arXiv research

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 …

The paper proves the existence of infinitely many minimal hypersurfaces in higher-dimensional manifolds.

Paper shows certain generalized Whitney topologies are Baire.

For almost all Riemannian metrics (in the $C^\infty$ Baire sense) on a closed manifold $M^{n+1}$, $3\leq (n+1)\leq 7$, we prove that the union of all closed, smooth, embedded minimal hypersurfaces is dense. This implies there are infinitely many minimal hypersurfaces thus proving a conjecture of Yau (1982) for generic …

Minimal surfaces exist for most metrics on compact manifolds with boundary.

Generic metrics make geodesic nets dense.

The paper proves generic transversality and regularity for minimal submanifolds and area-minimizing currents.

New manifold construction yields Baire-1 functions as cohomotopy groups.

The Baire metric induces an ultrametric on a dataset and is of linear computational complexity, contrasted with the standard quadratic time agglomerative hierarchical clustering algorithm. We apply the Baire distance to spectrometric and photometric redshifts from the Sloan Digital Sky Survey using, in this work, about…

The Baire metric induces an ultrametric on a dataset and is of linear computational complexity, contrasted with the standard quadratic time agglomerative hierarchical clustering algorithm. In this work we evaluate empirically this new approach to hierarchical clustering. We compare hierarchical clustering based on the …

The paper explores generic properties of minimal surfaces in high dimensions.

Theorem shows generic metrics yield non-degenerate geodesic nets.

Can the Minkowski sum of two compact convex bodies be made smoother by rotating one of them? We construct two infinitely differentiable strictly convex plane bodies such that after any generic rotation (in the Baire category sense) of one of the summands the Minkowski sum is not five times differentiable. On the other …

For almost all Riemannian metrics (in the $C^\infty$ Baire sense) on a closed manifold $M^{n+1}$, $3\leq (n+1)\leq 7$, we prove that there is a sequence of closed, smooth, embedded, connected minimal hypersurfaces that is equidistributed in $M$. This gives a quantitative version of the main result of \cite{irie-marques…

New criteria for Cantor set tameness and wildness via projections.

All projections of typical Cantor sets in high dimensions are Cantor sets.

We describe many vantage points on the Baire metric and its use in clustering data, or its use in preprocessing and structuring data in order to support search and retrieval operations. In some cases, we proceed directly to clusters and do not directly determine the distances. We show how a hierarchical clustering can …

We show that the topological groups $Diff_{+}^{1}(I)$ and $Diff_{+}^{1}(\mathbb{S}^1)$ of orientation-preserving $C^1$-diffeomorphisms of the interval and the circle, respectively, admit finitely generated dense subgroups. We also investigate the question of genericity (in the sense of Baire category) of such finite to…

The premier exhibition of the following phenomenon: The fundamental group of any Peano continuum constructed in similar fashion to the Hawaiian earring admits two natural distinct topological group structures. However despite being uncountable and regular, neither group is a Baire space and hence neither group admits a…

The paper proves bounds on the Morse index of free boundary minimal hypersurfaces.

Generic geodesic nets are dense in high-dimensional manifolds.

We introduce the natural and fairly general notion of a subanalytic bundle (with a finite dimensional vector space $P$ of sections) on a subanalytic subset $X$ of a real analytic manifold $M$, and prove that when $M$ is compact, there is a Baire subset $U$ of sections in $P$ whose zero-loci in $X$ have tubular neighbou…

Improved Kuznecov remainder estimates for generic metrics.

New proof for weak mixing in polygonal billiards.

In this paper, we study Lipschitz-Fredholm vector fields on Bounded-Fréchet-Finsler manifolds. In this context we generalize the Morse-Sard-Brown theorem, asserting that if $M$ is a connected smooth bounded-Fréchet-Finsler manifold endowed with a strengthened connection $\mathcal{K}$ and if $ξ$ is a smooth Lipschitz-Fr…

The study shows that certain metrics on spheres prevent stable tangent cones for area-minimizing boundaries.

The paper connects Diophantine approximation to black hole behavior, proving blow-up conditions.

Classifies geodesic planes outside convex core of geometrically finite 3-manifolds.

A map $f:X\to Y$ between topological spaces is defined to be {\em scatteredly continuous} if for each subspace $A\subset X$ the restriction $f|A$ has a point of continuity. We show that for a function $f:X\to Y$ from a perfectly paracompact hereditarily Baire Preiss-Simon space $X$ into a regular space $Y$ the scattere…

A new video prediction model treats videos as continuous processes, reducing sampling steps and improving efficiency.

In this partly expository monograph we develop a general framework for producing uncountable families of exotic actions of certain classically studied groups acting on the circle. We show that if $L$ is a nontrivial limit group then the nonlinear representation variety $\mathrm{Hom}(L,\mathrm{Homeo}_+(S^1))$ contains u…

Paper proposes MMD-Sense-Analysis for detecting word sense shifts.

Mobile sensing is an emerging technology that utilizes agent-participatory data for decision making or state estimation, including multimedia applications. This article investigates the structure of mobile sensing schemes and introduces crowdsourcing methods for mobile sensing. Inspired by social network, one can estab…

New method for sensing non-planar surfaces using ERT.

Compressed sensing improves MRI scans with data-driven learning.

This paper proposes a simple adaptive sensing and group testing algorithm for sparse signal recovery. The algorithm, termed Compressive Adaptive Sense and Search (CASS), is shown to be near-optimal in that it succeeds at the lowest possible signal-to-noise-ratio (SNR) levels, improving on previous work in adaptive comp…

Paper tackles online task allocation in multi-attribute social sensing.

DisCor corrects reinforcement learning issues by re-weighting collected data.

Neural story generation gains common sense through targeted training.

Study uses remotely sensed data to infer economic outcomes in experiments and quasi-experiments.

We describe our language-independent unsupervised word sense induction system. This system only uses topic features to cluster different word senses in their global context topic space. Using unlabeled data, this system trains a latent Dirichlet allocation (LDA) topic model then uses it to infer the topics distribution…

Review of image compressive sensing algorithms for beginners.

The paper improves conditions for unique recovery in homomorphic sensing of subspaces.

Novel algorithm estimates local permutations in unlabeled multi-view sensing.

Paper offers robust recovery for 1-bit sensing with partial Gaussian circulant matrices.

Paper improves compressed sensing with prior probability information.

Study evaluates progress in common-sense reasoning tasks.

CNN model for efficient wireless spectrum sensing and signal identification.