Study on MHD equilibria on curved spaces without symmetries.
problem Analyzing MHD equilibria on curved spaces without symmetries.
method Examined MHD equilibria on Riemannian 3-manifolds with various adapted metrics.
result Found that for an open and dense set of adapted metrics, MHD equilibria on compact 3-manifolds without boundary admit no continuous Killing symmetries.
The paper surveys pressure metrics in geometry and dynamics.
problem Understanding pressure metrics in various deformation spaces.
method Survey and discussion of pressure semi-norms and their degeneracy loci.
result Discussion of pressure semi-norms and their degeneracy loci in quasi-Blaschke products.
Paper introduces a new metric for deforming surfaces with parabolics.
problem Deformation spaces of quasifuchsian groups with parabolics.
method Developed a mapping class group invariant pressure metric on QF(S).
result Hausdorff dimension of limit sets varies analytically over QF(S).
This paper describes the Pressure Ulcers Online Website, which is a first step solution towards a new and innovative platform for helping people to detect, understand and manage pressure ulcers. It outlines the reasons why the project has been developed and provides a central point of contact for pressure ulcer analysi…
The study examines entropy and pressure at infinity in negatively curved manifolds, linking them to strong positive recurrence.
problem Investigating strong positive recurrence in negatively curved manifolds.
method Defining and comparing entropy and pressure at infinity through different measures.
result Strong positive recurrence potentials admit finite Gibbs measures.
Deep learning speeds up pressure prediction in carbon storage reservoirs.
problem Accurately forecasting reservoir pressure in geologic carbon storage projects with sparse well data.
method Combining InSAR surface displacement data with deep learning and data assimilation techniques.
result Workflow can predict reservoir pressure with high efficiency and uncertainty quantification.
Study pressure metrics for cusped Hitchin representations.
problem Characterize cusped Hitchin representations of Fuchsian groups.
method Develop pressure metrics associated to fundamental weights and roots.
result New pressure metrics for Hilbert length when d=3. Develops discrete geometry for non-constant curvature surfaces.
problem Modeling surfaces of non-constant curvature, especially with non-constant negative curvature.
method Derived and numerically integrated Lelieuvre formulas for C1,1 hyperbolic surfaces. Proposed iterative and fast marching methods for solving implicit equations and computing geodesic distances. result Explicit construction of immersions is not provided, but equations are described implicitly.
The paper establishes pressure gaps for manifolds with flat subtori singularities.
problem Understanding phase transitions in nonpositively curved manifolds with flat subtori.
method Derives a pressure gap criterion for closed rank 1 manifolds with specific singular sets and proves Hölder continuity of geometric potentials.
result Geometric potentials have pressure gaps and no phase transitions under certain curvature constraints.
A quaternionic version of Picard's theorem limits how many values a slice regular function can avoid.
problem How many values can a non-constant slice regular function of a quaternionic variable avoid?
method Investigates slice regular functions of quaternionic variables, extending the classical Picard theorem.
result A non-constant slice regular function of a quaternionic variable can avoid at most one value, similar to the classical Picard theorem.
Numerous studies have been carried out to measure wind pressures around circular cylinders since the early 20th century due to its engineering significance. Consequently, a large amount of wind pressure data sets have accumulated, which presents an excellent opportunity for using machine learning (ML) techniques to tra…
We prove that the pressure metric on the Teichmüller space of a bordered surface is incomplete and its partial completion can be given by the moduli space of metric graphs for a fat graph associated to the same bordered surface equipped with pressure metric. As a corollary, we show that the pressure metric is not a con…
By using the Hawking Taub-NUT metric, this note gives an explicit construction of a 3-parameter family of Einstein Finsler metrics of non-constant flag curvature in terms of navigation representation.
We prove a Gauss-Bonnet type formula for Riemann-Finsler surfaces of non-constant indicatrix volume and with regular piecewise smooth boundary. We give a Hadamard type theorem for N-parallels of a Landsberg surface.
A new option pricing model handles non-constant risk aversion and transaction costs.
problem Deriving a pricing model for options with varying risk aversion.
method Developed a transformation method to solve the penalized nonlinear PDE and used finite difference discretization.
result Derived bounds on option prices and proposed a numerical scheme.
Study develops a data-based model for in-cylinder pressure and cyclic variations in RCCI engines.
problem Lack of models capturing cyclic variations in combustion concepts like RCCI.
method Combines Principle Component Decomposition and Gaussian Process Regression.
result Model predicts combustion measures with high accuracy, especially peak-pressure rise-rate.
New smooth solutions of the Strominger system with non vanishing flux, non-trivial instanton and non-constant dilaton based on the quaternionic Heisenberg group are constructed. We show that through appropriate contractions the solutions found in the G2-heterotic case converge to the heterotic solutions on 6-dimensi…
A neural network models pressure-Hessian from local velocity gradients in turbulent flows.
problem Modeling the pressure-Hessian from local velocity gradients in turbulent flows.
method Tensor basis neural network (TBNN) trained on DNS data.
result Neural network accurately captures key alignment statistics of the pressure-Hessian tensor.
The paper examines geometric curvatures in generalized Riemannian spaces.
problem Understanding the physical meaning of scalar curvatures in generalized Riemannian spaces.
method Developed Madsen's formulae for pressures and energy-densities, analyzed with different concepts of generalized Riemannian spaces.
result Linearities of energy-momentum tensor, pressure, energy-density, and state-parameter are examined.
Study forecasts aortic pressure with deep learning models.
problem Forecasting noisy, non-stationary aortic pressure.
method Used deep learning models, specifically recurrent neural networks with Legendre Memory Unit, on 25 Hz time series data.
result Recurrent neural networks with Legendre Memory Unit achieved the best performance with an overall forecasting error of 1.8 mmHg.
The paper studies Blaschke products, proving uniformization and non-degeneracy of pressure metrics.
problem Analytic aspects of Blaschke products and their moduli space.
method Definition of complex structure and proof of uniformization theorem.
result Pressure semi-norms are non-degenerate outside the super-attracting locus.
Recent advances in deep pose estimation models have proven to be effective in a wide range of applications such as health monitoring, sports, animations, and robotics. However, pose estimation models fail to generalize when facing images acquired from in-bed pressure sensing systems. In this paper, we address this chal…
The paper extends Menelaus' and Ceva's theorems to translation triangles in various Thurston geometries.
problem Extending classical theorems to non-Euclidean geometries.
method Using projective models of Thurston geometries and defining a ``surface of a translation-like triangle".
result Generalization of Menelaus' and Ceva's theorems to non-constant curvature Thurston geometries.
The paper defines a path metric on a stable component of polynomial families.
problem Understanding the geometry of polynomial families with parabolic relations.
method Constructing a positive semi-definite pressure form on a bounded stable component of the moduli space.
result The pressure form defines a path metric on the stable component.
Deep learning reconstructs pressure fields and classifies leakage rates in CCS storage sites.
problem Monitoring CO2 leakage in CCS storage sites.
method Variational auto-encoder tailored for pressure field reconstruction and leakage rate classification.
result Uncertainty estimates of predictions illustrated on synthetic data.
We prove that the Hitchin parametrization provides geodesic coordinates at the Fuchsian locus for the pressure metric in the Hitchin component H3(S) of surface group representations into PSL(3,R). The proof consists of the following elements: we compute first derivatives of the pressure metric…
In this paper, we extend the construction of pressure metrics to Teichmüller spaces of surfaces with punctures. This construction recovers Thurston's Riemannian metric on Teichmüller spaces. Moreover, we prove the real analyticity and the convexity of Manhattan curves of the finite area type-preserving Fuchsian represe…
In this article we construct the pressure form on the moduli space of higher dimensional Margulis spacetimes without cusps and study its properties. We show that the Margulis spacetimes are infinitesimally determined by their marked Margulis invariant spectrums. We use it to show that the restrictions of the pressure f…
Funds inflate their returns due to price pressure, leading to wealth reallocation and market crashes.
problem Funds inflate their returns due to price pressure, leading to wealth reallocation and market crashes.
method Decomposed fund returns into price pressure and fundamental components, and identified the impact of price chasing on fund flows.
result Funds' self-inflated returns lead to wealth reallocation and market crashes, and can be predicted by fund illiquidity.
A new algorithm optimizes time-varying functions with non-constant evaluation times.
problem Optimizing functions that change over time with varying evaluation times.
method Proposes a novel time-varying Bayesian optimization algorithm.
result Establishes a regret bound for the proposed algorithm.
This paper defines the pressure metric on the Moduli space of Margulis spacetimes without cusps and shows that it is positive definite on the constant entropy sections. It also demonstrates an identity regarding the variation of the cross-ratios.
Bayesian inference calibrates Hall thruster model uncertainty at varying pressures.
problem Quantifying uncertainty in a multi-component Hall thruster model at different facility pressures.
method Bayesian inference applied to calibrate and quantify prediction uncertainty in a coupled multi-component Hall thruster model.
result Model reduces predictive errors in thrust and discharge current by more than 50% compared to a previous model.
Hybrid model predicts flow and pressure in water systems.
problem Predicting flow and pressure in water distribution systems with complex spatial-temporal correlations.
method Hybrid dual-stage spatial-temporal attention-based recurrent neural networks (hDS-RNN).
result Our model outperformed 9 baseline models in flow and pressure series prediction.
The study improves fundamental gap estimates for surfaces with non-constant positive curvature.
problem Estimating the fundamental gap for surfaces with non-constant positive curvature.
method Using a two-point maximum principle, the study establishes log-concavity and fundamental gap estimates.
result Corresponding log-concavity and fundamental gap estimates for surfaces with non-constant positive curvature are derived.
Conformally compact and complete smooth solutions to the Strominger system with non vanishing flux, non-trivial instanton and non-constant dilaton using the first Pontrjagin form of the (-)-connection} on 6-dimensional non-Kaehler nilmanifold are presented. In the conformally compact case the dilaton is determined by t…
Paper classifies special slant surfaces with varying curvature.
problem Classifying surfaces with non-constant mean curvature.
method Analyzing special slant surfaces in complex space forms.
result Complete classification of surfaces with non-constant mean curvature.
Soap films collapse only if their bulk has negative pressure, forming convex shapes.
problem Understanding soap film behavior and collapse conditions.
method Variational analysis of capillarity theory.
result Soap films collapse only if their bulk has negative pressure, forming convex shapes.
ANN model predicts zinc leaching filter cake moisture accurately.
problem Modeling cake moisture in zinc leaching pressure filtration.
method Developed ANN model using 7 parameters.
result High accuracy in predicting cake moisture (R2 > 0.8, MSE < 1e-6).
We prove a uniqueness theorem for immersed spheres of prescribed (non-constant) mean curvature in homogeneous three-manifolds. In particular, this uniqueness theorem proves a conjecture by A.D. Alexandrov about immersed spheres of prescribed Weingarten curvature in R3 for the special but important case of prescribed me…
Proves closure for specific spacetimes with certain conditions.
problem Proving closure for globally hyperbolic spacetimes.
method Using a Bonnet-Myers type result.
result Proves closure for spacetimes with specific conditions.
In this paper we consider the Ricci curvature of a Ricci soliton. In particular, we have showed that a complete gradient Ricci soliton with non-negative Ricci curvature possessing a non-constant convex potential function having finite weighted Dirichlet integral satisfying an integral condition is Ricci flat and also i…
It is well-known that non-constant holomorphic functions do not exist on a compact complex manifold. This statement is false for a supermanifold with a compact reduction. In this paper we study the question under what conditions non-constant holomorphic functions do not exist on a compact homogeneous complex supermanif…
A new method splits surface flow discretizations into streamfunctions and harmonic fields.
problem Discretizing incompressible flows on surfaces with pressure and saddle-point structure.
method Discrete Helmholtz-Hodge decomposition for BDM elements on surfaces.
result Eliminates pressure and saddle-point structure, ensuring exact tangentiality and divergence-freeness.
Study equilibrium measures on manifolds without conjugate points with visibility covering.
problem Uniqueness and properties of equilibrium measures on manifolds without conjugate points.
method Analysis of geodesic flows, study of equilibrium measures, ergodic properties, and pressure gap.
result Equilibrium measures satisfy a weak pressure gap under certain conditions.
Deep learning has been used in many areas, such as feature detections in images and the game of go. This paper presents a study that attempts to use the deep learning method to predict turbomachinery performance. Three different deep neural networks are built and trained to predict the pressure distributions of turbine…
The dynamics of representations into PSL_d(R) are studied for surfaces of genus at least 3.
problem Dynamics of representations into PSL_d(R) for surfaces of genus at least 3.
method Showed quasi-convex subsets of infinite diameter for the Weil--Petersson metric have finite diameter for the path metric of the pressure metric through controlled bounded length of biinfinite paths of bending deformations.
result Biinfinite paths of bending deformations have controlled bounded length.
The fact that every human has a distinctive walking style has prompted a proposal to use gait recognition as an identification criterion. Using end-to-end learning, I investigated whether the center-of-pressure trajectory is sufficiently unique to identify a person with a high certainty. Thirty-six adults walked on a t…
Study evaluates uncertainty in BP estimation from PPG signals under domain shift.
problem Uncertainty quantification in healthcare, especially for cuffless BP estimation.
method Compared deep ensembles, Monte Carlo dropout, and various recalibration techniques.
result Deep ensembles provide stronger robustness under domain shift.