Study joint spectrum of sub-Laplacian and Reeb vector field on Heisenberg Bieberbach manifolds.
problem Computing the joint spectrum of sub-Laplacian and Reeb vector field on specific manifolds.
method Explicit computation using theta functions and character theory of finite groups.
result Explicitly computed multiplicities of the joint spectrum.
End-to-end denoising framework improves SDR and PESQ metrics.
problem Spectrum and metric mismatches in speech enhancement networks.
method Optimizes network on time-domain signals after ISTFT and uses improved loss functions.
result Significantly improved SDR and PESQ performance.
A method for identifying joint and individual subspaces from multi-view data.
problem Unclear conditions for reliably identifying joint and individual subspaces from noisy, high-dimensional measurements.
method Rigorously quantifies conditions based on signal rank, principal angles, and noise levels. Characterizes spectrum perturbations of product of projection matrices.
result Estimates joint and individual subspaces more accurately than existing approaches in simulations and real-world applications.
Paper uses non-Euclidean analysis to classify brain structure variations.
problem Classifying joint variations in multi-object brain structures.
method Combines non-Euclidean statistics and non-parametric integrative analysis.
result Effective, robust, and interpretable joint structure found.
Algorithm learns graph ARMA processes for missing signal estimation.
problem Missing signal estimation in time-varying graph signals.
method Learning joint time-vertex power spectral density through convex relaxations.
result High accuracy in time-vertex signal estimation.
Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this paper, we address the problem of combining different layers of the multi-layer gra…
FreST Loss decorrelates spatio-temporal dependencies in graph signals.
problem Complex spatio-temporal dependencies in graph-structured signals are not well captured by standard forecasting models.
method FreST Loss extends supervision to the joint spatio-temporal spectrum using Joint Fourier Transform (JFT).
result FreST Loss reduces estimation bias and improves forecasting accuracy on real-world datasets.
Any two compact, complete, one-dimensional geodesic spaces with identical marked length spectrum have isometric π1-hull. The present version contains errors, notably in Lemmas 2.2 and 2.3 (path cancellations can be more complicated), which then propagate through the paper. The main result is correct as stated, and a…
Proposes a novel graph signal model using narrowband kernels.
problem Graph signals with multiple concentrated frequency regions.
method Jointly learns graph signal model parameters and coefficients.
result Joint learning improves signal interpolation accuracy.
A new method for analyzing multifractal cross correlations in complex systems.
problem Characterizing long-range cross-correlations in complex systems.
method Multifractal Cross Wavelet Analysis (MFXWT)
result MFXWT accurately captures joint multifractality in binomial multifractal measures but may produce spurious results for bivariate fractional Brownian motions.
New resonance theory for Anosov flows connects spectral properties to mixing measures.
problem Defining and analyzing Ruelle-Taylor resonances for Anosov actions.
method Combining microlocal methods and J. Taylor's cohomological theory, defining Ruelle-Taylor resonances and proving Fredholm theory.
result Ruelle-Taylor resonances form a discrete subset of Cκ with λ=0 being a leading resonance. Framework predicts clinical severity from rs-fMRI data using network optimization.
problem Predicting clinical severity from rs-fMRI data.
method Joint network optimization framework combining sparse subnetworks and linear regression.
result Framework outperforms standard methods and identifies clinically relevant ASD networks.
Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only o…
In this talk, I will discuss the use of harmonic functions to study the geometry and topology of complete manifolds. In my previous joint work with Luen-fai Tam, we discovered that the number of infinities of a complete manifold can be estimated by the dimension of a certain space of harmonic functions. Applying this t…
In this paper, we address the general case of a coordinated secondary network willing to exploit communication opportunities left vacant by a licensed primary network. Since secondary users (SU) usually have no prior knowledge on the environment, they need to learn the availability of each channel through sensing techn…
Generative models for graphs have been typically committed to strong prior assumptions concerning the form of the modeled distributions. Moreover, the vast majority of currently available models are either only suitable for characterizing some particular network properties (such as degree distribution or clustering coe…
The paper explores cost-aware spectrum access strategies in cognitive radio systems.
problem Optimizing spectrum usage in cognitive radio systems with uncertain channel states and costs.
method Discrete time model with sensing and transmission phases, considering random costs and rewards.
result The optimal policy for spectrum access has a recursive double threshold structure, and online algorithms achieve near-optimal performance.
Model improves covariance estimation from shared and distinct datasets.
problem Limited sample sizes and shared covariance structure across related datasets.
method Spiked covariance model with shared subspace, closed-form pooling weight, and asymptotic guarantees.
result Improves estimation of high-dimensional covariance matrices from related datasets.
Asymptotic factorizations for the small-ball probability (SmBP) of a Hilbert valued random element X are rigorously established and discussed. In particular, given the first d principal components (PCs) and as the radius ε of the ball tends to zero, the SmBP is asymptotically proportional to (a) the joi…
DSL estimates heterogeneous treatment effects over time in survival settings.
problem Complicated by right censoring and time-varying treatment effects.
method Deep survival learner (DSL) for estimating CATEs over a clinically relevant time spectrum.
result DSL reveals heterogeneity in perioperative chemotherapy effects over time.
The subject of this paper is the relationship among the marked length spectrum, the length spectrum, the Laplace spectrum on functions, and the Laplace spectrum on forms on Riemannian nilmanifolds. In particular, we show that for a large class of three-step nilmanifolds, if a pair of nilmanifolds in this class has the …
The subject of this paper is the relationship among the marked length spectrum, the length spectrum, the Laplace spectrum on functions, and the Laplace spectrum on forms on Riemannian nilmanifolds. In particular, we show that for a large class of three-step nilmanifolds, if a pair of nilmanifolds in this class has the …
We define a new spectrum for compact length spaces and Riemannian manifolds called the "covering spectrum" which roughly measures the size of the one dimensional holes in the space. More specifically, the covering spectrum is a set of real numbers δ>0 which identify the distinct δ covers of the space. We investigat…
UWM-JEPA predicts future scenarios in belief space, improving accuracy in partially observed environments.
problem Predicting future scenarios in partially observed environments with uncertainty.
method Introduces UWM-JEPA, a JEPA world model with a density-matrix latent and learned unitary predictor.
result UWM-JEPA achieves 0.77 accuracy on a hidden-velocity indicator task, outperforming LSTM-JEPA.
ASD-DiagNet uses fMRI data to improve ASD diagnosis accuracy.
problem Difficult diagnosis of Autism Spectrum Disorder (ASD) due to symptom observation.
method Hybrid learning approach combining autoencoder and single layer perceptron.
result Improved classification accuracy up to 80% with 20% increase over state-of-the-art methods.
This paper shows a unique spectrum for hyperbolic surfaces.
problem The rigidity of marked length spectrum for closed hyperbolic surfaces is not true for unmarked spectra.
method Introducing the length-angle spectrum and proving its uniqueness.
result The length-angle spectrum determines the surface uniquely.
Study the energy spectrum of metrics on surfaces and its relation to simple length spectrum.
problem Relate the energy spectrum to the simple length spectrum of metrics on surfaces.
method Analyze the energy spectrum of metrics on surfaces and their Teichmüller spaces, considering homotopy conditions.
result The energy spectrum determines the simple length spectrum under certain conditions.
The paper compares two spectrum definitions and finds stability in one modification.
problem Generalizing eigenvalues to arbitrary functionals with stability.
method Comparison of Gromov's homotopy significant spectrum and Krasnoskii spectrum, with a modified definition of the homotopy significant spectrum.
result The modified homotopy significant spectrum is stable, and Cheeger constant corresponds to Krasnoskii eigenvalue.
Proofs high-dimensional spectrum convergence of weighted sample covariance.
problem High-dimensional spectrum convergence of weighted sample covariance.
method Proposes a new, concise proof with stronger assumptions.
result Spectrum convergence proven for different weight distributions.
Study shows spectrum properties for specific Hadamard manifolds.
problem Spectrum properties of Hadamard manifolds.
method Absolute continuity and spectrum determination for two classes of Hadamard manifolds.
result Spectrum properties determined for specific Hadamard manifolds.
Iterative method 'Concent' corrects spectrum bias in covariance matrices.
problem Consistent bias in the spectrum of covariance matrices.
method 'Concent' iterative algorithm.
result Corrects spectrum bias for small and moderate dimensions.
Develops a new spectrum for annular links, recovering a transverse invariant at extreme gradings.
problem Understanding transverse link invariants in the annular setting.
method Constructs a stable homotopy type for annular links and defines a map to the Khovanov skein spectrum.
result At extreme gradings, the map from the Khovanov spectrum to the Khovanov skein spectrum recovers the cohomotopy transverse invariant.
Constructs manifolds with specific spectral properties.
problem Spectral properties of Riemannian manifolds.
method Asymptotically hyperbolic manifolds with sharp curvature bounds.
result Embeds singular continuous spectrum into the essential spectrum of the Laplacian.
The spectrum of certain manifolds matches that of hyperbolic space if the bottom spectrum is maximal.
problem Investigating spectral rigidity of manifolds with Ricci bounded below and maximal bottom spectrum.
method Analyzing the spectrum of the Laplacian on manifolds with specific Ricci curvature bounds.
result The spectrum of the manifold coincides with that of hyperbolic space if the bottom spectrum is maximal.
Lower bounds for Hodge-Laplacian spectrum on orbifolds.
problem Finding bounds for the essential spectrum of Hodge-Laplacian.
method Deriving lower bounds for the essential spectrum of the Hodge-Laplacian on geometrically finite orbifolds and their suborbifolds.
result Lower bounds for the essential spectrum of the Hodge-Laplacian.
Rigidity of spectral data for spherical manifolds with boundary.
problem Determining the length spectrum of spherically symmetric manifolds with boundary.
method Proving a trace formula and using it to show spectral rigidity.
result The Neumann spectrum uniquely determines the length spectrum for spherically symmetric manifolds with boundary.
A machine learning approach for efficient spectrum sharing in distributed DSA networks.
problem Effective spectrum sharing among secondary users (SUs) and primary users (PUs) in a distributed network.
method Deep reinforcement learning (DRL) combined with reservoir computing (RC) for distributed spectrum access decisions.
result The RC-based spectrum access strategy significantly reduces collision chances and outperforms other methods.
Trapezoids uniquely identified by their Dirichlet Laplace spectrum.
problem Identifying trapezoids based on their spectral properties.
method Analyzing the Dirichlet Laplace spectrum of non-obtuse trapezoids.
result Non-obtuse trapezoids are uniquely determined by their Dirichlet Laplace spectrum.
In 2004, Sormani and Wei introduced the covering spectrum: a geometric invariant that isolates part of the length spectrum of a Riemannian manifold. In their paper they observed that certain Sunada isospectral manifolds share the same covering spectrum, thus raising the question of whether the covering spectrum is a sp…
Survey on bottom of spectrum of Hodge Laplacian on complete noncompact Kähler manifolds
problem Bottom of the spectrum of Hodge Laplacian on complete noncompact Kähler manifolds
method Survey on Kähler hyperbolic manifolds and bounded symmetric domains
result Proposed several open problems
The paper extends decay estimates to graphs with positive spectrum.
problem Proving decay estimates for nonnegative functions on graphs.
method Sharp ℓ2 decay estimates for nonnegative generalized subharmonic functions. result Extends Li and Wang's result to graphs with positive Laplacian spectrum.
Upper bounds for essential spectrum of minimal submanifolds linked to volume growth.
problem Estimating the essential spectrum of minimal submanifolds.
method Using volume growth to bound the bottom of the essential spectrum.
result Improved essential spectrum estimate for minimal submanifolds.
Upper bounds for volume spectrum depend on volume, dimension, and a conformal invariant.
problem Bounding the volume spectrum of Riemannian manifolds.
method Proves upper bounds that depend on volume, dimension, and a conformal invariant.
result Upper bounds for the volume spectrum are established.
Study on magnetic Dirac operators and their spectrum.
problem Understanding the spectrum of magnetic Dirac operators.
method Analysis of magnetic Dirac operators over complete Riemannian manifolds.
result Find sufficient conditions for maximal or discrete spectrum.
Study shows Riemannian manifold volume spectrum follows a Weyl law.
problem Understanding volume spectrum of Riemannian manifolds.
method Proved a Weyl law for volume spectrum.
result Volume spectrum of Riemannian manifolds follows a Weyl law.
Covering preserves bottom spectrum, implies amenable covering.
problem Spectral preservation in Riemannian coverings.
method Proving spectral properties of Schrödinger operators on coverings.
result Covering preserving bottom spectrum implies amenability.
Notes on continuity of discrete-spectrum Fredholm operators.
problem Continuity properties of discrete-spectrum families of Fredholm operators.
method Relates recent work on discrete-spectrum families to classical continuity properties.
result Establishes connections between new and classical concepts.
Study shows ortho spectrum doesn't fully determine systolic length but limits the number of possible structures.
problem Determining the systolic length of hyperbolic surfaces with boundary.
method Analyzing the ortho spectrum of hyperbolic surfaces with totally geodesic boundary.
result There are only finitely many possibilities for the ortho spectrum and corresponding hyperbolic structures.