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.

Biological evolution of replicator systems: towards a quantitative approach

The aim of this work is to study the features of a simple replicator chemical model of the relation between kinetic stability and entropy production under the action of external perturbations. We quantitatively explore the different paths leading to evolution in a toy model where two independent replicators compete for the same substrate. To do that, the same scenario described originally by Pross (J Phys Org Chem 17:312–316, 2004) is revised and new criteria to define the kinetic stability are proposed. Our results suggest that fast replicator populations are continually favored by the effects of strong stochastic environmental fluctuations capable to determine the global population, the former assumed to be the only acting evolution force. We demonstrate that the process is continually driven by strong perturbations only, and that population crashes may be useful proxies for these catastrophic environmental fluctuations. As expected, such behavior is particularly enhanced under very large scale perturbations, suggesting a likely dynamical footprint in the recovery patterns of new species after mass extinction events in the Earth’s geological past. Furthermore, the hypothesis that natural selection always favors the faster processes may give theoretical support to different studies that claim the applicability of maximum principles like the Maximum Metabolic Flux (MMF) or Maximum Entropy Productions Principle (MEPP), seen as the main goal of biological evolution.

Motion control and real-time systems: an approach to trajectory rebuilding in non-deterministic networks

Motion control is a sub-field of automation, in which the position and/or velocity of machines are controlled using some type of device. In motion control the position, velocity, force, pressure, etc., profiles are designed in such a way that the different mechanical parts work as an harmonious whole in which a perfect synchronization must be achieved. The real-time exchange of information in the distributed system that is nowadays an industrial plant plays an important role in order to achieve always better performance, better effectiveness and better safety. The network for connecting field devices such as sensors, actuators, field controllers such as PLCs, regulators, drive controller etc., and man-machine interfaces is commonly called fieldbus. Since the motion transmission is now task of the communication system, and not more of kinematic chains as in the past, the communication protocol must assure that the desired profiles, and their properties, are correctly transmitted to the axes then reproduced or else the synchronization among the different parts is lost with all the resulting consequences. In this thesis, the problem of trajectory reconstruction in the case of an event-triggered communication system is faced. The most important feature that a real-time communication system must have is the preservation of the following temporal and spatial properties: absolute temporal consistency, relative temporal consistency, spatial consistency. Starting from the basic system composed by one master and one slave and passing through systems made up by many slaves and one master or many masters and one slave, the problems in the profile reconstruction and temporal properties preservation, and subsequently the synchronization of different profiles in network adopting an event-triggered communication system, have been shown. These networks are characterized by the fact that a common knowledge of the global time is not available. Therefore they are non-deterministic networks. Each topology is analyzed and the proposed solution based on phase-locked loops adopted for the basic master-slave case has been improved to face with the other configurations.

The port-Hamiltonian framework as a comprehensive approach to model and simulate complex systems

This thesis describes modelling tools and methods suited for complex systems (systems that typically are represented by a plurality of models). The basic idea is that all models representing the system should be linked by well-defined model operations in order to build a structured repository of information, a hierarchy of models. The port-Hamiltonian framework is a good candidate to solve this kind of problems as it supports the most important model operations natively. The thesis in particular addresses the problem of integrating distributed parameter systems in a model hierarchy, and shows two possible mechanisms to do that: a finite-element discretization in port-Hamiltonian form, and a structure-preserving model order reduction for discretized models obtainable from commercial finite-element packages.

Reconstruction and analysis of the NF-kB pathway interactome: a systems biology approach

Background. One of the phenomena observed in human aging is the progressive increase of a systemic inflammatory state, a condition referred to as “inflammaging”, negatively correlated with longevity. A prominent mediator of inflammation is the transcription factor NF-kB, that acts as key transcriptional regulator of many genes coding for pro-inflammatory cytokines. Many different signaling pathways activated by very diverse stimuli converge on NF-kB, resulting in a regulatory network characterized by high complexity. NF-kB signaling has been proposed to be responsible of inflammaging. Scope of this analysis is to provide a wider, systemic picture of such intricate signaling and interaction network: the NF-kB pathway interactome. Methods. The study has been carried out following a workflow for gathering information from literature as well as from several pathway and protein interactions databases, and for integrating and analyzing existing data and the relative reconstructed representations by using the available computational tools. Strong manual intervention has been necessarily used to integrate data from multiple sources into mathematically analyzable networks. The reconstruction of the NF-kB interactome pursued with this approach provides a starting point for a general view of the architecture and for a deeper analysis and understanding of this complex regulatory system. Results. A “core” and a “wider” NF-kB pathway interactome, consisting of 140 and 3146 proteins respectively, were reconstructed and analyzed through a mathematical, graph-theoretical approach. Among other interesting features, the topological characterization of the interactomes shows that a relevant number of interacting proteins are in turn products of genes that are controlled and regulated in their expression exactly by NF-kB transcription factors. These “feedback loops”, not always well-known, deserve deeper investigation since they may have a role in tuning the response and the output consequent to NF-kB pathway initiation, in regulating the intensity of the response, or its homeostasis and balance in order to make the functioning of such critical system more robust and reliable. This integrated view allows to shed light on the functional structure and on some of the crucial nodes of thet NF-kB transcription factors interactome. Conclusion. Framing structure and dynamics of the NF-kB interactome into a wider, systemic picture would be a significant step toward a better understanding of how NF-kB globally regulates diverse gene programs and phenotypes. This study represents a step towards a more complete and integrated view of the NF-kB signaling system.

A Unitary Approach to Information and Estimation Theory in Digital Communication Systems

This thesis presents the outcomes of a Ph.D. course in telecommunications engineering. It is focused on the optimization of the physical layer of digital communication systems and it provides innovations for both multi- and single-carrier systems. For the former type we have first addressed the problem of the capacity in presence of several nuisances. Moreover, we have extended the concept of Single Frequency Network to the satellite scenario, and then we have introduced a novel concept in subcarrier data mapping, resulting in a very low PAPR of the OFDM signal. For single carrier systems we have proposed a method to optimize constellation design in presence of a strong distortion, such as the non linear distortion provided by satellites' on board high power amplifier, then we developed a method to calculate the bit/symbol error rate related to a given constellation, achieving an improved accuracy with respect to the traditional Union Bound with no additional complexity. Finally we have designed a low complexity SNR estimator, which saves one-half of multiplication with respect to the ML estimator, and it has similar estimation accuracy.

Quantum effects and dynamics in hydrogen-bonded systems: a first-principles approach to spectroscopic experiments

Computer simulations have become an important tool in physics. Especially systems in the solid state have been investigated extensively with the help of modern computational methods. This thesis focuses on the simulation of hydrogen-bonded systems, using quantum chemical methods combined with molecular dynamics (MD) simulations. MD simulations are carried out for investigating the energetics and structure of a system under conditions that include physical parameters such as temperature and pressure. Ab initio quantum chemical methods have proven to be capable of predicting spectroscopic quantities. The combination of these two features still represents a methodological challenge. Furthermore, conventional MD simulations consider the nuclei as classical particles. Not only motional effects, but also the quantum nature of the nuclei are expected to influence the properties of a molecular system. This work aims at a more realistic description of properties that are accessible via NMR experiments. With the help of the path integral formalism the quantum nature of the nuclei has been incorporated and its influence on the NMR parameters explored. The effect on both the NMR chemical shift and the Nuclear Quadrupole Coupling Constants (NQCC) is presented for intra- and intermolecular hydrogen bonds. The second part of this thesis presents the computation of electric field gradients within the Gaussian and Augmented Plane Waves (GAPW) framework, that allows for all-electron calculations in periodic systems. This recent development improves the accuracy of many calculations compared to the pseudopotential approximation, which treats the core electrons as part of an effective potential. In combination with MD simulations of water, the NMR longitudinal relaxation times for 17O and 2H have been obtained. The results show a considerable agreement with the experiment. Finally, an implementation of the calculation of the stress tensor into the quantum chemical program suite CP2K is presented. This enables MD simulations under constant pressure conditions, which is demonstrated with a series of liquid water simulations, that sheds light on the influence of the exchange-correlation functional used on the density of the simulated liquid.

Modelling and simulating in systems biology: an approach based on multi-agent systems

Systems Biology is an innovative way of doing biology recently raised in bio-informatics contexts, characterised by the study of biological systems as complex systems with a strong focus on the system level and on the interaction dimension. In other words, the objective is to understand biological systems as a whole, putting on the foreground not only the study of the individual parts as standalone parts, but also of their interaction and of the global properties that emerge at the system level by means of the interaction among the parts. This thesis focuses on the adoption of multi-agent systems (MAS) as a suitable paradigm for Systems Biology, for developing models and simulation of complex biological systems. Multi-agent system have been recently introduced in informatics context as a suitabe paradigm for modelling and engineering complex systems. Roughly speaking, a MAS can be conceived as a set of autonomous and interacting entities, called agents, situated in some kind of nvironment, where they fruitfully interact and coordinate so as to obtain a coherent global system behaviour. The claim of this work is that the general properties of MAS make them an effective approach for modelling and building simulations of complex biological systems, following the methodological principles identified by Systems Biology. In particular, the thesis focuses on cell populations as biological systems. In order to support the claim, the thesis introduces and describes (i) a MAS-based model conceived for modelling the dynamics of systems of cells interacting inside cell environment called niches. (ii) a computational tool, developed for implementing the models and executing the simulations. The tool is meant to work as a kind of virtual laboratory, on top of which kinds of virtual experiments can be performed, characterised by the definition and execution of specific models implemented as MASs, so as to support the validation, falsification and improvement of the models through the observation and analysis of the simulations. A hematopoietic stem cell system is taken as reference case study for formulating a specific model and executing virtual experiments.

A landscape mosaics approach for characterizing swidden systems from a REDD+ perspective

Swidden agriculture is often deemed responsible for deforestation and forest degradation in tropical regions, yet swidden landscapes are commonly not visible on land cover/use maps, making it difficult to prove this assertion. For a future REDD+ scheme, the correct identification of deforestation and forest degradation and linking these processes to land use is crucial. However, it is a key challenge to distinguish degradation and deforestation from temporal vegetation dynamics inherent to swiddening. In this article we present an approach for spatial delineation of swidden systems based on landscape mosaics. Furthermore we introduce a classification for change processes based on the change matrix of these landscape mosaics. Our approach is illustrated by a case study in Viengkham district in northern Laos. Over a 30-year time period the swidden landscapes have increased in extent and they have degraded, shifting from long crop–fallow cycles to short cycles. From 2007 to 2009 degradation within the swidden system accounted for half of all the landscape mosaics change processes. Pioneering shifting cultivation did not prevail. The landscape mosaics approach could be used in a swidden compatible monitoring, reporting and verification (MRV) system of a future REDD+ framework.

A Systems-Level Approach to Human Epileptic Seizures

Epileptic seizures are due to the pathological collective activity of large cellular assemblies. A better understanding of this collective activity is integral to the development of novel diagnostic and therapeutic procedures. In contrast to reductionist analyses, which focus solely on small-scale characteristics of ictogenesis, here we follow a systems-level approach, which combines both small-scale and larger-scale analyses. Peri-ictal dynamics of epileptic networks are assessed by studying correlation within and between different spatial scales of intracranial electroencephalographic recordings (iEEG) of a heterogeneous group of patients suffering from pharmaco-resistant epilepsy. Epileptiform activity as recorded by a single iEEG electrode is determined objectively by the signal derivative and then subjected to a multivariate analysis of correlation between all iEEG channels. We find that during seizure, synchrony increases on the smallest and largest spatial scales probed by iEEG. In addition, a dynamic reorganization of spatial correlation is observed on intermediate scales, which persists after seizure termination. It is proposed that this reorganization may indicate a balancing mechanism that decreases high local correlation. Our findings are consistent with the hypothesis that during epileptic seizures hypercorrelated and therefore functionally segregated brain areas are re-integrated into more collective brain dynamics. In addition, except for a special sub-group, a highly significant association is found between the location of ictal iEEG activity and the location of areas of relative decrease of localised EEG correlation. The latter could serve as a clinically important quantitative marker of the seizure onset zone (SOZ).

A Historical-Institutional Study of the Welfare Systems in the United States and Sweden: Net Social Wage Approach

In this study I first look at the historical developments of the welfare systems in Sweden and the United States to understand why these countries have produced two distinct systems over the years. After understanding their historical context I turn to the question of the relationship between the welfare system and economic growth. Policy makers and the mainstream media commonly cite the critique that through government deficit and public debt, welfare systems are a drag on the economy. By calculating the net social wage, the difference in taxes paid and benefits received by workers, I test this hypothesis to see if welfare systems are self-financed by the workers. My findings demonstrate that the net social wage has been negative in the U.S. from 1962 to the early 2000s and in Sweden from 1965 to 2012. This shows that the welfare systems are entirely self-financed by the workers for the full period in Sweden and until the recent financial crisis in the U.S.