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 restrictions on digitally continuous functions and their effects.
Survey on affine Anosov representations and their implications.
In this purely expository note, we recall a few known properties of 3-dimensional singularity models. These properties are direct consequences of Perelman's canonical neighborhood theorem for 3-dimensional Ricci flow and compactness theorem for 3-dimensional kappa-solutions.
The Bergman metric on symmetrized bidisc has negative curvature properties.
Just as the Jacobi identity of vector fields is a natural consequence of the general Jacobi identity of microcubes in synthetic differential geometry, it is to be shown in this paper that the graded Jacobi identity of the Frolicher-Nijenhuis bracket is also a natural consequence of the general Jacobi identity.
We present, solve and numerically simulate a simple model that describes the consequences of increased longevity on fertility rates, population growth and the distribution of wealth in developed societies. We look at the consequences of the repeated use of life extension techniques and show that they represent a novel …
We show that the analog of Hamilton's Ricci flow in the combinatorial setting produces solutions which converge exponentially fast to Thurston's circle packing on surfaces. As a consequence, a new proof of Thurston's existence of circle packing theorem is obtained. As another consequence, Ricci flow suggests a new algo…
We describe, in the general setting of closed cone fields, the set of causal functions which can be approximated by smooth Lyapunov. We derive several consequences on causality theory. Dans le contexte général des champs de cones fermés, on décrit l'ensemble des fonctions causales qui peuvent être approchées par des fo…
Homotopy proof for pseudomanifolds via branched covers.
Using a maximum principle for self-shrinkers of the mean curvature flow, we give new proofs of a rigidity theorem for rotationally symmetric compact self-shrinkers and a result about the asymptotic behavior of self-shrinkers. This comparison argument also implies a linear bound for the second fundamental form of self-s…
Machine Learning models become increasingly proficient in complex tasks. However, even for experts in the field, it can be difficult to understand what the model learned. This hampers trust and acceptance, and it obstructs the possibility to correct the model. There is therefore a need for transparency of machine learn…
We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data. We challenge t…
A gauged bi-differential calculus over an associative (and not necessarily commutative) algebra A is an N-graded left A-module with two covariant derivatives acting on it which, as a consequence of certain (e.g., nonlinear differential) equations, are flat and anticommute. As a consequence, there is an iterative constr…
VB uses natural gradients in information geometry.
Knowing and modelling the migration phenomena and especially the social and economic consequences have a theoretical and practical importance, being related to their consequences for development, economic progress (or as appropriate, regression), environmental influences etc. One of the causes of migration, especially …
The paper discusses various practical consequences of treating economics and finance as an inherently dynamic and chaotic system. On the theoretical side this looks at the general applicability of the market-making pricing approach to economics in general. The paper also discuses the consequences of the endogenous crea…
We observe that Whitehead's lemma is an immediate consequence of Stallings folds.
We study algebro-geometric consequences of the quantised extremal Kähler metrics, introduced in the previous work of the author. We prove that the existence of quantised extremal metrics implies weak relative Chow polystability. As a consequence, we obtain asymptotic weak relative Chow polystability and -semistabili…
We use a weighted variant of the frequency functions introduced by Almgren to prove sharp asymptotic estimates for almost eigenfunctions of the drift Laplacian associated to the Gaussian weight on an asymptotically conical end. As a consequence, we obtain a purely elliptic proof of a result of L. Wang on the uniqueness…
We use computer algebra to demonstrate the existence of a multilinear polynomial identity of degree 8 satisfied by the bilinear operation in every Lie-Yamaguti algebra. This identity is a consequence of the defining identities for Lie-Yamaguti algebras, but is not a consequence of anticommutativity. We give an explicit…
We show that instanton knot homology is mutation-invariant, as a consequence of earlier work of the third author.
In this paper we investigate two variants of association rules for preference data, Label Ranking Association Rules and Pairwise Association Rules. Label Ranking Association Rules (LRAR) are the equivalent of Class Association Rules (CAR) for the Label Ranking task. In CAR, the consequent is a single class, to which th…
Isometric embeddings of Teichmüller spaces are derived from branched coverings.
In this study, we determine some special Smarandache curves in E1 3.We give some characterizations consequences of Smarandache curves.
Holomorphic actions on complex spaces for nilpotent groups.
As machine learning (ML) increasingly affects people and society, awareness of its potential unwanted consequences has also grown. To anticipate, prevent, and mitigate undesirable downstream consequences, it is critical that we understand when and how harm might be introduced throughout the ML life cycle. In this paper…
We review two strands of conceptual approaches to the formal representation of a decision maker's non-knowledge at the initial stage of a static one-person, one-shot decision problem in economic theory. One focuses on representations of non-knowledge in terms of probability measures over sets of mutually exclusive and …
We have one more look at the (homological) perturbation lemma and we point out some non-standard consequences, including the relevance to deformations.
In this article we will propose a completely new point of view for solving one of the most important paradoxes concerning game theory. The solution develop shifts the focus from the result to the strategy s ability to operate in a cognitive way by exploiting useful information about the system. In order to determine fr…
Study evaluates how framing affects machine learning models for sepsis prediction.
We summarize properties of 3-manifold groups, with a particular focus on the consequences of the recent results of Ian Agol, Jeremy Kahn, Vladimir Markovic and Dani Wise.
We determine the algebra of isovectors for the Black--Scholes equation. As a consequence, we obtain some previously unknown families of transformations on the solutions.
We show that contact homology distinguishes infinitely many tight contact structures on any orientable, toroidal, irreducible 3-manifold. As a consequence of the contact homology computations, on a very large class of toroidal manifolds, all known examples of universally tight contact structures with nonvanishing torsi…
A 2-manifold's group structure is deduced from orbit configuration spaces.
In this study, we determine some special Smarandache curves according to Darboux frame in E3. We give some characterizations and consequences of Smarandache curves.
The consequences of the splitting of higher jet sequences of vector bundles on a compact complex (Kaehler) manifold are studied, proving an infinitesimal convers to a result of I.Biswas.
Medial quandles are represented using a heterogeneous affine structure. As a consequence, we obtain numerous structural properties, including enumeration of isomorphism classes of medial quandles up to 13 elements.
In this paper we give a proof of an index theorem by Bismut. As a consequence we obtain another proof of the Grothendieck-Riemann-Roch theorem in differential cohomology.
Inspired by the bankruptcy of Lehman Brothers and its consequences on the global financial system, we develop a simple model in which the Lehman default event is quantified as having an almost immediate effect in worsening the credit worthiness of all financial institutions in the economic network. In our stylized desc…
We find all 2-Bridge links up to 11 crossings and locate them in Thistlethwaite's link table. The splitting numbers of some links are calculated as a consequence of this identification.
We discuss an elementary consequence of the works of (1) Brett Kotschwar and Lu Wang and (2) Ovidiu Munteanu and Jiaping Wang.
Why the results of that article [arXiv:1304.3212] are immediate consequences of known ones.
Any quasi-isometry of the complex of curves is bounded distance from a simplicial automorphism. As a consequence, the quasi-isometry type of the curve complex determines the homeomorphism type of the surface.
We show that Chern-Weil theory for tensor bundles over manifolds is a consequence of the existence of natural closed differential forms on total spaces of torsion free connections on frame bundles.
Random hyperbolic surfaces are mostly tangle-free, with geometric implications.
We first show that hypergeometric functions appear naturally as spectral functions when applying pseudo-differential calculus to decipher heat kernel asymptotic in the situation where the symbol algebra is noncommutative. Such observation leads to a unified (works for arbitrary dimension) method of computing the modula…
The study examines geometric properties of complex Hermitian manifolds and their holonomy groups.
Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical copulas with the same unconditional correlation. Furthermore, for Gaussian and Stude…