On the Solution of Markov-switching Rational Expectations Models

This paper describes a method for solving a class of forward-looking Markov-switching Rational Expectations models under noisy measurement, by specifying the unobservable expectations component as a general-measurable function of the observable states of the system, to be determined optimally via stochastic control and filtering theory. Solution existence is proved by setting this function to the regime-dependent feedback control minimizing the mean-square deviation of the equilibrium path from the corresponding perfect-foresight autoregressive Markov jump state motion. As the exact expression of the conditional (rational) expectations term is derived both in finite and infinite horizon model formulations, no (asymptotic) stationarity assumptions are needed to solve forward the system, for only initial values knowledge is required. A simple sufficient condition for the mean-square stability of the obtained rational expectations equilibrium is also provided.Rational Expectations, Markov-switching dynamic systems, Dynamic programming, Time-varying Kalman filter

On a stochastic approach to model the double phosphorylation/dephosphorylation cycle

Because of the unavoidable intrinsic noise affecting biochemical processes, astochastic approach is usually preferred whenever a deterministic model givestoo rough information or, worse, may lead to erroneous qualitative behaviorsand/or quantitatively wrong results. In this work we focus on the chemicalmaster equation (CME)-based method which provides an accurate stochasticdescription of complex biochemical reaction networks in terms of the probabilitydistribution of the underlying chemical populations. Indeed, deterministic mod-els can be dealt with as first-order approximations of the average-value dynamicscoming from the stochastic CME approach. Here we investigate the double phos-phorylation/dephosphorylation cycle, a well-studied enzymatic reaction networkwhere the inherent double time scale requires one to exploit quasisteady stateapproximation (QSSA) approaches to infer qualitative and quantitative informa-tion. Within the deterministic realm, several researchers have deeply investi-gated the use of the proper QSSA, agreeing to highlight that only one type ofQSSA (the total QSSA) is able to faithfully replicate the qualitative behaviorof bistability occurrences, as well as the correct assessment of the equilibriumpoints, accordingly to the not approximated (full) model. Based on recent resultsproviding CME solutions that do not resort to Monte Carlo simulations, the pro-posed stochastic approach shows some counterintuitive facts arising when tryingto straightforwardly transfer bistability deterministic results into the stochasticrealm, and suggests how to handle such cases according to both theoretical andnumerical results

Solid-state 3He^3\mathrm{He} NMR of the superconducting rubidium endofulleride Rb3(3He@C60)\mathrm{Rb_3(^3He@C_{60})}

A new variant of the superconducting fulleride $\mathrm{Rb_{3}C_{60}}$ is presented, with $\mathrm{^{3}He}$ atoms encapsulated in the $\mathrm{C_{60}}$ cages. The $\mathrm{^{3}He}$ nuclei act as sensitive NMR probes embedded in the material. The superconducting and normal states are characterised by $\mathrm{^{3}He}$ NMR. Evidence is found for co-existing vortex liquid and vortex solid phases below the superconducting transition temperature. A strong dependence of the spin-lattice relaxation time constant on spectral frequency is observed in the superconducting state, as revealed by two-dimensional NMR utilising an inverse Laplace transform. Surprisingly, this phenomenon persists, in attenuated form, at temperatures well above the superconducting transition.Comment: 20 pages, 15 figure

Measuring the willingness to share personal health information: a systematic review

BackgroundIn the age of digitalization and big data, personal health information is a key resource for health care and clinical research. This study aimed to analyze the determinants and describe the measurement of the willingness to disclose personal health information.MethodsThe study conducted a systematic review of articles assessing willingness to share personal health information as a primary or secondary outcome. The review followed the Preferred Reporting Items for Systematic Reviews and Meta-Analysis protocol. English and Italian peer-reviewed research articles were included with no restrictions for publication years. Findings were narratively synthesized.ResultsThe search strategy found 1,087 papers, 89 of which passed the screening for title and abstract and the full-text assessment.ConclusionNo validated measurement tool has been developed for willingness to share personal health information. The reviewed papers measured it through surveys, interviews, and questionnaires, which were mutually incomparable. The secondary use of data was the most important determinant of willingness to share, whereas clinical and socioeconomic variables had a slight effect. The main concern discouraging data sharing was privacy, although good data anonymization and the high perceived benefits of sharing may overcome this issue

On the Nonlinear Stabilization Problem via Quadratic Immersion Part I: Sigma/Pi-systems and biased solutions of driver-type systems.

Based on our recently issued paper on Quadratic Immersion (QI), (also said 'exact quadratization') for nonlinear control systems, the present work aims to define the main features of a possible new approach in nonlinear control, able to exploit the structural properties of a quadratized system in order to design global, statefeedback- regulators, with an exponential, and tunable, performance, for a meaningful class of nonlinear systems. The paper is divided into two parts. In the Part I we go through the properties of QI and explore the possibility of writing explicitly the solution for the class of the, so called, Sigma/Pi-systems. The main result consists in showing that, under certain conditions, Sigma/Pi-systems are always forward complete, and the solution can be calculated at the steady-state

Filtraggio polinomiale per sistemi bilineari stocastici a tempo discreto

Dottorato di ricerca in ingegneria dei sistemi. 7. ciclo. A.a. 1993-94. Tutori Carlo Bruni e Alfredo GermaniConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

On the Nonlinear Stabilization Problem via Quadratic Immersion Part II: A QI-based approach for the design of nonlinear regulators having exponential-tunable performance

The results of Part I of the paper are here exploited in order to define a regulator design method for Sigma/Pi-systems, even non stationary, which makes use of a static state-feedback working in the same domain as the open-loop system. Sufficient conditions are given in order that a fixed performance, in terms of convergence rate, be achievable. Provided these conditions are satisfied the regulator steers the system state to zero, at an exponential, tunable, rate and the domain of \u27attraction\u27 of the zero will include all points from which the orbits of the closed-loop system are bounded. For stationary systems additional results are proven as far as the accessibility property