arXiv research

The study of random surfaces reveals asymptotic lengths of separating geodesics.

The study shows subgroup separability conditions for specific groups.

Classifies polynomial growth solutions to drift-harmonic equations on asymptotically paraboloidal manifolds.

Gradient methods avoid overfitting on separable data.

At critical coupling, the interactions of Ginzburg-Landau vortices are determined by the metric on the moduli space of static solutions. The asymptotic form of the metric for two well separated vortices is shown here to be expressible in terms of a Bessel function. A straightforward extension gives the metric for N vor…

For each $n$, we construct a separable metric space $\mathbb{U}_n$ that is universal in the coarse category of separable metric spaces with asymptotic dimension ($\mathop{asdim}$) at most $n$ and universal in the uniform category of separable metric spaces with uniform dimension ($\mathop{udim}$) at most $n$. Thus, $\m…

Robustly detects jumps in high-frequency CIR and CKLS models.

We prove the dimension of any asymptotic cone over a metric space X does not exceed the asymptotic Assouad-Nagata dimension of X. This improves a result of Dranishnikov and Smith who showed that dim(Y) does not exceed asymptotic Assouad-Nagata dimension of X for all separable subsets Y of special asymptotic cones of X …

We study the topological types of pants decompositions of a surface by associating to any pants decomposition $P,$ in a natural way its pants decomposition graph, $Γ(P).$ This perspective provides a convenient way to analyze the maximum distance in the pants complex of any pants decomposition to a pants decomposition c…

Novel framework for uncertainty quantification in metric spaces.

We give effective proofs of residual finiteness and conjugacy separability for finitely generated nilpotent groups. In particular, we give precise asymptotic bounds for a function introduced by Bou-Rabee that measures how large the quotients that are need to separate non-identity elements of bounded length from the ide…

We prove an exponential estimate for the asymptotics of Bergman kernels of a positive line bundle under hypotheses of bounded geometry. We give further Bergman kernel proofs of complex geometry results, such as separation of points, existence of local coordinates and holomorphic convexity by sections of positive line b…

Develops large-sample theory for non-stationary source separation.

New separation concepts for Anosov representations help bound Thurston asymmetric metric.

We construct a partial compactification of the moduli space, M_k, of SU(2) magnetic monopoles on R^3, wherein monopoles of charge k decompose into widely separated 'monopole clusters' of lower charge going off to infinity at comparable rates. The hyperKahler metric on M_k has a complete asymptotic expansion up to the b…

We study the asymptotic behaviour of regularized determinants of certain Laplace type operators with respect to singular deformations of the underlying manifold which are obtained by stretching a tubular neighborhood of an embedded separating hypersurface to a cylinder of infinite length. Using the asymptotic expansion…

For any asymptotically conical self-shrinker with entropy less than or equal to that of a cylinder we show that the link of the asymptotic cone must separate the unit sphere into exactly two connected components, both diffeomorphic to the self-shrinker. Combining this with recent work of Brendle, we conclude that the r…

New methods test discrete distributions faster with local privacy constraints.

SS-SARSA tackles recovering bandits by treating rounds as states.

SLOPE is a relatively new convex optimization procedure for high-dimensional linear regression via the sorted l1 penalty: the larger the rank of the fitted coefficient, the larger the penalty. This non-separable penalty renders many existing techniques invalid or inconclusive in analyzing the SLOPE solution. In this pa…

Paper studies second order tail probabilities in risk models.

Decomposes ultrametric spaces into scaled simplices.

The paper analyzes the risk of CV-tuned regularized estimators and connects it to SURE.

The paper proves uniqueness and convergence of asymptotically conical self-shrinkers and self-expanders.

Relative moduli spaces of periodic monopoles provide novel examples of Asymptotically Locally Flat hyperkahler manifolds. By considering the interactions between well-separated periodic monopoles, we infer the asymptotic behavior of their metrics. When the monopole moduli space is four-dimensional, this construction yi…

This paper deals with the notion of a large financial market and the concepts of asymptotic arbitrage and strong asymptotic arbitrage (both of the first kind), introduced by Yu.M. Kabanov and D.O. Kramkov. We show that the arbitrage properties of a large market are completely determined by the asymptotic behavior of th…

Paper develops robust methods for panel data with latent groups, improving inference under group separation violations.

New concept of regular separation for ODEs leads to improved Hardy field results.

A singularity theorem based on asymptotic volume growth

We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with the characteristics of separate processes. Bivariate Hurst exponent is then equa…

Paper proves a new criterion for time-like geodesics in flat spacetimes.

Study of Dirichlet minimizers on manifolds with boundary and their asymptotic behavior.

This paper shows how to combine optimal tests into log-optimal processes.

De Sitter spacetime can be separated into two parts along two kinds of hypersurfaces and the half-de Sitter spacetimes are covered by the planar and hyperbolic coordinates respectively. Two positive energy theorems were proved previously for certain $¶$-asymptotically de Sitter and $\H$-asymptotically de Sitter initial…

An important issue in neural network research is how to choose the number of nodes and layers such as to solve a classification problem. We provide new intuitions based on earlier results by An et al. (2015) by deriving an upper bound on the number of nodes in networks with two hidden layers such that linear separabili…

Derives asymptotic generalization error for large-margin classifiers.

We use planar coordinates as well as hyperbolic coordinates to separate the de Sitter spacetime into two parts. These two ways of cutting the de Sitter give rise to two different spatial infinities. For spacetimes which are asymptotic to either half of the de Sitter spacetime, we are able to provide definitions of the …

Unified bounds for iterative algorithms with Gaussian data matrices.

The simplicial condition and other stronger conditions that imply it have recently played a central role in developing polynomial time algorithms with provable asymptotic consistency and sample complexity guarantees for topic estimation in separable topic models. Of these algorithms, those that rely solely on the simpl…

Study on minimal surfaces in a specific homogeneous space with non-existence and construction results.

We introduce the notion of controlled Floyd separation between geodesic rays starting at the identity in a finitely generated group G. Two such geodesic rays are said to be Floyd separated with respect to quasigeodesics if the (Floyd) length of c-quasigeodesics (for fixed but arbitrary c) joining points on the geodesic…

Independent component analysis (ICA) has been widely used for blind source separation in many fields such as brain imaging analysis, signal processing and telecommunication. Many statistical techniques based on M-estimates have been proposed for estimating the mixing matrix. Recently, several nonparametric methods have…

We prove that each coarsely homogenous separable metric space $X$ is coarsely equivalent to one of the spaces: the sigleton, the Cantor macro-cube or the Baire macro-space. This classification is derived from coarse characterizations of the Cantor macro-cube and of the Baire macro-space given in this paper. Namely, we …

We express the Masur-Veech volume and the area Siegel-Veech constant of the moduli space of meromorphic quadratic differential with simple poles as polynomials in the intersection numbers of psi-classes supported on the boundary cycles of the Deligne-Mumford compactification of the moduli space of curves. Our formulae …

The paper analyzes heat kernel asymptotics for real powers of Laplacians on manifolds.

We consider the class of self-similar Gaussian stochastic volatility models, and compute the small-time (near-maturity) asymptotics for the corresponding asset price density, the call and put pricing functions, and the implied volatilities. Unlike the well-known model-free behavior for extreme-strike asymptotics, small…

We construct an example of an isometric action of $F(a,b)$ on a $δ$-hyperbolic graph $Y$, such that this action is acylindrical, purely loxodromic, has asymptotic translation lengths of nontrivial elements of $F(a,b)$ separated away from $0$, has quasiconvex orbits in $Y$, but such that the orbit map $F(a,b)\to Y$ is n…

The study calculates the risk of semi-supervised multitask learning on Gaussian mixtures.