Paper proposes a faster time series clustering method.
problem Efficiently clustering input/output time series with underlying dynamics.
method Extends Martin cepstral distance to efficiently cluster time series.
result New distance measure performs as well as explicit model identification but is much faster.
Paper extends cepstral distance for stable, minimum-phase models.
problem Quantifying similarity between data objects in deterministic systems.
method Combines insights from systems theory and machine learning to extend weighted cepstral distance.
result Extended weighted cepstral distance can be interpreted in terms of poles and zeros of the model.
Detects AI-synthesized speech using cepstral and bispectral analysis.
problem Validating the authenticity of speech from AI-generated content.
method Integrates cepstral and bispectral analysis for distinguishing human from AI-synthesized speech.
result Higher-order statistics show less correlation for human speech compared to AI-synthesis, and cepstral analysis reveals unique power components.
CycleGAN-VC2 improves voice conversion without parallel data.
problem Challenges in non-parallel voice conversion.
method Improved CycleGAN-VC with three techniques: two-step adversarial losses, 2-1-2D CNN generator, and PatchGAN discriminator.
result CycleGAN-VC2 significantly reduces the gap between converted and target speech.
New Gehring-Martin-Tan groups with elliptic generators found.
problem Finding discrete subgroups of PSL(2,C) satisfying Gehring-Martin-Tan inequality.
method Constructing groups with an elliptic generator of order four.
result Examples of Gehring-Martin-Tan groups with elliptic generators.
Study diffusions and random walks on hyperbolic spaces, focusing on their Martin boundaries.
problem Understanding diffusions and random walks on hyperbolic spaces.
method Analyzing specific diffusions and random walks on hyperbolic spaces, examining their Martin boundaries.
result Characterized the Martin boundaries of diffusions and random walks on hyperbolic spaces.
Study of Martin boundary for rank 1 manifolds with nonpositive curvature.
problem Understanding the Martin boundary for specific types of manifolds.
method Modification of Ancona's argument to analyze the geometric and Martin boundaries.
result A residual set in the geometric boundary corresponds naturally to a subset of the Martin boundary.
Characterizes Martin boundaries of certain hyperbolic groups.
problem Understanding the Martin boundaries of specific groups.
method Topological characterization using Green's function and random walks.
result Martin boundary matches CAT (0) boundary in some cases.
The Martin boundary of certain groups is stable under specific conditions.
problem Stability of Martin boundaries in relatively hyperbolic groups.
method Extending Floyd-Ancona inequalities, defining spectral degenerescence, and proving stability criteria.
result The Martin boundary of admissible symmetric finitely supported probability measures on geometrically finite Kleinian groups of dimension at most 5 is always strongly stable.
The Martin boundary of a Cartan-Hadamard manifold describes a fine geometric structure at infinity, which is a sub-space of positive harmonic functions. We describe conditions which ensure that some points of the sphere at infinity belong to the Martin boundary as well. In the case of the universal cover of a compact m…
Two singular mean curvature flows converge if Hausdorff distance decreases faster than inverse time.
problem Understanding convergence of singular mean curvature flows.
method Analyzing Hausdorff distance between flows approaching a singularity.
result Two flows become identical if Hausdorff distance decreases faster than inverse time.
Extends Martin boundary to Floyd boundary for random walks.
problem Mapping Martin boundary to Floyd boundary for random walks.
method Continuous equivariant surjection using Green and Floyd metrics.
result Identity map extends to continuous surjection with preimages being singletons.
The study provides criteria for solving the Dirichlet problem at infinity on Cartan-Hadamard surfaces.
problem Solvability of the Dirichlet problem at infinity on Cartan-Hadamard surfaces.
method General criterion and upper radial curvature bounds.
result Solvability of the Dirichlet problem at infinity implies a natural continuous surjection of the Martin boundary onto the geometric boundary.
Combines relatively hyperbolic groups over a complex.
problem Combining relatively hyperbolic groups.
method Generalization of Martin's theorem for hyperbolic groups.
result Combination theorem for relatively hyperbolic groups.
Extends Mahalanobis distance to Banach spaces for anomaly detection.
problem Anomaly detection in infinite-dimensional spaces.
method Generalizes Mahalanobis distance to Banach spaces via Cameron-Martin norm and variance norm.
result Kernelized nearest-neighbour Mahalanobis distance outperforms traditional methods for time series novelty detection.
A new robust speaker identification method using minimum divergence measures.
problem Improving speaker identification accuracy in the presence of outliers.
method Minimum divergence approach with modified distance measures (likelihood disparity, Hellinger, Pearson's chi-square).
result Significant improvement in classification accuracy on benchmark and new speech corpora.
Study transforms singular area minimizing hypersurfaces into hyperbolic spaces.
problem Understanding singular area minimizing hypersurfaces.
method Conformal unfolding to Gromov hyperbolic spaces.
result Recover singular set as Gromov and Martin boundaries.
We present two proofs of the fact, originally due to Reiner Martin, that any fully irreducible hyperbolic element of Out(FN) acts on the projectivized space of geodesic currents PCurr(FN) with uniform north-south dynamics. The first proof, using purely train-track methods, provides an elaborated and corr…
Geoffrey Martin's theorem proves normal forms for Lagrangian submanifolds in multisymplectic geometry.
problem Normal forms for Lagrangian submanifolds in multisymplectic geometry.
method Detailed, self-contained proof of normal form theorem, including necessary results in foliated differential topology.
result Geoffrey Martin's theorem provides a normal form for Lagrangian submanifolds in multisymplectic geometry.
Develops potential theory on singular almost minimizers.
problem Boundary value problems on singular spaces.
method Elliptic operators, hyperbolic unfoldings, boundary Harnack inequalities.
result Established robust boundary Harnack inequalities and Martin theory.
The purpose of this article is to describe all possible beliefs of market participants on objective measures under Markovian environments when a risk-neutral measure is given. To achieve this, we employ the Martin integral representation of Markovian pricing kernels. Then, we offer economic and financial implications o…
In this paper we examine the Laplacian on the product of two asymptotically hyperbolic (or conformally compact, as they are often called) spaces from the point of view of geometric scattering theory. In particular, we describe the asymptotic behavior of the resolvent applied to Schwartz functions and that of the resolv…
Machine learning classifies IoT noise in smart cities.
problem Noise classification in smart cities.
method Mel-frequency cepstral coefficients for audio features, supervised classification (SVM, k-NN), parameter optimization.
result Noise classification accuracy of 85% - 100%.
Bounds on Gaussian approximation for neural networks with novel smoothing techniques.
problem Approximating the distribution of wide random neural networks.
method Stein's method, Gaussian smoothing, Laplacian operators, Cameron-Martin space.
result First bounds on Gaussian approximation of wide random neural networks.
Polyconvex energies with conformal invariance have smooth stationary points outside a discrete set.
problem Stationary points of conformally invariant polyconvex energies
method Proving smoothness of stationary points
result Smooth stationary points outside a discrete set
We give elementary constructions for Satake-Furstenberg, Martin and Karpelevich boundaries of symmetric spaces. We also consruct some "new" boundaries
Potential theory extended to Gromov hyperbolic spaces.
problem Extending potential theory to a new class of spaces.
method Unified framework for Gromov hyperbolic metric measure spaces.
result Boundary Harnack inequalities and complete classification of positive harmonic functions.
Transform drift of diffusions without knowing if measure change is a martingale.
problem Transforming drift in diffusions without knowing if measure change is a martingale.
method Characterize when measure change local martingale is a true martingale.
result Complete characterization of measure change local martingale being a true martingale.
The study quantifies geodesic divergence on Riemannian planes with bounded geometry.
problem Understanding geodesic divergence on Riemannian planes with specific geometric constraints.
method Recalling quasi-redirection and using it to quantify geodesic divergence, compactifying Riemannian planes into D2 or S2. result Necessary and sufficient conditions for the quasi-redirecting compactification being S2 are derived in terms of asymptotic cones. New basis and Schur-Weyl duality for loop Hecke algebra defined.
problem Define a new basis for the loop Hecke algebra.
method Use higher linear rewriting theory and combinatorics of Dyck paths.
result Yields a conjecture of Damiani-Martin-Rowell and provides a representation theoretic interpretation.
A model classifies music genres from MP3 files using metric learning and feature extraction.
problem Classifying music genres from MP3 files efficiently and accurately.
method Metric learning and feature extraction using MFCC and PCA.
result Promising results in classification accuracy compared to baseline algorithms.
We construct open domains in Euclidean 3-space which do not admit complete properly immersed minimal surfaces with an annular end. These domains can not be smooth by a recent result of Martin and Morales
Functional inequality proves quasi-invariance in infinite dimensions.
problem Proving quasi-invariance of measures in infinite-dimensional spaces.
method Using a functional inequality to prove quasi-invariance of measures under group actions.
result Different proof of the Cameron-Martin theorem in infinite dimensions.
Estimates on Einstein manifolds improve Brownian motion behavior and curvature limits.
problem Improving estimates on Einstein manifolds for Brownian motion behavior.
method Generalizing Benjamini-Pemantle-Peres estimate to manifolds with Ricci curvature bounds.
result Sharp estimates for Brownian motion on high curvature parts of Ricci-flat manifolds.
Detects adversarial examples in deep speech recognition.
problem Vulnerability of deep speech recognition systems to adversarial attacks.
method Formulated as a classification problem, generated adversarial and normal datasets, trained CNN.
result Accurately distinguishes between adversarial and normal examples for known attacks.
Starting from works by Scherk (1835) and by Enneper-Weierstraß\ (1863), new minimal surfaces with Scherk ends were found only in 1988 by Karcher (see \cite{Karcher1,Karcher}). In the singly periodic case, Karcher's examples of positive genera had been unique until Traizet obtained new ones in 1996 (see \cite{Traizet}).…
New knot found with unique property.
problem Existence of hyperbolic fibered slice knots with specific monodromy.
method Constructed a specific type of hyperbolic fibered slice knot.
result Negative answer to a question posed by Hubbard et al.
In this paper we consider the Martin compactification, associated with the operator L=Δ−1, of a complete non-compact surface (Σ2,ds2) with negative curvature. In particular, we investigate positive eigenfunctions with eigenvalue one of the Laplace operator Δ of (Σ2,ds2) and prove a uniqueness …
Model classifies environment sounds using multiple feature channels and attention mechanisms.
problem Environment sound classification task.
method Multiple feature channels (MFCC, GFCC, CQT, Chromagram) and attention mechanism in a deep CNN.
result Achieves state-of-the-art performance on three benchmark datasets.
In his 1974 thesis, Martin Scharlemann constructed a fake homotopy equivalence from a closed smooth manifold f:Q -> S^3 x S^1 # S^2 x S^2 and asked whether the manifold Q itself is diffeomorphic to S^3 x S^1 # S^2 x S^2. Here we answer this question affirmatively.
Abstract: Generalizes SGMs to infinite-dimensional Hilbertian setting.
problem Difficulties in extending SGMs to infinite-dimensional settings.
method Uses Gamma and Malliavin Calculus, Dirichlet forms, Wiener chaoses, and time-reversal formula.
result Generalized SGMs to Hilbertian setting with finite-dimensional entropic convergence bounds.
Develops confidence intervals for unique elements in data streams.
problem Analyzing the number of unique elements in data streams.
method Uses Flajolet-Martin algorithms and Chernoff bounds for statistical analysis.
result Shows deep connections with mathematical special functions and extreme value theory.
This paper studies Brownian motion and heat kernel measure on a class of infinite dimensional Lie groups. We prove a Cameron-Martin type quasi-invariance theorem for the heat kernel measure and give estimates on the Lp norms of the Radon-Nikodym derivatives. We also prove that a logarithmic Sobolev inequality holds …
We generalize a class of groups introduced by Herbert Abels to produce examples of virtually torsion free groups that have Bredon-finiteness length m-1 and classical finiteness length n-1 for all 0 < m <= n. The proof illustrates how Bredon-finiteness properties can be verified using geometric methods and a version of …
ICML workshop on making machine learning models more understandable.
problem Making machine learning models more understandable to humans.
method Various presentations and discussions on interpretability techniques.
result Advancements in methods to improve model interpretability.
We show that the spectrum of a complete submanifold properly immersed into a ball of a Riemannian manifold is discrete, provided the norm of the mean curvature vector is sufficiently small. In particular, the spectrum of a complete minimal surface properly immersed into a ball of R3 is discrete. This give…
ResNet with Focal Loss improves speech emotion recognition.
problem Speech emotion recognition using plain text features is insufficient.
method Residual Convolutional Neural Network (ResNet) trained with Focal Loss.
result Focal Loss enhances model's focus on hard examples.
We study an integration theory in circle equivariant cohomology in order to prove a theorem relating the cohomology ring of a hyperkahler quotient to the cohomology ring of the quotient by a maximal abelian subgroup, analogous to a theorem of Martin for symplectic quotients. We discuss applications of this theorem to q…