Method constrains spectral gaps of hyperbolic spin surfaces using identities and semidefinite programming.
problem Bounding Laplacian and Dirac spectra of hyperbolic spin manifolds and orbifolds.
method Infinite family of spectral identities, semidefinite programming, and Selberg trace formula.
result Upper bounds on spectral gaps nearly saturated by specific orbifolds.
Defines spectral selectors on lens spaces for contactomorphisms.
problem Understanding the geometry of contactomorphism groups on lens spaces.
method Using Givental's non-linear Maslov index, defines spectral selectors.
result Standard Reeb flow is a geodesic for specific lens spaces.
Paper proves flat metrics on surfaces are uniquely determined by their lengths.
problem Proving uniqueness of flat metrics on surfaces based on closed curve lengths.
method Proves spectral rigidity of flat metrics on closed surfaces.
result Flat metrics on closed surfaces are uniquely determined by their lengths.
Develops a gradient estimator for implicit distributions using spectral methods.
problem Learning and inference with implicit distributions.
method Spectral decomposition of kernel operators and Nyström method for gradient estimation.
result Directly estimates the gradient function for implicit distributions.
The paper proves geometric and spectral alignment for deep neural networks.
problem Understanding the singular spectra of deep neural network layers.
method Proves deterministic quotient-geometric estimates for singular spectra of Frobenius-normalized layer factors.
result Exact power-law spectra form a trace-normalized Cartan orbit under Frobenius normalization.
Bounds on spectral gaps of hyperbolic 3-manifolds and orbifolds.
problem Constraining the spectra of Laplace operators on hyperbolic manifolds and orbifolds.
method Linear programming and spectral identities derived from the conformal bootstrap and Selberg trace formula.
result Upper bounds on the first and second Laplacian eigenvalues, and spectral gaps of hyperbolic 3-manifolds and orbifolds.
ARFF reduces spectral bias in SGD-trained neural networks.
problem Spectral bias in two-layer neural networks.
method Comparison of SGD and ARFF on spectral bias and robustness.
result ARFF yields a closer to zero spectral bias compared to SGD.
We construct a canonical noncommutative spectral triple for every oriented closed Riemannian manifold, which represents the fundamental class in the twisted K-homology of the manifold. This so-called "projective spectral triple" is Morita equivalent to the well-known commutative spin spectral triple provided that the m…
The paper extends McShane identities to higher Teichmüller theory and convex real projective surfaces.
problem Deriving McShane identities for higher Teichmüller theory.
method By studying mapping class group invariant functions and generalizing horocycle lengths.
result Established McShane-type identities for various surface group representations.
Study on spectral stability of an embedded annulus under curve shortening and Ricci flows.
problem Spectral stability of Dirichlet eigenvalues on an evolving annulus.
method Variational formulas, Rellich-type identities, and harmonic capacity methods.
result Established quantitative bounds comparing the spectrum of the evolving annulus with a flat cylinder.
The paper proves stability for a modified Bach flow on various manifolds.
problem Stability of gauge-modified Bach flow on manifolds.
method Linear stability proved via spectral bounds and Koiso identity generalization. Nonlinear stability for hyperbolic and Poincaré-Einstein spaces.
result Linear and nonlinear stability results for the Bach flow on specific manifolds.
We continue the study of the spectral theory associated to integrable metrics, started in our previous paper arXiv:1301.1793 [math.SP]. We introduce the notion of 1-integrable metric on line-bundles on a compact Riemann surface. We extend the spectral theory of generalized Laplacians to line-bundles equipped with 1-int…
This paper provides a full controlled version of algebraic K-theory. This includes a rich array of assembly maps; the controlled assembly isomorphism theorem identifying the controlled group with homology; and the stability theorem describing the behavior of the inverse limit as the control parameter goes to 0. There…
Improved covariance matrix estimation for portfolio optimization with guaranteed PSD and controlled conditioning.
problem Guaranteeing positive semidefinite ness and controlling spectral conditioning in IQ estimators.
method Introducing squeezing identity and atomic-IQ parameterization to construct structured channel matrices with PSD guarantees and analytic eigen floor for conditioning control.
result Atomic-IQ improves Sharpe ratios and delivers a more stable risk profile compared to standard estimators.
New gauge preserves Einstein metrics' interactions, proving rigidity on negatively curved manifolds.
problem Stability and deformation theory of Einstein metrics.
method Introduces Chen-Nagano gauge condition, linking Lichnerowicz Laplacian to shifted scalar operator.
result Chen-Nagano gauge collapses to classical transverse-traceless gauge under spectral pinching assumptions.
New kernel models multi-output Gaussian processes accurately.
problem Challenges in modelling cross-covariances for multiple-output Gaussian processes.
method Replaced Gaussian components with block components of finite bandwidth in spectral mixture kernel.
result First multi-output generalization of spectral mixture kernel that can approximate any stationary multi-output kernel to arbitrary precision.
The main goal in this paper is to point out that quantity ∣∣∇R∣∣2(p) on a harmonic space can not be determined by the spectra of local geodesic spheres or balls, therefore the main results of [AM-S] (quoted in the title) are wrong. My strong interest in the above theorem is motivated by the fact that it contra…
Spectral clustering is a technique that clusters elements using the top few eigenvectors of their (possibly normalized) similarity matrix. The quality of spectral clustering is closely tied to the convergence properties of these principal eigenvectors. This rate of convergence has been shown to be identical for both th…
Ridge regression linked to Poisson resetting in statistical physics.
problem Understanding and extending ridge regularization in machine learning.
method Connecting stochastic resetting from statistical physics with ridge regularization in machine learning, using renewal processes.
result Exact filter identities for ridge regularization in various reset laws, including exponential and non-exponential.
Spectral filters enhance option pricing methods using Hilbert transforms.
problem Improving convergence rates of option pricing methods.
method Using spectral filters to improve convergence of numerical schemes based on discrete Hilbert transforms.
result Improved convergence rates, especially polynomial convergence, achieved with spectral filtering.
The paper calculates spectral determinants for two complex surfaces.
problem Calculating spectral determinants for complex surfaces.
method Closed explicit formulas, multiplicative relations, Belyi maps, and constant-curvature spheres.
result Spectral determinants of the Bolza surface and Klein quartic are calculated.
This paper analyzes optimal stopping regions for American options with Poisson exercise opportunities.
problem Analyzing the optimal stopping regions for American options with Poisson exercise opportunities.
method Computing identities related to the first Poisson arrival time to an interval and applying them to the computation of the optimal strategies.
result Explicit expressions of the stopping and continuation regions and the value function are obtained.
Researchers find spectral gaps in quantum flag manifolds using twisted operators.
problem Finding spectral gaps in quantum flag manifolds.
method Tensoring Laplace and Dolbeault-Dirac operators with negative Hermitian holomorphic modules.
result Twisting Dirac and Laplace operators by negative line bundles produces a spectral gap for q close to 1.
Let M be an exact symplectic manifold equal to a symplectization near infinity and having stably trivializable tangent bundle, and φ be an exact symplectomorphism of M which, near infinity, is equal to either the identity or the symplectization of a contactomorphism φ^ such that neither φ^ nor φ^2…
New algorithm tests Markov chains without hitting.
problem Testing Markov chains with unknown transition matrix.
method Combining approximation algorithms and spectral analysis.
result Efficient testing of Markov chains without hitting time dependence.
Study on real projective spaces with odd dimensions, focusing on loop homology and geodesics.
problem Investigate the topological structure of non-contractible loop spaces on real projective spaces with odd dimensions.
method Use Chas-Sullivan theory on loop homology and Leray-Serre spectral sequence.
result Derive the resonance identity of non-contractible prime closed geodesics.
Study on spectral clustering phase transitions in noisy networks.
problem Detecting communities in noisy networks.
method Proved phase transitions using Erdos-Renyi random noise model.
result Critical external edge connection probability for community detectability.
Introduces a new spectral geometry framework with dissipative data.
problem Deforming spectral triples with dissipative Lindblad operators.
method Lindblad-deformed spectral geometry framework with heat-kernel asymptotics.
result First nontrivial dissipative effect appears at order gamma^4.
Augments GNNs with diversification to preserve node identity.
problem Current GNNs filter node information, potentially losing node identity.
method Integrates diversification operators with aggregation to enrich node representations.
result Significant performance boost on 9 node classification tasks.
New method deforms function algebras on manifolds using spectral decomposition.
problem Deforming function algebras on compact Riemannian manifolds.
method Introducing a bilinear product on the finite spectral core of smooth functions using unimodular phases.
result The product extends to a Sobolev algebra and admits iteration under certain conditions.
A new method simulates a lazy version of a Markov chain for empirical inference.
problem Estimating and testing unknown Markov chains with limited data.
method Simulates an α-lazy version of an unknown Markov chain, making it ergodic.
result The pseudo spectral gap can be applied to non-ergodic Markov chains.
We determine the structure of conformal powers of the Dirac operator on Einstein {\it Spin}-manifolds in terms of the product formula for shifted Dirac operators. The result is based on the techniques of higher variations for the Dirac operator on Einstein manifolds and spectral analysis of the Dirac operator on the as…
Paper compresses SM kernels with time-phase modulated dependency structures for better GP performance.
problem Improving the expressiveness and generalization of Gaussian processes with complex patterns.
method Introducing time-phase modulated dependency structures and a novel structure adaptation algorithm to compress SM kernels.
result The proposed SMD kernel shows improved performance on both synthetic and real-life applications.
Higher homotopy generalizations of Lie-Rinehart algebras, Gerstenhaber-, and Batalin-Vilkovisky algebras are explored. These are defined in terms of various antisymmetric bilinear operations satisfying weakened versions of the Jacobi identity, as well as in terms of operations involving more than two variables of the L…
We consider an elliptic self-adjoint first order pseudodifferential operator acting on columns of m complex-valued half-densities over a connected compact n-dimensional manifold without boundary. The eigenvalues of the principal symbol are assumed to be simple but no assumptions are made on their sign, so the operator …
This paper optimizes periodic dividend strategies for Lévy processes with transaction costs.
problem Maximizing dividends for spectrally negative Lévy processes with fixed transaction costs.
method Using periodic strategies and fixed transaction costs, the paper calculates the value function and shows optimality conditions.
result A sufficient condition for optimality is that the Lévy measure is completely monotonic.
We consider an elliptic self-adjoint first order differential operator acting on pairs (2-columns) of complex-valued half-densities over a connected compact 3-dimensional manifold without boundary. The principal symbol of our operator is assumed to be trace-free. We study the spectral function which is the sum of squar…
The optimal capital structure model with endogenous bankruptcy was first studied by Leland (1994) and Leland and Toft (1996), and was later extended to the spectrally negative Levy model by Hilberink and Rogers (2002) and Kyprianou and Surya (2007). This paper incorporates the scale effects by allowing the values of ba…
This paper tackles multilayer graph clustering via convex layer aggregation.
problem Challenges in clustering multilayer graphs and combining information from each layer.
method Theoretical framework for multilayer spectral graph clustering via convex layer aggregation.
result Establishes a critical value on the noise level for reliable cluster separation.
We develop the Ercolani-Sinha construction of SU(2) monopoles and make this effective for (a five parameter family of centred) charge 3 monopoles. In particular we show how to solve the transcendental constraints arising on the spectral curve. For a class of symmetric curves the transcendental constraints become a numb…
Optimizes hybrid dividend strategies in dual models with periodic and continuous payments.
problem Determining the best dividend strategy in a dual model with periodic and continuous payments.
method Generalizes results from a Brownian model to a dual (spectrally positive Lévy) model, using the scale function.
result The optimal strategy is of the hybrid-barrier type and can be expressed using the scale function.
The paper improves L2-estimates for Dirac-Dolbeault operators on complex manifolds.
problem Improving L2-estimates for Dirac-Dolbeault operators on complex manifolds. method Generalized classical method to handle mixed curvature cases and provided bounds on error terms.
result Full asymptotic expansion for Bergman kernel obtained.
Optimal dividend strategy found for risk models with regime switching.
problem Optimal dividend strategy for spectrally negative Markov additive models with regime switching.
method Introduced an auxiliary problem and transformed the original problem into a local optimization problem.
result The refraction-reflection strategy with regime-modulated thresholds is optimal.
A new method detects hidden driving forces in systems with multiple observables.
problem Hidden driving forces in systems with multiple observables cannot be detected by scalar statistics.
method Cross-spectral witness for hidden nonequilibrium.
result Two simultaneously observed channels retain an off-diagonal cross-spectral sector inaccessible to scalar reductions.
Transformer models show distinct spectral fingerprints under voice changes.
problem Detecting architectural biases in transformer models.
method Spectral analysis of attention-induced token graphs.
result Clear architectural signatures in model fingerprints correlate with language-specific behavior.
New method trains neural networks in spectral domain for improved performance.
problem Training deep neural networks in the space of nodes.
method Trains neural networks in the spectral domain, modifying eigenvalues and eigenvectors of transfer operators.
result Superior performance compared to standard methods, especially when adjusting eigenvalues.
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…
In this paper we study a spectrally negative Lévy process which is refracted at its running maximum and at the same time reflected from below at a certain level. Such a process can for instance be used to model an insurance surplus process subject to tax payments according to a loss-carry-forward scheme together with t…