Critical Setting Research Articles

Potential theory on an analytic surface

The work is devoted to the theory of pluripotential on analytic surfaces. The pluripotential theory on the complex space ${\mathbb C}^{n},$ as well as on the Stein complex manifold $X\subset{\mathbb C}^{N}$ (without a singular set) have been studied in enough detail. In this work, we propose a new approach for studying the main objects of potential theory on an analytic set with a non-empty singular (critical) set.

Digital Health Literacy and Its Association With Sociodemographic Characteristics, Health Resource Use, and Health Outcomes: Rapid Review.

Digital health literacy has emerged as a critical skill set to navigate the digital age. This review sought to broadly summarize the literature on associations between digital health literacy and (1) sociodemographic characteristics, (2) health resource use, and (3) health outcomes in the general population, patient groups, or parent or caregiver groups. A rapid review of literature published between January 2016 and May 2022 was conducted through a search of 4 web-based databases. Articles were included on the basis of the following keywords: "measured digital health literacy," "digital literacy," "ehealth literacy," "e-health literacy," "electronic health literacy," or "internet health literacy" in adult populations; participants were from countries where English was the primary language; studies had to be cross-sectional, longitudinal, prospective, or retrospective, and published in English. Thirty-six articles met the inclusion criteria. Evidence on the associations between digital health literacy and sociodemographic characteristics varied (27/36, 75% included studies), with higher education (16/21, 76.2% studies that examined the association) and younger age (12/21, 57.1% studies) tending to predict higher digital health literacy; however, other studies found no associations. No differences between genders were found across the majority of studies. Evidence across ethnic groups was too limited to draw conclusions; some studies showed that those from racial and ethnic minority groups had higher digital health literacy than White individuals, while other studies showed no associations. Higher digital health literacy was associated with digital health resource use in the majority of studies (20/36, 55.6%) that examined this relationship. In addition, higher digital health literacy was also associated with health outcomes across 3 areas (psychosocial outcomes; chronic disease and health management behaviors; and physical outcomes) across 17 included studies (17/36, 47.2%) that explored these relationships. However, not all studies on the relationship among digital health literacy and health resource use and health outcomes were in the expected direction. The review presents mixed results regarding the relationship between digital health literacy and sociodemographic characteristics, although studies broadly found that increased digital health literacy was positively associated with improved health outcomes and behaviors. Further investigations of digital health literacy on chronic disease outcomes are needed, particularly across diverse groups. Empowering individuals with the skills to critically access and appraise reliable health information on digital platforms and devices is critical, given emerging evidence that suggests that those with low digital health literacy seek health information from unreliable sources. Identifying cost-effective strategies to rapidly assess and enhance digital health literacy capacities across community settings thus warrants continued investigation.

Critical Data Visualization to Enhance Protection Schemes for State Estimation

Intelligent electrical power grids, widely referred to as smart grids (SGs), rely on digital technology resources, especially communication and measurement devices, becoming a cyber-physical energy system. Massive data flow between grid elements makes smart grids more vulnerable to cyber-attacks. Power system state estimation (SE)—an essential function of energy management systems—is one of these data integrity attacks’ targets. Integrity validation routines can fail when insufficient redundancy levels are reached, and spurious data occur. These levels are associated with critical data, i.e., those whose unavailability makes the grid unobservable. Data redundancy is a metric that gives a precarious indication that SE can run. Alternatively, it is more appropriate to quantify this function strength concerning its results’ reliability, which can be achieved by criticality analysis (CA). This paper proposes a novel approach to visualize the results of an extensive CA through representative graphs; they facilitate understanding the usefulness of CA. Critical sets of measurements are generalized, and several metrics are proposed to reveal measuring system vulnerabilities, assisting the design of protection schemes to resist cyber-attacks. Simulations attained on the IEEE-30bus system evince significant improvements in the interpretation/use of CA.

Influence of inflow directions and setting angle of inlet guide vane on hydraulic performance of an axial-flow pump

Inlet flow direction significantly affects the hydraulic performance of an axial-flow pump. Usually, the research papers ignore this phenomenon, resulting in discrepancies between simulation and experimental results. This study examines the influence of inflow direction in five cases (0%, 5%, 10%, 15%, and 30% pre-swirl intensities) to determine the relationship between the pre-swirl intensity and the hydraulic performance of the axial-flow pump. Based on this, changing the setting angle of the inlet guide vane (IGV) is proposed and thoroughly investigated to reduce the effect of inflow direction. In this study, the influence of clearances in IGV blades on hydraulic performance is also investigated in detail. Numerical simulations are performed using ANSYS–CFX and a shear stress transport reattachment modification (SST k-omega) turbulence model with small y+ values at all walls. Specifically, the hydraulic performance curves and internal flow characteristics, including contours and streamlines, are assessed and analyzed. The inflow direction significantly impacts the hydraulic efficiency of the axial-flow pump. Increased pre-swirl intensity causes more loss in the IGV passage. The internal flow field and performance are not affected by the clearance at the hub and shroud of the IGV. However, the tip clearance of the impeller causes a decrease in hydraulic efficiency due to the tip leakage vortex. By adjusting the setting angle of the IGV, the efficiency and head gradually increase from a negative to a positive setting angle. Additionally, 30° is considered the critical setting angle for IGV.

On $$SL(2,\mathbb{R})$$-Cocycles over Irrational Rotations with Secondary Collisions

We consider a skew product $F_{A} = (\sigma_{\omega}, A)$ over irrational rotation $\sigma_{\omega}(x) = x + \omega$ of a circle $\mathbb{T}^{1}$. It is supposed that the transformation $A: \mathbb{T}^{1} \to SL(2, \mathbb{R})$ being a $C^{1}$-map has the form $A(x) = R(\varphi(x)) Z(\lambda(x))$, where $R(\varphi)$ is a rotation in $\mathbb{R}^{2}$ over the angle $\varphi$ and $Z(\lambda)= diag\{\lambda, \lambda^{-1}\}$ is a diagonal matrix. Assuming that $\lambda(x) \ge \lambda_{0} > 1$ with a sufficiently large constant $\lambda_{0}$ and the function $\varphi$ be such that $\cos \varphi(x)$ possesses only simple zeroes, we study hyperbolic properties of the cocycle generated by $F_{A}$. We apply the critical set method to show that, under some additional requirements on the derivative of the function $\varphi$, the secondary collisions compensate weakening of the hyperbolicity due to primary collisions and the cocycle generated by $F_{A}$ becomes hyperbolic in contrary to the case when secondary collisions can be partially eliminated.

Veneto Region dementia-related mortality during the COVID-19 pandemic: multiple causes of death and time series analysis.

Older individuals with dementia have been severely affected by the COVID-19 pandemic. There is a lack of in-depth evaluation of mortality trends using both the underlying cause of death (UCOD) and the multiple causes of death (MCOD) approaches. The objective of this study was to determine the impact of the COVID-19 pandemic on dementia-related deaths considering comorbidities and the place of death. This retrospective, population-based study was conducted in Veneto, Italy. All the death certificates of individuals aged ≥65 years issued from 2008 to 2020 were analyzed for dementia-related mortality using age-standardized sex-stratified rates of dementia as UCOD and MCOD. Excess in monthly dementia-related mortality in 2020 was estimated by applying Seasonal Autoregressive Integrated Moving Average (SARIMA) model. Overall, 70301 death certificates reported dementia (MCOD proportional mortality: 12.9%), and 37604 cases identified it as UCOD (proportional mortality: 6.9%). In 2020, the MCOD proportional mortality increased to 14.3% whereas that of UCOD remained static (7.0%). Compared to the SARIMA prediction, MCOD increased by 15.5% in males and 18.3% in females in 2020. Compared to the 2018-19 average, deaths in nursing homes increased by 32% in 2020, at home by 26% and in hospitals by 12%. An increase in dementia-related mortality during the first months of the COVID-19 pandemic could only be detected using the MCOD approach. MCOD proved to be more robust, and hence, should be included in future analyses. Nursing homes appeared to be the most critical setting which should guide establishing protective measures for similar situations.

Long time behaviour of the discrete volume preserving mean curvature flow in the flat torus

We show that the discrete approximate volume preserving mean curvature flow in the flat torus $$\mathbb {T}^N$$ starting near a strictly stable critical set E of the perimeter converges in the long time to a translate of E exponentially fast. As an intermediate result we establish a new quantitative estimate of Alexandrov type for periodic strictly stable constant mean curvature hypersurfaces. Finally, in the two dimensional case a complete characterization of the long time behaviour of the discrete flow with arbitrary initial sets of finite perimeter is provided.

Topological approaches to knotted electric charge distributions

Consider a knot K in S^3 with uniformly distributed electric charge. Whilst solutions to the Laplace equation in terms of Dirichlet integrals are readily available, it is still of theoretical and physical interest to understand the qualitative behavior of the potential, particularly with respect to critical points and equipotential surfaces. In this paper, we demonstrate how techniques from geometric topology can yield novel insights from the perspective of electrostatics. Specifically, we show that when the knot is sufficiently close to a planar projection, we get a lower bound on the size of the critical set based on the projection’s crossings, improving a 2021 result of the author. We then classify the equipotential surfaces of a charged knot distribution by tracking how the topology of the knot complement restricts the Morse surgeries associated to the critical points of the potential.

Machine learning for acute kidney injury: Changing the traditional disease prediction mode.

Acute kidney injury (AKI) is a serious clinical comorbidity with clear short-term and long-term prognostic implications for inpatients. The diversity of risk factors for AKI has been recognized in previous studies, and a series of predictive models have been developed using traditional statistical methods in conjunction with its preventability, but they have failed to meet the expectations in limited clinical applications, the rapid spread of electronic health records and artificial intelligence machine learning technology has brought new hope for the construction of AKI prediction models. In this article, we systematically review the definition and classification of machine learning methods, modeling ideas and evaluation methods, and the characteristics and current status of modeling studies. According to the modeling objectives, we subdivided them into critical care medical setting models, all medical environment models, special surgery models, special disease models, and special nephrotoxin exposure models. As the first review article to comprehensively summarize and analyze machine learning prediction models for AKI, we aim to objectively describe the advantages and disadvantages of machine learning approaches to modeling, and help other researchers more quickly and intuitively understand the current status of modeling research, inspire ideas and learn from experience, so as to guide and stimulate more research and more in-depth exploration in the future, which will ultimately provide greater help to improve the overall status of AKI diagnosis and treatment.

An improved local error estimate in adaptive finite element analysis based on element energy projection technique

PurposeAn improved adaptive finite element analysis based on local error estimate is proposed via the element energy projection (EEP) technique. This paper aims to discuss the aforementioned idea.Design/methodology/approachThe computational region for a posteriori error estimation based on EEP method is further confined to a critical set of local elements generated in the previous adaptive step, enhancing efficiency while maintaining accuracy. The adaptive procedure incorporated with hierarchical mesh refinement is then developed.FindingsThe effectiveness of the improved error estimation of the overall adaptive analysis is confirmed by several benchmark examples. The results show that the shrinkage of the local computational region has little negative influence on the accuracy of a posteriori error estimation, thus yielding an improved adaptive procedure with simplified logic and reduced cost.Originality/valueBy localizing the computational region for error estimation, two crucial but cumbersome tricks, i.e. treatments of virtual elements and hanging nodes, are removed, giving the proposed approach full clarity and flexibility. The improved adaptive procedure characterizes simpler and faster computational algorithm and can produce results with required accuracy measured in maximum norm.

Partially dissipative systems in the critical regularity setting, and strong relaxation limit

Many physical phenomena may be modeled by first order hyperbolic equations with degenerate dissipative or diffusive terms. This is the case for example in gas dynamics, where the mass is conserved during the evolution, but the momentum balance includes a diffusion (viscosity) or damping (relaxation) term, or, in numerical simulations, of conservation laws by relaxation schemes. Such so-called partially dissipative systems have been first pointed out by S. K. Godunov in a short note in 1961. Much later, in 1984, S. Kawashima highlighted in his PhD thesis a simple criterion ensuring the existence of global strong solutions in the vicinity of a linearly stable constant state. This criterion has been revisited in a number of research works. In particular, K. Beauchard and E. Zuazua proposed in 2010 an explicit method for constructing a Lyapunov functional allowing to refine Kawashima’s results and to establish global existence results in some situations that were not covered before. These notes originate essentially from the PhD thesis of T. Crin-Barat that was initially motivated by an earlier observation of the author in a chapter of the handbook edited by Y. Giga and A. Novotný. Our main aim is to adapt the method of Beauchard and Zuazua to a class of symmetrizable quasilinear hyperbolic systems (containing the compressible Euler equations), in a critical regularity setting that allows to keep track of the dependence with respect to e.g. the relaxation parameter. Compared to Beauchard and Zuazua’s work, we exhibit a ‘damped mode’ that will have a key role in the construction of global solutions with critical regularity, in the proof of optimal time-decay estimates and, last but not least, in the study of the strong relaxation limit. For simplicity, we here focus on a simple class of partially dissipative systems, but the overall strategy is rather flexible, and adaptable to much more general situations.

Measurable Residual Disease and Clonal Evolution in Acute Myeloid Leukemia from Diagnosis to Post-Transplant Follow-Up: The Role of Next-Generation Sequencing

It has now been ascertained that acute myeloid leukemias-as in most type of cancers-are mixtures of various subclones, evolving by acquiring additional somatic mutations over the course of the disease. The complexity of leukemia clone architecture and the phenotypic and/or genotypic drifts that can occur during treatment explain why more than 50% of patients-in hematological remission-could relapse. Moreover, the complexity and heterogeneity of clone architecture represent a hindrance for monitoring measurable residual disease, as not all minimal residual disease monitoring methods are able to detect genetic mutations arising during treatment. Unlike with chemotherapy, which imparts a relatively short duration of selective pressure on acute myeloid leukemia clonal architecture, the immunological effect related to allogeneic hematopoietic stem cell transplant is prolonged over time and must be overcome for relapse to occur. This means that not all molecular abnormalities detected after transplant always imply inevitable relapse. Therefore, transplant represents a critical setting where a measurable residual disease-based strategy, performed during post-transplant follow-up by highly sensitive methods such as next-generation sequencing, could optimize and improve treatment outcome. The purpose of our review is to provide an overview of the role of next-generation sequencing in monitoring both measurable residual disease and clonal evolution in acute myeloid leukemia patients during the entire course of the disease, with special focus on the transplant phase.

Optimization of Flow Cytometric Sorting Parameters for High-Throughput Isolation and Purification of Small Extracellular Vesicles.

Small extracellular vesicles (sEV) can be released from all cell types and carry protein, DNA, and RNA. Signaling molecules serve as indicators of the physiological and pathological state of a cell. However, there is no standard method for sEV isolation, which prevents downstream biomarker identification and drug intervention studies. In this article, we provide a detailed protocol for the isolation and purification of 50-200 nm sEV by a flow cell sorter. For this, a 50 µm nozzle and 80 psi sheath fluid pressure were selected to obtain a good sorting rate and stable side stream. Standard sized polystyrene microspheres were used to locate populations of 100, 200, and 300 nm particles. With additional optimization of the voltage, gain, and forward scatter (FSC) triggering threshold, the sEV signal could be separated from the background noise. These optimizations provide a panel of critical sort settings that enables one to obtain a representative population of sEV using FSC vs. side scatter (SSC) only. The flow cytometry-based isolation method not only allows for high-throughput analysis but also allows for synchronous classification or proteome analysis of sEV based on the biomarker expression, opening numerous downstream research applications.

Flexible Networked Machine Integrated Scheduling Algorithm Based on the Dynamic Root Node Operation Set Considering Reverse Scheduling

Aiming at the problem that the previous flexible machine network integrated scheduling algorithm only considers positive sequence scheduling, which leads to the extension of product completion time, a reverse-order machine network integrated scheduling algorithm based on the dynamic root node operation set is proposed. In order to avoid the constraints of multi-predecessor operations in the process of forward-order scheduling, an encoding method based on dynamic root node operation set is proposed to ensure the validity of constraints among operations. The crossover methods based on crossover row vector and subtree are proposed to ensure the legitimacy of offspring individuals. The chaotic mutation method based on sibling operation and the random mutation method based on mutation row vector are proposed, respectively, to ensure the diversity of the population. A local search strategy based on the critical operation machine set is proposed, which enhances the search ability of the algorithm for optimal solutions. The comparative experimental results show that the proposed algorithm’s solving speed and solution quality outperform other comparison algorithms.

Singular cotangent models in fluids with dissipation

In this article we analyze several mathematical models with singularities where the classical cotangent model is replaced by a b-cotangent model. We provide physical interpretations of the singular symplectic geometry underlying in b-cotangent bundles featuring two models: the canonical (or non-twisted) model and the twisted one. The canonical one models systems on manifolds with boundary and the twisted one represents Hamiltonian systems with a singularity on the fiber. The twisted cotangent model includes (for linear potentials) the case of fluids with dissipation. We prove (non)-existence of cotangent lift dynamics and show the existence of an infinite number of escape orbits in this model. We also discuss more general physical interpretations of the twisted and non-twisted b-symplectic models. Twisted b-symplectic models yield in a natural way escape orbits that go to the critical set. Under compactness assumptions those escape orbits are continued as singular periodic orbits in the sense of Miranda and Oms (2021) and Miranda (2020). These models offer a Hamiltonian formulation for systems which are dissipative, extending the horizons of Hamiltonian dynamics and opening a new approach to study non-conservative systems.

Positive and negative exact controllability results for the linear Biharmonic Schrödinger equation

In this paper, we study the exact boundary controllability of the linear Biharmonic Schrödinger equation on a bounded domain with hinged boundary conditions and boundary control acts on the second spatial derivative at the left endpoint. We prove that this system is exactly controllable at any positive time $ T $, if and only if, the group velocity dispersion (GVD) coefficient does not belong to a critical countable set of negative real numbers. The analysis in this work is based on spectral analysis together with the nonharmonic Fourier series method.

“In All Ages and All Churches”: Anti-Mormonism and the Making of Antebellum Evangelicalism

“In All Ages and All Churches”: Anti-Mormonism and the Making of Antebellum Evangelicalism

Global existence, blow-up and mass concentration for the inhomogeneous nonlinear Schrödinger equation with inverse-square potential

<abstract><p>In the current paper, the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation including inverse-square potential is considered. First, some criteria of global existence and finite-time blow-up in the mass-critical and mass-supercritical settings with $ 0 < c\leq c^{*} $ are obtained. Then, by utilizing the potential well method and the sharp Sobolev constant, the sharp condition of blow-up is derived in the energy-critical case with $ 0 < c < \frac{N^{2}+4N}{(N+2)^{2}}c^{*} $. Finally, we establish the mass concentration property of explosive solutions, as well as the dynamic behaviors of the minimal-mass blow-up solutions in the $ L^{2} $-critical setting for $ 0 < c < c^{*} $, by means of the variational characterization of the ground-state solution to the elliptic equation, scaling techniques and a suitable refined compactness lemma. Our results generalize and supplement the ones of some previous works.</p></abstract>

Decompositions of moduli spaces of vector bundles and graph potentials

Abstract We propose a conjectural semiorthogonal decomposition for the derived category of the moduli space of stable rank 2 bundles with fixed determinant of odd degree, independently formulated by Narasimhan. We discuss some evidence for and furthermore propose semiorthogonal decompositions with additional structure. We also discuss two other decompositions. One is a decomposition of this moduli space in the Grothendieck ring of varieties, which relates to various known motivic decompositions. The other is the critical value decomposition of a candidate mirror Landau–Ginzburg model given by graph potentials, which in turn is related under mirror symmetry to Muñoz’s decomposition of quantum cohomology. This corresponds to an orthogonal decomposition of the Fukaya category. We discuss how decompositions on different levels (derived category of coherent sheaves, Grothendieck ring of varieties, Fukaya category, quantum cohomology, critical sets of graph potentials) are related and support each other.

The Learning Practices of the Students with Physical Disabilities

In this research article the current learning practices to the students with physical disabilities are discussed. It is a qualitative study. The main objective of the study is to analyze current learning practices used for students with physical disabilities in Kailali district. Interview schedule and classed observation were the major tools for the collection of data in the study. The researcher chose case study as a research design. In this study, the organization is a case where physically disabled students stay and study. Among eight teachers three teachers were selected through Purposive sampling method. The data were collected from teachers who were teaching physically disabled students in school teaching. The findings of the study showed that the practice of teaching physically disabled students seemed to be difficult and challenging. The foremost reason behind this is the lack of disability-assistive infrastructure, parental support, social stigma, teachers training and awareness. Moreover, the findings revealed that teachers’ professionalism, engagement with students, planning for the lesson, inculcating the spirit of a creative and critical thinking and setting goals can prove instrumental to maximize students’ outcomes. The implication of the study is that the teachers should enhance special skills to deal with physically disabled students for their better performance.