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.
Efficient algorithm for clustering and classification using MBO scheme.
problem Data clustering and classification tasks.
method Introduces constraints on cluster size leading to a linear integer problem, proving it's induced by a novel order statistic. Develops exact and efficient algorithms based on variational viewpoint connecting to volume-preserving mean curvature flow.
result Estimates computational complexity better than state-of-the-art, proving rigorous analysis.
The paper studies groupoid structures from different viewpoints.
problem Understanding groupoid morphisms and their structures.
method Constructing two groupoids from morphisms of groupoids, one from a categorical viewpoint and the other from a geometric viewpoint. Showing equivalence of the two kinds of groupoids of morphisms.
result Equivalence of two kinds of groupoids of morphisms for each pair of groupoids.
We report a statistical analysis of the Island ECN (NASDAQ) order book. We determine the static and dynamic properties of this system, and then analyze them from a physicist's viewpoint using an equivalent particle system obtained by treating orders as massive particles and price as position. We identify the fundamenta…
The quantum cohomology of CP^1 provides a distinguished solution of the third Painleve equation. S. Cecotti and C. Vafa discovered this from a physical viewpoint. We derive it from a differential geometric viewpoint, using the theory of harmonic maps and in particular the generalized Weierstrass representation (DPW rep…
Multi-class classification methods based on both labeled and unlabeled functional data sets are discussed. We present a semi-supervised logistic model for classification in the context of functional data analysis. Unknown parameters in our proposed model are estimated by regularization with the help of EM algorithm. A …
We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label (based on a Shannon entropy measure). By harnessing a recent theoretical result on…
We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable for regression, robust regression and classification that is lower bound of the…
This paper is devoted to the development and applications of some (new) basic concepts in Lie theory, both from `computational" and "observability" viewpoint. We specify set of all "G-equivariant" maps from a given Lie group G to the underlying manifold M, namely G-set, and also we introduce "conjugacy" in Lie group …
Unified framework for imitating tasks across domains with discrepancies.
problem Learning tasks across domains with embodiment, viewpoint, and dynamics mismatches.
method Two-step approach: alignment followed by adaptation. Alignment uses Generative Adversarial MDP Alignment (GAMA) for state and action correspondences from unpaired, unaligned demonstrations. Adaptation leverages these correspondences for zero-shot imitation.
result Effectiveness of the proposed approach in embodiment, viewpoint, and dynamics mismatch scenarios.
We consider a triality between the Zermelo navigation problem, the geodesic flow on a Finslerian geometry of Randers type, and spacetimes in one dimension higher admitting a timelike conformal Killing vector field. From the latter viewpoint, the data of the Zermelo problem are encoded in a (conformally) Painleve-Gullst…
In an informal way, a number of thoughts on the financial crisis 2008 are presented from a physicist's viewpoint, considering the problem as a nonergodicity transition of a spin-glass type of system. Some tentative suggestions concerning the way out of the crisis are also discussed, concerning Keynesian "deficit spendi…
A conceptual framework for cluster analysis from the viewpoint of p-adic geometry is introduced by describing the space of all dendrograms for n datapoints and relating it to the moduli space of p-adic Riemannian spheres with punctures using a method recently applied by Murtagh (2004b). This method embeds a dendrogram …
Currently, machine learning plays an important role in the lives and individual activities of numerous people. Accordingly, it has become necessary to design machine learning algorithms to ensure that discrimination, biased views, or unfair treatment do not result from decision making or predictions made via machine le…
The change of numeraire gives very important computational simplification in option pricing. This technique reduces the number of sources of risks that need to be accounted for and so it is useful in pricing complicated derivatives that have several sources of risks. In this article, we considered the underlying mathem…
In 1929, Paul Funk and Ludwig Berwald gave a characterization of Hilbert geometries from the Finslerian viewpoint. They showed that a smooth Finsler metric in a convex bounded domain of Rn is the Hilbert geometry in that domain if and only if it is complete, if its geodesics are straight lines and if its fl…
The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry.