Level Sets of the Takagi Function: Local Level Sets

The Takagi function \tau : [0, 1] \to [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. The level sets L(y) = {x : \tau(x) = y} of the Takagi function \tau(x) are studied by introducing a notion of local level set into which level sets are partitioned. Local level sets are simple to analyze, reducing questions to understanding the relation of level sets to local level sets, which is more complicated. It is known that for a "generic" full Lebesgue measure set of ordinates y, the level sets are finite sets. Here it is shown for a "generic" full Lebesgue measure set of abscissas x, the level set L(\tau(x)) is uncountable. An interesting singular monotone function is constructed, associated to local level sets, and is used to show the expected number of local level sets at a random level y is exactly 3/2.Comment: 32 pages, 2 figures, 1 table. Latest version has updated equation numbering. The final publication will soon be available at springerlink.co

Effects of Fasting and Transportation on Pork Quality Development and Extent of Postmortem Metabolism

One hundred seventy-seven pigs were used to determine the interaction effects of fasting and length of transport prior to harvest on pork muscle quality. The study design was a 2 × 2 × 3 factorial, which involved two genetic sources, fasting (F) or no fasting (N) of pigs 48-h prior to harvest, and three transport times (0.5, 2.5, or 8.0 h) on a semitrailer to the packing plant. Genetic source was a significant source of variation (P \u3c 0.05) for most composition and muscle quality variables. Fasting reduced hot carcass weight 3.6% (P \u3c 0.05), but length of transport did not affect hot carcass weight (P \u3e 0.05). There were no differences (P \u3e 0.05) in percent lean among fasting and transport treatments. Fasted pigs had higher longissimus dorsi (LD) ultimate pH (pHu), darker lean color, higher marbling score and lower 7-d purge loss, 24-h drip loss, and cooking loss (P \u3c 0.05) than nonfasted pigs. Meat from pigs that were transported 8.0 h had lower glycolytic potential (GP), higher LD and semimembranosus (SM) pHu, darker lean color, and lower L*, 7-d purge loss, 24-h drip loss, cooking loss, and shear force values than meat from pigs transported 0.5 h (P \u3c 0.05). Meat from pigs transported 2.5 h had higher LD and SM pHu and lower L*, 7-d purge loss, 24-h drip loss, and cooking loss than meat from pigs transported 0.5 h (P \u3c 0.05). Meat from pigs transported 8.0 h had higher LD pHu and color scores and lower L* and cooking loss than meat from pigs transported 2.5 h (P \u3c 0.05). The fasting × transport interaction was significant for SM pHu, L*, color score, and drip loss. Fasting improved SM pHu, L*, color score, and drip loss for pigs that were transported 0.5 h (P \u3c 0.05), but when pigs were transported for 2.5 h or 8.0 h, fasting had little or no effect on these muscle quality traits. Fasting lowered GP and increased LD pHu for pigs from the genetic source with the higher initial pork quality (P \u3c 0.05), while fasting had no effect on pork quality for pigs from the genetic source with the lower initial pork quality (P \u3e 0.05). Longer transport times resulted in lower GP and higher LD pHu regardless of genetic source. Fasting and length of transport each had positive effects on pork quality, but length of transport effects was greater in magnitude. When pigs were transported for 0.5 h, fasting for 48 h prior to harvest improved pork quality, but when pigs were transported 2.5 or 8.0 h, fasting had little effect on pork quality

The evaluation of treatment services and systems for substance use disorders

Scientific research and program evaluation have not played a major role in shaping the development of treatment services and systems in most countries. This has led to disparities in the development, management and monitoring of national treatment systems. In the evaluation of treatment for substance use disorders, the evaluation practitioner will usually be working at one of five levels: single case, treatment activity, treatment service, treatment agency or treatment system. One of the major barriers to undertaking internal program evaluation is the belief that it is a complicated research process best left to those with specific research training. Program managers and staff can plan and initiate an evaluation process for their program if they have access to research expertise when needed for certain parts of the process. There are seven main components of an evaluation process that can be planned and implemented: need assessment; evaluation planning, process evaluation, cost analysis, client satisfaction evaluation, outcome evaluation and economic evaluation. However, evaluation is more than the techniques and technology required to implement these types of activities. It also involves the routine questioning of current practice even if the feedback may be less positive than anticipated. A healthy culture for evaluation is one in which feedback loops are woven into the fabric of the treatment service or system. There are many barriers to evaluation in substance abuse services but these barriers can be overcome with careful planning and commitment to the delivery of evidence-based services

Outpatient hospital attendances in people with rheumatoid arthritis during the COVID-19 pandemic and beyond: a cohort study in three nations of the UK

Objectives We aimed to estimate how rheumatology outpatient hospital attendances have changed since the COVID-19 pandemic and determine demographic characteristics associated with observed changes. Methods Using three primary and secondary care electronic health record datasets in England (with the approval of NHS England), Scotland and Wales, we identified people with a diagnosis of RA before 1 April 2019. We determined the proportion of people with rheumatology hospital outpatient appointments each month [April 2019 to December 2022 (Wales and Scotland), November 2023 (England)] and quantified changes using interrupted time-series analysis. We used logistic regression to determine characteristics associated with having fewer appointments compared with 2019. Results We identified 145 065, 3813 and 13 637 people coded with RA in England, Scotland and Wales, respectively. At the start of the COVID-19 pandemic the number of rheumatology outpatient appointments dropped sharply across all nations. In England and Scotland, the percentage of monthly appointments has continued to decline. In Wales, while there was a gradual recovery, rheumatology services have not returned to pre-pandemic levels. In contrast, the number of appointments for other specialties has recovered in all nations. People with no rheumatology outpatient appointments were more often aged over 80, male and living in rural areas. Ethnic minorities, those living in more deprived and urban areas had fewer appointments after the start of the pandemic compared with 2019. Conclusion For the first time, we compared healthcare use across three UK nations and found rheumatology outpatient appointments had not recovered to pre-COVID-19 pandemic levels, particularly in Scotland and England

Factors Associated with Revision Surgery after Internal Fixation of Hip Fractures

Background: Femoral neck fractures are associated with high rates of revision surgery after management with internal fixation. Using data from the Fixation using Alternative Implants for the Treatment of Hip fractures (FAITH) trial evaluating methods of internal fixation in patients with femoral neck fractures, we investigated associations between baseline and surgical factors and the need for revision surgery to promote healing, relieve pain, treat infection or improve function over 24 months postsurgery. Additionally, we investigated factors associated with (1) hardware removal and (2) implant exchange from cancellous screws (CS) or sliding hip screw (SHS) to total hip arthroplasty, hemiarthroplasty, or another internal fixation device. Methods: We identified 15 potential factors a priori that may be associated with revision surgery, 7 with hardware removal, and 14 with implant exchange. We used multivariable Cox proportional hazards analyses in our investigation. Results: Factors associated with increased risk of revision surgery included: female sex, [hazard ratio (HR) 1.79, 95% confidence interval (CI) 1.25-2.50; P = 0.001], higher body mass index (fo