Proposes a multi-stage algorithm for efficient spectrum access in CR networks.
problem High demand for wireless spectrum and need for high throughput and energy efficiency in SUs.
method Centralized multi-stage algorithm with non-parametric learning and adaptive collision avoidance.
result Ensures minimum interference to licensed users while providing high throughput and energy efficiency.
Spectrum selectively trains LLMs based on SNR to save resources.
problem Efficiently training large language models with limited resources.
method Targeting layer modules based on SNR for selective training.
result Spectrum achieves similar performance to full fine-tuning but with reduced VRAM usage.
A machine learning approach for efficient spectrum sharing in distributed DSA networks.
problem Effective spectrum sharing among secondary users (SUs) and primary users (PUs) in a distributed network.
method Deep reinforcement learning (DRL) combined with reservoir computing (RC) for distributed spectrum access decisions.
result The RC-based spectrum access strategy significantly reduces collision chances and outperforms other methods.
CNN model for efficient wireless spectrum sensing and signal identification.
problem Efficient utilization of scarce wireless spectrum.
method Convolutional Neural Network (CNN) based on spectral correlation function.
result Significant performance gains over existing methods.
A robust method for decomposing spectral peaks robust to distortion and interference.
problem Decomposing spectral peaks in the presence of distortion and interference.
method Optimizing a nonparametric approach using pseudo-symmetric functions with nonincreasing behavior.
result Decomposed spectral peaks show pseudo-orthogonal behavior and power preserving equality.
Study deepnet Hessians, revealing spiked spectrum with SGD and sample size effects.
problem Understanding the spectrum of deepnet Hessians at scale.
method Applied modern numerical linear algebra tools to approximate Hessian spectrum of large deepnets.
result Deepnet Hessians exhibit spiked behavior with outliers isolated from a continuous bulk.
Proposes a new sparse spectrum method for Bayesian optimization.
problem Overconfidence in GP models for Bayesian optimization.
method Derives a new regularized marginal likelihood to balance predictive mean and variance.
result Significant improvement in Bayesian optimization convergence rate.
ARISE models efficient markets without periodogram or Gaussianity assumptions.
problem Mimicking and learning long-term memory in efficient markets.
method ARISE process using aperiodic spectrum estimation and infinite-sum function of known processes.
result ARISE process has mean-square convergence, consistency, and asymptotic normality without periodogram and Gaussianity assumptions.
New method prunes recurrent networks efficiently, improving performance.
problem Pruning recurrent neural networks (RNNs) is challenging and often leads to poor performance.
method Data-efficient pruning objective derived from the spectrum of the recurrent Jacobian.
result 95% sparse GRUs significantly improve on existing baselines.
Opportunistic spectrum access is one of the emerging techniques for maximizing throughput in congested bands and is enabled by predicting idle slots in spectrum. We propose a kernel-based reinforcement learning approach coupled with a novel budget-constrained sparsification technique that efficiently captures the envir…
A new method warps inputs to learn nonstationary kernels efficiently.
problem Learning nonstationary patterns in data with varying smoothness.
method Sparse spectrum Gaussian processes with input warping as conditional Gaussian measures.
result Efficient learning of nonstationary patterns with fewer parameters.
A strategy for spectrum sharing in CRNs with multiple PT power levels.
problem Efficient spectrum usage for secondary users in CRNs with multiple PT power levels.
method Data-driven/machine learning based multi-level spectrum sensing and prediction-transmission structures.
result The proposed strategy effectively aligns the ST with the PT power levels, improving spectrum usage.
This paper uses spectrum analysis to understand price behavior in the Indian stock market.
problem Understanding price formation and discovery in the Indian stock market.
method Adapting mathematical physics theories and spectrum analysis to decompose price cycles.
result Decomposing price cycles helps in understanding the effect of information on price formation and discovery.
EEG measures brain activity to diagnose ASD more efficiently.
problem Lack of objective measures for early ASD diagnosis.
method Use EEG to classify ASD using machine learning.
result EEG can be a biomarker for ASD.
Simple method solves Quanto Skew problem.
problem Quanto Skew problem in Equities and FX.
method Analytical method that accommodates Equity and FX volatility skew.
result Highly efficient and fast performance.
VAE improves MCMC efficiency by generating diverse prior proposals.
problem Inefficient MCMC methods in Bayesian inverse problems, especially subsurface flow modeling.
method Uses Variational Autoencoder (VAE) to generate broader-spectrum prior proposals.
result VAE achieves comparable accuracy to Karhunen-Loève Expansion (KLE) and outperforms it when correlation length is unknown.
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency, thereby resulting in a coherent design. The popular convex compressed sensing methods…
New method designs antimicrobial peptides with high potency and low toxicity.
problem Designing potent antimicrobial drugs with low toxicity.
method CLaSS method using deep generative autoencoder and atomistic simulations.
result Design and synthesis of two novel AMPs with high potency and low toxicity.
We develop and analyze efficient "coordinate-wise" methods for finding the leading eigenvector, where each step involves only a vector-vector product. We establish global convergence with overall runtime guarantees that are at least as good as Lanczos's method and dominate it for slowly decaying spectrum. Our methods a…
Deep autoencoder network solves spectrum sharing problems efficiently.
problem Resource allocation in wireless communications and D2D networks.
method Generative neural network (autoencoder) for solving linear sum assignment problems.
result Hybrid autoencoder architecture outperforms other methods in accuracy and speed.
The subject of this paper is the relationship among the marked length spectrum, the length spectrum, the Laplace spectrum on functions, and the Laplace spectrum on forms on Riemannian nilmanifolds. In particular, we show that for a large class of three-step nilmanifolds, if a pair of nilmanifolds in this class has the …
The subject of this paper is the relationship among the marked length spectrum, the length spectrum, the Laplace spectrum on functions, and the Laplace spectrum on forms on Riemannian nilmanifolds. In particular, we show that for a large class of three-step nilmanifolds, if a pair of nilmanifolds in this class has the …
We define a new spectrum for compact length spaces and Riemannian manifolds called the "covering spectrum" which roughly measures the size of the one dimensional holes in the space. More specifically, the covering spectrum is a set of real numbers δ>0 which identify the distinct δ covers of the space. We investigat…
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.
Algorithm for stable allocation in heterogeneous ad-hoc networks.
problem Decentralized spectrum allocation in dynamic, heterogeneous networks.
method Multi-armed bandit based distributed algorithm for static and dynamic networks.
result Achieves stable orthogonal allocation in finite time with low complexity.
Study the energy spectrum of metrics on surfaces and its relation to simple length spectrum.
problem Relate the energy spectrum to the simple length spectrum of metrics on surfaces.
method Analyze the energy spectrum of metrics on surfaces and their Teichmüller spaces, considering homotopy conditions.
result The energy spectrum determines the simple length spectrum under certain conditions.
The paper compares two spectrum definitions and finds stability in one modification.
problem Generalizing eigenvalues to arbitrary functionals with stability.
method Comparison of Gromov's homotopy significant spectrum and Krasnoskii spectrum, with a modified definition of the homotopy significant spectrum.
result The modified homotopy significant spectrum is stable, and Cheeger constant corresponds to Krasnoskii eigenvalue.
Proofs high-dimensional spectrum convergence of weighted sample covariance.
problem High-dimensional spectrum convergence of weighted sample covariance.
method Proposes a new, concise proof with stronger assumptions.
result Spectrum convergence proven for different weight distributions.
Study shows spectrum properties for specific Hadamard manifolds.
problem Spectrum properties of Hadamard manifolds.
method Absolute continuity and spectrum determination for two classes of Hadamard manifolds.
result Spectrum properties determined for specific Hadamard manifolds.
Iterative method 'Concent' corrects spectrum bias in covariance matrices.
problem Consistent bias in the spectrum of covariance matrices.
method 'Concent' iterative algorithm.
result Corrects spectrum bias for small and moderate dimensions.
Develops a new spectrum for annular links, recovering a transverse invariant at extreme gradings.
problem Understanding transverse link invariants in the annular setting.
method Constructs a stable homotopy type for annular links and defines a map to the Khovanov skein spectrum.
result At extreme gradings, the map from the Khovanov spectrum to the Khovanov skein spectrum recovers the cohomotopy transverse invariant.
Constructs manifolds with specific spectral properties.
problem Spectral properties of Riemannian manifolds.
method Asymptotically hyperbolic manifolds with sharp curvature bounds.
result Embeds singular continuous spectrum into the essential spectrum of the Laplacian.
The spectrum of certain manifolds matches that of hyperbolic space if the bottom spectrum is maximal.
problem Investigating spectral rigidity of manifolds with Ricci bounded below and maximal bottom spectrum.
method Analyzing the spectrum of the Laplacian on manifolds with specific Ricci curvature bounds.
result The spectrum of the manifold coincides with that of hyperbolic space if the bottom spectrum is maximal.
Lower bounds for Hodge-Laplacian spectrum on orbifolds.
problem Finding bounds for the essential spectrum of Hodge-Laplacian.
method Deriving lower bounds for the essential spectrum of the Hodge-Laplacian on geometrically finite orbifolds and their suborbifolds.
result Lower bounds for the essential spectrum of the Hodge-Laplacian.
While the harmonic function solution performs well in many semi-supervised learning (SSL) tasks, it is known to scale poorly with the number of samples. Recent successful and scalable methods, such as the eigenfunction method focus on efficiently approximating the whole spectrum of the graph Laplacian constructed from …
Trapezoids uniquely identified by their Dirichlet Laplace spectrum.
problem Identifying trapezoids based on their spectral properties.
method Analyzing the Dirichlet Laplace spectrum of non-obtuse trapezoids.
result Non-obtuse trapezoids are uniquely determined by their Dirichlet Laplace spectrum.
We present a new random sampling strategy for k-bandlimited signals defined on graphs, based on determinantal point processes (DPP). For small graphs, ie, in cases where the spectrum of the graph is accessible, we exhibit a DPP sampling scheme that enables perfect recovery of bandlimited signals. For large graphs, ie, …
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…
Random SNNs are stable and simple, with low-frequency Fourier spectra.
problem Stability and robustness of spiking neural networks.
method Boolean function analysis and Fourier spectrum concentration.
result Random LIF-SNNs are stable and biased towards simple functions.
Survey on bottom of spectrum of Hodge Laplacian on complete noncompact Kähler manifolds
problem Bottom of the spectrum of Hodge Laplacian on complete noncompact Kähler manifolds
method Survey on Kähler hyperbolic manifolds and bounded symmetric domains
result Proposed several open problems
The paper extends decay estimates to graphs with positive spectrum.
problem Proving decay estimates for nonnegative functions on graphs.
method Sharp ℓ2 decay estimates for nonnegative generalized subharmonic functions. result Extends Li and Wang's result to graphs with positive Laplacian spectrum.
Upper bounds for essential spectrum of minimal submanifolds linked to volume growth.
problem Estimating the essential spectrum of minimal submanifolds.
method Using volume growth to bound the bottom of the essential spectrum.
result Improved essential spectrum estimate for minimal submanifolds.
Upper bounds for volume spectrum depend on volume, dimension, and a conformal invariant.
problem Bounding the volume spectrum of Riemannian manifolds.
method Proves upper bounds that depend on volume, dimension, and a conformal invariant.
result Upper bounds for the volume spectrum are established.
Study on magnetic Dirac operators and their spectrum.
problem Understanding the spectrum of magnetic Dirac operators.
method Analysis of magnetic Dirac operators over complete Riemannian manifolds.
result Find sufficient conditions for maximal or discrete spectrum.
Covering preserves bottom spectrum, implies amenable covering.
problem Spectral preservation in Riemannian coverings.
method Proving spectral properties of Schrödinger operators on coverings.
result Covering preserving bottom spectrum implies amenability.
Notes on continuity of discrete-spectrum Fredholm operators.
problem Continuity properties of discrete-spectrum families of Fredholm operators.
method Relates recent work on discrete-spectrum families to classical continuity properties.
result Establishes connections between new and classical concepts.
Study shows ortho spectrum doesn't fully determine systolic length but limits the number of possible structures.
problem Determining the systolic length of hyperbolic surfaces with boundary.
method Analyzing the ortho spectrum of hyperbolic surfaces with totally geodesic boundary.
result There are only finitely many possibilities for the ortho spectrum and corresponding hyperbolic structures.
The rigidity of marked length spectrum for closed hyperbolic surfaces due to Fricke-Klein [7] has been the motivation of many different rigidity results, specially for manifolds of negative curvature. From the works of Vigneras [18], Sunada [17] and many other authors this result is far from being true for the unmarked…