A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.

Potential Analysis for Hypoelliptic Second Order PDEs with Nonnegative Characteristic Form

In this Thesis we consider a class of second order partial differential operators with non-negative characteristic form and with smooth coefficients. Main assumptions on the relevant operators are hypoellipticity and existence of a well-behaved global fundamental solution. We first make a deep analysis of the L-Green function for arbitrary open sets and of its applications to the Representation Theorems of Riesz-type for L-subharmonic and L-superharmonic functions. Then, we prove an Inverse Mean value Theorem characterizing the superlevel sets of the fundamental solution by means of L-harmonic functions. Furthermore, we establish a Lebesgue-type result showing the role of the mean-integal operator in solving the homogeneus Dirichlet problem related to L in the Perron-Wiener sense. Finally, we compare Perron-Wiener and weak variational solutions of the homogeneous Dirichlet problem, under specific hypothesis on the boundary datum.

A Clarke–Ledyaev Type Inequality for Certain Non–Convex Sets

We consider the question whether the assumption of convexity of the set involved in Clarke-Ledyaev inequality can be relaxed. In the case when the point is outside the convex hull of the set we show that Clarke-Ledyaev type inequality holds if and only if there is certain geometrical relation between the point and the set.

Exponential Rates of Convergence in the Ergodic Theorem: A Constructive Approach

We prove that, once an algorithm of perfect simulation for a stationary and ergodic random field F taking values in S(Zd), S a bounded subset of R(n), is provided, the speed of convergence in the mean ergodic theorem occurs exponentially fast for F. Applications from (non-equilibrium) statistical mechanics and interacting particle systems are presented.

A new approach to the initial value problem

5th Portuguese Conference on Automatic Control, September, 5-7, 2002, Aveiro, Portugal

Integrating postoperative value of cardiac Troponin I for a better correlation with in-hospital outcomes after congenital heart surgery.

Objective: Cardiac Troponin-I (cTnI) is a well-recognized early postoperative marker for myocardial damage in adults and children after heart surgery. The present study was undertaken to evaluate whether the integrated value (area under the curve(AUC)) of postoperative cTnI is a better mode to predict long-term outcome than post operative cTnI maximum value, after surgery for congenital heart defects (CHD). Methods: retrospective cohort study. 279 patients (mean age 4.6 years; range 0-17 years-old, 185 males) with congenital heart defect repair on cardiopulmonary by-pass were retrieved from our database including postoperative cTnI values. Maximal post operative cTnI value, post operative cTnI AUC value at 48h and total post operative cTnI AUC value were calculated and then correlated with duration of intubation, duration of ICU stay and mortality. Results: the mean duration of mechanical ventilation was 5.1+/-7.2 days and mean duration of ICU stay was 11.0+/- 13.3 days,11 patients (3.9%) died in post operative period. When comparing survivor and deceased groups, there was a significant difference in the mean value for max cTnI (16.7+/- 21.8 vs 59.2+/-41.4 mcg/l, p+0.0001), 48h AUC cTnI (82.0+/-110.7 vs 268.8+/-497.7 mcg/l, p+0.0001) and total AUC cTnI (623.8+/-1216.7 vs 2564+/-2826.0, p+0.0001). Analyses for duration of mechanical ventilation and duration of ICU stay by linear regression demonstrated a better correlation for 48h AUC cTnI (ventilation time r+0.82, p+0.0001 and ICU stay r+0.74, p+0.0001) then total AUC cTnI (ventilation time r+0.65, p+0.0001 and ICU stay r+0.60, p+0.0001) and max cTnI (ventilation time r+0.64, p+0.0001 and ICU stay r+0.60, p+0.0001). Conclusion: Cardiac Troponin I is a specific and sensitive marker of myocardial injury after congenital heart surgery and it may predict early in-hospital outcomes. Integration of post operative value of cTnI by calculation of AUC improves prediction of early in-hospital outcomes. It probably takes into account, not only the initial surgical procedure, but probably also incorporates the occurrence of hypoxic-ischemic phenomena in the post-operative period.

Inference about the number of contributors to a DNA mixture: Comparative analyses of a Bayesian network approach and the maximum allele count method.

In the forensic examination of DNA mixtures, the question of how to set the total number of contributors (N) presents a topic of ongoing interest. Part of the discussion gravitates around issues of bias, in particular when assessments of the number of contributors are not made prior to considering the genotypic configuration of potential donors. Further complication may stem from the observation that, in some cases, there may be numbers of contributors that are incompatible with the set of alleles seen in the profile of a mixed crime stain, given the genotype of a potential contributor. In such situations, procedures that take a single and fixed number contributors as their output can lead to inferential impasses. Assessing the number of contributors within a probabilistic framework can help avoiding such complication. Using elements of decision theory, this paper analyses two strategies for inference on the number of contributors. One procedure is deterministic and focuses on the minimum number of contributors required to 'explain' an observed set of alleles. The other procedure is probabilistic using Bayes' theorem and provides a probability distribution for a set of numbers of contributors, based on the set of observed alleles as well as their respective rates of occurrence. The discussion concentrates on mixed stains of varying quality (i.e., different numbers of loci for which genotyping information is available). A so-called qualitative interpretation is pursued since quantitative information such as peak area and height data are not taken into account. The competing procedures are compared using a standard scoring rule that penalizes the degree of divergence between a given agreed value for N, that is the number of contributors, and the actual value taken by N. Using only modest assumptions and a discussion with reference to a casework example, this paper reports on analyses using simulation techniques and graphical models (i.e., Bayesian networks) to point out that setting the number of contributors to a mixed crime stain in probabilistic terms is, for the conditions assumed in this study, preferable to a decision policy that uses categoric assumptions about N.

Value of sTREM-1, procalcitonin and CRP as laboratory parameters for postmortem diagnosis of sepsis.

OBJECTIVES: Triggering receptor expressed on myeloid cells-1 (TREM-1) was reported to be up-regulated in various inflammatory diseases as well as in bacterial sepsis. Increased cell-surface TREM-1 expression was also shown to result in marked plasma elevation of the soluble form of this molecule (sTREM-1) in patients with bacterial infections. In this study, we investigated sTREM-1, procalcitonin and C-reactive protein in postmortem serum in a series of sepsis-related fatalities and control individuals who underwent medico-legal investigations. sTREM-1 was also measured in pericardial fluid and urine. METHODS: Two study groups were prospectively formed, a sepsis-related fatalities group and a control group. The sepsis-related fatalities group consisted of sixteen forensic autopsy cases. Eight of these had a documented clinical diagnosis of sepsis in vivo. The control group consisted of sixteen forensic autopsy cases with various causes of death. RESULTS: Postmortem serum sTREM-1 concentrations were higher in the sepsis group with a mean value of 173.6 pg/ml in septic cases and 79.2 pg/ml in control individuals. The cutoff value of 90 pg/ml provided the best sensitivity and specificity. Pericardial fluid sTREM-1 values were higher in the septic group, with a mean value of 296.7 pg/ml in septic cases and 100.9 pg/ml in control individuals. The cutoff value of 135 pg/ml provided the best sensitivity and specificity. Mean urine sTREM-1 concentration was 102.9 pg/ml in septic cases and 89.3 pg/ml in control individuals. CONCLUSIONS: Postmortem serum sTREM-1, individually considered, did not provide better sensitivity and specificity than procalcitonin in detecting sepsis. However, simultaneous assessment of procalcitonin and sTREM-1 in postmortem serum can be of help in clarifying contradictory postmortem findings. sTREM-1 determination in pericardial fluid can be an alternative to postmortem serum in those situations in which biochemical analyses are required and blood collected during autopsy proves insufficient.

Electrical colonic stimulation reduces mean transit time in a porcine model.

Abstract Electrical stimulation is a new way to treat digestive disorders such as constipation. Colonic propulsive activity can be triggered by battery operated devices. This study aimed to demonstrate the effect of direct electrical colonic stimulation on mean transit time in a chronic porcine model. The impact of stimulation and implanted material on the colonic wall was also assessed. Three pairs of electrodes were implanted into the caecal wall of 12 anaesthetized pigs. Reference colonic transit time was determined by radiopaque markers for each pig before implantation. It was repeated 4 weeks after implantation with sham stimulation and 5 weeks after implantation with electrical stimulation. Aboral sequential trains of 1-ms pulse width (10 V; 120 Hz) were applied twice daily for 6 days, using an external battery operated stimulator. For each course of markers, a mean value was computed from transit times obtained from individual pig. Microscopic examination of the caecum was routinely performed after animal sacrifice. A reduction of mean transit time was observed after electrical stimulation (19 +/- 13 h; mean +/- SD) when compared to reference (34 +/- 7 h; P = 0.045) and mean transit time after sham stimulation (36 +/- 9 h; P = 0.035). Histological examination revealed minimal chronic inflammation around the electrodes. Colonic transit time measured in a chronic porcine model is reduced by direct sequential electrical stimulation. Minimal tissue lesion is elicited by stimulation or implanted material. Electrical colonic stimulation could be a promising approach to treat specific disorders of the large bowel.

A quantitative view on fuzzy numbers

Since its introduction, fuzzy set theory has become a useful tool in the mathematical modelling of problems in Operations Research and many other fields. The number of applications is growing continuously. In this thesis we investigate a special type of fuzzy set, namely fuzzy numbers. Fuzzy numbers (which will be considered in the thesis as possibility distributions) have been widely used in quantitative analysis in recent decades. In this work two measures of interactivity are defined for fuzzy numbers, the possibilistic correlation and correlation ratio. We focus on both the theoretical and practical applications of these new indices. The approach is based on the level-sets of the fuzzy numbers and on the concept of the joint distribution of marginal possibility distributions. The measures possess similar properties to the corresponding probabilistic correlation and correlation ratio. The connections to real life decision making problems are emphasized focusing on the financial applications. We extend the definitions of possibilistic mean value, variance, covariance and correlation to quasi fuzzy numbers and prove necessary and sufficient conditions for the finiteness of possibilistic mean value and variance. The connection between the concepts of probabilistic and possibilistic correlation is investigated using an exponential distribution. The use of fuzzy numbers in practical applications is demonstrated by the Fuzzy Pay-Off method. This model for real option valuation is based on findings from earlier real option valuation models. We illustrate the use of number of different types of fuzzy numbers and mean value concepts with the method and provide a real life application.

Neural network detection of grinding burn from acoustic emission

An artificial neural network (ANN) approach is proposed for the detection of workpiece `burn', the undesirable change in metallurgical properties of the material produced by overly aggressive or otherwise inappropriate grinding. The grinding acoustic emission (AE) signals for 52100 bearing steel were collected and digested to extract feature vectors that appear to be suitable for ANN processing. Two feature vectors are represented: one concerning band power, kurtosis and skew; and the other autoregressive (AR) coefficients. The result (burn or no-burn) of the signals was identified on the basis of hardness and profile tests after grinding. The trained neural network works remarkably well for burn detection. Other signal-processing approaches are also discussed, and among them the constant false-alarm rate (CFAR) power law and the mean-value deviance (MVD) prove useful.

The mean corpuscular volume and hydroxyurea in brazilian patients with sickle cell anemia: a surrogate marker of compliance

The suppression of erythropoiesis by Hydroxyurea (HU) therapy is associated with increase in mean corpuscular volume, in addition to the increase in Hb F. Monitoring the mean corpuscular volume values and the presence of macrocytosis are effective tools of adherence to the treatment with HU in patients with sickle cell anemia. The aim of this study is to monitor the mean corpuscular volume values after starting treatment with HU to determine if macrocytosis can be used as a surrogate marker of compliance with therapy. We conducted a prospective cohort study over one year with measurements of blood counts and mean corpuscular volume after starting therapy with HU in 95 patients with sickle cell anemia who were regularly followed in our ambulatory outpatient unit. In one-year of successful use of HU the mean value of the mean corpuscular volume increased significantly. The Andersen and Gill model demonstrated that the increase of one unit of MCV implies a 5% reduction in the risk of visiting the emergency room. Monitoring mean corpuscular volume values after prescribing HU alerts the provider of noncompliance in order to counsel the patient in question for better adherence to the use of HU that could improve the quality of care and to reduce morbidity and the frequency of acute pain crises and associated healthcare costs.

Supporting interoperable interpolation: the INTAMAP approach

In many Environmental Information Systems the actual observations arise from a discrete monitoring network which might be rather heterogeneous in both location and types of measurements made. In this paper we describe the architecture and infrastructure for a system, developed as part of the EU FP6 funded INTAMAP project, to provide a service oriented solution that allows the construction of an interoperable, automatic, interpolation system. This system will be based on the Open Geospatial Consortium’s Web Feature Service (WFS) standard. The essence of our approach is to extend the GML3.1 observation feature to include information about the sensor using SensorML, and to further extend this to incorporate observation error characteristics. Our extended WFS will accept observations, and will store them in a database. The observations will be passed to our R-based interpolation server, which will use a range of methods, including a novel sparse, sequential kriging method (only briefly described here) to produce an internal representation of the interpolated field resulting from the observations currently uploaded to the system. The extended WFS will then accept queries, such as ‘What is the probability distribution of the desired variable at a given point’, ‘What is the mean value over a given region’, or ‘What is the probability of exceeding a certain threshold at a given location’. To support information-rich transfer of complex and uncertain predictions we are developing schema to represent probabilistic results in a GML3.1 (object-property) style. The system will also offer more easily accessible Web Map Service and Web Coverage Service interfaces to allow users to access the system at the level of complexity they require for their specific application. Such a system will offer a very valuable contribution to the next generation of Environmental Information Systems in the context of real time mapping for monitoring and security, particularly for systems that employ a service oriented architecture.

Moral reasoning in sport: validation of the Portuguese version of the RSBH value-judgement inventory in adolescents

The purpose of this study was to examine the validity and reliability of the Portuguese version of the Rudd Stoll Beller Hahm Value-judgement Inventory (RSBHVI) in a sample of adolescents. The RSBHVI, which measures moral and social reasoning, was translated using a back translation method. A sample of 238 10th to 12th grade high school students (age mean value 16.93 years, s = 1.34) completed the Portuguese versions of RSBH, and the Task and Ego-orientation Questionnaire. Partial support for the original structure of the moral reasoning scale, but not the social reasoning scale, was found. Females, and non-athletes and individual sport athletes scored significantly higher than males and team sport athletes in moral reasoning, respectively. Moral reasoning was negatively correlated with ego-orientation (r = −30; p <. 001) and uncorrelated with task-orientation (r = .10, p > .05). Participants who were low-ego scored higher in moral reasoning than those who were high-ego. It is suggested that decreasing levels of ego-orientation may be necessary to improve athletes’ moral reasoning.

Is Sport Practice A Risk Factor For Shoulder Injuries In Tetraplegic Individuals?

A retrospective cohort. To report the incidence rates of shoulder injuries diagnosed with magnetic resonance imaging (MRI) in tetraplegic athletes and sedentary tetraplegic individuals. To evaluate whether sport practice increases the risk of shoulder injuries in tetraplegic individuals. Campinas, Sao Paulo, Brazil. Ten tetraplegic athletes with traumatic spinal cord injury were selected among quad rugby athletes and had both the shoulders evaluated by MRI. They were compared with 10 sedentary tetraplegic individuals who were submitted to the same radiological protocol. All athletes were male with a mean age of 32.1 years (range 25-44 years, s.d.=6.44). Time since injury ranged from 6 to 17 years, with a mean value of 9.7 years and s.d. of 3.1 years. All sedentary individuals were male with a mean age of 35.9 years (range 22-47 years, s.d.=8.36). Statistical analysis showed a protective effect of sport in the development of shoulder injuries, with a weak correlation for infraspinatus and subscapularis tendinopathy (P=0.09 and P=0.08, respectively) and muscle atrophy (P=0.08). There was a strong correlation for acromioclavicular joint (ACJ) and labrum injuries (P=0.04), with sedentary individuals at a higher risk for these injuries. Tetraplegic athletes and sedentary individuals have a high incidence of supraspinatus tendinosis, bursitis and ACJ degeneration. Statistical analysis showed that there is a possible protective effect of sport in the development of shoulder injuries. Weak evidence was encountered for infraspinatus and subscapularis tendinopathy and muscle atrophy (P=0.09, P=0.08 and P=0.08, respectively). Strong evidence with P=0.04 suggests that sedentary tetraplegic individuals are at a greater risk for ACJ and labrum injuries.Spinal Cord advance online publication, 17 March 2015; doi:10.1038/sc.2014.248.