arXiv research

Note removes degeneracy in Kähler geometry estimates.

It is shown that $m$ disjoint sets with fixed Gaussian volumes that partition $\mathbb{R}^{n}$ with minimum Gaussian surface area must be $(m-1)$-dimensional. This follows from a second variation argument using infinitesimal translations. The special case $m=3$ proves the Double Bubble problem for the Gaussian measure,…

In this survey, a short introduction in the recent discovery of log-normally distributed market-technical trend data will be given. The results of the statistical evaluation of typical market-technical trend variables will be presented. It will be shown that the log-normal assumption fits better to empirical trend data…

Study conformal product structures on reducible Riemannian manifolds.

Paper presents a randomized algorithm for SPCA with high probability approximation.

We derive, under a technical assumption, the first variation formula for the eigenvalues of the Laplacian on a closed manifold evolving by the Ricci flow and give some applications.

In this note under a crucial technical assumption we derive a differential equality of the Yamabe constant $\mathcal{Y} (g (t))$ where $g (t)$ is a solution of the Ricci flow on a closed manifold.

We prove precompactness in an orbifold Cheeger-Gromov sense of complete gradient Ricci shrinkers with a lower bound on their entropy and a local integral Riemann bound. We do not need any pointwise curvature assumptions, volume or diameter bounds. In dimension four, under a technical assumption, we can replace the loca…

Study finds traditional technical indicators underperform in high-frequency trading, suggesting risk management over prediction.

Let $(M, g)$ be an $n$-dimensional complete Riemannian manifold with $Ric(M)\geq-(n-1)Q$, where $Q\geq0$ is a constant. We obtain an interior gradient bound for minimal graphs in $M\times R$ under some technical assumptions. For details, see Theorem 2.

This note removes technical assumptions and characterizes relatively dominated representations.

We solve the $n$-marginal Skorokhod embedding problem for a continuous local martingale and a sequence of probability measures $μ_1,...,μ_n$ which are in convex order and satisfy an additional technical assumption. Our construction is explicit and is a multiple marginal generalisation of the Azema and Yor (1979) soluti…

Inspired by recent work of S. K. Donaldson on constant scalar curvature metrics on toric complex surfaces, we study obstructions to the extension of the Calabi flow on a polarized toric variety. Under some technical assumptions, we prove that the Calabi flow can be extended for all time.

The study redefines algorithmic fairness as a sociotechnical concept.

Away from the central axis, we prove the stability of the Positive Mass Theorem in the $W^{1,p}$ sense for asymptotically flat axisymmetric manifolds with nonnegative scalar curvature satisfying some additional technical assumptions. We also derive estimates for the volumes of regions, the areas of axisymmetric surface…

We describe, under some additional technical assumptions, the Gromov boundary of the free product of several $G_i$'s amalgamated wrt. $H$, where $G_i$ are hyperbolic groups with boundary homeomorphic to a densely punctured $n$-sphere, and $H$ is their common subgroup corresponding to a peripheral sphere in each of the …

Paper converts quantiles to cumulative distribution functions to simplify risk measures.

These are lecture notes for the course "Analysis and X-ray tomography". The course is a broad overview of various tools in analysis that can be used to study X-ray tomography. The focus is on tools and ideas, not so much on technical details and minimal assumptions. Only very basic functional analysis is assumed as bac…

As an application of his entropy formula, Perelman proved that every compact shrinking breather is a shrinking gradient Ricci soliton. We give a proof for the complete noncompact case by using Perelman's $\mathcal{L}$-geometry. Our proof follows the argument in Lu and Zheng of constructing an ancient solution, and remo…

In this article we consider outer Galois actions on a free profinite group of rank two, induced by the étale fundamental group of a projective line minus three points or of a pointed elliptic curve over a number field. Under mild technical assumptions their respective images uniquely determine the curves and the number…

We study the Yang-Mills flow on a holomorphic vector bundle E over a compact Kahler manifold X. We construct a natural barrier function along the flow, and introduce some techniques to study the blow-up of the curvature along the flow. Making some technical assumptions, we show how our techniques can be used to prove t…

Investor finds a fair outcome in complex financial markets.

We prove (under some technical assumptions) that each surface in $\mathbb R^3$ containing two arcs of parabolas with axes parallel to $Oz$ through each point has a parametrization $\left(\frac{P(u,v)}{R(u,v)},\frac{Q(u,v)}{R(u,v)},\frac{Z(u,v)}{R^2(u,v)}\right)$ for some $P,Q,R,Z\in\mathbb R[u,v]$ such that $P,Q,R$ hav…

Order matching systems form the backbone of modern equity exchanges, used by millions of investors daily. Thus, their operation is strictly controlled through numerous regulatory directives to ensure that markets are fair and transparent. Despite these efforts, market manipulation remains an open problem. In this work,…

Let $G$ be a group with a finite balanced presentation $P$. We associate a Heegaard Floer homology group $\widehat{HF}_P(G)$ with the pair $(G,P)$ based on some extra choices and technical assumptions. We show that $\widehat{HF}_P(G)$ is independent from these choices and also is invariant under stable Andrews-Curtis t…

We study power utility maximization for exponential Lévy models with portfolio constraints, where utility is obtained from consumption and/or terminal wealth. For convex constraints, an explicit solution in terms of the Lévy triplet is constructed under minimal assumptions by solving the Bellman equation. We use a nove…

We generalize the Weinstein-Moser theorem on the existence of nonlinear normal modes (i.e., periodic orbits) near an equilibrium in a Hamiltonian system to a theorem on the existence of relative periodic orbits near a relative equilibrium in a Hamiltonian system with continuous symmetries. More specifically we signific…

Wave equation map reveals manifold's structure.

These are extended notes of the course given by the author at RIMS, Kyoto, in October 2016. The aim is to give a self-contained overview on the recently developed approach to differential calculus on metric measure spaces. The effort is directed into giving as many ideas as possible, without losing too much time in tec…

This article serves a few purposes. First of all, it reviews polyfold--Kuranishi correspondence I (http://arxiv.org/abs/1402.7008) and previews and samples some results from four papers I have been preparing. It is also a written-up and expanded version of a talk I gave at a symplectic conference in Chengdu on June 28,…

Method detects batch heterogeneity in genomic data.

We introduce a convex approach for mixed linear regression over $d$ features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $\mathbb{R}^{d}$ for each data point. These estimates can then be clustered using, for example, $k$-means. For problem…

New test for point processes without strong model assumptions.

Improved Sobolev mappings in Carnot groups with weaker assumptions.

Let $Y$ be a closed $3$-manifold such that all flat $SU(2)$-connections on $Y$ are $non$-$degenerate$. In this article, we prove a Uhlenbeck-type compactness theorem on $Y$ for stable flat $SL(2,\mathbb{C})$ connections satisfying an $L^{2}$-bound for the real curvature. Combining the compactness theorem and a previous…

Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions -- e.g. locality or measurement independence -- have to be relaxed in order to allo…

In order to apply variational methods to the action functional for geodesics of a stationary spacetime, some hypotheses, useful to obtain classical Palais-Smale condition, are commonly used: pseudo-coercivity, bounds on certain coefficients of the metric, etc. We prove that these technical assumptions admit a natural i…

For bicovariant differential calculi on quantum matrix groups a generalisation of classical notions such as metric tensor, Hodge operator, codifferential and Laplace-Beltrami operator for arbitrary k-forms is given. Under some technical assumptions it is proved that Woronowicz' external algebra of left-invariant differ…

The paper limits the profitability of technical trading rules and finds they are not better than random trading.

We consider the problem of Bayesian optimization (BO) in one dimension, under a Gaussian process prior and Gaussian sampling noise. We provide a theoretical analysis showing that, under fairly mild technical assumptions on the kernel, the best possible cumulative regret up to time $T$ behaves as $Ω(\sqrt{T})$ and $O(\s…

New PAC-Bayes bounds for heavy-tailed losses using supermartingales.

We extend the concept of genuine rigidity of submanifolds by allowing mild singularities, mainly to obtain new global rigidity results and unify the known ones. As one of the consequences, we simultaneously extend and unify Sacksteder and Dajczer-Gromoll theorems by showing that any compact $n$-dimensional submanifold …

For i = 1,2, let Gamma_i be a lattice in a simply connected, solvable Lie group G_i, and let X_i be a connected Lie subgroup of G_i. The double cosets Gamma_igX_i provide a foliation F_i of the homogeneous space Gamma_i\G_i. Let f be a continuous map from Gamma_1\G_1 to Gamma_2\G_2 whose restriction to each leaf of F_1…

Classifies pure mapping class groups based on surface properties.

The paper suggests new topological lower bounds for the number of zeros of closed 1-forms within a given cohomology class. The main new technical tool is the deformation complex, which allows to pass to a singular limit and reduce the original problem with a closed 1-form to a traditional problem with a Morse function.…

A well known question of Gromov asks whether every one-ended hyperbolic group $Γ$ has a surface subgroup. We give a positive answer when $Γ$ is the fundamental group of a graph of free groups with cyclic edge groups. As a result, Gromov's question is reduced (modulo a technical assumption on 2-torsion) to the case when…

We study active learning where the labeler can not only return incorrect labels but also abstain from labeling. We consider different noise and abstention conditions of the labeler. We propose an algorithm which utilizes abstention responses, and analyze its statistical consistency and query complexity under fairly nat…

We study the generic invariant probability measures for the geodesic flow on connected complete nonpositively curved manifolds. Under a mild technical assumption, we prove that ergodicity is a generic property in the set of probability measures defined on the unit tangent bundle of the manifold and supported by traject…