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 cryptocurrency price dynamics using adaptive EMD and spectral analysis.
problem Analyze the time-varying volatility of cryptocurrency prices.
method Adaptive complementary ensemble empirical mode decomposition (ACE-EMD) and Hilbert spectral analysis.
result Reveal the properties of various timescales in cryptocurrency price dynamics.
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.
Estimates chirp signal frequencies using probabilistic models.
problem Estimating instantaneous frequencies of chirp signals when true forms are unknown.
method Non-linear Gaussian processes and stochastic filters/smothers for posterior estimation.
result The method outperforms state-of-the-art methods on synthetic and real-world datasets.
Modeling continuous movement of entities in latent space for interaction timing.
problem Analyzing timing and frequency of instantaneous interactions.
method Latent position model with continuous trajectories.
result Individual trajectories estimated from interaction data.
Study high-frequency trading game with price impact, finding unique equilibrium.
problem Optimal execution in a trading game with transient price impact.
method Analyzes high-frequency limit of an n-trader optimal execution game. result High-frequency limit converges to a continuous-time model with quadratic costs.
Study compares Fourier estimators to mitigate asynchrony effects in finance.
problem Impact of asynchrony on instantaneous financial estimates.
method Comparison of Malliavin-Mancino and Cuchiero-Teichmann estimators.
result Malliavin-Mancino estimator produces more stable estimates under asynchrony.
GANSynth uses GANs to efficiently synthesize high-fidelity audio.
problem Efficient and high-fidelity audio synthesis is challenging.
method Model log magnitudes and instantaneous frequencies with GANs.
result GANSynth outperforms WaveNet on automated and human evaluation metrics.
HHT feature generation enhances financial time series forecasting.
problem Forecasting nonstationary financial time series.
method CEEMD and HHT for decomposition, machine learning integration.
result HHT-enhanced models outperform traditional models in forecasting.
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.
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.
Motivated by the need for accurate frequency information, a novel algorithm for estimating the fundamental frequency and its rate of change in three-phase power systems is developed. This is achieved through two stages of Kalman filtering. In the first stage a quaternion extended Kalman filter, which provides a unified…
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…
The paper introduces a new volatility model for state heterogeneous financial markets using high-frequency data.
problem State heterogeneity in financial volatility processes.
method Developed a state heterogeneous GARCH-Ito (SG-Ito) model based on continuous Ito diffusion process.
result Empirical studies reveal various state heterogeneities in S&P 500 index volatility.
New neural network extracts signal components and their IFs from non-uniform samples.
problem Recovering signal components and their IFs from discrete blind-source data.
method Inspired by theory, deep neural network extends Hilbert transform and synchrosqueezed wavelet transform.
result Neural network resolves inverse problem for non-uniformly sampled data.
Proposes overnight volatility model for better market dynamics.
problem Lack of high-frequency data during close-to-open period.
method Itô diffusion model with weighted least squares estimation.
result Developed and validated overnight volatility model.
In this paper, a genetic algorithm-based frequency-domain feature search (GAFDS) method is proposed for the electroencephalogram (EEG) analysis of epilepsy. In this method, frequency-domain features are first searched and then combined with nonlinear features. Subsequently, these features are selected and optimized to …
Study finds roughness in volatility despite diffusive instantaneous volatility.
problem Determining the roughness of volatility in financial assets.
method Non-parametric method based on normalized p-th variation for estimating roughness of sample paths. result Realized volatility exhibits rough behavior with a significantly smaller Hurst exponent than instantaneous volatility.
Modeling price clustering in financial markets using discrete distributions.
problem Price clustering phenomenon in financial markets.
method Discrete price model based on mixture of double Poisson distributions with dynamic volatility and proportions.
result Higher instantaneous volatility weakens price clustering at ultra-high frequencies.
We uniquely and explicitly reconstruct the instantaneous intrinsic metric of the Kerr-Newman Event Horizon from the spectrum of its Laplacian. In the process we find that the angular momentum parameter, radius, area; and in the uncharged case, mass, can be written in terms of these eigenvalues. In the uncharged case th…
A system is presented that segments, clusters and predicts musical audio in an unsupervised manner, adjusting the number of (timbre) clusters instantaneously to the audio input. A sequence learning algorithm adapts its structure to a dynamically changing clustering tree. The flow of the system is as follows: 1) segment…
We prove uniqueness of instantaneously complete Ricci flows on surfaces. We do not require any bounds of any form on the curvature or its growth at infinity, nor on the metric or its growth (other than that implied by instantaneous completeness). Coupled with earlier work, particularly [23, 11], this completes the well…
Paper tackles invariance of demodulation in shallow water acoustic communications.
problem Frequency-selective signal distortion (Doppler effect) in shallow water environments.
method Developed ML-based demodulation methods using DBN-NN and DBN-CNN.
result Demonstrated invariance of the proposed method to Doppler effect with 2dB error margin.
Deep model generates high-quality speech from spectrograms.
problem Speech reconstruction from spectrograms.
method Deep generative model with Gaussian and von Mises distributions for magnitude and phase, variational autoencoder framework.
result Generated speech has high perceptual quality and intelligibility.
New framework IDOL identifies latent causal processes with instantaneous relations from time series data.
problem Identifying latent causal processes with instantaneous relations from time series data.
method Sparse influence constraint and variational inference architecture with sparsity regularization.
result Our method can identify latent causal processes with instantaneous relations.
This paper studies the concept of instantaneous arbitrage in continuous time and its relation to the instantaneous CAPM. Absence of instantaneous arbitrage is equivalent to the existence of a trading strategy which satisfies the CAPM beta pricing relation in place of the market. Thus the difference between the arbitrag…
iCITRIS learns causal variables from interactive systems with instantaneous effects.
problem Identifying causal variables from temporal sequences with instantaneous effects.
method iCITRIS method for causal representation learning that handles instantaneous effects in intervened temporal sequences.
result iCITRIS accurately identifies causal variables and their causal graph from three interactive system datasets.
Study revisits Leland-Toft model with Poisson observation intervals.
problem Optimal capital structure under discrete asset value updates.
method Spectrally negative Lévy model with Poisson observation process.
result Optimal bankruptcy strategy and capital structure derived.
Many problems on signal processing reduce to nonparametric function estimation. We propose a new methodology, piecewise convex fitting (PCF), and give a two-stage adaptive estimate. In the first stage, the number and location of the change points is estimated using strong smoothing. In the second stage, a constrained s…
The Ricci flow preserves product structures with instantaneous curvature bounds.
problem Preserving product structures under Ricci flow with curvature constraints.
method Proving a constant ε exists such that if a solution splits as a product at time 0 and has bounded curvature, it splits for all time.
result A constant ε exists depending on dimension such that if a solution splits as a product at time 0 and has curvature bounded by ε/t, it splits for all time.
Instantaneous volatility estimated from traded volume and spread.
problem Estimating market volatility accurately and quickly.
method Developed a new market invariant linking volatility, traded volume, spread, and order book volume. Used this invariant for instantaneous volatility estimation.
result Instantaneous volatility estimation reproduces realised volatility better than GARCH(1,1) prediction.
We study hedging and pricing of unattainable contingent claims in a non-Markovian regime-switching financial model. Our financial market consists of a bank account and a risky asset whose dynamics are driven by a Brownian motion and a multivariate counting process with stochastic intensities. The interest rate, drift, …
We propose a limit order book (LOB) model with dynamics that account for both the impact of the most recent order and the shape of the LOB. We present an empirical analysis showing that the type of the last order significantly alters the submission rate of immediate future orders, even after accounting for the state of…
A new stochastic volatility model with quadratic drift prevents moment explosions and preserves stock price martingale property.
problem Avoiding moment explosions and preserving stock price martingale property in stochastic volatility models.
method Introduces a one-factor stochastic volatility model with quadratic drift and a linear dispersion function, showing that the quadratic term is crucial.
result The model prevents moment explosions and preserves the martingale property of the stock price process.
Study on Yamabe flow on manifolds with singularities, proving removability.
problem Yamabe flow on manifolds with submanifold singularities.
method Analyzing the Yamabe flow on Riemannian manifolds of dimension m≥3 minus a closed submanifold of dimension n. result Removability of singularities preserved along the Yamabe flow in certain cases.
Collective behaviours taking place in financial markets reveal strongly correlated states especially during a crisis period. A natural hypothesis is that trend reversals are also driven by mutual influences between the different stock exchanges. Using a maximum entropy approach, we find coordinated behaviour during tre…
Study optimal execution in a transient price impact model with multiple traders.
problem Optimal execution among multiple traders with transient price impact.
method Analyzed N-player optimal execution games in an Obizhaeva--Wang model with and without regularization. Derived equilibrium solutions and explained their behavior. result Existence of equilibrium restored with a specific time-dependent cost on block trades, and equilibrium is tractable.
The paper solves portfolio liquidation under transient price impact for 100 NASDAQ stocks.
problem Determining optimal trading strategies under various market impact models.
method Derives explicit solutions for market impact parameters in a portfolio liquidation model.
result The derived strategy achieves significant cost savings compared to benchmark models.
New networks interpret kernel decompositions for signal analysis.
problem Mode decomposition in signal analysis.
method Programmable and interpretable regression networks using kernels and data.
result Near machine precision recovery of signal modes under regularity and separation assumptions.
A new principle minimizes residual and introduces momentum to improve PDE solution dynamics.
problem Ill-conditioning in Dirac-Frenkel residual minimization leads to non-unique parameter dynamics.
method Introduces a history variable (momentum) to select better-conditioned parameter velocities, preserving residual minimization while promoting smooth parameter evolutions.
result The approach leads to increased robustness in singular and near-singular PDE solution regimes.
New model identifies regimes in non-stationary data.
problem Identifying latent regimes in non-stationary systems with instantaneous effects.
method Identifiable Markov Switching Models with exponential family noise.
result Established identifiability of latent regimes and causal structures.
The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued signal into its quadrature component. In this paper, we define a probabilistic gene…
Unified framework for optimal liquidation with small market impact and semimartingale strategies.
problem Optimal liquidation under small market impact and portfolio liquidation.
method Semimartingale strategies and convergence results for BSDEs with singular terminal conditions.
result Unified framework for embedding two common liquidation models and microscopic foundation for semimartingale strategies.
To convert standard Brownian motion Z into a positive process, Geometric Brownian motion (GBM) eβZt,β>0 is widely used. We generalize this positive process by introducing an asymmetry parameter α≥0 which describes the instantaneous volatility whenever the process reaches a new low. For our new process, …
This paper uses deep learning to classify different types of cracks from acoustic emission events.
problem Classifying different types of cracks from acoustic emission events.
method Combining deep neural networks with Bidirectional Long Short Term Memory and statistical analysis.
result Achieves 92% accuracy in classifying different types of cracks.
An average instantaneous cross-correlation function is introduced to quantify the interaction of the financial market of a specific time. Based on the daily data of the American and Chinese stock markets, memory effect of the average instantaneous cross-correlations is investigated over different price return time inte…
We develop a theory for valuing non-diversifiable mortality risk in an incomplete market. We do this by assuming that the company issuing a mortality-contingent claim requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. We apply our method to value life annuities. One result of…
We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. First, we apply our method to price opt…