Study extends quantum density spectra of knots.
problem Understanding quantum density spectra of knots.
method Examined new quantum invariants and sequences of knots.
result Proposed conjectures for maximal sequences.
New ICA method for sources with mixed spectra.
problem Inaccurate separation of sources with temporal autocorrelations and mixed spectra.
method Estimates spectral density functions and line spectra using cubic splines and indicator functions, then maximizes the Whittle likelihood function.
result Outperforms existing ICA methods in simulations and EEG data applications.
A new method matches moments exactly for large graphs, improving spectral learning.
problem Lack of exact moment matching in spectral density approximations for large graphs.
method Maximum Entropy method for spectral density approximation, with a new algorithm.
result The new method outperforms existing approaches in learning graph spectra.
We derive the exact form of the eigenvalue spectra of correlation matrices derived from a set of time-shifted, finite Brownian random walks (time-series). These matrices can be seen as random, real, asymmetric matrices with a special structure superimposed due to the time-shift. We demonstrate that the associated eigen…
DenSNet learns electron densities for molecular dynamics, enabling accurate spectroscopic predictions.
problem Lack of accurate electronic observables in MLIPs for molecular dynamics.
method DenSNet uses SE(3)-equivariant neural networks to predict electron densities and total energy.
result DenSNet predicts infrared spectra with excellent agreement to experimental data.
The study explores the densities of volume and determinant for hyperbolic links.
problem Understanding the densities of volume and determinant for hyperbolic links.
method Defined and analyzed volume and determinant densities for hyperbolic links.
result The set of volume densities is dense in [0, v_8], and the closure of the set of determinant densities contains [0, v_8].
We show that the set of k-dimensional isoperimetric exponents of finitely presented groups is dense in the interval [1, \infty) for k > 1. Hence there is no higher-dimensional analogue of Gromov's gap (1,2) in the isoperimetric spectrum.
Study reveals pathological eigenvalue spectra in FIM and its variants of DNNs.
problem Understanding sharp local shapes in DNN loss landscapes.
method Analysis of FIM and its variants in regression and classification DNNs.
result Pathological eigenvalue spectra appear in FIM and its variants, indicating sharp local shapes in specific directions.
This work uses neural density estimation to analyze laser-induced breakdown spectroscopy data, enabling accurate predictions and uncertainty quantification.
problem Inference of probability densities in high-dimensional spectral data is often intractable.
method Normalizing flows on structured spectral latent spaces for density estimation and uncertainty quantification.
result The approach enables generation of realistic spectral samples and accurate prediction of state vectors with well-calibrated uncertainties.
We derive expressions for the predicitive information rate (PIR) for the class of autoregressive Gaussian processes AR(N), both in terms of the prediction coefficients and in terms of the power spectral density. The latter result suggests a duality between the PIR and the multi-information rate for processes with mutua…
LGKDE learns graph density using neural networks and perturbations.
problem Graph density estimation challenges in capturing structural patterns and semantic variations.
method LGKDE uses graph neural networks to represent graphs as discrete distributions and learns graph metrics via maximum mean discrepancy.
result LGKDE outperforms state-of-the-art baselines in graph anomaly detection.
Bayesian framework estimates noise variance and peak number from noisy spectra.
problem Misunderstanding of physical properties from noisy spectra.
method Bayesian inference with two steps: hyperparameter estimation and peak fitting.
result Framework prevents overfitting and overpenalizing, improving parameter estimation.
Optimizes graph spectral density learning for large networks.
problem Ad-hoc kernel function and bandwidth selection in graph spectral techniques.
method Maximum Entropy approach to learn a smooth graph spectral density.
result Outperforms comparable iterative spectral approaches on synthetic and real graphs.
Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails, that can be modelled with Levy stable distributions. We review comprehensively …
A new method clusters hyperspectral images using spatially regularized diffusion.
problem Clustering hyperspectral images effectively.
method Spatially regularized random walks and diffusion geometry.
result The method outperforms state-of-the-art algorithms on real data.
Study bridge spectra of 2-bridge knots and their cables.
problem Computing bridge spectra for 2-bridge knots and their cables.
method Computed bridge spectra of cables of 2-bridge knots.
result Results on bridge spectra and distance of Montesinos knots.
We apply random matrix theory to derive spectral density of large sample covariance matrices generated by multivariate VMA(q), VAR(q) and VARMA(q1,q2) processes. In particular, we consider a limit where the number of random variables N and the number of consecutive time measurements T are large but the ratio N/T is fix…
We analyze the Hessian spectra of large models up to 100B parameters.
problem Accurate Hessian spectra of large foundation models are difficult to obtain.
method We use shard-local finite-difference Hessian vector products and stochastic Lanczos quadrature.
result We produce the first large-scale spectral density estimates of foundation models.
Investigates point spectra of vector fields and their properties.
problem Understanding the point spectra of vector fields.
method Define and study point spectra, prove properties under isometries, and analyze compactly supported fields.
result Point spectra are well-behaved under isometries and trivial for compactly supported fields.
Khovanov spectra are shown to be functorial under certain conditions.
problem Understanding functoriality of Khovanov spectra.
method Proving functoriality up to homotopy and sign for Khovanov spectra.
result Khovanov spectra are functorial under specific conditions.
New matrix ensembles better match deep neural network spectral densities.
problem Theoretical spectral density models for deep networks do not match empirical observations.
method Introduced new matrix ensemble classes to better fit observed spectral densities.
result Theoretical models for deep networks are significantly flawed.
Paper finds knots with stair-step bridge spectra but are not high distance.
problem Understanding the relationship between bridge spectra and knot distance.
method Computed bridge spectra and distances of generalized Montesinos knots, including pretzel and Montesinos knots.
result First example of knots with stair-step bridge spectra but not high distance.
We give a simple sufficient condition for Quinn's "bordism-type spectra" to be weakly equivalent to strictly associative ring spectra. We also show that Poincare bordism and symmetric L-theory are naturally weakly equivalent to monoidal functors. Part of the proof of these statements involves showing that Quinn's funct…
Method calculates spectra of Rarita-Schwinger operator on symmetric spaces.
problem Calculating spectra of the Rarita-Schwinger operator on compact symmetric spaces.
method Using Weitzenböck formulas, Laplace operator, Casimir operator, Freudenthal's formula, and branching rules.
result Obtained spectra on the sphere, complex projective space, and quaternionic projective space.
Proves spectra equivalence for Riemannian manifolds.
problem Equivalence of Almgren-Pitts and phase-transition half-volume spectra.
method Proof of spectra equivalence for Riemannian manifolds.
result Confirms conjecture about spectra equivalence.
Paper resolves decades-old problem about L-spectra.
problem Identifying L-spectra local information with geometric data. method Proved equivalence of L-orientations and characteristic classes. result Levitt-Ranicki's theory equivalent to Brumfiel-Morgan's classes.
Study calculates spectra of minimal hypersurfaces in hyperbolic space.
problem Computing Laplacian spectra of minimal hypersurfaces.
method Analyzes hypersurfaces in hyperbolic space with specific asymptotic data.
result Obtains spectra and extremal properties of the bottom of the spectrum.
New metrics compare rational spectra using optimal transport.
problem Comparing rational spectra efficiently and accurately.
method Optimal transport and linear-systems theory.
result Established connection to Wasserstein distance.
Defines higher order spectra for complex manifolds with group actions and equations.
problem Understanding spectra of complex manifolds with group actions.
method Introduces higher order spectra, defines refinements, and provides Macdonald type equations.
result Macdonald type equations for higher order spectra of complex manifolds with group actions.
Study how bottom of spectra changes with Riemannian coverings.
problem Behavior of bottom of spectra under Riemannian coverings.
method Analysis of scalar Schrödinger operators on Riemannian manifolds.
result Changes in the bottom of spectra observed under coverings.
In this paper, we numerically investigate the length spectra and the low-lying eigenvalue spectra of the Laplace-Beltrami operator for a large number of small compact(closed) hyperbolic (CH) 3-manifolds. The first non-zero eigenvalues have been successfully computed using the periodic orbit sum method, which are compar…
Graphs approximate Laplacian spectra on manifolds.
problem Approximating Laplacian spectra on complex manifolds.
method Graph Laplacians on proximity graphs.
result Spectra of graph Laplacians approximate the Laplacian spectra of manifolds.
Jones-Wenzl projectors lifted to Khovanov spectra, proving knot conjectures.
problem Understanding Jones-Wenzl projectors in Khovanov spectra.
method Constructing and studying lifted projectors via maps and polynomial actions.
result Complete computation of 3-colored Khovanov spectrum of the unknot, proving conjectures.
We introduce a framework, twisted parametrized stable homotopy theory, for describing semi-infinite homotopy types. A twisted parametrized spectrum is a section of a bundle whose fibre is the category of spectra. We define these bundles in terms of modules over a stack of parametrized spectra and in terms of diagrams o…
Functor decomposes Khovanov spectra for non-alternating diagrams.
problem Computing Khovanov spectra for diagrams without alternating pairs.
method Functor from cube to Burnside 2-category, decomposition into simplicial complexes.
result Homotopy type of almost-extreme Khovanov spectra computed.
Covering spectra match if the covering is amenable, with conditions on curvature.
problem Matching spectra of Riemannian coverings under amenability conditions.
method Analyzing spectra of Riemannian manifolds and their coverings under completeness and curvature constraints.
result Spectra match if the covering is amenable, with conditions on curvature.
The paper studies knot densities under various constraints and degenerations.
problem Understanding knot densities under different constraints and their degenerations.
method Introduces and analyzes unconstrained and ropelength-windowed p-densities of knot types. result The degenerations in the unconstrained theory and the introduction of ropelength-windowed densities.
CRBM extracts speech features from complex spectra directly.
problem Speech coding ignores phase information in complex spectra.
method CRBM learns relationships between visible and hidden units from complex-valued spectra.
result CRBM outperforms conventional methods in speech coding.
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.
Novel construction of Bauer--Furuta invariant using sheaves of spectra.
problem Constructing the Bauer--Furuta invariant without finite-dimensional approximations.
method Using sheaves of spectra and Borel--Moore homology, avoiding approximations.
result Defines the shriek functors and Thom spectra for index calculations.
Study on sine-cones' spectra and stability under Ricci-de Turck flow.
problem Analyzing stability and rigidity of sine-cones.
method Computed spectra of specific operators on sine-cones.
result Conditions for sine-cones' dynamic stability and rigidity.
We prove explicit upper and lower bounds for the L1-moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds Pm in ambient Riemannian spaces Nn. We assume that P and N both have controlled radial curvatures (mean curvature and sectional curvature, respectively) as view…
The paper describes correlations of spectra for higher rank Anosov representations.
problem Understanding correlations of spectra for Anosov representations of higher rank groups.
method Relates correlation problem to counting projections in truncated hypertubes.
result Extends previous work on rank one representations to higher rank.
Formulas for spectra of higher spin operators on sphere subbundles.
problem Finding spectra of higher spin operators on specific subbundles of spinor-valued tensors.
method Explicit formulas derived for spectra in both even and odd dimensions.
result Spectra formulas for higher spin operators and their squares.
Study bottom of spectra on orbifolds via coverings.
problem Behavior of bottom of spectra under orbifold coverings.
method Analysis of scalar Schrödinger operators on orbifolds.
result Results apply to geometrically finite and conformally compact orbifolds.
Integrally splits L-spectra of integers into simpler components.
problem Understanding the homotopy type of L-spectra of integers.
method Using Anderson duality and splitting into simpler spectra.
result Splits L-spectra of integers into simpler components.
We view strict ring spectra as generalized rings. The study of their algebraic K-theory is motivated by its applications to the automorphism groups of compact manifolds. Partial calculations of algebraic K-theory for the sphere spectrum are available at regular primes, but we seek more conceptual answers in terms of lo…
Splits a spectrum related to Madsen-Tillmann spectra at prime 2.
problem Homotopy equivalence and splitting of Madsen-Tillmann spectra.
method Uses Steinberg idempotents and Whitehead conjecture.
result Splits MTO(n) off BO(n)+ at prime 2.