Flat bundles, von Neumann algebras and KK-theory with R/Z\R/\Z-coefficients

Let $M$ be a closed manifold and $\alpha : \pi_1(M)\to U_n$ a representation. We give a purely $K$-theoretic description of the associated element $[\alpha]$ in the $K$-theory of $M$ with $\R/\Z$-coefficients. To that end, it is convenient to describe the $\R/\Z$-$K$-theory as a relative $K$-theory with respect to the inclusion of \C in a finite von Neumann algebra $B$. We use the following fact: there is, associated with $\alpha$, a finite von Neumann algebra $B$ together with a flat bundle \cE\to M with fibers $B$, such that E_\a\otimes \cE is canonically isomorphic with \C^n\otimes \cE, where $E_\alpha$ denotes the flat bundle with fiber \C^n associated with $\alpha$. We also discuss the spectral flow and rho type description of the pairing of the class $[\alpha]$ with the $K$-homology class of an elliptic selfadjoint (pseudo)-differential operator $D$ of order 1

Towards the use of vector based GP to predict physiological time series

Azzali, I., Vanneschi, L., Bakurov, I., Silva, S., Ivaldi, M., & Giacobini, M. (2020). Towards the use of vector based GP to predict physiological time series. Applied Soft Computing Journal, 89(April), [106097]. https://doi.org/10.1016/j.asoc.2020.106097-----------------------------------------------------------------This work was partially supported by FCT, Portugal, through funding of LASIGE Research Unit (UIDB/00408/2020) and projects INTERPHENO (PTDC/ASP-PLA/28726/2017), PERSEIDS (PTDC/EMS -SIS/0642/2014), OPTOX (PTDC/CTA-AMB/30056/2017), BINDER (PTDC/CCI-INF/29168/2017), AICE (DSAIPA/DS/0113/2019), GADgET (DSAIPA/DS/0022/2018), and PREDICT (PTDC/CCI-CIF/29877/2017). This study was also supported by Ministero dell'Istruzione, dell'Universita e della Ricerca (MIUR) under the programme "Dipartimenti di Eccellenza ex L.232/2016'' to the Department of Veterinary Science, University of Turin.Prediction of physiological time series is frequently approached by means of machine learning (ML) algorithms. However, most ML techniques are not able to directly manage time series, thus they do not exploit all the useful information such as patterns, peaks and regularities provided by the time dimension. Besides advanced ML methods such as recurrent neural network that preserve the ordered nature of time series, a recently developed approach of genetic programming, VE-GP, looks promising on the problem in analysis. VE-GP allows time series as terminals in the form of a vector, including new strategies to exploit this representation. In this paper we compare different ML techniques on the real problem of predicting ventilation flow from physiological variables with the aim of highlighting the potential of VE-GP. Experimental results show the advantage of applying this technique in the problem and we ascribe the good performances to the ability of properly catching meaningful information from time series.authorsversionpublishe

ANHEDONIA IN THE PSYCHOSIS RISK SYNDROME: STATE AND TRAIT CHARACTERISTICS

Background: Previous studies reported deficits in pleasure experience in schizophrenia, but little is known about anhedonia in psychosis risk syndrome. Aim of this study was: (1) to assess anhedonia in distinct help-seeking subgroups of young people identified through the Ultra-High Risk (UHR) criteria, (2) to explore its association with functioning and psychopathology in the UHR group, and (3) to monitor longitudinally its stability in UHR individuals along 1-year follow-up period. Subjects and methods: All participants (78 UHR, 137 with a First Episode Psychosis (FEP), and 95 non-UHR/FEP), aged 13-35 years, completed the Comprehensive Assessment of At-Risk Mental States (CAARMS), the Beck Depression Inventory-II (BDI-II), the Schizotypal Personality Questionnaire - Brief version (SPQ-B), the Brief O-LIFE questionnaire (BOL), and the World Health Organization Quality of Life - Brief version (WHOQOL-BREF). We adopted two different indexes of anhedonia: i.e. CAARMS “Anhedonia” item 4.3 and BOL “Introvertive Anhedonia” subscale scores. Results: In comparison with non-UHR/FEP, UHR individuals showed higher baseline CAARMS item 4.3 and BOL “Introvertive Anhedonia” subscale scores. No difference in anhedonia scores between UHR and FEP patients was found. After 1-year follow up period, UHR subjects had a significant decrease in severity exclusively on CAARMS item 4.3 subscore. Conclusions: In the UHR group, CAARMS anhedonia showed significant correlations with functioning deterioration, negative symptoms, and comorbid depression (including suicide ideation), while BOL anhedonia with a poorer self-perceived quality of life and specific schizotypal personality traits (i.e. interpersonal deficits and disorganization). Anhedonia is prominent in the psychosis risk syndrome and its severity is indistinguishable from that of FEP patients

Anhedonia and suicidal ideation in young people with early psychosis: Further findings from the 2-year follow-up of the ReARMS program.

Hedonic deficits have been extensively studied in schizophrenia, but little is known about their association with suicidal ideation in early psychosis. The aim of this research was to examine the relationship between anhedonia and suicidal thoughts across a 2-year follow-up period in people with First Episode Psychosis (FEP) and at Ultra High Risk (UHR) of psychosis. Ninty-six UHR and 146 FEP, aged 13–35 years, completed the Comprehensive Assessment of At-Risk Mental States (CAARMS) and the Beck Depression Inventory-II (BDI-II). The BDI-II “Anhedonia” subscale score to assess anhedonia and the CAARMS “Depression” item 7.2 subscore to measure depression were used across the 2 years of follow-up. Hierarchical regression analyses were performed. No difference in anhedonia scores between FEP and UHR individuals was found. In the FEP group, a significant enduring association between anhedonia and suicidal ideation was found at baseline and across the follow-up, independent of clinical depression. In the UHR subgroup, the enduring relationship between anhedonia and suicidal thoughts were not completely independent from depression severity. Anhedonia is relevant in predicting suicidal ideation in early psychosis. Specific pharmacological and/or psychosocial interventions on anhedonia within specialized EIP program could reduce suicide risk overtime

L^2 rho form for normal coverings of fibre bundles

We define the secondary invariants L^2- eta and -rho forms for families of generalized Dirac operators on normal coverings of fibre bundles. On the covering family we assume transversally smooth spectral projections, and Novikov--Shubin invariants bigger than 3(dim B+1) to treat the large time asymptotic for general operators. In the particular case of a bundle of spin manifolds, we study the L^2- rho class in relation to the space of positive scalar curvature vertical metrics.Comment: 21 pages, revised versio

The Baum--Connes conjecture localised at the unit element of a discrete group

We construct a Baum--Connes assembly map localised at the unit element of a discrete group $Gamma$. This morphism, called $mu_ au$, is defined in $KK$-theory with coefficients in $mathbb{R}$ by means of the action of the projection $[ au ] in KK_{mathbb{R}}^Gamma(mathbb{C},mathbb{C})$ canonically associated to the group trace of $Gamma$. We show that the corresponding $au$-Baum--Connes conjecture is weaker then the classical one but still implies the strong Novikov conjecture. The right hand side of $mu_ au$ is functorial with respect to the group $Gamma$