Primitive Words, Free Factors and Measure Preservation

Let F_k be the free group on k generators. A word w \in F_k is called primitive if it belongs to some basis of F_k. We investigate two criteria for primitivity, and consider more generally, subgroups of F_k which are free factors. The first criterion is graph-theoretic and uses Stallings core graphs: given subgroups of finite rank H \le J \le F_k we present a simple procedure to determine whether H is a free factor of J. This yields, in particular, a procedure to determine whether a given element in F_k is primitive. Again let w \in F_k and consider the word map w:G x G x ... x G \to G (from the direct product of k copies of G to G), where G is an arbitrary finite group. We call w measure preserving if given uniform measure on G x G x ... x G, w induces uniform measure on G (for every finite G). This is the second criterion we investigate: it is not hard to see that primitivity implies measure preservation and it was conjectured that the two properties are equivalent. Our combinatorial approach to primitivity allows us to make progress on this problem and in particular prove the conjecture for k=2. It was asked whether the primitive elements of F_k form a closed set in the profinite topology of free groups. Our results provide a positive answer for F_2.Comment: This is a unified version of two manuscripts: "On Primitive words I: A New Algorithm", and "On Primitive Words II: Measure Preservation". 42 pages, 14 figures. Some parts of the paper reorganized towards publication in the Israel J. of Mat

Weight-bearing bones are more sensitive to physical exercise in boys than in girls during pre- and early puberty: a cross-sectional study

Summary: We carried out a cross-section study of the sex-specific relationship between bone mineral content and physical activity at sites with different loading in pre- and early pubertal girls and boys. There was significant sensitivity of bone mineral content of the hip to physical exercise in boys, but not in girls. Background: Since little is known whether there are sex differences in sensitivity of bone to loading, we investigated sex differences in the cross-sectional association between measures of physical activity (PA) and bone mass and size in pre- and early pubertal children of both sexes. Methods: We measured bone mineral content/density (BMC/BMD) and fat-free mass (FFM) in 269 6- to 13-year-old children from randomly selected schools by dual-energy X-ray absorptiometry. Physical activity (PA) was measured by accelerometers and lower extremity strength by a jump-and-reach test. Results: Boys (n = 128) had higher hip and total body BMC and BMD, higher FFM, higher muscle strength and were more physically active than girls (n = 141). Total hip BMC was positively associated with time spent in total and vigorous PA in boys (r = 0.20-0.33, p < 0.01), but not in girls (r = 0.02-0.04, p=ns), even after adjusting for FFM and strength. While boys and girls in the lowest tertile of vigorous PA (22min/day) did not differ in hip BMC (15.62 vs 15.52g), boys in the highest tertile (72min/day) had significantly higher values than the corresponding girls (16.84 vs 15.71g, p < 0.05). Conclusions: Sex differences in BMC during pre- and early puberty may be related to a different sensitivity of bone to physical loading, irrespective of muscle mas

Copeptin Levels Remain Unchanged during the Menstrual Cycle.

BACKGROUND: Copeptin, a surrogate marker for arginin vasopressin production, is evaluated as an osmo-dependent stress and inflammatory biomarker in different diseases. We investigated copeptin during the menstrual cycle and its relationship to sex hormones, markers of subclinical inflammation and estimates of body fluid. METHODS: In 15 healthy women with regular menstrual cycles, blood was drawn on fifteen defined days of their menstrual cycle and was assayed for copeptin, progesterone, estradiol, luteinizing hormone, high-sensitive C-reactive protein, tumor necrosis factor-alpha and procalcitonin. Symptoms of fluid retention were assessed on each visit, and bio impedance analysis was measured thrice to estimate body fluid changes. Mixed linear model analysis was performed to assess the changes of copeptin across the menstrual cycle and the relationship of sex hormones, markers of subclinical inflammation and estimates of body fluid with copeptin. RESULTS: Copeptin levels did not significantly change during the menstrual cycle (p = 0.16). Throughout the menstrual cycle, changes in estradiol (p = 0.002) and in the physical premenstrual symptom score (p = 0.01) were positively related to copeptin, but changes in other sex hormones, in markers of subclinical inflammation or in bio impedance analysis-estimated body fluid were not (all p = ns). CONCLUSION: Although changes in estradiol and the physical premenstrual symptom score appear to be related to copeptin changes, copeptin does not significantly change during the menstrual cycle

Isoperimetric Inequalities in Simplicial Complexes

In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expansion for simplicial complexes of general dimension, and prove that similar connections exist between the combinatorial expansion of a complex, and the spectrum of the high dimensional Laplacian defined by Eckmann. In particular, we present a Cheeger-type inequality, and a high-dimensional Expander Mixing Lemma. As a corollary, using the work of Pach, we obtain a connection between spectral properties of complexes and Gromov's notion of geometric overlap. Using the work of Gunder and Wagner, we give an estimate for the combinatorial expansion and geometric overlap of random Linial-Meshulam complexes

Equating accelerometer estimates among youth : the Rosetta Stone 2

Different accelerometer cutpoints used by different researchers often yields vastly different estimates of moderate-to-vigorous intensity physical activity (MVPA). This is recognized as cutpoint non-equivalence (CNE), which reduces the ability to accurately compare youth MVPA across studies. The objective of this research is to develop a cutpoint conversion system that standardizes minutes of MVPA for six different sets of published cutpoint

USE of Mine Pool Water for Power Plant Cooling.

Water and energy production issues intersect in numerous ways. Water is produced along with oil and gas, water runs off of or accumulates in coal mines, and water is needed to operate steam electric power plants and hydropower generating facilities. However, water and energy are often not in the proper balance. For example, even if water is available in sufficient quantities, it may not have the physical and chemical characteristics suitable for energy or other uses. This report provides preliminary information about an opportunity to reuse an overabundant water source--ground water accumulated in underground coal mines--for cooling and process water in electric generating facilities. The report was funded by the U.S. Department of Energy's (DOE's) National Energy Technology Laboratory (NETL), which has implemented a water/energy research program (Feeley and Ramezan 2003). Among the topics studied under that program is the availability and use of ''non-traditional sources'' of water for use at power plants. This report supports NETL's water/energy research program

Associations of sleep and chronotype with mental health and well-being in women with gestational diabetes during the perinatal period: A prospective cohort study.

During pregnancy, short sleep duration is associated with obesity, risk of gestational diabetes (GDM), and adverse mental health outcomes. Chronotype reflects an individual's preference for activity and sleep-wake cycle during a 24 h period. Evening chronotypes have been associated with poorer mental health and unhealthy lifestyle habits. We evaluated the associations between chronotype, sleep, and mental health in women with GDM, during the perinatal period. We included 214 women with GDM followed in 2021-2022 from the third trimester of pregnancy up to 6-8 weeks postpartum. We assessed sleep quality, the chronotype (Morning-Eveningness Questionnaire), depressive symptoms, intuitive eating behaviors, and well-being. We adjusted for potential confounders. In pregnancy, reduced sleep duration, sleep efficiency, and subjective sleep quality were associated with higher depressive symptoms or lower well-being (all p ≤ 0.03). Later bedtime was linked to eating as a means of coping with emotional distress and a lower awareness of internal hunger and satiety cues (both p ≤ 0.02). An earlier chronotype was associated with improved well-being (p = 0.002). At 6-8 weeks postpartum, reduced subjective sleep quality, sleep duration, and later bedtime was associated with higher depressive symptoms, while an earlier chronotype was associated with reduced depressive symptoms (all p ≤ 0.02). Longitudinal analyses revealed that later bedtime during pregnancy predicted more depressive symptoms in the early postpartum (p = 0.04). Casual pathways cannot be determined in an observational study. This study lacks objective sleep measurements. Our results highlight the associations between sleep patterns and chronotype with mental health and eating behavior in women with GDM

Survey of Nutrition Management Practices in Centers for Pediatric Intestinal Rehabilitation

Background: Nutrition management of pediatric intestinal failure (IF) requires interdisciplinary coordination of parenteral nutrition (PN) and enteral nutrition (EN) support. Nutrition strategies used by specialists in pediatric intestinal rehabilitation to promote gut adaptation and manage complications have not been previously summarized. Methods: A practice survey was distributed to members of the dietitian subgroup of the American Society for Parenteral and Enteral Nutrition Pediatric Intestinal Failure Section. The survey included 24 open‐ended questions related to PN and enteral feeding strategies, nutrition management of PN‐associated liver disease, and laboratory monitoring. Results: Dietitians from 14 centers completed the survey. Management components for patients at risk for cholestasis were consistent and included fat minimization, trace element modification, avoiding PN overfeeding, and providing EN. Parenteral amino acid solutions designed for infants/young children are used in patients <1 or 2 years of age. Trace minerals are dosed individually in 10 of 14 centers. Eleven centers prescribe a continuous infusion of breast milk or elemental formula 1–2 weeks after resection while 3 centers determine the formula type by the extent of resection. Most (86%) centers do not have a protocol for initiating oral/motor therapy. Laboratory panel composition varied widely by center. The selection and frequency of use depended on clinical variables, including cholestatic status, exclusive vs partial PN dependence, postrepletion verification vs routine monitoring, intestinal anatomy, and acuity of care. Conclusion: EN and PN management strategies are relatively consistent among U.S. centers. Collaborative initiatives are necessary to define better practices and establish laboratory monitoring guidelines.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/145220/1/ncp10040_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/145220/2/ncp10040.pd

Dietary ω-3 fatty acid supplementation improves murine sickle cell bone disease and reprograms adipogenesis

Sickle cell disease (SCD) is a genetic disorder of hemoglobin, leading to chronic hemolytic anemia and multiple organ damage. Among chronic organ complications, sickle cell bone disease (SBD) has a very high prevalence, resulting in long-term disability, chronic pain and fractures. Here, we evaluated the effects of ω-3 (fish oil-based, FD)-enriched diet vs. ω-6 (soybean oil-based, SD)-supplementation on murine SBD. We exposed SCD mice to recurrent hypoxia/reoxygenation (rec H/R), a consolidated model for SBD. In rec H/R SS mice, FD improves osteoblastogenesis/osteogenic activity by downregulating osteoclast activity via miR205 down-modulation and reduces both systemic and local inflammation. We also evaluated adipogenesis in both AA and SS mice fed with either SD or FD and exposed to rec H/R. FD reduced and reprogramed adipogenesis from white to brown adipocyte tissue (BAT) in bone compartments. This was supported by increased expression of uncoupling protein 1(UCP1), a BAT marker, and up-regulation of miR455, which promotes browning of white adipose tissue. Our findings provide new insights on the mechanism of action of ω-3 fatty acid supplementation on the pathogenesis of SBD and strengthen the rationale for ω-3 fatty acid dietary supplementation in SCD as a complementary therapeutic intervention