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.

Norm and difference : Stone Age dietary practice in the Baltic region

Stone Age research on Northern Europe frequently makes gross generalizations about the Mesolithic and Neolithic, although we still lack much basic knowledge on how the people lived. The transition from the Mesolithic to the Neolithic in Europe has been described as a radical shift from an economy dominated by marine resources to one solely dependent on farming. Both the occurrence and the geographical extent of such a drastic shift can be questioned, however. It is therefore important to start out at a more detailed level of evidence in order to present the overall picture, and to account for the variability even in such regional or chronological overviews. Fifteen Stone Age sites were included in this study, ranging chronologically from the Early Mesolithic to the Middle or Late Neolithic, c. 8300–2500 BC, and stretching geographically from the westernmost coast of Sweden to the easternmost part of Latvia within the confines of latitudes 55–59° N. The most prominent sites in terms of the number of human and faunal samples analysed are Zvejnieki, Västerbjers and Skateholm I–II. Human and faunal skeletal remains were subjected to stable carbon and nitrogen isotope analysis to study diet and ecology at the sites. Stable isotope analyses of human remains provide quantitative information on the relative importance of various food sources, an important addition to the qualitative data supplied by certain artefacts and structures or by faunal or botanical remains. A vast number of new radiocarbon dates were also obtained. In conclusion, a rich diversity in Stone Age dietary practice in the Baltic Region was demonstrated. Evidence ranging from the Early Mesolithic to the Late Neolithic show that neither chronology nor location alone can account for this variety, but that there are inevitably cultural factors as well. Food habits are culturally governed, and therefore we cannot automatically assume that people at similar sites will have the same diet. Stable isotope studies are very important here, since they tell us what people actually consumed, not only what was available, or what one single meal contained. We should not be deceived in inferring diet from ritually deposited remains, since things that were mentally important were not always important in daily life. Thus, although a ritual and symbolic norm may emphasize certain food categories, these may in fact contribute very little to the diet. By the progress of analysis of intra-individual variation, new data on life history changes have been produced, revealing mobility patterns, breastfeeding behaviour and certain dietary transitions. The inclusion of faunal data has proved invaluable for understanding the stable isotope ecology of a site, and thereby improve the precision of the interpretations of human stable isotope data. The special case of dogs, though, demonstrates that these animals are not useful for inferring human diet, since, due to the number of roles they possess in human society, dogs could deviate significantly from humans in their diet, and in several cases have been proved to do so. When evaluating radiocarbon data derived from human and animal remains from the Pitted-Ware site of Västerbjers on Gotland, the importance of establishing the stable isotope ecology of the site before making deductions on reservoir effects was further demonstrated. The main aim of this thesis has been to demonstrate the variation and diversity in human practices, challenging the view of a “monolithic” Stone Age. By looking at individuals and not only at populations, the whole range of human behaviour has been accounted for, also revealing discrepancies between norm and practice, which are frequently visible both in the archaeological record and in present-day human behaviour.

Improving approximate inverses based on Frobenius norm minimization

[EN]Approximate inverses, based on Frobenius norm minimization, of real nonsingular matrices are analyzed from a purely theoretical point of view. In this context, this paper provides several sufficient conditions, that assure us the possibility of improving (in the sense of the Frobenius norm) some given approximate inverses. Moreover, the optimal approximate inverses of matrix A ∈ R n×n , among all matrices belonging to certain subspaces of R n×n , are obtained. Particularly, a natural generalization of the classical normal equations of the system Ax = b is given, when searching for approximate inverses N 6= AT such that AN is symmetric and kAN − IkF < AAT − I F …

Ab-initio determination of x-ray absorption near edge structure (xanes) spectra in an ultrasoft and norm conserving pseudopotentials scheme

X-ray absorption spectroscopy (XAS) is a powerful means of investigation of structural and electronic properties in condensed -matter physics. Analysis of the near edge part of the XAS spectrum, the so – called X-ray Absorption Near Edge Structure (XANES), can typically provide the following information on the photoexcited atom: - Oxidation state and coordination environment. - Speciation of transition metal compounds. - Conduction band DOS projected on the excited atomic species (PDOS). Analysis of XANES spectra is greatly aided by simulations; in the most common scheme the multiple scattering framework is used with the muffin tin approximation for the scattering potential and the spectral simulation is based on a hypothetical, reference structure. This approach has the advantage of requiring relatively little computing power but in many cases the assumed structure is quite different from the actual system measured and the muffin tin approximation is not adequate for low symmetry structures or highly directional bonds. It is therefore very interesting and justified to develop alternative methods. In one approach, the spectral simulation is based on atomic coordinates obtained from a DFT (Density Functional Theory) optimized structure. In another approach, which is the object of this thesis, the XANES spectrum is calculated directly based on an ab – initio DFT calculation of the atomic and electronic structure. This method takes full advantage of the real many-electron final wavefunction that can be computed with DFT algorithms that include a core-hole in the absorbing atom to compute the final cross section. To calculate the many-electron final wavefunction the Projector Augmented Wave method (PAW) is used. In this scheme, the absorption cross section is written in function of several contributions as the many-electrons function of the finale state; it is calculated starting from pseudo-wavefunction and performing a reconstruction of the real-wavefunction by using a transform operator which contains some parameters, called partial waves and projector waves. The aim of my thesis is to apply and test the PAW methodology to the calculation of the XANES cross section. I have focused on iron and silicon structures and on some biological molecules target (myoglobin and cytochrome c). Finally other inorganic and biological systems could be taken into account for future applications of this methodology, which could become an important improvement with respect to the multiscattering approach.

Kindersegen und effektive Rituale: Die Jesuiten in China zwischen lokalen Heilspraktiken, tridentinischer Norm und konfuzianischer Obrigkeit

In christlichen Gemeinden, die im 17. Jahrhundert in zahlreichen chinesischen Provinzen entstanden, versuchten die Jesuiten deshalb vor allem, die Heilsbedürfnisse der Gläubigen vor Ort zu befriedigen. Da in der chinesischen Gesellschaft die Fortsetzung der männlichen Linie von grosser Wichtigkeit war, war Kindersegen ein Anliegen erster Ordnung, dem die Jesuiten mit ihren Ritualen zu begegnen hatten. Sie setzten christliche Heilsobjekte oft gegen Kinderlosigkeit ein und standen Frauen bei schwierigen Niederkünften bei. Mit solchen Heilspraktiken, die in China traditionellerweise von lokalen religiösen Spezialisten ausgeführt wurden, traten die Missionare in Konkurrenz mit anderen Anbietern auf dem chinesischen Heilsmarkt. Der Vortrag beleuchtet die Rolle der Jesuiten als religiöse Spezialisten in lokalen christlichen Gemeinden und fragt nach den Spannungen, die sich zwischen dieser Rolle einerseits und den Rollen als katholische Missionare und konfuzianische Literati andererseits ergaben.

The mentalizing network orchestrates the impact of parochial altruism on social norm enforcement.

Parochial altruism - a preference for altruistic behavior towards ingroup members and mistrust or hostility towards outgroup members--is a pervasive feature in human society and strongly shapes the enforcement of social norms. Since the uniqueness of human society critically depends on the enforcement of norms, the understanding of the neural circuitry of the impact of parochial altruism on social norm enforcement is key, but unexplored. To fill this gap, we measured brain activity with functional magnetic resonance imaging (fMRI) while subjects had the opportunity to punish ingroup members and outgroup members for violating social norms. Findings revealed that subjects' strong punishment of defecting outgroup members is associated with increased activity in a functionally connected network involved in sanction-related decisions (right orbitofrontal gyrus, right lateral prefrontal cortex, right dorsal caudatus). Moreover, the stronger the connectivity in this network, the more outgroup members are punished. In contrast, the much weaker punishment of ingroup members who committed the very same norm violation is associated with increased activity and connectivity in the mentalizing-network (dorsomedial prefrontal cortex, bilateral temporo-parietal junction), as if subjects tried to understand or justify ingroup members' behavior. Finally, connectivity analyses between the two networks suggest that the mentalizing-network modulates punishment by affecting the activity in the right orbitofrontal gyrus and right lateral prefrontal cortex, notably in the same areas showing enhanced activity and connectivity whenever third-parties strongly punished defecting outgroup members.