相关论文: Symmetric resonance based integrators and forest f…
Random forests are a learning algorithm proposed by Breiman [Mach. Learn. 45 (2001) 5--32] that combines several randomized decision trees and aggregates their predictions by averaging. Despite its wide usage and outstanding practical…
For a system of partial differential equations admitting point, contact, or higher symmetries, the framework of invariant reduction systematically computes how invariant geometric structures, such as conservation laws, presymplectic…
Computational approaches in historical linguistics have been increasingly applied during the past decade and many new methods that implement parts of the traditional comparative method have been proposed. Despite these increased efforts,…
We study the problem of determining whether a given temporal specification can be implemented by a symmetric system, i.e., a system composed from identical components. Symmetry is an important goal in the design of distributed systems,…
In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting…
Many problems in areas such as compressive sensing and coding theory seek to design a set of equal-norm vectors with large angular separation. This idea is essentially equivalent to constructing a frame with low coherence. The elements of…
A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi…
This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…
We prove that the asymptotic distribution of resonances has a multilevel internal structure for the following classes of Hamiltonians H: Schr\"odinger operators with point interactions in $\mathbb{R}^3$, quantum graphs, and 1-D photonic…
This paper is the first in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. Our immediate motivation is a specific model, involving…
Unit norm finite frames are generalizations of orthonormal bases with many applications in signal processing. An important property of a frame is its coherence, a measure of how close any two vectors of the frame are to each other. Low…
Quantum systems governed by non-Hermitian Hamiltonians with $\PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We argue that $\PT$ symmetry may also be important and present at the level…
Robots exhibit a rich variety of symmetries arising from their mechanical structure and the properties of their tasks. Although many robotics problems exhibit several symmetries simultaneously, existing approaches typically treat them in…
I review the formalism, Feynman rules, and combinatorics that constrain a field to propagate ``classically", strictly in tree diagrams, either by itself, or interacting with other, purely quantum fields. The perturbation theory is…
Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram. From a statistical perspective, however, persistence diagrams…
A promising way to reconcile naturalness with a decoupling solution to the SUSY flavor and CP problems is suggested by models with a radiatively driven inverted mass hierarchy (RIMH). The RIMH models arise naturally within the context of…
A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and…
We introduce a unified framework for random forest prediction error estimation based on a novel estimator of the conditional prediction error distribution function. Our framework enables simple plug-in estimation of key prediction…
We discuss a path toward the generalisation of the nested soft-collinear subtraction scheme to arbitrary $2\rightarrow n$ processes. The scheme is designed to provide an efficient and process-independent procedure to extract and regulate…
Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of applications in machine learning, data science and statistics. Classically, such problems are solved via…