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Separable Bregman divergences induce Riemannian metric spaces that are isometric to the Euclidean space after monotone embeddings. We investigate fixed rate quantization and its codebook Voronoi diagrams, and report on experimental…
We present an alternative technique for evaluating multiloop Feynman diagrams, using the integration by fractional expansion method. Here we consider generic diagrams that contain propagators with radiative corrections which topologically…
In this paper, the notion of strongly typed language will be borrowed from the field of computer programming to introduce a calculational framework for linear algebra and tensor calculus for the purpose of detecting errors resulting from…
The Berger-Ebin and York $L^2$-orthogonal decompositions of the vector space of symmetric bilinear differential two-forms are fundamental tools in global Riemannian geometry. In this paper, we investigate the structure of Ricci tensors on…
Equivalence classes of $n$-point configurations in Euclidean, Hermitian, and quaternionic spaces are related, respectively, to classical determinantal varieties of symmetric, general, and skew-symmetric bilinear forms. Cayley-Menger…
It is well accepted that image segmentation can benefit from utilizing multilevel cues. The paper focuses on utilizing the FCNN-based dense semantic predictions in the bottom-up image segmentation, arguing to take semantic cues into account…
Chord diagrams and combinatorics of word algebras are used to model products of Dirac matrices, their traces, and contractions. A simple formula for the result of arbitrary contractions is derived, simplifying and extending an old…
The content of this paper can be roughly organized into a three-level hierarchy of generality. At the first, most general level, we introduce a new language which allows us to express various categorical structures in a systematic and…
Tensors, also known as multidimensional arrays, are useful data structures in machine learning and statistics. In recent years, Bayesian methods have emerged as a popular direction for analyzing tensor-valued data since they provide a…
This paper consists of real and complex affine techniques for studying the Abreu equation on toric surfaces. In particular, an interior estimate for Ricci tensor is given.
A geometrical way to calculate N-point Feynman diagrams is reviewed. As an example, the dimensionally-regulated three-point function is considered, including all orders of its epsilon-expansion. Analytical continuation to other regions of…
Twisted period integrals are ubiquitous in theoretical physics and mathematics, where they inhabit a finite-dimensional vector space governed by an inner product known as the intersection number. In this work, we uncover the associated…
Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…
Methods from learning theory are used in the state space of linear dynamical and control systems in order to estimate the system matrices. An application to stabilization via algebraic Riccati equations is included. The approach is…
The analysis of 3D symmetric second-order tensor fields often relies on topological features such as degenerate tensor lines, neutral surfaces, and their generalization to mode surfaces, which reveal important structural insights into the…
Efficient and stable algorithms for the calculation of spectral quantities and correlation functions are some of the key tools in computational condensed matter physics. In this article we review basic properties and recent developments of…
Developing non-perturbative methods to reveal exotic properties of strongly correlated fermionic systems remains one of the most essential tasks of theoretical physics. Tensor network methods with Grassmann algebra offer powerful numerical…
There is strong interest in developing mathematical methods that can be used to understand complex neural networks used in image analysis. In this paper, we introduce techniques from Linear Algebra to model neural network layers as maps…
Feynman diagrams are an essential tool for simulating strongly correlated electron systems. However, stochastic quantum Monte Carlo sampling suffers from the sign problem, particularly when solving a multiorbital quantum impurity model.…
We study a recently-proposed approach to the numerical evaluation of multi-loop Feynman integrals using available sector decomposition programs. As our main example, we consider the two-loop integrals for the $\alpha \alpha_s$ corrections…