Study describes frequencies of geodesics on hyperbolic surfaces as genus grows.
problem Large genus asymptotic behaviors of geodesic frequencies on hyperbolic surfaces.
method Proof of conjecture involving separating and nonseparating geodesics.
result Explicit function $f( rac{n}{g})$ for frequency ratio given.
Study on frequencies of non-simple curves in surfaces of large genus.
problem Frequency of non-simple curves in surfaces of large genus.
method Expression for frequency, large genus asymptotics, comparison with previous work.
result Identify most common types of non-simple curves with K intersections.
Modeling implied volatility surface dynamics with Hawkes kernels.
problem Understanding and predicting high-frequency dynamics of the implied volatility surface.
method Hawkes modeling of the volatility surface, with coefficients governing skew and convexity.
result Simple conditions on Hawkes kernel coefficients ensure no-arbitrage and reduce parameter estimation.
A new method to estimate local volatility from high-frequency data.
problem Quantitative trading risk management needs a better way to estimate volatility.
method Realized local volatility surface estimated via high-frequency data and Bayesian nonparametric estimation.
result The method can capture counterfactual volatility and improve risk management.
Study growth rates of harmonic functions on curved surfaces.
problem Understanding the growth rates of harmonic functions on curved surfaces.
method Gradient estimate and frequency analysis on complete surfaces and manifolds with non-negative curvature.
result Existence and properties of nonconstant polynomial growth harmonic functions on manifolds with maximal volume growth.
Study uses sentiment analysis to predict implied volatility surface, improving prediction accuracy.
problem Improving prediction accuracy of implied volatility surface.
method Constructed daily high-frequency sentiment data, used VAR method, deep learning (BERT, LSTM), FFT, EMD for sentiment decomposition.
result High-frequency sentiment correlates with ATM options' implied volatility, low-frequency with DOTM options.
New kernels model non-stationary data efficiently.
problem Efficiently modeling non-stationary data with Gaussian processes.
method Model spectral density as a mixture of frequency surfaces, solve generalised Fourier transform.
result Derives efficient inference methods for non-stationary kernels.
The paper studies counting problems on square-tiled surfaces.
problem Understanding the frequency of properties in square-tiled surfaces.
method Examining properties of the square torus and their implications in translation surfaces.
result Implications between properties and their frequency in translation surfaces.
On a fixed smooth compact Riemann surface with boundary (M0,g), we show that the Cauchy data space (or Dirichlet-to-Neumann map $\mc{N}$) of the Schrödinger operator Δ+V with V∈C2(M0) determines uniquely the potential V. We also discuss briefly the corresponding consequences for potential scattering at 0 …
We consider globally hyperbolic flat spacetimes in 2+1 and 3+1 dimensions, in which a uniform light signal is emitted on the r-level surface of the cosmological time for r→0. We show that the frequency of this signal, as perceived by a fixed observer, is a well-defined, bounded function which is generally not co…
Formulae for Masur-Veech volumes and frequencies of geodesics derived from intersection numbers.
problem Calculating volumes and frequencies of geodesics in moduli spaces.
method Lattice point counts and intersection numbers of ψ-classes, with explicit rational coefficients.
result Formulae for Masur-Veech volumes and frequencies of simple closed geodesics.
On a fixed smooth compact Riemann surface with boundary (M0,g), we show that for the Schrödinger operator Δ+V with potential V∈C1,α(M0) for some α>0, the Dirichlet-to-Neumann map N∣Γ measured on an open set Γ⊂∂M0 determines uniquely the potential V. We also discuss briefly the cor…
Bayesian method suppresses low-frequency pulses in audio recordings.
problem Suppressing long pulses caused by mechanical defects in audio recordings.
method Bayesian approach using Gaussian Process for pulse location, signal interpolation, and tail estimation.
result Perceptual results similar to previous methods, performs well on naturally degraded signals.
Study proves uniqueness of certain minimal surfaces in spherical and hyperbolic spaces.
problem Proving uniqueness of free boundary minimal annuli in geodesic balls.
method Using Steklov problem frequency and antipodal map invariance.
result Minimal annuli are congruent to a critical rotational annulus.
Study proper sampling for X-ray transforms on simple surfaces.
problem Proper discretizing and sampling issues related to geodesic X-ray transforms on simple surfaces.
method Provide minimal sampling rates for faithful reconstruction, quantify sampling quality, and predict artifacts.
result Minimal sampling rates and artifact prediction for geodesic X-ray transforms on simple surfaces.
Paper reduces recommender system model size by 90%.
problem Large model size in recommender systems.
method Hybrid frequency and double hashing for model size reduction.
result 90% reduction in model size with no performance loss.
Formulae for Masur-Veech volumes derived from intersection numbers of curves.
problem Computing volumes and densities of geodesics and surfaces.
method Intersection numbers of psi-classes and lattice point count.
result Formulae for Masur-Veech volumes as polynomials in intersection numbers.
HyFAD improves time series imputation by combining time and frequency diffusion.
problem Improve time series imputation by handling frequency-sensitive denoising and balancing global and local dynamics.
method HyFAD is a hybrid time-frequency diffusion model with frequency-aware embedding, built on DDPM paradigm.
result HyFAD achieves state-of-the-art performance in time series imputation.
SSMs have a built-in bias towards low-frequency components, which can be adjusted.
problem Frequency bias in SSMs affects their performance on long-range sequences.
method Proposed two mechanisms to tune frequency bias: scaling initialization or applying a Sobolev-norm-based filter.
result Tuning frequency bias improves SSMs' performance on long-range sequence learning tasks.
Geometrically interprets frequency in electric circuits.
problem Conventional frequency definition limitations.
method Introduces a multivector definition of frequency.
result Conventional frequency is a special case of the new framework.
Trading affects grid frequency fluctuations, making them more extreme.
problem Impact of trading on grid frequency stability.
method Analysis of frequency time series from 2011 and 2017.
result Trading modifies frequency fluctuation statistics, making large deviations more likely.
CNNs show sensitivity to low-frequency signals due to image frequency distribution.
problem Understanding why CNNs are sensitive to low-frequency signals.
method Theoretical analysis of CNN representations in frequency space.
result CNNs sensitivity to low-frequency signals is due to the frequency distribution of natural images.
The paper examines how parabolic frequency behaves under Ricci flow and Ricci-harmonic flow on manifolds.
problem Understanding the behavior of parabolic frequency under Ricci flow and Ricci-harmonic flow.
method Investigates the monotonicity of parabolic frequency for solutions of linear and heat equations with bounded curvatures.
result Establishes monotonicity results for parabolic frequency under specific curvature conditions.
New method constrains CNN filter frequencies to improve robustness.
problem CNN bias towards low frequency components, leading to poor performance in scenario transformations.
method Frequency domain regularization by constraining filter spectra, training valid frequency range end-to-end.
result Demonstrated effectiveness in defending adversarial perturbations, reducing generalization gap, and improving transfer learning.
Paper extends SI method for detecting CPs in complex systems' frequency domain.
problem Identifying change points in complex systems' frequency domain.
method Extends SI framework to frequency domain using DFT properties and develops valid p-values.
result Reliable detection of genuine CPs with strong statistical guarantees.
Study uses multi-kernel Hawkes models to analyze high-frequency price dynamics.
problem Understanding responsive speeds of market participants in high-frequency trading.
method Multi-kernel Hawkes models with conditional Hessian analysis for optimization.
result Existence of multi-kernels (UHF, VHF, HF) in high-frequency price dynamics.
The paper defines a frequency for mean curvature flow and proves its monotonicity.
problem Backwards uniqueness for solutions of mean curvature flow.
method Defining and proving monotonicity of a parabolic frequency for mean curvature flows.
result Frequency monotonicity implies backwards uniqueness for mean curvature flow solutions.
PhaseDNN speeds up learning of high-dimensional functions across wide frequencies.
problem Training high-dimensional functions at wide frequencies is slow and inefficient.
method Parallel DNNs with frequency-specific training and phase shifts.
result PhaseDNN achieves uniform learning across wide frequencies.
Low frequency perturbations improve model robustness, contrary to high frequency attacks.
problem Improving model robustness against adversarial attacks.
method Systematic control of frequency components in perturbations.
result Low frequency perturbations improve model robustness, especially in white-box and black-box settings.
Paper defines parabolic frequency for Ricci flow solutions, proving monotonicity and uniqueness.
problem Backwards uniqueness for solutions of parabolic equations on Ricci flows.
method Defines and proves monotonicity of parabolic frequency for Ricci flow solutions.
result Backwards uniqueness for solutions of parabolic equations on Ricci flows.
New Fourier-based diffusion model improves high-frequency generation quality.
problem Diffusion models struggle with high-frequency details.
method Analyzed and modified the forward process in Fourier space to equalize noise corruption across frequencies.
result Improved generation quality for high-frequency components.
Proves monotonicity of parabolic frequency on all manifolds without curvature assumptions.
problem Monotonicity of parabolic frequency on manifolds.
method Analyzes parabolic frequency function on manifolds, proving monotonicity without curvature assumptions.
result Monotonicity of parabolic frequency on all manifolds, no curvature assumption needed.
Proposes a conservative LR estimator for infrequent data near a frequency threshold.
problem Overestimation of likelihood ratios for infrequent data near a frequency threshold.
method Conservative likelihood ratio estimator for frequencies slightly above a threshold.
result Improves prediction accuracy in named entity context prediction.
We build an agent-based model to study how the interplay between low- and high-frequency trading affects asset price dynamics. Our main goal is to investigate whether high-frequency trading exacerbates market volatility and generates flash crashes. In the model, low-frequency agents adopt trading rules based on chronol…
Deeper neural networks learn lower frequency functions faster, according to a new principle.
problem Understanding why deeper learning is faster.
method Fourier analysis and filtering method to separate and analyze the frequency distribution of neural network outputs.
result Deeper hidden layers in neural networks bias towards lower frequency functions during training.
Wavelet analysis reveals non-linear dynamics in cryptocurrency prices.
problem Understanding non-linear dynamics in high-frequency cryptocurrency prices.
method Wavelet analysis of frequency and time variables.
result Cyclical persistence at different frequencies in cryptocurrency prices.
Local convolutions bias neural networks towards high-frequency adversarial examples.
problem High-frequency adversarial examples in neural networks.
method Analysis of different linear and nonlinear architectures, focusing on the impact of local convolution operations.
result Local convolutions induce an implicit bias towards high frequency features, leading to high-frequency adversarial examples.
Study shows neural networks learn low frequencies first, proposing solutions.
problem Frequency bias in neural network learning process.
method Developed a PDE to unravel frequency dynamics, used Fourier Features model.
result Appropriate weight initialization can eliminate or control frequency bias.
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.
Complex frequency generalizes eigenvalues in LTI systems.
problem Characterizing dynamics of signals with complex values.
method Geometric frequency interpretation and transformation analysis.
result Complex frequencies in LTI systems match eigenvalues.
The paper studies frequency monotonicity for solutions of nonlinear equations under Ricci flow.
problem Frequency monotonicity for positive solutions of nonlinear equations under Ricci flow.
method Obtained parabolic frequency monotonicity for solutions of two nonlinear parabolic equations with bounded Ricci curvature.
result Established integral type Harnack inequalities using parabolic frequency monotonicity.
Study of large-n asymptotics for Weil-Petersson volumes of hyperbolic surfaces with cusps.
problem Understanding the geometry and spectral properties of random hyperbolic surfaces with many cusps.
method Large-n asymptotic analysis, spectral theory, and moduli space volumes. result Linear number of small Laplacian eigenvalues and relative frequency of simple vs. non-simple closed geodesics.
Convolutional GANs favor low spatial frequencies, affecting fine detail generation.
problem Understanding GANs' limitations in high spatial frequency learning.
method Proposed method to manipulate GANs' bias against high spatial frequencies.
result Convolutional GANs have a bias against learning high spatial frequencies.
The paper introduces a frequency-domain estimator for low-order systems from noisy data.
problem Estimating frequency responses of low-order systems from noisy measurements.
method Uses a quadratic data-fitting term regularized by the nuclear norm of a Loewner matrix, subject to a convex stability constraint.
result Proves a finite-sample error bound and extends it to all frequencies through rational interpolation.
The paper explains how neural networks learn less salient frequency components during training.
problem Understanding the grokking phenomenon in neural networks.
method Empirical frequency analysis of training data.
result Neural networks initially learn less salient frequency components of the test data.
A predictor improves power grid frequency forecasts up to one hour.
problem Improving frequency forecast for better power system stability.
method Developed a weighted-nearest-neighbor (WNN) predictor.
result Forecasts for up to one hour are more precise than averaged daily profiles.
Study on parabolic frequency monotonicity on compact manifolds.
problem Analyzing solutions of the heat equation on Riemannian manifolds.
method Generalization of R. Hamilton's matrix Harnack inequality for small time.
result Parabolic frequency functional is almost increasing on compact manifolds with nonnegative sectional curvature.
FreSh shifts model's initial frequency spectrum to match target signal, improving neural representation performance.
problem MLPs' low-frequency bias limits capturing high-frequency details accurately.
method FreSh selects embedding hyperparameters to align model's initial output spectrum with target signal's spectrum.
result FreSh improves performance across various neural representation methods and tasks with minimal computational overhead.