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.
Generalizes string-net modular functors to non-spherical categories.
Study spherical twists on K3 surfaces, compute their centers.
Racks and quandles are rich algebraic structures that are strong enough to classify knots. Here we develop several fundamental categorical aspects of the theories of racks and quandles and their relation to the theory of permutations. In particular, we compute the centers of the categories and describe power operations…
Study of generalized Legendrian racks and their GL-structures.
The paper proves a theorem linking convex body centroids and category theory.
The center Z(C) of a spherical fusion category C (over an arbitrary commutative ring) is modular. We give an algorithm for computing the Reshetikhin-Turaev invariant defined with Z(C). It is based on Hopf diagrams and an explicit description of the structure of the coend of Z(C).
3D HQFT comparison proves state sum equals surgery.
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first consider the similarity of elements in the data as the connectivity of nodes in an…
Study partially hyperbolic dynamics on 3-manifolds with quasi-isometric center.
For a group G, the notion of a ribbon G-category was introduced by the second author in a previous work with a view towards constructing 3-dimensional homotopy quantum field theories (HQFT's) with target K(G,1). We discuss here how to derive ribbon G-categories from a simple complex Lie algebra g where G is the center …
This paper introduces quantum invariants for 3-alterfolds and proves their consistency with topological moves.
Let C be a spherical fusion category. We prove that the Turaev-Viro-Barrett-Westbury state sum invariant of 3-manifolds derived from C is equal to the Reshetikhin-Turaev surgery invariant of 3-manifolds derived from Z(C), where Z(C) is the Drinfeld-Joyal-Street center of C.
In this paper we show how one can extend Turaev-Viro invariants, defined for an arbitrary spherical fusion category , to 3-manifolds with corners. We demonstrate that this gives an extended TQFT which conjecturally coincides with the Reshetikhin-Turaev TQFT corresponding to the Drinfeld center . In the present…
In this paper is proposed a kind of model theory for our axiomatic differential geometry. It is claimed that smooth manifolds, which have occupied the center stage in differential geometry, should be replaced by functors on the category of Weil algebras. Our model theory is geometrically natural and conceptually motiva…
Language models allocate information storage, not collapsing into uniform representations.
Unified understanding of neural representation similarity measures.
3D topological order linked to Seifert manifolds and gauge groups.
Geometrically computes sheaves linking HOMFLY-PT homology to Hilbert schemes.
This paper deals with sheaves of differential operators on noncommutative algebras. The sheaves are defined by quotienting a the tensor algebra of vector fields (suitably deformed by a covariant derivative) to ensure zero curvature. As an example we can obtain enveloping algebra like relations for Hopf algebras with di…
A new method for optimizing functions with both categorical and continuous variables.
Following widely used in visual recognition concept of relative attributes, the article establishes definition of the relative PCA attributes for a class of objects defined by vectors of their parameters. A new rating model (RELARM) is built using relative PCA attribute ranking functions for rating object description a…
This paper updates knot invariants using Hopf algebras and categorifies their structure.
The HKR (Hennings-Kauffman-Radford) framework is used to construct invariants of 4-thickenings of 2-dimensional CW complexes under 2-deformations (1- and 2- handle slides and creations and cancellations of 1-2 handle pairs). The input of the invariant is a finite dimensional unimodular ribbon Hopf algebra A and an elem…
Blockchain aims to improve trust in AI systems, but lacks systematic studies.
A new method centers outliers in robust PCA without manual intervention.
Center identified in stated skein algebra for quantum traces.
The object of our investigation is a point that gives the maximum value of a potential with a strictly decreasing radially symmetric kernel. It defines a center of a body in Rm. When we choose the Riesz kernel or the Poisson kernel as the kernel, such centers are called a radial center or an illuminating center, respec…
Refines geometric center of mass analysis for Einstein field equations.
Let f:M->M be a partially hyperbolic diffeomorphism such that all of its center leaves are compact. We prove that Sullivan's example of a circle foliation that has arbitrary long leaves cannot be the center foliation of f. This is proved by thorough study of the accessible boundaries of the center-stable and the center…
We investigate centers of a body (the closure of a bounded open set) defined as maximum points of potentials. In particular, we study centers defined by the Riesz potential and by Poisson's integral. These centers, in general, depend on parameters and move with respect to the parameters. We give a necessary and suffici…
We prove the existence of a center, or continuous selection of a point, in the relative interior of embedded -disks in Riemannian -manifolds. If the center can be made equivariant with respect to the isometries of the manifold, and under mild assumptions the same holds for . By contrast, for…
This work analyzes centered binary Restricted Boltzmann Machines (RBMs) and binary Deep Boltzmann Machines (DBMs), where centering is done by subtracting offset values from visible and hidden variables. We show analytically that (i) centering results in a different but equivalent parameterization for artificial neural …
The paper quantizes concatenated noisy vectors to a common cluster center, improving performance over naive methods.
In this study, we investigate the locus of the centers of the Meusnier spheres. Just as focal curve is the locus of the centers of the osculating spheres, we investigate the geometrical interpretation on the locus of the centers of the Meusnier spheres. We proved that if the curve is a principal line, the locus of the …
This article briefly introduced Arthur and Vassilvitshii's work on \textbf{k-means++} algorithm and further generalized the center initialization process. It is found that choosing the most distant sample point from the nearest center as new center can mostly have the same effect as the center initialization process in…
Absolutely partially hyperbolic surface endomorphisms have a coherent center foliation.
Suppose one is faced with the challenge of tissue segmentation in MR images, without annotators at their center to provide labeled training data. One option is to go to another medical center for a trained classifier. Sadly, tissue classifiers do not generalize well across centers due to voxel intensity shifts caused b…
Introduces Quantum Data Center for quantum era benefits.
Studies amenable category's monotonicity and its relation to topological complexity.
To each oriented surface S, we associate a differential graded category Ko(S). The homotopy category Ho(Ko(S)) is a triangulated category which satisfies properties akin to those of the contact categories studied by K. Honda. These categories are also related to the algebraic contact categories of Y. Tian and to the bo…
Unified theory linking atom-centered and message-passing models for molecular properties.
Characterizes G2-structures on Lie algebras with non-trivial center.
Paper introduces new center of mass for flat manifolds.
Simplified proof of mass center system's uniqueness and generalized Pappus' theorem across Euclidean, spherical, and hyperbolic geometries.
New features for quantum calculations learn N-center Hamiltonian matrix elements.
For nearly spherical bodies, the unique center is proven under certain conditions.
Formulates a new connection between topological and geometric categories.
We show that the center of the Goldman algebra associated to a closed oriented hyperbolic surface is trivial. For a hyperbolic surface of finite type with nonempty boundary, the center consists of closed curves which are homotopic to boundary components or punctures.