A new method estimates nonhomogeneous Poisson process intensities with super-resolution.
problem Estimating cyclic arrival rates of nonhomogeneous Poisson processes.
method Super-resolution estimation using sinusoidal waves with unknown parameters.
result Finite sample guarantees for super-resolution estimation under suitable conditions.
New method learns complex brain signal patterns from EEG/MEG data.
problem Complex waveforms in brain signals not captured by linear filters.
method Multivariate convolutional sparse coding (CSC) algorithm.
result Reveals non-sinusoidal mu-shaped patterns in brain signals.
Algorithm finds frequencies, amplitudes, and phases of sinusoids in noisy data.
problem Finding frequencies, amplitudes, and phases of sinusoids in noisy data.
method Maximum likelihood approach to estimate tone parameters from contaminated observations. Successively estimates frequencies and jointly optimizes amplitudes and phases.
result Near-linear computational complexity (O(N)) for estimating M number of sinusoidal sources. New method recovers sparse vectors from random sinusoidal features.
problem Recovering sparse vectors from random sinusoidal features.
method Proposes a numerically stable algorithm for sparse vector reconstruction.
result Sparse vectors can be reliably recovered from random sinusoidal features.
Paper proposes robust LAD estimators for 2D sinusoidal model, proving consistency and normality.
problem Estimation of parameters in 2D sinusoidal models with outliers or heavy-tailed noise.
method Least absolute deviation (LAD) estimators for robust parameter estimation.
result Strong consistency and asymptotic normality of LAD estimators for 2D sinusoidal model parameters.
Periodic activation functions improve neural network reliability and interpretability.
problem Neural networks reinforce hidden biases, making them unreliable and hard to interpret.
method Introduce periodic activation functions in Bayesian neural networks to establish a connection with stationary Gaussian process priors.
result Periodic activation functions, including sinusoidal, triangular, and ReLU, improve model performance and sensitivity to perturbations.
WaveQ uses sinusoidal regularization to optimize deep quantization for neural networks, improving both efficiency and accuracy.
problem Deep quantization reduces bitwidth but can lead to significant accuracy loss due to inter-layer dependencies.
method WaveQ employs sinusoidal regularization to learn multiple quantization parameters during gradient-based training, balancing compute efficiency and accuracy.
result WaveQ achieves accuracy preservation and efficiency gains across various deep networks, outperforming state-of-the-art techniques.
SinReQ adds sinusoidal regularization to improve quantized neural networks.
problem Accuracy loss in quantized deep neural networks.
method SinReQ adds a periodic term to the objective function of quantized training algorithms.
result SinReQ closes the accuracy gap by 32.4% and 27.5% compared to DoReFa and WRPN respectively.
Autoencoder estimates parameters of noisy, multi-component damped signals.
problem Parameter estimation of damped sinusoidal signals under rapid decay and noise.
method Autoencoder-based approach using latent space for frequency, phase, decay, and amplitude estimation.
result High accuracy in parameter estimation, robustness to subdominant components and phase differences.
A new KAN variant uses sinusoidal activations to approximate functions.
problem Approximating multivariable functions using neural networks.
method Replacing inner and outer functions in Kolmogorov-Arnold representation with weighted sinusoidal functions.
result The new KAN variant outperforms fixed-frequency Fourier transform and achieves comparable performance to MLPs.
A new method uses sinusoidal functions to represent timestamps as dense vectors for improving irregularly sampled time series learning.
problem Challenges in supervised learning with irregularly sampled time series due to irregular time intervals.
method Proposes a novel method to represent timestamps as dense vectors using sinusoidal functions, called Time Embeddings.
result Improves LSTM-based and classical machine learning models, especially with very irregular data.
Paper revises power theory using classical mechanics concepts.
problem Clarifying instantaneous power definitions for circuit elements.
method Defines power using classical mechanics concepts like velocity and momentum.
result General and compact expression for inductance, capacitance, and resistance powers.
Deep ReLU networks can approximate various signal types with exponential error decay.
problem Approximating different signal structures with deep neural networks.
method Demonstrated approximation of polynomials, sinusoidal functions, oscillatory textures, and fractals.
result Finite-width deep ReLU networks require fewer connections than wide finite-depth networks for smooth function approximation.
A new neural network improves frequency estimation from noisy signals.
problem Estimating frequencies of sinusoidal components in noisy signals.
method A novel neural network architecture combined with a module to detect the number of frequencies.
result Significantly more accurate frequency estimation at medium-to-high noise levels.
Generative Adversarial Networks create time series data from images.
problem Generating realistic time series data from images.
method Wasserstein GANs with gradient penalty for stability, synthesizing sinusoidal, PPG, and ECG data.
result Successfully generated time series data using image-based GANs.
Method interprets LSTMs at the cell level for better understanding of their dynamics.
problem Understanding the dynamics of LSTMs at the cell level.
method A systematic pipeline for interpreting individual hidden state dynamics using response characterization methods.
result Identifies neurons with insightful dynamics and quantifies their impact on network performance.
Spiking neural networks maintain robust classification even with perturbed inputs.
problem Maintaining robustness of spiking neural networks under perturbed inputs.
method Extensive experiments on the XOR problem and benchmark datasets using SpikeProp algorithm.
result Classification ability of spiking neural networks is not significantly reduced by sinusoidal and Gaussian perturbations.
The study proposes a new interest rate model that captures long-term periodicity in U.S. Treasury yields.
problem The conventional Hull-White model fails to adequately capture long-term economic cycles in interest rates.
method The study introduces a sinusoidal Hull-White model with a time-varying mean reversion speed.
result The proposed model improves bond pricing and interest rate derivative valuation, especially for longer maturities.
Study wave front singularities and their geometric properties.
problem Characterize singularities of focal surfaces of wave fronts.
method Characterization through differential geometric properties.
result Relationships between focal surfaces and initial wave fronts' geometric invariants.
Study proves interaction of three impulsive gravitational waves, showing local solution and Lipschitz continuity.
problem Interaction of three impulsive gravitational waves in Einstein vacuum equations.
method Geometric estimates and wave estimates to prove local solution and continuity.
result Local solution to Einstein vacuum equations with three impulsive gravitational waves, Lipschitz continuity.
New Galilean spacetimes found as pp-wave reductions.
problem Understanding isotropic homogeneous Galilean spacetimes.
method Null reductions of pp-wave spacetimes.
result Found novel torsional Galilean spacetimes.
Model-free reinforcement learning agents outperform traditional portfolio management models in asset allocation.
problem Optimizing asset allocation in financial markets with limited historical data.
method Developed and compared model-based and model-free reinforcement learning agents (DSRQN, MSM) for trading efficiency.
result Model-free reinforcement learning agents achieve superior performance in asset allocation, outperforming traditional models by 9.2% in annualized cumulative returns and 13.4% in annualized Sharpe Ratio.
Analyzes Gerstner's trochoidal waves and their geometric properties.
problem Understanding the geometry and kinematics of trochoidal waves.
method Derives velocity and arc length conditions for cycloidal, curtate, and prolate trochoids using Galilean transformations.
result Conditions for arc lengths of prolate and curtate trochoids to coincide over a wave cycle.
Wave fronts on certain surfaces become dense.
problem Density of wave fronts on surfaces.
method Proof of density for specific surfaces.
result Wave fronts become dense on flat torus, square billiard, Klein bottle, and cube surface.
Investigates curvature properties of generalized pp-wave metric.
problem Examines curvature characteristics of generalized pp-wave metric.
method Analyzes Ricci, quasi-Einstein, and pseudosymmetric properties.
result Shows various curvature properties and sufficient conditions.
Analyzes properties of stiffness tensors for elastic wave imaging.
problem Characterizing stiffness tensor fields for elastic wave imaging.
method Finsler-geometric methods applied to anisotropic stiffness tensor fields.
result Conditions for Finsler-geometric methods to be applicable.
Deep learning model predicts wind-wave relationship.
problem Characterize ocean wave climate for engineering applications.
method Two-stage deep learning model: CNN for spatial features, LSTM for temporal dependencies.
result Predicts spatio-temporal relationship between wind and significant wave height.
Impulsive waves contradict a 1962 conjecture about pp-waves.
problem The failure of the Ehlers--Kundt conjecture in the impulsive case.
method Summarized completeness results for impulsive wave spacetimes.
result Impulsive pp-waves are complete, contradicting the conjecture.
Extends Penrose limit to Finsler spacetimes.
problem Extending Penrose limit to Finsler spacetimes.
method Introducing lightlike coordinates and adapting Lorentzian pp-wave definition.
result New examples of Finsler pp-waves presented.
New findings on plane waves in 3D spacetimes, showing non-unimodular elliptic plane waves are unique.
problem Classifying Lorentz homogeneous spaces of dimension 3, focusing on plane waves.
method Revisiting and relaxing usual completeness assumptions, characterizing homogeneous plane waves.
result Non-unimodular elliptic plane waves are unique and non-extendable, geodesically complete only if symmetric.
Classifies solutions to vacuum weighted Einstein equations on pr-waves.
problem Classifying solutions to vacuum weighted Einstein field equations on pr-waves.
method Classifying solutions using smooth metric measure spacetimes of dimension 4.
result Provides examples of solutions with special geometric properties.
High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points are moving along rays. As it appears, their motion can be described by Hamilton e…
Study compact plane waves, showing they are essentially standard.
problem Understanding the topology and dynamics of compact plane waves.
method Analyzing quotients of homogeneous plane waves by discrete subgroups.
result Compact quotients of homogeneous plane waves are essentially standard.
New method finds precise late-time behavior of wave equations.
problem Analyzing late-time behavior of wave equations with inverse-square potentials.
method Physical-space-based method for deriving late-time asymptotics.
result Sharp, uniform decay estimates in time for asymptotic late-time tails.
Paper explores non-uniqueness and uniqueness class for wave equations on graphs.
problem Non-uniqueness of solutions to wave equations on infinite graphs.
method Analyticity of solutions in the uniqueness class, extension to a wide class of linear evolution equations.
result Sharp uniqueness class for solutions of wave equations on graphs.
New metrics link Kähler and pp-wave spacetimes.
problem Connecting Kähler and pp-wave spacetimes.
method Constructing families of complete almost Kähler metrics by deforming pp-waves.
result Established a one-to-one correspondence between almost Kähler metrics and pp-wave spacetimes.
The financial rogue waves are reported analytically in the nonlinear option pricing model due to Ivancevic, which is nonlinear wave alternative of the Black-Scholes model. These solutions may be used to describe the possible physical mechanisms for rogue wave phenomenon in financial markets and related fields.
Study on wave fronts' singularities and parallel surfaces.
problem Understanding singularities of wave fronts and their parallel surfaces.
method Using geometric invariants to analyze principal curvatures and singular points.
result Criteria for bounded principal curvatures at non-degenerate singular points.
Simple conformally recurrent spaces are identified as pp-waves.
problem Characterizing conformally recurrent space-times.
method Analyzing dimension n>3 space-times.
result Simple conformally recurrent space-times are conformally recurrent pp-waves.
Wave maps into negatively curved targets can blow up stably.
problem Existence and stability of blowup for wave maps.
method Construction of a self-similar wave map for a negatively curved target.
result Stable blowup mechanism for wave maps in high dimensions.
New method detects spike-and-wave epileptiform discharges using Kendall's Tau-b.
problem Detecting spike-and-wave epileptiform discharges in EEG signals.
method Proposes a new method based on Kendall's Tau-b coefficient.
result High Specificity and rule in (SpPIn) for spike-and-wave discharge detection.
We show that every n-dimensional locally homogeneous pp-wave is a plane wave, provided it is indecomposable and its curvature operator, when acting on 2-forms, has rank greater than one. As a consequence we obtain that indecomposable, Ricci-flat locally homogeneous pp-waves are plane waves. This generalises a classic…
The paper shows how null hypersurfaces behave in Lorentz-Minkowski space.
problem Understanding null hypersurfaces in Lorentz-Minkowski space.
method Analyzing L-complete null hypersurfaces as wave fronts in Euclidean space. result Most null wave fronts can be realized as restrictions of certain L-complete null wave fronts. New metrics constructed dual to specific wave-like geometries.
problem Constructing metrics dual to general plane-fronted wave Lorentzian metrics.
method Explains construction of extremal and non-Kähler almost-Kähler metrics.
result Constructs canonical almost-Kähler metrics dual to general plane-fronted wave Lorentzian metrics.
Improved F0 estimation in noisy speech with neural networks.
problem Difficult F0 estimation at low SNRs in unexpected noise.
method Waveform-to-sinusoid regression using RNN trained on supervised data.
result Significant improvement in FPE and GPE rates compared to existing methods.
Study pp-waves with lightlike parallel spinors in vacuum spacetimes.
problem Characterize pp-waves with lightlike parallel spinors in vacuum spacetimes.
method Parametrize pp-wave spacetimes, show correspondence with Riemannian metrics, prove parallel spinor condition.
result A pp-wave spacetime with a lightlike parallel spinor corresponds to a Ricci-flat metric with a parallel spinor.
This paper solves a complex equation using Lie symmetry approach to find solitary wave and multiple soliton solutions.
problem Solving a (3 + 1)-dimensional KdV type equation.
method Lie group of transformation method to find infinitesimal generators and commutator table.
result Exact solutions of KdV type equation in explicit form.
Develops methods to construct harmonic and wave maps into variable-curvature surfaces.
problem Limited explicit constructions for harmonic and wave maps in variable-curvature settings.
method Reduction framework for pseudo-Riemannian surfaces, geometric ansatz, first-order ODEs.
result Constructs explicit harmonic and wave maps into ellipsoids, hyperboloids, and Schwarzschild exterior.