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

Remotely Sensed Assessment of the Preferred Habitat of Alexandrium catenella in the Gulf of Maine and the Bay of Fundy

Harmful Algal Blooms (HABs) of the toxic dinoflagellate Alexandrium catenella are an annually recurring problem in the Gulf of Maine (GoM), resulting in risks to human health and substantial economic losses due to shellfish harvesting closures. The monitoring approaches in the region are restricted to real-time identification of the HABs events, when they are clearly underway and already causing deleterious effects to the environment. To fully function as an early warning system rather than an immediate response, monitoring strategies need to be focused on environmental conditions preceding A. catenella HABs. However, the current understanding of the preferred habitat for A. catenella in the GoM is still scarce due to the complex interactions between this organism and the environment. My dissertation research contributes to the solution of these problems by determining the preferred thermal habitat for A. catenella, contrasting environmental conditions for two extremes in A. catenella concentration, and exploring the benefits of using high resolution spectral data to characterize the GoM surface waters. This dissertation is focused on the application of current and future remote sensing technology to the measurement and management of GoM HABs. Chapter 1 briefly introduces the problematic of HABs, monitoring efforts and the study species. Chapter 2 characterizes the interannual variability in the thermal habitat and bloom phenology of A. catenella in the Bay of Fundy, identifying the environmental conditions associated with this variability and its responses to climate change. Chapter 3 contrasts the optical and thermal conditions associated with two extremes in A. catenella concentration over multiple years and areas in the GoM and establishes a set of typical water types for each concentration category. Chapter 4 characterizes the spatial and temporal variability of hyperspectral reflectance of surface waters in the GoM and determines the advantage of hyperspectral resolution over multispectral to identify important spatial patterns and regions. Chapter 5 will conclude with a discussion on the implications of these results to monitoring efforts in the GoM, implications of climate change, and discusses future directives to further explore habitat suitability approaches in monitoring efforts

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

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

Effectiveness of surgical procedures in the acceleration of orthodontic tooth movement: Findings from systematic reviews and meta-analyses

The current overview aimed to summarise the findings provided by systematic reviews (SRs) on the effect of surgical procedures in the acceleration of tooth movement and to assess the methodological quality of the included SRs. Three electronic databases have been explored. SRs addressing the effects of surgical procedures on the acceleration of tooth movement were included. The methodological quality of the included SRs was assessed using the updated version of “A Measurement Tool to Assess Systematic Review” (AMSTAR-2). Twenty-eight (28) SRs were included. The methodological quality of the included reviews ranged between critically low (6 studies) and high (12 studies). The most common critical weakness in the included reviews was the absence of clearly a-prior established review methods and any significant deviations from the protocol. The most studied surgical procedure was corticotomy, followed by micro-osteoperforation, piezocision and periodontally accelerated osteogenic orthodontics. The majority of the included SRs supported short-term favourable effects of corticotomy on treatment time and tooth movement rate, in the short-term. However, the authors of the included SRs reported that results were based on weak quality evidence. Conflicting results arise from the existent SRs with regards to the effectiveness of piezocision and micro-osteoperforation. Few SRs summarised complications and side effects of surgical techniques, supporting absence of loss of tooth vitality, periodontal problems, or severe root resorption. The current overview of SRs highlighted the need of high quality SRs comparing different surgical approaches for tooth movement acceleration though network meta-analysis, in order to determine the most efficient instrument for orthodontic movement acceleration

Analyzing the 20-year declining trend of hospital length-of-stay in European countries with different healthcare systems and reimbursement models

The study aims to investigate the last 20-year (2000–2019) of hospital length of stay (LOS) trends and their association with different healthcare systems (HS) among 25 European countries. A panel dataset was created using secondary data from Eurostat and Global Burden of Disease study databases, with dependent and control variables aggregated at the national level over a period of 20 years. A time trend analysis was conducted using a weighted least squares model for panel data to investigate the association between LOS, HS models [National Health Service (NHS), National Health Insurance, Social Health Insurance (SHI), and Etatist Social Health Insurance], healthcare reimbursement schemes [Prospective Global Budget (PGB), Diagnosis Related Groups (DRG), and Procedure Service Payment (PSP)], and control variables. The study showed a reduction of average LOS from 9.20 days in 2000 to 7.24 in 2019. SHI was associated with a lower LOS compared to NHS (b = − 0.6327, p < 0.05). Both DRG (b = 1.2399, p < 0.05) and PSP (b = 1.1677, p < 0.05) reimbursement models were positively associated with LOS compared to PGB. Our results confirmed the downward trend of LOS in the last 20 years, its multifactorial nature, and the influence of the SHI model of HS. This could be due to the financial incentives present in fee-for-service payment models and the role of competition in creating a market for healthcare services. These results offer insight into the factors influencing healthcare utilization and can inform the design of more effective, efficient, and sustainable HS. © The Author(s) 2024