arXiv research

Note establishes a local maximum principle for Ricci flow under curvature conditions.

Extremal length systole is maximized at the Bolza surface.

We consider two connected aspects of maximum likelihood estimation of the parameter for high-dimensional discrete graphical models: the existence of the maximum likelihood estimate (mle) and its computation. When the data is sparse, there are many zeros in the contingency table and the maximum likelihood estimate of th…

Assuming local uniform bounds on the metric for a solution of the Chern-Ricci flow, we establish local Calabi and curvature estimates using the maximum principle.

The study finds a unique systole maximum in non-hyperelliptic surfaces.

Paper proposes methods to localize sources in WSNs without knowing sensor parameters.

Alternative hypothesis tests for class-conditional noise using local maximum likelihood.

We consider the volume-normalized Ricci flow close to compact shrinking Ricci solitons. We show that if a compact Ricci soliton $(M,g)$ is a local maximum of Perelman's shrinker entropy, any normalized Ricci flow starting close to it exists for all time and converges towards a Ricci soliton. If $g$ is not a local maxim…

Many mathematical imaging problems are posed as non-convex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally convergent algorithm has found the globally optimal solution. When the problem is formu…

Maximum principle proves positivity of forward rates in stochastic models.

SGD transitions between maxima and minima with varying time scales.

We give a maximum principle proof of interior derivative estimates for the Kähler-Ricci flow, assuming local uniform bounds on the metric.

New boundary condition for Black-Scholes equations in strict local martingale models.

One of the earliest conjectures in computational learning theory-the Sample Compression conjecture-asserts that concept classes (equivalently set systems) admit compression schemes of size linear in their VC dimension. To-date this statement is known to be true for maximum classes---those that possess maximum cardinali…

We propose a generic calibration framework to both vanilla and no-touch options for a large class of continuous semi-martingale models. The method builds upon the forward partial integro-differential equation (PIDE) derived in Hambly et al. (2016), which allows fast computation of up-and-out call prices for the complet…

Let $A$ be a finite-dimensional local commutative algebra over $R$, $\dim_RA=n$. In this work we consider compact manifolds over $A$, and prove that the real part of an $A$-differentiable function is constant. Also we find estimates for the dimensions of some spaces of 1-form.

Sublinear LSVI via LSH reduces runtime to sublinear in actions.

New variational method solves submodular maximum coverage problem efficiently.

We study the strong maximum principle for horizontal (p-) mean curvature operator and p-(sub)laplacian operator on subriemannian manifolds including, in particular, Heisenberg groups and Heisenberg cylinders. Under a certain Hormander type condition on vector fields, we show the strong maximum principle holds in higher…

The multivariate normal density is a monotonic function of the distance to the mean, and its ellipsoidal shape is due to the underlying Euclidean metric. We suggest to replace this metric with a locally adaptive, smoothly changing (Riemannian) metric that favors regions of high local density. The resulting locally adap…

The paper solves a maximum entropy sampling problem with efficient algorithms and performance guarantees.

New GP model estimates piecewise continuous functions.

Inverted file and asymmetric distance computation (IVFADC) have been successfully applied to approximate nearest neighbor search and subsequently maximum inner product search. In such a framework, vector quantization is used for coarse partitioning while product quantization is used for quantizing residuals. In the ori…

Chow and Liu (1968) studied the problem of learning a maximumlikelihood Markov tree. We generalize their work to more complexMarkov networks by considering the problem of learning a maximumlikelihood Markov network of bounded complexity. We discuss howtree-width is in many ways the appropriate measure of complexity and…

MCN improves deep neural networks by bettering local minima and generalizing well.

In this paper we consider Riemannian manifolds $(M^n,g)$ of dimension $n \geq 5$, with semi-positive $Q$-curvature and non-negative scalar curvature. Under these assumptions we prove $(i)$ the Paneitz operator satisfies a strong maximum principle; $(ii)$ the Paneitz operator is a positive operator; and $(iii)$ its Gree…

Study on isoperimetric problem in Randers planes achieving maximum area.

Graph Shift (GS) algorithms are recently focused as a promising approach for discovering dense subgraphs in noisy data. However, there are no theoretical foundations for proving the convergence of the GS Algorithm. In this paper, we propose a generic theoretical framework consisting of three key GS components: simplex …

The EM algorithm is a novel numerical method to obtain maximum likelihood estimates and is often used for practical calculations. However, many of maximum likelihood estimation problems are nonconvex, and it is known that the EM algorithm fails to give the optimal estimate by being trapped by local optima. In order to …

On the ground of origins of the theory of Lie groups and Lie algebras, their (co)adjoint representations, and the Pontryagin maximum principle for the time-optimal problem are given an independent foundation for methods of geodesic vector field to search for normal geodesics of left-invariant (sub-)Finsler metrics on L…

Constructs expanding gradient Ricci solitons with unique properties.

An efficient LDP protocol for QMLE with improved practicality and theoretical guarantees.

We propose the Legendrian web in a contact three manifold as a second order generalization of the planar web. An Abelian relation for a Legendrian web is analogously defined as an additive equation among the first integrals of its foliations. For a class of Legendrian $\, d$-webs defined by simple second order ODE's, w…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance matrix, which can be computationally intensive in large dimensions. Approximate infer…

We describe the local structure of Riemannian manifolds with harmonic curvature which admit a maximum number, in a well-defined sense, of local warped-product decompositions, and at the same time their Ricci tensor has, at some point, only simple eigenvalues. We also prove that, in every given dimension greater than tw…

The paper studies global Yamabe flow on AF manifolds, preserving ADM mass.

We provide the classification of locally conformally flat gradient Yamabe solitons with positive sectional curvature. We first show that locally conformally flat gradient Yamabe solitons with positive sectional curvature have to be rotationally symmetric and then give the classification and asymptotic behavior of all r…

EntroPath learns manifold geometry from diffusion paths.

LOCAL learns dynamic causal structures from time series data efficiently.

Correntropy is a local similarity measure defined in kernel space and the maximum correntropy criterion (MCC) has been successfully applied in many areas of signal processing and machine learning in recent years. The kernel function in correntropy is usually restricted to the Gaussian function with center located at ze…

The study describes the structure of surfaces with constant mean curvature in 3-manifolds.

TMDA aligns subdomain data distribution discrepancies across domains using manifold representations.

Tricks improve retail product image classification accuracy.

A characterization of the C-projective vector fields on a Randers spaces is presented in terms of a recently introduced non-Riemannian quantity defined by Z. Shen and denoted by ${\bfΞ}$; It is proved that the quantity ${\bfΞ}$ is invariant for C-projective vector fields. Therefore, the dimension of the algebra of the …

Researchers compute quasi-local mass of Kerr black hole horizon.

New algorithms find half-optimal independent sets in sparse graphs.

We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds, more precisely, on $S^n\times T^m$, where $T^m$ is a torus of dimension $m\ge 2$ and $S^n$ is a sphere of dimension $n\ge 4$. These metrics are not locally homogeneous; in particu…

This paper proposes and evaluates the k-greedy equivalence search algorithm (KES) for learning Bayesian networks (BNs) from complete data. The main characteristic of KES is that it allows a trade-off between greediness and randomness, thus exploring different good local optima. When greediness is set at maximum, KES co…