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.
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.
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.
The paper extends the Manhattan curve concept to complex dynamics and studies its relation to multiplier spectra.
problem Understanding the growth rate of lengths of closed geodesics in complex dynamics.
method Defining and studying the Manhattan curve for holomorphic endomorphisms of CPk and relating it to multiplier spectra. result The Manhattan curve for two holomorphic endomorphisms is related to the correlation number of their multiplier spectra.
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…
We study the length, weak length and complex length spectrum of closed geodesics of a compact flat Riemannian manifold, comparing length-isospectrality with isospectrality of the Laplacian acting on p-forms. Using integral roots of the Krawtchouk polynomials, we give many pairs of p-isospectral flat manifolds having di…
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…
Study of group actions on CAT(0) cube complexes, focusing on marked length spectra.
problem Comparing marked length spectra of group actions on CAT(0) cube complexes.
method Use of finite-state automata and thermodynamic formalism for suspension flows over subshifts of finite type.
result Prove that the Manhattan curve is analytic and convex, and a straight line if and only if marked length spectra are homothetic.
We define notions of higher order spectra of a complex quasi-projective manifold with an action of a finite group G and with a G-equivariant automorphism of finite order, some of their refinements and give Macdonald type equations for them.
A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors followed by (2) taking the absolute value of every entry…
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.
We give a simple geometric characterization of isospectral orbifolds covered by spheres, complex projective spaces and the quaternion projective line having cyclic fundamental group. The differential operators considered are Laplace-Beltrami operators twisted by characters of the corresponding fundamental group. To pro…
This paper studies torsion obstructions to complex sections on manifolds.
problem Torsion obstructions to finding complex sections on almost complex manifolds.
method Calculations using the Adams-Novikov spectral sequence for Thom spectra.
result Torsion obstructions for finding r complex sections of order p vanish for r<p2−p. Algorithms compute length spectra of torus graphs efficiently.
problem Computing length spectra of graphs embedded on a torus.
method Preprocessing and algorithms based on polyhedral norms.
result Efficient computation of length spectra and spectrum comparison.
Deep neural networks correct Mie scattering in FTIR spectra of biological samples.
problem Mie scattering obscures biochemically relevant spectral information in FTIR spectra of biological samples.
method Deep neural networks to approximate the preprocessing function that removes Mie scattering.
result The model is faster and more generalizable across different tissue types.
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.
Unified method to compute Laplace spectra on homogeneous principal bundles.
problem Computing the Laplace-Beltrami spectrum on homogeneous principal bundles.
method Unified representation-theoretic approach using generalized canonical variations and spectral branching criterion.
result Explicit formulas for the full spectra of several geometric families.
spectra2pix generates nanostructure images from spectra using DNN.
problem Designing nanostructures is complex and relies on intuition.
method Trained a DNN to infer nanostructure images from spectra.
result spectra2pix successfully designs unseen nanostructures.
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.
Adaptive Bayesian model for covariate-dependent power spectra analysis.
problem Estimating complex relationships and interactions between covariates and power spectra.
method Bayesian sum of trees model with local power spectrum estimation and reversible-jump MCMC for tree modifications.
result The method can accurately recover both smooth and abrupt changes in power spectra across multiple covariates.
This work analyzes neural scaling laws using power-law data spectra and derives analytical expressions for generalization error.
problem Understanding how neural network performance scales with key factors like data size and model complexity.
method Statistical mechanics techniques applied to one-pass stochastic gradient descent in a student-teacher framework.
result Derivation of analytical expressions for generalization error under power-law data spectra and identification of conditions for power-law scaling.
Analyzes neural networks using spectral perspectives.
problem Understanding neural network initialization and training.
method Examines the Conjugate Kernel and Neural Tangent Kernel spectra.
result Lends insights into neural network initialization and training properties.
We compute the eigenvalues with multiplicities of the Lichnerowicz Laplacian acting on the space of complex symmetric covariant tensor fields on the complex projective space $P^n(\comp)$. The spaces of symmetric eigentensors are explicitly given.
Machine learning models simulate molecular spectra and reactions in solvents.
problem Accurate simulation of molecular spectra and reactions in solvent environments.
method Introduced FieldSchNet, a deep neural network for modeling molecular interactions with external fields.
result Demonstrated significant lowering of Claisen rearrangement reaction activation barrier using FieldSchNet.
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…
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.
We compute the bridge spectra of cables of 2-bridge knots. We also give some results about bridge spectra and distance of Montesinos knots.
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.
SPT predicts age and mass of red giants from spectra.
problem Challenges in age and mass estimation of red giants using traditional methods.
method SPT framework with Multi-head Hadamard Self-Attention and Mahalanobis distance-based loss function.
result Remarkable age and mass estimations with low errors and uncertainties.
Neural networks learn simpler features first, then more complex ones; Fourier analysis reveals this pattern.
problem Understanding the learning dynamics of neural networks, especially with natural image data.
method Fourier analysis of translation-invariant and power-law spectra to study feature learning.
result Simple neural networks first rely on amplitude information, then phase information, and power-law spectra can accelerate learning phase information.
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.
Generative model gradients enhance MS/MS peptide identification.
problem Improving peptide identification from MS/MS spectra.
method Leverage log-likelihood gradients of generative models in a kernel-based classifier.
result Fisher kernel outperforms other methods on MS/MS datasets.
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…
We construct homology theories with coefficients in L-spectra on the category of ball complexes and we define products in this setting. We also obtain signatures of geometric situations in these homology groups and prove product formulae which we hope will clarify products used in the theory of the total surgery obstru…
Tomova, along with results of Bachman and Schleimer, showed that any high distance knot has a stair-step bridge spectrum. In this paper, we compute the bridge spectra and distance of generalized Montesinos knots. In particular, we produce the first example of a class of knots which attain the stair-step bridge spectra …
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.
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.
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.