Quantum vacuum energy (Casimir energy) is reviewed for a mathematical audience as a topic in spectral theory. Then some one-dimensional systems are solved exactly, in terms of closed classical paths and periodic orbits. The relations among local spectral densities, energy densities, global eigenvalue densities, and tot…
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48 results for “Spectral energy distribution”
Many spectral unmixing methods rely on the non-negative decomposition of spectral data onto a dictionary of spectral templates. In particular, state-of-the-art music transcription systems decompose the spectrogram of the input signal onto a dictionary of representative note spectra. The typical measures of fit used to …
New method estimates Nishimori temperature for node classification in weighted graphs.
problem Estimating Nishimori temperature for Bayesian inference.
method Spectral method using eigenvalues of Bethe Hessian matrix.
result Spectral method outperforms existing approaches in node classification.
New method improves speech synthesis quality.
problem Efficiently train parallel speech synthesis models.
method Spectral energy distance for implicit generative models.
result State-of-the-art generation quality achieved.
The paper proves optimal estimates and inequalities for spectral functions on certain manifolds.
problem Optimal estimates and inequalities for spectral functions on weakly 1-complete manifolds.
method Establishes optimal fundamental estimates and weak Morse inequalities for lower energy forms.
result Optimal fundamental estimates and weak Morse inequalities are proven for lower energy forms on weakly 1-complete manifolds.
Study small perturbations on low energy Laplace eigenfunctions.
problem Understanding small changes in low energy Laplace eigenfunctions.
method Investigates nodal geometry and topology, focusing on low frequency regimes and small perturbations.
result Highlight interesting aspects of spectral theory and nodal phenomena tied to ground state/low energy eigenfunctions.
D-LinOSS models learn to dissipate energy, improving performance on long-range tasks.
problem Representational limitations of LinOSS models in long-range reasoning.
method Introducing Damped Linear Oscillatory State-Space models (D-LinOSS) that learn to dissipate latent state energy on arbitrary time scales.
result D-LinOSS consistently outperforms previous LinOSS methods on long-range learning tasks, achieving faster convergence and reducing hyperparameter search space.
Graph Laplacians adapt to different manifold dimensions, while Dirichlet energies converge to a tensorized Dirichlet energy.
problem Understanding machine learning methods for data with varying intrinsic dimensions.
method Γ-convergence of graph Dirichlet energies and spectral convergence of graph Laplacians on intersecting manifolds of varying dimensions.
result Normalized Dirichlet energy converges to a tensorized Dirichlet energy that adapts to all dimensions simultaneously.
Spectral estimation (SE) aims to identify how the energy of a signal (e.g., a time series) is distributed across different frequencies. This can become particularly challenging when only partial and noisy observations of the signal are available, where current methods fail to handle uncertainty appropriately. In this c…
Study smooth linear statistics on random covers of hyperbolic surfaces, showing central limit and variance results.
problem Analyzing fluctuations and energy variance of random covers of compact hyperbolic surfaces.
method Examining fluctuations in a small energy window around a fixed energy level, considering the variance of a typical surface, using a double limit where and go to infinity.
result Distribution of fluctuations tends to a Gaussian with variance of GOE/GUE, and energy variance of a typical random -cover is that of GOE/GUE.
Study identifies cancer genes through graph anomaly analysis of protein interactions.
problem Insufficient modeling of biological information in protein interaction networks for cancer gene identification.
method Proposes HIerarchical-Perspective Graph Neural Network (HIPGNN) to detect weight heterogeneity and spectral flattening in cancer gene nodes.
result HIPGNN detects weight heterogeneity and spectral flattening, leading to improved cancer gene identification.
Under a spectral assumption on the Laplacian of a Poincaré--Einstein manifold, we establish an energy inequality relating the energy of a fractional GJMS operator of order or and the energy of the weighted conformal Laplacian or weighted Paneitz operator, respectively. This spectral assumption…
Study cryptocurrency price dynamics using adaptive EMD and spectral analysis.
problem Analyze the time-varying volatility of cryptocurrency prices.
method Adaptive complementary ensemble empirical mode decomposition (ACE-EMD) and Hilbert spectral analysis.
result Reveal the properties of various timescales in cryptocurrency price dynamics.
FAST selects coresets more efficiently by matching distributions in the frequency domain.
problem Efficiently selecting representative subsets of large datasets for deep learning.
method FAST uses spectral graph theory and CFD to match distributions, addressing limitations of existing methods.
result FAST significantly outperforms state-of-the-art coreset selection methods in accuracy and energy efficiency.
EGO-MDA identifies optimal spectral-bands for process discrimination.
problem Optimal spectral-bands for process discrimination.
method EGO-MDA, an unsupervised method using EGO and Mixture Discriminant Analysis.
result EGO-MDA achieves at least 70% improvement in median deviance.
Graph signal processing detects hallucinations in large language models.
problem Detecting factual reasoning from hallucinations in large language models.
method Modeling transformer layers as dynamic graphs, using spectral analysis to define diagnostics.
result Spectral signatures can distinguish different types of hallucinations and achieve high accuracy.
Graph classification improved using spectral features and wavelet filters.
problem Categorizing graphs based on their structure and node attributes.
method Derived spectral features from graph signal processing, designed two Gaussian process models: one simple and one sophisticated.
result Simple and sophisticated Gaussian process models yield competitive performance, including well-calibrated uncertainty estimates.
JNR Monopolesmath.DG
We review the theory of JNR, mass 1/2 hyperbolic monopoles in particular their spectral curves and rational maps. These are used to establish conditions for a spectral curve to be the spectral curve of a JNR monopole and to show that that rational map of a JNR monopole monopole arises by scattering using results of Ati…
We formulate a noncommutative generalization of the Ricci flow theory in the framework of spectral action approach to noncommutative geometry. Grisha Perelman's functionals are generated as commutative versions of certain spectral functionals defined by nonholonomic Dirac operators and corresponding spectral triples. W…
Novel framework for learning infinitesimal generator of stochastic processes.
problem Challenges in learning infinitesimal generator due to unbounded nature and state space dimensionality.
method Introduces a novel framework based on energy functional, integrates physical priors, and uses reduced-rank estimator in RKHS.
result Learning bounds independent of state space dimension and non-spurious spectral estimation.
Generalized Dirichlet Energy and Graph Laplacians for Clustering Directed and Undirected Graphsstat.ML
New method clusters directed and undirected graphs without losing directional information.
problem Clustering directed graphs due to asymmetry in edge connectivity.
method Generalized Dirichlet Energy (GDE) and generalized spectral clustering (GSC).
result GSC outperforms existing methods in clustering accuracy and robustness.
New method speeds up galaxy analysis from hours to seconds.
problem Infeasibility of state-of-the-art SED analyses for large surveys.
method Amortized Neural Posterior Estimation (ANPE) for scalable Bayesian inference.
result Posterior distributions of 12 model parameters estimated in seconds per galaxy.
We describe two-dimensional potential Schrodinger and Dirac operators which are finite-gap at one energy level and have singular spectral curves. It appears that the singularities can be rather complicated. Such Dirac operators appear as the spectral curves of tori immersed into the three-space.
Study low energy resolvent behavior on fibred boundary metrics.
problem Analyze the resolvent of Hodge Laplacian on manifolds with fibred boundary metrics.
method Develop a 'split' pseudodifferential calculus to handle different asymptotic behaviors.
result Precise asymptotic behavior of resolvent as a fibred boundary pseudodifferential operator.
A conformal immersion of a 2-torus into the 4-sphere is characterized by an auxiliary Riemann surface, its spectral curve. This complex curve encodes the monodromies of a certain Dirac type operator on a quaternionic line bundle associated to the immersion. The paper provides a detailed description of the geometry and …
Proves positive mass theorem for hyperbolic manifolds with ends.
problem Establishing positive mass theorem for complex initial data sets.
method Used spectral PSC, Jang equation, and quantitative shielding theorem.
result Proved positive mass theorem for asymptotically hyperbolic manifolds.
Unified framework explains why overfitting is benign in interpolating learning.
problem Understanding why overfitting is benign in highly overparameterized models.
method Spectral-transport stability framework.
result Sharp benign-overfitting criterion and explicit phase-transition rates.
Detects corruption in agentic models during execution.
problem Inconsistent context, retrieval errors, or adversarial inputs corrupt intermediate steps of reasoning chains.
method Analyzes token graphs induced by attention and computes spectral statistics to emit accept/reject signals.
result A single threshold on the high frequency energy ratio optimally detects context inconsistency in agentic models.
S-GAI initializes MLPs using spectral geometry from data, improving performance.
problem Lack of guidance on initial weights encoding data geometry.
method S-GAI uses SVD to estimate spectral class geometry, initializing MLPs from training data.
result S-GAI-initialized MLPs start from a more informative hidden state and achieve comparable accuracy.
The paper studies spectral analysis on complex spaces and finds explicit formulas for eigensections.
problem Understanding eigensections on complex projective spaces and Grassmannians.
method Using creation and annihilation operators, converting higher energy eigensections to lower energy holomorphic sections.
result Explicit formulas for the dimension of higher-level eigensections on .
New method compresses non-Gaussian distributions exponentially.
problem Efficiently representing and computing non-Gaussian probability distributions.
method Tensor-Network Fourier Methods using QTT representation.
result Exponential compression of non-Gaussian distributions.
In this paper we study equivariant constrained Willmore tori in the 3-sphere. These tori admit a 1-parameter group of Möbius symmetries and are critical points of the Willmore energy under conformal variations. We show that the associated spectral curve of an equivariant torus is given by a double covering of $\mathbb …
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.
This article determines the spectral data, in the integrable systems sense, for all weakly conformally immersed Hamiltonian stationary Lagrangian in . This enables us to describe their moduli space and the locus of branch points of such an immersion. This is also an informative example in integrable systems geome…
SPECTRA improves probabilistic energy forecasting by separating trends and uncertainties.
problem Interacting uncertainties from renewable intermittency, demand flexibility, market volatility, and weather impact probabilistic forecasts.
method Adaptive state-space exogenous context and temporal-frequency resolution architecture.
result Achieved best CRPS in 14 out of 18 settings, reducing CRPS by 5.74% and upper-tail quantile risk by 7.27%.
We present a novel spectral embedding of graphs that incorporates weights assigned to the nodes, quantifying their relative importance. This spectral embedding is based on the first eigenvectors of some properly normalized version of the Laplacian. We prove that these eigenvectors correspond to the configurations of lo…
EBM model for functional data using path measure tilting.
problem Modeling distributions of functions from irregularly sampled data.
method Spectral decomposition of an energy-based model with a Gaussian Process path measure to reweight the distribution.
result Effective approach to up-scaling functional data.
Estimates for Schrödinger operators on manifolds with bounded Ricci curvature.
problem Quantifying unique continuation for Schrödinger operators on manifolds with specific curvature conditions.
method Proving quantitative unique continuation estimates for Schrödinger operators on manifolds with Ricci curvature bounded below.
result Upper bound for energy range and constant in terms of Ricci curvature and parameters of relatively dense set.
Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions-e.g., based on wavelets and Slepians-that can be applied to filter signals defined on the g…
Study spectral invariants over integers, discovering unboundedness and field-dependence.
problem Dependence of spectral invariants on integer coefficients.
method Floer homology theory, focusing on Hamiltonian Floer homology.
result Spectral norm is unbounded over integers for complex projective spaces.
Introduce Collapsed Effective Operators for higher-order structures.
problem Existing spectral operators decompose topology into separate ranks, leaving practitioners to fuse information back to vertices.
method Introduce Collapsed Effective Operators via Schur complementation of a graded Laplacian.
result Preserves positive semi-definiteness, lowers system energy under higher-order connectivity.
Classifies charge-3 monopoles with symmetry, identifying new spectral curves.
problem Classifying charge-3 monopoles with symmetry.
method Constructing Nahm data and identifying spectral curves with elliptic quotients.
result New monopole spectral curves with and symmetry identified.
Proves the index of a Möbius band in 4D ball equals 5.
problem Determining the Morse index of critical non-orientable surfaces.
method Comparison theorem between Steklov spectral index and energy index.
result Proves the index of critical Möbius band in equals 5.
We consider a class of time dependent finite energy multi-soliton solutions of the U(N) integrable chiral model in dimensions. The corresponding extended solutions of the associated linear problem have a pole with arbitrary multiplicity in the complex plane of the spectral parameter. Restrictions of these exten…
This paper bridges Kahler geometry and quantum mechanics in lognormal statistical models.
problem Evolution of spectral curves in Siegel Jacobi space through Schrodinger equation.
method Kahler geometry induced on lognormal statistical manifold, Dombrowski's construction.
result Time-dependent Schrodinger equation with varying energy.
Spectral flow connects manifold geometry to rigidity criteria.
problem Tackling rigidity of simply-connected closed manifolds.
method Spectral deformation flow and invariant-based approach.
result Spherical profile is the unique manifold-compatible asymptotic realization.
Energy statistics was proposed by Sz\' ekely in the 80's inspired by Newton's gravitational potential in classical mechanics and it provides a model-free hypothesis test for equality of distributions. In its original form, energy statistics was formulated in Euclidean spaces. More recently, it was generalized to metric…
We consider the energy-critical half-wave maps equation for . We give a complete classification of all traveling solitary waves with finite energy. The proof is based on a geometric characterizat…