Mathematical study of complex networks : brain, internet, and power grid

The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored, which are motivated by power systems. The first one is “flow optimization over a flow network” and the second one is “nonlinear optimization over a generalized weighted graph”. The results derived in this dissertation are summarized below.

Brain Networks: Neuroimaging data reveals the coordinated activity of spatially distinct brain regions, which may be represented mathematically as a network of nodes (brain regions) and links (interdependencies). To obtain the brain connectivity network, the graphs associated with the correlation matrix and the inverse covariance matrix—describing marginal and conditional dependencies between brain regions—have been proposed in the literature. A question arises as to whether any of these graphs provides useful information about the brain connectivity. Due to the electrical properties of the brain, this problem will be investigated in the context of electrical circuits. First, we consider an electric circuit model and show that the inverse covariance matrix of the node voltages reveals the topology of the circuit. Second, we study the problem of finding the topology of the circuit based on only measurement. In this case, by assuming that the circuit is hidden inside a black box and only the nodal signals are available for measurement, the aim is to find the topology of the circuit when a limited number of samples are available. For this purpose, we deploy the graphical lasso technique to estimate a sparse inverse covariance matrix. It is shown that the graphical lasso may find most of the circuit topology if the exact covariance matrix is well-conditioned. However, it may fail to work well when this matrix is ill-conditioned. To deal with ill-conditioned matrices, we propose a small modification to the graphical lasso algorithm and demonstrate its performance. Finally, the technique developed in this work will be applied to the resting-state fMRI data of a number of healthy subjects.

Communication Networks: Congestion control techniques aim to adjust the transmission rates of competing users in the Internet in such a way that the network resources are shared efficiently. Despite the progress in the analysis and synthesis of the Internet congestion control, almost all existing fluid models of congestion control assume that every link in the path of a flow observes the original source rate. To address this issue, a more accurate model is derived in this work for the behavior of the network under an arbitrary congestion controller, which takes into account of the effect of buffering (queueing) on data flows. Using this model, it is proved that the well-known Internet congestion control algorithms may no longer be stable for the common pricing schemes, unless a sufficient condition is satisfied. It is also shown that these algorithms are guaranteed to be stable if a new pricing mechanism is used.

Electrical Power Networks: Optimal power flow (OPF) has been one of the most studied problems for power systems since its introduction by Carpentier in 1962. This problem is concerned with finding an optimal operating point of a power network minimizing the total power generation cost subject to network and physical constraints. It is well known that OPF is computationally hard to solve due to the nonlinear interrelation among the optimization variables. The objective is to identify a large class of networks over which every OPF problem can be solved in polynomial time. To this end, a convex relaxation is proposed, which solves the OPF problem exactly for every radial network and every meshed network with a sufficient number of phase shifters, provided power over-delivery is allowed. The concept of “power over-delivery” is equivalent to relaxing the power balance equations to inequality constraints.

Flow Networks: In this part of the dissertation, the minimum-cost flow problem over an arbitrary flow network is considered. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which always finds the optimal injections. A primary application of this work is in the OPF problem. The results of this work on GNF prove that the relaxation on power balance equations (i.e., load over-delivery) is not needed in practice under a very mild angle assumption.

Generalized Weighted Graphs: Motivated by power optimizations, this part aims to find a global optimization technique for a nonlinear optimization defined over a generalized weighted graph. Every edge of this type of graph is associated with a weight set corresponding to the known parameters of the optimization (e.g., the coefficients). The motivation behind this problem is to investigate how the (hidden) structure of a given real/complex valued optimization makes the problem easy to solve, and indeed the generalized weighted graph is introduced to capture the structure of an optimization. Various sufficient conditions are derived, which relate the polynomial-time solvability of different classes of optimization problems to weak properties of the generalized weighted graph such as its topology and the sign definiteness of its weight sets. As an application, it is proved that a broad class of real and complex optimizations over power networks are polynomial-time solvable due to the passivity of transmission lines and transformers.

Identification of fucose-α(1-2)-galactose binding proteins in the mammalian brain

Fucose-α(1-2)-galactose (Fucα(1-2)Gal) carbohydrates have been implicated in cognitive functions. However, the underlying molecular mechanisms that govern these processes are not well understood. While significant progress has been made toward identifying glycoconjugates bearing this carbohydrate epitope, a major challenge remains the discovery of interactions mediated by these sugars. Here, we employ the use of multivalent glycopolymers to enable the proteomic identification of weak affinity, low abundant Fucα(1-2)Gal-binding proteins (i.e. lectins) from the brain. End-biotinylated glycopolymers containing photoactivatable crosslinkers were used to capture and enrich potential Fucα(1-2)Gal-specific lectins from rat brain lysates. Candidate lectins were tested for their ability to bind Fucα(1-2)Gal, and the functional significance of the interaction was investigated for one such candidate, SV2a, using a knock-out mouse system. Our results suggest an important role for this glycan-lectin interaction in facilitating synaptic changes necessary for neuronal communication. This study highlights the use of glycopolymer mimetics to discover novel lectins and identify functional interactions between fucosyl carbohydrates and lectins in the brain.

Flood circulation in oligomictic lakes: an undervalued reason for restriction of zooplankton production [Translation from: Memorie dell'Istituto Italiano di Idrobiologia Dott.Marco de Marchi 22 9-52, 1967]

Dormancy has been observed in several species of Cyclops. Animals in dormancy are characterised by almost complete inactivity of the main appendages and sluggish intestinal peristalsis. In Cyclops vicinus dormancy can take place in copepod stages III (19%), IV (78%) and V (3%) but one and the same animal only in one developmental stage. The author gives his own results between frequency of dormancy and photoperiod (20 C, 1000 lux). He concludes that dormancy in C. vicinus can be influenced by day length and can be ended prematurely by short day length.

Delivery of Targeted Nanoparticles Across the Blood-Brain Barrier Using a Detachable Targeting Ligand

Chronic diseases of the central nervous system are poorly treated due to the inability of most therapeutics to cross the blood-brain barrier. The blood-brain barrier is an anatomical and physiological barrier that severely restricts solute influx, including most drugs, from the blood to the brain. One promising method to overcome this obstacle is to use endogenous solute influx systems at the blood-brain barrier to transport drugs. Therapeutics designed to enter the brain through transcytosis by binding the transferrin receptor, however, are restricted within endothelial cells. The focus of this work was to develop a method to increase uptake of transferrin-containing nanoparticles into the brain by overcoming these restrictive processes.

To accomplish this goal, nanoparticles were prepared with surface transferrin molecules bound through various liable chemical bonds. These nanoparticles were designed to shed the targeting molecule during transcytosis to allow increased accumulation of nanoparticles within the brain.

Transferrin was added to the surface of nanoparticles through either redox or pH sensitive chemistry. First, nanoparticles with transferrin bound through disulfide bonds were prepared. These nanoparticles showed decreased avidity for the transferrin receptor after exposure to reducing agents and increased ability to enter the brain in vivo compared to those lacking the disulfide link.

Next, transferrin was attached through a chemical bond that cleaves at mildly acidic pH. Nanoparticles containing a cleavable link between transferrin and gold nanoparticle cores were found to both cross an in vitro model of the blood-brain barrier and accumulate within the brain in significantly higher numbers than similar nanoparticles lacking the cleavable bond. Also, this increased accumulation was not seen when using this same strategy with an antibody to transferrin receptor, indicating that behavior of nanoparticles at the blood-brain barrier varies depending on what type of targeting ligand is used.

Finally, polymeric nanoparticles loaded with dopamine and utilizing a superior acid-cleavable targeting chemistry were investigated as a potential treatment for Parkinson’s disease. These nanoparticles were capable of increasing dopamine quantities in the brains of healthy mice, highlighting the therapeutic potential of this design. Overall, this work describes a novel method to increase targeted nanoparticle accumulation in the brain.

Never-resting microglia: physiological roles in the healthy brain and pathological implications

Microglia are largely known as the major orchestrators of the brain inflammatory response. As such, they have been traditionally studied in various contexts of disease, where their activation has been assumed to induce a wide range of detrimental effects. In the last few years, a series of discoveries have challenged the current view of microglia, showing their active and positive contribution to normal brain function. This Research Topic will review the novel physiological roles of microglia in the developing, mature and aging brain, under non-pathological conditions. In particular, this Research Topic will discuss the cellular and molecular mechanisms by which microglia contribute to the formation, pruning and plasticity of synapses; the maintenance of the blood brain barrier; the regulation of adult neurogenesis and hippocampal learning; and neuronal survival, among other important roles. Because these novel findings defy our understanding of microglial function in health as much as in disease, this Research Topic will also summarize the current view of microglial nomenclature, phenotypes, origin and differentiation, sex differences, and contribution to various brain pathologies. Additionally, novel imaging approaches and molecular tools to study microglia in their non-activated state will be discussed. In conclusion, this Research Topic seeks to emphasize how the current research in neuroscience is challenged by never-resting microglia.

Cytokine pathway disruption in a mouse model of schizophrenia induced by Munc18-1a overexpression in the brain

Background: An accumulating body of evidence points to the significance of neuroinflammation and immunogenetics in schizophrenia, and an imbalance of cytokines in the central nervous system (CNS) has been suggested to be associated with the disorder. Munc18-overexpressing mice (Munc18-OE) have provided a model for the study of the alterations that may underlie the symptoms of subjects with schizophrenia. The aim of the present study was to elucidate the involvement of neuroinflammation and cytokine imbalance in this model. Methods: Cytokines were evaluated in the cortex and the striatum of Munc18-OE and wild-type (WT) mice by enzyme-linked immunosorbent assay (ELISA). Protein levels of specific microglia and macrophage, astrocytic and neuroinflammation markers were quantified by western blot in the cortex and the striatum of Munc18-OE and WT mice. Results: Each cytokine evaluated (Interferon-gamma (IFN-gamma), Tumor Necrosis Factor-alpha (TNF-alpha), Interleukin-2 (IL-2) and CCL2 chemokine) was present at higher levels in the striatum of Munc18-OE mice than WT. Cortical TNF-alpha and IL-2 levels were significantly lower in Munc18-OE mice than WT mice. The microglia and macrophage marker CD11b was lower in the cortexes of Munc18-OE mice than WT, but no differences were observed in the striatum. Glial Fibrillary Acidic Protein (GFAP) and Nuclear Factor-kappaB (NF-kappa B)p65 levels were not different between the groups. Interleukin-1beta (IL-1 beta) and IL-6 levels were beneath detection limits. Conclusions: The disrupted levels of cytokines detected in the brain of Munc18-OE mice was found to be similar to clinical reports and endorses study of this type for analysis of this aspect of the disorder. The lower CD11b expression in the cortex but not in the striatum of the Munc18-OE mice may reflect differences in physiological activity. The cytokine expression pattern observed in Munc18-OE mice is similar to a previously published model of schizophrenia caused by maternal immune activation. Together, these data suggest a possible role for an immune imbalance in this disorder.

Altered expression of Alzheimer's disease-related genes in the cerebellum of autistic patients: a model for disrupted brain connectome and therapy

Autism and Alzheimer's disease (AD) are, respectively, neurodevelopmental and degenerative diseases with an increasing epidemiological burden. The AD-associated amyloid-beta precursor protein-alpha has been shown to be elevated in severe autism, leading to the 'anabolic hypothesis' of its etiology. Here we performed a focused microarray analysis of genes belonging to NOTCH and WNT signaling cascades, as well as genes related to AD and apoptosis pathways in cerebellar samples from autistic individuals, to provide further evidence for pathological relevance of these cascades for autism. By using the limma package from R and false discovery rate, we demonstrated that 31% (116 out of 374) of the genes belonging to these pathways displayed significant changes in expression (corrected P-values <0.05), with mitochondria- related genes being the most downregulated. We also found upregulation of GRIN1, the channel-forming subunit of NMDA glutamate receptors, and MAP3K1, known activator of the JNK and ERK pathways with anti-apoptotic effect. Expression of PSEN2 (presinilin 2) and APBB1 (or F65) were significantly lower when compared with control samples. Based on these results, we propose a model of NMDA glutamate receptor-mediated ERK activation of alpha-secretase activity and mitochondrial adaptation to apoptosis that may explain the early brain overgrowth and disruption of synaptic plasticity and connectome in autism. Finally, systems pharmacology analyses of the model that integrates all these genes together (NOWADA) highlighted magnesium (Mg2+) and rapamycin as most efficient drugs to target this network model in silico. Their potential therapeutic application, in the context of autism, is therefore discussed.

Incidences de la modification de la circulation des eaux sur l'hydrochimie et le degré de contamination bacterienne d'un estuaire eutrophe tropical

In order to control the proliferation of floating aquatic vegetation in Côte d'Ivoire, a coastal inlet, allowing a direct communication between the Comoe river and the ocean, was created in September 1987. The impact of this operation on the hydrochemistry (salinity, nutrients, algal biomass) and the bacterial contamination level was studied in the area close to the Vridi canal.

La circulation superficielle dans la partie occidentale du Golfe de Guinée

Direct current measurements carried out for 10 years in the Gulf of Guinea clearly show the importance of transverse circulation. The general pattern of currents is characterized by an anticyclonic gyre. The seasonal variations of this circulation are calculated through the study of the 3-monthly averaged geostrophic currents. The biological consequences of such a circulation are outlined.

Alcohol-Related Brain Damage in Humans

Chronic excessive alcohol intoxications evoke cumulative damage to tissues and organs. We examined prefrontal cortex (Brodmann's area (BA) 9) from 20 human alcoholics and 20 age, gender, and postmortem delay matched control subjects. H & E staining and light microscopy of prefrontal cortex tissue revealed a reduction in the levels of cytoskeleton surrounding the nuclei of cortical and subcortical neurons, and a disruption of subcortical neuron patterning in alcoholic subjects. BA 9 tissue homogenisation and one dimensional polyacrylamide gel electrophoresis (PAGE) proteomics of cytosolic proteins identified dramatic reductions in the protein levels of spectrin beta II, and alpha- and beta-tubulins in alcoholics, and these were validated and quantitated by Western blotting. We detected a significant increase in a-tubulin acetylation in alcoholics, a non-significant increase in isoaspartate protein damage, but a significant increase in protein isoaspartyl methyltransferase protein levels, the enzyme that triggers isoaspartate damage repair in vivo. There was also a significant reduction in proteasome activity in alcoholics. One dimensional PAGE of membrane-enriched fractions detected a reduction in beta-spectrin protein levels, and a significant increase in transmembranous alpha 3 (catalytic) subunit of the Na+, K+-ATPase in alcoholic subjects. However, control subjects retained stable oligomeric forms of a-subunit that were diminished in alcoholics. In alcoholics, significant loss of cytosolic alpha-and beta-tubulins were also seen in caudate nucleus, hippocampus and cerebellum, but to different levels, indicative of brain regional susceptibility to alcohol-related damage. Collectively, these protein changes provide a molecular basis for some of the neuronal and behavioural abnormalities attributed to alcoholics

Circulation dans la partie orientale de l'Atlantique sud

The authors studied the circulation in the South Tropical Atlantic from hydrology and current measurements made during a cruise of the N.O. Capricorne in Nov 1971. Direct current measurements confirm the existence of the eastwards South Equatorial Counter-Current. The authors discuss the counter-current as confirmed by current measurements and high salinity core.

Variabilité, circulation et chlorophylle dans la région du Dôme d'Angola en février-mars 1971

In February-March 1971 the hydrological conditions off Angola did not display the thermal dome mapped by Mazeika's averages (1967). Cold water cells observed are connected at the surface to a sinuous boundary between low-salinity coastal waters and high-salinity tropical oceanic waters. That boundary coincides rather regularly with an area where trades and SW winds alternate; photosynthesis growths rapidly in a thermoclinal layer that rises until 10 m of the surface but never outcrops. Below a poor and permanent homogeneous surface layer, chlorophyll concentrations show a distribution which is typical of divergence areas. Geostrophical and measured currents show off a transient process in horizontal and vertical movements, however the general curvature of the circulation is propitious to upwelling. Oxygen oversaturations of about 110%, suggest a moderate potential primary production which confirms slowness and alternation of movements. Also, the regular range of the various chemical and biological levels and moderate chlorophyll concentrations suggest an ecosystem where nutrients supply rapidly equilibrate phytoplankton consumption and not at all a 'phytoplankton bloom' area as that which exists in coastal upwelling. Values of Richardson's number show that instability becomes visible at the bottom of the euphotic layer. An evaluation of the vertical motion is inferred by the peculiar distribution and diurnal alternance of the winds shows that 'doming' structures may be sustained by local meteorological events.

Neuroprotective effects of resveratrol and docosahexaenoic acid antioxidants in perinatal hypoxic-ischemic brain injury in rats

295 p.

Hóspedes do Profeta sem Morada: estudo sobre modos de subjetivação da migração, a partir das experiências de estudantes de pós-graduação participantes de programas de intercâmbio internacional

Este trabalho problematiza a experiência migratória do estudante de pós-graduação participante de programas de intercâmbio internacional, entendendo que este é um trabalhador cognitivo que sofre a extração de sua força de trabalho segundo os mesmos padrões sofridos pelos demais trabalhadores, regulado pela universidade que tem sido atravessada por uma lógica administrativa repleta de imperativos de normatizações, padrões de eficiência e modelos bem-sucedidos. A partir da articulação entre a Análise Institucional, Filosofia da Diferença e Autonomia das Migrações, discute analisadores que atravessam a formação, como o efeito lattes, que incita o produtivismo; a tara contemporânea que nos impele a um estado permanente de formação; o aumento de programas de intercâmbio internacional, que tornam-se mais uma griffe em busca do status de excelência, e o processo de êxodo de cérebros, caracterizado pela migração de trabalhadores qualificados que não encontram, em suas cidades ou países, oportunidades para canalizar sua qualificação. Estes processos são analisadores de uma política que incita o processo de circulação, e também a delimita e a esquadrinha, como pode ser percebido pelas experiências dos sete estudantes que compuseram as travessias em estudo, cujos vestígios deixados pelos fragmentos das histórias/ modos de funcionamento encarnaram os personagens conceituais, conforme Deleuze. As experiências de intercâmbio internacional exprimem o mais alto grau da exigência do atual modo de subjetivação acadêmico por sua característica de se dar como longa imersão e em país estranho capaz de graves efeitos positivos e negativos em sua subjetivação, denotando que o paradoxo e o sofrimento são constitutivos da migração e da formação.