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.
Study natural and conjugate mates of Frenet curves in Lie groups.
New method proves mateability of triangle groups with Blaschke products.
Unified and generalized mating frameworks for Kleinian groups and rational maps.
This note gives sufficient conditions (isothermic or totally nonisothermic) for an immersion of a compact surface to have no Bonnet mate.
New framework mated Kleinian groups with complex polynomials, revealing unique group properties.
The paper connects reflection groups to maps with specific dynamical properties.
In this work, we studied the properties of the spherical indicatrices of a Bertrand curve and its mate curve and presented some characteristic properties in the cases that Bertrand curve and its mate curve are slant helices, spherical indicatrices are slant helices and we also researched that whether the spherical indi…
Overview of dynamics in algebraic correspondences and their connections.
We present a novel method for solving Canonical Correlation Analysis (CCA) in a sparse convex framework using a least squares approach. The presented method focuses on the scenario when one is interested in (or limited to) a primal representation for the first view while having a dual representation for the second view…
The Bonnet problem is solved for specific Thurston geometries.
The paper studies degenerations of rational maps and their limits as geometrically finite rational maps.
In this work, we study plane and spherical curves in Euclidean and Lorentz-Minkowski 3-spaces by employing rotation minimizing (RM) frames. By conveniently writing the curvature and torsion for a curve on a sphere, we show how to find the angle between the principal normal and an RM vector field for spherical curves. L…
Automated model tracks mouse behavior in home cages.
Study of holomorphic correspondences combining entire maps and Fuchsian groups.
The study of Bonnet surfaces in 4D space forms reveals new conformally invariant properties and characterizes proper Bonnet surfaces.
In this article, we introduce rack invariants of oriented Legendrian knots in the 3-dimensional Euclidean space endowed with the standard contact structure, which we call Legendrian racks. These invariants form a generalization of the quandle invariants of knots. These rack invariants do not result in a complete invari…
Develops analogs of character varieties for algebraic correspondences, proving boundedness and compactifications.
With recent advances in high throughput technology, researchers often find themselves running a large number of hypothesis tests (thousands+) and esti- mating a large number of effect-sizes. Generally there is particular interest in those effects estimated to be most extreme. Unfortunately naive estimates of these effe…
We propose the Legendrian web in a contact three manifold as a second order generalization of the planar web. An Abelian relation for a Legendrian web is analogously defined as an additive equation among the first integrals of its foliations. For a class of Legendrian -webs defined by simple second order ODE's, w…
Single-cell RNA sequencing (scRNA-seq) is a fast growing approach to measure the genome-wide transcriptome of many individual cells in parallel, but results in noisy data with many dropout events. Existing methods to learn molecular signatures from bulk transcriptomic data may therefore not be adapted to scRNA-seq data…
Survey explores interactions between four conformal dynamics branches.
Optimizing a neural network's performance is a tedious and time taking process, this iterative process does not have any defined solution which can work for all the problems. Optimization can be roughly categorized into - Architecture and Hyperparameter optimization. Many algorithms have been devised to address this pr…
An important task for many if not all the scientific domains is efficient knowledge integration, testing and codification. It is often solved with model construction in a controllable computational environment. In spite of that, the throughput of in-silico simulation-based observations become similarly intractable for …
Meta-learning framework improves explainability of GNNs.
Enhanced evolutionary algorithms solve NP-hard portfolio optimization with cardinality constraints.
Study quantifies firm risks from nature decline, showing significant equity losses.
When a gauge-natural invariant variational principle is assigned, to determine {\em canonical} covariant conservation laws, the vertical part of gauge-natural lifts of infinitesimal principal automorphisms -- defining infinitesimal variations of sections of gauge-natural bundles -- must satisfy generalized Jacobi equat…
A new method for classifying naturally reductive spaces is presented. This method relies on the structure theory of naturally reductive spaces developed in \cite{Storm2018a} and the new construction of naturally reductive spaces in \cite{Storm2018}. We obtain the classification of all naturally reductive spaces in dime…
Generates natural product-like compounds using GPT models.
Defines and proves the uniqueness of a second natural connection on Riemannian Π-manifolds.
New definition of naturally reductive Finsler manifolds using geodesic graphs.
Study characterizes naturally reductive metrics on homogeneous manifolds.
A new construction of naturally reductive spaces is presented. This construction gives a large amount of new families of naturally reductive spaces. First the infinitesimal models of the new naturally reductive spaces are constructed. A concrete transitive group of isometries is given for the new spaces and also the na…
Natural gradient simplification for deep learning networks.
Study finds real-world datasets contain natural experiments that can improve model performance.
We prove that the natural principal parameters on a given Weingarten surface are also natural principal parameters for the parallel surfaces of the given one. As a consequence of this result we obtain that the natural PDE of any Weingarten surface is the natural PDE of its parallel surfaces. We show that the linear fra…
Paper shows spectra can't distinguish naturally reductive manifolds.
In the present paper we study naturally reductive homogeneous -metric spaces. Under some conditions, we give some necessary and sufficient conditions for a homogeneous -metric space to be naturally reductive. Then we show that for such spaces the two definitions of naturally reductive homogeneous Finsler …
I.A.B. Strachan introduced the notion of a natural Frobenius submanifold of a Frobenius manifold and gave a sufficient but not necessary condition for a submanifold to be a natural Frobenius submanifold. This paper will give a necessary and sufficient condition and classify the natural Frobenius hypersurfaces.
Introduces a natural parallel translation for navigation data.
Study proves naturality and functoriality in a type of Heegaard Floer homology.
The natural gradient method has been used effectively in conjugate Gaussian process models, but the non-conjugate case has been largely unexplored. We examine how natural gradients can be used in non-conjugate stochastic settings, together with hyperparameter learning. We conclude that the natural gradient can signific…
A reductive structure is associated here with Lagrangian canonically defined conserved quantities on gauge-natural bundles. Parametrized transformations defined by the gauge-natural lift of infinitesimal principal automorphisms induce a variational sequence such that the generalized Jacobi morphism is naturally self-ad…
Defines a new natural connection on Riemannian Π-manifolds.
We discuss natural transformations in the context of Lie groupoids, and their infinitesimal counterpart. Our main result is an integration procedure that provides smooth natural transformations between Lie groupoid morphisms.
Square-root natural-gradient improves variational inference convergence.
Paper proposes a natural hedging framework with graphical assessment for longevity risk management.
Study natural invariants for differential operators, simplifying their equivalence problem.