Related papers: A simplified algorithm for the topological entropy…
A homotopy method for multi-objective optimization that produces uniformly sampled Pareto fronts by construction is presented. While the algorithm is general, of particular interest is application to simulation-based engineering…
A continuous-time path integral Quantum Monte Carlo method using the directed-loop algorithm is developed to simulate the Anderson single-impurity model in the occupation number basis. Although the method suffers from a sign problem at low…
A multimodal network encodes relationships between the same set of nodes in multiple settings, and network alignment is a powerful tool for transferring information and insight between a pair of networks. We propose a method for multimodal…
We combine standard persistent homology with image persistent homology to define a novel way of characterizing shapes and interactions between them. In particular, we introduce: (1) a mixup barcode, which captures geometric-topological…
There is no closed form analytical equation or quick method to calculate probabilities based only on the entropy of a signal or process. Except in the cases where there are constraints on the state probabilities, one must typically derive…
We introduce an algorithmic model of heat conduction, the thermodynamic graph. The thermodynamic graph is analogous to meshes in the finite difference method in the sense that the calculation of temperature is carried out at the vertices of…
Measure-theoretic slow entropy is a more refined invariant than the classical measure-theoretic entropy to characterize the complexity of dynamical systems with subexponential growth rates of distinguishable orbit types. In this paper we…
\emph{Maximal ancestral graph} (MAGs) is a class of graphical model that extend the famous \emph{directed acyclic graph} in the presence of latent confounders. Most score-based approaches to learn the unknown MAG from empirical data rely on…
Maximum a posteriori (MAP) inference is a fundamental computational paradigm for statistical inference. In the setting of graphical models, MAP inference entails solving a combinatorial optimization problem to find the most likely…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…
The topological entropy of a continuous self-map of a compact metric space can be defined in several distinct ways; when the space is not assumed compact, these definitions can lead to distinct invariants. The original, purely topological…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
We investigate the use of the Multiple Optimised Parameter Estimation and Data compression algorithm (MOPED) for data compression and faster evaluation of likelihood functions. Since MOPED only guarantees maintaining the Fisher matrix of…
Topological data analysis provides a collection of tools to encapsulate and summarize the shape of data. Currently it is mainly restricted to \emph{mapper algorithm} and \emph{persistent homology}. In this paper we introduce new…
Consider a collection of competing machine learning algorithms. Given their performance on a benchmark of datasets, we would like to identify the best performing algorithm. Specifically, which algorithm is most likely to rank highest on a…
A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
We present an algorithm for computing the main topological characteristics of three-dimensional bodies. The algorithm is based on a discretization of Morse theory and uses discrete analogs of smooth functions with only nondegenerate (Morse)…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…