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.
In this paper we study the ergodic theory of the geodesic flow on negatively curved geometrically finite manifolds. We prove that the measure theoretic entropy is upper semicontinuous when there is no loss of mass. In case we are losing mass, the critical exponents of parabolic subgroups of the fundamental group have a…
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…
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.
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.
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.
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.
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.
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.
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.
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.
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…
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. 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.
An innovative method optimizes engine calibration to improve efficiency and reduce emissions.
problem Complex engines with many tunable parameters require efficient calibration methods.
method Combines Principal Component Decomposition with constrained Bayesian Optimization to minimize pressure curve deviation.
result Optimal engine calibration found after 64.4s with a 0.017% efficiency gain.
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…
Study infinitesimal characters on semi-groups to prove interior properties and apply to Teichmüller spaces.
problem Properties of infinitesimal characters and their applications in Teichmüller spaces.
method Analyzing integrable tangent vectors on character varieties and applying to pressure forms and Teichmüller spaces.
result Non-empty interior of the cone of Jordan variations and length-normalized variations for split groups.
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.
The paper introduces two new metrics on outer space and shows fixed points for their actions.
problem Analyzing metrics on outer space and their geometric group theory implications.
method Defined and analyzed entropy and pressure metrics on outer space, comparing to Weil-Petersson metric.
result For rank r≥4, the metrics have fixed points in their actions on outer space. We discuss how one uses the thermodynamic formalism to produce metrics on higher Teichmüller spaces. Our higher Teichmüller spaces will be spaces of Anosov representations of a word-hyperbolic group into a semi-simple Lie group. We begin by discussing our construction in the classical setting of the Teichmüller space o…
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…
A new definition of umbilic points at infinity for polynomial surfaces.
problem Defining umbilic points at infinity for homogeneous polynomial graphs.
method Proposed a stronger definition than Toponogov's, proving all are isolated and pairs, with geometric interpretation.
result All umbilic points at infinity are isolated and occur in pairs, being zeroes of the projective extension of the third fundamental form.
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.
Simulation of high-speed train aerodynamics using RANS and machine learning.
problem Aerodynamic analysis of high-speed trains under turbulent flow conditions.
method RANS equations with turbulence model, machine learning (GEP, GPR, RF) for predictions.
result Random Forest (RF) provides the most accurate predictions for aerodynamic coefficients.
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…
Hyperflux models pruning as a system to reveal weight importance.
problem Pruning large neural networks to reduce latency and power consumption.
method Introduces Hyperflux, a novel L0 method that models pruning as flux and pressure. result Achieves competitive results with ResNet-50, VGG-19, and DeiT-T/S on various datasets.
The paper proves mapping class groups of closed surfaces are simply connected at infinity.
problem Understanding connectivity at infinity for mapping class groups of surfaces.
method Proved a general simply connected at infinity result for finitely presented groups.
result All mapping class groups of closed surfaces of genus ≥ 3 are simply connected at infinity.
We study connected sum at infinity on smooth, open manifolds. This operation requires a choice of proper ray in each manifold summand. In favorable circumstances, the connected sum at infinity operation is independent of ray choices. For each m at least 3, we construct an infinite family of pairs of m-manifolds on whic…
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…
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.
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.
Nonlinear embedding manifold learning methods provide invaluable visual insights into the structure of high-dimensional data. However, due to a complicated nonconvex objective function, these methods can easily get stuck in local minima and their embedding quality can be poor. We propose a natural extension to several …
The paper examines mass aspects at future null infinity and limits of quasilocal mass.
problem Understanding mass aspects and limits of quasilocal mass at future null infinity.
method Review and extension of Bondi mass and mass loss formula in Bondi-Sachs coordinate system.
result New results about the limit of quasilocal mass of unit spheres at null infinity.
Framework improves health by planning actionable treatment processes.
problem Developing objective treatment processes in clinical settings.
method Surrogate Bayesian model combined with ML for personalized health improvement.
result Computed treatment processes are actionable and consistent with clinical knowledge.
The paper defines curvature at infinity for flat manifolds.
problem Defining curvature at the boundary of flat manifolds.
method Constructing coordinates at infinity for asymptotically flat ends.
result A Weyl tensor and renormalized volume defined at infinity.
We study the geometry at infinity of expanding gradient Ricci solitons of dimension greater than two with finite asymptotic curvature ratio without curvature sign assumptions. We mainly prove that they have a cone structure at infinity.
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.
Let F be R or C, d the dimension of F over R. Denote by P(F) either the affine plane A(F) or the hyperbolic plane H(F) over F. An arrangement L of k lines in P(F) (pairwise non-parallel in the hyperbolic case) has a link at infinity K(L) comprising k unknotted (d-1)-spheres in the (2d-1)-sphere, whose topology reflects…
Study asymptotic behavior of Weingarten surfaces at infinity.
problem Understanding the behavior of Weingarten surfaces at infinity.
method Derive asymptotic expansion and solve Dirichlet problem.
result Established maximum principle and solved Dirichlet problem.
Positive injectivity radius for manifolds with Lie structure at infinity.
problem Injectivity radius positivity for manifolds with specific boundary conditions.
method Lie groupoids to prove injectivity radius positivity.
result Injectivity radius is positive for manifolds with Lie structure at infinity.
We look at complete minimal surfaces of finite total curvature in R4. Similarly to the case of complex curves in C2 we introduce their {\it link at infinity}; we derive the {\it writhe number at infinity} which gives a formula for the total normal curvature of the surface. The knowledge of the l…
This paper develops a Carleman type estimate for immersed surface in Euclidean space at infinity. With this estimate, we obtain an unique continuation property for harmonic functions on immersed surfaces vanishing at infinity, which leads to rigidity results in geometry.