In spatially distributed cellular systems, it is often convenient to represent complicated auxiliary pathways and spatial transport by time-delayed reaction rates. Furthermore, many of the reactants appear in low numbers necessitating a probabilistic description. The coupling of delayed rates with stochastic dynamics leads to a probability conservation equation characterizing a non-Markovian pr...

Blade-to-blade variations can significantly impact the operation of bladed disks. In this paper, a method is presented for assessing the effects of these variations using a high-fidelity aerodynamic analysis. Systematic model reduction is applied to a high-order computational fluid dynamics code using the proper orthogonal decomposition technique. This results in a low-order model suitable for ...

In a conformational nonequilibrium steady state (cNESS), enzyme turnover is modulated by the underlying conformational dynamics. On the basis of a discrete kinetic network model, we use an integrated probability flux balance method to derive the cNESS turnover rate for a conformation-modulated enzymatic reaction. The traditional Michaelis-Menten (MM) rate equation is extended to a generalized f...

To describe the slow dynamics of a system out of equilibrium, but close to a dynamical arrest, we generalize the ideas of previous work to the case where timetranslational invariance is broken. We introduce a model of the dynamics that is reasonably general, and show how all of the unknown parameters of this model may be related to the observables or to averages of the noise. One result is a ge...

We show examples which reveal influences of spatial topologies to dynamics, using a class of spatially closed inhomogeneous cosmological models. The models, called the locally U(1)×U(1) symmetric models (or the generalized Gowdy models), are characterized by the existence of two commuting spatial local Killing vectors. For systematic investigations we first present a classification of possible ...

An atomistic level stress tensor is defined with physical clarity, based on the SPH method. This stress tensor rigorously satisfies the conservation of linear momentum, and is appropriate for both homogeneous and inhomogeneous deformations. The formulation is easier to implement than other stress tensors that have been widely used in atomistic analysis, and is validated by numerical examples. T...

Motivated by the pursuit of a systematic computational and algorithmic understanding of Generative Adversarial Networks (GANs), we present a simple yet unified non-asymptotic local convergence theory for smooth two-player games, which subsumes several discrete-time gradientbased saddle point dynamics. The analysis reveals the surprising nature of the off-diagonal interaction term as both a bles...

Phenotype measurements frequently take the form of time series, but we currently lack a systematic method for relating these complex data streams to scientifically meaningful outcomes, such as relating the movement dynamics of organisms to their genotype or measurements of brain dynamics of a patient to their disease diagnosis. Previous work addressed this problem by comparing implementations o...

In conventional sliding-mode control systems, the sliding-mode motion is of reduced order. Two main problems hindering the application of the sliding-mode control are the singularity in terminal slidingmode control systems and the chattering in both the conventional linear sliding-mode and the terminal sliding-mode control systems. This paper proposes a chattering-free full-order terminal-slidi...

Complex animal behaviors are likely built from simpler modules, but their systematic identification in mammals remains a significant challenge. Here we use depth imaging to show that 3D mouse pose dynamics are structured at the sub-second timescale. Computational modeling of these fast dynamics effectively describes mouse behavior as a series of reused and stereotyped modules with defined trans...