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.
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48 results for “geometric frequency”
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.
Paper shows geometric frequency and Lagrange derivative equivalence for electric and fluid systems.
problem Understanding and classifying system operating conditions based on electric quantity waveform distortions.
method Demonstrates equivalence between geometric frequency and Lagrange derivative through numerical examples.
result Identifies components of Lagrange derivative that relate to geometric frequency and waveform distortions.
The paper uses Frenet frame to unify electrical and geometric quantities.
problem Defining time derivatives of electrical quantities in various conditions.
method Utilizes Frenet frame from differential geometry to define time derivatives in both stationary and transient conditions.
result Unifies and generalizes time- and phasor-domain frameworks.
New formula for instantaneous frequency in unbalanced systems.
problem Estimating frequency in unbalanced electrical systems.
method Utilizes affine differential geometry to link frequency and voltage derivatives.
result Proposes a new formula for instantaneous frequency estimation.
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.
Analyzes branch points of area-minimizing currents with non-2 planar frequency.
problem Understanding the structure of area-minimizing currents near branch points.
method Intrinsic frequency function and geometric arguments avoiding center manifolds.
result Establishes higher order asymptotics and topological control near branch points.
Paper revisits five IF paradoxes using differential geometry.
problem Five paradoxes of Instantaneous Frequency in three-phase systems.
method Geometric interpretation of frequency to explain IF paradoxes.
result Revisits and explains five IF paradoxes through a common framework.
Zipfian Whiteningcs.CL
PCA whitening weighted by Zipfian word frequencies improves task performance.
problem Skewed word embedding spaces in neural models.
method PCA whitening weighted by empirical word frequencies following Zipf's law.
result Significantly improves task performance, surpassing baselines.
FRA-Attack improves adversarial transferability for closed-source MLLMs by aligning visual focus across models.
problem Improving adversarial transferability for closed-source MLLMs, especially with high accuracy.
method Unified frequency-domain regularization approach: high-pass DCT objective for feature alignment and Frequency-domain Gradient Regularization (FGR) for gradient optimization.
result FRA-Attack achieves superior cross-model transferability, especially on GPT-5.4, Claude-Opus-4.6, and Gemini-3-flash.
Lazy, perfectly informed investors trade infrequently due to costs.
problem The paradox of an omniscient yet lazy investor trading infrequently.
method Formalized the paradox using geometric and fractional Brownian motion models, derived closed-form profit functions, and proved existence and uniqueness of the optimal trading frequency.
result The optimal trading frequency can be interpreted through the fractal dimension of the price path.
We prove sharp bounds for the growth rate of eigenfunctions of the Ornstein-Uhlenbeck operator and its natural generalizations. The bounds are sharp even up to lower order terms and have important applications to geometric flows.
A natural way of handling imbalanced data is to attempt to equalise the class frequencies and train the classifier of choice on balanced data. For two-class imbalanced problems, the classification success is typically measured by the geometric mean (GM) of the true positive and true negative rates. Here we prove that G…
Zipf Distributions from Two-Stage Symbolic Processes: Stability Under Stochastic Lexical Filteringstat.ME
Study explains Zipf's law using geometric mechanisms from a finite alphabet.
problem Explains Zipf's law in language without relying on linguistic elements.
method Uses the Full Combinatorial Word Model (FCWM) to generate geometric distributions of word lengths.
result Supports predictions of power-law rank-frequency curves, matching various languages.
The paper models financial order books using geometric shears and directional liquidity.
problem Understanding the geometry and dynamics of financial order books.
method Structural framework modeling liquidity as emergent observables, geometric shears, and directional imbalances.
result The geometry of financial order books can be described by a rigid drift and geometric shear, leading to a gamma-like profile of projected liquidity.
LEGO estimates tangent spaces more robustly than LPCA in noisy data.
problem Estimating tangent spaces in high-noise settings.
method Spectral method using graph Laplacian eigenvectors and gradient orthogonization.
result LEGO yields more robust tangent space estimates than LPCA.
Developed a diffusion model on spherical data, addressing geometric and stochastic challenges.
problem Diffusion models on spherical data face unique geometric and stochastic issues.
method Extended spectral diffusion to spherical harmonics, introducing modified stochastic differential equations.
result Introduced a geometry-dependent inductive bias in spectral diffusion models.
This work analyzes how often to update the target network in Q-learning.
problem Understanding the optimal frequency of target network updates in Q-learning.
method Formulated target updates as a nested optimization scheme, derived finite-time convergence analysis.
result Optimal target update frequency increases geometrically over time.
GSAN learns adaptive node representations using geometric scattering and attention.
problem Oversmoothing in node representation learning.
method Attention-based architecture integrating geometric scattering and GCN channels.
result GSAN outperforms previous networks in semi-supervised node classification.
The paper introduces a new price model based on entropy that better fits high-frequency market data.
problem Understanding fair prices in high-frequency markets with bid-ask imbalance.
method A parametrized family of prices derived from the Maximum Entropy Principle, minimizing bias given volume imbalance.
result The model can generate higher kurtosis and heavy-tailed distributions compared to standard models.
In this article we introduce an approach for studying the geodesic X-ray transform and related geometric inverse problems by using Carleman estimates. The main result states that on compact negatively curved manifolds (resp. nonpositively curved simple or Anosov manifolds), the geodesic vector field satisfies a Carlema…
While ubiquitous, textual sources of information such as company reports, social media posts, etc. are hardly included in prediction algorithms for time series, despite the relevant information they may contain. In this work, openly accessible daily weather reports from France and the United-Kingdom are leveraged to pr…
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time sy…
Study on the nodal set of Dirac equation solutions on manifolds.
problem Understanding the structure of nodal sets of solutions to Dirac equations.
method Proved Hausdorff dimension of nodal sets, extended to locally Lipschitz coefficients, provided stratification results.
result Stratification result for nodal sets, providing new insights even in the smooth case.
A new geometrically-motivated algorithm for nonnegative matrix factorization is developed and applied to the discovery of latent "topics" for text and image "document" corpora. The algorithm is based on robustly finding and clustering extreme points of empirical cross-document word-frequencies that correspond to novel …
FiberNet integrates geometry into machine learning for clearer classification.
problem Lack of interpretability in traditional deep learning.
method Reformulates classification as geometric optimization on fiber bundles, introducing learnable Riemannian metrics and variational prototype optimization.
result Clear geometric interpretability and efficiency in classification.
Study on singularities of area-minimizing currents, focusing on frequency and branch points.
problem Understanding the nature of singular points in area-minimizing currents.
method Intrinsic frequency function and decomposition theorem for singular set.
result Established properties of the planar frequency function and decomposition of singular set.
New method learns dynamics from sparse data using geometric constraints.
problem Learning dynamics from sparse, undersampled data.
method Reformulates inference as a stochastic control problem, using geometry-driven path augmentation.
result Accurately recovers stochastic dynamics from extremely undersampled data.
HyFAD: Hybrid Time-Frequency Diffusion with Frequency-Aware Embedding for Time Series Imputationstat.ML
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.
Study shows invariant curves in tubular origami dynamics, revealing geometric barriers to folding transitions.
problem Understanding the dynamics and geometric barriers in tubular origami structures.
method Kolmogorov--Arnold--Moser (KAM) theory and numerical simulations.
result Invariant curves persist in large module limits, providing phase-space interpretation of folding modes.
Lower bounds for eigenvalues on manifolds with negative Ricci curvature.
problem Estimating eigenvalues on non-compact manifolds with negative Ricci curvature.
method Using a one-dimensional differential equation model to bound the principal frequency.
result The lower bound for the principal frequency is sharp and depends on the diameter and curvature.
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.
A quasi-Lie scheme is a geometric structure that provides t-dependent changes of variables transforming members of an associated family of systems of first-order differential equations into members of the same family. In this note we introduce two quasi-Lie schemes for studying second-order Gambier equations in a geome…
Two algorithms converge to dictionary learning with geometric rate for non-uniform data.
problem Dictionary learning for non-uniform data models.
method Derivation of convergence conditions for MOD and ODL.
result Both algorithms converge to the generating dictionary with geometric rate under certain conditions.
Lower bounds for eigenvalues on manifolds with negative Ricci curvature.
problem Estimating eigenvalues on non-compact manifolds with negative Ricci curvature.
method Using a one-dimensional differential equation model, the paper establishes a lower bound for the principal frequency.
result The lower bound for the principal frequency is sharp and depends on the diameter and curvature.
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.
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.
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.
Parabolic frequency monotonicity on Ricci flow and Ricci-harmonic flow with bounded curvaturesmath.DG
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.
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.
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.
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.
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.
Conservative Likelihood Ratio Estimator for Infrequent Data Slightly above a Frequency Thresholdstat.ML
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.