AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the postjump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach. Two examples are presented illustrating the possible applications of the results developed in the paper.

Experimental study of a Tollmien-Schlichting wave interacting with a shallow 3D roughness element

The paper is devoted to an experimental study of the effect of a shallow 3D roughness element on the evolution of a 2D Tollmien-Schlichting wave in a Blasius boundary layer. The experiments were carried out under controlled disturbance conditions on an airfoil section which could provide a long run with zero pressure gradient flow. A pneumatically driven slit source was used to introduce the Tollmien-Schilichting wave upstream of the lower branch of the neutral stability curve. A few wavelengths downstream, the T-S wave interacts with a cylindrical roughness element. The height of the roughness was slowly oscillating in time, which allows a continuous measurement of the T-S wave response downstream the roughness. The oscillation frequency was approximately 1500 times lower than the frequency of the studied Tollmien-Schlichting wave and therefore, behaved as a steady roughness with respect to the T-S wave. Hot wire anemometry was used to measure wall normal profiles and spanwise scans close to the maximum of the eigenfunction of the T-S wave. The oscillation of the roughness and the synchronization of all-equipments permitted the use of ensemble average techniques. Two different amplitudes of T-S waves with a non-dimensional frequency of F120E-06 were studied. They show a strong amplification of the disturbances in a small spanwise wave number range. The analysis of the wall normal T-S profiles suggests the growth of oblique modes.

The Policy Iteration Algorithm for Average Continuous Control of Piecewise Deterministic Markov Processes

The main goal of this paper is to apply the so-called policy iteration algorithm (PIA) for the long run average continuous control problem of piecewise deterministic Markov processes (PDMP`s) taking values in a general Borel space and with compact action space depending on the state variable. In order to do that we first derive some important properties for a pseudo-Poisson equation associated to the problem. In the sequence it is shown that the convergence of the PIA to a solution satisfying the optimality equation holds under some classical hypotheses and that this optimal solution yields to an optimal control strategy for the average control problem for the continuous-time PDMP in a feedback form.

THE VANISHING DISCOUNT APPROACH FOR THE AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the alpha-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

Use of an Inflatable Silicone Balloon Improves the Success Rate of Bladder Autoaugmentation at Long-Term Followup

Purpose: Most groups have reported disappointing results with autoaugmentation or detrusor myectomy for low capacity/compliance neuropathic bladders. Failure may be due to an ischemic diverticulum or mucosal shrinkage. We investigated whether a Silimed (R) silicone balloon placed in the bladder after autoaugmentation could prevent these problems, improving surgical results. Materials and Methods: We compared the results of standard bladder autoaugmentation in 12 children (group 1) with those in 10 (group 2) who underwent the same surgery using a bladder conformer. The conformer was a silicone balloon filled with saline that remained in the bladder for 2 weeks. All patients had a neuropathic bladder with poor capacity and compliance, resulting in urinary leakage between catheterizations. Preoperative and postoperative evaluation included a voiding diary, ultrasound, voiding cystourethrogram and urodynamics. Results: In group 1 only 1 patient became dry, 4 had little improvement in continence, 4 remained unchanged and 3 became worse. In group 2, 6 patients (60%) become continent without medication, 2 (20%) become continent with oxybutynin and 2 remained unchanged. Bladder capacity and compliance did not change significantly in group 1. However, in group 2 capacity changed from a mean of 140 to 240 ml and mean +/- SD compliance increased from 15.6 +/- 16.8 to 34.3 +/- 22.8 ml/cm H(2)O (p = 0.02). Conclusions: The inflatable balloon improved our long-term results of bladder auto-augmentation. A larger series may be necessary to confirm procedure efficacy and safety.

Catheter ablation of severe neurally meditated reflex (neurocardiogenic or vasovagal) syncope: cardioneuroablation long-term results

Aims Neurally meditated reflex or neurocardiogenic or vasovagal syncope (NMS) is usually mediated by a massive vagal reflex. This study reports the long-term outcome of NMS therapy based on endocardial radiofrequency (RF) catheter ablation of the cardiac vagal nervous system aiming permanent attenuation or elimination of the cardioinhibitory reflex (cardioneuroablation). Methods and results A total of 43 patients (18F/25M, 32.9+/-15 years) without apparent cardiopathy (left ventricular ejection fraction=68.6+/-5%) were included. All had recurrent NMS (4.7+/-2 syncope/patient) with important cardioinhibition (pauses=13.5+/-13 s) at head-up tilt test (HUT), normal electrocardiogram (ECG), and normal atropine test (AT). The patients underwent atrial endocardial RF ablation using spectral mapping to track the neurocardiac interface (AF Nest Mapping). The follow-up (FU) consisted of clinical evaluation, ECG (1 month/every 6 months/or symptoms), Holter (every 6 months/or symptoms), HUT (>= 4 months/or symptoms), and AT (end of ablation and >= 6 months). A total of 44 ablations (48+/-9 points/patient) were performed. Merely three cases of spontaneous syncope occurred in 45.1+/-22 months (two vasodepressor, one undefined). Only four partial cardioinhibitory responses occurred in post-ablation HUT without pauses or asystole (sinus bradycardia). Long-term AT (21.7+/-11 months post) was negative in 33 (76.7%, P<0.01), partially positive in 7(16.3%), and normal in three patients only (6.9%) reflecting long-term vagal denervation (AT-Delta% HR pre 79.4% x 23.2% post). The post-ablation stress test and Holter showed no abnormalities. No major complications occurred. Conclusion Endocardial RF catheter ablation of severe neurally meditated reflex syncope prevented pacemaker implantation and showed excellent long-term results in well selected patients. Despite no action in vasodepression it seems to cause enough long-term vagal reflex attenuation, eliminating the cardioinhibition, and keeping most patients asymptomatic. Indication was based on clinical symptoms, reproduction of severe cardioinhibitory syncope, and normal atropine response.

Association between degenerative aortic valve disease and long-term exposure to cardiovascular risk factors: results of the longitudinal population-based KORA/MONICA survey

Degenerative aortic valve disease (DAVD), a common finding in the elderly, is associated with an increased risk of death due to cardiovascular causes. Taking advantage of its longitudinal design, this study evaluates the prevalence of DAVD and its temporal associations with long-term exposure to cardiovascular risk factors in the general population. We studied 953 subjects (aged 25-74 years) from a random sample of German residents. Risk factors had been determined at a baseline investigation in 1994/95. At a follow-up investigation, 10 years later, standardized echocardiography determined aortic valve morphology and aortic valve area (AVA) as well as left ventricular geometry and function. At the follow-up study, the overall prevalence of DAVD was 28%. In logistic regression models adjusting for traditional cardiovascular risk factors at baseline age (OR 2.0 [1.7-2.3] per 10 years, P < 0.001), active smoking (OR 1.7 [1.1-2.4], P = 0.009) and elevated total cholesterol levels (OR 1.2 [1.1-1.3] per increase of 20 mg/dL, P < 0.001) were significantly related to DAVD at follow-up. Furthermore, age, baseline status of smoking, and total cholesterol level were significant predictors of a smaller AVA at follow-up study. In contrast, hypertension and obesity had no detectable relationship with long-term changes of aortic valve structure. In the general population we observed a high prevalence of DAVD that is associated with long-term exposure to elevated cholesterol levels and active smoking. These findings strengthen the notion that smoking cessation and cholesterol lowering are promising treatment targets for prevention of DAVD.

Histologic Study of Urethral Extracellular Matrix and Collagen From Aging and Long-Term Alloxan-induced Diabetic Male Rats

OBJECTIVES To evaluate the histological alterations of extracellular matrix in long-term alloxan-induced diabetes and aging urethras of male rats with descriptions of total connective tissue, muscle layer and collagen types I and III relative amounts. METHODS Histologic evaluations were performed in 3 animal groups: group 1, 8 weeks old; group 2, 44 weeks old; and group 3, 44 weeks old with alloxan-induced diabetes. The muscle layer thickness, extracellular matrix fibrosis, and collagen were quantified on digital images of the urethral samples. RESULTS A higher total thickness and muscle layer thickness and higher connective tissue and collagen content were observed in the urethras of group 3. No changes in the collagen type III/I ratio were found in the urethra of groups 2 and 3. CONCLUSIONS Our results suggest that the morphologic alterations of the urethra should also be considered in long-term studies of diabetic lower urinary tract dysfunction. These morphologic alterations due to diabetes differ from the changes induced by aging itself and could represent a final stage in decompensate urethras. Further studies are necessary to establish the real influence of the urethral morphologic changes on lower urinary tract diabetes dysfunction. UROLOGY 77: 510.e6-510.e11, 2011. (C) 2011 Elsevier Inc.