Related papers: A theoretical framework and the experimental datas…

High-fidelity pedestrian tracking in real-life conditions has been an important tool in fundamental crowd dynamics research allowing to quantify statistics of relevant observables including walking velocities, mutual distances and body…

The objective for establishing dense correspondence between paired images consists of two terms: a data term and a prior term. While conventional techniques focused on defining hand-designed prior terms, which are difficult to formulate,…

The aim of the present contribution is to provide a framework for analyzing and visualizing the correlated many-electron dynamics of molecular systems, where an explicitly time-dependent electronic wave packet is represented as a linear…

Diffusion models have achieved remarkable performance on a wide range of generative tasks, yet training them from scratch is notoriously resource-intensive, typically requiring millions of training images and many GPU days. Motivated by a…

DC has proved to be a promising tool for the specification and verification of functional requirements on the design of hard real-time systems. Many works were devoted to develop effective techniques for checking the models of hard…

Quantum computing holds immense potential, yet its practical success depends on multiple factors, including advances in quantum circuit design. In this paper, we introduce a generative approach based on denoising diffusion models (DMs) to…

The Dirichlet process mixture model and more general mixtures based on discrete random probability measures have been shown to be flexible and accurate models for density estimation and clustering. The goal of this paper is to illustrate…

Discrete Combinatorial Problems (DCPs) are prevalent in industrial decision-making and optimisation. However, while constraint solving technologies for DCPs have advanced significantly, the core process of formalising them, namely…

We propose a new binary classification model called Phase Separation Binary Classifier (PSBC). It consists of a discretization of a nonlinear reaction-diffusion equation coupled with an Ordinary Differential Equation, and is inspired by…

Reconstructing high derivatives of noisy measurements is an important step in many control, identification and diagnosis problems. In this paper, a heuristic is proposed to address this challenging issue. The framework is based on a…

Model Predictive Control (MPC) offers a versatile framework for constraint handling and multi-objective optimisation, yet practical application faces challenges regarding initial and recursive feasibility, robustness against model…

The gradient discretisation method (GDM) is a generic framework for designing and analysing numerical schemes for diffusion models. In this paper, we study the GDM for the porous medium equation, including fast diffusion and slow diffusion…

We introduce PPL Bench, a new benchmark for evaluating Probabilistic Programming Languages (PPLs) on a variety of statistical models. The benchmark includes data generation and evaluation code for a number of models as well as…

Previous work on learning physical systems from data has focused on high-resolution grid-structured measurements. However, real-world knowledge of such systems (e.g. weather data) relies on sparsely scattered measuring stations. In this…

For the sake of computational efficiency and for theoretical purposes, in mathematical modelling, the Dirac Delta distributions are often utilized as a replacement for cells or vesicles, since the size of cells or vesicles is much smaller…

Modern control theory provides us with a spectrum of methods for studying the interconnection of dynamic systems using input-output properties of the interconnected subsystems. Perhaps the most advanced framework for such input-output…

The main components of an atmospheric model for numerical weather prediction are the dynamical core, which describes the resolved flow, and the physical parametrisations, which capture the effects of unresolved processes. Additionally,…

We propose a systematic framework to conduct design-technology pathfinding for PPAC in advanced nodes. Our goal is to provide configurable, scalable generation of process design kit (PDK) and standard-cell library, spanning key scaling…

We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing…

This paper presents a novel theoretical framework for understanding how diffusion models can learn disentangled representations. Within this framework, we establish identifiability conditions for general disentangled latent variable models,…