Il problema di Dirichlet per equazioni lineari ellittiche in forma di divergenza

The purpose of this dissertation is to prove that the Dirichlet problem in a bounded domain is uniquely solvable for elliptic equations in divergence form. The proof can be achieved by Hilbert space methods based on generalized or weak solutions. Existence and uniqueness of a generalized solution for the Dirichlet problem follow from the Fredholm alternative and weak maximum principle.

Stationary states in random walks on networks

In this thesis we dealt with the problem of describing a transportation network in which the objects in movement were subject to both finite transportation capacity and finite accomodation capacity. The movements across such a system are realistically of a simultaneous nature which poses some challenges when formulating a mathematical description. We tried to derive such a general modellization from one posed on a simplified problem based on asyncronicity in particle transitions. We did so considering one-step processes based on the assumption that the system could be describable through discrete time Markov processes with finite state space. After describing the pre-established dynamics in terms of master equations we determined stationary states for the considered processes. Numerical simulations then led to the conclusion that a general system naturally evolves toward a congestion state when its particle transition simultaneously and we consider one single constraint in the form of network node capacity. Moreover the congested nodes of a system tend to be located in adjacent spots in the network, thus forming local clusters of congested nodes.

Model Predictive Control for Vehicle Stabilization at the Limits of Handling

Recent developments in vehicle steering systems offer new opportunities to measure the steering torque and reliably estimate the vehicle sideslip and the tire-road friction coefficient. This paper presents an approach to vehicle stabilization that leverages these estimates to define state boundaries that exclude unstable vehicle dynamics and utilizes a model predictive envelope controller to bound the vehicle motion within this stable region of the state space. This approach provides a large operating region accessible by the driver and smooth interventions at the stability boundaries. Experimental results obtained with a steer-by-wire vehicle and a proof of envelope invariance demonstrate the efficacy of the envelope controller in controlling the vehicle at the limits of handling.

Enumerating constrained elementary flux vectors of metabolic networks

The concept of elementary vector is generalised to the case where the steady-state space of the metabolic network is not a flux cone but is a general polyhedron due to further inhomogeneous constraints on the flows through some of the reactions. On one hand, this allows to selectively enumerate elementary modes which satisfy certain optimality criteria and this can yield a large computational gain compared with full enumeration. On the other hand, in contrast to the single optimum found by executing a linear program, this enables a comprehensive description of the set of alternate optima often encountered in flux balance analysis. The concepts are illustrated on a metabolic network model of human cardiac mitochondria.

Ultrasound-guided paravertebral puncture and placement of catheters in human cadavers: an imaging study

BACKGROUND: During paravertebral block, the anterolateral limit of the paravertebral space, which consists of the pleura, should preferably not be perforated. Also it is possible that, during the block, the constant superior costotransverse ligament can be missed in the loss-of-resistance technique. We therefore aimed to develop a new technique for an ultrasound-guided puncture of the paravertebral space. METHODS: We performed 20 punctures and catheter placements in 10 human cadavers. A sonographic view showing the pleura and the superior costotransverse ligament was obtained with a slightly oblique scan using a curved array transducer. After inline approach, injection of 10 ml normal saline confirmed the correct position of the needle tip, distended the space, and enabled catheter insertion. The spread of contrast dye injected through the catheters was assessed by CT scans. RESULTS: The superior costotransverse ligament and the paravertebral space were easy to identify. The needle tip reached the paravertebral space without problems under visualization. In contrast, the introduction of the catheter was difficult. The CT scan revealed a correct paravertebral spread of contrast in 11 cases. Out of the remaining, one catheter was found in the pleural space, in six cases there was an epidural, and in two cases there was a prevertebral spread of contrast dye. CONCLUSIONS: We successfully developed a technique for an accurate ultrasound-guided puncture of the paravertebral space. We also showed that when a catheter is introduced through the needle with the tip lying in the paravertebral space, there is a high probability of catheter misplacement into the epidural, mediastinal, or pleural spaces.

Automated design of self-stabilization

Self-stabilization is a property of a distributed system such that, regardless of the legitimacy of its current state, the system behavior shall eventually reach a legitimate state and shall remain legitimate thereafter. The elegance of self-stabilization stems from the fact that it distinguishes distributed systems by a strong fault tolerance property against arbitrary state perturbations. The difficulty of designing and reasoning about self-stabilization has been witnessed by many researchers; most of the existing techniques for the verification and design of self-stabilization are either brute-force, or adopt manual approaches non-amenable to automation. In this dissertation, we first investigate the possibility of automatically designing self-stabilization through global state space exploration. In particular, we develop a set of heuristics for automating the addition of recovery actions to distributed protocols on various network topologies. Our heuristics equally exploit the computational power of a single workstation and the available parallelism on computer clusters. We obtain existing and new stabilizing solutions for classical protocols like maximal matching, ring coloring, mutual exclusion, leader election and agreement. Second, we consider a foundation for local reasoning about self-stabilization; i.e., study the global behavior of the distributed system by exploring the state space of just one of its components. It turns out that local reasoning about deadlocks and livelocks is possible for an interesting class of protocols whose proof of stabilization is otherwise complex. In particular, we provide necessary and sufficient conditions – verifiable in the local state space of every process – for global deadlock- and livelock-freedom of protocols on ring topologies. Local reasoning potentially circumvents two fundamental problems that complicate the automated design and verification of distributed protocols: (1) state explosion and (2) partial state information. Moreover, local proofs of convergence are independent of the number of processes in the network, thereby enabling our assertions about deadlocks and livelocks to apply on rings of arbitrary sizes without worrying about state explosion.

Multichannel EEG fields during and without visual input: frequency domain model source locations and dimensional complexities

27-Channel EEG potential map series were recorded from 12 normals with closed and open eyes. Intracerebral dipole model source locations in the frequency domain were computed. Eye opening (visual input) caused centralization (convergence and elevation) of the source locations of the seven frequency bands, indicative of generalized activity; especially, there was clear anteriorization of α-2 (10.5–12 Hz) and β-2 (18.5–21 Hz) sources (α-2 also to the left). Complexity of the map series' trajectories in state space (assessed by Global Dimensional Complexity and Global OMEGA Complexity) increased significantly with eye opening, indicative of more independent, parallel, active processes. Contrary to PET and fMRI, these results suggest that brain activity is more distributed and independent during visual input than after eye closing (when it is more localized and more posterior).

Single-dose piracetam effects on global complexity measures of human spontaneous multichannel EEG

Global complexity of 47-channel resting electroencephalogram (EEG) of healthy young volunteers was studied after intake of a single dose of a nootropic drug (piracetam, Nootropil® UCB Pharma) in 12 healthy volunteers. Four treatment levels were used: 2.4, 4.8, 9.6 g piracetam and placebo. Brain electric activity was assessed through Global Dimensional Complexity and Global Omega-Complexity as quantitative measures of the complexity of the trajectory of multichannel EEG in state space. After oral ingestion (1–1.5 h), both measures showed significant decreases from placebo to 2.4 g piracetam. In addition, Global Dimensional Complexity showed a significant return to placebo values at 9.6 g piracetam. The results indicate that a single dose of piracetam dose-dependently affects the spontaneous EEG in normal volunteers, showing effects at the lowest treatment level. The decreased EEG complexity is interpreted as increased cooperativity of brain functional processes.

Spatio-temporal dynamics of alpha brain electric fields, and cognitive modes

Brian electric activity is viewed as sequences of momentary maps of potential distribution. Frequency-domain source modeling, estimation of the complexity of the trajectory of the mapped brain field distributions in state space, and microstate parsing were used as analysis tools. Input-presentation as well as task-free (spontaneous thought) data collection paradigms were employed. We found: Alpha EEG field strength is more affected by visualizing mentation than by abstract mentation, both input-driven as well as self-generated. There are different neuronal populations and brain locations of the electric generators for different temporal frequencies of the brain field. Different alpha frequencies execute different brain functions as revealed by canonical correlations with mentation profiles. Different modes of mentation engage the same temporal frequencies at different brain locations. The basic structure of alpha electric fields implies inhomogeneity over time — alpha consists of concatenated global microstates in the sub-second range, characterized by quasi-stable field topographies, and rapid transitions between the microstates. In general, brain activity is strongly discontinuous, indicating that parsing into field landscape-defined microstates is appropriate. Different modes of spontaneous and induced mentation are associated with different brain electric microstates; these are proposed as candidates for psychophysiological ``atoms of thought''.

Brain electric correlates of strong belief in paranormal phenomena: intracerebral EEG source and regional Omega complexity analyses

The neurocognitive processes underlying the formation and maintenance of paranormal beliefs are important for understanding schizotypal ideation. Behavioral studies indicated that both schizotypal and paranormal ideation are based on an overreliance on the right hemisphere, whose coarse rather than focussed semantic processing may favor the emergence of 'loose' and 'uncommon' associations. To elucidate the electrophysiological basis of these behavioral observations, 35-channel resting EEG was recorded in pre-screened female strong believers and disbelievers during resting baseline. EEG data were subjected to FFT-Dipole-Approximation analysis, a reference-free frequency-domain dipole source modeling, and Regional (hemispheric) Omega Complexity analysis, a linear approach estimating the complexity of the trajectories of momentary EEG map series in state space. Compared to disbelievers, believers showed: more right-located sources of the beta2 band (18.5-21 Hz, excitatory activity); reduced interhemispheric differences in Omega complexity values; higher scores on the Magical Ideation scale; more general negative affect; and more hypnagogic-like reveries after a 4-min eyes-closed resting period. Thus, subjects differing in their declared paranormal belief displayed different active, cerebral neural populations during resting, task-free conditions. As hypothesized, believers showed relatively higher right hemispheric activation and reduced hemispheric asymmetry of functional complexity. These markers may constitute the neurophysiological basis for paranormal and schizotypal ideation.

Chewing-gum flavor affects measures of global complexity of multichannel EEG

Global complexity of spontaneous brain electric activity was studied before and after chewing gum without flavor and with 2 different flavors. One-minute, 19-channel, eyes-closed electroencephalograms (EEG) were recorded from 20 healthy males before and after using 3 types of chewing gum: regular gum containing sugar and aromatic additives, gum containing 200 mg theanine (a constituent of Japanese green tea), and gum base (no sugar, no aromatic additives); each was chewed for 5 min in randomized sequence. Brain electric activity was assessed through Global Omega (Ω)-Complexity and Global Dimensional Complexity (GDC), quantitative measures of complexity of the trajectory of EEG map series in state space; their differences from pre-chewing data were compared across gum-chewing conditions. Friedman Anova (p < 0.043) showed that effects on Ω-Complexity differed significantly between conditions and differences were maximal between gum base and theanine gum. No differences were found using GDC. Global Omega-Complexity appears to be a sensitive measure for subtle, central effects of chewing gum with and without flavor.

Paraseptal accessory pathway in Wolff-Parkinson- White-Syndrom: ablation from the right, from the left or within the coronary sinus/middle cardiac vein?

AIMS In 1999 the consensus statement "living anatomy of the atrioventricular junctions" was published. With that new nomenclature the former posteroseptal accessory pathway (APs) are termed paraseptal APs. The aim of this study was to identify ECG features of manifest APs located in this complex paraseptal space. METHODS AND RESULTS ECG characteristics of all patients who underwent radiofrequency ablation of an AP during a 3 year period were analyzed. Of the 239 patients with one or more APs, 30 patients had a paraseptal AP with preexcitation. Compared to APs within the coronary sinus (CS) or the middle cardiac vein (MCV) the right sided paraseptal APs significantly more often showed an isoelectric delta wave in lead II and/or a negative delta wave in aVR. The left sided paraseptal APs presented a negative delta wave in II significantly more often compared to the right sided APs. CONCLUSIONS According to the site of radiofrequency ablation, paraseptal APs are classified into 4 subgroups: paraseptal right, paraseptal left, inside the CS or inside the MCV. Subtle differences in preexcitation patterns of the delta wave as well as of the QRS complex exist. However, the definitive localization of APs remains reserved to the periinterventional intracardiac electrogram analysis.

Differential dynamic properties of scleroderma fibroblasts in response to perturbation of environmental stimuli.

Diseases are believed to arise from dysregulation of biological systems (pathways) perturbed by environmental triggers. Biological systems as a whole are not just the sum of their components, rather ever-changing, complex and dynamic systems over time in response to internal and external perturbation. In the past, biologists have mainly focused on studying either functions of isolated genes or steady-states of small biological pathways. However, it is systems dynamics that play an essential role in giving rise to cellular function/dysfunction which cause diseases, such as growth, differentiation, division and apoptosis. Biological phenomena of the entire organism are not only determined by steady-state characteristics of the biological systems, but also by intrinsic dynamic properties of biological systems, including stability, transient-response, and controllability, which determine how the systems maintain their functions and performance under a broad range of random internal and external perturbations. As a proof of principle, we examine signal transduction pathways and genetic regulatory pathways as biological systems. We employ widely used state-space equations in systems science to model biological systems, and use expectation-maximization (EM) algorithms and Kalman filter to estimate the parameters in the models. We apply the developed state-space models to human fibroblasts obtained from the autoimmune fibrosing disease, scleroderma, and then perform dynamic analysis of partial TGF-beta pathway in both normal and scleroderma fibroblasts stimulated by silica. We find that TGF-beta pathway under perturbation of silica shows significant differences in dynamic properties between normal and scleroderma fibroblasts. Our findings may open a new avenue in exploring the functions of cells and mechanism operative in disease development.

Differential dynamic properties of scleroderma fibroblasts in response to perturbation of environmental stimuli.

Diseases are believed to arise from dysregulation of biological systems (pathways) perturbed by environmental triggers. Biological systems as a whole are not just the sum of their components, rather ever-changing, complex and dynamic systems over time in response to internal and external perturbation. In the past, biologists have mainly focused on studying either functions of isolated genes or steady-states of small biological pathways. However, it is systems dynamics that play an essential role in giving rise to cellular function/dysfunction which cause diseases, such as growth, differentiation, division and apoptosis. Biological phenomena of the entire organism are not only determined by steady-state characteristics of the biological systems, but also by intrinsic dynamic properties of biological systems, including stability, transient-response, and controllability, which determine how the systems maintain their functions and performance under a broad range of random internal and external perturbations. As a proof of principle, we examine signal transduction pathways and genetic regulatory pathways as biological systems. We employ widely used state-space equations in systems science to model biological systems, and use expectation-maximization (EM) algorithms and Kalman filter to estimate the parameters in the models. We apply the developed state-space models to human fibroblasts obtained from the autoimmune fibrosing disease, scleroderma, and then perform dynamic analysis of partial TGF-beta pathway in both normal and scleroderma fibroblasts stimulated by silica. We find that TGF-beta pathway under perturbation of silica shows significant differences in dynamic properties between normal and scleroderma fibroblasts. Our findings may open a new avenue in exploring the functions of cells and mechanism operative in disease development.

Existence and Uniqueness of Equilibrium in Nonoptimal Unbounded Infinite Horizon Economies

In applied work in macroeconomics and finance, nonoptimal infinite horizon economies are often studied in the the state space is unbounded. Important examples of such economies are single vector growth models with production externalities, valued fiat money, monopolistic competition, and/or distortionary government taxation. Although sufficient conditions for existence and uniqueness of Markovian equilibrium are well known for the compact state space case, no similar sufficient conditions exist for unbounded growth. This paper provides such a set of sufficient conditions, and also present a computational algorithm that will prove asymptotically consistent when computing Markovian equilibrium.