The Gabor wave front set in spaces of ultradifferentiable functions

[EN] We consider the spaces of ultradifferentiable functions S as introduced by Bjorck (and its dual S) and we use time-frequency analysis to define a suitable wave front set in this setting and obtain several applications: global regularity properties of pseudodifferential operators of infinite order and the micro-pseudolocal behaviour of partial differential operators with polynomial coefficients and of localization operators with symbols of exponential growth. Moreover, we prove that the new wave front set, defined in terms of the Gabor transform, can be described using only Gabor frames. Finally, some examples show the convenience of the use of weight functions to describe more precisely the global regularity of (ultra)distributions.The authors were partially supported by the INdAM-Gnampa Project 2016 "Nuove prospettive nell'analisi microlocale e tempo-frequenza", by FAR2013, FAR2014 (University of Ferrara) and by the project "Ricerca Locale - Analisi di Gabor, operatori pseudodifferenziali ed equazioni differenziali" (University of Torino). The research of the second author was partially supported by the project MTM2016-76647-P.Boiti, C.; Jornet Casanova, D.; Oliaro, A. (2019). The Gabor wave front set in spaces of ultradifferentiable functions. Monatshefte für Mathematik. 188(2):199-246. https://doi.org/10.1007/s00605-018-1242-3S1992461882Albanese, A., Jornet, D., Oliaro, A.: Quasianalytic wave front sets for solutions of linear partial differential operators. Integr. Equ. Oper. 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The Roles of Glycated Albumin as Intermediate Glycation Index and Pathogenic Protein

The conventional glycemic indices used in management of diabetic patients includes A1c, fructosamine, 1,5-anhydroglucitol, and glycated albumin (GA). Among these indices, A1c is currently used as the gold standard. However, A1c cannot reflect the glycemic change over a relatively short period of time, and its accuracy is known to decrease when abnormalities in hemoglobin metabolism, such as anemia, coexist. When considering these weaknesses, there have been needs for finding a novel glycemic index for diagnosing and managing diabetes, as well as for predicting diabetic complications properly. Recently, several studies have suggested the potential of GA as an intermediate-term glycation index in covering the short-term effect of treatment. Furthermore, its role as a pathogenic protein affecting the worsening of diabetes and occurrence of diabetic complications is receiving attention as well. Therefore, in this article, we wanted to review the recent status of GA as a glycemic index and as a pathogenic protein

Treatment of relapsing mild-to-moderate ulcerative colitis with the probiotic VSL#3 as adjunctive to a standard pharmaceutical treatment: a double-blind, randomized, placebo-controlled study

JECTIVES: VSL#3 is a high-potency probiotic mixture that has been used successfully in the treatment of pouchitis. The primary end point of the study was to assess the effects of supplementation with VSL#3 in patients affected by relapsing ulcerative colitis (UC) who are already under treatment with 5-aminosalicylic acid (ASA) and/or immunosuppressants at stable doses. METHODS: A total of 144 consecutive patients were randomly treated for 8 weeks with VSL#3 at a dose of 3,600 billion CFU/day (71 patients) or with placebo (73 patients). RESULTS: In all, 65 patients in the VSL#3 group and 66 patients in the placebo group completed the study. The decrease in ulcerative colitis disease activity index (UCDAI) scores of 50% or more was higher in the VSL#3 group than in the placebo group (63.1 vs. 40.8; per protocol (PP) P=0.010, confidence interval (CI)??(%) 0.51-0.74; intention to treat (ITT) P=0.031, CI??(%) 0.47-0.69). Significant results with VSL#3 were recorded in an improvement of three points or more in the UCDAI score (60.5% vs. 41.4%; PP P=0.017, CI??(%) 0.51-0.74; ITT P=0.046, CI??(%) 0.47-0.69) and in rectal bleeding (PP P=0.014, CI??(%) 0.46-0.70; ITT P=0.036, CI??(%) 0.41-0.65), whereas stool frequency (PP P=0.202, CI??(%) 0.39-0.63; ITT P=0.229, CI??(%) 0.35-0.57), physician's rate of disease activity (PP P=0.088, CI??(%) 0.34-0.58; ITT P=0.168, CI??(%) 0.31-0.53), and endoscopic scores (PP P=0.086, CI??(%) 0.74-0.92; ITT P=0.366, CI??(%) 0.66-0.86) did not show statistical differences. Remission was higher in the VSL#3 group than in the placebo group (47.7% vs. 32.4%; PP P=0.069, CI??(%) 0.36-0.60; ITT P=0.132, CI??(%) 0.33-0.56). Eight patients on VSL#3 (11.2%) and nine patients on placebo (12.3%) reported mild side effects. CONCLUSIONS: VSL#3 supplementation is safe and able to reduce UCDAI scores in patients affected by relapsing mild-to-moderate UC who are under treatment with 5-ASA and/or immunosuppressants. Moreover, VSL#3 improves rectal bleeding and seems to reinduce remission in relapsing UC patients after 8 weeks of treatment, although these parameters do not reach statistical significance