A new method integrates Fourier basis expansion and mapping for improved time series forecasting.
problem Inconsistent starting cycles and series length issues in Fourier-based methods.
method Fourier Basis Mapping (FBM) method that integrates time-frequency features through Fourier basis expansion and mapping.
result FBM addresses inconsistencies and preserves temporal characteristics, achieving SOTA performance.
CMC method detects causal relationships in time series data.
problem Understanding causal relationships in nonlinear systems.
method Cross-Mapping Coherence method, based on nonlinear state-space reconstruction and coherence metrics.
result CMC accurately identifies causal connections in various systems.
Study reveals how neural network biases align with adversarial attack frequencies.
problem Correlation between neural network biases and adversarial attacks.
method Fourier transform analysis of network implicit bias and adversarial perturbations.
result Network bias and adversarial attack frequencies are highly correlated.
A new WNN framework selects wavelet bases for efficient learning.
problem Challenges in constructing accurate wavelet bases and high computational costs in WNN.
method Introduces a constructive WNN that selects initial bases and trains functions by introducing new bases for predefined accuracy while reducing computational costs.
result Significantly improves computational efficiency through a frequency estimator and wavelet-basis increase mechanism.
Speech separation has been very successful with deep learning techniques. Substantial effort has been reported based on approaches over spectrogram, which is well known as the standard time-and-frequency cross-domain representation for speech signals. It is highly correlated to the phonetic structure of speech, or "how…
We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional datasets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other non-linear dimensionality reduction methods. MFVDM combines different nonlinear emb…
Enhances uncertainty estimation in medical image segmentation.
problem Frequency-related noise in medical imaging leads to biased uncertainty estimates.
method Extends MC-Dropout to the frequency domain for better uncertainty estimation.
result MC-Frequency Dropout improves calibration and uncertainty in semantic segmentation.
Neural networks are known to be a class of highly expressive functions able to fit even random input-output mappings with 100% accuracy. In this work, we present properties of neural networks that complement this aspect of expressivity. By using tools from Fourier analysis, we show that deep ReLU networks are biased…
A new Hawkes process model captures order book dynamics in high-frequency trading.
problem Capturing the complex dynamics of high-frequency trading with large datasets.
method Estimation of an order book dependent Hawkes process using a product of a Hawkes process and covariates.
result Capturing the nonlinearity of order book information improves the model's performance.
This paper proposes a framework based on deep convolutional neural networks (CNNs) for automatic heart sound classification using short-segments of individual heart beats. We design a 1D-CNN that directly learns features from raw heart-sound signals, and a 2D-CNN that takes inputs of two- dimensional time-frequency fea…
Deep neural network learns optimal trading controls for high-frequency finance.
problem Optimal trading on high-frequency data with market impact and limited data.
method Deep neural network, Monte-Carlo initialization, transfer learning, explainable controls.
result Neural network learns optimal controls for trader preferences.
Optimizes natural frequencies of cellular composites with various microstructures.
problem Designing cellular composites with diverse microstructures for maximizing natural frequencies.
method Data-driven topology optimization with a latent-variable Gaussian process model.
result Cellular designs with multiclass microstructures achieve higher natural frequencies.
CNNs use a bottleneck structure to focus on a few frequencies, affecting function representation.
problem Understanding how CNNs focus on specific frequencies in their feature learning.
method Defined Convolution Bottleneck (CBN) structure, measured CBN rank, and analyzed parameter norms.
result Parameter norm scales with depth and CBN rank, and networks with optimal parameters exhibit this structure.
Study evaluates three ML models for high-frequency trading.
problem Improving accuracy and reliability of high-frequency trading strategies.
method Compared three models: cross-entropy loss + quasi-Newton, FCNN, and vector machine.
result Combination of cross-entropy loss and quasi-Newton outperformed other models.
Large textual corpora are often represented by the document-term frequency matrix whose elements are the frequency of terms; however, this matrix has two problems: sparsity and high dimensionality. Four dimension reduction strategies are used to address these problems. Of the four strategies, unsupervised feature trans…
Recently, the field of adversarial machine learning has been garnering attention by showing that state-of-the-art deep neural networks are vulnerable to adversarial examples, stemming from small perturbations being added to the input image. Adversarial examples are generated by a malicious adversary by obtaining access…
In this manuscript we present a comprehensive study on the multifractal properties of high-frequency price fluctuations and instantaneous volatility of the equities that compose Dow Jones Industrial Average. The analysis consists about quantification of dependence and non-Gaussianity on the multifractal character of fi…
Quantum models can approximate any function if data encoding allows for a rich enough frequency spectrum.
problem Theoretical properties of quantum machine learning models, particularly their expressive power.
method Investigated how data encoding affects the expressive power of parametrized quantum circuits.
result Quantum models can access increasingly rich frequency spectra by repeating data encoding gates, potentially making them universal function approximators.
We introduce a new non parametric method that allows for a direct, fast and efficient estimation of the matrix of kernel norms of a multivariate Hawkes process, also called branching ratio matrix. We demonstrate the capabilities of this method by applying it to high-frequency order book data from the EUREX exchange. We…
Deep learning maps tongue movements to speech sounds for voiceless individuals.
problem Developing silent speech interfaces for individuals without a larynx.
method Hybrid spatio-temporal 3D convolutions and feature shuffling for formant estimation and tracking from ultrasound tongue images.
result Best model achieves R-squared of 99.96% for vowel formant regression.
Deep learning has become an area of interest in most scientific areas, including physical sciences. Modern networks apply real-valued transformations on the data. Particularly, convolutions in convolutional neural networks discard phase information entirely. Many deterministic signals, such as seismic data or electrica…
A musical instrument based on moduli spaces lets users hear geometric concepts.
problem Understanding geometric structures through auditory means.
method Developed a plastic hormonica based on Farey tessellations and Poincaré disk decorations.
result Users can audibly experience paths in Riemann moduli spaces and listen to mapping classes.
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.
Bayesian optimization with RPCE reduces MAP estimation for structural dynamics models.
problem Estimating parameters of structural dynamic models efficiently.
method Bayesian optimization with RPCE surrogate model.
result Effective reduction in model evaluations for MAP estimation.
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 …
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.
CycleGAN-VC3 improves CycleGAN-VCs for mel-spectrogram conversion.
problem Ambiguity in CycleGAN-VC/VC2 effectiveness for mel-spectrogram conversion.
method Proposes CycleGAN-VC3 with time-frequency adaptive normalization (TFAN).
result CycleGAN-VC3 outperforms or matches CycleGAN-VC2 for mel-spectrogram conversion.
A nonlinear channel estimator using complex Least Square Support Vector Machines (LS-SVM) is proposed for pilot-aided OFDM system and applied to Long Term Evolution (LTE) downlink under high mobility conditions. The estimation algorithm makes use of the reference signals to estimate the total frequency response of the …
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.
Power spectral density (PSD) maps providing the distribution of RF power across space and frequency are constructed using power measurements collected by a network of low-cost sensors. By introducing linear compression and quantization to a small number of bits, sensor measurements can be communicated to the fusion cen…
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.
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.
In this paper, we continue our previous work on the Dirichlet mixture model (DMM)-based VQ to derive the performance bound of the LSF VQ. The LSF parameters are transformed into the ΔLSF domain and the underlying distribution of the ΔLSF parameters are modelled by a DMM with finite number of mixture components. The…
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.
Axial-LOB predicts stock prices from LOB data using attention layers.
problem Predicting stock price from LOB data with long-range dependencies.
method Axial-LOB uses gated position-sensitive axial attention layers to incorporate global interactions.
result Axial-LOB achieves state-of-the-art performance in stock price prediction.
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.
Study finds anomalies in high-frequency S&P 500 price changes.
problem Anomalies in high-frequency S&P 500 price changes.
method Using NBBO event-time data, the study forms pairs of backward and forward price increments, standardizes them, and estimates expected responses on a fine grid of push magnitudes.
result Persistent structural shift in expected responses: near zero for short lags, pronounced tails for long lags, indicating correlation between larger historical pushes and nonzero responses.
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.
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.
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…
Complex analysis techniques link Gaussian RBF kernels to quantum mechanics.
problem Understanding the Gaussian RBF kernel in machine learning and SVMs.
method Using Fock space and Segal-Bargmann theories in complex analysis.
result Proves connections between Gaussian RBF kernels and quantum mechanics operators.