How large are the level sets of the Takagi function?

Let T be Takagi's continuous but nowhere-differentiable function. This paper considers the size of the level sets of T both from a probabilistic point of view and from the perspective of Baire category. We first give more elementary proofs of three recently published results. The first, due to Z. Buczolich, states that almost all level sets (with respect to Lebesgue measure on the range of T) are finite. The second, due to J. Lagarias and Z. Maddock, states that the average number of points in a level set is infinite. The third result, also due to Lagarias and Maddock, states that the average number of local level sets contained in a level set is 3/2. In the second part of the paper it is shown that, in contrast to the above results, the set of ordinates y with uncountably infinite level sets is residual, and a fairly explicit description of this set is given. The paper also gives a negative answer to a question of Lagarias and Maddock by showing that most level sets (in the sense of Baire category) contain infinitely many local level sets, and that a continuum of level sets even contain uncountably many local level sets. Finally, several of the main results are extended to a version of T with arbitrary signs in the summands.Comment: Added a new Section 5 with generalization of the main results; some new and corrected proofs of the old material; 29 pages, 3 figure

Fast, Linear Time, m-Adic Hierarchical Clustering for Search and Retrieval using the Baire Metric, with linkages to Generalized Ultrametrics, Hashing, Formal Concept Analysis, and Precision of Data Measurement

We describe many vantage points on the Baire metric and its use in clustering data, or its use in preprocessing and structuring data in order to support search and retrieval operations. In some cases, we proceed directly to clusters and do not directly determine the distances. We show how a hierarchical clustering can be read directly from one pass through the data. We offer insights also on practical implications of precision of data measurement. As a mechanism for treating multidimensional data, including very high dimensional data, we use random projections.Comment: 17 pages, 45 citations, 2 figure

Training adults and children with an autism spectrum disorder to be compliant with a clinical dental assessment using a TEACCH-based approach

The specific neuropsychological and sensory profile found in persons with autism spectrum disorders complicate dental procedures and as a result of this, most are treated under general anesthesia or unnecessary sedation. The main goal of the present study was to evaluate the effectiveness of a short treatment and education of autistic and related communication-handicapped children-based intervention program (five sessions) to facilitate a 10-component oral assessment in children (n = 38, aged 4¿9 years) and adults (n = 34, aged 19¿41) with autism spectrum disorder (with or without associated intellectual disability). The assessment ranges from entering into the examination room to the evaluation of the dental occlusion. There were statistically significant differences in the number of components reached and in compliance before and after the training program

Somatic mutations of GNA11 and GNAQ in CTNNB1-mutant aldosterone-producing adenomas presenting in puberty, pregnancy or menopause.

Most aldosterone-producing adenomas (APAs) have gain-of-function somatic mutations of ion channels or transporters. However, their frequency in aldosterone-producing cell clusters of normal adrenal gland suggests a requirement for codriver mutations in APAs. Here we identified gain-of-function mutations in both CTNNB1 and GNA11 by whole-exome sequencing of 3/41 APAs. Further sequencing of known CTNNB1-mutant APAs led to a total of 16 of 27 (59%) with a somatic p.Gln209His, p.Gln209Pro or p.Gln209Leu mutation of GNA11 or GNAQ. Solitary GNA11 mutations were found in hyperplastic zona glomerulosa adjacent to double-mutant APAs. Nine of ten patients in our UK/Irish cohort presented in puberty, pregnancy or menopause. Among multiple transcripts upregulated more than tenfold in double-mutant APAs was LHCGR, the receptor for luteinizing or pregnancy hormone (human chorionic gonadotropin). Transfections of adrenocortical cells demonstrated additive effects of GNA11 and CTNNB1 mutations on aldosterone secretion and expression of genes upregulated in double-mutant APAs. In adrenal cortex, GNA11/Q mutations appear clinically silent without a codriver mutation of CTNNB1

Determinants of preventable readmissions in the United States: a systematic review

<p>Abstract</p> <p>Background</p> <p>Hospital readmissions are a leading topic of healthcare policy and practice reform because they are common, costly, and potentially avoidable events. Hospitals face the prospect of reduced or eliminated reimbursement for an increasing number of preventable readmissions under nationwide cost savings and quality improvement efforts. To meet the current changes and future expectations, organizations are looking for potential strategies to reduce readmissions. We undertook a systematic review of the literature to determine what factors are associated with preventable readmissions.</p> <p>Methods</p> <p>We conducted a review of the English language medicine, health, and health services research literature (2000 to 2009) for research studies dealing with unplanned, avoidable, preventable, or early readmissions. Each of these modifying terms was included in keyword searches of readmissions or rehospitalizations in Medline, ISI, CINAHL, The Cochrane Library, ProQuest Health Management, and PAIS International. Results were limited to US adult populations.</p> <p>Results</p> <p>The review included 37 studies with significant variation in index conditions, readmitting conditions, timeframe, and terminology. Studies of cardiovascular-related readmissions were most common, followed by all cause readmissions, other surgical procedures, and other specific-conditions. Patient-level indicators of general ill health or complexity were the commonly identified risk factors. While more than one study demonstrated preventable readmissions vary by hospital, identification of many specific organizational level characteristics was lacking.</p> <p>Conclusions</p> <p>The current literature on preventable readmissions in the US contains evidence from a variety of patient populations, geographical locations, healthcare settings, study designs, clinical and theoretical perspectives, and conditions. However, definitional variations, clear gaps, and methodological challenges limit translation of this literature into guidance for the operation and management of healthcare organizations. We recommend that those organizations that propose to reward reductions in preventable readmissions invest in additional research across multiple hospitals in order to fill this serious gap in knowledge of great potential value to payers, providers, and patients.</p

Effects of rare kidney diseases on kidney failure: a longitudinal analysis of the UK National Registry of Rare Kidney Diseases (RaDaR) cohort

\ua9 2024 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 licenseBackground: Individuals with rare kidney diseases account for 5–10% of people with chronic kidney disease, but constitute more than 25% of patients receiving kidney replacement therapy. The National Registry of Rare Kidney Diseases (RaDaR) gathers longitudinal data from patients with these conditions, which we used to study disease progression and outcomes of death and kidney failure. Methods: People aged 0–96 years living with 28 types of rare kidney diseases were recruited from 108 UK renal care facilities. The primary outcomes were cumulative incidence of mortality and kidney failure in individuals with rare kidney diseases, which were calculated and compared with that of unselected patients with chronic kidney disease. Cumulative incidence and Kaplan–Meier survival estimates were calculated for the following outcomes: median age at kidney failure; median age at death; time from start of dialysis to death; and time from diagnosis to estimated glomerular filtration rate (eGFR) thresholds, allowing calculation of time from last eGFR of 75 mL/min per 1\ub773 m2 or more to first eGFR of less than 30 mL/min per 1\ub773 m2 (the therapeutic trial window). Findings: Between Jan 18, 2010, and July 25, 2022, 27 285 participants were recruited to RaDaR. Median follow-up time from diagnosis was 9\ub76 years (IQR 5\ub79–16\ub77). RaDaR participants had significantly higher 5-year cumulative incidence of kidney failure than 2\ub781 million UK patients with all-cause chronic kidney disease (28% vs 1%; p&lt;0\ub70001), but better survival rates (standardised mortality ratio 0\ub742 [95% CI 0\ub732–0\ub752]; p&lt;0\ub70001). Median age at kidney failure, median age at death, time from start of dialysis to death, time from diagnosis to eGFR thresholds, and therapeutic trial window all varied substantially between rare diseases. Interpretation: Patients with rare kidney diseases differ from the general population of individuals with chronic kidney disease: they have higher 5-year rates of kidney failure but higher survival than other patients with chronic kidney disease stages 3–5, and so are over-represented in the cohort of patients requiring kidney replacement therapy. Addressing unmet therapeutic need for patients with rare kidney diseases could have a large beneficial effect on long-term kidney replacement therapy demand. Funding: RaDaR is funded by the Medical Research Council, Kidney Research UK, Kidney Care UK, and the Polycystic Kidney Disease Charity

Is teacher happiness contagious? A study of the link between perceptions of language teacher happiness and student attitudes

There remains a dearth of research on the effects of student perception of teacher happiness and the ramifications of those perceptions on student feelings and attitudes. Using an online questionnaire, data were collected from 129 adult students of ESL/EFL across the world who were enrolled in formal English classes of intermediate to advanced level proficiency. Participants were asked about their perception of various aspects of their teachers’ happiness, and about their own attitudes and motivation to learn English. Statistical analyses revealed that student perception of teacher happiness was significantly (and positively) linked with students’ Overall attitude and motivation, as well as students’ Attitude towards the teacher. This is interpreted as an illustration of the process of positive emotional contagion between teachers and students. Pedagogical implications of the results are discussed