Mean-field solution of the Hubbard model: the magnetic phase diagram

The present paper is based on our graduate lectures in condensed-matter physics. We found that the mean-field solution of the Hubbard model is an excellent tool to stimulate students' reflections towards the treatment of realistic magnetic interactions. We show by detailed analytical and numerical calculations how to find the mean-field solution of the model on a square lattice. We then interpret the physical implications of the ground-state magnetic phase diagram in terms of the electron density and the ratio between the Coulomb repulsion and the electron-structure bandwidth.Comment: 14 pages, 7 figure

On the relation between thermodynamical and statistical entropy: The origin of the N!

The division by N! in the expression of statistical entropy is usually justified to students by the statement that classical particles should be counted as indistinguishable. Sometimes, quantum indistinguishability is invoked to explain it. In this paper, we try to clarify the issue starting from Clausius thermodynamical entropy and deriving from it Boltzmann statistical entropy for the ideal gas. This approach appears interesting for two reasons: Firstly, it provides a direct heuristic link between thermodynamical and statistical expressions of entropy that is missing in the usual approach. In second place, it explicitly reminds that also statistical entropy is defined with respect to a reference state, chosen to be the quantum-mechanical (T=0) ground state of the N-particles in a box. Both factors $h^{3N}$ and $N!$ at the denominator of the statistical entropy are a consequence of the quantum nature of the reference state: in particular, the $N!$ is not related to the particle identity, but to the identity of the boundary conditions on the quantum-mechanical ground-state momenta, and to a general statistical maximization principle. The introduction of a reference state also allows to reinterpret the standard case of two mixing gases.Comment: 11 pages, 2 figure

Regole di tutela e sanzioni: il caso della patente a punti

Economic theory does not seem to have a valid explanation of the emergence and success of demerit point based driving licenses across many countries. In fact, the theory of optimal deterrence would imply, in such circumstances, a system based on monetary sanctions. Some extensions of the standard theory have been explored, however they do not seem to size both the nature of the sanctioning mechanism applied and the goals of the lawmaker. In this paper we try to frame the demerit point mechanism within the conceptual co-ordinates of the property rules and liability rules as stylised by Calabresi and Melamed (1972). We enlighten how circulation laws address the problem of the protection of different entitlements, of both public and private, monetary and non monetary nature, which, moreover, are protected through a plurality of rules of protection. The demerit point mechanism has been simply added to this portfolio of tools and has been specifically deployed for the pursuit of the entitlement of the "health of all those involved in circulation". Moreover, we show how such a mechanism addresses the incoherence of punishing the violation of an inalienable entitlement, such as the "right of health", with a sanction which is more consistent with a property rule. Some results might be generalised. An in-depth analysis of the plurality of entitlements protected by a certain law may entail the need of a plurality of rules of protection. Moreover, the deterrence effect of a specific rule may crucially depend on the consistency between the nature of the entitlement and the rule of protection applied.

Cosmogenic neutrinos and gamma-rays and the redshift evolution of UHECR sources

If ultra-high-energy cosmic rays (UHECRs) have extragalactic origins, as is widely assumed to be the case at least for the majority of cosmic rays with energies above a few EeV, secondary neutrinos and photons can be expected to be produced during the propagation of UHECRs through intergalactic space via interactions with cosmic background photons. The fluxes of such secondary particles are strongly dependent on the redshift evolution of the emissivity (number density times luminosity) of UHECR sources. We show how cosmic rays, neutrinos, and gamma rays can potentially provide complementary information about UHECR source evolution.Comment: 6 pages, 3 figures; published in the proceedings of the Neutrino Oscillation Workshop, 4-11 September 2016, Otranto, Ital

An economic evaluation of aripiprazole vs olanzapine adapted to the Italian setting using outcomes of metabolic syndrome and risk for diabetes in patients with schizophrenia

Giorgio L Colombo1, Mauro Caruggi2, Sergio Di Matteo1, Alessandro Rossi31S.A.V.E. Studi Analisi Valutazioni Economiche, Milano, Italy; 2Università degli Studi dell’Insubria, Varese, Italy; 3Università de L’Aquila, ItalyObjective: To evaluate the cost-effectiveness of aripiprazole and olanzapine in patients with schizophrenia.Methods: Data from a double-blind, randomized study demonstrating the efficacy of aripiprazole and olanzapine were used to observe new incidence of metabolic syndrome (26-week therapy) and to model the risk of developing diabetes over 5 years of therapy. Cumulative incidence of metabolic syndrome was compared using Kaplan–Meier estimates; diabetes risk was estimated using a validated, general population risk-prediction model. Economic assessment was conducted from the third-party payer perspective by evaluating pharmacotherapy costs of treating schizophrenia and medical costs associated with treating adverse metabolic effects in a hypothetical cohort of 1000 patients. Resource utilization and costs were derived from the underlying study and published data, using a 3% rate to discount costs and benefits.Results: For the patients switched from olanzapine to aripiprazole, treatment with aripiprazole was a dominant cost-saving strategy. Use of aripiprazole avoided 184 events of metabolic syndrome over 26 weeks of treatment, contributing to a real-world (RW) cost savings of €2.53 per patient and a total savings of approximately €465.52 over a 5-year period. For the same cohort, the risk-prediction model indicated that 34 occurrences of diabetes could be avoided over 5 years, corresponding to a RW cost savings of €56.86 per patient and a total saving of approximately €1,933.24. These savings reflect avoided costs in treating adverse metabolic events and comparable costs in the acquisition of aripiprazole.Conclusions: Maintenance aripiprazole therapy offers medical and economic benefits over olanzapine, reflected by reduced incidence of metabolic syndrome and diabetes and associated lower costs.Keywords: schizophrenia, cost-consequences, apripiprazole, olanzapine, metabolic syndrome, diabete

Combined Point of Care Tools Are Able to Improve Treatment Adherence and Health-Related Quality of Life in Patients with Severe Hemophilia: An Observational Prospective Study

Introduction: Ultrasound (US) assessment of joints is an evolving point of care tool for the detection of early joint arthropathy (Napolitano M, Kessler CM. Hemophilia A and B. Consultative Hemostasis and Thrombosis, Kitchens, 4th edition); population pharmacokinetic (pop-PK) studies are adopted as a useful instrument to set the prophylaxis regimen for patients with hemophilia, they may improve adherence (Nagao A.et al. Thromb Res. 2019 Jan; 173:79-84) and reduce the annual bleeding rate (ABR). Adherence to continuous intravenous administrations of factor VIII or Factor IX products is challenging, thus patients may experience breakthrough bleedings while on prophylaxis. Repeated US examinations of joint status have recently been advocated to attempt to remedy sub-optimal medication adherence (Di Minno A et al., Blood Rev. 2019 Jan;33:106-116). Aim of the current prospective analysis was to evaluate the impact of combined US assessment and pop-PK study on adherence to treatment and health related quality of life in patients with severe hemophilia A(HA) and B (HB) under regular prophylaxis. Material and methods: This prospective observational study was performed at a single tertiary center from January 2017 to June 2019. Research was conducted following the Helsinki Declaration. All patients included in the study provided a written informed consent for study participation. Patients with severe HA and HB routinely underwent, as part of regular 12-months follow-up visits, the following: US joints evaluation of elbows, knees and ankles using the HEAD-US protocol, treatment adherence evaluation by VERITAS-Pro questionnaire, health –related quality of life assessment by the standardized EQ-5D,EQ-VAS and pop-PK study (WAPPS-Hemo, McMaster University) as needed (i.e.in case of changes in life style, planned treatment switch); each patient visualised US and his estimated PK profile during medial encounters. Compliance to the prescribed treatment was also determined by analysis of patient diaries with infusion logs. Statistical analysis was performed using the SPSS software version 25.0 (SPSS Chicago, IL). Statistical tests were 2-sided, with a significance threshold of 0.05. Results: Twenty consecutive males with severe haemophilia were included in the current analysis, 13 with severe HA, 2 with HA with previous inhibitors and 5 HB, with a median age of 30 (range 14- 56) years and a median ABR of 5 (range:0-12). Nine patients were under primary prophylaxis, 8 under secondary prophylaxis and 3 under tertiary prophylaxis, they all self-infused at home. Four patients had one target joint and 3 patients had multiple target joints. For each enrolled subject, HEAD-US score, VERITAS-pro, EQ5D and EQ-VAS score were assessed at enrolment (T0) and at 12 (T12) and 24 (T24) months follow-up visits, respectively. Pop-PK was assessed in 11 patients: in 7 (5 HA,2 HB) it was assessed twice, before and after treatment switch to extended half-life (EHL) products, in 4 it was assessed once to modify prophylaxis treatment schedules for a more active life-style (N=2) or weight changes (N=2). Median ABR was 4 at T12 and 3.8 at T24. Reported breakthrough bleeds at T12 were 14, mainly trauma-related (N= 8) or affecting target joints (N=4), they were not reported at T24 in patients with PK-driven modified schedules (N=4) and in 4 patients under EHL treatments. Mean HEAD-US score at T0 resulted 8 (range:0-16), at T24 it was 6 (range:0-16). Mean Veritas-Pro score values were 42.7 at TO, 40.1 at T12 and 38.7 at T24. At T0, EQ-5D mean utility score was 0.82 (range: 0.68-1), at T24, the mean was 0.87 (range:0.72-1). In detail, at 24 months follow-up, there was a statistically significant (p<0.05) improvement in adherence to treatment with particular reference to the dimensions of communication and skipped doses. A tendency toward improved HEAD-US score, higher adherence and better quality of life scores, was observed in particular in patients switched to EHL products at T24, at a mean of 10 months after switching (range: 6-22 months). Conclusion: Several combined measures of haemophilia treatment monitoring, allowing visual assessment of joints status and PK profile estimates by patients have here shown to improve treatment adherence and quality of life in patients with HA and HB, this may be not only related to new available treatments but also to an increased awareness and education of patients