A theory of the infinite horizon LQ-problem for composite systems of PDEs with boundary control

We study the infinite horizon Linear-Quadratic problem and the associated algebraic Riccati equations for systems with unbounded control actions. The operator-theoretic context is motivated by composite systems of Partial Differential Equations (PDE) with boundary or point control. Specific focus is placed on systems of coupled hyperbolic/parabolic PDE with an overall `predominant' hyperbolic character, such as, e.g., some models for thermoelastic or fluid-structure interactions. While unbounded control actions lead to Riccati equations with unbounded (operator) coefficients, unlike the parabolic case solvability of these equations becomes a major issue, owing to the lack of sufficient regularity of the solutions to the composite dynamics. In the present case, even the more general theory appealing to estimates of the singularity displayed by the kernel which occurs in the integral representation of the solution to the control system fails. A novel framework which embodies possible hyperbolic components of the dynamics has been introduced by the authors in 2005, and a full theory of the LQ-problem on a finite time horizon has been developed. The present paper provides the infinite time horizon theory, culminating in well-posedness of the corresponding (algebraic) Riccati equations. New technical challenges are encountered and new tools are needed, especially in order to pinpoint the differentiability of the optimal solution. The theory is illustrated by means of a boundary control problem arising in thermoelasticity.Comment: 50 pages, submitte

Spectral properties of incommensurate charge-density wave systems

The concept of frustrated phase separation is applied to investigate its consequences for the electronic structure of the high T_c cuprates. The resulting incommensurate charge density wave (CDW) scattering is most effective in creating local gaps in k-space when the scattering vector connects states with equal energy. Starting from an open Fermi surface we find that the resulting CDW is oriented along the (10)- and (or) (01)-direction which allows for a purely one-dimensional or a two-dimensional ``eggbox type'' charge modulation. In both cases the van Hove singularities are substantially enhanced, and the spectral weight of Fermi surface states near the M-points, tends to be suppressed. Remarkably, a leading edge gap arises near these points, which, in the eggbox case, leaves finite arcs of the Fermi surface gapless. We discuss our results with repect to possible consequences for photoemission experiments

Measles in Italy: Viral strains and crossing borders.

In 2017, Italy experienced one of the largest outbreaks of measles in recent years, with 5404 notified cases and 4347 confirmed cases. A further 2029 cases were notified during the first 6 months of 2018, and 1516 of them were laboratory-confirmed. The B3 and D8 genotypes were identified as those responsible for the outbreak. Possible transmission routes can be established by monitoring the circulating measles virus strains in support of the national health authorities to warn people and travellers

Long-term prediction of adherence to continuous positive air pressure therapy for the treatment of moderate/severe obstructive sleep apnea syndrome

BACKGROUND: Continuous positive airway pressure (CPAP) therapy is a highly effective treatment for obstructive sleep apnea syndrome (OSAS). However, poor adherence is a limiting factor, and a significant proportion of patients are unable to tolerate CPAP. The aim of this study was to determine predictors of long-term non-compliance with CPAP. METHODS: CPAP treatment was prescribed to all consecutive patients with moderate or severe OSAS (AHI ≥15 events/h) (n = 295) who underwent a full-night CPAP titration study at home between February 1, 2002 and December 1, 2016. Adherence was defined as CPAP use for at least 4 h per night and five days per week. Subjects had periodical follow-up visits including clinical and biochemical evaluation and assessment of adherence to CPAP. RESULTS: Median follow-up observation was 74.8 (24.2/110.9) months. The percentage of OSAS patients adhering to CPAP was 41.4% (42.3% in males and 37.0% in females), and prevalence was significantly higher in severe OSAS than in moderate (51.8% vs. 22.1%; p < 0.001; respectively). At multivariate analysis, lower severity of OSAS (HR = 0.66; CI 95 0.46-0.94) p < 0.023), cigarette smoking (HR = 1.72; CI 95 1.13-2.61); p = 0.011), and previous cardiovascular events (HR = 1.95; CI 95 1.03-3.70; p = 0.04) were the only independent predictors of long-term non-adherence to CPAP after controlling for age, gender, and metabolic syndrome. CONCLUSIONS: In our cohort of patients with moderate/severe OSAS who were prescribed CPAP therapy, long-term compliance to treatment was present in less than half of the patients. Adherence was positively associated with OSAS severity and negatively associated with cigarette smoking and previous cardiovascular events at baseline

Monte Carlo evaluation of the external gamma, neutron and muon induced background sources in the CUORE experiment

CUORE is a 1 ton scale cryogenic experiment aiming at the measurement of the Majorana mass of the electron neutrino. The detector is an array of 988 TeO2 bolometers used for a calorimetric detection of the two electrons emitted in the BB0n of 130Te. The sensitivity of the experiment to the lowest Majorana mass is determined by the rate of background events that can mimic a BB0n. In this paper we investigate the contribution of external sources i.e. environmental gammas, neutrons and cosmic ray muons to the CUORE background and show that the shielding setup designed for CUORE guarantees a reduction of this external background down to a level <1.0E-02 c/keV/kg/y at the Q-value, as required by the physical goal of the experiment.Comment: 14 pages, 7 figure

Interleukin-1beta tear concentration in glaucomatous and ocular hypertensive patients treated with preservative-free nonselective beta-blockers

PURPOSE: To evaluate the ocular surface inflammatory response to the presence of preservatives in nonselective beta-blocker eyedrops. DESIGN: Prospective, crossover, single-masked, randomized clinical study. METHODS: STUDY POPULATION: Twenty primary open angle glaucoma or ocular hypertensive patients were divided in two groups, one treated with preservative-free timolol 0.5% (group 1) and the other with preserved timolol 0.5% (group 2) eyedrops. After 60 days of therapy and 3 more weeks of washout, the two groups switched to the other therapy. PROCEDURE: At each visit,basal tear samples were collected from the inferior conjunctival fornix for the determination of interleukin (IL)-1 tear concentrations by an enzyme-linked immunosorbent assay. Intraocular pressure measurement, conjunctival hyperemia, superficial punctate keratitis, and tear film breakup time were evaluated. MAIN OUTCOME MEASURE: IL-1 concentration in tears following the use of preserved eyedrops. RESULTS: IL-1 tear concentrations increased significantly in both groups, compared with baseline values,during preserved timolol therapy. There were no statistically significant changes in hyperemia and superficial punctate keratitis throughout the study in either group.A statistically significant breakup time reduction was observed in both groups after 30 days and after 60 days of preserved therapy. CONCLUSION: The use of preservatives in timolol 0.5% eyedrops leads to tear film instability and ocular surface inflammatory changes documented by a reduction of breakup time and an increase of IL-1 tear concentrations.Preservative-free beta-blockers are preferable for long-term hypotensive therapy to prevent ocular surface inflammation

Delayed-onset muscle soreness does not influence occlusal sensitivity and position sense of the mandible

Masticatory muscle-pain patients often complain about sensorimotor changes, but the effects of pain on the psychophysical properties remain unclear. This study aimed to investigate the effects of delayed-onset muscle soreness (DOMS) on the jaw's position sense (PS) and occlusal sensitivity (OS). In all, 12 participants underwent intense concentric–eccentric jaw exercises. Self-reported muscle fatigue and pain, pain-free maximum mouth opening (MMO), pain pressure thresholds (PPTs) at right and left masseter and right and left anterior temporalis, maximum voluntary bite force (MVBF), PS and OS were recorded before, immediately after, 24 h, 48 h and 1 week after the exercises. Data were analysed with repeated measures anova. Pain and fatigue increased significantly after the exercises, while fatigue also increased 24 h afterwards. Time and site had a significant effect for PPTs, not for MVBF. MMO decreased significantly 24 h after the exercises. OS and PS did not change significantly. Experimentally induced DOMS does not influence the psychophysical properties of the masticatory system

Invariance: a Theoretical Approach for Coding Sets of Words Modulo Literal (Anti)Morphisms

Let $A$ be a finite or countable alphabet and let $\theta$ be literal (anti)morphism onto $A^*$ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under $\theta$ ($\theta$-invariant for short).We establish an extension of the famous defect theorem. Moreover, we prove that for the so-called thin $\theta$-invariant codes, maximality and completeness are two equivalent notions. We prove that a similar property holds in the framework of some special families of $\theta$-invariant codes such as prefix (bifix) codes, codes with a finite deciphering delay, uniformly synchronized codes and circular codes. For a special class of involutive antimorphisms, we prove that any regular $\theta$-invariant code may be embedded into a complete one.Comment: To appear in Acts of WORDS 201

Vertical distribution of aerosol optical properties in the Po Valley during the 2012 summer campaigns

Studying the vertical distribution of aerosol particle physical and chemical properties in the troposphere is essential to understand the relative importance of local emission processes vs. long-range transport for column-integrated aerosol properties (e.g. the aerosol optical depth, AOD, affecting regional climate) as well as for the aerosol burden and its impacts on air quality at the ground. The main objective of this paper is to investigate the transport of desert dust in the middle troposphere and its intrusion into the planetary boundary layer (PBL) over the Po Valley (Italy), a region considered one of the greatest European pollution hotspots for the frequency that particulate matter (PM) limit values are exceeded. Events of mineral aerosol uplift from local (soil) sources and phenomena of hygroscopic growth at the ground are also investigated, possibly affecting the PM concentration in the region as well. During the PEGASOS 2012 field campaign, an integrated observing–modelling system was set up based on near-surface measurements (particle concentration and chemistry), vertical profiling (backscatter coefficient profiles from lidar and radiosoundings) and Lagrangian air mass transport simulations by FLEXPART model. Measurements were taken at the San Pietro Capofiume supersite (44°39′ N, 11°37′ E; 11 m a.s.l.), located in a rural area relatively close to some major urban and industrial emissive areas in the Po Valley. Mt. Cimone (44°12′ N, 10°42′ E; 2165 m a.s.l.) WMO/GAW station observations are also included in the study to characterize regional-scale variability. Results show that, in the Po Valley, aerosol is detected mainly below 2000 m a.s.l. with a prevalent occurrence of non-depolarizing particles ( > 50 % throughout the campaign) and a vertical distribution modulated by the PBL daily evolution. Two intense events of mineral dust transport from northern Africa (19–21 and 29 June to 2 July) are observed, with layers advected mainly above 2000 m, but subsequently sinking and mixing in the PBL. As a consequence, a non-negligible occurrence of mineral dust is observed close to the ground (  ~7 % of occurrence during a 1-month campaign). The observations unambiguously show Saharan dust layers intruding the Po Valley mixing layer and directly affecting the aerosol concentrations near the surface. Finally, lidar observations also indicate strong variability in aerosol on shorter timescales (hourly). Firstly, these highlight events of hygroscopic growth of anthropogenic aerosol, visible as shallow layers of low depolarization near the ground. Such events are identified during early morning hours at high relative humidity (RH) conditions (RH  > 80 %). The process is observed concurrently with high PM1 nitrate concentration (up to 15 µg cm−3) and hence mainly explicable by deliquescence of fine anthropogenic particles, and during mineral dust intrusion episodes, when water condensation on dust particles could instead represent the dominant contribution. Secondly, lidar images show frequent events (mean daily occurrence of  ~ 22 % during the whole campaign) of rapid uplift of mineral depolarizing particles in afternoon–evening hours up to 2000 m a.s.l. height. The origin of such particles cannot be directly related to long-range transport events, being instead likely linked to processes of soil particle resuspension from agricultural lands