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

Observability and nonlinear filtering

This paper develops a connection between the asymptotic stability of nonlinear filters and a notion of observability. We consider a general class of hidden Markov models in continuous time with compact signal state space, and call such a model observable if no two initial measures of the signal process give rise to the same law of the observation process. We demonstrate that observability implies stability of the filter, i.e., the filtered estimates become insensitive to the initial measure at large times. For the special case where the signal is a finite-state Markov process and the observations are of the white noise type, a complete (necessary and sufficient) characterization of filter stability is obtained in terms of a slightly weaker detectability condition. In addition to observability, the role of controllability in filter stability is explored. Finally, the results are partially extended to non-compact signal state spaces

Definitions, Criteria and Global Classification of Mast Cell Disorders with Special Reference to Mast Cell Activation Syndromes: A Consensus Proposal

Activation of tissue mast cells (MCs) and their abnormal growth and accumulation in various organs are typically found in primary MC disorders also referred to as mastocytosis. However, increasing numbers of patients are now being informed that their clinical findings are due to MC activation (MCA) that is neither associated with mastocytosis nor with a defined allergic or inflammatory reaction. In other patients with MCA, MCs appear to be clonal cells, but criteria for diagnosing mastocytosis are not met. A working conference was organized in 2010 with the aim to define criteria for diagnosing MCA and related disorders, and to propose a global unifying classification of all MC disorders and pathologic MC reactions. This classification includes three types of `MCA syndromes' (MCASs), namely primary MCAS, secondary MCAS and idiopathic MCAS. MCA is now defined by robust and generally applicable criteria, including (1) typical clinical symptoms, (2) a substantial transient increase in serum total tryptase level or an increase in other MC-derived mediators, such as histamine or prostaglandin D 2, or their urinary metabolites, and (3) a response of clinical symptoms to agents that attenuate the production or activities of MC mediators. These criteria should assist in the identification and diagnosis of patients with MCAS, and in avoiding misdiagnoses or overinterpretation of clinical symptoms in daily practice. Moreover, the MCAS concept should stimulate research in order to identify and exploit new molecular mechanisms and therapeutic targets. Copyright (C) 2011 S. Karger AG, Base

International consensus on (ICON) anaphylaxis

ICON: Anaphylaxis provides a unique perspective on the principal evidence-based anaphylaxis guidelines developed and published independently from 2010 through 2014 by four allergy/immunology organizations. These guidelines concur with regard to the clinical features that indicate a likely diagnosis of anaphylaxis -- a life-threatening generalized or systemic allergic or hypersensitivity reaction. They also concur about prompt initial treatment with intramuscular injection of epinephrine (adrenaline) in the mid-outer thigh, positioning the patient supine (semi-reclining if dyspneic or vomiting), calling for help, and when indicated, providing supplemental oxygen, intravenous fluid resuscitation and cardiopulmonary resuscitation, along with concomitant monitoring of vital signs and oxygenation. Additionally, they concur that H1-antihistamines, H2-antihistamines, and glucocorticoids are not initial medications of choice. For self-management of patients at risk of anaphylaxis in community settings, they recommend carrying epinephrine auto-injectors and personalized emergency action plans, as well as follow-up with a physician (ideally an allergy/immunology specialist) to help prevent anaphylaxis recurrences. ICON: Anaphylaxis describes unmet needs in anaphylaxis, noting that although epinephrine in 1 mg/mL ampules is available worldwide, other essentials, including supplemental oxygen, intravenous fluid resuscitation, and epinephrine auto-injectors are not universally available. ICON: Anaphylaxis proposes a comprehensive international research agenda that calls for additional prospective studies of anaphylaxis epidemiology, patient risk factors and co-factors, triggers, clinical criteria for diagnosis, randomized controlled trials of therapeutic interventions, and measures to prevent anaphylaxis recurrences. It also calls for facilitation of global collaborations in anaphylaxis research. In addition to confirming the alignment of major anaphylaxis guidelines, ICON: Anaphylaxis adds value by including summary tables and citing 130 key references. It is published as an information resource about anaphylaxis for worldwide use by healthcare professionals, academics, policy-makers, patients, caregivers, and the public

Delayed prandial insulin boluses are an important determinant of blood glucose control and relate to fear of hypoglycemia in people with type 1 diabetes on advanced technologies

Aims: Automated insulin delivery systems improve blood glucose control in patients with type 1 diabetes (T1D). However, optimizing their performance requires patient's proper compliance to meal insulin bolus administration. We explored real-life prevalence of delayed prandial boluses (DBs) in adults with T1D on advanced technologies, and their association with glycemic control and fear of hypoglycemia (FH). Methods: In the last two-week web-based reports of 152 adults with T1D on Hybrid Closed Loop Systems (HCLS) or Sensor Augmented Pump (SAP), DBs were identified when a steep increase in blood glucose occurred at CGM before the prandial bolus, and CGM metrics were evaluated. All participants completed an online questionnaire on FH. Results: Mean DBs over two weeks were 10.2 ± 4.7 (M ± SD, range 1–23) and more frequent in women than men (11.0 ± 4.6 vs. 9.4 ± 4.7, p = 0.036). Participants with more DBs (>12) showed significantly lower Time-In-Range (62.4 ± 13.8 vs. 76.6 ± 9.0 %) than those with less DBs (<7.7), along with higher Time-Above-Range, GMI, and Coefficient-of-Variation (ANOVA, p < 0.001 for all). Participants with higher FH score showed more DBs (11.6 ± 5.0) than those in lower tertiles (9.57 ± 4.59 and 9.47 ± 4.45, ANOVA p = 0.045). Conclusions: In patients on advanced technologies, delayed boluses are extremely common, and associate with significantly worse glycemic control. Utmost attention is needed to bolus timing, mainly tackling fear of hypoglycemia