Optimal network topologies for local search with congestion

The problem of searchability in decentralized complex networks is of great importance in computer science, economy, and sociology. We present a formalism that is able to cope simultaneously with the problem of search and the congestion effects that arise when parallel searches are performed, and we obtain expressions for the average search cost both in the presence and the absence of congestion. This formalism is used to obtain optimal network structures for a system using a local search algorithm. It is found that only two classes of networks can be optimal: starlike configurations, when the number of parallel searches is small, and homogeneous-isotropic configurations, when it is large.

Generation of uncorrelated random scale-free networks

Uncorrelated random scale-free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable of generating random uncorrelated scale-free networks with no multiple and self-connections. The model is based on the classical configuration model, with an additional restriction on the maximum possible degree of the vertices. We check numerically that the proposed model indeed generates scale-free networks with no two- and three-vertex correlations, as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k, respectively.

Protein-protein interactions between adenovirus DNA polymerase and nuclear factor I mediate formation of the DNA replication preinitiation complex.

The in vitro adenovirus (Ad) DNA replication system provides an assay to study the interaction of viral and host replication proteins with the DNA template in the formation of the preinitiation complex. This initiation system requires in addition to the origin DNA sequences 1) Ad DNA polymerase (Pol), 2) Ad preterminal protein (pTP), the covalent acceptor for protein-primed DNA replication, and 3) nuclear factor I (NFI), a host cell protein identical to the CCAAT box-binding transcription factor. The interactions of these proteins were studied by coimmunoprecipitation and Ad origin DNA binding assays. The Ad Pol can bind to origin sequences only in the presence of another protein which can be either pTP or NFI. While NFI alone can bind to its origin recognition sequence, pTP does not specifically recognize DNA unless Ad Pol is present. Thus, protein-protein interactions are necessary for the targetting of either Ad Pol or pTP to the preinitiation complex. DNA footprinting demonstrated that the Ad DNA site recognized by the pTP.Pol complex was within the first 18 bases at the end of the template which constitutes the minimal origin of replication. Mutagenesis studies have defined the Ad Pol interaction site on NFI between amino acids 68-150, which overlaps the DNA binding and replication activation domain of this factor. A putative zinc finger on the Ad Pol has been mutated to a product that fails to bind the Ad origin sequences but still interacts with pTP. These results indicate that both protein-protein and protein-DNA interactions mediate specific recognition of the replication origin by Ad DNA polymerase.

Statistical mechanics of multi-edge networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.

Computer-simulation study of magnetic relaxation in anisotropic magnetic systems

We present a computer-simulation study of the effect of the distribution of energy barriers in an anisotropic magnetic system on the relaxation behavior of the magnetization. While the relaxation law for the magnetization can be approximated in all cases by a time logarithmic decay, the law for the dependence of the magnetic viscosity with temperature is found to be quite sensitive to the shape of the distribution of barriers. The low-temperature region for the magnetic viscosity never extrapolates to a positive no-null value. Moreover our computer simulation results agree reasonably well with some recent relaxation experiments on highly anisotropic single-domain particles.

Local optima networks of hard combinatorial landscapes

Combinatorial optimization involves finding an optimal solution in a finite set of options; many everyday life problems are of this kind. However, the number of options grows exponentially with the size of the problem, such that an exhaustive search for the best solution is practically infeasible beyond a certain problem size. When efficient algorithms are not available, a practical approach to obtain an approximate solution to the problem at hand, is to start with an educated guess and gradually refine it until we have a good-enough solution. Roughly speaking, this is how local search heuristics work. These stochastic algorithms navigate the problem search space by iteratively turning the current solution into new candidate solutions, guiding the search towards better solutions. The search performance, therefore, depends on structural aspects of the search space, which in turn depend on the move operator being used to modify solutions. A common way to characterize the search space of a problem is through the study of its fitness landscape, a mathematical object comprising the space of all possible solutions, their value with respect to the optimization objective, and a relationship of neighborhood defined by the move operator. The landscape metaphor is used to explain the search dynamics as a sort of potential function. The concept is indeed similar to that of potential energy surfaces in physical chemistry. Borrowing ideas from that field, we propose to extend to combinatorial landscapes the notion of the inherent network formed by energy minima in energy landscapes. In our case, energy minima are the local optima of the combinatorial problem, and we explore several definitions for the network edges. At first, we perform an exhaustive sampling of local optima basins of attraction, and define weighted transitions between basins by accounting for all the possible ways of crossing the basins frontier via one random move. Then, we reduce the computational burden by only counting the chances of escaping a given basin via random kick moves that start at the local optimum. Finally, we approximate network edges from the search trajectory of simple search heuristics, mining the frequency and inter-arrival time with which the heuristic visits local optima. Through these methodologies, we build a weighted directed graph that provides a synthetic view of the whole landscape, and that we can characterize using the tools of complex networks science. We argue that the network characterization can advance our understanding of the structural and dynamical properties of hard combinatorial landscapes. We apply our approach to prototypical problems such as the Quadratic Assignment Problem, the NK model of rugged landscapes, and the Permutation Flow-shop Scheduling Problem. We show that some network metrics can differentiate problem classes, correlate with problem non-linearity, and predict problem hardness as measured from the performances of trajectory-based local search heuristics.

Reconstruction of networks from their betweenness centrality

In this paper we study the reconstruction of a network topology from the values of its betweenness centrality, a measure of the influence of each of its nodes in the dissemination of information over the network. We consider a simple metaheuristic, simulated annealing, as the combinatorial optimization method to generate the network from the values of the betweenness centrality. We compare the performance of this technique when reconstructing different categories of networks –random, regular, small-world, scale-free and clustered–. We show that the method allows an exact reconstruction of small networks and leads to good topological approximations in the case of networks with larger orders. The method can be used to generate a quasi-optimal topology fora communication network from a list with the values of the maximum allowable traffic for each node.

Glassy magnetic phase driven by short range charge and magnetic ordering in nanocrystalline La1/3Sr2/3FeO3-δ: Magnetization, Mössbauer, and polarized neutron studies

The charge ordered La1/3Sr2/3FeO3−δ (LSFO) in bulk and nanocrystalline forms are investigated using ac and dc magnetization, M¨ossbauer, and polarized neutron studies. A complex scenario of short-range charge and magnetic ordering is realized from the polarized neutron studies in nanocrystalline specimen. This short-range ordering does not involve any change in spin state and modification in the charge disproportion between Fe3+ and Fe5+ compared to bulk counterpart as evident in the M¨ossbauer results. The refinement of magnetic diffraction peaks provides magnetic moments of Fe3+ and Fe5+ are about 3.15 μB and 1.57 μB for bulk, and 2.7 μB and 0.53 μB for nanocrystalline specimen, respectively. The destabilization of charge ordering leads to magnetic phase separation, giving rise to the robust exchange bias (EB) effect. Strikingly, EB field at 5 K attains a value as high as 4.4 kOe for average size ∼70 nm, which is zero for the bulk counterpart. A strong frequency dependence of ac susceptibility reveals cluster-glass-like transition around ∼65 K, below which EB appears. Overall results propose that finite-size effect directs the complex glassy magnetic behavior driven by unconventional short-range charge and magnetic ordering, and magnetic phase separation appears in nanocrystalline LSFO.

Statistical mechanics of multi-edge networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.

Spectral properties of the Laplacian of multiplex networks.

One of the more challenging tasks in the understanding of dynamical properties of models on top of complex networks is to capture the precise role of multiplex topologies. In a recent paper, Gómez et al. [ Phys. Rev. Lett. 110 028701 (2013)], some of the authors proposed a framework for the study of diffusion processes in such networks. Here, we extend the previous framework to deal with general configurations in several layers of networks and analyze the behavior of the spectrum of the Laplacian of the full multiplex. We derive an interesting decoupling of the problem that allow us to unravel the role played by the interconnections of the multiplex in the dynamical processes on top of them. Capitalizing on this decoupling we perform an asymptotic analysis that allow us to derive analytical expressions for the full spectrum of eigenvalues. This spectrum is used to gain insight into physical phenomena on top of multiplex, specifically, diffusion processes and synchronizability.

Structure-related magnetic fabric studies : implications for deformed and undeformed Precambrian rocks

The aim of this thesis research was to gain a better understanding of the emplacement of rapakivi granite intrusions, as well as the emplacement of gold-bearing hydrothermal fluids in structurally controlled mineralizations. Based on investigations of the magnetic fabric, the internal structures could be analysed and the intrusion mechanisms for rapakivi granite intrusions and respectively different deformation stages within gold-bearing shear and fault zones identified. Aeromagnetic images revealed circular structures within the rapakivi granite batholiths of Wiborg, Vehmaa and Åland. These circular structures represent intrusions that eventually build up these large batholiths. The rapakivi granite intrusions of Vehmaa, Ruotsinpyhtää within the Wiborg batholith and Saltvik intrusions within the Åland batholith all show bimodal magnetic susceptibilities with paramagnetic and ferromagnetic components. The distribution of the bimodality is related to different magma batches of the studied intrusions. The anisotropy of magnetic susceptibility (AMS) reveals internal structures that cannot be studied macroscopically or by microscope. The Ruotsinpyhtää and Vehmaa intrusions represent similar intrusion geometries, with gently to moderately outward dipping magnetic foliations. In the case of Vehmaa, the magnetic lineations are gently plunging and trend in the directions of the slightly elongated intrusion. The magnetic lineations represent magma flow. The shapes of the AMS ellipsoids are also more planar (oblate) in the central part of the intrusion, whereas they become more linear (prolate) near the margin. These AMS results, together with field observations, indicate that the main intrusion mechanism has involved the subsidence of older blocks with successive intrusion of fractionated magma during repeated cauldron subsidence. The Saltvik area within the Åland batholith consists of a number of smaller elliptical intrusions of different rapakivi types forming a multiple intrusive complex. The magnetic fabric shows a general westward dipping of the pyterlite and eastward dipping of the contiguous even-grained rapakivi granite, which indicates a central inflow of magma batches towards the east and west resulting from a laccolitic emplacement of magma batches, while the main mechanism for space creation was derived from subsidence. The magnetic fabric of structurally controlled gold potential shear and fault zones in Jokisivu, Satulinmäki and Koijärvi was investigated in order to describe the internal structures and define the deformation history and emplacement of hydrothermal fluids. A further aim of the research was to combine AMS studies with palaeomagnetic methods to constrain the timing for the shearing event relative to the precipitation of ferromagnetic minerals and gold. All of the studied formations are dominated by monoclinic pyrrhotite. The AMS directions generally follow the tectonic structures within the formations. However, internal variations in the AMS direction as well as the shapes of the AMS ellipsoids are observed within the shear zones. In Jokisivu and Satulinmäki in particular, the magnetic signatures of the shear zone core differ from the margins. Furthermore, the shape of the magnetic fabric in the shear zone core of Jokisivu is dominated by oblate shapes, whereas the margins exhibit prolate shapes. These variations indicate a later effect of the hydrothermal fluids on the general shear event. The palaeo-magnetic results reveal a deflection from the original Svecofennian age geomagnetic direction. These results, coupled with correlations between the orientation of the NRM vectors and the magnetic and rock fabrics, imply that the gold-rich hydrothermal fluids were emplaced pre/syntectonically during the late stages of the Svecofennian orogeny.

Network Similarity Measures and Automatic Construction of Graph Models using Genetic Programming

A complex network is an abstract representation of an intricate system of interrelated elements where the patterns of connection hold significant meaning. One particular complex network is a social network whereby the vertices represent people and edges denote their daily interactions. Understanding social network dynamics can be vital to the mitigation of disease spread as these networks model the interactions, and thus avenues of spread, between individuals. To better understand complex networks, algorithms which generate graphs exhibiting observed properties of real-world networks, known as graph models, are often constructed. While various efforts to aid with the construction of graph models have been proposed using statistical and probabilistic methods, genetic programming (GP) has only recently been considered. However, determining that a graph model of a complex network accurately describes the target network(s) is not a trivial task as the graph models are often stochastic in nature and the notion of similarity is dependent upon the expected behavior of the network. This thesis examines a number of well-known network properties to determine which measures best allowed networks generated by different graph models, and thus the models themselves, to be distinguished. A proposed meta-analysis procedure was used to demonstrate how these network measures interact when used together as classifiers to determine network, and thus model, (dis)similarity. The analytical results form the basis of the fitness evaluation for a GP system used to automatically construct graph models for complex networks. The GP-based automatic inference system was used to reproduce existing, well-known graph models as well as a real-world network. Results indicated that the automatically inferred models exemplified functional similarity when compared to their respective target networks. This approach also showed promise when used to infer a model for a mammalian brain network.

Development and Evaluation of Blind Identification Techniques for Nonlinear Systems

Identification and Control of Non‐linear dynamical systems are challenging problems to the control engineers.The topic is equally relevant in communication,weather prediction ,bio medical systems and even in social systems,where nonlinearity is an integral part of the system behavior.Most of the real world systems are nonlinear in nature and wide applications are there for nonlinear system identification/modeling.The basic approach in analyzing the nonlinear systems is to build a model from known behavior manifest in the form of system output.The problem of modeling boils down to computing a suitably parameterized model,representing the process.The parameters of the model are adjusted to optimize a performanace function,based on error between the given process output and identified process/model output.While the linear system identification is well established with many classical approaches,most of those methods cannot be directly applied for nonlinear system identification.The problem becomes more complex if the system is completely unknown but only the output time series is available.Blind recognition problem is the direct consequence of such a situation.The thesis concentrates on such problems.Capability of Artificial Neural Networks to approximate many nonlinear input-output maps makes it predominantly suitable for building a function for the identification of nonlinear systems,where only the time series is available.The literature is rich with a variety of algorithms to train the Neural Network model.A comprehensive study of the computation of the model parameters,using the different algorithms and the comparison among them to choose the best technique is still a demanding requirement from practical system designers,which is not available in a concise form in the literature.The thesis is thus an attempt to develop and evaluate some of the well known algorithms and propose some new techniques,in the context of Blind recognition of nonlinear systems.It also attempts to establish the relative merits and demerits of the different approaches.comprehensiveness is achieved in utilizing the benefits of well known evaluation techniques from statistics. The study concludes by providing the results of implementation of the currently available and modified versions and newly introduced techniques for nonlinear blind system modeling followed by a comparison of their performance.It is expected that,such comprehensive study and the comparison process can be of great relevance in many fields including chemical,electrical,biological,financial and weather data analysis.Further the results reported would be of immense help for practical system designers and analysts in selecting the most appropriate method based on the goodness of the model for the particular context.

W3233 -- Networks and Complexity in Social Systems (Collective Dynamics Group ISERP -- Columbia University) Course Syllabus

The Networks and Complexity in Social Systems course commences with an overview of the nascent field of complex networks, dividing it into three related but distinct strands: Statistical description of large scale networks, viewed as static objects; the dynamic evolution of networks, where now the structure of the network is understood in terms of a growth process; and dynamical processes that take place on fixed networks; that is, "networked dynamical systems". (A fourth area of potential research ties all the previous three strands together under the rubric of co-evolution of networks and dynamics, but very little research has been done in this vein and so it is omitted.) The remainder of the course treats each of the three strands in greater detail, introducing technical knowledge as required, summarizing the research papers that have introduced the principal ideas, and pointing out directions for future development. With regard to networked dynamical systems, the course treats in detail the more specific topic of information propagation in networks, in part because this topic is of great relevance to social science, and in part because it has received the most attention in the literature to date.

Self-organized sociopolitical interactions as the best way to achieve organized patterns in human social systems: going beyond the top-down control of classical political regimes

La monografía presenta la auto-organización sociopolítica como la mejor manera de lograr patrones organizados en los sistemas sociales humanos, dada su naturaleza compleja y la imposibilidad de las tareas computacionales de los regímenes políticos clásico, debido a que operan con control jerárquico, el cual ha demostrado no ser óptimo en la producción de orden en los sistemas sociales humanos. En la monografía se extrapola la teoría de la auto-organización en los sistemas biológicos a las dinámicas sociopolíticas humanas, buscando maneras óptimas de organizarlas, y se afirma que redes complejas anárquicas son la estructura emergente de la auto-organización sociopolítica.