This paper presents a new algorithm, termed \emph{truncated amplitude flow} (TAF), to recover an unknown vector from a system of quadratic equations of the form , where 's are given random measurement vectors. This problem is known to be \emph{NP-hard} in genera…
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48 results for “amplitude flow”
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.
Solving Large-scale Systems of Random Quadratic Equations via Stochastic Truncated Amplitude Flowcs.IT
A novel approach termed \emph{stochastic truncated amplitude flow} (STAF) is developed to reconstruct an unknown -dimensional real-/complex-valued signal from `phaseless' quadratic equations of the form . This problem, also known as phase retrieval from magnitude-onl…
A new deep learning model improves phase retrieval performance.
problem Recovering signals from phaseless measurements.
method Hybrid model-based data-driven deep architecture (Unfolded Phase Retrieval, UPR).
result Significant improvement in phase retrieval performance.
A new RBM model handles both linear and log-amplitude spectrograms.
problem Handling amplitude spectra with existing models.
method Proposed gamma-Bernoulli RBM that uses gamma distribution.
result The model can naturally handle positive numbers and log-amplitude spectrograms.
A new spinorial heat flow framework studies geometric degeneration on 3-manifolds.
problem Analyzing geometric degeneration on 3-manifolds via spinor dynamics.
method Introducing a spinorial heat flow governed by the squared Dirac operator, where the metric is induced conformally by the spinor amplitude.
result Degeneration of the induced metric corresponds to nodal behavior of the spinor field.
Quantum computer method for pricing rainbow options efficiently.
problem Pricing rainbow options with quantum computers.
method Iterative Quantum Amplitude Estimation and amplitude loading techniques.
result Validation of quantum pricing model on IBM QASM simulator.
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.
New insights connect strong coupling SYM amplitudes to hyperkähler geometry.
problem Understanding strong coupling SYM amplitudes.
method Integrable systems, pseudo-hyperkähler geometry, twistor theory.
result Remainder function is a pseudo-Kähler scalar in hyperkähler geometry.
A fast method for estimating radar amplitude density parameters.
problem Accurate estimation of amplitude density function parameters in radar applications.
method Projecting amplitude data onto horizontal and vertical axes, then using MLE for -stale distribution parameters.
result The average of computed MLEs based on two projections is a fast and accurate estimator for amplitude distribution parameters.
Improved formulation of spinfoam quantum gravity with cosmological constant, ensuring all amplitudes are finite and providing semiclassical asymptotics.
problem Ensuring the finiteness of spinfoam amplitudes and providing semiclassical asymptotics for quantum gravity.
method Using state-integral model of PSL(2, ) Chern-Simons theory and implementing simplicity constraint.
result All spinfoam amplitudes are finite and provide semiclassical asymptotics with oscillatory terms related to the Regge action.
Atiyah classes of DG manifolds of positive amplitude are invariant under weak equivalences.
problem Defining and studying Hochschild cohomology of DG manifolds of positive amplitude.
method Using poly-differential operators and derived intersection, proving invariance under weak equivalences.
result Hochschild cohomology of DG manifolds of positive amplitude is invariant under weak equivalences.
Exact Multivariate Amplitude Distributions for Non-Stationary Gaussian or Algebraic Fluctuations of Covariances or Correlationscond-mat.dis-nn
The paper provides exact multivariate amplitude distributions for non-stationary Gaussian or algebraic fluctuations.
problem Capturing the statistical properties of fluctuating correlations in non-stationary systems.
method Developed a random matrix model to average multivariate amplitude distributions from short time scales to large time scales.
result Explicit multivariate distributions for non-stationary correlation systems are provided, capturing the degree of non-stationarity.
We define a topological quantum membrane theory on a seven dimensional manifold of holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is quantum amplitudes of non-local observables …
Paper computes Atiyah class for DG manifolds of amplitude +1.
problem Computing the Atiyah class for DG manifolds of specific amplitude.
method Computed the Atiyah class by encoding the derived intersection of sections and zero sections of vector bundles.
result Atiyah class vanishes if and only if the intersection is clean.
We demonstrate the equivalence of all loop closed topological string amplitudes on toric local Calabi-Yau threefolds with computations of certain knot invariants for Chern-Simons theory. We use this equivalence to compute the topological string amplitudes in certain cases to very high degree and to all genera. In parti…
PolarBM models complex-valued audio signals in polar coordinates, improving over conventional methods.
problem Discarding structural information in complex-valued problems simplifies models but loses important amplitude-phase relationships.
method Proposes PolarBM, a novel Boltzmann machine for complex-valued variables in polar coordinates, and LogPolarBM for logarithmic amplitude.
result PolarBM and LogPolarBM achieve superior modeling accuracy compared to conventional models, including deep neural networks.
We introduce a fully coherent spin network amplitude whose expansion generates all SU(2) spin networks associated with a given graph. We then give an explicit evaluation of this amplitude for an arbitrary graph. We show how this coherent amplitude can be obtained from the specialization of a generating functional obtai…
Common perpendiculars equidistribute in negatively curved spaces.
problem Equidistribution of common perpendiculars in negatively curved spaces.
method Analyzing the Bowen-Margulis measure and geodesic flow properties.
result Lebesgue measures of common perpendiculars equidistribute to the Bowen-Margulis measure.
We study topological open string amplitudes on orientifolds without fixed planes. We determine the contributions of the untwisted and twisted sectors as well as the BPS structure of the amplitudes. We illustrate our general results in various examples involving D-branes in toric orientifolds. We perform the computation…
The paper proves a category of dg manifolds with finite positive amplitude.
problem Understanding the structure of dg manifolds with finite positive amplitude.
method Using path spaces and homotopy transfer theorem for curved -algebras.
result Proves that dg manifolds of finite positive amplitude form a category of fibrant objects.
Algorithm finds frequencies, amplitudes, and phases of sinusoids in noisy data.
problem Finding frequencies, amplitudes, and phases of sinusoids in noisy data.
method Maximum likelihood approach to estimate tone parameters from contaminated observations. Successively estimates frequencies and jointly optimizes amplitudes and phases.
result Near-linear computational complexity (O(N)) for estimating number of sinusoidal sources.
We decompose the exchange rates returns of 41 currencies (incl. gold) into their sign and amplitude components. Then we group together all exchange rates with a common base currency, construct Minimal Spanning Trees for each group independently, and analyze properties of these trees. We show that both the sign and the …
Geodesics in Sol geometry described with invariant k and spiral properties.
problem Understanding the geodesic flow in the Sol geometry.
method Self-contained geometric description and analysis of geodesics.
result Characterization of geodesic segments, cut locus, and asymptotic distance growth.
We show how the amplitude of holonomies on a vector bundle can be controlled by the integral of the curvature of the connection on a surface enclosed by the curve.
Spectral flow connects manifold geometry to rigidity criteria.
problem Tackling rigidity of simply-connected closed manifolds.
method Spectral deformation flow and invariant-based approach.
result Spherical profile is the unique manifold-compatible asymptotic realization.
The paper analyzes the amplitude of functions on the sphere, improving FDA methods.
problem Analyzing trajectories on non-linear manifolds with time variability.
method Developed tools for temporal alignment, geodesic computation, and mean calculation on .
result Efficient and accurate tools for analyzing manifold-valued functions on .
Transformers predict scattering amplitudes in theoretical physics.
problem Computing exact coefficients of scattering amplitudes in N = 4 SYM theory.
method Applied Transformers to predict integer coefficients of scattering amplitudes.
result Transformers achieve high (> 98%) accuracy on predicting scattering amplitudes.
The transition amplitudes between coherent states on a coherent state manifold are expressed in terms of the embedding of the coherent state manifold into a projective Hilbert space. Consequences for the dimension of projective Hilbert space and a simple geometric interpretation of Calabi's diastasis follows.
Proposes a new complex Gaussian distribution for better modeling of complex-valued signals.
problem Limited ability of Gaussian distribution to represent diverse amplitude characteristics.
method Introduces a power-weighted noncentral complex Gaussian distribution on the complex plane.
result Consistently outperforms conventional distributions in log-likelihood for speech power spectra.
Improves generative models by adding jump-diffusion noise.
problem Limited performance of diffusion models in generating samples from unknown distributions.
method Generalizes diffusion processes to include jump-diffusion noise, deriving closed-form generalized score functions.
result Jump-diffusion models outperform Gaussian models in specific parameter regimes.
Geometric phase and modulus relations for SU(n) matrix elements in the defining representationmath-ph
A set of relations between the modulus and phase is derived for amplitudes of the form $\mels{\hatu(x)}$ where in the fundamental representation and denotes the coordinates on the group manifold. An illustration is given for the case as well as a brief discussion of phase singularities …
Gaussian beams describe the amplitude and phase of rays and are widely used to model acoustic propagation. This paper describes four new results in the theory of Gaussian beams. (1) A new version of the Červený equations for the amplitude and phase of Gaussian beams is developed by applying the equivalence of Hamilton-…
NeuralFLoC unifies registration and clustering of functional data, overcoming phase variation challenges.
problem Challenges in clustering functional data due to phase variation and temporal misalignment.
method NeuralFLoC uses Neural ODE-driven diffeomorphic flows and spectral clustering for joint registration and clustering.
result NeuralFLoC effectively disentangles phase and amplitude variation, achieving state-of-the-art performance.
Quantum tech speeds up financial risk assessment.
problem Improving credit valuation adjustments using quantum mechanics.
method Developed a quantum algorithm using Bayesian quantum amplitude estimation and engineered likelihood functions.
result Significant speedup in quantum computations for CVA over classical methods.
Study uses ML to forecast ionospheric scintillation severity.
problem Predicting amplitude scintillation severity using real-time data.
method Developed and tested six ML models, XGBoost being the most effective.
result XGBoost model achieved 77% prediction accuracy for scintillation severity.
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For a real mode, we wish to infer its damping rate and mode shape. For a complex mod…
Enhances quantum sensing by eliminating multiple oscillations in field amplitude estimation.
problem Multiple oscillations in field amplitude estimation due to inter-qubit interactions at high qubit densities.
method Adopting a quantum circuit learning framework to approximate a target function by optimizing gate parameters.
result Elimination of multiple oscillations, leading to enhanced dynamic range of quantum sensing.
Quantum algorithm speeds up pricing of financial derivatives.
problem Pricing autocallable options efficiently.
method Integration-based exponential amplitude loading technique.
result 50x reduction in circuit depth for payoff component.
Adaptive sampling results in dramatic improvements in the recovery of sparse signals in white Gaussian noise. A sequential adaptive sampling-and-refinement procedure called Distilled Sensing (DS) is proposed and analyzed. DS is a form of multi-stage experimental design and testing. Because of the adaptive nature of the…
Developing tools for computing string amplitudes with hyperbolic vertices.
problem Computing off-shell string amplitudes with new vertices.
method Constructing local coordinates and investigating limits for hyperbolic three-string vertex.
result Derived conservation laws and performed sample computations.
Quantum method improves CVaR evaluation under correlated fields.
problem Accurately evaluating CVaR in high-dimensional, correlated material uncertainty.
method Quantum-enhanced inference framework using stabilized IQAE.
result Quantum method achieves lower oracle complexity than classical methods.
We derive an analytic formula for the hydrodynamic Green function and the Robin function on every orientable surface admitting a hydrodynamic Killing vector field. Closed-form expressions are provided for all fourteen canonical Riemann surfaces, covering both compact and non-compact cases; the formulae satisfy the slip…
Algorithm samples constrained stochastic differential equations.
problem Sampling stochastic differential equations with complex constraints.
method Pathspace Metropolis-adjusted manifold sampling.
result Demonstrated effectiveness in various constrained conditions.
New sigma models compute graviton scattering amplitudes from quaternionic geometry.
problem Computing graviton scattering amplitudes from quaternionic geometry.
method Introducing new twistor sigma models that encode finite non-linear perturbations of flat structures.
result Provides a first-principles derivation of Hodges' formula for MHV graviton amplitudes.
A Björling Representation for Jacobi Fields on Minimal Surfaces and Soap Film Instabilitiescond-mat.soft
We develop a general framework for the description of instabilities on soap films using the Björling representation of minimal surfaces. The construction is naturally geometric and the instability has the interpretation as being specified by its amplitude and transverse gradient along any curve lying in the minimal sur…
This letter presents a novel Block Bayesian Hypothesis Testing Algorithm (Block-BHTA) for reconstructing block sparse signals with unknown block structures. The Block-BHTA comprises the detection and recovery of the supports, and the estimation of the amplitudes of the block sparse signal. The support detection and rec…
In order to understand the origin of stock price jumps, we cross-correlate high-frequency time series of stock returns with different news feeds. We find that neither idiosyncratic news nor market wide news can explain the frequency and amplitude of price jumps. We find that the volatility patterns around jumps and aro…