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.
The paper characterizes Conway-Coxeter friezes using rational links.
We construct a finite dimensional quiver algebra from the non-simply laced type Dynkin diagram, which we call the type zigzag algebra. This leads to a faithful categorical action of the type braid group , acting on the homotopy category of its projective modules. This categorical action is a…
New categorical actions link topological and algebraic structures.
A zigzag in a plane graph is a circuit of edges, such that any two, but no three, consecutive edges belong to the same face. A railroad in a plane graph is a circuit of hexagonal faces, such that any hexagon is adjacent to its neighbors on opposite edges. A graph without a railroad is called tight. We consider the zigz…
Study Lagrangian zigzag cobordisms for Legendrian knots, comparing to smooth concordance.
Zigzag sampling algorithm efficiently samples from strongly log-concave distributions with low computational cost.
The study explores cohomological invariants and decomposes them into irreducible parts, focusing on zigzags.
We construct an action of the free group on the homotopy category of projective modules over a finite dimensional zigzag algebra. The main theorem in the paper is that this action is faithful. We describe the relationship between homotopy classes of paths in the punctured disc and complexes of projective zigzag m…
Z-GCNETs uses topological data to improve time series forecasting.
We give a simple proof of the Emch closing theorem by introducing a new invariant measure on the circle. Special cases of that measures are well-known and have been used in the literature to prove Poncelet's and Zigzag theorems. Some further generalizations are also obtained by applying the new measure.
In the present paper, we build a bridge between Conway-Coxeter friezes and rational tangles through the Kauffman bracket polynomials. One can compute a Kauffman bracket polynomials attached to rational links by using Conway-Coxeter friezes. As an application one can give a complete invariant on Conway-Coxeter friezes o…
We consider here 6-regular plane graphs whose faces have size 1, 2 or 3. In Section 2 a practical enumeration method is given that allowed us to enumerate them up to 53 vertices. Subsequently, in Section 3 we enumerate all possible symmetry groups of the spheres that showed up. In Section 4 we introduce a new Goldberg-…
In this paper, a new higher Hochschild Complex is defined with an Iterated Integral map to locally model differential forms on the space of bigons on . In particular, given the local data for a gerbe with structure 2-group given by a crossed module of matrix-groups, there is an element in our curved zigzag Hochschil…
A zigzag in a map (a -cell embedding of a connected graph in a connected closed -dimensional surface) is a cyclic sequence of edges satisfying the following conditions: 1) any two consecutive edges lie on the same face and have a common vertex, 2) for any three consecutive edges the first and the third edges are …
Study cohomology of Bigolin complex on complex manifolds.
We determine all critical configurations for the Area function on polygons with vertices on a circle or an ellipse. For isolated critical points we compute their Morse index, resp index of the gradient vector field. We relate the computation at an isolated degenerate point to an eigenvalue question about combinations. …
TabPFN's internal geometry topology correlates with dataset reliability.
Complete classification of rod complements in 3-torus using topology.
Traditional models of macroeconomic dynamics are fundamentally incorrect. The reason lies in a misunderstanding of peculiarities of the analysis of infinitesimal quantities. However, even those types of solutions that are envisaged by the above-mentioned models are nonrepresentative in the sense of the reflection of re…
An i-hedrite is a 4-regular plane graph with faces of size 2, 3 and 4. We do a short survey of their known properties and explain some new algorithms that allow their efficient enumeration. Using this we give the symmetry groups of all i-hedrites and the minimal representative for each. We also review the link of 4-hed…
We develop a novel family of algorithms for the online learning setting with regret against any data sequence bounded by the empirical Rademacher complexity of that sequence. To develop a general theory of when this type of adaptive regret bound is achievable we establish a connection to the theory of decoupling inequa…
We study consequences and applications of the folklore statement that every double complex over a field decomposes into so-called squares and zigzags. This result makes questions about the associated cohomology groups and spectral sequences easy to understand. We describe a notion of `universal' quasi-isomorphism, inve…
Develops a first-order interior-point method for solving constrained variational inequalities.
Typilus predicts types for Python programs using neural networks.
LambdaNet infers TypeScript types using graph neural networks.
Study shows partially-typed NER datasets can match fully-typed ones in model performance.
The generic fiber of a Lagrangian fibration on an irreducible holomorphic symplectic manifold is an abelian variety. Associate a polarization type to such Lagrangian fibrations coming from polarizations on a generic fiber. We prove that this polarization type is constant in families of Lagrangian fibrations. Further, w…
We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type. We obtain a full classification of all operators that admit Wronskian type Darboux transformations of first order and a …
Category theory generalizes finite type invariants using diagrams systems.
New spherical curve deformations solve a conjecture.
Despite the great success of deep neural networks, the adversarial attack can cheat some well-trained classifiers by small permutations. In this paper, we propose another type of adversarial attack that can cheat classifiers by significant changes. For example, we can significantly change a face but well-trained neural…
Finite-type surfaces have a topological Hopf property.
As entity type systems become richer and more fine-grained, we expect the number of types assigned to a given entity to increase. However, most fine-grained typing work has focused on datasets that exhibit a low degree of type multiplicity. In this paper, we consider the high-multiplicity regime inherent in data source…
Kähler-Ricci flow singularity type is independent of initial metric.
In the theory of finite type submanifolds, null 2-type submanifolds are the most simple ones, besides 1-type submanifolds (cf. e.g., [3, 12]). In particular, the classification problems of null 2-type hypersurfaces are quite interesting and of fundamentally important. In this paper, we prove that every (3)-ideal nul…
We describe a bordered version of totally twisted Khovanov homology. We first twist Roberts's type structure by adding a "vertical" type structure which generalizes the vertical map in twisted tangle homology. One of the distinct advantages of our type structure is that it is homotopy equivalent to a type $…
The paper defines a new equivalence relation for knot projections and finds an infinite number of distinct classes.
It is known that all left-invariant pseudo-Riemannian metrics on are algebraic Ricci solitons. We consider generalizations of Riemannian -type, namely pseudo-type and -type. We study algebraic Ricci solitons of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups of both types.
Study BF invariants using simple type concepts.
We study Legendrian knots in a cabled knot type. Specifically, given a topological knot type K, we analyze the Legendrian knots in knot types obtained from K by cabling, in terms of Legendrian knots in the knot type K. As a corollary of this analysis, we show that the (2,3)-cable of the (2,3)-torus knot is not transver…
Study flip graphs for surfaces of infinite type, finding uncountably many connected components.
Crowdsourced labeling recovers task types with minimal queries.
Nearly Kähler and Kähler-Codazzi type manifolds are defined in a very similar way. We prove that nearly Kähler type manifolds have sense just in Hermitian and para-Hermitian contexts, and that Kähler-Codazzi type manifolds reduce to Kähler type manifolds in all the four Hermitian, para-Hermitian, Norden and product Rie…
Constructs two types of Eguchi-Hanson metrics with negative scalar curvature.
We define a notion of finite type invariants for links with a fixed linking matrix. We show that Milnor's triple link homotopy invariant is a finite type invariant, of type 1, in this sense. We also generalize the approach to Milnor's higher order homotopy invariants and show that they are also, in a sense, of finite t…
In this paper, we obtain a Cartan type identity for curvature-adapted isoparametric hypersurfaces in symmetric spaces of compact type or non-compact type. This identity is a generalization of Cartan-D'Atri's identity for curvature-adapted(=amenable) isoparametric hypersurfaces in rank one symmetric spaces. Furthermore,…
Extends A-type coefficient polynomials to B-type setting, introducing new invariants.
Paper shows certain algebra types are not differentially smooth.