Study proves existence of weak solutions for volume-preserving mean curvature flow using phase field method.
problem Existence of weak solutions for volume-preserving mean curvature flow.
method Phase field method applied to reaction-diffusion equation with nonlocal term.
result Existence of weak solutions proved for the volume-preserving mean curvature flow.
Data-driven approach learns effective equations for phase field interfaces.
problem Learning accurate equations for phase field interface dynamics.
method Data-driven identification of partial differential equations from phase field data.
result Data-driven equations outperform analytical approximations in certain regimes.
We explore a computational model of an incompressible fluid with a multi-phase field in three-dimensional Euclidean space. By investigating an incompressible fluid with a two-phase field geometrically, we reformulate the expression of the surface tension for the two-phase field found by Lafaurie, Nardone, Scardovelli, …
A time schedule simplifies learning in flow-based models for high-dimensional data.
problem Disappearance of relative probability phase in high-dimensional Gaussian mixture sampling.
method Introduces a time dilation schedule to characterize phases of learning.
result Autoencoder learns to simplify by focusing on relevant parameters for each phase.
New methods reveal compatible liquid crystal phases in 3D.
problem Understanding compatible director fields in 3D liquid crystals.
method Re-derived compatibility conditions using vector calculus.
result Characterized a wide range of compatible liquid crystal phases.
Deep learning predicts phase segregation in binary mixtures.
problem Predicting phase segregation in binary mixtures.
method Conditional generative convolutional neural networks.
result Deep learning model accurately predicts phase segregation up to 98%.
Optimizes structure topology for ductile and brittle fracture resistance.
problem Minimizing mass while ensuring structural damage and fracture resistance.
method Phase-field approach for modeling fracture, level-set topology optimization.
result Enhanced fracture resistance through two formulations.
Method generates dense fields from sparse measurements without needing spatial statistics or examples.
problem Generating dense physical fields from sparse measurements.
method Introduces a differentiable numerical simulator into neural network training.
result Superior results on fluid mechanics problems compared to statistical and neural network methods.
In this paper we study vector fields on the big phase space of Gromov-Witten theory which are idempotents of the quantum product. Such vector fields can be used to simplify universal equations for higher genus Gromov-Witten invariants.
Analyzes market phases using bipartite model to predict crises.
problem Identifying market phases and predicting crises.
method Bipartite market model, mean field approximation, analytical derivation.
result Identifies three phases: stable, unstable, and boom-bust periods.
We start by analysing the Lie algebra of Hermitian vector fields of a Hermitian line bundle. Then, we specify the base space of the above bundle by considering a Galilei, or an Einstein spacetime. Namely, in the first case, we consider, a fibred manifold over absolute time equipped with a spacelike Riemannian metric, a…
Study shows reverberant phase is not essential for weakly-supervised dereverberation.
problem Evaluating the role of reverberant phase in weakly-supervised dereverberation.
method Statistical Wave Field Theory and recent weak supervision framework.
result Wet phase carries limited useful information and is not essential for weakly supervised dereverberation.
LoRA fine-tuning causes forgetting, studied via particle system dynamics.
problem Catastrophic forgetting in LoRA fine-tuning.
method Mean-field self-attention model, partial differential equations, dynamical systems.
result Characterization of phase transitions in forgetting behavior.
Stability inequalities for specific solutions in high dimensions.
problem Stability of solutions to the one-phase Bernoulli problem.
method Proving strict stability inequalities for cohomogeneity one solutions with bi-orthogonal symmetry.
result Strict stability for cohomogeneity one solutions in dimensions 7 and above.
Universal model for soft tissue mechanics under shock waves.
problem Modeling shock wave mechanics in soft biological tissues.
method Continuum mixture theory with phase-field mechanics.
result Universal thermodynamically consistent formulation for soft porous tissues.
The dynamics of an ideal fluid or plasma is constrained by topological invariants such as the circulation of (canonical) momentum or, equivalently, the flux of the vorticity or magnetic fields. In the Hamiltonian formalism, topological invariants restrict the orbits to submanifolds of the phase space. While the coadjoi…
Generative diffusion models exhibit phase transitions in statistical mechanics, impacting their performance.
problem Understanding the performance and capabilities of generative diffusion models.
method Reformulating generative diffusion models using statistical mechanics, focusing on phase transitions and symmetry breaking.
result Generative diffusion models undergo second-order phase transitions with mean-field universality, critical instability, and mean-field critical exponents.
Paper proposes a new method for sparse phase retrieval with fewer measurements.
problem Sparse phase retrieval in various fields.
method Stochastic alternating minimizing method (StormSpar) with HTP algorithm.
result The method recovers sparse signals from fewer measurements than existing methods.
The covariant phase space of a Lagrangian field theory is the solution space of the associated Euler-Lagrange equations. It is, in principle, a nice environment for covariant quantization of a Lagrangian field theory. Indeed, it is manifestly covariant and possesses a canonical (functional) "presymplectic structure" w …
New method optimizes objective function for vector field dynamics.
problem Neuroscientists' doubts about backpropagation algorithm.
method Two-phase learning procedure for fixed point recurrent networks.
result Algorithm optimizes objective function without computing true gradient.
Study sharp interface limit of Allen-Cahn equation to characterize mean curvature flow with boundary conditions.
problem Characterizing mean curvature flow with Dirichlet or dynamic boundary conditions.
method Varifold formulation, phase field method, extending Brakke flow.
result Sharp interface limit of Allen-Cahn equation converges to mean curvature flow with boundary conditions.
A learning algorithm optimizes beamforming for holographic transceivers in far-field communication.
problem Optimal phase-shifts for beamforming in holographic transceivers are challenging due to unknown receiver locations and large phase-shifts.
method Developed a learning algorithm using a fixed-budget multi-armed bandit framework to learn optimal phase-shifts.
result The algorithm, HoloBeam, outperforms state-of-the-art methods in beamforming optimization.
New method for flux quantization on phase space stacks.
problem Defining and constructing flux-quantized phase space stacks.
method Observation of flux densities and characterization of Cauchy data.
result Flux-quantized phase space stacks have classifying spaces with rational Whitehead L-infinity algebra.
Unified method for constructing non-vacuum initial data sets in general relativity.
problem Constructing solutions of Einstein constraint equations with coupled matter sources.
method Phase space representation and scaling of matter fields.
result Semi-decoupling of conformal constraint equations for constant-mean curvature initial data.
Improved QSM maps from MRI using deep learning.
problem Inaccurate susceptibility maps due to ill-posed dipole inversion.
method 3D GAN with increased receptive field and WGAN with gradient penalty.
result Significantly better QSM maps from single orientation phase maps.
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.
New algorithm reduces autocorrelation in HMC for lattice field theories.
problem Reduction of autocorrelation in HMC for lattice field theories.
method Hybrid Monte-Carlo algorithm with restricted Boltzmann machine.
result Reduction of autocorrelation in both symmetric and broken phases.
We present a generalization of the Nambu mechanics on the base of Liouville's theorem. We prove that the Poisson structure of an n-dimensional multisymplectic phase space is induced by (n-1)-Hamiltonian k-vector field seach of which requires introduction of k-Hamiltonians.
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.
New method shows stable phase synchronised patterns in EEG signals during face perception tasks.
problem Traditional phase synchronisation measures do not capture temporal evolution.
method Proposes a new method to identify synchrostates, small sets of unique phase synchronised patterns.
result Consistent existence of synchrostates in multi-channel EEG recordings across different subject groups.
In this work, we use the Sternberg phase space (which may be considered as the classical phase space of particles in gauge fields) in order to explore the dynamics of such particles in the context of Hamilton-Dirac systems and their associated Hamilton-Pontryagin variational principles. For this, we develop an analogue…
Gradient descent variants improve phase retrieval accuracy.
problem Phase retrieval problem in high-dimensional spaces.
method Gradient descent, stochastic gradient descent, Langevin algorithm, dynamical mean-field theory.
result Stochastic variants of gradient descent achieve better generalization in phase retrieval.
Novel M-theory approach classifies topological phases of matter.
problem Classifying and understanding topological phases of matter.
method Establishing a correspondence between (2+1)d topological field theories and non-hyperbolic 3-manifolds, identifying topological phases from internal wrapped 3-manifolds.
result Paves a new route toward the classification of topological phases of matter, including fermionic and non-unitary phases.
The paper simplifies complex gauge field theory using symplectic methods.
problem Simplifying complex gauge field theory models.
method Singular symplectic cotangent bundle reduction in the Fréchet setting.
result The Higgs sector's singular structure is encoded in a finite-dimensional Lie group action.
Continuum mechanics theory describes skin's complex anisotropic behavior.
problem Modeling the anisotropic tearing of skin.
method Finsler geometry fiber bundle approach, variational method, phase-field mechanics.
result Analytical solutions capture experimental data on skin tearing.
A k-space deep learning method corrects EPI ghost artifacts without a reference scan.
problem Nyquist ghost artifacts in EPI MRI due to phase mismatch between even and odd echoes.
method Structured low-rank Hankel matrix approaches combined with data-driven Hankel matrix decomposition and deep convolutional neural networks.
result The proposed k-space deep learning method outperforms existing methods in image quality and computing time.
New model considers spontaneous curvature for lipid bilayer membranes, including discontinuities.
problem Modeling discontinuities at interfaces in lipid bilayer membranes.
method Introduced a family of energies for smooth surfaces and phase fields, derived a sharp interface limit.
result Theoretical result extends classical model by assigning bending energy to tangential discontinuities.
Machine learning predicts failure in brittle materials with high accuracy.
problem Predicting failure in brittle materials under repetitive loads.
method Phase-field model combined with supervised machine learning.
result Framework predicts failure with acceptable accuracy even in noisy data.
Researchers found 5 local fields to uniquely describe 3D director fields, related through 6 differential relations.
problem Understanding the compatibility conditions for 3D director fields.
method Employed the method of moving frames.
result A director field is fully determined by five local fields related through six differential relations.
We study the indefinite metric G in the contact phase space (P,θ) of a homogeneous thermodynamical system introduced by R. Mrugala. We calculate the curvature tensor, Killing vector fields, second fundamental form of Legendre submanifolds of P - constitutive surfaces of different homogeneous thermodynamical syste…
The paper analyzes the dynamics of tokens in transformer models at moderate interaction levels.
problem Understanding the evolution of tokens in transformer models at moderate interaction levels.
method Modeling transformer models as a system of particles interacting in a mean-field way and studying the corresponding dynamics.
result Characterization and convergence of the limiting dynamics in different phases of the system.
This paper is concerned with basic geometric properties of the phase space of a classical general relativistic particle, regarded as the 1st jet space of motions, i.e. as the 1st jet space of timelike 1--dimensional submanifolds of spacetime. This setting allows us to skip constraints. Our main goal is to determine the…
Study detects signal in financial stock correlations using phase-ordering kinetics.
problem Detecting meaningful signals in financial stock return correlations.
method Stochastic field theory model to establish a detection threshold.
result Detection of a signal in the largest eigenvalues of the stock return correlation matrix.
Study of kinks in curves mimicking lipid bilayers.
problem Understanding spontaneous curvature in lipid bilayers.
method Introducing energies for smooth curves and phase fields, showing Γ-convergence to curves with kinks.
result Theoretical result of energies converging to curves with a finite number of kinks.
We consider the problem of learning the structure of Ising models (pairwise binary Markov random fields) from i.i.d. samples. While several methods have been proposed to accomplish this task, their relative merits and limitations remain somewhat obscure. By analyzing a number of concrete examples, we show that low-comp…
High-dimensional random geometry shows phase transitions in various problems.
problem Phase transitions in high-dimensional random geometry.
method Analysis of various financial, optimization, and ecological problems.
result Links between seemingly distant fields and further ramifications.
New proof confirms De Giorgi's conjecture about phase-field approximation of Willmore functional.
problem Proving a conjecture about the phase-field approximation of the Willmore functional.
method Using Γ-convergence and properties of the Allen-Cahn energy and its variations.
result The original De Giorgi conjecture holds with k=0.
Formula for integral on supermanifolds using stationary phase approximation.
problem Calculating integrals on supermanifolds with invariant densities.
method Stationary phase approximation and Morse-Bott Lemma extension to supermanifolds.
result Formula for integral in terms of neighborhood values of invariant density.