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 honors Lai's contributions to multi-armed bandits and establishes new regret bounds.
In this paper, two sequences of minimal isoparametric hypersurfaces are constructed via representations of Clifford algebras. Based on these, we give estimates on eigenvalues of the Laplacian of the focal submanifolds of isoparametric hypersurfaces in unit spheres. This improves results of [TY13] and [TXY14]. Eells and…
In this article, we give a geometric proof of the classification of complex vector cross product due to Lee-Leung.
In this paper we show how hypercomplex function theoretical objects can be used to construct explicitly self-dual SU(2)-Yang-Mills instanton solutions on certain classes of conformally flat 4-manifolds. We use a hypercomplex argument principle to establish a natural link between the fundamental solutions of …
We define an (equivariant) quaternionic analytic torsion for antiselfdual vector bundles on quaternionic Kaehler manifolds, using ideas by Leung and Yi. We compute this torsion for vector bundles on quaternionic homogeneous spaces with respect to any isometry in the component of the identity, in terms of roots and Weyl…
In this thesis, we study a class of special Lagrangian submanifolds of toric Calabi-Yau manifolds and construct their mirrors using some techniques developed in the SYZ programme. We present a justification on the conjecture on the mirror construction of D- branes in Aganagic-Vafa [2]. We apply the techniques employed …
Generalizing some results from R. Leung's thesis, we compute, in rational cohomology, the Poincare dual of the degeneracy locus of the family of Dirac operators parameterized by the moduli space of projectively anti-self-dual $\SO(3)$ connections. This is the first step in a program to derive a relation between the Don…
Let be a compact Kähler manifold, a Hermitian vector bundle and an ample line bundle. We construct a non-linear heat flow corresponding to the almost Hermitian-Einstein equation introduced by N.C. Leung, and prove that the solution exists for a short time. We also construct a potential function $D…
The paper examines properties of deformed Donaldson-Thomas connections on G2-manifolds.
Alternative definition of dDT connections for Spin(7) manifolds.
Generates new human genomic sequences for LAI training.
This is a survey on the recent progress in several applications of isoparametric theory, including an affirmative answer to Yau's conjecture on the first eigenvalue of Laplacian in the isoparametric case, a negative answer to Yau's 76th problem in his Problem Section, new examples of Willmore submanifolds in spheres, a…
The present volume is the written version of the series of lectures the author delivered at the Catholic University of Leuven, Belgium during the period of June-July, 1990. The main purpose of these talks is to present some of author's work and also his joint works with Professor T. Nagano and Professor Y. Tazawa of Ja…
Geometric interpretation of 2d-4d wall-crossing formulas.
From string theory, the notion of deformed Hermitian Yang-Mills connections has been introduced by Mariño, Minasian, Moore and Strominger. After that, Leung, Yau and Zaslow proved that it naturally appears as mirror objects of special Lagrangian submanifolds via Fourier-Mukai transform between dual torus fibrations. In…
The famous theorems of Cartan, related to the axiom of -planes, and Leung-Nomizu about the axiom of -spheres were extended to Kähler geometry by several authors. In this paper we replace the strong notions of totally geodesic submanifolds (-planes) and extrinsic spheres (-spheres) by a wider class of specia…
Survey of Thurston's impact on knot theory.
The paper examines stability of subelliptic harmonic maps with potential.
Polynomial-time method solves complex combinatorial semi-bandits.
Extends quantization theory to mixed polarizations using transverse differential operators.
This paper connects symplectic and Kähler manifolds via brane quantization.
We lay foundations of the subject in the title, on which we build in another paper devoted to isometries in spaces of Kähler metrics.
Inspired by the work of Leung-Wan, we study the mean curvature flow in hyperkähler manifolds starting from hyper-Lagrangian submanifolds, a class of middle dimensional submanifolds, which contains the class of complex Lagrangian submanifolds. For each hyper-Lagrangian submanifold, we define a new energy concept called …
New method fuses optical and SAR data to fill LAI gaps during cloudy periods.
Develops a correspondence between symplectic orbits and Grassmannians.
We compute the first Dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the Brownian motion exit times from the ball. This expression implies an estimate as exact as you want for the first Dirichlet eigenvalue of a geodesic ball in these rotationally symm…
We study a stochastic equation modeling the lay-down of fibers in the production process of nonwovens. The equation can be formulated as some manifold-valued Stratonovich stochastic differential equation. Especially, we study the long time behaviour of the stochastic process. Demanding mathematical difficulties arising…
In this paper we try to design the necessary calculation needed for backtesting trading systems when only candle chart data are available. We lay particular emphasis on situations which are not or not uniquely decidable and give possible strategies to handle such situations.
Quantizes Kähler manifolds using sheaves and differential operators.
In this article we lay out the details of Fukaya's -structure of the Morse complexe of a manifold possibly with boundary. We show that this -structure is homotopically independent of the made choices. We emphasize the transversality arguments that make some fiber products smooth.
By Markowitz geometry we mean the intersection theory of ellipsoids and affine subspaces in a real finite-dimensional linear space. In the paper we give a meticulous and self-contained treatment of this arch-classical subject, which lays a solid mathematical groundwork of Markowitz mean-variance theory of efficient por…
New proof shows inequality without restrictions.
Sharp eigenvalue estimates for submanifolds of asymptotically hyperbolic spaces.
Complete Ricci flow from singular 3D manifold with pseudolocality.
New ancient curve shortening flows created from grim reapers.
We study the J-flow from the point of view of an algebro-geometric stability condition. In terms of this we give a lower bound for the natural associated energy functional, and we show that the blowup behavior found by Fang-Lai is reflected by the optimal destabilizer. Finally we prove a general existence result on com…
New bounds for Bayesian bandits show prior improves performance.
Classifies ancient ovals in higher dimensional mean curvature flow.
Issues regarding explainable AI involve four components: users, laws & regulations, explanations and algorithms. Together these components provide a context in which explanation methods can be evaluated regarding their adequacy. The goal of this chapter is to bridge the gap between expert users and lay users. Different…
New rational curvature measures for 2-complexes.
We study the J-flow on the toric manifolds, through study the transition map between the moment maps induced by two Kähler metrics, which is a diffeomorphism between polytopes. This is similar to the work of Fang-Lai, under the assumption of Calabi symmetry, they study the monotone map between two intervals. We get a p…
Constructing brane quantization for -resolutions using SYZ mirror symmetry.
Develops a Barta theorem for p-Laplacian on manifolds.
We propose the kl-UCB ++ algorithm for regret minimization in stochastic bandit models with exponential families of distributions. We prove that it is simultaneously asymptotically optimal (in the sense of Lai and Robbins' lower bound) and minimax optimal. This is the first algorithm proved to enjoy these two propertie…
Paper tightens statistical aggregation results using local complexity.
In this article a class of closed convex sets in the Euclidean -space which are the convex hull of their profiles is described. Thus a generalization of Krein-Milman theorem\cite{Lay:1982} to a class of closed non-compact convex sets is obtained. Sufficient and necessary conditions for convexity, affinity and starsh…
New steady gradient Ricci solitons found with specific symmetry.
We lay the foundations for a theory of divergence-measure fields in noncommutative stratified nilpotent Lie groups. Such vector fields form a new family of function spaces, which generalize in a sense the fields. They provide the most general setting to establish Gauss-Green formulas for vector fields of low regul…