Two species competitive model with the Allee effect

We consider the following system of difference equations: [Mathematical equations cannot be displayed here, refer to PDF], where a, b, c, d are positive constants and x0, y0 ≥ 0 are initial conditions. This system has interesting dynamics and can have up to nine equilibrium points. The most complex and perhaps most interesting case is the case of nine equilibrium points, four of which are local attractors, four of which are saddle points, and one of which is a repeller. Using recent results of Kulenović and Merino we are able to characterize the basins of attractions of all local attractors and thus to describe the global dynamics of this system. This case can be considered as a two-dimensional version of the Allee effect for competitive systems

Taking a Day off to Pray: Closing Schools for Religious Observance in Increasingly Diverse Schools

States and public schools across the Nation consistently debate the number of days students must be in attendance, the length of the day, and the configuration of those days to maximize learning opportunities. Establishing the school calendar within each state’s statutory minimum can be challenging as many states still maintain somewhat traditional (albeit antiquated) calendars, which commence the school year around Labor Day and conclude shortly after June begins.1 Public schools are generally in session for 180 school days. Some states have been more creative in their scheduling by reducing the number of days required of student attendance in favor of expanded school days, citing reduced costs. Attempting to schedule 180 school days in the period of late August through early June does not provide schools with much flexibility should they be required to close for exigent circumstances such as inclement weather. Providing students with additional days off for holidays and religious observances only increases the complexity of meeting the required number of school days in a respective state given these calendar constraints

When Speech Is Your Stock in Trade: What Kennedy v. Bremerton School District Reveals about the Future of Employee Speech and Religion Jurisprudence

Coaches play an important role in establishing a nondiscriminatory environment in public-school athletics, both on and off the field. In addition to the duties associated with training a team for athletic competition, coaches, like teachers, are hired to communicate with players and spectators both verbally and demonstratively. Coaches are expected to not only teach sports techniques, but also teach character, leadership, sportsmanship, and other positive character traits. In Kennedy v. Bremerton School District, courts from the district level to the Supreme Court have considered how Coach Joe Kennedy\u27s role as a coach factored into his right to pray on the 50-yard line directly following his team\u27s high school football games. This Article reviews Kennedy v. Bremerton School District, from its inception through its current status, including the significance of Justice Alito\u27s concurring opinion issued in conjunction with the United States Supreme Court\u27s denial of Coach Kennedy\u27s Petition for Writ of Certiorari. After discussing the underlying facts, Part I provides an overview and analysis of the district and circuit courts\u27 rulings focusing particularly on the relationship between employee speech and the First Amendment religion clauses. Part II discusses the implications of Justice Alito\u27s concurring opinion in denying Coach Kennedy\u27s petition. And finally, Part III discusses the future of religious speech jurisprudence for public school employees, now that Justices Gorsuch and Kavanaugh are on the Supreme Court bench

What is the initial work-up in the diagnosis of hypertension?

Patients with a new diagnosis of hypertension should be evaluated with a history and physical exam and the following initial studies: serum potassium and creatinine, fasting serum glucose and lipid panel, hematocrit, urinalysis, and electrocardiogram (strength of recommendation [SOR]: C, based on a consensus of expert opinion). Consensus is lacking for measuring serum sodium, calcium, and uric acid. Testing for microalbuminuria is optional in the work-up for a patient without diabetes (SOR: C, expert consensus). Some expert panels list limited echocardiography as another option

Liver Disease in Burn Injury: Evidence From a National Sample of 31,338 Adult Patients

Objective: To assess mortality risk and extent of increased length of hospital stay in patients with burn injury with preexisting liver disease. Methods: Records of 31,338 adults who were admitted with burns to 70 burn centers were reviewed from the American Burn Association National Burn Repository. Demographics, percentage burn, and medical characteristics of 180 patients with liver disease were compared with all patients without liver disease and to a propensity score–matched sample of 180 patients without liver disease. Risk of mortality as well as lengths of both intensive care and total stay were compared after matching for demographics, burn injury, and preexisting medical conditions. Results: Patients with liver disease were significantly more likely to have a history of a number of medical comorbidities, including alcohol abuse, drug abuse, a psychiatric diagnosis, chronic pulmonary disease, hypertension, and diabetes. Patients with liver disease were significantly more likely to die in the hospital (27.2% vs 6.9%, odds ratio = 5.0, 95% confidence interval = 3.6–7.0, P < .01), and this held even when compared with a propensity score–matched group of patients without liver disease, but with similar demographics, burn injury, and medical profiles. Lengths of both intensive care and total hospital stay were 122.5% (P < .01) and 86.7% (P < .01) longer, respectively, among patients with liver disease than among all other patients. In a matched sample, lengths of both intensive care and total stays were longer, albeit not significantly so (41.6%, P = .12; 35.5%, P = .07). Conclusions: Liver impairment worsens the prognosis in patients with thermal injury

Values of sleep/wake, activity/rest, circadian rhythms, and fatigue prior to adjuvant breast cancer chemotherapy.

Fatigue is the most prevalent and distressing symptom experienced by patients receiving adjuvant chemotherapy for early stage breast cancer. Higher fatigue levels have been related to sleep maintenance problems and low daytime activity in patients who have received chemotherapy, but knowledge describing these relationships prior to chemotherapy is sparse. The Piper Integrated Fatigue Model guided this study, which describes sleep/wake, activity/rest, circadian rhythms, and fatigue and how they interrelate in women with Stage I, II, or IIIA breast cancer during the 48 hours prior to the first adjuvant chemotherapy treatment. The present report describes these variables in 130 females, mean age=51.4 years; the majority were married and employed. Subjective sleep was measured by the Pittsburgh Sleep Quality Index and fatigue was measured by the Piper Fatigue Scale. Wrist actigraphy was used to objectively measure sleep/wake, activity/rest, and circadian rhythms. Mean Pittsburgh Sleep Quality Index score was 6.73+/-3.4, indicating poor sleep. Objective sleep/wake results were within normal limits established for healthy individuals, except for the number and length of night awakenings. Objective activity/rest results were within normal limits except for low mean daytime activity. Circadian rhythm mesor was 132.3 (24.6) and amplitude was 97.2 (22.8). Mean Piper Fatigue Scale score was 2.56+/-2, with 72% reporting mild fatigue. There were significant relationships between subjective and objective sleep, but no consistent patterns. Higher total and subscale fatigue scores were correlated with most components of poorer subjective sleep quality (r=0.25-0.42, P\u3c or =0.005)

Using Group Model Building to Understand Factors That Influence Childhood Obesity in an Urban Environment

Background: Despite increased attention, conventional views of obesity are based upon individual behaviors, and children and parents living with obesity are assumed to be the primary problem solvers. Instead of focusing exclusively on individual reduction behaviors for childhood obesity, greater focus should be placed on better understanding existing community systems and their effects on obesity. The Milwaukee Childhood Obesity Prevention Project is a community-based coalition established to develop policy and environmental change strategies to impact childhood obesity in Milwaukee, Wisconsin. The coalition conducted a Group Model Building exercise to better understand root causes of childhood obesity in its community. Methods: Group Model Building is a process by which a group systematically engages in model construction to better understand the systems that are in place. It helps participants make their mental models explicit through a careful and consistent process to test assumptions. This process has 3 main components: (1) assembling a team of participants; (2) conducting a behavior-over-time graphs exercise; and (3) drawing the causal loop diagram exercise. Results: The behavior-over-time graph portion produced 61 graphs in 10 categories. The causal loop diagram yielded 5 major themes and 7 subthemes. Conclusions: Factors that influence childhood obesity are varied, and it is important to recognize that no single solution exists. The perspectives from this exercise provided a means to create a process for dialogue and commitment by stakeholders and partnerships to build capacity for change within the community

Conditionally Calibrated Predictive Distributions by Probability-Probability Map: Application to Galaxy Redshift Estimation and Probabilistic Forecasting

Uncertainty quantification is crucial for assessing the predictive ability of AI algorithms. Much research has been devoted to describing the predictive distribution (PD) $F(y|\mathbf{x})$ of a target variable $y \in \mathbb{R}$ given complex input features $\mathbf{x} \in \mathcal{X}$. However, off-the-shelf PDs (from, e.g., normalizing flows and Bayesian neural networks) often lack conditional calibration with the probability of occurrence of an event given input $\mathbf{x}$ being significantly different from the predicted probability. Current calibration methods do not fully assess and enforce conditionally calibrated PDs. Here we propose \texttt{Cal-PIT}, a method that addresses both PD diagnostics and recalibration by learning a single probability-probability map from calibration data. The key idea is to regress probability integral transform scores against $\mathbf{x}$. The estimated regression provides interpretable diagnostics of conditional coverage across the feature space. The same regression function morphs the misspecified PD to a re-calibrated PD for all $\mathbf{x}$. We benchmark our corrected prediction bands (a by-product of corrected PDs) against oracle bands and state-of-the-art predictive inference algorithms for synthetic data. We also provide results for two applications: (i) probabilistic nowcasting given sequences of satellite images, and (ii) conditional density estimation of galaxy distances given imaging data (so-called photometric redshift estimation). Our code is available as a Python package https://github.com/lee-group-cmu/Cal-PIT .Comment: 21 pages, 11 figures. Under review. Code available as a Python package https://github.com/lee-group-cmu/Cal-PI

Regulation of human mononuclear phagocyte migration by cell surface-binding proteins for advanced glycation end products.

This is the published version. Copyright 1993 American Society for Clinical Investigation.Nonenzymatic glycation of proteins occurs at an accelerated rate in diabetes and can lead to the formation of advanced glycation end products of proteins (AGEs), which bind to mononuclear phagocytes (MPs) and induce chemotaxis. We have isolated two cell surface-associated binding proteins that mediate the interaction of AGEs with bovine endothelial cells. One of these proteins is a new member of the immunoglobulin superfamily of receptors (termed receptor for AGEs or RAGE); and the second is a lactoferrin-like polypeptide (LF-L). Using monospecific antibodies to these two AGE-binding proteins, we detected immunoreactive material on Western blots of detergent extracts from human MPs. Radioligand-binding studies demonstrated that antibody to the binding proteins blocked 125I-AGE-albumin binding and endocytosis by MPs. Chemotaxis of human MPs induced by soluble AGE-albumin was prevented in a dose-dependent manner by intact antibodies raised to the AGE-binding proteins, F(ab')2 fragments of these antibodies and by soluble RAGE. When MP migration in response to N-formyl-Met-Leu-Phe was studied in a chemotaxis chamber with AGE-albumin adsorbed to the upper surface of the chamber membrane, movement of MPs to the lower compartment was decreased because of interaction of the glycated proteins with RAGE and LF-L on the cell surface. The capacity of AGEs to attract and retain MPs was shown by implanting polytetrafluoroethylene (PTFE) mesh impregnated with AGE-albumin into rats: within 4 d a florid mononuclear cell infiltrate was evident in contrast to the lack of a significant cellular response to PTFE with adsorbed native albumin. These data indicate that RAGE and LF-L have a central role in the interaction of AGEs with human mononuclear cells and that AGEs can serve as a nidus to attract MPs in vivo