Towards robust network based complex systems : from evolutionary cellular automata to biological models

Abstract Sitting between your past and your future doesn't mean you are in the present. Dakota Skye Complex systems science is an interdisciplinary field grouping under the same umbrella dynamical phenomena from social, natural or mathematical sciences. The emergence of a higher order organization or behavior, transcending that expected of the linear addition of the parts, is a key factor shared by all these systems. Most complex systems can be modeled as networks that represent the interactions amongst the system's components. In addition to the actual nature of the part's interactions, the intrinsic topological structure of underlying network is believed to play a crucial role in the remarkable emergent behaviors exhibited by the systems. Moreover, the topology is also a key a factor to explain the extraordinary flexibility and resilience to perturbations when applied to transmission and diffusion phenomena. In this work, we study the effect of different network structures on the performance and on the fault tolerance of systems in two different contexts. In the first part, we study cellular automata, which are a simple paradigm for distributed computation. Cellular automata are made of basic Boolean computational units, the cells; relying on simple rules and information from- the surrounding cells to perform a global task. The limited visibility of the cells can be modeled as a network, where interactions amongst cells are governed by an underlying structure, usually a regular one. In order to increase the performance of cellular automata, we chose to change its topology. We applied computational principles inspired by Darwinian evolution, called evolutionary algorithms, to alter the system's topological structure starting from either a regular or a random one. The outcome is remarkable, as the resulting topologies find themselves sharing properties of both regular and random network, and display similitudes Watts-Strogtz's small-world network found in social systems. Moreover, the performance and tolerance to probabilistic faults of our small-world like cellular automata surpasses that of regular ones. In the second part, we use the context of biological genetic regulatory networks and, in particular, Kauffman's random Boolean networks model. In some ways, this model is close to cellular automata, although is not expected to perform any task. Instead, it simulates the time-evolution of genetic regulation within living organisms under strict conditions. The original model, though very attractive by it's simplicity, suffered from important shortcomings unveiled by the recent advances in genetics and biology. We propose to use these new discoveries to improve the original model. Firstly, we have used artificial topologies believed to be closer to that of gene regulatory networks. We have also studied actual biological organisms, and used parts of their genetic regulatory networks in our models. Secondly, we have addressed the improbable full synchronicity of the event taking place on. Boolean networks and proposed a more biologically plausible cascading scheme. Finally, we tackled the actual Boolean functions of the model, i.e. the specifics of how genes activate according to the activity of upstream genes, and presented a new update function that takes into account the actual promoting and repressing effects of one gene on another. Our improved models demonstrate the expected, biologically sound, behavior of previous GRN model, yet with superior resistance to perturbations. We believe they are one step closer to the biological reality.

FAM161A, associated with retinitis pigmentosa, is a component of the cilia-basal body complex and interacts with proteins involved in ciliopathies.

Retinitis pigmentosa (RP) is a retinal degenerative disease characterized by the progressive loss of photoreceptors. We have previously demonstrated that RP can be caused by recessive mutations in the human FAM161A gene, encoding a protein with unknown function that contains a conserved region shared only with a distant paralog, FAM161B. In this study, we show that FAM161A localizes at the base of the photoreceptor connecting cilium in human, mouse and rat. Furthermore, it is also present at the ciliary basal body in ciliated mammalian cells, both in native conditions and upon the expression of recombinant tagged proteins. Yeast two-hybrid analysis of binary interactions between FAM161A and an array of ciliary and ciliopathy-associated proteins reveals direct interaction with lebercilin, CEP290, OFD1 and SDCCAG8, all involved in hereditary retinal degeneration. These interactions are mediated by the C-terminal moiety of FAM161A, as demonstrated by pull-down experiments in cultured cell lines and in bovine retinal extracts. As other ciliary proteins, FAM161A can also interact with the microtubules and organize itself into microtubule-dependent intracellular networks. Moreover, small interfering RNA-mediated depletion of FAM161A transcripts in cultured cells causes the reduction in assembled primary cilia. Taken together, these data indicate that FAM161A-associated RP can be considered as a novel retinal ciliopathy and that its molecular pathogenesis may be related to other ciliopathies.

Resting-state temporal synchronization networks emerge from connectivity topology and heterogeneity.

Spatial patterns of coherent activity across different brain areas have been identified during the resting-state fluctuations of the brain. However, recent studies indicate that resting-state activity is not stationary, but shows complex temporal dynamics. We were interested in the spatiotemporal dynamics of the phase interactions among resting-state fMRI BOLD signals from human subjects. We found that the global phase synchrony of the BOLD signals evolves on a characteristic ultra-slow (<0.01Hz) time scale, and that its temporal variations reflect the transient formation and dissolution of multiple communities of synchronized brain regions. Synchronized communities reoccurred intermittently in time and across scanning sessions. We found that the synchronization communities relate to previously defined functional networks known to be engaged in sensory-motor or cognitive function, called resting-state networks (RSNs), including the default mode network, the somato-motor network, the visual network, the auditory network, the cognitive control networks, the self-referential network, and combinations of these and other RSNs. We studied the mechanism originating the observed spatiotemporal synchronization dynamics by using a network model of phase oscillators connected through the brain's anatomical connectivity estimated using diffusion imaging human data. The model consistently approximates the temporal and spatial synchronization patterns of the empirical data, and reveals that multiple clusters that transiently synchronize and desynchronize emerge from the complex topology of anatomical connections, provided that oscillators are heterogeneous.

Regional deterministic characterization of fracture networks and its application to GIS-based rock fall risk assessment

The study investigates the possibility to incorporate fracture intensity and block geometry as spatially continuous parameters in GIS-based systems. For this purpose, a deterministic method has been implemented to estimate block size (Bloc3D) and joint frequency (COLTOP). In addition to measuring the block size, the Bloc3D Method provides a 3D representation of the shape of individual blocks. These two methods were applied using field measurements (joint set orientation and spacing) performed over a large field area, in the Swiss Alps. This area is characterized by a complex geology, a number of different rock masses and varying degrees of metamorphism. The spatial variability of the parameters was evaluated with regard to lithology and major faults. A model incorporating these measurements and observations into a GIS system to assess the risk associated with rock falls is proposed. The analysis concludes with a discussion on the feasibility of such an application in regularly and irregularly jointed rock masses, with persistent and impersistent discontinuities.

Complex formation by the human RAD51C and XRCC3 recombination repair proteins.

In vertebrates, the RAD51 protein is required for genetic recombination, DNA repair, and cellular proliferation. Five paralogs of RAD51, known as RAD51B, RAD51C, RAD51D, XRCC2, and XRCC3, have been identified and also shown to be required for recombination and genome stability. At the present time, however, very little is known about their biochemical properties or precise biological functions. As a first step toward understanding the roles of the RAD51 paralogs in recombination, the human RAD51C and XRCC3 proteins were overexpressed and purified from baculovirus-infected insect cells. The two proteins copurify as a complex, a property that reflects their endogenous association observed in HeLa cells. Purified RAD51C--XRCC3 complex binds single-stranded, but not duplex DNA, to form protein--DNA networks that have been visualized by electron microscopy.

Kernel-based Mapping of Meteorological Fields in Complex Orography

Due to the advances in sensor networks and remote sensing technologies, the acquisition and storage rates of meteorological and climatological data increases every day and ask for novel and efficient processing algorithms. A fundamental problem of data analysis and modeling is the spatial prediction of meteorological variables in complex orography, which serves among others to extended climatological analyses, for the assimilation of data into numerical weather prediction models, for preparing inputs to hydrological models and for real time monitoring and short-term forecasting of weather.In this thesis, a new framework for spatial estimation is proposed by taking advantage of a class of algorithms emerging from the statistical learning theory. Nonparametric kernel-based methods for nonlinear data classification, regression and target detection, known as support vector machines (SVM), are adapted for mapping of meteorological variables in complex orography.With the advent of high resolution digital elevation models, the field of spatial prediction met new horizons. In fact, by exploiting image processing tools along with physical heuristics, an incredible number of terrain features which account for the topographic conditions at multiple spatial scales can be extracted. Such features are highly relevant for the mapping of meteorological variables because they control a considerable part of the spatial variability of meteorological fields in the complex Alpine orography. For instance, patterns of orographic rainfall, wind speed and cold air pools are known to be correlated with particular terrain forms, e.g. convex/concave surfaces and upwind sides of mountain slopes.Kernel-based methods are employed to learn the nonlinear statistical dependence which links the multidimensional space of geographical and topographic explanatory variables to the variable of interest, that is the wind speed as measured at the weather stations or the occurrence of orographic rainfall patterns as extracted from sequences of radar images. Compared to low dimensional models integrating only the geographical coordinates, the proposed framework opens a way to regionalize meteorological variables which are multidimensional in nature and rarely show spatial auto-correlation in the original space making the use of classical geostatistics tangled.The challenges which are explored during the thesis are manifolds. First, the complexity of models is optimized to impose appropriate smoothness properties and reduce the impact of noisy measurements. Secondly, a multiple kernel extension of SVM is considered to select the multiscale features which explain most of the spatial variability of wind speed. Then, SVM target detection methods are implemented to describe the orographic conditions which cause persistent and stationary rainfall patterns. Finally, the optimal splitting of the data is studied to estimate realistic performances and confidence intervals characterizing the uncertainty of predictions.The resulting maps of average wind speeds find applications within renewable resources assessment and opens a route to decrease the temporal scale of analysis to meet hydrological requirements. Furthermore, the maps depicting the susceptibility to orographic rainfall enhancement can be used to improve current radar-based quantitative precipitation estimation and forecasting systems and to generate stochastic ensembles of precipitation fields conditioned upon the orography.

Bayesian Networks and the Value of the Evidence for the Forensic Two-Trace Transfer Problem

Forensic scientists face increasingly complex inference problems for evaluating likelihood ratios (LRs) for an appropriate pair of propositions. Up to now, scientists and statisticians have derived LR formulae using an algebraic approach. However, this approach reaches its limits when addressing cases with an increasing number of variables and dependence relationships between these variables. In this study, we suggest using a graphical approach, based on the construction of Bayesian networks (BNs). We first construct a BN that captures the problem, and then deduce the expression for calculating the LR from this model to compare it with existing LR formulae. We illustrate this idea by applying it to the evaluation of an activity level LR in the context of the two-trace transfer problem. Our approach allows us to relax assumptions made in previous LR developments, produce a new LR formula for the two-trace transfer problem and generalize this scenario to n traces.

Implicit methods for qualitative modeling of gene regulatory networks.

Advancements in high-throughput technologies to measure increasingly complex biological phenomena at the genomic level are rapidly changing the face of biological research from the single-gene single-protein experimental approach to studying the behavior of a gene in the context of the entire genome (and proteome). This shift in research methodologies has resulted in a new field of network biology that deals with modeling cellular behavior in terms of network structures such as signaling pathways and gene regulatory networks. In these networks, different biological entities such as genes, proteins, and metabolites interact with each other, giving rise to a dynamical system. Even though there exists a mature field of dynamical systems theory to model such network structures, some technical challenges are unique to biology such as the inability to measure precise kinetic information on gene-gene or gene-protein interactions and the need to model increasingly large networks comprising thousands of nodes. These challenges have renewed interest in developing new computational techniques for modeling complex biological systems. This chapter presents a modeling framework based on Boolean algebra and finite-state machines that are reminiscent of the approach used for digital circuit synthesis and simulation in the field of very-large-scale integration (VLSI). The proposed formalism enables a common mathematical framework to develop computational techniques for modeling different aspects of the regulatory networks such as steady-state behavior, stochasticity, and gene perturbation experiments.

Tissue-specific regulatory circuits reveal variable modular perturbations across complex diseases.

Mapping perturbed molecular circuits that underlie complex diseases remains a great challenge. We developed a comprehensive resource of 394 cell type- and tissue-specific gene regulatory networks for human, each specifying the genome-wide connectivity among transcription factors, enhancers, promoters and genes. Integration with 37 genome-wide association studies (GWASs) showed that disease-associated genetic variants-including variants that do not reach genome-wide significance-often perturb regulatory modules that are highly specific to disease-relevant cell types or tissues. Our resource opens the door to systematic analysis of regulatory programs across hundreds of human cell types and tissues (http://regulatorycircuits.org).

Automobile Corporate Networks in Europe : Sectoral Specialization of Central and Eastern European Cities

The global automobile industry is made up of very large corporations and their various subsidiaries containing different functions that create complex locational structures. The networks formed by the 19 largest automobile transnational corporations constitute an automobile "oligopoly" representing more than 90% (OICA, 2012) of the world's production. Since the mid-1990s, Central and Eastern European cities have become attractive for transnational corporations and particularly for the production functions in the automobile sector. This leads to a crucial question. Are strategic functions (such as R&D) within these networks also located in Central and Eastern Europe, or is the region still manufacturing-oriented in the automobile industry? This paper focuses on the patterns and the main factors influencing the role of some of these new central and Eastern European cities that have become integrated in the global value chain of the automobile industry. By analysing the various locations of the specialized functions within the corporations, this study aims to extend the research on global value chains (Gereffi and Korzeniewicz; 1994, Sturgeon, 2000; Krätke, 2014). The spatial patterns of the various functions and the ownerships networks of the automobile industry are constructed in order to identify the cities supporting it. In particular, the way that national metropolises bring their national territories into the globalization of the automobile industry is addressed. For example, are there some specific advantages of capital cities compared to cities that have less integration in globalization terms?