Related papers: Conformal Mesh Parameterization Using Discrete Cal…
We present a viable solution to the challenging question of change detection in complex networks inferred from large dynamic data sets. Building on Forman's discretization of the classical notion of Ricci curvature, we introduce a novel…
In this paper, we establish a connection between the parameterization of flow-based and energy-based generative models, and present a new flow-based modeling approach called energy-based normalizing flow (EBFlow). We demonstrate that by…
Algorithms based on the particle flow approach are becoming increasingly utilized in collider experiments due to their superior jet energy and missing energy resolution compared to the traditional calorimeter-based measurements. Such…
Estimating three-dimensional conformations of a molecular graph allows insight into the molecule's biological and chemical functions. Fast generation of valid conformations is thus central to molecular modeling. Recent advances in…
In this paper we propose the use of a continuous data assimilation algorithm for miscible flow models in a porous medium. In the absence of initial conditions for the model, observed sparse measurements are used to generate an approximation…
In this paper a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced. The method is parameterized in order to affect…
Machine-learning techniques are essential in modern collider research, yet their probabilistic outputs often lack calibrated uncertainty estimates and finite-sample guarantees, limiting their direct use in statistical inference and…
We provide a new algebraic technique to solve the sequential flow problem in polynomial space. The task is to maximise the flow through a graph where edge capacities can be changed over time by choosing a sequence of capacity labelings from…
Energy based models (EBMs) are appealing for their generality and simplicity in data likelihood modeling, but have conventionally been difficult to train due to the unstable and time-consuming implicit MCMC sampling during contrastive…
Mass spectrometry (MS) stands as a cornerstone analytical technique for molecular identification, yet de novo structure elucidation from spectra remains challenging due to the combinatorial complexity of chemical space and the inherent…
In this paper, we extend the work of Ge-Hua-Zhou \cite{GHZ} on combinatorial Ricci flows for ideal circle patterns to combinatorial Calabi flows in both hyperbolic and Euclidean background geometry. We prove the solution to the…
In this paper, a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced. The method is parameterized in order to affect…
Generative models have emerged as a powerful paradigm for solving physics systems and modeling complex spatiotemporal dynamics. However, achieving high physical accuracy without incurring high computational cost remains a fundamental…
In this paper, we continue to study the Calabi flow on complex tori. We develop a new method to obtain an explicit bound of the curvature of the Calabi flow. As an application, we show that when $n=2$, the Calabi flow starting from a weak…
In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…
Calibrating mathematical models of biological processes is essential for achieving predictive accuracy and gaining mechanistic insight. However, this task remains challenging due to limited and noisy data, significant biological…
Assuming local uniform bounds on the metric for a solution of the Chern-Ricci flow, we establish local Calabi and curvature estimates using the maximum principle.
In this note, we study the long time existence of the Calabi flow on $X = \mathbb{C}^n/\mathbb{Z}^n + i\mathbb{Z}^n$. Assuming the uniform bound of the total energy, we establish the non-collapsing property of the Calabi flow by using…
Recent learning-based methods for event-based optical flow estimation utilize cost volumes for pixel matching but suffer from redundant computations and limited scalability to higher resolutions for flow refinement. In this work, we take…
Optimal-order uniform-in-time $H^1$-norm error estimates are given for semi- and full discretizations of mean curvature flow of surfaces in arbitrarily high codimension. The proposed and studied numerical method is based on a parabolic…