Let p be a graph parameter that assigns a positive integer value to every graph. The inverse problem for p asks for a graph within a prescribed class (here, we will only be concerned with trees), given the value of p. In this context, it is of interest to know whether such a graph can be found for all or at least almost all integer values of p. We will provide a very general setting for this ty...

A robust fixed-lag smoothing approach is proposed in the case there a mismatch between nominal model and actual model. The resulting smoother characterized by dynamic game two players: one player selects least favorable prescribed ambiguity set, while other minimizing error with respect to We propose an efficient implementation of smoother. Moreover, we characterize corresponding over finite ti...

We calculate the probability distribution of work for an exactly solvable model of a system interacting with its environment. The system of interest is a harmonic oscillator with a time-dependent control parameter, the environment is modeled by N-independent harmonic oscillators with arbitrary frequencies, and the system-environment coupling is bilinear and not necessarily weak. The initial con...

This paper is an analysis of a model for the structure in a liquid crystal medium that arises when the material is cooled from the smectic-A to the chiral smectic-C phase in a surface-stabilized cell with prescribed boundary conditions under a given electric field. This phenomenon causes V-shaped (chevron-like) defects to form in liquid crystal display devices and has attracted interest from bo...

We aim at constructing a smooth basis for isogeometric function spaces on domains of reduced geometric regularity. In this context an isogeometric function is the composition of a piecewise rational function with the inverse of a piecewise rational geometry parameterization. We consider two types of singular parameterizations, domains where a part of the boundary is mapped onto one point and do...

This paper is concerned with the problems of robust stochastic stabilization and robust H1 control for uncertain discrete-time stochastic bilinear systems with Markovian switching. The parameter uncertainties are time-varying norm-bounded. For the robust stochastic stabilization problem, the purpose is the design of a state feedback controller which ensures the robust stochastic stability of th...

How to design a robust gene network to tolerate more intrinsic kinetic parameter variations and to attenuate more extrinsic environmental noises to achieve a desired filtering level will be an important topic for systems biology and synthetic biology. At present, there is no good systematic design method to achieve robust gene network design. In this study, a gene network suffering from intrins...

We implemented a pharmacokinetics-based mathematical modeling technique using algebra to assist prescribers with point-of-care opioid dosing. We call this technique computational opioid prescribing (COP). Because population pharmacokinetic parameter values are needed to estimate drug dosing regimen designs for individual patients using COP, and those values are not readily available to prescrib...

In this paper, a new robust filtering problem is investigated for a class of time-varying nonlinear system with norm-bounded parameter uncertainties, bounded state delay, sector-bounded nonlinearity and probabilistic sensor gain faults. The probabilistic sensor reductions are modeled by using a random variable that obeys a specific distribution in a known interval , which accounts for the follo...

We construct local minimizers to the Ginzburg-Landau functional of superconductivity whose number of vortices N is prescribed and blows up as the parameter ε, inverse of the Ginzburg-Landau parameter κ, tends to 0. We treat the case of N as large as |log ε|, and a wide range of intensity of external magnetic field. The vortices of our solutions arrange themselves with uniform density over a sub...