Related papers: The recursive structure of Baikov representations …
Fast and sensitive detector arrays enable image scanning microscopy (ISM), overcoming the trade-off between spatial resolution and signal-to-noise ratio (SNR) typical of confocal microscopy. However, current ISM approaches cannot provide…
Deep neural networks have evolved to become power demanding and consequently difficult to apply to small-size mobile platforms. Network parameter reduction methods have been introduced to systematically deal with the computational and…
We elucidate the vector space (twisted relative cohomology) that is Poincar\'e dual to the vector space of Feynman integrals (twisted cohomology) in general spacetime dimension. The pairing between these spaces - an algebraic invariant…
In several domains, data objects can be decomposed into sets of simpler objects. It is then natural to represent each object as the set of its components or parts. Many conventional machine learning algorithms are unable to process this…
Top-down instance segmentation framework has shown its superiority in object detection compared to the bottom-up framework. While it is efficient in addressing over-segmentation, top-down instance segmentation suffers from over-crop…
This paper aims to use topological methods to compute $\mathrm{Ext}$ between an irreducible representation of a finite monoid inflated from its group completion and one inflated from its group of units, or more generally coinduced from a…
In many field theoretical models one has to resum two- and four-legged subdiagrams in order to determine their behaviour. In this article we present a novel formalism which does this in a nice way. It is based on the central limit theorem…
Pattern recognition is generally assumed as an interaction of two inversely directed image-processing streams: the bottom-up information details gathering and localization (segmentation) stream, and the top-down information features…
We establish a recursive representation that fully decouples jumps from a large class of multivariate inhomogeneous stochastic differential equations with jumps of general time-state dependent unbounded intensity, not of L\'evy-driven type…
Topology Optimization (TO), which maximizes structural robustness under material weight constraints, is becoming an essential step for the automatic design of mechanical parts. However, existing TO algorithms use the Finite Element Analysis…
Integrated Computational Materials Engineering (ICME) aims to accelerate optimal design of complex material systems by integrating material science and design automation. For tractable ICME, it is required that (1) a structural feature…
We introduce an adaptive structured low rank algorithm to recover MR images from their undersampled Fourier coefficients. The image is modeled as a combination of a piecewise constant component and a piecewise linear component. The Fourier…
Since its introduction in 2011, the partial information decomposition (PID) has triggered an explosion of interest in the field of multivariate information theory and the study of emergent, higher-order ("synergistic") interactions in…
A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model.…
We present a simplification of the recursive algorithm for the evaluation of intersection numbers for differential $n$-forms, by combining the advantages emerging from the choice of delta-forms as generators of relative twisted cohomology…
In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…
The goal of data selection is to capture the most structural information from a set of data. This paper presents a fast and accurate data selection method, in which the selected samples are optimized to span the subspace of all data. We…
We consider conformal four-point Feynman integrals to investigate how much of their mathematical structure in two spacetime dimensions carries over to higher dimensions. In particular, we discuss recursions in the loop order and spacetime…
We present ReCAT, a recursive composition augmented Transformer that is able to explicitly model hierarchical syntactic structures of raw texts without relying on gold trees during both learning and inference. Existing research along this…
We study the class structure of finite-alphabet Markov chains with arbitrary memory length. To capture the structural constraints induced by prohibited transitions, we introduce the skeleton of a higher-order transition kernel, defined as a…