Critical Point Research Articles

Using Version Control Information to Visualize Developers' Knowledge

It is not always clear in case of a software project who has the right amount of knowledge concerning a certain module or file. Programmers frequently ask questions like "Who knows the most about this code?" or "Who can I ask for help when I work on this module?". In a large, long-term software product, knowledge is distributed in an uneven way among developers. Developer fluctuation during the product lifetime might cause some parts of the code to be known very well by a multitude of developers, while other parts might sink to the "gray zone", where developer competence is dangerously scarce. It is important for the project management to identify such critical points, to avoid the complete loss of competence. Version control repositories contain loads of useful information about the evolution of a software project. This paper presents a developer-centered visualization that is intended to show individual, team-bound and company-bound knowledge of large legacy projects. The competence information is computed from the extracted version control information from Git repositories. The calculated competence value is based on the number of commits per developer and their significance. Aggregated views for teams and companies are available based on various heuristics. The visualization is implemented as a new plugin in CodeCompass, a standalone, open-source code comprehension software. Project managers and individual developers may both profit from the tool, whether it concerns software evolution, human-resource management, architecture, knowledge catch-up, or blame.

Crystallization and the liquid-liquid critical point in nonbonded modified-WAC models.

For decades, it has been known that Liquid-Liquid Critical Points (LLCPs) can exist in one-component liquids, yet a comprehensive understanding of the conditions under which they arise remains elusive. To better comprehend the possible interplay between the LLCP and the crystalline phase, we conduct molecular dynamics simulations using the nonbonded family of modified-WAC (mWAC) models, which are known to exhibit a LLCP for certain parameter values. By comparing different versions of the mWAC model-those featuring a LLCP and those lacking one-we identify several key differences between the models relating to crystallization. Those models that do have a LLCP are found to have multiple stable crystalline phases, one of them being a solid-state ionic conductor similar to superionic ice. Moreover, we find that for models that do not have a LLCP, the liquid becomes a glass at a larger range of temperatures, possibly preventing the occurrence of a LLCP. Further studies are required to determine if these results are general or model-specific.

Sheet Forming via Limiting Dome Height (LDH) Test: Influence of the Application of Lubricants, Location and Sheet Thickness on the Micro-Mechanical Properties of X8CrMnNi19-6-3

This work is concerned with forming, specifically deep drawing, and its influence on the micro-mechanical properties of sheet metal. In practice, there are several applications in which fractions can occur due to weak spots in the deep-drawn sheet metal, especially after long-term use. The deep drawing process was carried out on BUP–600 machines using the LHD (Limiting Dome Height) method, which uses a forming tool with a diameter of 100 mm and bead groove. Sheet metals X8CrMnNi19-6-3 (1.4376) with thicknesses of 1, 1.5, and 3 mm were selected for this process. To study the effect of a lubricant on the formability of the sheet metal, deep drawing without and with a lubricant was compared. An FEM analysis was conducted to identify critical points in the deep drawing process, and the results were later compared with real results. The analysis was conducted using the AutoForm program. The micro-mechanical properties of these points were subsequently examined. The specified points on the formed part showed significant differences in their micro-mechanical properties, suggesting a higher strength but also less resistance to fractures. The difference in micro-mechanical properties (indentation and Vickers hardness) in points that were not deep-drawn and points located in critical areas was up to 86%. Significant changes in behavior were found in the indentation modulus and plastic/elastic deformation work as well. This study demonstrates the significant effect of the use of a lubricant in achieving the deep drawing of the sheet metal. The application of a lubricant resulted in a 33% increase in drawing range compared to drawing without lubrication. This study has a significant influence on the deep drawing of sheet metals in practice, showing the fundamental influence of the lubricant on the drawing process and also showing the problem of critical points that need to be eliminated.

Analyzing sensitivity and multi-soliton solutions in the Estevez–Mansfield–Clarkson equation: Insights into dynamics of bifurcation and chaos

In this investigation, an analysis of the Estevez–Mansfield–Clarkson equation, a model equation employed in the examination of shape formation in liquid drops, optics, and mathematical physics, is undertaken. Firstly, multiple wave solitons, including 1-soliton, 2-soliton, and 3-soliton structures, are successfully generated through the utilization of a multiple exp-function technique. Subsequently, the conversion of the partial differential equation into an ordinary differential equation is executed. The extraction of various traveling wave patterns, such as kink, anti-kink, periodic, and exponential functions, is then carried out using the new auxiliary equation method. The outcomes are visually represented through 3-dimensional, 2-dimensional, and density plots, employing Mathematica software. Following this, an investigation into the qualitative dynamics of the equation is conducted, examining aspects such as bifurcation and chaos. Critical points are identified for bifurcation, and the dynamical system undergoes an outward force, resulting in the identification of chaotic patterns. Furthermore, the model’s sensitivity across different initial values is explored. These solutions hold immense significance in the domains of nonlinear fiber optics and telecommunications that help in deepening our knowledge about the basic physical model.

Measurement and thermodynamic correlation of liquid–liquid equilibria of water + n-propanol + toluene at 20°C and atmospheric pressure

Although the system water + n-propanol + toluene is important for research and industry, its liquid–liquid equilibria LLE are scarcely covered in literature, with no thermodynamic modeling reported using typical equations of state or activity coefficient models. The current work addresses this gap by presenting the equilibria of the system at 20°C and atmospheric pressure. That includes the binodal curve and twelve tie lines covering the entire miscibility gap, whereby the compositions of the conjugate phases are determined using high-precision refractive index measurements. The quality of the data is verified by applying the techniques of conjugate lines and mass balances, whereas it is shown that empirical correlations cannot be used for that purpose. Three different methods to extrapolate the critical point are then employed and, using the more reliable one, that point is located and added to the dataset. Further thermodynamic correlation of the data is conducted using the activity coefficient models, UNIQUAC and NRTL. While the former did not perform well, the latter was able to model the LLE and adapt to temperature changes.

Enhancing payload capacity to low earth orbit via a relay solution trajectory with laser-powered vehicles

ABSTRACT Low Earth Orbit (LEO) stands as the primary access point for deep space exploration endeavors, encompassing a variety of space missions such as communication satellites, Earth observation platforms, and scientific research missions. In light of the expanding scope of human activities in space, the cost associated with accessing LEO has emerged as a critical focal point for spacecraft designers. Within the spectrum of proposed solutions, laser-powered vehicle has emerged as a viable avenue toward achieving cost-effective launch options. In order to significantly augment the payload capacity of laser-powered launch vehicles destined for LEO, this study introduced a novel Relay Solution Trajectory Flight Scheme. Central to this scheme was the implementation of a relay mirror system affixed to a satellite, which served to stabilize the incident angle of the laser beam directed toward the laser-powered vehicle, thereby ensuring continuous alignment between the laser beam and the vehicle’s axis throughout the duration of the flight. Following the development of comprehensive structural, propulsive, aerodynamic, and trajectory models tailored for the laser-powered vehicle, an optimization of its flight trajectory was conducted, comparing this innovative strategy with two conventional flight strategies. The outcomes of this analysis showcased a notable enhancement of 269.29% in payload capacity compared to conventional strategies that lacked a relay satellite system, within a designated 400 km LEO flight scenario. This endeavor underscored the transformative potential of advanced relay systems in reshaping payload delivery mechanisms and elevating mission feasibility levels, notwithstanding the intricate coordination challenges posed by intricate satellite systems.

Investigation of nano-confinement effects on asphaltenic crude oil phase behavior in tight and shale reservoirs: Modeling using CPA-EOS

As a result of strong molecule–molecule and molecule–wall interactions, phase behavior in confined fluids differs significantly from that in bulk fluids. Asphaltene precipitation is a challenging issue for both conventional and unconventional (nano-scale) porous media. In this study, a new model based on cubic-plus-association equation of state (CPA-EOS) was developed for studying phase behavior of asphaltenic crude oil and asphaltene precipitation in nanoporous media. The developed model considers confinement phenomena including shift in the critical properties of components, high capillary pressure, and adsorption/desorption of fluid components on rock surface. For this purpose, necessary modifications were performed on both the EOS and phase equilibria calculations. The developed model was then used to analyze two-phase (vapor–liquid) and three-phase (vapor–liquid–asphaltene) behavior in confined systems. Results demonstrated that confinement phenomena shrink the two-phase envelope and shift the critical point of the mixture. It is also shown that instability of asphaltene in the solution is higher in nanoporous media and increases with reducing pore size. Therefore, the amount of precipitated asphaltene in nanoporous media is higher than that in conventional systems. As adsorption of components with higher molecular weights is more than that of low-molecular weight compounds, the crude oil sample is enriched with lighter components and hence, due to adsorption, bubble point pressure increases, upper branch of dew point curve shifts downward and its lower branch shifts upward, and asphaltene instability increases. Neglecting confinement phenomena results in overestimation or underestimation of saturation pressures as well as asphaltene upper and lower onset points and the proposed model can be of high importance in predicting the extent of asphaltene precipitation during natural depletion or solvent injection in tight oil reservoirs.

Convergence of gradient descent for learning linear neural networks

We study the convergence properties of gradient descent for training deep linear neural networks, i.e., deep matrix factorizations, by extending a previous analysis for the related gradient flow. We show that under suitable conditions on the stepsizes gradient descent converges to a critical point of the loss function, i.e., the square loss in this article. Furthermore, we demonstrate that for almost all initializations gradient descent converges to a global minimum in the case of two layers. In the case of three or more layers, we show that gradient descent converges to a global minimum on the manifold matrices of some fixed rank, where the rank cannot be determined a priori.

An improved artificial spin ice structure for restoring ice degeneracy

It is known that rare-earth-based pyrochlore oxide may accommodate the well-defined two-in-two-out spin ice state with its tetrahedral unit. Low-energy excitation is argued to favor the highly concerned monopole state which attracts essential attention. However, such an excitation cannot be directly tracked and imaged using advanced characterizations, raising challenges to our understanding of the physics of monopoles. In this work, we propose an improved two-dimensional artificial spin ice structure on the Shastry–Sutherland lattice to restore the degeneracy of realistic pyrochlore systems. Such a structure avoids the deficiency of inequivalent nearest and next-nearest exchanges in the planar quadrate unit, which, however, is equivalent to the tetrahedral unit of realistic pyrochlore oxides. Therefore, this spin ice model restores state degeneracy that is lost in conventional planar artificial spin ice structures, representing an improved simulator of real spin ice systems. Our careful investigations of such improved structures reveal the rich physics of spin ice excitations, including the phase diagram, which allows different ordered phases and interesting critical phase transitions between spin ice phase I and phase II. Energy spectrum analysis suggests that restoration of state degeneracy substantially reduces monopole excitation energy, resulting in a striking monopole emergency at the critical point. Furthermore, the emergent spin dimer phase in this improved model allows high-density monopole excitations and exhibits high-correlated monopole fluid states.

Privacy implications of central bank digital currencies (CBDCs): a systematic review of literature

This study employs a systematic review of the literature to critically analyze the privacy implications of central bank digital currencies (CBDCs) by examining 50 pertinent papers. Against the backdrop of a global digital revolution spurred by financial crises and the rise of cryptocurrencies, the emergence of CBDCs has garnered substantial attention from central banks worldwide. The study’s main objective is to fill a significant gap in the literature by providing an evidence-based assessment of the privacy issues of CBDCs. Through a meticulous analysis of the 46 selected papers, the study identifies key findings, including diverse perspectives on CBDC models, aspects and gaps in CBDC research, and various privacy concerns, such as extensive data collection in the direct CBDC model, challenges related to central bank data retention in the hybrid CBDC model, and increased operational complexity in the intermediated CBDC approach associated with CBDC implementation. The critical analysis points toward the urgent need for more extensive research into the privacy and security aspects of CBDCs to ensure user protection and trust. The findings contribute valuable insights for policymakers, regulators, and stakeholders in shaping the responsible creation and use of CBDCs.

Spatial Variation of Oomycetes and Bacteria on Surfaces, Solutions, and Plants from a Commercial Hydroponic Greenhouse

The spatial distribution and diversity of plant pathogens and other microbial communities in commercial operations is the first step in identifying critical control points where crops may be at risk of disease. Our objective was to characterize the spatial variation of oomycete pathogens and bacteria across the production system of a greenhouse producing lettuce in hydroponics. We utilized DNA metabarcoding to identify oomycetes and 16S rRNA gene sequencing of bacteria from different production stages and sample types (surfaces, solutions, and roots) collected from a commercial greenhouse producing lettuce in deepwater culture. Pythium was the genus with the highest relative abundance (41 to 100%) across all production stages. P. dissotocum was detected in most samples, except for sowing and seedling surfaces and municipal water, where P. myriotylum was the most abundant species. Oomycete communities showed distinct clustering by production stages and sample types, where sowing and seedling surfaces and municipal water were separated from the rest. Proteobacteria had the highest relative abundance in the surfaces at the sowing (98%) and seedling (85%) stages. Municipal water was the only sample with less than 20% relative abundance of Proteobacteria and dominated by Cyanobacteria. Negative correlations between Pythium and 13 bacteria genera point to potential antagonists in hydroponics that should be further studied. Mapping the spatial variation of oomycetes and bacterial communities in a commercial greenhouse indicates that production stage and sample type influence microbial composition and potentially the risk to disease.

Short Communication: Microbiological Quality of Food Purchased from Home-Based Dark Kitchens

Purchase of locally processed food from home-based dark kitchens is common in Mauritius. This study aimed to compare the microbiological quality of locally processed food purchased from HACCP (hazard analysis critical control point) certified suppliers and non-HACCP certified foods purchased from home-based dark kitchens. A total of 16 food samples were collected and processed. Bacterial growth was observed in 87.5% of the non-HACCP samples and 25% of HACCP samples. The colony forming units were significantly higher in non-HACCP samples compared to HACCP samples (p = 0.04). E. coli was isolated from 25% and 37.5% of HACCP and non-HACCP food samples, respectively. It was noted that 64.3% of the bacteria isolated were resistant to amoxicillin, and 100% of the Pseudomonas spp. was resistant to ampicillin (10 μg), chloramphenicol (30 μg), and tetracycline (10 μg). There is a need to educate the population on food safety and the risks associated with the purchase of food from unregulated suppliers.

Preparation and Properties of Composite Double-Network Gel for Inhibiting Coal Spontaneous Combustion.

In order to improve the inhibition effect of gel on coal spontaneous combustion, a chitosan (CS)/polyacrylamide (PAM)/metal ion (Al3+) composite double-network gel was developed in this study. The optimum formula of the composite double-network gel was determined using orthogonal experimentation. The microstructure, water retention, compressibility, and anti-destruction properties of the composite double-network gel were analyzed. The inhibition effect of the composite double-network gel on coal spontaneous combustion was studied via infrared spectroscopy and a synchronous thermal analyzer from the micro and macro perspectives. The results show that the composite double-network gel has a denser interpenetrating double-network structure and a larger void ratio than the ordinary gel. The water retention rate was 55% after standing at 150 °C for 12 h. The deformation memory ratio of the composite double-network gel was 78%, which was 26.8% higher than that of the ordinary gel, and the compressive strength also increased by 59.96%. In addition, the critical temperature point and the maximum thermal weight-loss rate temperature point decreased by 7.01 °C and 39.62 °C, respectively, and the composite double-network gel effectively reduced active functional groups in the treated coal sample, such as hydroxyl and aliphatic hydrocarbons. In this study, a CS/PAM/Al3+ composite double-network gel was produced, which exhibited good gel performance and inhibition effects, with physical effects such as the covering, wetting, and cementation of coal.

Production of an introperative safety list in interventional cardiology. From pilot project to clinical practice guidelines hospital

Abstract Introduction The safety list was created to respond to two complexities: the first is the fallibility of human memory and attention; The second is the tendency to skip some operations even when remembering that they should be performed: not all operations in the supply chain of a process are always considered important so the shortcut is taken, motivated by the fact that nothing has ever happened so far. Safety in Interventional Cardiology laboratories is characterized by the intrinsic complexity that characterizes all interventional procedures, even the simplest ones: complexity due to the number of people and professionals involved, the acute and/or serious conditions of the patients, the amount of information required, the urgency with which the processes must be performed, the high technological and high level of specialization and the multiplicity of critical points of the processes that can cause serious harm to patients. For this reason, an intraoperative safety list for interventional cardiology has been designed and drawn up. Aim In view of Law no. 24 of 8 March 2017, a provision on the safety of care and the assisted person, it was necessary to have a document aimed at: improving the quality and safety of surgical interventions and interventional/structural procedures, dissemination of recommendations and safety standards aimed at strengthening pre- intra and post-operative processes, Implementation of safety standards through the application of the safety list, adapting it to the characteristics of your organization. Materials and methods The trial phase began in 2021 and was tested on about 800 patients, in 2022 on about 900 patients. The safety list has been designed to combine an intraoperative "check list" with a "nursing card", collecting information relating to the individual people assisted, in order to promote continuity and personalization of care, represents a resource for research on nursing care, for the analysis of care complexity and allows the traceability of the actions carried out. Results and conclusions After years of constant reviews and updates with the collaboration of the Risk Management and Quality staff, the safety list has become a fundamental part of the work of the operating room, supporting both system and individual changes, strengthening standards for safety and communication processes, counteracting possible failure factors, having been included in the hospital Guidelines on the management of patients undergoing surgery.

Relaxation dynamics in the alternating XY chain following a quantum quench

We investigate the relaxation dynamics of the fermion two-point correlation function Cmn(t)=〈ψ(t)∣cm†cn∣ψ(t)〉 in the XY chain with alternating nearest-neighbor hopping interaction after a quench. We find that the deviation δ C mn (t) = C mn (t) − C mn (∞) decays with time following the power law behavior t −μ , where the exponent μ depends on whether the quench is to the commensurate phase (μ = 1) or incommensurate phase ( μ=12 ). This decay of δ C mn (t) arises from the transient behavior of the double-excited quasiparticle occupations and the transitions between different excitation spectra. Furthermore, we find that the steady value C mn (∞) only involves the average fermion occupation numbers (i.e. the average excited single particle) over the time-evolved state, which are different from the ground state expectation values. We also observe nonanalytic singularities in the steady value C mn (∞) for the quench to the critical points of the quantum phase transitions (QPTs), suggesting its potential use as a signature of QPTs.

Structure and scaling of Kitaev chain across a quantum critical point in real space.

The spatial Kibble-Zurek mechanism (KZM) is applied to the Kitaev chain with inhomogeneous pairing interactions that vanish in half of the lattice and result in a quantum critical point separating the superfluid and normal-gas phases in real space. The weakly-interacting BCS theory predicts scaling behavior of the penetration of the pair wavefunction into the normal-gas region different from conventional power-law results due to the non-analytic dependence of the BCS order parameter on the interaction. The Bogoliubov-de Gennes (BdG) equation produces numerical results confirming the scaling behavior and hints complications in the strong-interaction regime. The limiting case of the step-function quench reveals the dominance of the BCS coherence length in absence of additional length scale. Furthermore, the energy spectrum and wavefunctions from the BdG equation show abundant in-gap states from the normal-gas region in addition to the topological edge states.

On the Shape of Hypersurfaces with Boundary Which Have Zero Fractional Mean Curvature

We consider compact hypersurfaces with boundary in RN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {R}}^N$$\\end{document} that are the critical points of the fractional area introduced by Paroni et al. (Commun Pure Appl Anal 17:709–727, 2018). In particular, we study the shape of such hypersurfaces in several simple settings. First we consider the critical points whose boundary is a smooth, orientable, closed manifold Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma $$\\end{document} of dimension N-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N-2$$\\end{document} and lies in a hyperplane H⊂RN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H \\subset {\\mathbb {R}}^N$$\\end{document}. Then we show that the critical points coincide with a smooth manifold N⊂H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {N}}\\subset H$$\\end{document} of dimension N-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N-1$$\\end{document} with ∂N=Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial {\\mathcal {N}}= \\Gamma $$\\end{document}. Second we consider the critical points whose boundary consists of two smooth, orientable, closed manifolds Γ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma _1$$\\end{document} and Γ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma _2$$\\end{document} of dimension N-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N-2$$\\end{document} and suppose that Γ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma _1$$\\end{document} lies in a hyperplane H perpendicular to the xN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x_N$$\\end{document}-axis and that Γ2=Γ1+deN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma _2 = \\Gamma _1 + d \\, e_N$$\\end{document} (d>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d >0$$\\end{document} and eN=(0,⋯,0,1)∈RN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e_N = (0,\\cdots ,0,1) \\in {\\mathbb {R}}^N$$\\end{document}). Then, assuming that Γ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma _1$$\\end{document} has a non-negative mean curvature, we show that the critical points do not coincide with the union of two smooth manifolds N1⊂H\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {N}}_1 \\subset H$$\\end{document} and N2⊂H+deN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {N}}_2 \\subset H + d \\, e_N$$\\end{document} of dimension N-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N-1$$\\end{document} with ∂Ni=Γi\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial {\\mathcal {N}}_i = \\Gamma _i$$\\end{document} for i∈{1,2}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$i \\in \\{1,2\\}$$\\end{document}. Moreover, the interior of the critical points does not intersect the boundary of the convex hull in RN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {R}}^N$$\\end{document} of Γ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma _1$$\\end{document} and Γ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma _2$$\\end{document}, while this can occur in the codimension-one situation considered by Dipierro et al. (Proc Am Math Soc 150:2223–2237, 2022). We also obtain a quantitative bound which may tell us how different the critical points are from N1∪N2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {N}}_1 \\cup {\\mathcal {N}}_2$$\\end{document}. Finally, in the same setting as in the second case, we show that, if d is sufficiently large, then the critical points are disconnected and, if d is sufficiently small, then Γ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma _1$$\\end{document} and Γ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma _2$$\\end{document} are in the same connected component of the critical points when N≥3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N \\ge 3$$\\end{document}. Moreover, by computing the fractional mean curvature of a cone whose boundary is Γ1∪Γ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma _1 \\cup \\Gamma _2$$\\end{document}, we also obtain that the interior of the critical points does not touch the cone if the critical points are contained in either the inside or the outside of the cone.

Simulations of Stochastic Fluid Dynamics near a Critical Point in the Phase Diagram

Simulations of Stochastic Fluid Dynamics near a Critical Point in the Phase Diagram

Concept Analysis of Woman-Centered Care: Implications for Postpartum Care.

Approximately two-thirds of pregnancy-related deaths in the United States occur during the postpartum period, yet there is minimal research focusing on the postpartum hospital stay, a critical point of contact between women and the health care system and an important opportunity for intervention. A new approach to postpartum care is needed. "Woman-centered" postpartum care is recommended to improve maternal outcomes, but the concept of woman-centered care is not well-defined. Using Walker & Avant's method of concept analysis, we identified four defining attributes of woman-centered care in the literature: 1) choice, control, and involvement in decision-making; 2) communication and collaboration in the caregiver-woman relationship; 3) individualized and holistic care; and 4) continuity of care. Using these findings, we offer a conceptual definition of woman-centered care and apply the attributes to the postpartum hospitalization in the model and contrary cases. We discuss the potential of the concept to improve maternal health care during this critical period.

The shape of the filling-systole subspace in surface moduli space and critical points of the systole function

The shape of the filling-systole subspace in surface moduli space and critical points of the systole function