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HOOK-SHAPE IMMANANT CHARACTERS FROM STANLEY-STEMBRIDGE CHARACTERS

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arXiv 2023年

作者： Lesnevich, Nathan R.T. Department of Mathematics and Statistics Washington University in St. Louis One Brookings Drive St. LouisMO63130 United States

We consider the Schur-positivity of monomial immanants of Jacobi-Trudi matrices, in particular whether a non-negative coefficient of the trivial Schur function implies non-negative coefficients for other Schur functions in said immanants. We prove that this true for hook-shape Schur functions using combinatorial methods in a representation theory setting. Our main theorem proves that hook-shape immanant characters can be written as finite non-negative integer sums of Stanley-Stembridge characters, and provides an explicit combinatorial formula for these sums. This resolves a special case of a longstanding conjecture of Stanley and Stembridge that posits such a sum exists for all immanant characters. We also provide several simplifications for computing immanant characters, and several corollaries applying the main result to cases where the coefficient of the trivial Schur function in monomial immanants of Jacobi-Trudi matrices is known to be *** Codes 05E05 (Primary) 05E10 (Secondary) Copyright © 2023, The Authors. All rights reserved.

关键词： computation theory

A FINITE ELEMENT IMPLEMENTATION OF FINITE DEFORMATION SURFACE AND BULK POROELASTICITY

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arXiv 2023年

作者： Kim, Jaemin Ang, Ida Ballarin, Francesco Hui, Chung-Yuen Bouklas, Nikolaos Sibley School of Mechanical and Aerospace Engineering Cornell University IthacaNY14853 United States Dipartimento di Matematica e Fisica "N. Tartaglia" Università Cattolica del Sacro Cuore via della Garzetta 48 Brescia25133 Italy Field of Theoretical and Applied Mechanics Cornell University IthacaNY14853 United States Global Station for Soft Matter GI-CoRE Hokkaido University Sapporo Japan

We present a theoretical and computational model for the behavior of a porous solid undergoing two interdependent processes, the finite deformation of a solid and species migration through the solid, which are distinct in bulk and on surface. Nonlinear theories allow us to systematically study porous solids in a wide range of applications, such as drug delivery, biomaterial design, fundamental study of biomechanics and mechanobiology, and the design of sensors and actuators. As we aim to understand the physical phenomena at a smaller length scale towards comprehending the fundamental biological processes and the miniaturization of devices, the surface effect becomes more pertinent. Although existing methodologies provide the necessary tools to study coupled bulk effects for deformation and diffusion;however, very little is known about fully coupled bulk and surface poroelasticity at finite strain. Here we develop a thermodynamically consistent formulation for multiphysics processes of surface and bulk poroelasticity, specialized for soft hydrated solids, along with a corresponding finite element implementation. Our multiphysical approach captures the interplay between competing processes of finite deformation and species diffusion through the bulk and surface, and provides invaluable insight when surface effects are important. © 2023, CC BY.

关键词： computation theory

Elliptic genera from classical error-correcting codes

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arXiv 2023年

作者： Kawabata, Kohki Yahagi, Shinichiro Department of Physics Faculty of Science The University of Tokyo Bunkyo-Ku Tokyo113-0033 Japan Department of Physics Osaka University Machikaneyama-Cho 1-1 Toyonaka560-0043 Japan

We consider chiral fermionic conformal field theories constructed from classical error-correcting codes and provide a systematic way of computing their elliptic genera. We exploit the U(1) current of the N = 2 superconformal algebra to obtain the U(1)-graded partition function that is invariant under the modular transformation and the spectral flow. We demonstrate our method by constructing extremal N = 2 elliptic genera from classical codes for relatively small central charges. Also, we give near-extremal elliptic genera and decompose them into N = 2 superconformal characters. Copyright © 2023, The Authors. All rights reserved.

关键词： computation theory

A Mean Field Game Approach to Optimal Investment and Risk Control for Competitive Insurers

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SSRN

SSRN 2023年

作者： Bo, Lijun Wang, Shihua Zhou, Chao School of Mathematics and Statistics Xidian University Xi’an710126 China School of Mathematical Sciences University of Science and Technology of China Hefei230026 China Department of Mathematics National University of Singapore 10 Lower Kent Ridge Rd. 119076 Singapore

We consider an insurance market consisting of multiple competitive insures with a mean filed interaction via their terminal wealths under the exponential performance. It is assumed that each insurer regulates her risk by controlling the number of polices. We respectively establish the constant Nash equilibrium (independent of time) on the investment and risk control strategy for finite n-insurer and the constant mean field equilibrium for the corresponding mean field game (MFG) problem (when the number of insurers tends to infinite). We examine the convergence relationship between the constant Nash equilibrium of finite-n insurer and the mean field equilibrium of the corresponding MFG game. © 2023, The Authors. All rights reserved.

关键词： computation theory

THH OF THE MORAVA E-theory SPECTRUM E2

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arXiv 2023年

作者： Agarwal, Sanjana

The Morava E-theories, En, are complex-oriented 2-periodic ring spectra, with homotopy groups WFpn [[u1, u2, ..., un−1]][u, u−1]. Here W denotes the Witt vector ring. En is a Landweber exact spectrum and hence uniquely determined by this ring as BP∗-algebra. Algebraic K-theory of En is a key ingredient towards analyzing the layers in the p-complete Waldhausen’s K-theory chromatic tower. One hopes to use the machinery of trace methods to get results towards K-theory once the computation for T HH(En) is known. In this paper we describe T HH(E2) as part of consecutive chain of cofiber sequences where each cofiber sits in the next cofiber sequence and the first term of each cofiber sequence is describable completely in terms of suspensions and localisations of E2. For these results, we first calculate K(i)-homology of T HH(E2) using a Bökstedt spectral sequence and then lift the generating classes of K(1)-homology to fundamental classes in homotopy group of T HH(E2). These lifts allow us to construct terms of the cofiber sequence and explicitly understand how they map to T HH(E2). Copyright © 2023, The Authors. All rights reserved.

关键词： computation theory

ADAMS SPECTRAL SEQUENCES FOR NON-VECTOR-BUNDLE THOM SPECTRA

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arXiv 2023年

作者： Debray, Arun Yu, Matthew Purdue University West LafayetteIN United States Perimeter Institute for Theoretical Physics WaterlooON Canada

When R is one of the spectra ku, ko, tmf , MTSpinc, MTSpin, or MTString, there is a standard approach to computing twisted R-homology groups of a space X with the Adams spectral sequence, by using a change-of-rings isomorphism to simplify the E2-page. This approach requires the assumption that the twist comes from a vector bundle, i.e. the twist map X → BGL1(R) factors through BO. We show this assumption is unnecessary by working with Baker-Lazarev’s Adams spectral sequence of R-modules and computing its E2-page for a large class of twists of these spectra. We then work through two example computations motivated by anomaly cancellation for supergravity theories. © 2023, CC BY.

关键词： computation theory

Equidistribution of lattice orbits in the space of homothety classes of rank 2 sublattices in R3

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arXiv 2023年

作者： Bersudsky, Michael Xing, Hao Department of mathematics The Ohio State University United States

We study the distribution of orbits of a lattice Γ ≤ SL(3, R) in the moduli space X2,3 of covolume one rank-two discrete subgroups in R3. Each orbit is dense, and our main result is the limiting distribution of these orbits with respect to norm balls, where the norm is given by the sum of squares. Specifically, we consider ΓT = {γ ∈ Γ: kγk ≤ T } and show that, for any fixed x0 ∈ X2,3 and (Equation presented), where ν˜x0 is an explicit probability measure on X2,3 depending on x0. To prove our result, we use the duality principle developed by Gorodnik and Weiss which recasts the above problem into the problem of computation of certain volume estimates of growing skewed balls in H and proving ergodic theorems of the left action of the skewed balls on SL(3, R)/Γ. The ergodic theorems are proven by applying theorems of Shah building on the linearisation technique. The main contribution of the paper is the application of the duality principle in the case where H has infinitely many non-compact connected *** Codes 37 © 2023, CC BY.

关键词： computation theory

Conformal field theory-data analysis for N = 4 Super-Yang-Mills at strong coupling

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arXiv 2023年

作者： Julius, Julius Sokolova, Nika Harish-Chandra Research Institute Homi Bhabha National Institute Chhatnag Road Jhunsi Allahabad211019 India Department of Mathematics King’s College London Strand WC2R 2LS United Kingdom

We analyse the CFT-data of planar 4D N = 4 Super-Yang-Mills theory at strong coupling. By combining spectral data extracted from integrability, with recent advances in computing the AdS Virasoro-Shapiro amplitude, we extract predictions for leading order OPE coefficients on entire Kaluza-Klein (KK-)towers of states. We observe that the appropriately normalised leading order OPE coefficients for all states in a given KK-tower are the same. Furthermore, we also notice that, in many cases, the leading order OPE coefficients of all states in the KK-tower vanish, suggesting a simplification of the physics in this limit. Copyright © 2023, The Authors. All rights reserved.

关键词： computation theory

computational Adequacy for Substructural Lambda Calculi 3

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Computational Adequacy for Substructural Lambda Calculi

Proceedings of the 3rd Annual International Applied Category theory Conference

作者： Zamdzhiev, Vladimir Univ Lorraine CNRS Inria LORIA F-54000 Nancy France

Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum programming. We describe one linear and one affine type systems and we formulate abstract categorical models for both of them which are sound and computationally adequate. We also show, under basic assumptions, that interpreting lambda abstractions via a monoidal closed structure (a popular method for linear type systems) necessarily leads to degenerate and inadequate models for call-by-value affine type systems with recursion. In our categorical treatment, a solution to this problem is clearly presented. Our categorical models are more general than linear/non-linear models used to study linear logic and we present a homogeneous categorical account of both linear and affine type systems in a call-by-value setting. We also give examples with many concrete models, including classical and quantum ones.

关键词： computation theory