相关论文: A fixed-point approach to history-dependent sweepi…

We propose a constructive approach to building temporal point processes that incorporate dependence on their history. The dependence is modeled through the conditional density of the duration, i.e., the interval between successive event…

Practical implementations of Gaussian smoothing algorithms have received a great deal of attention in the last 60 years. However, almost all work focuses on estimating complete time series (''fixed-interval smoothing'', $\mathcal{O}(K)$…

We consider a controlled evolution problem for a set $\Omega(t)\in\mathbb{R}^d$, originally motivated by a model where a dog controls a flock of sheep. Necessary conditions and sufficient conditions are given, in order that the evolution be…

We introduce and analyze a **memory-weighted velocity operator** \(\mathscr{V}_{\alpha,\beta}\) as a mathematical framework for describing rates of change in systems with time-varying, power-law memory. The operator employs two independent…

The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…

We study a fundamental instability mechanism in nonlinear, nonlocal dynamical systems arising from the interaction of long-range memory and stochastic regime switching. The dynamics are governed by network-coupled, operator-valued Volterra…

We establish well-posedness results for systems of a finite number of stochastic particles driven by independent Brownian motions and subject to a strongly singular drift induced by a Lennard-Jones interaction. In addition to the pairwise…

In this paper we study well posedness of a certain nonlinear Volterra-Fredholm dynamic integral and integro-dynamic equations on unbounded interval from arbitrary time scale. We derive the time scale analogue of certain integral…

In this paper, we study a new variant of Moreau's sweeping process with velocity constraint. Based on an adapted version of Moreau's catching-up algorithm, we show the well-posedness (in the sense existence and uniqueness) of this problem…

We propose and analyze a simple model for the evolution of an immersed, inextensible filament which incorporates linear viscoelastic effects of the surrounding fluid. The model is a closed-form system of equations along the curve only which…

Effectively learning from sequential data is a longstanding goal of Artificial Intelligence, especially in the case of long sequences. From the dawn of Machine Learning, several researchers have pursued algorithms and architectures capable…

Reinforcement learning (RL) with continuous time and state/action spaces is often data-intensive and brittle under nuisance variability and shift, motivating methods that exploit value-preserving structures to stabilize and improve…

We consider the problem of efficiently learning optimal control policies and value functions over large state spaces in an online setting in which estimates must be available after each interaction with the world. This paper develops an…

Continual learning, the setting where a learning agent is faced with a never ending stream of data, continues to be a great challenge for modern machine learning systems. In particular the online or "single-pass through the data" setting…

We are concerned with the well-posedness of the density-dependent incompressible viscoelastic fluid system. By Schauder-Tychonoff fixed point argument, when $\|{1}/{\rho_0}-1\|_{\dot{B}_{p,1}^{{N}/{p}}}$ is small, local well-posedness is…

Instruction tuning has been central to the success of recent vision-language models (VLMs), but it remains expensive-requiring large-scale datasets, high-quality annotations, and large compute budgets. We propose PRioritized cOncept…

A controlled sweeping process with prox-regular set, $W^{1,2}$-controls, and separable endpoints constraints is considered in this paper. Existence of optimal solutions is established and local optimality conditions are derived via strong…

We consider the problem of building a state representation model in a continual fashion. As the environment changes, the aim is to efficiently compress the sensory state's information without losing past knowledge. The learned features are…

A higher-order nonlinear Boussinesq system with a time-dependent boundary delay is considered. Sufficient conditions are presented to ensure the well-posedness of the problem by utilizing Kato's variable norm technique and the Fixed-Point…

Fixed-point iterative sweeping methods were developed in the literature to efficiently solve steady state solutions of Hamilton-Jacobi equations and hyperbolic conservation laws. Similar as other fast sweeping schemes, the key components of…