Critical Setting Research Articles

The Maxwell-scalar field system near spatial infinity

We make use of Friedrich’s representation of spatial infinity to study asymptotic expansions of the Maxwell-scalar field system near spatial infinity. The main objective of this analysis is to understand the effects of non-linearities of this system on the regularity of solutions and polyhomogeneous expansions at null infinity and, in particular, at the critical sets where null infinity touches spatial infinity. The main outcome from our analysis is that the nonlinear interaction makes both fields more singular at the conformal boundary than what is seen when the fields are non-interacting. In particular, we find a whole new class of logarithmic terms in the asymptotic expansions, which depend on the coupling constant between the Maxwell and scalar fields. We analyze the implications of these results on the peeling (or rather lack thereof) of the fields at null infinity.

The effect of reparixin on survival in patients at high riskfor in-hospital mortality: a meta-analysis of randomized trials.

IntroductionA great number of anti-inflammatory drugs have been suggested in the treatment of SARS-CoV-2 infection. Reparixin, a non-competitive allosteric inhibitor of the CXCL8 (IL-8) receptors C-X-C chemokine receptor type 1 (CXCR1) and C-X-C chemokine receptor type 2 (CXCR2), has already been tried out as a treatment in different critical settings. Due to the contrasting existing literature, we decided to perform the present meta-analysis of randomized controlled trials (RCTs) to investigate the effect of the use of reparixin on survival in patients at high risk for in-hospital mortality.MethodsWe created a search strategy to include any human RCTs performed with reparixin utilization in patients at high risk for in-hospital mortality, excluding oncological patients. Two trained, independent authors searched PubMed, EMBASE, and the Cochrane Central Register of Controlled Trials (CENTRAL) for appropriate studies. Furthermore, references of review articles and included RCTs were screened to identify more studies. No language restrictions were enforced. To assess the risk of bias of included trials, the Revised Cochrane risk-of-bias tool for randomized trials (RoB 2) was used.ResultsOverall, six studies were included and involved 406 patients (220 received reparixin and 186 received the comparator). The all-cause mortality in the reparixin group was significantly lower than that in the control group [5/220 (2.3%) in the reparixin group vs. 12/186 (6.5%) in the control group, odds ratio = 0.33 (95% confidence interval 0.12 to 0.96), p-value for effect 0.04, p for heterogeneity 0.20, I 2 = 36%]. In addition, no difference in the rate of pneumonia, sepsis, or non-serious infections was shown between the two groups.ConclusionOur meta-analysis of randomized trials suggests that short-term inhibition of CXCL8 activity improved survival in patients at high risk for in-hospital mortality without increasing the risk of infection.Meta-analysis registrationPROSPERO, identifier CRD42021254467.

Off-road testing scenario design and library generation for intelligent vehicles

To realize the widespread application and continuous functional development of intelligent vehicles, test and evaluation of vehicle's functionality and Safety Performance in complex off-road scenarios are fundamental. Since traditional distance-based road tests cannot meet the evolving test requirements, a method to design the function-based off-road testing scenario library for intelligent vehicles(IV) is proposed in this paper. The testing scenario library is defined as a critical set of scenarios that can be used for IV tests. First, for the complex and diverse off-road scenarios, a hierarchical, structural model of the test scenario is built. Then, the critical test scenarios are selected adaptively according to the vehicle model to be tested. Next, those parameters representing the challenging test scenarios are selected. The selected parameters need to fit the natural distribution probability of scenarios. The critical test-scenario library is built combing these parameters with the structural model. Finally, the test scenarios that are most approximate to the natural driving scenario are determined with importance sampling theory. The test-scenario library built with this method can provide more critical test scenarios, and is widely applicable despite different vehicle models. Verified by simulation in the off-road interaction scenarios, test would be accelerated significantly with this method, about 800 times faster than testing in the natural road environment.

The Identification of Subphenotypes and Associations with Health Outcomes in Patients with Opioid-Related Emergency Department Encounters Using Latent Class Analysis.

The emergency department (ED) is a critical setting for the treatment of patients with opioid misuse. Detecting relevant clinical profiles allows for tailored treatment approaches. We sought to identify and characterize subphenotypes of ED patients with opioid-related encounters. A latent class analysis was conducted using 14,057,302 opioid-related encounters from 2016 through 2017 using the National Emergency Department Sample (NEDS), the largest all-payer ED database in the United States. The optimal model was determined by face validity and information criteria-based metrics. A three-step approach assessed class structure, assigned individuals to classes, and examined characteristics between classes. Class associations were determined for hospitalization, in-hospital death, and ED charges. The final five-class model consisted of the following subphenotypes: Chronic pain (class 1); Alcohol use (class 2); Depression and pain (class 3); Psychosis, liver disease, and polysubstance use (class 4); and Pregnancy (class 5). Using class 1 as the reference, the greatest odds for hospitalization occurred in classes 3 and 4 (Ors 5.24 and 5.33, p < 0.001) and for in-hospital death in class 4 (OR 3.44, p < 0.001). Median ED charges ranged from USD 2177 (class 1) to USD 2881 (class 4). These subphenotypes provide a basis for examining patient-tailored approaches for this patient population.

Well-Being and Safety in the Workplace

The workplace represents a critical and time-consuming exposure setting in which workers are continuously exposed to the heterogeneity of hazards, including physical, biological, chemical, and organizational risk factors [...].

Embracing Complexity in Policy Implementation Research: A Comparative Analysis of Water Policy Implementation in the Great Lakes and Rio-Grande/Bravo Regions

Scholars and practitioners must increasingly embrace complexity in policy implementation research and practice. This article presents findings from in-depth comparative qualitative analysis of two complex transboundary water policy cases, the North American Great Lakes and Rio Grande/Bravo Basin, to highlight the value of focusing on four sets of factors (contextual, institutional, engagement, and knowledge factors) to understand why complex policy regimes continue to face limited policy implementation success in achieving policy goals decades after initiating implementation efforts. The findings outline the value of focusing on critical sets of factors in comparative policy implementation research that embraces complexity.

Assessment of Racial and Ethnic Differences in Oxygen Supplementation Among Patients in the Intensive Care Unit

Pulse oximetry (SpO2) is routinely used for transcutaneous monitoring of blood oxygenation, but it can overestimate actual oxygenation. This is more common in patients of racial and ethnic minority groups. The extent to which these discrepancies are associated with variations in treatment is not known. To determine if there are racial and ethnic disparities in supplemental oxygen administration associated with inconsistent pulse oximeter performance. This retrospective cohort study was based on the Medical Information Mart for Intensive Care (MIMIC)-IV critical care data set. Included patients were documented with a race and ethnicity as Asian, Black, Hispanic, or White and were admitted to the intensive care unit (ICU) for at least 12 hours before needing advanced respiratory support, if any. Oxygenation levels and nasal cannula flow rates for up to 5 days from ICU admission or until the time of intubation, noninvasive positive pressure ventilation, high-flow nasal cannula, or tracheostomy were analyzed. The primary outcome was time-weighted average supplemental oxygen rate. Covariates included race and ethnicity, sex, SpO2-hemoglobin oxygen saturation discrepancy, data duration, number and timing of blood gas tests on ICU days 1 to 3, partial pressure of carbon dioxide, hemoglobin level, average respiratory rate, Elixhauser comorbidity scores, and need for vasopressors or inotropes. This cohort included 3069 patients (mean [SD] age, 66.9 [13.5] years; 83 were Asian, 207 were Black, 112 were Hispanic, 2667 were White). In a multivariable linear regression, Asian (coefficient, 0.602; 95% CI, 0.263 to 0.941; P = .001), Black (coefficient, 0.919; 95% CI, 0.698 to 1.140; P < .001), and Hispanic (coefficient, 0.622; 95% CI, 0.329 to 0.915; P < .001) race and ethnicity were all associated with a higher SpO2 for a given hemoglobin oxygen saturation. Asian (coefficient, -0.291; 95% CI, -0.546 to -0.035; P = .03), Black (coefficient, -0.294; 95% CI, -0.460 to -0.128; P = .001), and Hispanic (coefficient, -0.242; 95% CI, -0.463 to -0.020; P = .03) race and ethnicity were associated with lower average oxygen delivery rates. When controlling for the discrepancy between average SpO2 and average hemoglobin oxygen saturation, race and ethnicity were not associated with oxygen delivery rate. This discrepancy mediated the effect of race and ethnicity (-0.157; 95% CI, -0.250 to -0.057; P = .002). In this cohort study, Asian, Black, and Hispanic patients received less supplemental oxygen than White patients, and this was associated with differences in pulse oximeter performance, which may contribute to known race and ethnicity-based disparities in care.

UAV Trajectory Planning from a Comprehensive Energy Efficiency Perspective in Harsh Environments

As a highly promising application paradigm, unmanned aerial vehicles (UAVs) in wireless communications have gained widespread attention by virtue of their advantages, such as low cost and high agility. Unfortunately, the discharge capacity of onboard batteries will be greatly weakened in harsh environments, thereby reducing the expected endurance of the UAV. To this end, a UAV data distribution system with expected data requirements is considered in this article. Our objective is to reassess the trade-off between UAV mission time and its propulsion energy consumption (PEC), and provide a novel designing perspective for energy-efficient UAV deployment based on trajectory planning. First, we analyze the energy consumption composition and approximate the PEC to the total energy consumption of the UAV. Then, based on the “hover-fly-communicate” design, we focus on the factors that affect mission time and PEC. Furthermore, the simulation results illustrate the influence of critical system parameter settings on the propulsion energy consumption efficiency (PEC-E) of the UAV. Finally, future research is discussed, and the article is concluded.

An Interactive Explanatory AI System for Industrial Quality Control

Machine learning based image classification algorithms, such as deep neural network approaches, will be increasingly employed in critical settings such as quality control in industry, where transparency and comprehensibility of decisions are crucial. Therefore, we aim to extend the defect detection task towards an interactive human-in-the-loop approach that allows us to integrate rich background knowledge and the inference of complex relationships going beyond traditional purely data-driven approaches. We propose an approach for an interactive support system for classifications in an industrial quality control setting that combines the advantages of both (explainable) knowledge-driven and data-driven machine learning methods, in particular inductive logic programming and convolutional neural networks, with human expertise and control. The resulting system can assist domain experts with decisions, provide transparent explanations for results, and integrate feedback from users; thus reducing workload for humans while both respecting their expertise and without removing their agency or accountability.

Electron acoustic singular solitons interaction in the Earth’s magnetotail region

Electron acoustic potential structures are generated in the presence of a large-amplitude electric field in Earth’s magnetotail region, Earth’s magnetosphere according to the numerous space observations by satellites. In this article, we study the electron-acoustic solitary waves (EASWs) in an unmagnetized electron–ion plasma consisting of cold electrons and isothermal ions with two different temperatures. Nonlinear evolution equations are derived from the hydrodynamic model of collisionless, unmagnetized electron–ion plasma. Exact analytic solutions are obtained from derived Korteweg-de Vries (KdV) equations and modified Korteweg-de Vries (MKdV) equations separately with the aid of the Hirota Bilinear method. Two singular soliton solutions of both KdV and MKdV equations are obtained separately. The efficiency and interactive approach of the heuristic Hirota Bilinear method leads to multiple singular soliton solutions for its beautiful algebraic technique which generates solitons solutions as well as singular solitons explicitly. Then the significant multi singular soliton interaction has been studied for KdV singular solitons and MKdV singular solitons in the critical parameter set.

A Bi-Objective Model for Scheduling Construction Projects Using Critical Chain Method and Interval-Valued Fuzzy Sets

Numerous constraints affect construction projects, and lack of management may lead to schedule deviation. In the execution phase of the project, due to the lack of timely access to the required resources and the existence of uncertainty, the project activities do not progress following the schedule, and as a result, schedule deviation occurs. The scheduling addresses resource constraints by the critical chain method and deals with delays in activities by placing buffers that have emerged as a method for scheduling construction projects. This paper presents a new bi-objective mathematical model which aims to reduce delay and increase quality, based on the critical chain method and resource constraint for scheduling construction projects. In the proposed model, the activities have been considered multi-mode ones. Moreover, this paper has assumed each activity to be executed in a normal or crashing way. Due to the uncertainty in real-world problems, the duration of the activity is expressed using triangular interval-valued fuzzy numbers. A new interval-valued fuzzy solution process is presented in this paper using a two-step approach. First, the equivalent crisp model is given; then in the second step, a goal programming approach is applied for transforming the bi-objective model into the single-objective one. Finally, the mathematical model is implemented on a case study adapted from the literature, and sensitivity analysis of the results is conducted.

How do intensive work environments affect nurses' absenteeism and turnover intent?

BackgroundIntensive hospital work environments can affect staff, patient, and organizational outcomes. Purpose(1) To assess quantitatively the relationship between critical care registered nurses' perceptions of their workplace, their absenteeism, and their turnover intent; and (2) to analyze nurses' recommendations for improvements for critical patient care. MethodsFollowing STROBE guidelines, a cross-sectional survey sampled registered nurses (n = 302), across the Canadian province of Alberta, in October 2018. We assessed nurses' perceptions of their work environment relative to their absenteeism and turnover intent utilizing regression modelling and the Practice Environment Scale of the Nursing Work Index. FindingsA negative binomial analysis indicated that RNs' positive perceptions about their workplace had significant associations with lower rates of absenteeism. Additionally, participants who scored their work environment higher were found to have decreased intentions of leaving the workplace. RNs ranked their “participation in hospital affairs” lowest when comparing practice environment domains and recommended optimizing staffing as the most important improvement for their work environment and patient care. DiscussionConsidering the demands associated with critical care patient settings, stakeholders can consider these findings that significant associations exist between nursing staffs' perceptions of the workplace relative to their absenteeism and their turnover intent. Implications for Policy: Value-based solutions are needed in optimizing these key factors, and staffs' participation in hospital affairs appears vital for organizational success.

Reproductive-Stage Heat Stress in Cereals: Impact, Plant Responses and Strategies for Tolerance Improvement.

Reproductive-stage heat stress (RSHS) poses a major constraint to cereal crop production by damaging main plant reproductive structures and hampering reproductive processes, including pollen and stigma viability, pollination, fertilization, grain setting and grain filling. Despite this well-recognized fact, research on crop heat stress (HS) is relatively recent compared to other abiotic stresses, such as drought and salinity, and in particular, RSHS studies in cereals are considerably few in comparison with seedling-stage and vegetative-stage-centered studies. Meanwhile, climate change-exacerbated HS, independently or synergistically with drought, will have huge implications on crop performance and future global food security. Fortunately, due to their sedentary nature, crop plants have evolved complex and diverse transient and long-term mechanisms to perceive, transduce, respond and adapt to HS at the molecular, cell, physiological and whole plant levels. Therefore, uncovering the molecular and physiological mechanisms governing plant response and tolerance to RSHS facilitates the designing of effective strategies to improve HS tolerance in cereal crops. In this review, we update our understanding of several aspects of RSHS in cereals, particularly impacts on physiological processes and yield; HS signal perception and transduction; and transcriptional regulation by heat shock factors and heat stress-responsive genes. We also discuss the epigenetic, post-translational modification and HS memory mechanisms modulating plant HS tolerance. Moreover, we offer a critical set of strategies (encompassing genomics and plant breeding, transgenesis, omics and agronomy) that could accelerate the development of RSHS-resilient cereal crop cultivars. We underline that a judicious combination of all of these strategies offers the best foot forward in RSHS tolerance improvement in cereals. Further, we highlight critical shortcomings to RSHS tolerance investigations in cereals and propositions for their circumvention, as well as some knowledge gaps, which should guide future research priorities. Overall, our review furthers our understanding of HS tolerance in plants and supports the rational designing of RSHS-tolerant cereal crop cultivars for the warming climate.

In vivo Mouse Intervertebral Disc Degeneration Models and Their Utility as Translational Models of Clinical Discogenic Back Pain: A Comparative Review.

Low back pain is a leading cause of disability worldwide and studies have demonstrated intervertebral disc (IVD) degeneration as a major risk factor. While many in vitro models have been developed and used to study IVD pathophysiology and therapeutic strategies, the etiology of IVD degeneration is a complex multifactorial process involving crosstalk of nearby tissues and systemic effects. Thus, the use of appropriate in vivo models is necessary to fully understand the associated molecular, structural, and functional changes and how they relate to pain. Mouse models have been widely adopted due to accessibility and ease of genetic manipulation compared to other animal models. Despite their small size, mice lumbar discs demonstrate significant similarities to the human IVD in terms of geometry, structure, and mechanical properties. While several different mouse models of IVD degeneration exist, greater standardization of the methods for inducing degeneration and the development of a consistent set of output measurements could allow mouse models to become a stronger tool for clinical translation. This article reviews current mouse models of IVD degeneration in the context of clinical translation and highlights a critical set of output measurements for studying disease pathology or screening regenerative therapies with an emphasis on pain phenotyping. First, we summarized and categorized these models into genetic, age-related, and mechanically induced. Then, the outcome parameters assessed in these models are compared including, molecular, cellular, functional/structural, and pain assessments for both evoked and spontaneous pain. These comparisons highlight a set of potential key parameters that can be used to validate the model and inform its utility to screen potential therapies for IVD degeneration and their translation to the human condition. As treatment of symptomatic pain is important, this review provides an emphasis on critical pain-like behavior assessments in mice and explores current behavioral assessments relevant to discogenic back pain. Overall, the specific research question was determined to be essential to identify the relevant model with histological staining, imaging, extracellular matrix composition, mechanics, and pain as critical parameters for assessing degeneration and regenerative strategies.

Abstract 2923: New insights into interactions of the androgen receptor with ELK1 and the platform antagonist KCI807

Abstract Prostate cancer (PC) is generally dependent on the androgen signaling axis for growth. Advanced PC is managed by androgen deprivation therapy (ADT). However, the tumors frequently progress by restoring AR signaling that is either androgen-independent or hypersensitive to androgen, leading to castration resistant prostate cancer (CRPC). CRPC is also supported by hormone-independent actions of AR splice variants which lack the ligand binding domain. Additionally, ADT has many undesirable side effects on a variety of normal tissues that depend on androgen for non-growth related functions, including effects on the cardiovascular system, central nervous system (cognitive effects), bone and muscle. Therefore, a more strategic therapy approach would be to disrupt a functional arm of AR-signaling that is critical for PC/CRPC growth but not for the essential physiological roles of AR in normal tissues. Previous studies in this laboratory have identified ELK1 as an AR tethering protein essential for activation of a critical set of androgen/AR growth genes in various PC model cell line models, both in vitro and in vivo, including those resistant to castration and enzalutamide. It was also established that the N-terminal A/B domain of AR binds to ELK1 by co-opting the two ERK docking sites on ELK1 to constitutively activate genes enriched for cell growth functions in PC cells. A platform antagonist (KCI807) was discovered that bound to AR (Kd = 7x10-8 M), blocking its association with ELK1 and inhibiting PC/CRPC tumor growth. KCI807 has a limited target gene set (a subset of AR target genes) that is primarily and highly enriched for functions in cell cycle progression and mitosis. To further drug development, we must identify the ELK1 docking site recognition sites in AR and the KCI807 binding site. Using a variety of complimentary approaches, we have now mapped and validated the ELK1 docking site recognition sites in the AR A/B domain and also the binding site of KCI807 in AR. The two docking site recognition sites in the AR A/B domain for the two docking sites in ELK1 span amino acids 358-456 and amino acids 514-557. We have also developed a working model in which KCI807 binds in a cleft adjacent to the downstream ELK1-binding site, within the DBD, displacing an alpha helix which in turn disrupts ELK1 binding. Further structural and functional studies based on this knowledge will directly aid in design of next-generation antagonists to selectively target ELK1-dependent growth signaling by AR in PC/CRPC tumors. Citation Format: Claire L. Soave, Charles Ducker, Nathan Nicely, Yanfang Huang, Luke Pardy, Peter Shaw, Manohar Ratnam. New insights into interactions of the androgen receptor with ELK1 and the platform antagonist KCI807 [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 2923.

Singular solitons interaction of dust ion acoustic waves in the framework of Korteweg de Vries and Modified Korteweg‐de Vries equations with (r,q) distributed electrons

AbstractTwo nonlinear evolution equations (NLEEs), namely, Korteweg‐de Vries (KdV) and modified Korteweg‐de Vries (MKdV) are derived from the dust hydrodynamic model of collisionless, unmagnetized dusty plasma with electrons following double spectral velocity distribution, that is, (r,q) distribution. Regular as well as singular analytic solutions of derived KdV equations and MKdV equations are obtained separately with the aid of the Hirota Bilinear method. Two singular soliton solutions of both KdV and MKdV equations are obtained separately. The efficiency and interactive approach of the heuristic Hirota Bilinear method leads to multiple singular soliton solutions for its beautiful algebraic technique which generates solitons solutions as well as singular solitons explicitly. Then the significance of multi singular soliton interaction has been studied for KdV singular solitons and for MKdV singular solitons in the critical parameter set.

The level sets of functions with bounded criticalsets and bounded Hess+ complements

"We denote by ${\rm Hess}^+(f)$ the set of all points $p\in\mathbb{R}^n$ such that the Hessian matrix $H_p(f)$ of the $C^2$-smooth function $f:\mathbb{R}^n\longrightarrow\mathbb{R}$ is positive definite. In this paper we prove several properties of real-valued functions of several variables by showing the connectedness of their level sets for sufficiently high levels, under the boundedness assumption on the critical set. In the case of three variables we also prove the convexity of the levels surfaces for sufficiently high levels, under the additional boundedness assumption on the ${\rm Hess}^+$ complement. The selection of the {\em a priori} convex levels, among the connected regular ones, is done through the positivity of the Gauss curvature function which ensure an ovaloidal shape of the levels to be selected. The ovaloidal shape of a level set makes a diffeomorphism out of the associated Gauss map. This outcome Gauss map diffeomorphism is then extended to a smooth homeomorphism which is used afterwards to construct one-parameter families of smooth homeomorphisms of Loewner chain flavor. "

Philosophy Examined: Metaphilosophy in Pragmatic Perspective by Nicholas Rescher

Reviewed by: Philosophy Examined: Metaphilosophy in Pragmatic Perspective by Nicholas Rescher Daniel Pierson RESCHER, Nicholas. Philosophy Examined: Metaphilosophy in Pragmatic Perspective. Berlin: De Gruyter, 2021. xii + 216 pp. Cloth, $100.99 Nicholas Rescher's Philosophy Examined: Metaphilosophy in Pragmatic Perspective is a refreshing book. Rescher brings his decades of experience in the field to bear on the topic of metaphilosophy, which he describes as "the study of the nature and methodology of the discipline." The book provides an opportunity to reflect on basic philosophical commitments that might otherwise be sedimented over in the highly specialized environment of academic philosophy. His careful formulations along the way are both instructive and delightful; the reader finds himself in the presence of an original and systematic thinker. At the same time, the book is sometimes needlessly repetitious. It is episodic in the sense that no internal references are made to earlier parts of the book, even when the same topics arise or the same examples are used. At several points, paragraphs from earlier in the book are repeated verbatim in later chapters. (In addition, it should be noted that the present state of the text is marred by a distracting number of typographical errors: over 200 or so, in its 210 pages!) The book is divided into fourteen chapters of uneven length: Four are brief (4–8 pages), five are mid-length (11–14 pages), and five are relatively long (16+ pages). Whereas the shorter and mid-length chapters are somewhat matter-of-factly stated, along the lines of a textbook, the long chapters are more involved scholarly contributions, which have been published—sometimes in a less revised version—in other places. Chapter 1 is a brief chapter in which philosophy is distinguished from science. Whereas the latter deals with "the real world," the former profitably makes use of speculative thought maneuvers, such as "what-if" scenarios, paradox, and thought experiments. As Rescher states very nicely, the contemplation of what is not can lead us to understand and appreciate "the offerings and arrangements of the real." In a mid-length chapter 2, Rescher points to the inherent tension that he sees in philosophical claims, such that they aim for a likelihood of correctness that can be purchased only by sacrificing informativeness; that is, they demand "conjoint precision and generality." In the face of the "problems of getting it right" discussed in chapter 2, a brief chapter 3 advocates for a "rational contextualism" founded on [End Page 825] separate "zones of acceptability." Rescher proposes this as the best way of dealing with the "information glut" caused by the pragmatic shift from absolute truth as the standard of acceptability to the less rigid "warranted assertability." A mid-length chapter 4 notes that philosophy aims at the best available answer to its questions, not "the best possible answer (in some rarified sense of the term)." Ultimately, it is the task of philosophy to "impart systemic order into the manifold of relevant data." But the relevant data of the discipline comes from diverse sources (such as common sense, science, tradition, and so forth) that serve up mutually inconsistent statements, all of which have plausibility. Given the inherent inconsistencies of the data set, Rescher defends the coherentist approach as the most "natural" for the field. After chapter 4 begins a sequence of four long chapters. Chapter 5 is an insightful discussion of the role that aporias and strategic distinctions can play in the task of philosophy. In chapter 6, Rescher defends his philosophy against two sets of critics: those who claim that his metaphilosophical coherentism is ultimately a "crypto-relativism" and others who take it to be more consistent with an "evidentialist absolutism." In chapter 7, Rescher suggests that recasting the philosophical enterprise as a "quest for plausibility" rather than for truth would help to overcome a major obstacle to systematization, namely, treating philosophical claims as rival truth claims. Chapter 8 examines the nature, function, and ultimate justification for first principles. Rescher concludes that any given first principles are defeasible since they are ultimately justified pragmatically. A brief chapter 9 is an exhortation for intellectual modesty concerning our philosophical views, given certain cognitive limitations that we must acknowledge. A...

Critical points of solutions to a kind of linear elliptic equations in multiply connected domains

In this paper, we mainly study the critical points and critical zero points of solutions u to a kind of linear elliptic equations with nonhomogeneous Dirichlet boundary conditions in a multiply connected domain Ω in ℝ2. Based on the delicate analysis about the distributions of connected components of the super-level sets {x ∈ Ω: u(x) > t} and sub-level sets {x ∈ Ω: u(x) < t} for some t, we obtain the geometric structure of interior critical point sets of u. Precisely, let Ω be a multiply connected domain with the interior boundary γI and the external boundary γE, where u∣γI = ψ1(x), u∣γE = ψ2(x). When ψ1(x) and ψ2(x) have N1 and N2 local maximal points on γI and γE respectively, we deduce that \(\sum\nolimits_{i = 1}^k {{m_i} \le {N_1} + {N_2}} \), where m1,…,mk are the respective multiplicities of interior critical points x1,…,xk of u. In addition, when \({\min _{{\gamma _E}}}{\psi _2}\left( x \right) \ge {\max _{{\gamma _I}}}{\psi _1}\left( x \right)\) and u has only N1 and N2 equal local maxima relative to \(\overline \Omega \) on γI and γe respectively, we develop a new method to show that one of the following three results holds \(\sum\nolimits_{i = 1}^k {{m_i} = {N_1} + {N_2}} \) or \(\sum\nolimits_{i = 1}^k {{m_i} + 1 = {N_1} + {N_2}} \) or \(\sum\nolimits_{i = 1}^k {{m_i} + 2 = {N_1} + {N_2}} \). Moreover, we investigate the geometric structure of interior critical zero points of u. We obtain that the sum of multiplicities of the interior critical zero points of u is less than or equal to the half of the number of its isolated zero points on the boundaries.

Understanding Uncertainty Maps in Vision with Statistical Testing.

Quantitative descriptions of confidence intervals and uncertainties of the predictions of a model are needed in many applications in vision and machine learning. Mechanisms that enable this for deep neural network (DNN) models are slowly becoming available, and occasionally, being integrated within production systems. But the literature is sparse in terms of how to perform statistical tests with the uncertainties produced by these overparameterized models. For two models with a similar accuracy profile, is the former model's uncertainty behavior better in a statistically significant sense compared to the second model? For high resolution images, performing hypothesis tests to generate meaningful actionable information (say, at a user specified significance level ) is difficult but needed in both mission critical settings and elsewhere. In this paper, specifically for uncertainties defined on images, we show how revisiting results from Random Field theory (RFT) when paired with DNN tools (to get around computational hurdles) leads to efficient frameworks that can provide a hypothesis test capabilities, not otherwise available, for uncertainty maps from models used in many vision tasks. We show via many different experiments the viability of this framework.