Torus graphs analyze multivariate phase coupling among brain signals.
problem Identifying coordinated phase changes across multiple brain regions.
method Torus graphs based on full exponential family with pairwise interactions.
result Torus graphs accurately identify conditional associations in multivariate phase data.
M-CaStLe discovers causal structures in multivariate space-time data.
problem Challenges in causal graph discovery for high-dimensional gridded data.
method Generalizes CaStLe to multivariate analyses, using local embeddings and pooling spatial replicates.
result More accurately recovers multivariate causal structure and identifies physical dynamics.
This paper shows how learning the phase-amplitude coupling improves bio-signal classification.
problem Discarding phase component in bio-signal feature extraction leads to poor generalization.
method Introducing a novel self-supervised learning task called Phase-Swap to detect phase-amplitude coupling.
result Neural networks trained on Phase-Swap task generalize better across subjects and recording sessions.
Study oscillatory integrals with degenerate singular points in multivariable phase functions.
problem Analyzing oscillatory integrals with degenerate singular points in phase functions.
method Using asymptotic expansions and results from one variable, the study examines multivariable phase functions.
result Asymptotic expansions of oscillatory integrals for multivariable phase functions with degenerate singular points.
We describe a model for capturing the statistical structure of local amplitude and local spatial phase in natural images. The model is based on a recently developed, factorized third-order Boltzmann machine that was shown to be effective at capturing higher-order structure in images by modeling dependencies among squar…
A new model integrates LSTM and copulas for high-dimensional financial data.
problem Modeling high-dimensional dependencies across financial markets.
method Variational LSTM with regular vine copulas.
result Outperforms benchmarks in cross-market portfolio forecasting.
CAP-BM learns complex-valued data's amplitude and phase distributions.
problem Learning from complex-valued data with amplitude variation.
method Complex Amplitude-Phase Boltzmann machine (CAP-BM) with Gibbs sampling.
result Necessity of amplitude-amplitude coupling term in CAP-BM.
Proves well-posedness for hard phase model in general relativity.
problem Modeling fluid dynamics in curved spacetime.
method A priori estimates and well-posedness in Sobolev spaces, coupled interior-boundary system of wave equations.
result Proves existence and uniqueness of solutions in Sobolev spaces.
This paper presents an introduction to the stochastic concepts of \emph{coupling} and \emph{copula}. Coupling means the construction of a joint distribution of two or more random variables that need not be defined on one and the same probability space, whereas a copula is a function that joins a multivariate distributi…
Study of phase separation and geometry on a closed elastic curve, including dynamics and free energy minimization.
problem Free energy and dynamics of a closed elastic filament coupled to a scalar concentration field.
method Analytical and numerical simulations of coupled Willmore flow and Cahn--Hilliard gradient flow on differential geometry.
result Qualitative changes in free energy landscape due to closure constraint, leading to metastable and stable multi-domain morphologies.
KuramotoGNN uses Kuramoto model to prevent over-smoothing in graph neural networks.
problem Over-smoothing in graph neural networks where node features become indistinguishable.
method Integrates Kuramoto model to prevent phase synchronization and instead achieve frequency synchronization.
result KuramotoGNN reduces over-smoothing on various graph deep learning tasks.
Quantum algorithm estimates multivariate mean with near-optimal efficiency.
problem Estimating the mean of multivariate random variables efficiently in quantum computing.
method Combines amplitude amplification, quantum singular value transformation, and Bernstein-Vazirani algorithm.
result Quantum estimator outperforms classical estimators outside low-precision regime.
New method identifies sepsis-related patient features in EMR data.
problem Identify sepsis-related patient features in EMR data.
method Linear multivariate Hawkes process model with ReLU link function, coupled with gradient-based method.
result Identifies several interpretable GC chains that precede sepsis.
5D SCFTs can have confining vacua with strings and unbroken symmetries.
problem Investigating phases of 5D SCFTs by varying couplings.
method Using geometric realisation of M-theory on metrically conical Calabi-Yau threefolds.
result Many 5D SCFTs have couplings leading to massive, confining vacua with strings and unbroken symmetries.
We examine the out-of-equilibrium phase reported by Plerou {\it et. al.} in Nature, {\bf 421}, 130 (2003) using the data of the New York stock market (NYSE) between the years 2001 --2002. We find that the observed two phase phenomenon is an artifact of the definition of the control parameter coupled with the nature of …
New method tackles convergence issues in approximating FBSDEs.
problem Convergence issues in approximating coupled FBSDEs.
method Approximates initial condition for a family of FBSDEs, then uses it to approximate the original FBSDE.
result Method converges even when standard deep BSDE method fails.
Proposes M-CHMM for robust modeling of multivariate healthcare time series.
problem Challenges in analyzing multivariate healthcare time series data.
method Mixture of coupled hidden Markov models (M-CHMM) with two sampling algorithms.
result Improves data fit, handles missing and noisy measurements, and enhances prediction accuracy.
New method uses spherical convolutional Wasserstein distance to validate climate models.
problem Ensuring the accuracy of global climate models.
method Spherical convolutional Wasserstein distance to measure model differences.
result Phase 6 models show modest improvements in realistic climatologies.
While it is an important problem to identify the existence of causal associations between two components of a multivariate time series, a topic addressed in Runge et al. (2012), it is even more important to assess the strength of their association in a meaningful way. In the present article we focus on the problem of d…
SLS optimizes minimum-volume regions for conditional quantiles, bypassing density estimation.
problem Constructing minimum-volume prediction regions that satisfy conditional coverage.
method Super-level-set regression (SLS) directly optimizes geometric boundaries of conditional level sets.
result SLS optimizes regions directly, capturing complex conditional structures end-to-end.
New method assesses multivariate stochastic dominance using Optimal Transport.
problem Benchmarking models across multiple metrics considering dependencies.
method Characterization of multivariate first stochastic dominance via couplings, entropic regularization, and Optimal Transport.
result Established CLT and consistency for the empirical statistic, enabling hypothesis testing.
Long-term prediction of multivariate time series is still an important but challenging problem. The key to solve this problem is to capture the spatial correlations at the same time, the spatio-temporal relationships at different times and the long-term dependence of the temporal relationships between different series.…
Paper proposes a coupling-based diagnostic for SGD stepsize optimization.
problem Optimizing stepsize for SGD convergence.
method Coupling-based convergence diagnostic for monitoring stationarity.
result Proposed stepsize scheme achieves superior performance across convex and non-convex problems.
Study on synchronization in financial markets with time delays.
problem Understanding market dynamics and synchronization in financial systems with time delays.
method Examined a system of coupled non-linear delay-differential equations, linearized for small delays, and analyzed collective dynamics using bifurcation diagrams and numerical solutions.
result Demonstrated that limit cycles can be maintained in coupled N-asset models with appropriate parameterization, leading to market synchronization.
Stein's method for measuring convergence to a continuous target distribution relies on an operator characterizing the target and Stein factor bounds on the solutions of an associated differential equation. While such operators and bounds are readily available for a diversity of univariate targets, few multivariate targ…
A criterion for training-free time-lagged spectral embeddings of multivariate time series
problem Applicability of fixed-length descriptors for multivariate time series
method Using a stationary Gaussian VAR(1) model and cosine similarity to classify descriptors
result D(τ) separates two classes when signals are approximately stationary and cross-channel temporal coupling is present
Study local topological constraints on Berry curvature in spin-orbit coupled Bose-Einstein condensates.
problem Understanding local topological obstructions to flattening Berry curvature in spin-orbit-coupled Bose-Einstein condensates.
method Adapting Pigazzini-Toda lower bound to Kaluza-Klein setting, analyzing harmonic part of torsion 3-form, and using exact pointwise curvature analysis.
result Obstruction kernel vanishes, preventing complete gauging-away of Berry phases even at zero net topological charge.
Study shows how anisotropic data affects learning dynamics in phase retrieval.
problem Understanding learning dynamics in phase retrieval with anisotropic Gaussian inputs.
method Developed a tractable reduction to reveal a three-phase trajectory and derived scaling laws.
result Found that anisotropy leads to a three-phase trajectory: fast escape, slow convergence, and spectral-tail learning.
We obtain all possible solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield equation exactly, containing configurations made of walls, vortices and monopoles in the Higgs phase. We use supersymmetric U(N_C) gauge theories with eight supercharges with N_F fundamental hypermultiplets in the strong coupling limit. The moduli…
Study of deformed Hermitian Yang-Mills equations with variable Kähler metrics.
problem Solving special Lagrangian type equations with variable metrics.
method Introducing extended gauge group to couple moment maps and scalar curvature.
result Solutions satisfy a mixture of K-stability and Bridgeland-type stability.
Early approaches to multiple-output Gaussian processes (MOGPs) relied on linear combinations of independent, latent, single-output Gaussian processes (GPs). This resulted in cross-covariance functions with limited parametric interpretation, thus conflicting with the ability of single-output GPs to understand lengthscal…
SchNarc combines SchNet and SHARC for efficient photodynamics simulations.
problem Efficiently simulate excited-state dynamics of complex molecules.
method Combines SchNet for multiple electronic states with SHARC for molecular dynamics, learning energies, forces, and couplings.
result Paves the way for efficient photodynamics simulations of complex systems.
Continuous phase transitions identified in Doi-Onsager, noisy transformer, and Hegselmann-Krause models.
problem Phase transitions in multimodal models and their properties.
method Sharp coercivity estimate and constrained Lebedev--Milin inequality.
result Continuous phase transitions at critical coupling strengths for Doi-Onsager, noisy transformer, and Hegselmann-Krause models.
A new method for functional data classification using supervised manifold learning.
problem Improving classification of functional data.
method Supervised manifold learning approach considering label information.
result The proposed method achieves highly competitive performance compared to existing methods.
Probability Density Estimation (PDE) is a multivariate discrimination technique based on sampling signal and background densities defined by event samples from data or Monte-Carlo (MC) simulations in a multi-dimensional phase space. In this paper, we present a modification of the PDE method that uses a self-adapting bi…
We have analyzed the Indices of Industrial Production (Seasonal Adjustment Index) for a long period of 240 months (January 1988 to December 2007) to develop a deeper understanding of the economic shocks. The angular frequencies estimated using the Hilbert transformation, are almost identical for the 16 industrial secto…
We use principle component analysis (PCA) of cross correlations in European government bonds and European stocks to investigate the systemic risk contained in the European economy. We tackle the task to visualize the evolution of risk, introducing the conditional average rolling sum (CARS). Using this tool we see that …
In a complex system, the interactions between individual agents often lead to emergent collective behavior like spontaneous synchronization, swarming, and pattern formation. The topology of the network of interactions can have a dramatic influence over those dynamics. In many studies, researchers start with a specific …
This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the training sample. The estimated uncertainties can be propagated into the optimal…
CoCAI uses copulas for accurate multivariate time-series forecasting and anomaly detection.
problem Accurate multivariate time-series forecasting and robust anomaly detection.
method Copula-based conformal prediction for multivariate time-series analysis.
result CoCAI provides statistically valid predictive regions and robust anomaly scores.
Phase synchronisation in multichannel EEG is known as the manifestation of functional brain connectivity. Traditional phase synchronisation studies are mostly based on time average synchrony measures hence do not preserve the temporal evolution of the phase difference. Here we propose a new method to show the existence…
PH-VAE models heavy-tailed data with flexible Phase-Type distributions.
problem Standard VAEs fail to capture heavy-tailed behavior in real-world data.
method PH-VAE uses Phase-Type distributions defined by continuous-time Markov chains to adaptively model tail behavior.
result PH-VAE significantly outperforms existing heavy-tail-aware VAEs in approximating diverse heavy-tailed distributions.
We show that multivariate Hawkes processes coupled with the nonparametric estimation procedure first proposed in Bacry and Muzy (2015) can be successfully used to study complex interactions between the time of arrival of orders and their size, observed in a limit order book market. We apply this methodology to high-fre…
Metabolic flux balance analyses are a standard tool in analysing metabolic reaction rates compatible with measurements, steady-state and the metabolic reaction network stoichiometry. Flux analysis methods commonly place unrealistic assumptions on fluxes due to the convenience of formulating the problem as a linear prog…
We study cascades on a two-layer multiplex network, with asymmetric feedback that depends on the coupling strength between the layers. Based on an analytical branching process approximation, we calculate the systemic risk measured by the final fraction of failed nodes on a reference layer. The results are compared with…
Cryptocurrencies are increasingly correlated with traditional financial markets.
problem Determining the independence of cryptocurrencies from traditional financial markets.
method High-frequency detrended cross-correlation analysis over various time scales and market periods.
result Cryptocurrencies have become more aligned with traditional financial markets, especially during bear phases.
Deep neural network approximates multivariate option pricing.
problem High-dimensional partial differential equations in option pricing.
method Deep parametric PDE method using neural networks.
result Option prices computed in milliseconds for up to 25 dimensions.
Researchers calculate Hofer-Zehnder capacity for twisted tangent bundles over surfaces.
problem Determining the Hofer-Zehnder capacity for specific geometric configurations.
method Analyzing constant magnetic fields on closed surfaces and using equivariant compactification.
result Explicit calculations and compactifications for phase and configuration spaces.