Related papers: State evolution beyond first-order methods I: Rigo…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
This paper investigates the iterates $\hbb^1,\dots,\hbb^T$ obtained from iterative algorithms in high-dimensional linear regression problems, in the regime where the feature dimension $p$ is comparable with the sample size $n$, i.e., $p…
The development of surrogate models to study uncertainties in hydrologic systems requires significant effort in the development of sampling strategies and forward model simulations. Furthermore, in applications where prediction time is…
The behavior and architecture of large scale discrete state systems found in computer software and hardware can be specified and analyzed using a particular class of primitive recursive functions. This paper begins with an illustration of…
This paper presents finite-time and fixed-time stabilization results for inhomogeneous abstract evolution problems, extending existing theories. We prove well-posedness for strong and weak solutions, and estimate upper bounds for settling…
Variational quantum algorithms (VQAs) are prominent candidates for near-term quantum advantage but lack rigorous guarantees of convergence and generalization. By contrast, quantum phase estimation (QPE) provides provable performance under…
This paper is about the state estimation of timed probabilistic discrete event systems. The main contribution is to propose general procedures for developing state estimation approaches based on artificial neural networks. It is assumed…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
Finding the ground state of a Hamiltonian system is of great significance in many-body quantum physics and quantum chemistry. We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian. The crucial point…
State estimation or filtering serves as a fundamental task to enable intelligent decision-making in applications such as autonomous vehicles, robotics, healthcare monitoring, smart grids, intelligent transportation, and predictive…
Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid…
Evolutionary processes proved very useful for solving optimization problems. In this work, we build a formalization of the notion of cooperation and competition of multiple systems working toward a common optimization goal of the population…
Many living and complex systems exhibit second order emergent dynamics. Limited experimental access to the configurational degrees of freedom results in data that appears to be generated by a non-Markovian process. This poses a challenge in…
Computer modelling for evolutionary systems consists in: 1) to store in the memory the individual features of each member of a large population; and 2) to update the whole system repeatedly, as time goes by, according to some prescribed…
This paper presents a generic motion model to capture mobile robots' dynamic behaviors (translation and rotation). The model is based on statistical models driven by white random processes and is formulated into a full state estimation…
We present a unified deductive verification framework for first-order temporal properties based on well-founded rankings, where verification conditions are discharged using SMT solvers. To that end, we introduce a novel reduction from…
We study the stability of posterior predictive inferences to the specification of the likelihood model and perturbations of the data generating process. In modern big data analyses, useful broad structural judgements may be elicited from…
The task of artificial intelligence is to provide representation techniques for describing problems, as well as search algorithms that can be used to answer our questions. A widespread and elaborated model is state-space representation,…
This work is on constrained large-scale non-convex optimization where the constraint set implies a manifold structure. Solving such problems is important in a multitude of fundamental machine learning tasks. Recent advances on Riemannian…
In our previous work, we introduced the rule-based Bayesian Regression, a methodology that leverages two concepts: (i) Bayesian inference, for the general framework and uncertainty quantification and (ii) rule-based systems for the…