Structural Analysis of Networks

Network analysis naturally relies on graph theory and, more particularly, on the use of node and edge metrics to identify the salient properties in graphs. When building visual maps of networks, these metrics are turned into useful visual cues or are used interactively to filter out parts of a graph while querying it, for instance. Over the years, analysts from different application domains have designed metrics to serve specific needs. Network science is an inherently cross-disciplinary field, which leads to the publication of metrics with similar goals; different names and descriptions of their analytics often mask the similarity between two metrics that originated in different fields. Here, we study a set of graph metrics and compare their relative values and behaviors in an effort to survey their potential contributions to the spatial analysis of networks.

Comparing Multilevel Clustering Methods on Weighted Graphs : The Case of Worldwide Air Passenger Traffic 2000-2004

Specific properties emerge from the structure of large networks, such as that of worldwide air traffic, including a highly hierarchical node structure and multi-level small world sub-groups that strongly influence future dynamics. We have developed clustering methods to understand the form of these structures, to identify structural properties, and to evaluate the effects of these properties. Graph clustering methods are often constructed from different components: a metric, a clustering index, and a modularity measure to assess the quality of a clustering method. To understand the impact of each of these components on the clustering method, we explore and compare different combinations. These different combinations are used to compare multilevel clustering methods to delineate the effects of geographical distance, hubs, network densities, and bridges on worldwide air passenger traffic. The ultimate goal of this methodological research is to demonstrate evidence of combined effects in the development of an air traffic network. In fact, the network can be divided into different levels of âeurooecohesionâeuro, which can be qualified and measured by comparative studies (Newman, 2002; Guimera et al., 2005; Sales-Pardo et al., 2007).

Parts, places, and perspectives : a theory of spatial relations based an mereotopology and convexity

This thesis suggests to carry on the philosophical work begun in Casati's and Varzi's seminal book Parts and Places, by extending their general reflections on the basic formal structure of spatial representation beyond mereotopology and absolute location to the question of perspectives and perspective-dependent spatial relations. We show how, on the basis of a conceptual analysis of such notions as perspective and direction, a mereotopological theory with convexity can express perspectival spatial relations in a strictly qualitative framework. We start by introducing a particular mereotopological theory, AKGEMT, and argue that it constitutes an adequate core for a theory of spatial relations. Two features of AKGEMT are of particular importance: AKGEMT is an extensional mereotopology, implying that sameness of proper parts is a sufficient and necessary condition for identity, and it allows for (lower- dimensional) boundary elements in its domain of quantification. We then discuss an extension of AKGEMT, AKGEMTS, which results from the addition of a binary segment operator whose interpretation is that of a straight line segment between mereotopological points. Based on existing axiom systems in standard point-set topology, we propose an axiomatic characterisation of the segment operator and show that it is strong enough to sustain complex properties of a convexity predicate and a convex hull operator. We compare our segment-based characterisation of the convex hull to Cohn et al.'s axioms for the convex hull operator, arguing that our notion of convexity is significantly stronger. The discussion of AKGEMTS defines the background theory of spatial representation on which the developments in the second part of this thesis are built. The second part deals with perspectival spatial relations in two-dimensional space, i.e., such relations as those expressed by 'in front of, 'behind', 'to the left/right of, etc., and develops a qualitative formalism for perspectival relations within the framework of AKGEMTS. Two main claims are defended in part 2: That perspectival relations in two-dimensional space are four- place relations of the kind R(x, y, z, w), to be read as x is i?-related to y as z looks at w; and that these four-place structures can be satisfactorily expressed within the qualitative theory AKGEMTS. To defend these two claims, we start by arguing for a unified account of perspectival relations, thus rejecting the traditional distinction between 'relative' and 'intrinsic' perspectival relations. We present a formal theory of perspectival relations in the framework of AKGEMTS, deploying the idea that perspectival relations in two-dimensional space are four-place relations, having a locational and a perspectival part and show how this four-place structure leads to a unified framework of perspectival relations. Finally, we present a philosophical motivation to the idea that perspectival relations are four-place, cashing out the thesis that perspectives are vectorial properties and argue that vectorial properties are relations between spatial entities. Using Fine's notion of "qua objects" for an analysis of points of view, we show at last how our four-place approach to perspectival relations compares to more traditional understandings.

Structural covariance of superficial white matter in mild Alzheimer's disease compared to normal aging.

INTRODUCTION: Interindividual variations in regional structural properties covary across the brain, thus forming networks that change as a result of aging and accompanying neurological conditions. The alterations of superficial white matter (SWM) in Alzheimer's disease (AD) are of special interest, since they follow the AD-specific pattern characterized by the strongest neurodegeneration of the medial temporal lobe and association cortices. METHODS: Here, we present an SWM network analysis in comparison with SWM topography based on the myelin content quantified with magnetization transfer ratio (MTR) for 39 areas in each hemisphere in 15 AD patients and 15 controls. The networks are represented by graphs, in which nodes correspond to the areas, and edges denote statistical associations between them. RESULTS: In both groups, the networks were characterized by asymmetrically distributed edges (predominantly in the left hemisphere). The AD-related differences were also leftward. The edges lost due to AD tended to connect nodes in the temporal lobe to other lobes or nodes within or between the latter lobes. The newly gained edges were mostly confined to the temporal and paralimbic regions, which manifest demyelination of SWM already in mild AD. CONCLUSION: This pattern suggests that the AD pathological process coordinates SWM demyelination in the temporal and paralimbic regions, but not elsewhere. A comparison of the MTR maps with MTR-based networks shows that although, in general, the changes in network architecture in AD recapitulate the topography of (de)myelination, some aspects of structural covariance (including the interhemispheric asymmetry of networks) have no immediate reflection in the myelination pattern.

The evolution of helping and harming on graphs: the return of the inclusive fitness effect.

Evolutionary graph theory has been proposed as providing new fundamental rules for the evolution of co-operation and altruism. But how do these results relate to those of inclusive fitness theory? Here, we carry out a retrospective analysis of the models for the evolution of helping on graphs of Ohtsuki et al. [Nature (2006) 441, 502] and Ohtsuki & Nowak [Proc. R. Soc. Lond. Ser. B Biol. Sci (2006) 273, 2249]. We show that it is possible to translate evolutionary graph theory models into classical kin selection models without disturbing at all the mathematics describing the net effect of selection on helping. Model analysis further demonstrates that costly helping evolves on graphs through limited dispersal and overlapping generations. These two factors are well known to promote relatedness between interacting individuals in spatially structured populations. By allowing more than one individual to live at each node of the graph and by allowing interactions to vary with the distance between nodes, our inclusive fitness model allows us to consider a wider range of biological scenarios leading to the evolution of both helping and harming behaviours on graphs.

[(18)F]FDG-PET Standard Uptake Value as a Metabolic Predictor of Bone Marrow Response to Radiation: Impact on Acute and Late Hematological Toxicity in Cervical Cancer Patients Treated With Chemoradiation Therapy.

PURPOSE: To quantify the relationship between bone marrow (BM) response to radiation and radiation dose by using (18)F-labeled fluorodeoxyglucose positron emission tomography [(18)F]FDG-PET standard uptake values (SUV) and to correlate these findings with hematological toxicity (HT) in cervical cancer (CC) patients treated with chemoradiation therapy (CRT). METHODS AND MATERIALS: Seventeen women with a diagnosis of CC were treated with standard doses of CRT. All patients underwent pre- and post-therapy [(18)F]FDG-PET/computed tomography (CT). Hemograms were obtained before and during treatment and 3 months after treatment and at last follow-up. Pelvic bone was autosegmented as total bone marrow (BMTOT). Active bone marrow (BMACT) was contoured based on SUV greater than the mean SUV of BMTOT. The volumes (V) of each region receiving 10, 20, 30, and 40 Gy (V10, V20, V30, and V40, respectively) were calculated. Metabolic volume histograms and voxel SUV map response graphs were created. Relative changes in SUV before and after therapy were calculated by separating SUV voxels into radiation therapy dose ranges of 5 Gy. The relationships among SUV decrease, radiation dose, and HT were investigated using multiple regression models. RESULTS: Mean relative pre-post-therapy SUV reductions in BMTOT and BMACT were 27% and 38%, respectively. BMACT volume was significantly reduced after treatment (from 651.5 to 231.6 cm(3), respectively; P<.0001). BMACT V30 was significantly correlated with a reduction in BMACT SUV (R(2), 0.14; P<.001). The reduction in BMACT SUV significantly correlated with reduction in white blood cells (WBCs) at 3 months post-treatment (R(2), 0.27; P=.04) and at last follow-up (R(2), 0.25; P=.04). Different dosimetric parameters of BMTOT and BMACT correlated with long-term hematological outcome. CONCLUSIONS: The volumes of BMTOT and BMACT that are exposed to even relatively low doses of radiation are associated with a decrease in WBC counts following CRT. The loss in proliferative BM SUV uptake translates into low WBC nadirs after treatment. These results suggest the potential of intensity modulated radiation therapy to spare BMTOT to reduce long-term hematological toxicity.

Kernel-based mapping of orographic rainfall enhancement in the Swiss Alps as detected by weatherradar

In this paper, we develop a data-driven methodology to characterize the likelihood of orographic precipitation enhancement using sequences of weather radar images and a digital elevation model (DEM). Geographical locations with topographic characteristics favorable to enforce repeatable and persistent orographic precipitation such as stationary cells, upslope rainfall enhancement, and repeated convective initiation are detected by analyzing the spatial distribution of a set of precipitation cells extracted from radar imagery. Topographic features such as terrain convexity and gradients computed from the DEM at multiple spatial scales as well as velocity fields estimated from sequences of weather radar images are used as explanatory factors to describe the occurrence of localized precipitation enhancement. The latter is represented as a binary process by defining a threshold on the number of cell occurrences at particular locations. Both two-class and one-class support vector machine classifiers are tested to separate the presumed orographic cells from the nonorographic ones in the space of contributing topographic and flow features. Site-based validation is carried out to estimate realistic generalization skills of the obtained spatial prediction models. Due to the high class separability, the decision function of the classifiers can be interpreted as a likelihood or susceptibility of orographic precipitation enhancement. The developed approach can serve as a basis for refining radar-based quantitative precipitation estimates and short-term forecasts or for generating stochastic precipitation ensembles conditioned on the local topography.

Extreme prematurity and intra uterine growth restriction effects in brain network topology at school age

Higher risk for long-term behavioral and emotional sequelae, with attentional problems (with or without hyperactivity) is now becoming one of the hallmarks of extreme premature (EP) birth and birth after pregancy conditions leading to poor intra uterine growth restriction (IUGR) [1,2]. However, little is know so far about the neurostructural basis of these complexe brain functional abnormalities that seem to have their origins in early critical periods of brain development. The development of cortical axonal pathways happens in a series of sequential events. The preterm phase (24-36 post conecptional weeks PCW) is known for being crucial for growth of the thalamocortical fiber bundles as well as for the development of long projectional, commisural and projectional fibers [3]. Is it logical to expect, thus, that being exposed to altered intrauterine environment (altered nutrition) or to extrauterine environment earlier that expected, lead to alterations in the structural organization and, consequently, alter the underlying white matter (WM) structure. Understanding rate and variability of normal brain development, and detect differences from typical development may offer insight into the neurodevelopmental anomalies that can be imaged at later stages. Due to its unique ability to non-invasively visualize and quantify in vivo white matter tracts in the brain, in this study we used diffusion MRI (dMRI) tractography to derive brain graphs [4,5,6]. This relatively simple way of modeling the brain enable us to use graph theory to study topological properties of brain graphs in order to study the effects of EP and IUGR on childrens brain connectivity at age 6 years old.

Spatial prediction of monthly wind speeds in complex terrain with adaptive general regression neural networks

This paper presents the general regression neural networks (GRNN) as a nonlinear regression method for the interpolation of monthly wind speeds in complex Alpine orography. GRNN is trained using data coming from Swiss meteorological networks to learn the statistical relationship between topographic features and wind speed. The terrain convexity, slope and exposure are considered by extracting features from the digital elevation model at different spatial scales using specialised convolution filters. A database of gridded monthly wind speeds is then constructed by applying GRNN in prediction mode during the period 1968-2008. This study demonstrates that using topographic features as inputs in GRNN significantly reduces cross-validation errors with respect to low-dimensional models integrating only geographical coordinates and terrain height for the interpolation of wind speed. The spatial predictability of wind speed is found to be lower in summer than in winter due to more complex and weaker wind-topography relationships. The relevance of these relationships is studied using an adaptive version of the GRNN algorithm which allows to select the useful terrain features by eliminating the noisy ones. This research provides a framework for extending the low-dimensional interpolation models to high-dimensional spaces by integrating additional features accounting for the topographic conditions at multiple spatial scales. Copyright (c) 2012 Royal Meteorological Society.

From bird to sparrow: Learning-induced modulations in fine-grained semantic discrimination.

Recognition of environmental sounds is believed to proceed through discrimination steps from broad to more narrow categories. Very little is known about the neural processes that underlie fine-grained discrimination within narrow categories or about their plasticity in relation to newly acquired expertise. We investigated how the cortical representation of birdsongs is modulated by brief training to recognize individual species. During a 60-minute session, participants learned to recognize a set of birdsongs; they improved significantly their performance for trained (T) but not control species (C), which were counterbalanced across participants. Auditory evoked potentials (AEPs) were recorded during pre- and post-training sessions. Pre vs. post changes in AEPs were significantly different between T and C i) at 206-232ms post stimulus onset within a cluster on the anterior part of the left superior temporal gyrus; ii) at 246-291ms in the left middle frontal gyrus; and iii) 512-545ms in the left middle temporal gyrus as well as bilaterally in the cingulate cortex. All effects were driven by weaker activity for T than C species. Thus, expertise in discriminating T species modulated early stages of semantic processing, during and immediately after the time window that sustains the discrimination between human vs. animal vocalizations. Moreover, the training-induced plasticity is reflected by the sharpening of a left lateralized semantic network, including the anterior part of the temporal convexity and the frontal cortex. Training to identify birdsongs influenced, however, also the processing of C species, but at a much later stage. Correct discrimination of untrained sounds seems to require an additional step which results from lower-level features analysis such as apperception. We therefore suggest that the access to objects within an auditory semantic category is different and depends on subject's level of expertise. More specifically, correct intra-categorical auditory discrimination for untrained items follows the temporal hierarchy and transpires in a late stage of semantic processing. On the other hand, correct categorization of individually trained stimuli occurs earlier, during a period contemporaneous with human vs. animal vocalization discrimination, and involves a parallel semantic pathway requiring expertise.

Timing History: The Introduction of Graphical Analysis in 19th Century British Economics

The introduction of time-series graphs into British economics in the 19th century depended on the « timing » of history. This involved reconceptualizing history into events which were both comparable and measurable and standardized by time unit. Yet classical economists in Britain in the early 19th century viewed history as a set of heterogenous and complex events and statistical tables as giving unrelated facts. Both these attitudes had to be broken down before time-series graphs could be brought into use for revealing regularities in economic events by the century's end.