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.
Enhanced neural model detects misinformation by considering author context.
Survey on complex Monge-Ampère equations in Hermitian contexts.
The study of harmonicity for almost contact metric structures was initiated by Vergara-Díaz and Wood and continued by González-Dávila and the present author. By using the intrinsic torsion and some restriction on the type of almost contact metric structure, González-Dávila and the present author have characterised harm…
Language models are at the heart of numerous works, notably in the text mining and information retrieval communities. These statistical models aim at extracting word distributions, from simple unigram models to recurrent approaches with latent variables that capture subtle dependencies in texts. However, those models a…
Recently the authors have explored new concepts of plurisubharmonicity and pseudoconvexity, with much of the attendant analysis, in the context of calibrated manifolds. Here a much broader extension is made. This development covers a wide variety of geometric situations, including, for example, Lagrangian plurisubhamon…
Theorem ensures superior learning outcomes for authorized learners with quantum label encoding.
This work addresses the problem of author name homonymy in the Web of Science. Aiming for an efficient, simple and straightforward solution, we introduce a novel probabilistic similarity measure for author name disambiguation based on feature overlap. Using the researcher-ID available for a subset of the Web of Science…
The authors study the method of scaling in the context of the study of automorphism groups of complex domains in multiple dimensions. Various types of scaling techniques are compared and contrasted. Applications are given in a number of areas of complex geometric analysis. Relations with other parts of mathematics are …
These notes are based on a lecture course given by the first author in the Sedano Winter School on K-theory held in Sedano, Spain, on January 22-27th of 2007. They aim at introducing K-theory of C^*-algebras, equivariant K-homology and KK-theory in the context of the Baum-Connes conjecture.
Proved a combinatorial conjecture in machine learning.
Authors compute stable homology of torus knots using a new deformation technique.
We propose a means by which some categorifications can be evaluated at a root of unity. This is implemented using a suitable localization in the context of prior work by the authors on categorification of the Jones-Wenzl projectors. Within this construction we define objects, invariant under handle slides, which decate…
In this paper we show that a certain solvable Lie group constructed in a paper by Benson and Gordon has no lattices. This result answers (in the negative way) a question posed by several authors in the context of symplectic geometry. The main theorem is proved with the use of rational homotopy theory.
We propose a real-time context-aware learning system along with the architecture that runs on the mobile devices, provide services to the user and manage the IoT devices. In this system, an application running on mobile devices collected data from the sensors, learned about the user-defined context, made predictions in…
This article proposes a biologically inspired neurocomputational architecture which learns associations between words and referents in different contexts, considering evidence collected from the literature of Psycholinguistics and Neurolinguistics. The multi-layered architecture takes as input raw images of objects (re…
We show that every p-fold strictly-cyclic branched covering of a b-bridge link in admits a p-symmetric Heegaard splitting - in the sense of Birman and Hilden - of genus . This gives a complete converse of one of the results of the two authors. Moreover, we introduce the concept of weakly p-symmetric…
We first show that the connected sum along submanifolds introduced by the second author for compact initial data sets of the vacuum Einstein system can be adapted to the asymptotically Euclidean and to the asymptotically hyperbolic context. Then, we prove that in any case, and generically, the gluing procedure can be l…
We study effective potentials coming from compactifications of string theory. We show that, under mild assumptions, such potentials are bounded from below in four dimensions, giving an affirmative answer to a conjecture proposed by the second author in arXiv:0911.3378v4 [hep-th]. We also derive some sufficient conditio…
Investigates intrinsic Lipschitz sections in nonlinear quotient maps.
Our purpose is to pursue the rigorous construction of Liouville Quantum Field Theory on Riemann surfaces initiated by F. David, A. Kupiainen and the last two authors in the context of the Riemann sphere and inspired by the 1981 seminal work by Polyakov. In this paper, we investigate the case of simply connected domains…
The notion of local subgroupoid as a generalisation of a local equivalence relation was defined in a previous paper by the first two authors. Here we use the notion of star path connectivity for a Lie groupoid to give an important new class of examples, generalising the local equivalence relation of a foliation, and de…
Improved Kalman filter for non-linear, non-Gaussian data.
In an earlier paper of the authors it was shown that the sheaf theoretically based recently developed abstract differential geometry of the first author can in an easy and natural manner incorporate singularities on arbitrary closed nowhere dense sets in Euclidean spaces, singularities which therefore can have arbitrar…
New metric measure space theory for Lipschitz constants.
We establish a version of the complex Frobenius theorem in the context of a complex subbundle S of the complexified tangent bundle of a manifold, having minimal regularity. If the subbundle S defines the structure of a Levi-flat CR-manifold, it suffices that S be Lipschitz for our results to apply. A principal tool in …
This expository article is an introduction to the adjoint orbits of complex semisimple groups, primarily in the algebro-geometric and Lie-theoretic contexts, and with a pronounced emphasis on the properties of semisimple and nilpotent orbits. It is intended to build a foundation for more specialized settings in which a…
Author discusses the Poincaré conjecture from 40 years ago.
The paper is devoted to a detailed exposition of results outlined in author's 1983 note "On the virtual cohomology dimension of the Teichmüller modular group". The paper includes the full proofs and a discussion of the context which motivated both the results and the methods used. The reminiscences included into the la…
Proves a generalization of a multiplicity one theorem for specific groups.
Study strong inversions on knots using Khovanov homology.
We prove that smooth critical points of the Möbius energy parametrized by arc-length are analytic. Together with the main result in \cite{BRS16} this implies that critical points of the Möbius energy with merely bounded energy are not only but also analytic. Our proof is based on Cauchy's method of majorants…
The paper shows the computation of the noncommutative generalization of the A-polynomial of the trefoil knot. The classical A-polynomial was introduced by Cooper, Culler, Gillet, Long and Shalen, and was generalized to the context of Kauffman bracket skein modules by the author in joint work with Frohman and Lofaro. A …
Lecture notes on Heegaard Floer homology for beginners.
We prove here new results about transversality and related geometric properties of a holomorphic, formal, or CR mapping, sending one generic submanifold of $\bC^N$ into another. One of our main results is that a finite mapping is transversal to the target manifold provided this manifold is of finite type. For the case …
Previous work of the authors establishes a criterion on the fundamental group of a knot complement that determines when Dehn surgery on the knot will have a fundamental group that is not left-orderable. We provide a refinement of this criterion by introducing the notion of a decayed knot; it is shown that Dehn surgery …
This paper classifies all expanding Ricci solitons on surfaces.
New metric improves topic model evaluation.
We investigate a semi-continuity property for stability conditions for sheaves that is important for the problem of variation of the moduli spaces as the stability condition changes. We place this in the context of a notion of stability previously considered by the authors, called multi-Gieseker-stability, that general…
Researchers explore geometric dualities in statistical manifolds.
Modified Hennings invariant defined using quantum groups and integrals.
Generalizes bias-variance decomposition for Bregman divergences.
We study warped compactifications of string/M theory with the help of effective potentials, continuing previous work of the last two authors and Michael R. Douglas presented in arXiv:1206.1885. The dynamics of the conformal factor of the internal metric, which is responsible for instabilities in these constructions, is…
We introduce the author-topic model, a generative model for documents that extends Latent Dirichlet Allocation (LDA; Blei, Ng, & Jordan, 2003) to include authorship information. Each author is associated with a multinomial distribution over topics and each topic is associated with a multinomial distribution over words.…
Extends calculus to topological manifolds using generalized functions.
Study continuity of limit sets in symmetric spaces.
We prove that the cotangent of a double Lie groupoid S has itself a double groupoid structure with sides the duals of associated Lie algebroids, and double base the dual of the Lie algebroid of the core of S. Using this, we prove a result outlined by Weinstein in 1988, that the side groupoids of a general symplectic do…
About the economic growth the Keynesian theorists defend circular and cumulative processes, benefiting the rich localities and harming the poorest, without external interventions. In these processes the Verdoorn law has an important role. For Verdoorn (1949) the productivity growth rate is endogenous and depends of the…
Machine learning can provide efficient solutions to the complex problems encountered in autonomous driving, but ensuring their safety remains a challenge. A number of authors have attempted to address this issue, but there are few publicly-available tools to adequately explore the trade-offs between functionality, scal…