A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Paper quantifies neural operators' efficiency for solving nonlinear parabolic PDEs.
The paper establishes maximum principles and stochastic completeness for pseudo-Hermitian manifolds.
Islamic banks being commercial entities strive to earn profit within shariah ambit. Therefore, they seem to be basing themselves upon two knowledge streams namely i) Islamic jurisprudence principles, and ii) banking principles. Islamic jurisprudence principles primarily aim at bringing shariah compliance while banking …
The h-principle helps solve complex geometric problems.
The study establishes uncertainty principles on harmonic manifolds of rank one.
Shows flexible sheaves as fibrant objects for Gromov's h-principle.
A new method to break down insurance costs into risk and uncertainty.
Study on maximum principles for nonlinear equations on Riemannian manifolds.
Derives Fredholm criteria for isotypical components from a Simonenko principle.
Establishes a boundary maximum principle for varifolds with fixed contact angle.
Study proves Maximum Principles for unbounded Riemannian domains.
A pricing principle is introduced for non-attainable claims in incomplete markets.
We show that a well known uncertainty principle for functions on the circle can be derived from an uncertainty principle for the Euclidean motion group.
Proves a principle for one-phase Bernoulli problem minimizers.
New method proves -principles for stable forms on manifolds.
We give a version of the comparison principle from pluripotential theory where the Monge-Ampère measure is replaced by the Bergman kernel and use it to derive a maximum principle
In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the marginal distribution of the process itself. This technique is an extension of the classical reflection principle for Brownian motion, and it is o…
Note establishes a local maximum principle for Ricci flow under curvature conditions.
Along with fruitful applications of Deep Neural Networks (DNNs) to realistic problems, recently, some empirical studies of DNNs reported a universal phenomenon of Frequency Principle (F-Principle): a DNN tends to learn a target function from low to high frequencies during the training. The F-Principle has been very use…
Derives time-averaged active inference from control principles.
New principle for harmonic maps helps study higher-dimensional submanifolds.
In this paper we give three applications of a method to prove h-principles on closed manifolds. Under weaker conditions this method proves a homological h-principle, under stronger conditions it proves a homotopical one. The three applications are as follows: a homotopical version of Vassiliev's h-principle, the contra…
In this paper we prove two extensions of Hamilton's maximal principle for systems pf parabolic equations which sould be useful for the study of the Ricci flow and some other geometric evolution equations. One extension is a time-dependent maximum principle and the other is a time-dependent maximum principle subject to …
We present a new statistical learning paradigm for Boltzmann machines based on a new inference principle we have proposed: the latent maximum entropy principle (LME). LME is different both from Jaynes maximum entropy principle and from standard maximum likelihood estimation.We demonstrate the LME principle BY deriving …
3-manifolds study Hasse norm principle, akin to number fields.
New equivalences found linking parabolicity, comparison principle, and capacity on Riemannian manifolds.
Maps to manifolds transverse to certain distributions satisfy an -principle.
Paper proves h-principles for symplectic structures and foliations.
Previous studies have shown that deep neural networks (DNNs) with common settings often capture target functions from low to high frequency, which is called Frequency Principle (F-Principle). It has also been shown that F-Principle can provide an understanding to the often observed good generalization ability of DNNs. …
Study shows strong min-max principle for phase transitions.
We prove that for an algebraic curvature tensor on a pseudo-Euclidean space, the Jordan-Osserman condition implies the Rakić duality principle, and that the Osserman condition and the duality principle are equivalent in the diagonalisable case.
Why deep neural networks (DNNs) capable of overfitting often generalize well in practice is a mystery [#zhang2016understanding]. To find a potential mechanism, we focus on the study of implicit biases underlying the training process of DNNs. In this work, for both real and synthetic datasets, we empirically find that a…
Photography method solves manifold invariants.
New distance comparison principle for curve shortening flow in higher dimensions.
Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. In this survey we discuss the following two fundamental Discretization Principles: the transformation group principle (smooth geometric objects and their discretizations are invar…
The net-premium principle is considered to be the most genuine and fair premium principle in actuarial applications. However, an insurance company, applying the net-premium principle, goes bankrupt with probability one in the long run, even if the company covers its entire costs by collecting the respective fees from i…
Study h-principles for non-integrable distributions on manifolds.
Study shows distance to boundary is always attained on varifolds with bounded curvature.
We investigate a variety of stability properties of Haezendonck-Goovaerts premium principles on their natural domain, namely Orlicz spaces. We show that such principles always satisfy the Fatou property. This allows to establish a tractable dual representation without imposing any condition on the reference Orlicz func…
We study the training process of Deep Neural Networks (DNNs) from the Fourier analysis perspective. We demonstrate a very universal Frequency Principle (F-Principle) -- DNNs often fit target functions from low to high frequencies -- on high-dimensional benchmark datasets such as MNIST/CIFAR10 and deep neural networks s…
Proves h-principle for loose Legendrian embeddings in contact topology.
Study curve flows with global forcing terms using a distance comparison principle.
In this paper we characterize the degenerate elliptic equations F(D^2u)=0 whose viscosity subsolutions, (F(D^2u) \geq 0), satisfy the strong maximum principle. We introduce an easily computed function f(t) for t > 0, determined by F, and we show that the strong maximum principle holds depending on whether the integral …
We establish a general "boundedness implies convergence" principle for a family of evolving Riemannian metrics. We then apply this principle to collapsing Calabi-Yau metrics and normalized Kähler-Ricci flows on torus fibered minimal models to obtain convergence results.
In this paper we present a proof of a Neumann type maximum principle for the Laplace operator on compact Riemannian manifolds. A key p oint is the simple geometric nature of the constant in the a priori estimate of this maximum principle. In particular, this maximum principle can be applied to manifolds with Ricci curv…
Study of complex Hessian equations using subharmonic functions and geodesics.
In this work we consider viscosity solutions to second order partial differential equations on Riemannian manifolds. We prove maximum principles for solutions to Dirichlet problem on a compact Riemannian manifold with boundary. Using a different method, we generalize maximum principles of Omori and Yau to a viscosity v…
We explain the meaning of local symmetries in physics.