New algorithm recovers vectors from quadratic equations with high probability.
problem Recovering unknown vectors from quadratic equations with random measurements.
method Truncated Amplitude Flow (TAF) algorithm, two-stage approach.
result TAF recovers the solution exactly with high probability and linear complexity.
STAF solves large-scale phase retrieval problems from magnitude-only measurements.
problem Phase retrieval from magnitude-only quadratic equations.
method STAF is a novel iterative approach combining stochastic variance reduced gradient and stochastic truncated gradient iterations.
result STAF can recover any signal exactly from about 2.3n magnitude-only measurements, outperforming existing methods.
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.
The paper provides estimates for flows on Riemannian manifolds using truncated expansions.
problem Quantifying the relationship between flows on Riemannian manifolds and their truncated logarithms.
method Using truncated versions of the Magnus and Baker-Cambel-Hausdorff-Dynkin expansions.
result Quantitative estimates between flows and their truncated logarithms.
SeqRF straightens generative model flows to speed up sampling.
problem High global truncation error in ODE-based solvers for generative models.
method SeqRF, a learning technique that straightens the probability flow.
result Significantly improved sampling speed and synthesis quality.
We accelerate CNF by reducing ODE truncation errors with polynomial regularization.
problem High computation cost of CNF due to large truncation errors in solving ODEs.
method Add polynomial regularization to approximate ODE trajectories with polynomial functions.
result 42.3% to 71.3% reduction of NFE on density estimation, 19.3% to 32.1% on variational auto-encoder.
Derives equations for deep learning biases and weights, showing data complexity reduction.
problem Understanding interpretability in supervised learning.
method Gradient flow equations and dynamical truncation of training data.
result Data complexity reduction at an exponential rate with training.
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.
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.
Given a compact three-manifold together with a Riemannian metric, we prove the short-time existence of a solution to the renormalization group flow, truncated at the second order term, under a suitable hypothesis on the sectional curvature of the initial metric.
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.
A new method prices time-to-event cash flows using survival analysis.
problem Pricing insurance investment portfolios with time-to-event cash flows.
method Discrete-time survival analysis framework, hazard rate estimators, asymptotic multivariate normality.
result Pricing model yields estimates closer to actual cash flows than non-random models.
Ancient solutions to curve shortening flow are constructed and analyzed.
problem Constructing ancient solutions to curve shortening flow.
method Analyzing the rotating Yin-Yang soliton and Grim Reaper translating soliton to approximate the solution.
result An ancient solution to planar curve shortening is constructed and analyzed.
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 α-stale distribution parameters. result The average of computed MLEs based on two projections is a fast and accurate estimator for amplitude distribution parameters.
Study of flow in hyperbolic space with capillary boundary.
problem Optimizing hypersurfaces with capillary boundary in hyperbolic space.
method Mean curvature flow with capillary boundary, preserving volume and energy.
result Flow converges to a truncated umbilical hypersurface.
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, C) 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.
Holonomy amplitudes controlled by curvature on bundle surfaces.
problem Controlling holonomy amplitudes in vector bundles.
method Controlled by the integral of curvature on a surface.
result Holonomy amplitudes are bounded by curvature integrals.
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.
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 G2 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 CY3×S1 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.
New algorithm solves quadratic equations from magnitude measurements efficiently.
problem Solving quadratic system of equations from magnitude measurements.
method Gradient-like algorithm (RWF) minimizing nonconvex nonsmooth loss function.
result RWF converges geometrically to global optimal point with optimal sample complexity.
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.
Paper proposes a new generative model for discrete distributions using flows on submanifolds.
problem Discretization issues and complex statistical dependencies in discrete data.
method Continuous normalizing flows on factorizing discrete measures, geodesic flow matching.
result Efficient training and broad applicability demonstrated through experiments.
Reference metrics are used to define the differential structure on multicube representations of manifolds, i.e., they provide a simple and practical way to define what it means globally for tensor fields and their derivatives to be continuous. This paper introduces a general procedure for constructing reference metrics…
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…
Novel Bayesian prior for neural networks encodes amplitude and lengthscale.
problem Lack of user-friendly priors for specifying basic properties in Bayesian neural networks.
method Introduced Poisson Process Radial Basis Function Networks (PP-RBFN) as a novel prior.
result PP-RBFN allows decoupled specification of amplitude and lengthscale, and estimated function is consistent.
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 develops methods to infer modes of linear systems from noisy data.
problem Detecting oscillations in power flow in AC electrical networks.
method Develops methods to infer modes (real or complex) from observations of linear systems forced by Gaussian noise.
result Inference of damping rates, frequencies, and mode shapes for real and complex modes.
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 L∞[1]-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 M number of sinusoidal sources. 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.
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.
Empirical data of supermarket sales show stylised facts that are similar to stock markets, with a broad (truncated) Levy distribution of weekly sales differences in the baseline sales [R.D. Groot, Physica A 353 (2005) 501]. To investigate the cause of this, the influence of social interactions and advertisements are st…
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 …
This paper uses combinatorial Ricci flow to tackle Thurston's triangulation conjecture.
problem Thurston's triangulation conjecture for hyperbolic 3-manifolds.
method Combinatorial Ricci flow approach to prove convergence and geometric decompositions.
result Combinatorial Ricci flow converges if and only if the triangulation is geometric.
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 S2. result Efficient and accurate tools for analyzing manifold-valued functions on S2. 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.
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.
Normalizing flows model atomic solids without needing ground-truth samples.
problem Modeling atomic solids without ground-truth samples.
method Normalizing flows to transform a base distribution into the target solid.
result Excellent agreement between model estimates and literature values for Helmholtz free energy.
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-…
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.
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.