The results of our model fit in the parochialism framework. Retaliation and reputation effects are driven by the indirect reciprocity mechanism of the model and exclusion in terms of social capital in case of an aggregation event, both based on the agent’s reputation. Although all the members included in the model are supposed to belong to the same community, in some sense the segmentation effect is also present as a consequence of the concentration of the population towards the resource when there is **spatial** **correlation** in the distribution of the resource. As a matter of fact, **spatial** **correlation** empowers all the mechanisms of parochialism. The roaming paths are close to the resource for all the agents, so the frequency of interaction and the possibili- ty of gathering reliable information about the rest of the agents increase and the concentration of the population increases the odds of detecting a defector. The underlying network of vigilance is denser when the resource is not uniformly distributed, and higher clustering and interconnec- tedness promote cooperative social norms as previous research has indicated [86]. It is impor- tant to notice that this effect occurs even in this model in which the movement of the population is intentionally myopic. The agents are not endowed with memory about the location of the re- source or learning capabilities to figure out the distribution. Higher levels of cooperation must be expected in populations that include any learning dynamics.

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transformation of two parameters. Three special cases of ABCD systems are considered, namely a free-space segment, a quadratic index medium, and an unapertured thin lens. A complete characterization of these beams is made by studying their polarization properties and angular spectrum distribution. An important phenomenon known as the focal-shift is studied for the case of vector Mathieu- Gauss beams, and the existence of this shift is confirmed theoretically by means of two methods. All studies previously mentioned are performed assuming highly coherent sources. Partially coherent optical systems are considered as well, but we now look at singularities of the wave function describing the optical beam, which are commonly known as optical vortices. It is shown that partial coherence requires a beam to exhibit Rankine vortex characteristics, in analogy to vortices in fluids. We suggest a method to study the coherence properties of a beam by looking at its cross **correlation** function. Potential

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66 CHAPTER 7. GENERAL CONCLUSIONS In the last part of the thesis we studied optical vortices, and particularly we discussed how the **spatial** coherence properties of a beam carrying an optical vortex require them to exhibit Rankine vortex characteristics, analogous to vortex phenomena in other sys- tems such as fluids. An amazing feature of these optical Rankine vortices, is that they constitute a general state of optical vortices, regardless of their coherence properties. We proposed a method to measure the angular extent of distant objects, for instance we suggested a “vortex stellar interferometer” to determine the diameter of stars. An- other powerful method, coming out of this work on partially coherent vortices, is to use cross-**correlation** measurements to determine orbital angular momentum content. Fi- nally, we would like to comment that an optical vortex, exhibiting a behavior analogous to a mechanical system, may be telling us something more about the intrinsic nature of vortices in all physical systems, and therefore more research on this topic is required.

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For all of these statistics, it is necessary to design a matrix with **spatial** weights that identifies which areas we consider to be those of influence. The most widely used matrices are the contiguity matrix and the distance matrix. In the present paper, we basically use the first from two perspectives. Firstly, we consider contiguity from a purely geographical perspective at a provincial and regional scale. We identify whether there is a **correlation** between the total number of cases resolved in favour of the worker in each province (region) and in adjacent ones. Secondly, we adopt a legal and administrative perspective, using three different matrices where we consider courts in the same city, province, or region to be adjacent courts. In addition to calculating **spatial** **correlation** statistics, exploratory analysis of **spatial** data also draws on various graphical tools to identify **spatial** **correlation** visually. The most representative of these tools is Moran’s scatter plot, which shows the normalised object variable in the X axis and its **spatial** lag in the Y axis. A concentration of points in the first and third

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One important topic in the aeronautic and aerospace industries is the reproduction of random pressure field, with pre- scribed **spatial** **correlation** characteristics, in laboratory conditions. In particular, the random-wall pressure fluctua- tions induced by a Turbulent Boundary Layer (TBL) excitation are a major concern for cabin noise problem, as this excitation has been identified as the dominant contribution in cruise conditions. As in-flight measurements require costly and time-consuming measurement campaigns, the laboratory reproduction has attracted considerable attention in recent years. Some work has already been carried out for the laboratory simulation of the excitation pressure field for several random fields. It has been found that TBL reproduction is very demanding in terms of number of loud- speakers per **correlation** length, and it should require a dense and non-uniform arrangement of acoustic sources due to the different spanwise and streamwise **correlation** lengths involved. The present study addresses the problem of di- rectly simulating the vibroacoustic response of an aircraft skin panel using a near-field array of suitably driven loud- speakers. It is compared with the use of an array of shakers and piezoelectric actuators. It is shown how the wavenumber filtering capabilities of the panel reduces the number of sources required, thus dramatically enlarging the frequency range over which the TBL vibro-acoustic response is reproduced with accuracy. Direct reconstruction of the TBL-induced panel response is found to be feasible over the hydrodynamic coincidence frequency range using a limited number of actuators driven by optimal signals. It is shown that piezoelectric actuators, which have more practical implementation than shakers, provide a more effective reproduction of the TBL response than near-field loudspeakers.

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In this paper the distribution and **spatial** **correlation** patterns of tree species along an altitudinal gradient in the Metzabok Protected Natural Area (PNA) in the Selva Lacandona, Chiapas State was analyzed. A 20 × 50 m sampling unit (SU) was installed in each altitudinal strata (AS), and divided into 10 sampling subunits (SSU) of 10 x 10 m targeting pole-sized trees. Within each SSU, one 5 × 5 m plot was installed to register the saplings, and within this, another two 2 × 2 m plots were established for the sampling of seedlings. The **spatial** distribution of pole-sized trees, saplings and seedlings was analyzed with the Morisita-Horn index; whereas the distribution and **spatial** **correlation** of pole-sized trees by height categories (lower, middle and higher) and AS was evaluated using Ripley’s univariate K(t) and bivariate K 12 (t) functions. The mean **spatial**

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We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the **correlation** sum of a trajectory generated by a random walker navigating the network, and extends the classical Grassberger-Procaccia algorithm to the context of complex networks. The method is validated with reliable results for both synthetic networks and real-world networks such as the world air-transportation network or urban networks, and provides a computationally fast way for estimating the dimensionality of networks which only relies on the local information provided by the walkers.

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The management of any territory (e.g., state, region, city) is fraught with many hur- dles, especially in an open-access society linked together through networks of all kinds. Clearly, **spatial** justice as a policy objective calls for a balanced governance of regions and cities. The use of cognitive, technological and innovative mechanisms to steer the development of regions and cities towards prosperous, balanced and sustainable territo- ries has led to a new policy conceptualisation, nowadays often called smart governance (Scholl and AlAwadhi, 2016). This novel policy modus operando is strongly supported by digital technology (e.g., e-governance) and has to ensure a symbiosis of economic, social, ecological and technological conditions with a view to achieving a sustainable **spatial** development. Against this background, smart governance induces far-reaching questions on **spatial** competences of policies, on property rights and commons in a spa- tially heterogeneous world, on conflicting behaviours in a multi-actor **spatial** setting, and on fair financial mechanisms to care for the well-being of all citizens in the future.

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In the present paper, we have computed holographic **correlation** functions in Einstein-Weyl gravity at the critical point. We have applied holographic techniques to an equivalent form of the Critical Gravity action, given by eq. (2.2), where the curvature-squared part are expressed as the difference between the Weyl 2 and the GB terms. The GB term, with its coupling fixed by the above argument, provides partial renormalization of the variation of the action, such that the divergent pieces can be attributed to the non-Einstein part in the curvature (Bach tensor).

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Firstly, since the quantification of model uncertainties takes place by comparison with experimental data, an appropriate selection of the adequate experimental matrix is imperative. Choosing an appropriate experimental matrix will considerably reduce the compensating errors, which can mask the uncertainty estimation. The experimental data selected for quantification have to be representative of the considered application, including the scale of the analyzed facility. Secondly, the experiment-scaled EM is compared against SET data to estimate the uncertainty due to model/**correlation** inadequacy. This comparison makes possible to estimate the model capability in reproducing the experiment phenomena. Measurement uncertainties have to be accounted to avoid masking the model/**correlation** error. It has to be noted that scale distortions in code predictions are narrowed related with the **spatial** discretization used. Therefore, the EM nodalization has to be equivalent to as in the model/**correlation** validation process.

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Abstract The present work applies similarity theory to the plasma emanating from transferred arc, gas-vortex stabilized plasma cutting torches, to analyze the existing **correlation** between the arc temperature and the physical parameters of such torches. It has been found that the enthalpy number significantly influence the temperature of the electric arc. The obtained **correlation** shows an average deviation of 3 % from the temperature data points. Such **correlation** can be used, for instance, to predict changes in the peak value of the arc temperature at the nozzle exit of a geometrically similar cutting torch due to changes in its operation parameters.

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Here -1 indicates a perfect inverse linear relationship, i.e. “y” increases uniformly as “x” decreases, and 1 indicates a perfect direct linear relationship, i.e. “x” and “y” move uniformly together. A value of 0 indicates no relationship. Note that **correlation** can determine that a relationship exists between variables but says nothing about the cause or directional effect. For example, a known **correlation** exists between muggings and ice cream sales. However, one does not cause the other. Rather, a third variable, the warm weather which puts more people on the street both to mug and buy ice cream is a more direct cause of the **correlation**.

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Figure 12. Boerhaave’s syndrome. Barium study (a). Macroscopic **correlation** (b). The esophagogram demonstrates contrast me- dium extravasating from the left lateral wall of distal esophagus. Pneumomediastinum is evident. The pathologic specimen (pos- terior view) shows the typical localization of the spontaneous esophageal perforation that is secondary to a sudden increase in in- traluminal esophageal pressure.

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Second, since the SDM contains the SAR, it is necessary to discern about these two specifications. For this purpose, we use the likelihood ratio (LR) derived from the ML estimation, which allows us to test the hypothesis H 0 : θ = 0, which examines whether the spatially lagged inde- pendent variables are not jointly significant (i.e. the SDM can be simpli- fied to the SAR model). This test follows a chi-squared distribution with as many degrees of freedom as regression coefficients in the basic model, excluding the constant term (i.e. nine degrees of freedom in our case). As shown in Table 4, neither of the specifications can reject the null, which is consistent with the non-significant coefficients of the spatially lagged independent variables in the SDM (Model 1 in Table 2). Then the SAR is the model that best describes the data, since the robust LM tests also coincide in pointing to the SAR, and there is no reason to reject the **spatial** lag model in favor of the **spatial** Durbin model. Similarly, in most of the specifications in Table 4, we cannot reject the hypothesis that the SDM can be simplified to the SEM, as demonstrated by the common factor hypothesis: H 0 : θ = −λ·β (Anselin, 1988). 5

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The **correlation** is negative (-0.2). The United States spends in education the second most of any country, and has below average test-scores. Ethnically homogeneous Japan, South Korea and Finland spend at average rates and have the best test scores. Tiny, ethnically homogeneous and "hungry" Estonia spends less than half as much as the United States and Norway on education but has far better test scores. Source: Economy Industry USA View

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The SPS signals can be reproduced employing a suitable loudspeaker rig. This approach shares with Ambisonics the capability of rendering the signals over a generic loudspeaker array, in principle composed of an arbitrary number of transducer, and in arbitrary positions, as the SPS signals being transferred are not “speaker feeds”, such as in 5.1, 7.1, 10.2, 22.2, etc. Instead, the 32 signals of the SPS signal are a “**spatial** kernel”, codifying the whole **spatial** information, exactly as the Ambisonics signals. With the difference that the SPS signals are “PCM encoded”, whilst the Ambisonics signals are in the domain of “**spatial** frequency”.

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The main object of this study was to discover the relation with variables available in Eurostat and discover the pattern of those protests around Europe. Ordinary Least Squared Method and **Spatial** point pattern analysis methods were implemented in the R software environment for this purpose. Overall, the variables selected do not define the protests behaviour but some of them are related and increase with the protests. Protest tend to increase occur mostly when other protest have happened. Protest tend to create hotspots within Europe, their location are mostly in urban areas and close to the borders with other European countries. Resulting models discovered that protest/event distribution does not imitate to a Poisson process, and that their behaviour can be better described by interaction between protests.

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Abstract. The purpose of Functional Magnetic Resonance Imaging (fMRI) is to map areas of increased neuronal activity of the human brain. fMRI has been applied to inves- tigate a variety of neuronal processes from activities in the primary sensory and motor cortices to cognitive functions such as perception or learning. Robust anisotropic diffu- sion of statistical parametric maps (RADSPM) is a new technique to improve functional Magnetic Resonance Imaging. RADSPM attempts to improve voxel classification based on robust anisotropic diffusion (RAD) to include the **spatial** relationship between active voxels. This paper compares two fMRI postprocessing techniques used to identify areas of increased neuronal activity, a widely used method, **correlation** analysis, and RADSPM. In recent years, the use of ROC analysis has been extended from its original use in com- munication systems to machine learning, pattern classification and fMRI. We proposed to use ROC curves and the area under the curve (AUC) not only as a final performance evaluation and visualizing technique but as a gauging parameter procedure in RADSPM. We give a brief review of the main methods and conclude presenting experimental results and suggesting further research alternatives.

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La Correlación Nolineal Dual (DNC) es una operación general en reconocimiento óptico de patrones en la que el preprocesado nolineal introducido en el canal de referencia puede diferir del introducido en el canal de entrada. Abarca un gran número de métodos de filtrado lineal y nolineal y puede realizarse mediante un correlador optoelectrónico de transformadas conjuntas (JTC) en dos pasos. La capacidad del sistema depende finalmente de algunas condiciones experimentales tales como la discretización, el rango dinámico de niveles de gris, la saturación y otras características técnicas de la cámara y el modulador utilizados en el JTC. En este trabajo, presentamos una revisión de las técnicas de reconocimiento basadas en la DNC, centrándonos en primer lugar en la descripción de los fundamentos, las propiedades y la realización óptica de la correlación nolineal dual. Las posibilidades de la DNC en el reconocimiento de patrones con sensibilidad ajustable se presentan en un segundo trabajo (K. Chalasinska-Macukow et al.,” Dual Nonlinear **Correlation** in Optical Pattern Recognition II, Óptica Pura y Aplicada 38, núm. 2, 85- 97, 2005).

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NDVI — with monthly NDVI values being shown to correlate with field measurements of leaf cover and food availability for vervet monkeys (Willems et al. 2009). NDVI has, so far, been little used in studies on small mammals. Yet, this direction of research seems to have a great conceptual and methodological potential, especially when it comes to the question of spatiotem- poral dynamics of cyclic (or otherwise fluctuating) pop- ulations. Attempts to find the causal relationships between primary productivity and population density and/or fluctuations of rodents date go back to the years of the International Biological Programme. However, the studies conducted in the 1960s–1980s were per- formed at very small **spatial** scales (study sites usually encompassed one to a few hectares) as the methods of estimating habitat productivity relied on laborious direct sampling of vegetation (e.g. Grodzi ´nski 1971, Pelikan 1982). Since the 1980s, it has become more and more evident that patterns in small rodent abundance are better explained in macroecological scale, and sev- eral geographical gradients in vole population dynam- ics have been described (Hansson & Henttonen 1985, Mackin-Rogalska & Nagab8o 1990, Tkadlec & Stenseth 2001). So far, successful attempts have been under- taken to relate those large-scale patterns in small mammal populations to habitat productivity, using such indices derived from ground sampling as stand- ing crop and productivity of ground vegetation (J˛edrze- jewski & J˛edrzejewska 1996) and crop yield index (Tkadlec et al. 2006), or ranks of forest productivity (Niedzia8kowska et al. 2010). Examples of the great potential for using NDVI to study small rodents are provided by Andreo et al. (2009a,b), who investigated the relationships between small rodent population dynamics, climate and NDVI in an agricultural eco- system in Central Argentina. For Akodon azarae, the authors highlighted that large changes in land use were quite well captured by NDVI, which was the sole variable able to explain the sudden collapse exhibited by this rodent population.

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