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This paper investigates the exact controllability problem for multi-dimensional stochastic first-order symmetric hyperbolic systems with control inputs acting in two distinct ways: an internal control applied to the diffusion term and a…
In this paper, we study the partial differential equation models of neural networks. Neural network can be viewed as a map from a simple base model to a complicate function. Based on solid analysis, we show that this map can be formulated…
Diffusion models have demonstrated empirical successes in various applications and can be adapted to task-specific needs via guidance. This paper studies a form of gradient guidance for adapting a pre-trained diffusion model towards…
In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is…
This paper addresses the problems of stabilization, robust control, and observer design for nonlinear systems. We build upon recently a proposed method based on contraction theory and convex optimization, extending the class of systems to…
In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…
This work investigates the optimal control of the variable-exponent subdiffusion, which extends the work [Gunzburger and Wang, {\it SIAM J. Control Optim.} 2019] to the variable-exponent case to account for the multiscale and crossover…
This paper extends our recent results on multi-dimensional discrete-velocity models to the numerical level. By adopting an operator splitting scheme and introducing a suitable discrete Lyapunov function, we derive numerical control laws…
This paper deals with the problem of outliers in high frequency observation data from diffusion processes. Robust estimation methods are needed because the inclusion of outliers can lead to incorrect statistical inference even in the…
Dynamic phenomena in social and biological sciences can often be modeled by employing reaction-diffusion equations. When addressing the control of these modes, from a mathematical viewpoint one of the main challenges is that, because of the…
Diffusion-induced Ramsey narrowing that appears when atoms can leave the interaction region and repeatedly return without lost of coherence is investigated using strong collisions approximation. The effective diffusion equation is obtained…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
Due to network operation and maintenance relying heavily on network traffic monitoring, traffic matrix analysis has been one of the most crucial issues for network management related tasks. However, it is challenging to reliably obtain the…
The use of available disturbance predictions within a nominal model predictive control formulation is studied. The main challenge that arises is the loss of recursive feasibility and stability guarantees when a persistent disturbance is…
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
This paper investigates the optimal control problem for a class of parabolic equations where the diffusion coefficient is influenced by a control function acting nonlocally. Specifically, we consider the optimization of a cost functional…
Several theorems on the volume computing of the polyhedron spanned by a n-dimensional vector set with the finite-interval parameters are presented and proved firstly, and then are used in the analysis of the controllable regions of the…
A novel method for control of dynamical systems, proposed in the paper, ensures an output signal belonging to the given set at any time. The method is based on a special change of coordinates such that the initial problem with given…
In causal inference, sensitivity models assess how unmeasured confounders could alter causal analyses, but the sensitivity parameter -- which quantifies the degree of unmeasured confounding -- is often difficult to interpret. For this…