Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision and pattern...
Ever since its publication, the Griffith theory is the most widely used criterion for estimating the ideal strength and fracture strength of materials depending on whether the materials contain cracks or not. A Griffith strength limit of ~E/9 is the...
In this article we review Tononi's (2008) theory of consciousness as integrated information. We argue that previous formalizations of integrated information (e.g. Griffith, 2014) depend on information loss. Since lossy integration would necessitate c...
We study the excess growth rate -- a fundamental logarithmic functional arising in portfolio theory -- from the perspective of information theory. We show that the excess growth rate can be connected to the Rényi and cross entropies, the Helmholtz f...
We resolve a conjecture of Cooper-Fenner-Purewal that a certain sequence of combinatorial matrices which can be used to bound small product-Ramsey numbers is positive semidefinite. Because the connection to Ramsey Theory involves solving quadratic in...
We show that for any $n\geq 3$ the theory of open generalized $n$-gons is complete, decidable and strictly stable, yielding a new class of examples in the zoo of stable theories....
We present the expansion of stout smearing and the Wilson flow in lattice perturbation theory to order $g_0^3$, which is suitable for one-loop calculations. As the Wilson flow is generated by infinitesimal stout smearing steps, the results are relate...
These are notes of lectures on spinning particles and the worldline formalism originally given by Olindo Corradini and Christian Schubert at the School on Spinning Particles in Quantum Field Theory: Worldline Formalism, Higher Spins, and Conformal Ge...
This note contributes to the structure theory of abstract rigidity matroids in general dimension. In the spirit of classical matroid theory, we prove several cryptomorphic characterizations of abstract rigidity matroids (in terms of circuits, cocircu...
We generalize the van Est map and isomorphism theorem in three ways, and we discuss conjectured connections with homotopy theory, including a proposal of a category which unifies differentiable stacks, Lie algebroids and homotopy theory. In Part 2 of...
The classical Van Est theory relates the smooth cohomology of Lie groups with the cohomology of the associated Lie algebra, or its relative versions. Some aspects of this theory generalize to Lie groupoids and their Lie algebroids. In this paper, con...
Recently, Lad, Patel, and Pratap (LP&P) [Phys. Rev. E 105, 064107 (2022)] revisited a microscopic theory of molecular motion in liquids, proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)]. Coming from this theory, LP&P derived a new equation of...
We compare and contrast two different metric based formulations of non- linear cosmological perturbation theory: the MW2009 approach in [K. A. Malik and D. Wands, Phys. Rept. 475 (2009), 1.] following Bardeen and the recent approach of the paper KN20...
Integrated Information Theory (IIT) is an audacious attempt to pin down the abstract, phenomenological experiences of consciousness into a rigorous, mathematical framework. We show that IIT's stance in regards to neuronal noise is inconsistent with e...
In this contribution to the special issue "Celebrating 30 years of Steven Weinberg's papers on Nuclear Forces from Chiral Lagrangians," we emphasize the important role chiral effective field theory has played in leading nuclear physics into a precisi...
I understand everyone has their own opinions about PvP in this game, but this is speaking **strictly from a game-theory perspective and nothing else**: ARC isn’t a zero-sum game like Tarkov where k...
For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is smooth at eve...
Points: 3 | Comments: 1 | Author: indigodaddy
We show how to derive a consistent quantum theory of radiation reaction of a non-relativistic point-dipole quantum oscillator by including the dynamical fluctuations of the position of the dipole. The proposed non-linear theory displays neither runaw...
Points: 2 | Comments: 0 | Author: gansai