Regularity of maximal operators: recent progress and some open problems

This is an expository paper on the regularity theory of maximal operators, when these act on Sobolev and BV functions, with a special focus on some of the current open problems in the topic. Overall, a list of fifteen research problems is presented. It summarizes the contents of a talk delivered by the author at the CIMPA 2017 Research School - Harmonic Analysis, Geometric Measure Theory and Applications, in Buenos Aires, Argentina.Comment: 19 pages. Expository paper with the contents of a lecture given at the in the CIMPA 2017 Research School - Harmonic Analysis, Geometric Measure Theory and Applications, in Buenos Aires, Argentin

Pressure effects on the structural and superconducting transitions in La₃Co₄Sn₁₃

La3Co4Sn13 is a superconducting material with transition temperature at Tc = 2.70 K, which presents a superlattice structural transition at T ∗ ≃ 150 K, a common feature for this class of compounds. However, for this material, it is not clear that at T ∗ the lattice distortions arise from a charge density wave (CDW) or from a distinct microscopic origin. Interestingly, it has been suggested in isostructural non-magnetic intermetallic compounds that T ∗ can be suppressed to zero temperature, by combining chemical and external pressure, and a quantum critical point is argued to be observed near these critical doping/pressure. Our study shows that application of pressure on single-crystalline La3Co4Sn13 enhances Tc and decreases T ∗ . We observe thermal hysteresis loops for cooling/heating cycles around T ∗ for P & 0.6 GPa, in electrical resistivity measurements, which are not seen in x-ray diffraction data. The hysteresis in electrical measurements may be due to the pinning of the CDW phase to impurities/defects, while the superlattice structural transition maintains its ambient pressure second-order transition nature under pressure. From our experiments we estimate that T ∗ vanishes at around 5.5 GPa, though no quantum critical behavior is observed up to 2.53 GPa

Reduced pancreatic beta-cell mass is associated with decreased FoxO1 and Erk1/2 protein phosphorylation in low-protein malnourished rats

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)A low-protein diet leads to functional and structural pancreatic islet alterations, including islet hypotrophy. Insulin-signaling pathways are involved in several adaptive responses by pancreatic islets. We determined the levels of some insulin-signaling proteins related to pancreatic islet function and growth in malnourished rats. Adult male Wistar rats (N = 20 per group) were fed a 17% protein (normal-protein diet; NP) or 6% protein (low-protein diet; LP), for 8 weeks. At the end of this period, blood glucose and serum insulin and albumin levels were measured. The morphometric parameters of the endocrine pancreas and the content of some proteins in islet lysates were determined. The beta-cell mass was significantly reduced (congruent to 65%) in normoglycemic but hypoinsulinemic LP rats compared to NP rats. Associated with these alterations, a significant 30% reduction in insulin receptor substrate-1 and a 70% increase in insulin receptor substrate-2 protein content were observed in LP islets compared to NP islets. The phosphorylated serine-threonine protein kinase (pAkt)/Akt protein ratio was similar in LP and NP islets. The phosphorylated forkhead-O1 (pFoxO1)/FoxO1 protein ratio was decreased by 43% in LP islets compared to NP islets (P < 0.05). Finally, the ratio of phosphorylated-extracellular signal-related kinase 1/2 (pErk1/2) to total Erk1/2 protein levels was decreased by 71% in LP islets compared to NP islets (P < 0.05). Therefore, the reduced beta-cell mass observed in LP rats is associated with the reduction of phosphorylation in mitogenic-related signals, FoxO1 and Erk proteins. The cause/effect basis of this association remains to be determined.4210935941Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP [02/04310-4, 04/11684-9, 03/10829-0

Plasma glucose regulation and insulin secretion in hypertriglyceridemic mice

In this study, we examined glucose homeostasis and insulin secretion in transgenic mice overexpressing the human apolipoprotein CIII gene (apo CIII tg). These mice have elevated plasma levels of triglycerides, FFA and cholesterol compared to control mice. The body weight, plasma glucose, and insulin levels, glucose disappearance rates, areas under the ipGTT curve for adult (4-8 mo. old) and aged (20-24 mo. old) apo CIII tg mice and the determination of insulin during the ipGTT were riot different from those of control mice. However, an additional elevation of plasma FFA by treatment with heparin for 2-4h impaired the ipGTT responses in apo CIII tg mice compared to saline-treated mice. The glucose disappearance rate in heparin-treated transgenic mice was slightly lower than in heparin-treated controls. Glucose (22.2 mmol/l) stimulated insulin secretion in isolated islets to the same extent in saline-treated control and apo CIII tg mice. in islets from heparin-treated apo CIII tg mice, the insulin secretion at 2.8 and 22.2 mmol glucose/l was lower than in heparin-treated control mice. In conclusion, hypertriglyceridemia per se or a mild elevation in FFA did not affect insulin secretion or insulin resistance in adult or aged apo CIII tg mice. Nonetheless, an additional elevation of FFA induced by heparin in hypertriglyceridemic mice impaired the ipGTT by reducing insulin secretion.341212

A Case-base Approach to Workforces’ Satisfaction Assessment

It is well known that human resources play a valuable role in a sustainable organizational development. Indeed, this work will focus on the development of a decision support system to assess workers’ satisfaction based on factors related to human resources management practices. The framework is built on top of a Logic Programming approach to Knowledge Representation and Reasoning, complemented with a Case Based approach to computing. The proposed solution is unique in itself, once it caters for the explicit treatment of incomplete, unknown, or even self-contradictory information, either in terms of a qualitative or quantitative setting. Furthermore, clustering methods based on similarity analysis among cases were used to distinguish and aggregate collections of historical data or knowledge in order to reduce the search space, therefore enhancing the cases retrieval and the overall computational process

Family coordination in families who have a child with autism spectrum disorder

Little is known about the interactions of families where there is a child with autism spectrum disorder (ASD). The present study applies the Lausanne Trilogue Play (LTP) to explore both its applicability to this population as well as to assess resources and areas of deficit in these families. The sample consisted of 68 families with a child with ASD, and 43 families with a typically developing (TD) child. With respect to the global score for family coordination there were several negative correlations: the more severe the symptoms (based on the child’s ADOS score), the more family coordination was dysfunctional. This correlation was particularly high when parents had to play together with the child. In the parts in which only one of the parents played actively with the child, while the other was simply present, some families did achieve scores in the functional range, despite the child’s symptom severity. The outcomes are discussed in terms of their clinical implications both for assessment and for interventio