expression, which includes estimating transcription factor activities using a singular value…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
A comparison is made between conventional Michaelis-Menten kinetics and two models that take into account the duration of the conformational changes that take place at the molecular level during the catalytic cycle of a monomer. The models…
We study the dynamics of a delayed predator-prey system with Holling type II functional response, focusing on the interplay between time delay and carrying capacity. Using local and global Hopf bifurcation theory, we establish the existence…
In this paper, we consider a bidirectional relay network with half-duplex nodes and block fading where the nodes transmit with a fixed transmission rate. Thereby, user 1 and user 2 exchange information only via a relay node, i.e., a direct…
Time delay has been incorporated in models to reflect certain physical or biological meaning. The theory of delay differential equations (DDEs), which has seen extensive growth in the last seventy years or so, can be used to examine the…
This paper presents a characterization of distributed controllers subject to delay constraints induced by a strongly connected communication graph that achieve a prescribed closed loop $\mathcal{H}_\infty$ norm. Inspired by the solution to…
The mechanical model based on beads and springs, which we recently proposed to study non-specific DNA-protein interactions [J. Chem. Phys. 130, 015103 (2009)], was improved by describing proteins as sets of interconnected beads instead of…
This study investigates how the interaction between gene expression time delay and domain size governs spatio-temporal pattern formation in a reaction-diffusion system. To investigate these phenomena, we utilize a modified version of the…
We develop an approximate theoretical method to study discrete stochastic birth and death models that include a delay time. We analyze the effect of the delay in the fluctuations of the system and obtain that it can qualitatively alter…
There is increasing evidence that protein binding to specific sites along DNA can activate the reading out of genetic information without coming into direct physical contact with the gene. There also is evidence that these distant but…
The structure and dynamics of a typical biological system are complex due to strong and inhomogeneous interactions between its constituents. The investigation of such systems with classical mathematical tools, such as differential equations…
This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with quadratic term and delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try…
We propose a method of analysis of dynamical networks based on a recent measure of Granger causality between time series, based on kernel methods. The generalization of kernel Granger causality to the multivariate case, here presented,…
We provide a new theoretical framework for the variable-step deferred correction (DC) methods based on the well-known BDF2 formula. By using the discrete orthogonal convolution kernels, some high-order BDF2-DC methods are proven to be…
Modeling biological networks serves as both a major goal and an effective tool of systems biology in studying mechanisms that orchestrate the activities of gene products in cells. Biological networks are context specific and dynamic in…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
We study distributed stochastic convex optimization under the delayed gradient model where the server nodes perform parameter updates, while the worker nodes compute stochastic gradients. We discuss, analyze, and experiment with a setup…
Specific binding of proteins to DNA is one of the most common ways in which gene expression is controlled. Although general rules for the DNA-protein recognition can be derived, the ambiguous and complex nature of this mechanism precludes a…