The interplay between representable functionals and derivations on Banach quasi *-algebras

This note aims to highlight the link between representable functionals and derivations on a Banach quasi *-algebra, i.e. a mathematical structure that can be seen as the completion of a normed *-algebra in the case the multiplication is only separately continuous. Representable functionals and derivations have been investigated in previous papers for their importance concerning the study of the structure properties of a Banach quasi *-algebra and applications to quantum models.Comment: Contribution Proceedings of International Conference on Topological Algebras and Applications 201

Representable and continuous functionals on Banach quasi *-algebras

In the study of locally convex quasi *-algebras an important role is played by representable linear functionals; i.e., functionals which allow a GNS-construction. This paper is mainly devoted to the study of the continuity of representable functionals in Banach and Hilbert quasi *-algebras. Some other concepts related to representable functionals (full-representability, *-semisimplicity, etc) are revisited in these special cases. In particular, in the case of Hilbert quasi *-algebras, which are shown to be fully representable, the existence of a 1-1 correspondence between positive, bounded elements (defined in an appropriate way) and continuous representable functionals is proved

Fixed point and homotopy results for mixed multi-valued mappings in 0-complete partial metric spaces

We give sufficient conditions for the existence of common fixed points for a pair of mixed multi-valued mappings in the setting of 0-complete partial metric spaces. An example is given to demonstrate the usefulness of our results over the existing results in metric spaces. Finally, we prove a homotopy theorem via fixed point results

Wightman Fields for Two-Dimensional Conformal Field Theories with Pointed Representation Category

Two-dimensional full conformal field theories have been studied in various mathematical frameworks, from algebraic, operator-algebraic to categorical. In this work, we focus our attention on theories with chiral components having pointed braided tensor representation subcategories, namely having automorphisms whose equivalence classes necessarily form an abelian group. For such theories, we exhibit the explicit Hilbert space structure and construct primary fields as Wightman fields for the two-dimensional full theory. Given a finite collection of chiral components with automorphism categories with trivial total braiding, we also construct a local extension of their tensor product as a chiral component. We clarify the relations with the Longo-Rehren construction, and illustrate these results with concrete examples including the U(1)current

WHATSAPP MESSENGER AS A REAL-TIME TOOL FOR A LONG-DISTANCE ACTIVITY OF A MULTIDISCIPLINARY

Introduction: Communication between doctors is traditionally conducted by written clinical charts. Mobile health is becoming an integral part of modern medical systems, improving accessibility and quality of medical care. Recent papers suggest that an increasing number of doctors are using in their clinical practice mobile tools to communicate clinical informations (1, 2). The aim of our study was to verify the adoption of WhatsApp Messenger in everyday clinical practice to obtain a real-time multidisciplinary collaboration among medical centers located in different areas of the city. Materials and Methods: In January 2016 a WhatsApp Messenger group was created among 25 specialists: 9 urologists, 9 oncologists, 3 urology residents, 3 radiotherapists and 1 general practitioner. A general coordinator and a group coordinator for each specialty was monthly appointed. The participants were invited to interact within the group clinical cases of genitourinary tumors of particular complexity requiring a multidisciplinary approach. All the chats were registered. A preliminary analysis of the activity of the group was planned after the first 10 entered patients. An evaluation questionnaire was sent after 6 months to evaluate the level of appreciation. The questionnaire was composed of a first section investigating the appreciation among the members of the group and a second section analyzing the impact in their everyday clinical practice of whatsapp multidisciplinary consultation. Results: In 10 (91%) out of 11 patients the WhatsApp consultation was completed, one case was not of oncological interest. An average of 8 (range=2-13) specialists joined the chat for each patient. An average of 17.6 (range: 4-43) interventions for each clinical case was recorded. On the average, 27%, 54% and 19% of the interventions for each clinical case were provided by oncologists, urologists and radiotherapists respectively. In 9 (81.8%) cases a final agreement on the patient's management was reached. At the evaluation questionnaire in a scale 1-10, the average rating score of appreciation was 7.8 (range=4-10). Relevant suggestions to improve the Whatsapp Messenger consultation were obtained and will be considered for future application the ameliorate the tool. Discussion: WhatsApp is a useful alternative and powerful complementary communication tool because of its capability to rapidly transfer large amount of clinical and radiological data. In our experience this new approach for multidisciplinary consultations improved collaboration among different specialist in different areas of the city through an easier and more informal change of opinions. In difficult and complex cases a rapid multidisciplinary approach allowed to offer the patient a personalized and tailored therapy management. GSTU Foundation. 1Sidhoum N, Dast S, Abdulshakoor A, Assaf N, Herlin C and Sinna R: WhatsApp: Improvement tool for surgical team communication. J Plast Reconstr Aesthet Surg 69: 1562-1563, 2016. 2 Gould G and Nilforooshan R: WhatsApp Doc? BMJ Innov 2(3): 109-110, 201

NOTCH1-mutated chronic lymphocytic leukemia displays high endoplasmic reticulum stress response with druggable potential

IntroductionConstitutive activation of NOTCH1-wild-type (NT1-WT) signaling is associated with poor outcomes in chronic lymphocytic leukemia (CLL), and NOTCH1 mutation (c.7541_7542delCT), which potentiates NOTCH1 signaling, worsens the prognosis. However, the specific mechanisms of NOTCH1 deregulation are still poorly understood. Accumulative evidence mentioned endoplasmic reticulum (ER) stress/unfolded protein response (UPR) as a key targetable pathway in CLL. In this study, we investigated the impact of NOTCH1 deregulation on CLL cell response to ER stress induction, with the aim of identifying new therapeutic opportunities for CLL.MethodsWe performed a bioinformatics analysis of NOTCH1-mutated (NT1-M) and NT1-WT CLL to identify differentially expressed genes (DEGs) using the rank product test. Quantitative real-time polymerase chain reaction (qPCR), Western blotting, cytosolic Ca2+, and annexin V/propidium iodide (PI) assay were used to detect curcumin ER stress induction effects. A median-effect equation was used for drug combination tests. The experimental mouse model Eμ-TCL1 was used to evaluate the impact of ER stress exacerbation by curcumin treatment on the progression of leukemic cells and NOTCH1 signaling.Results and discussionBioinformatics analysis revealed gene enrichment of the components of the ER stress/UPR pathway in NT1-M compared to those in NT1-WT CLL. Ectopic expression of NOTCH1 mutation upregulated the levels of ER stress response markers in the PGA1 CLL cell line. Primary NT1-M CLL was more sensitive to curcumin as documented by a significant perturbation in Ca2+ homeostasis and higher expression of ER stress/UPR markers compared to NT1-WT cells. It was also accompanied by a significantly higher apoptotic response mediated by C/EBP homologous protein (CHOP) expression, caspase 4 cleavage, and downregulation of NOTCH1 signaling in NT1-M CLL cells. Curcumin potentiated the apoptotic effect of venetoclax in NT1-M CLL cells. In Eμ-TCL1 leukemic mice, the administration of curcumin activated ER stress in splenic B cells ex vivo and significantly reduced the percentage of CD19+/CD5+ cells infiltrating the spleen, liver, and bone marrow (BM). These cellular effects were associated with reduced NOTCH1 activity in leukemic cells and resulted in prolonged survival of curcumin-treated mice. Overall, our results indicate that ER stress induction in NT1-M CLL might represent a new therapeutic opportunity for these high-risk CLL patients and improve the therapeutic effect of drugs currently used in CLL