Connects 4-manifold topology to topological modular forms.
problem Understanding the topology of 4-manifolds.
method Topologically twisted compactification of 6d (1,0) theories on 4-manifolds.
result New invariant of 4-manifolds using equivariant weakly holomorphic modular forms.
New mathematical proposal for TQFTs using TMF-modules.
problem Constructing new types of TQFTs at the intersection of topology, algebra, physics, and homotopy theory.
method Defines TMF-modules associated with symmetric bilinear forms and assigns them to closed 3-manifolds and maps of TMF-modules to 4-dimensional cobordisms.
result Invariants of 4-manifolds arising from 6-dimensional superconformal field theories, conjecturally generalizing the theta function of a lattice.
Study TMF-valued TQFT for closed 3-manifolds using torsion linking pairings.
problem Explicit description of TMF-module state space for closed 3-manifolds.
method Construct canonical invariants and tokenization from torsion linking pairings.
result Explicit model for TMF-module state space in terms of rank-one TMF-module.
This work extends score-based methods to binary data on the Boolean hypercube.
problem Learning and sampling binary data on the Boolean hypercube.
method Adopting Bernoulli noise as a smoothing device, deriving a TMF-like expression for the optimal denoiser, and using a Langevin-like sampler.
result The method successfully samples noisy binary data and reduces effective noise through multiple measurements.
New methods improve recommendation accuracy for users and items with few ratings.
problem Skewed distribution and low ratings affect recommendation accuracy.
method Four matrix completion-based approaches: FARP, TMF, TMF + Dropout, IFWMF.
result Improved prediction accuracy for users and items with few ratings.
Using basic homotopy constructions, we show that isomorphism classes of string structures on spin bundles are naturally given by certain degree 3 cohomology classes, which we call string classes, on the total space of the bundle. Using a Hodge isomorphism, we then show that the harmonic representative of a string class…
The abstract discusses fiber sum formulas for 4-manifolds using topological modular forms.
problem Understanding fiber sum formulas for 4-manifolds.
method Using the connection between 4-manifolds and topological modular forms from 6d (1,0) SCFTs.
result Even free theories exhibit nontrivial fiber sum formulas, sensitive to individual theories and parameters.
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.
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.
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.
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…
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.
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.
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…
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.
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.
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.
This paper describes a novel energy-based probabilistic distribution that represents complex-valued data and explains how to apply it to direct feature extraction from complex-valued spectra. The proposed model, the complex-valued restricted Boltzmann machine (CRBM), is designed to deal with complex-valued visible unit…
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…
Length spectra for Riemannian metrics are well studied, while sub-Riemannian length spectra have been largely unexplored. Here we give the length spectrum for a canonical sub-Riemannian structure attached to any compact Lie group by restricting its Killing form to the sum of the root spaces. Surprisingly, the shortest …
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…
We introduce a new quasi-isometry invariant, called the divergence spectrum, to study finitely generated groups. We compare the concept of divergence spectrum with the other classical notions of divergence and we examine the divergence spectra of relatively hyperbolic groups. We show the existence of an infinite collec…
Bayesian framework integrates spectral deconvolution with expert reasoning for robust peak estimation.
problem Challenges in extracting meaningful peaks from noisy or complex spectra.
method Bayesian spectral deconvolution coupled with a physical-property regression layer.
result Recovery of weak peaks in poly(lactic acid) IR spectra related to degradation rates.
For mass spectra acquired from cancer patients by MALDI or SELDI techniques, automated discrimination between cancer types or stages has often been implemented by machine learnings. These techniques typically generate "black-box" classifiers, which are difficult to interpret biologically. We develop new and efficient s…
Spaces with similar long paths have similar shapes.
problem Comparing shapes of Gromov hyperbolic spaces.
method Examining asymptotic marked length spectra.
result Spaces with identical spectra are roughly isometric.
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.
Researchers describe a new method to compute Seiberg-Witten-Floer spectra for a specific class of manifolds.
problem Computing Seiberg-Witten-Floer spectra for a specific class of manifolds.
method Using lattice homology, they provide an explicit combinatorial description of the spectra.
result They calculate Manolescu's κ-invariant for certain connected sums of the spaces.
Spectral measurements reveal hidden representation geometry in language model training.
problem Hidden internal representation in language model training is hard to examine.
method Empirical protocol using activation covariance and per-sample gradient SVD spectra.
result Batch size affects representation geometry, and activation spectra predict token efficiency.