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.
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.
Formula for spectrum linking braid and bridge indices.
problem Understanding the relationship between braid and bridge indices.
method Foliation theory applied to booklink embeddings.
result Formula for link spectra of braid and bridge indices.
We compute the genus zero bridge numbers and give lower bounds on the genus one bridge numbers for a large class of sufficiently generic hyperbolic twisted torus knots. As a result, the bridge spectra of these knots have two gaps which can be chosen to be arbitrarily large, providing the first known examples of hyperbo…
We determine the set of all genus g bridge numbers of many iterated torus knots, listing these numbers in a sequence called the bridge spectrum. In addition, we prove a structural lemma about the decomposition of a strongly irreducible bridge surface induced by cutting along a collection of essential surfaces.
Cycle-StarNet bridges theory and data by adapting synthetic spectra to observational data.
problem Lack of consistency between theoretical stellar models and observational data.
method Hybrid generative domain adaptation using unsupervised learning on large spectroscopic surveys.
result Improved spectral fitting and reduced gap between synthetic and observational data.
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.
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.
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.
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.
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.
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.
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.
Unified view of spectral networks linking geometry and gauge theory.
problem Understanding BPS states in gauge theories.
method Unified geometric and physical approaches, focusing on spectral networks.
result Spectral networks provide a framework for determining BPS spectra.
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.
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. Study sub-Riemannian metrics on compact Lie groups, finding same shortest loops.
problem Exploring sub-Riemannian length spectra on compact Lie groups.
method Restricting Killing form to root spaces of compact Lie groups.
result Same shortest loops in Riemannian and sub-Riemannian cases.
Wavelet scattering spectra model non-Gaussian time-series, proving scale invariance for self-similar processes.
problem Modeling non-Gaussian time-series with stationary increments.
method Complex wavelet transform for scale variations, joint correlation matrix for scale dependencies, second wavelet transform for diagonalization, maximum entropy models conditioned by scattering spectra coefficients.
result Scattering spectra of self-similar processes are scale invariant, allowing statistical testing and generation of new time-series.
Constructs Khovanov spectra for periodic links, proving rank inequalities.
problem Understanding Khovanov homology for periodic links.
method Equivariant Khovanov spectra using Burnside functor construction.
result Rank inequalities for Khovanov homologies and annular filtrations of prime-periodic links.
New method to study group invariants using divergence spectra.
problem Understanding group invariants through divergence.
method Introducing divergence spectrum to compare classical notions and study relatively hyperbolic groups.
result Existence of groups with exponential divergence but different divergence spectra.
Manifold methods improve amino acid classification in LIBS spectra.
problem Improving classification accuracy of amino acids in LIBS spectra.
method Developed an information theoretic method for measuring LIBS energy spectra, implemented manifold methods for nonlinear dimensionality reduction.
result Nonlinear methods lead to increased classification accuracy in amino acid classification.
Study eigenvalues of orbifolds and manifolds, proving spectra convergence.
problem Comparing spectra of orbifolds and their boundaries.
method Generalized Hodge decomposition, collapsing connected sums, perturbation of metrics.
result Eigenvalues of orbifold spectra converge to those of manifolds.
Neural network predicts electron-ionization mass spectra quickly.
problem Identifying unknown molecules not in existing libraries.
method Lightweight neural network model for predicting mass spectra.
result High accuracy predictions of small molecule mass spectra.
Spectral bottoms match for Riemannian manifolds with amenable actions.
problem Matching spectral bottoms of manifolds under amenable actions.
method Analyzing Riemannian coverings and amenability of actions.
result Bottoms of spectra match for complete Riemannian manifolds with amenable actions.
Study shows how the spectra of negatively curved surfaces vary under certain conditions.
problem Understanding how the Laplace spectra of compact surfaces vary under specific conditions.
method Used time real analyticity of Ricci flow to extend a result from \cite{B} and provide a quantitative estimate of spectral variation.
result Laplace spectra of negatively curved compact surfaces with same genus, area, and curvature bounds vary in a controlled way.
We take prior-to-crash market prices (NASDAQ, Dow Jones Industrial Average) as a signal, a function of time, we project these discrete values onto a vertical axis, thus obtaining a Cantordust. We study said cantordust with the tools of multifractal analysis, obtaining spectra by definition and by lagrangian coordinates…
We prove an analogue of Farb-Masur's theorem that the length-spectra metric on moduli space is "almost isometric" to a simple model V(S) which is induced by the cone metric over the complex of curves. As an application, we know that the Teichmüller metric and the length-spectra metric are "almost isometric…
Characterizes isospectral orbifolds with cyclic groups.
problem Identifying orbifolds with cyclic groups that have the same spectrum.
method Geometric characterization and spectral analysis using Laplace-Beltrami operators.
result Explicit description and examples of isospectral orbifolds.
The paper shows that arithmetic hyperbolic 3-orbifolds have many non-commensurable pairs with similar geodesic spectra.
problem Understanding the relationship between geodesic length spectra and commensurability of arithmetic hyperbolic 3-orbifolds.
method Using a bounded gaps result for prime ideals in number fields, the paper constructs infinitely many non-commensurable pairs of arithmetic hyperbolic 3-orbifolds with similar geodesic spectra.
result Arithmetic hyperbolic 3-orbifolds can have many non-commensurable pairs with similar geodesic spectra.
In this article we use the "escape from subvarieties lemma" introduced by Eskin--Mozes--Oh to prove finite step rigidity results for the Jordan-Lyapunov projection spectra of Hitchin representations and the Margulis-Smilga invariant spectra of some special Margulis-Smilga spacetimes. In the process, we also prove a sim…