arXiv research

Characterizes minor-minimal separating projective planar graphs and their generalizations.

Study on minimal hypersurfaces in a special normed space.

Study on minimal surfaces in a 3D space with 2m-norm.

We solve minimal separator problems in AMP chain graphs and improve structure learning algorithms.

Some elementary considerations are presented concerning Catenoids and their stability, separable minimal hypersurfaces, minimal surfaces obtainable by rotating shapes, determinantal varieties, minimal tori in S3, the minimality in Rnk of the ordered set of k orthogonal equal-length n-vectors, and U(1)-invariant minimal…

Extends Newton's minimal resistance problem to Lorentz-Minkowski space.

Minimal simplicial complexes in high dimensions always contain complex links.

This paper develops a new nonlocal approximation method for minimal surfaces, proving robust estimates and separation properties.

Alternative proof of simplicial volume bound using area-minimizing sets.

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

Separable losses are inconsistent for structured prediction models.

Hierarchical clustering is a popular method for analyzing data which associates a tree to a dataset. Hartigan consistency has been used extensively as a framework to analyze such clustering algorithms from a statistical point of view. Still, as we show in the paper, a tree which is Hartigan consistent with a given dens…

Study of phase separation and geometry on a closed elastic curve, including dynamics and free energy minimization.

This paper proposes a new evaluation metric and boosting method for weight separability in neural network design. In contrast to general visual recognition methods designed to encourage both intra-class compactness and inter-class separability of latent features, we focus on estimating linear independence of column vec…

The generalized soap bubble problem seeks the least perimeter way to enclose and separate n given volumes in R^m. We study the possible configurations for perimeter minimizing bubble complexes enclosing more than two regions. We prove that perimeter minimizing planar bubble complexes with equal pressure regions and wit…

A new method separates data points using entropy minimization over a hypercube.

Optimal joint separation condition for radar and communications channels in dual-blind deconvolution.

We present a novel blind source separation (BSS) method, called information geometric blind source separation (IGBSS). Our formulation is based on the log-linear model equipped with a hierarchically structured sample space, which has theoretical guarantees to uniquely recover a set of source signals by minimizing the K…

We introduce a new metric to evaluate corruption robustness of ML classifiers.

Constructs classifiers for neural networks with specific data configurations.

Optimizes CM for stochastic convex optimization with progressive precision.

We prove a Weyl Law for the phase transition spectrum based on the techniques of Liokumovich-Marques-Neves. As an application we give phase transition adaptations of the proofs of the density and equidistribution of minimal hypersufaces for generic metrics by Irie-Marques-Neves and Marques-Neves-Song, respectively. We …

In this paper, we present a novel system that separates the voice of a target speaker from multi-speaker signals, by making use of a reference signal from the target speaker. We achieve this by training two separate neural networks: (1) A speaker recognition network that produces speaker-discriminative embeddings; (2) …

Adaptive clustering and personalization algorithms minimize regret in multi-agent stochastic linear bandits.

The investment risk minimization problem with budget and return constraints has been the subject of research using replica analysis but there are shortcomings in the extant literature. With respect to Tobin's separation theorem and the capital asset pricing model, it is necessary to investigate the implications of a ri…

Sparse Blind Source Separation (sparse BSS) is a key method to analyze multichannel data in fields ranging from medical imaging to astrophysics. However, since it relies on seeking the solution of a non-convex penalized matrix factorization problem, its performances largely depend on the optimization strategy. In this …

We present a conjecture, based on computational results, on the area minimizing way to enclose and separate two arbitrary volumes in the flat cubic 3-torus. For comparable small volumes, we prove that an area minimizing double bubble in the 3-torus is the standard double bubble from R^3.

Adaptive algorithm reduces regret in causal bandits.

This study examines abnormal geodesics in 2D-Zermelo navigation problems, revealing their role in separating time minimal and maximal curves.

DDICA separates nonlinear mixed signals robustly.

Minimal constructions of meanders and hyperelliptic pillowcase covers help in understanding ratio-optimizing pseudo-Anosovs.

Gradient flow on softmax attention minimizes nuclear norm of weight matrices.

Single-microphone, speaker-independent speech separation is normally performed through two steps: (i) separating the specific speech sources, and (ii) determining the best output-label assignment to find the separation error. The second step is the main obstacle in training neural networks for speech separation. Recent…

Adversarial training is a technique for training robust machine learning models. To encourage robustness, it iteratively computes adversarial examples for the model, and then re-trains on these examples via some update rule. This work analyzes the performance of adversarial training on linearly separable data, and prov…

SRTC model for background/foreground separation with missing pixels.

New method finds subsets of vertices to minimize interventions in causal discovery.

Study essential diagrams of knots in $S_{g} imes S^{1}$ and their relation to virtual knots.

We propose a new stochastic coordinate descent method for minimizing the sum of convex functions each of which depends on a small number of coordinates only. Our method (APPROX) is simultaneously Accelerated, Parallel and PROXimal; this is the first time such a method is proposed. In the special case when the number of…

Four counterexamples in surface homology.

Enhanced Hopfield model boosts memory retrieval capacity.

New approach for classification using trigonometric polynomial kernels from signal processing.

New deep-unfolded network improves video background separation.

Let $f : U\subset\Rm \to \calQ_Q(\ell_2)$ be of Sobolev class $W^{1,p}$, $1 < p < \infty$. If $f$ almost minimizes its $p$ Dirichlet energy then $f$ is Hölder continuous. If $p=2$ and $f$ is squeeze and squash stationary then $f$ is in VMO.

We consider the problem of estimating the phases of K mixed complex signals from a multichannel observation, when the mixing matrix and signal magnitudes are known. This problem can be cast as a non-convex quadratically constrained quadratic program which is known to be NP-hard in general. We propose three approaches t…

Let $M$ be a compact Riemannian manifold of nonnegative Ricci curvature and $Σ$ a compact embedded 2-sided minimal hypersurface in $M$. It is proved that there is a dichotomy: If $Σ$ does not separate $M$ then $Σ$ is totally geodesic and $M\setminusΣ$ is isometric to the Riemannian product $Σ\times(a,b)$, and if $Σ$ se…

This paper proposes RAS, a novel unsupervised loss function for speech separation.

Recently, the principal component pursuit has received increasing attention in signal processing research ranging from source separation to video surveillance. So far, all existing formulations are real-valued and lack the concept of phase, which is inherent in inputs such as complex spectrograms or color images. Thus,…

We bound the locations of outermost minimal surfaces in geometrostatic manifolds whose ADM mass is small relative to the separation between the black holes and prove the Intrinsic Flat Stability of the Positive Mass Theorem in this setting.