Study uses neural networks to predict wall quantities in turbulent flows.
problem Predicting wall quantities in turbulent open channel flows.
method Training convolutional neural networks (FCN) and a proposed R-Net architecture to predict wall-shear-stress and wall pressure.
result R-Net architecture performs better and predicts wall quantities with around 10% error.
Neural networks predict flow and elastic stresses in viscoelastic turbulence.
problem Predicting flow and elastic stresses in viscoelastic turbulent flows using limited experimental data.
method Convolutional neural networks trained on wall-normal velocity and pressure data.
result Neural networks accurately predict flow and elastic stresses, especially during low-drag events.
Modeling aortic wall inhomogeneities to predict dissection risks.
problem Predicting localized stress accumulations in the aortic wall due to inhomogeneities.
method Stochastic constitutive model with random field realizations, coupled with a convolutional neural network surrogate.
result The neural network accurately predicts stress distributions and assesses uncertainty in aortic wall stress.
ZerNet improves aneurysm wall stress estimation.
problem Estimating wall stress of cerebral aneurysms using ConvNets.
method ZerNet, a geometric ConvNet that generalizes convolution and pooling operations on manifolds.
result ZerNet outperforms state-of-the-art geometric ConvNets in aneurysm wall stress estimation.
Neural network predicts turbulence from wall shear stress.
problem Predicting wall-bounded turbulence from wall quantities.
method Fully-convolutional neural network trained on DNS data.
result Improved prediction of turbulence fields and statistics.
Convolutional networks predict turbulence from wall quantities.
problem Predicting turbulence fields from wall-shear-stress components and wall pressure.
method Two CNN models: FCN and FCN-POD, trained on DNS data.
result FCN and FCN-POD models outperform EPOD in predicting turbulence fields.
Study rigidity in Riemannian manifolds using Pohozoaev and P-function approaches.
problem Rigidity in Serrin's overdetermined problems in Riemannian manifolds.
method Prove a Pohozoaev-type identity, use conformal vector field, and apply P-function approach.
result Show Serrin's type rigidity result in Riemannian manifolds.
New framework predicts arterial blood pressure from MRI data using physics-informed neural networks.
problem Clinical applicability of predictive cardiovascular flow models is hindered by computational cost and tedious pre-processing.
method Physics-informed neural networks constrained by conservation of mass and momentum principles.
result Deep neural networks provide physically consistent predictions for arterial blood pressure without conventional simulators.
Describes Wall's finiteness obstruction.
problem Finiteness obstruction in algebraic topology.
method Self-contained description of Wall's finiteness obstruction.
result Comprehensive explanation of Wall's finiteness obstruction.
A new ES method improves reinforcement learning speed and accuracy.
problem Slow convergence and local maxima in reinforcement learning.
method Directional Gaussian Smoothing Evolution Strategy (DGS-ES)
result DGS-ES accelerates RL training with high accuracy and nonlocal search direction.
This paper studies the interplay between the N=2 gauge theories in three and four dimensions that have a geometric description in terms of twisted compactification of the six-dimensional (2,0) SCFT. Our main goal is to construct the three-dimensional domain walls associated to any three-dimensional cobordism. We find t…
New G2-holonomy manifolds from 5d N=1 theories domain walls.
problem Geometrizing domain walls in 5d N=1 theories.
method Constructing 7-manifolds by fibering a Calabi-Yau over a real line.
result 7-manifolds with G2-holonomy from domain walls in 5d theories. Paper solves Serrin problem for ring-shaped domains, showing velocity has finitely many maxima.
problem Characterizing rotationally symmetric solutions to a specific PDE on a ring-shaped domain.
method Introduced new arguments in the spirit of comparison geometry to overcome the lack of monotonicity.
result Simplest conditions are not sufficient; rotational symmetry requires finitely many maxima.
HFNO enhances interpretability of turbulent flows through parallel wavenumber bin processing.
problem Opaque inner workings of Fourier Neural Operators (FNOs) hinder physical interpretability.
method Introduces HFNO, a novel FNO-based architecture that processes wavenumber bins in parallel, enhancing interpretability.
result HFNO decomposes turbulent flows across various scales, enabling increased interpretability and multiscale modeling.
Study connects Morse theory with cluster variables for wall-crossing in Cerf diagrams.
problem Understanding wall-crossing in Cerf theory.
method Relates Bruhat numbers in real Morse theory to cluster variables in braid varieties.
result Provides wall-crossing coordinates in Cerf diagrams.
We explain how to adapt a construction of M. Sageev's to construct a proper action on a CAT(0) cube complex starting from a proper action on a wall space, and use this to deduce that if G is a group containing an amenable subgroup H of super-polynomial growth and G acts properly on a space with walls then there are arb…
Neural network predicts turbulence near-wall regions efficiently.
problem Reducing computational cost in turbulent flow simulations.
method Fully-convolutional neural network trained on DNS data.
result FCN predicts velocity fluctuations at y+=50 with less than 20% error. Farrell and Hsiang noticed that the geometric surgery groups defined By Wall, Chapter 9, do not have the naturality Wall claims for them. They were able to fix the problem by augmenting Wall's definitions to keep track of a line bundle. The definition of geometric Wall groups involves homology with local coefficients a…
The index theorem connects anomalies on a domain wall to global integrals.
problem Relating anomalies on a domain wall to global integrals.
method Formulated and proved an analog of the Atiyah-Patodi-Singer theorem.
result The index is expressed through global chiral and parity anomalies.
Analyzes how quadratic differential trajectories change with variation, proving a wall-crossing formula.
problem Analyzing how the number of trajectories of quadratic differentials changes with variation.
method Proves an analytic wall-crossing formula using Fock-Goncharov coordinates and characterizes birational automorphisms.
result Characterizes certain birational automorphisms and computes Stokes automorphisms.
Wall's result extended to 4-manifolds with definite intersection forms.
problem Realizing automorphisms of definite intersection forms.
method Using a specific 4-manifold construction and Wall's original result.
result Automorphisms of definite intersection forms are realized by diffeomorphisms of the constructed 4-manifold.
Extends index theorem to domain walls with discontinuous Riemannian connections.
problem Index theorem for domain walls with discontinuous Yang-Mills and Riemannian connections.
method Extension of index theorem to new conditions.
result Validates index theorem for more complex discontinuities.
Study wall singularities in spaces with upper curvature bounds.
problem Understanding singularities in spaces with curvature constraints.
method Geometric structure theorem and geometric characterization for codimension one and two.
result Necessary and sufficient conditions for singular sets to be of codimension at least two.
We describe a correspondence between spaces with walls and CAT(0) cube complexes.
Study of stability conditions on 3-folds, focusing on walls and intersections.
problem Understanding stability conditions and numerical walls on 3-folds.
method Differential geometry analysis of numerical walls, proving intersections and maximum turning points.
result Gieseker semistability equivalent to asymptotic semistability along paths in the upper half plane.
Proposes a reverse stress testing framework for dynamic models.
problem Finding plausible models under adverse stresses.
method Compound Poisson process, Kullback-Leibler divergence, optimization problem.
result Intensity and severity of process depend on time and state.
Study reviews machine learning techniques for stress monitoring.
problem Improving accuracy of stress monitoring devices.
method Reviewed machine learning techniques for various stress indicators.
result Choosing the right classifier depends on multiple factors.
Method generates plausible financial stress scenarios using large deviations.
problem Misleading risk management by overlooking or overemphasizing implausible scenarios.
method Exploits large-deviations principle to concentrate risk factors near most likely stress configurations.
result Can generate informative stress scenarios even with limited historical data.
Geometric interpretation of 2d-4d wall-crossing formulas.
problem Understanding wall-crossing phenomena in coupled 2d-4d systems.
method Deformation theory of holomorphic pairs and relation to scattering diagrams.
result Geometric interpretation of wall-crossing formulas.
Proof of wall-crossing formula using spectral networks.
problem Proving the Kontsevich-Soibelman wall-crossing formula.
method Path-lifting rules for spectral networks, convergence justification.
result Definition and justification of path lifting rules for spectral networks.
Physics-informed neural networks simulate solute dispersion in shear flows, validating complex transport mechanisms.
problem Simulating complex solute dispersion in asymmetric reactive environments.
method Physics-informed neural networks (PINNs) embedded with governing equations and boundary conditions.
result PINNs accurately predict solute dispersion, validating transport diagnostics.
The paper constructs K-moduli spaces for plane curves and describes wall crossings.
problem Constructing and understanding K-moduli spaces for plane curves.
method Constructing proper good moduli spaces and establishing wall-crossing framework.
result The first wall crossing of K-moduli spaces for plane curves of degree 4 is a weighted blow-up of Kirwan type.
Geometric Algebra Transformer (GATr) handles various geometric data types efficiently.
problem Lack of a single architecture for diverse geometric data types.
method GATr uses projective geometric algebra, equivariant to E(3), and is a Transformer architecture.
result GATr outperforms non-geometric and equivariant baselines in various geometric tasks.
We review our recent work on solitons in the Higgs phase. We use U(N_C) gauge theory with N_F Higgs scalar fields in the fundamental representation, which can be extended to possess eight supercharges. We propose the moduli matrix as a fundamental tool to exhaust all BPS solutions, and to characterize all possible modu…
When formulated in twistor space, the D-instanton corrected hypermultiplet moduli space in N=2 string vacua and the Coulomb branch of rigid N=2 gauge theories on R3×S1 are strikingly similar and, to a large extent, dictated by consistency with wall-crossing. We elucidate this similarity by showing that these…
Derives stress-energy tensor for polyharmonic maps.
problem Characterizing polyharmonic maps between Riemannian manifolds.
method Derives stress-energy tensor and uses it to characterize polyharmonic maps.
result Characterizes polyharmonic maps, focusing on triharmonic maps.
Abstract: Mapping 3-manifold bordisms to topological orders and domain walls.
problem Mapping spin 3-manifolds to topological orders and their domain walls.
method Defining topological orders from torsion elements in H1(N), linking form, and quadratic refinement. Extending to spin bordisms and domain walls. result Constructing domain walls between topological orders from spin bordisms.
This note improves correlation stress tests using geodesic distance.
problem Improving financial risk management through better covariance stress tests.
method Proposes a new geometrically invariant definition of correlation stress tests.
result Demonstrates a submanifold approach to stress testing covariance matrices.
Mathematician-friendly formulation of Atiyah-Patodi-Singer index.
problem Boundary conditions and edge modes in domain-wall fermions.
method Mathematician-friendly derivation of Atiyah-Patodi-Singer index.
result New insights into the interplay of boundary conditions, domain-wall fermions, and edge modes.
Study classifies long-term stress using EEG and expert labeling.
problem Classifying long-term stress using EEG signals.
method Baseline EEG recordings, perceived stress scale scores, expert evaluation, frequency domain features, alpha asymmetry, t-test, support vector machine.
result Expert evaluation improves classification accuracy to 85.20%.
Improved algorithm for multidimensional scaling reduces stress.
problem Stress in multidimensional scaling.
method Proposed modifications of the smacof algorithm.
result Convergent majorization algorithm for Kruskal's stress formula two.
Reformulates mod-two APS index using domain-wall fermion.
problem Non-local APS boundary condition and global anomalies.
method Physicist-friendly reformulation of APS index using domain-wall fermion.
result Equivalence between two formulations of APS index.
The MSPI predicts market stress with machine learning.
problem Estimating the probability of high market stress.
method L1-regularized logistic regression on stock fragility signals.
result MSPI tracks major stress episodes and improves accuracy.
We study commensurating actions of groups and the associated properties FW and PW, in connection with wallings, median graphs, CAT(0) cubings and multi-ended Schreier graphs.
Examines stress tests in European banking supervision.
problem Ensuring financial stability in European banks.
method Reviews existing financial stability institutions and stress testing.
result Stress tests are crucial for European banking supervision.
We use localization formulas in the theory of equivariant cohomology to rederive the wall crossing formulas of Li-Liu and Okonek-Teleman for Seiberg-Witten invariants.
End-to-end transformer model improves lexical stress detection accuracy.
problem Inaccurate phoneme boundaries and limited features for stress classification.
method End-to-end sequence to sequence model using transformer trained on feature sequences and phoneme sequences with stress marks.
result End-to-end model achieves better performance and lower phoneme error rate (6.36%) compared to syllable segmentation methods.
We present a systematic method to construct exactly all Bogomol'nyi-Prasad-Sommerfield (BPS) multi-wall solutions in supersymmetric (SUSY) U(N_C) gauge theories in five dimensions with N_F hypermultiplets in the fundamental representation for infinite gauge coupling. The moduli space of these non-Abelian walls is found…