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Nilpotency concepts for skew braces are among the main tools with which we are nowadays classifying certain special solutions of the Yang–Baxter equation, a consistency equation that plays a relevant role in quantum statistical mechanics and in many areas of mathematics. In this context, two relevant questions have been raised in F. Cedó, A. Smoktunowicz and L. Vendramin (Skew left braces of nilpotent type. Proc. Lond. Math. Soc. (3) 118 (2019), 1367–1392) (see questions 2.34 and 2.35) concerning right- and central nilpotency. The aim of this short note is to give a negative answer to both questions: thus, we show that a finite strong-nil brace B need not be right-nilpotent. On a positive note, we show that there is one (and only one, by our examples) special case of the previous questions that actually holds. In fact, we show that if B is a skew brace of nilpotent type and 
$b\ \ast \ b=0$ for all 
$b\in B$, then B is centrally nilpotent.
In mental health prevention, person-centered, and rights-based approaches, the role of recovery is highlighted (WHO, 2021). Various evaluation tools are used in rehabilitation objectives and programs, including the Specific Levels of Functioning Scale (SLOF) (Mucci et al. Schizophr Res 2014;159 144-50) and the Recovery Assessment Scale – Domains and Stages (RAS-DS), a self-measure of mental health recovery. It includes 38 items clustered into four recovery domains and meets two functions. In addition to measuring self-reported outcomes, it increases service-user control towards objectives and recovery action plans (Honey et al. BMC Psychiatry 2023;23 500).
To evalue the efficacy of RAD-DS in a psychiatric rehabilitation facility to be used as a routine tool in daily rehabilitation activity.
In our observational study, we recruited 103 inpatients (total: 103 patients, females: 38 patients, males: 65 patients) in a psychiatric rehabilitation facility. The patient presented with psychiatric disorders that met the diagnostic criteria of DMS-5 (schizophrenia, bipolar disorder, MDD, personality borderline disorder). Epidemiological data are shown in Table 1.
All patients were undergoing a psychiatric rehabilitation program and were observed during a one-year evaluation.
In all patients, the following rating scales were administered at baseline (T0) and after a year (T1):
For the evaluation of social measures, life outcomes, and functioning and recovery:
- Recovery Assessment Scale – Domains and Stages RAS-DS
- Specific Levels of Functioning Scale (SLOF)
- Global Assessment of Functioning (GAF)
For psychopathological evaluation:
- Brief Psychiatric Rating Scale (BPRS)
The data were statistically analyzed with the EZAnalyze 3.0 software for the Excel platform.
The RAS-DS total score results (Table 2) show a not significant difference between T0 vs. T1 (mean: 101.80 vs. 104.37, p. 0.193). An improvement in the score was observed after one year of rehabilitation treatment in the subgroup “Doing things I value” (T0 vs. T1: mean 16.15 vs. 18.77, p 0.001). Statistically significant differences were observed in the subgroups “Mastering my illness” (T0 vs. T1: mean 18.3 vs. 20.85, p. 0.021). In the other subgroups, the differences were not statistically significant. Interestingly, these results are comparable to those found with SLOF and GAF (respectively, p. 0.972 and p. 0.873).
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The current trend of research and clinical practice is to give more importance to psychiatric rehabilitation treatment (Franza Psychiatr Danub 2022;34(Suppl 8) 9-13). The results obtained with our observational study indicate the possible usefulness of indicators of patient well-being, as well as the RAS-DS in the management of psychiatric rehabilitation programs. The expectations, indications, and perceptions of psychiatric patients can be decisive in improving recovery.
None Declared
The aim of this paper is to study supersoluble skew braces, a class of skew braces that encompasses all finite skew braces of square-free order. It turns out that finite supersoluble skew braces have Sylow towers and that in an arbitrary supersoluble skew brace B many relevant skew brace-theoretical properties are easier to identify: For example, a centrally nilpotent ideal of B is B-centrally nilpotent, a fact that simplifies the computational search for the Fitting ideal; also, B has finite multipermutational level if and only if 
$(B,+)$ is nilpotent.
Given a finite presentation of the structure skew brace 
$G(X,r)$ associated with a finite nondegenerate solution of the Yang–Baxter equation (YBE), there is an algorithm that decides if 
$G(X,r)$ is supersoluble or not. Moreover, supersoluble skew braces are examples of almost polycyclic skew braces, so they give rise to solutions of the YBE on which one can algorithmically work on.
The evaluation of healthcare pathways must be considered of fundamental importance. The quality of care provided to patients with severe mental disorders (SMD) does not correspond to the standards set by the recommendations. Therefore, measures such as the real coverage rate of psychiatric patients’ needs (contact coverage), by comparing epidemiological prevalence rates and the number of patients receiving adequate care, could be a valuable resource for implementing the transition to community mental health. However, simple assessment and reporting of rates of contact with mental healthcare potentially overestimate the full expected health benefits of services. Therefore, in addition to monitor the coverage rate achieved by the services, the evaluation of the effectiveness of the care provided (effective coverage) [De Silva et al. Int J Epidemiol 2014;43(2):341–53] is also of relevant importance.
To measure the gap between contact and effective coverage of mental healthcare, i.e., the effectiveness of interventions provided by services for the treatment of SMD in preventing an exacerbation of psychiatric symptoms.
Data were retrieved from Healthcare Utilization databases of four Italian Regions (Lombardy, Emilia-Romagna, Lazio, Sicily). 45,761 newly taken-in-care cases of depression, schizophrenia, bipolar, and personality disorder were included. A variant of the self-controlled case series method was used to estimate the incidence rate ratio (IRR) for the relationship between exposure (use of different types of mental healthcare such as pharmacotherapy, generic contacts with the outpatient service, psychosocial interventions, and psychotherapies) and relapse episodes (mental illness emergency hospital admissions).
11,500 relapses occurred. Relapse risk was reduced (Figure) during periods covered by (i) psychotherapy for patients with depression (IRR 0.67; 95% CI, 0.49 to 0.91) and bipolar disorder (0.64; 0.29 to 0.99); (ii) psychosocial interventions for those with depression (0.74; 0.56 to 0.98), schizophrenia (0.83; 0.68 to 0.99) and bipolar disorder (0.55; 0.36 to 0.84), (iii) pharmacotherapy for those with schizophrenia (0.58; 0.49 to 0.69), and bipolar disorder (0.59; 0.44 to 0.78). Coverage with generic mental healthcare, in the absence of psychosocial/psychotherapeutic interventions, did not affect the risk of relapse.
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Psychosocial interventions, psychotherapies and specific pharmacotherapies can be considered particularly effective in treating patients with bipolar, depressive, and schizophrenic disorders. This study ascertained the gap between utilization of mental healthcare and effective coverage, showing that real-world data can represent a useful resource to monitor mental healthcare paths and to assess the effectiveness of a mental health system.
None Declared
A subgroup H of a group G is said to be pronormal in G if each of its conjugates 
$H^g$ in G is already conjugate to it in the subgroup 
$\langle H,H^g\rangle $. The aim of this paper is to classify those (locally) finite simple groups which have only nilpotent or pronormal subgroups.
