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.
Curved spaces form a category of fibrant objects.
Objects are represented in sensory systems by continuous manifolds due to sensitivity of neuronal responses to changes in physical features such as location, orientation, and intensity. What makes certain sensory representations better suited for invariant decoding of objects by downstream networks? We present a theory…
Theory for soft-margin classifiers on object manifolds.
Perceptual manifolds arise when a neural population responds to an ensemble of sensory signals associated with different physical features (e.g., orientation, pose, scale, location, and intensity) of the same perceptual object. Object recognition and discrimination requires classifying the manifolds in a manner that is…
The paper proposes a method to learn 3D object pose manifolds using GANs and elasticae.
Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as Riemannian cubics on object manifolds that are endowed with norm…
Study KKT conditions for multi-objective optimization on Hadamard manifolds.
The Lagrangian formalism on a arbitrary non-fibrating manifold is considered. The kinematical description of this generic situation is based on the concept of (higher-order) Grassmann manifolds which is the factorization of the regular velocity manifold to the action of the differential group. Here we introduce in this…
Optimizes functions on manifolds using Gaussian processes and graph models.
The paper shows objective derivatives are covariant derivatives on Riemannian metrics.
Introduces intrinsic Riemannian cross-covariance for manifold-valued random objects.
New discrete cobordism category for nested manifolds and relations to algebraic structures.
On the product of two Finsler manifolds M1 M2, we consider the twisted metric F which is construct by using Finsler metrics F1 and F2 on the manifolds M1 and M2, respectively. We introduce horizontal and vertical distributions on twisted product Finsler manifold and study Creducible and semi-C-reducible properties of t…
A modular object in a symmetric monoidal bicategory is a Frobenius algebra object whose product and coproduct are biadjoint, equipped with a braided structure and a compatible twist, satisfying rigidity, ribbon, pivotality, and modularity conditions. We prove that the oriented 3-dimensional bordism bicategory of 1-, 2-…
We discuss corks, and introduce new objects which we call plugs. Though plugs are fundamentally different objects, they also detect exotic smooth structures in 4-manifolds like corks. We discuss relation between corks, plugs and rational blow-downs. We show how to detect corks and plugs inside of some exotic manifolds.…
We introduce the notion of a symplectic hopfoid, which is a "groupoid-like" object in the category of symplectic manifolds where morphisms are given by canonical relations. Such groupoid-like objects arise when applying a version of the cotangent functor to the structure maps of a Lie groupoid. We show that such object…
Study optimality conditions for interval-valued optimization problems on Riemannian manifolds.
Nonlinear embedding manifold learning methods provide invaluable visual insights into the structure of high-dimensional data. However, due to a complicated nonconvex objective function, these methods can easily get stuck in local minima and their embedding quality can be poor. We propose a natural extension to several …
The theory of ambient spaces is useful to define CR invariant objects, such as CR invariant powers of the sub-Laplacian, the -prime operators, and -prime curvature. However in general, it is difficult to write down these objects in terms of the Tanaka-Webster connection. In this paper, we give those explicit form…
Let C be some class of objects equipped with a set of simplifying moves. When we apply these to a given object M in C as long as possible, we get a root of M. Our main result is that under certain conditions the root of any object exists and is unique. We apply this result to different situations and get several new re…
Abstract: Tangent categories get a Cartan calculus with scalar multiplication by a commutative ring.
Introduces VB-structures for geometric objects on manifolds.
In this paper, we aim to provide a notion of "relative objects", i.e. objects equipped with some sort of subobjects, in differential topology. In spite of active researches relating them, e.g. knot theory or the theory of manifolds with corners, there seem to be poor general notions to deal with them. Moreover, we want…
Study para-Ricci-like solitons on special Riemannian manifolds, proving geometric properties and providing an example.
Variational approach to basic manifold structures.
We study some sub-Riemannian objects (such as horizontal connectivity, horizontal connection, horizontal tangent plane, horizontal mean curvature) in hypersurfaces of sub-Riemannian manifolds. We prove that if a connected hypersurface in a contact manifold of dimension more than three is noncharacteristic or with isola…
This survey article describes the algorithmic approaches successfully used over the time to construct hyperbolic structures on 3-dimensional topological "objects" of various types, and to classify several classes of such objects using such structures.
The object of the present paper is to study the locally - semisymmetric Kenmotsu manifolds along with the characterization of such notion.
We define a sutured cobordism category of surfaces with boundary and 3-manifolds with corners. In this category a sutured 3-manifold is regarded as a morphism from the empty surface to itself. In the process we define a new class of geometric objects, called bordered sutured manifolds, that generalize both sutured 3-ma…
Study on hermitian Yang-Mills connections on blown-up manifolds.
This paper develops a method to approximate the whole Pareto set for expensive multi-objective optimization.
The aim of the present paper is to provide an \emph{intrinsic} investigation of the properties of the most important geometric objects associated with the fundamental linear connections in Finsler geometry. We investigate intrinsically the most general relations concerning the torsion tensor fields and the curvature te…
New invariants derived from a modular category for links and 3-manifolds.
Galatius, Madsen, Tillmann and Weiss have identified the homotopy type of the classifying space of the cobordism category with objects (d-1)-dimensional manifolds embedded in R^\infty. In this paper we apply the techniques of spaces of manifolds, as developed by the author and Galatius, to identify the homotopy type of…
Stability conditions on K3 surfaces are linked to the masses of spherical objects.
A new privacy-preserving mechanism for shapes on manifolds.
The paper studies HYM connections on stable vector bundles over Kähler manifolds.
The object of study are almost complex manifolds with a pair of Norden metrics, mutually associated by means of the almost complex structure. More precisely, a torsion-free connection and tensors with geometric interpretation are found which are invariant under the twin interchange, i.e. the swap of the counterparts of…
Paper extends tail bounds to high-dimensional random objects on Riemannian manifolds.
The paper proves a category of dg manifolds with finite positive amplitude.
Score matching provides an effective approach to learning flexible unnormalized models, but its scalability is limited by the need to evaluate a second-order derivative. In this paper, we present a scalable approximation to a general family of learning objectives including score matching, by observing a new connection …
The object of study is almost paracomplex pseudo-Riemannian manifolds with a pair of metrics associated each other by the almost paracomplex structure. A torsion-free connection and tensors with geometric interpretation are found which are invariant under the twin interchange, i.e. the swap of the counterparts of the p…
The object of the present note is to discuss about the defining condition of weakly cyclic Ricci symmetric manifolds and weakly cyclic -symmetric manifolds \cite{DMS15} and the existence of such notion by proper examples.
Develops derived differential geometry theory.
Advances M-polyfolds for complex geometry applications.
If M is a manifold with compressible boundary, we analyze essential disks in M, as well as incompressible, but not necessarily boundary incompressible, surfaces in M. We are most interested in the case where M is a handlebody or compression body. The analysis depends on a new normal surface theory. We hope the normal s…
The paper explores how regularization can improve multi-objective learning with high-dimensional data.
We extend the problem of finding Hamiltonian-invariant volume forms on a Poisson manifold to the problem of construction of Hamiltonian-invariant generalized functions. For this we introduce the notion of generalized center of a Poisson algebra, which is the space of generalized Casimir functions. We study as the case …