Walter Rudin meets Elias M. Stein

Walter Rudin and Elias M. Stein were giants in the world of mathemat- ics. They were loved and admired from students and researchers to teachers and academics, both young and old. They touched many of us through their inspiring books at the undergraduate and postgraduate level. Although they were leading researchers in both harmonic analysis and several complex vari- ables, we are not aware whether they interacted and discussed mathematics. In this article, Rudin and Stein meet mathematically through a reformulation of the beautiful theory of Fourier series with gaps that Rudin developed in the 1950s as an equivalent Fourier restriction problem from the 1970s, a problem Stein proposed and which remains a fundamental, central problem in Euclidean harmonic analysis today. Walter Rudin was born in Vienna on 2 May, 1921 and emigrated to the US in 1945, completing his PhD at Duke University in 1949. While a C. L. E. Moore Instructor at MIT in the early 1950s, Walter was asked to teach a real analysis course but he could not find a textbook that he liked so he decided to write Principles of Mathematical Analysis which despite its age, has remained the paragon of high quality. After a stint of teaching at the University of Rochester, he took up a position at the University of Wisconsin, Madison in 1959 where he remained until his retirement as Vilas Professor in 1991. He died at his home in Madison on 20 May, 2010. Elias M. Stein (known to friends and colleagues as Eli) was born in Antwerp on 13 January, 1931 and emigrated with his family to the US in 1941, settling in New York where Eli attended high school. He went to the University of Chicago, received his PhD in 1955, and then went to MIT as a C.L.E. Moore Instructor before Antoni Zygmund told Eli “it’s time to return to Chicago.” In 1963, Stein moved to Princeton University as a full professor where he remained until he died on 23 December, 2018. Between 2003 and 2011, Eli expanded the presentation of Walter’s Principles and published a series of four books aimed at advanced undergraduates. This series is quickly becoming an important part of any young analyst’s education.However the majority of books written by Rudin and Stein are postgraduate textbooks and research monographs (too many to list here), mainly in the areas of harmonic analysis and several complex variables where both men were central figures. In this article, these two luminaries meet in the world of mathematical anal- ysis. We look back at some important work Rudin did in the 1950s and recast it in terms of a far-reaching problem from the 1970s that Stein gave us

Regularized transport between singular covariance matrices

We consider the problem of steering a linear stochastic system between two end-point degenerate Gaussian distributions in finite time. This accounts for those situations in which some but not all of the state entries are uncertain at the initial, t = 0, and final time, t = T. This problem entails non-trivial technical challenges as the singularity of terminal state-covariance causes the control to grow unbounded at the final time T. Consequently, the entropic interpolation (Schroedinger Bridge) is provided by a diffusion process which is not finite-energy, thereby placing this case outside of most of the current theory. In this paper, we show that a feasible interpolation can be derived as a limiting case of earlier results for non-degenerate cases, and that it can be expressed in closed form. Moreover, we show that such interpolation belongs to the same reciprocal class of the uncontrolled evolution. By doing so we also highlight a time-symmetry of the problem, contrasting dual formulations in the forward and reverse time-directions, where in each the control grows unbounded as time approaches the end-point (in the forward and reverse time-direction, respectively)

The Na+/Ca2+ Exchanger 3 Is Functionally Coupled With the NaV1.6 Voltage-Gated Channel and Promotes an Endoplasmic Reticulum Ca2+ Refilling in a Transgenic Model of Alzheimer’s Disease

The remodelling of neuronal ionic homeostasis by altered channels and transporters is a critical feature of the Alzheimer’s disease (AD) pathogenesis. Different reports converge on the concept that the Na+/Ca2+ exchanger (NCX), as one of the main regulators of Na+ and Ca2+ concentrations and signalling, could exert a neuroprotective role in AD. The activity of NCX has been found to be increased in AD brains, where it seemed to correlate with an increased neuronal survival. Moreover, the enhancement of the NCX3 currents (INCX) in primary neurons treated with the neurotoxic amyloid β 1–42 (Aβ1–42) oligomers prevented the endoplasmic reticulum (ER) stress and neuronal death. The present study has been designed to investigate any possible modulation of the INCX, the functional interaction between NCX and the NaV1.6 channel, and their impact on the Ca2+ homeostasis in a transgenic in vitro model of AD, the primary hippocampal neurons from the Tg2576 mouse, which overproduce the Aβ1–42 peptide. Electrophysiological studies, carried in the presence of siRNA and the isoform-selective NCX inhibitor KB-R7943, showed that the activity of a specific NCX isoform, NCX3, was upregulated in its reverse, Ca2+ influx mode of operation in the Tg2576 neurons. The enhanced NCX activity contributed, in turn, to increase the ER Ca2+ content, without affecting the cytosolic Ca2+ concentrations of the Tg2576 neurons. Interestingly, our experiments have also uncovered a functional coupling between NCX3 and the voltage-gated NaV1.6 channels. In particular, the increased NaV1.6 currents appeared to be responsible for the upregulation of the reverse mode of NCX3, since both TTX and the Streptomyces griseolus antibiotic anisomycin, by reducing the NaV1.6 currents, counteracted the increase of the INCX in the Tg2576 neurons. In agreement, our immunofluorescence analyses revealed that the NCX3/NaV1.6 co-expression was increased in the Tg2576 hippocampal neurons in comparison with the WT neurons. Collectively, these findings indicate that NCX3 might intervene in the Ca2+ remodelling occurring in the Tg2576 primary neurons thus emerging as a molecular target with a neuroprotective potential, and provide a new outcome of the NaV1.6 upregulation related to the modulation of the intracellular Ca2+ concentrations in AD neurons

ALDH3A1 overexpression in melanoma and lung tumors drives cancer stem cell expansion, impairing immune surveillance through enhanced PD-L1 output

Melanoma and non-small-cell lung carcinoma (NSCLC) cell lines are characterized by an intrinsic population of cancer stem-like cells (CSC), and high expression of detoxifying isozymes, the aldehyde dehydrogenases (ALDHs), regulating the redox state. In this study, using melanoma and NSCLC cells, we demonstrate that ALDH3A1 isozyme overexpression and activity is closely associated with a highly aggressive mesenchymal and immunosuppressive profile. The contribution of ALDH3A1 to the stemness and immunogenic status of melanoma and NSCLC cells was evaluated by their ability to grow in 3D forming tumorspheres, and by the expression of markers for stemness, epithelial to mesenchymal transition (EMT), and inflammation. Furthermore, in specimens from melanoma and NSCLC patients, we investigated the expression of ALDH3A1, PD-L1, and cyclooxygenase-2 (COX-2) by immunohistochemistry. We show that cells engineered to overexpress the ALDH3A1 enzyme enriched the CSCs population in melanoma and NSCLC cultures, changing their transcriptome. In fact, we found increased expression of EMT markers, such as vimentin, fibronectin, and Zeb1, and of pro-inflammatory and immunosuppressive mediators, such as NFkB, prostaglandin E2, and interleukin-6 and-13. ALDH3A1 overexpression enhanced PD-L1 output in tumor cells and resulted in reduced proliferation of peripheral blood mononuclear cells when co-cultured with tumor cells. Furthermore, in tumor specimens from melanoma and NSCLC patients, ALDH3A1 expression was invariably correlated with PD-L1 and the pro-inflammatory marker COX-2. These findings link ALDH3A1 expression to tumor stemness, EMT and PD-L1 expression, and suggest that aldehyde detoxification is a redox metabolic pathway that tunes the immunological output of tumors

A Systematic Review of the Efficacy and Safety of Direct Oral Anticoagulants in Atrial Fibrillation Patients with Diabetes Using a Risk Index

Diabetes mellitus (DM) represents an independent risk factor for chronic AF and is associated with unfavorable outcomes. We aimed to evaluate the efficacy and safety of direct oral anticoagulants (DOACs) in patients with atrial fibrillation (AF), with and without diabetes mellitus (DM), using a new risk index (RI) defined as: RI = Rate of Events/Rate of Patients at Risk. In particular, an RI lower than 1 suggests a favorable treatment effect. We searched MEDLINE, MEDLINE In-Process, EMBASE, PubMed, and the Cochrane Central Register of Controlled Trials. The risk index (RI) was calculated in terms of efficacy (rate of stroke/systemic embolism (stroke SEE)/rate of patients with and without DM; rate of cardiovascular death/rate of patients with and without DM) and safety (rate of major bleeding/rate of patients with and without DM) outcomes. AF patients with DM (n = 22,057) and 49,596 without DM were considered from pivotal trials. DM doubles the risk index for stroke/SEE, major bleeding (MB), and cardiovascular (CV) death. The RI for stroke/SEE, MB, and CV death was comparable in patients treated with warfarin or DOACs. The lowest RI was in DM patients treated with Rivaroxaban (stroke/SEE, RI = 0.08; CV death, RI = 0.13). The RIs for bleeding were higher in DM patients treated with Dabigatran (RI110 = 0.32; RI150 = 0.40). Our study is the first to use RI to homogenize the efficacy and safety data reported in the DOACs pivotal studies against warfarin in patients with and without DM. Anticoagulation therapy is effective and safe in DM patients. DOACs appear to have a better efficacy and safety profile than warfarin. The use of DOACs is a reasonable alternative to vitamin-K antagonists in AF patients with DM. The RI can be a reasonable tool to help clinicians choose between DOACs or warfarin in the peculiar set of AF patients with DM

The home-court advantage in NCAA Division-I men’s basketball

The purpose of the present study was to examine the differences in game-related statistics between home and away games at the NCAA Division-I level of men’s basketball competition. The data scraping technique was used to obtain publicly available box scores during the 2018-19 competitive season. Throughout this period, 2181 home and 2205 away box scores were randomly selected across 353 teams, regardless of the winning or losing game outcome. The findings of the present study revealed that the game-related statistics influenced by the game location, listed in descending order of magnitude, were: assists (AS), personal fouls (PF), field-goal percentage (FG%), free-throw attempts (FTA), blocks (BL), defensive rebounds (DRB), turnovers (TO), steals (ST), and three-point shooting percentage (3P%). During home games, the teams tended to display better decision-making processes (i.e., more AS and ST, and less TO), defensive performance (i.e., more DRB and BL), shooting efficiency (i.e., greater FT% and 3P%), and minimize tactical errors (i.e., less PF and more FTA). Overall, these findings suggest that playing on a home-court provides a significant advantage in securing the desired game outcome and provides insight into what game-related statistics contribute most to this effect

Effects of resveratrol on bone health in type 2 diabetic patients. A double-blind randomized-controlled trial

Abstract Objectives Patients with type 2 diabetes (T2DM) are at increased fracture risk. Resveratrol has shown beneficial effects on bone health in few studies. The aim of this trial was to investigate the effects of resveratrol on bone mineral density (BMD) and on calcium metabolism biomarkers in T2DM patients. Methods In this double-blind randomized placebo-controlled trial 192 T2DM outpatients were randomized to receive resveratrol 500 mg/day (Resv500 arm), resveratrol 40 mg/day (Resv40 arm) or placebo for 6 months. BMD, bone mineral content (BMC), serum calcium, phosphorus, alkaline phosphatase, and 25-hydroxy vitamin D were measured at baseline and after 6 months. Results At follow-up, calcium concentrations increased in all patients, while within-group variations in alkaline phosphatase were higher in both resveratrol arms, and 25-hydroxy vitamin D increased in the Resv500 arm only, without between-group differences. Whole-body BMD significantly decreased in the placebo group, while whole-body BMC decreased in both the placebo and Resv40 arms. No significant changes in BMD and BMC values occurred in the Resv500 arm. The adjusted mean differences of change from baseline were significantly different in the Resv500 arm vs placebo for whole-body BMD (0.01 vs −0.03 g/cm2, p = 0.001), whole-body BMC (4.04 vs −58.8 g, p < 0.001), whole-body T-score (0.15 vs −0.26), and serum phosphorus (0.07 vs −0.01 µmol/L, p = 0.002). In subgroup analyses, in Resv500 treated-patients BMD values increased to higher levels in those with lower calcium and 25-hydroxy vitamin D values, and in alcohol drinkers. Conclusions Supplementation with 500 mg resveratrol prevented bone density loss in patients with T2DM, in particular, in those with unfavorable conditions at baseline