Academic literature on the topic 'Complex conductance networks'

Abstract In past decades, a lot of studies have been carried out on complex networks and heat conduction in regular lattices. However, very little attention has been paid to the heat conduction in complex networks. In this work, we study (both thermal and electric) energy transport in physical networks rewired from 2D regular lattices. It is found that the network can be transferred from a good conductor to a poor conductor, depending on the rewired network structure and coupling scheme. Two interesting phenomena were discovered: (i) the thermal-siphon effect—namely the heat flux can go from a low-temperature node to a higher-temperature node and (ii) there exits an optimal network structure that displays small thermal conductance and large electrical conductance. These discoveries reveal that network-structured materials have great potential in applications in thermal-energy management and thermal-electric-energy conversion.

A previously developed method for efficiently simulating complex networks of integrate-and-fire neurons was specialized to the case in which the neurons have fast unitary postsynaptic conductances. However, inhibitory synaptic conductances are often slower than excitatory ones for cortical neurons, and this difference can have a profound effect on network dynamics that cannot be captured with neurons that have only fast synapses. We thus extend the model to include slow inhibitory synapses. In this model, neurons are grouped into large populations of similar neurons. For each population, we calculate the evolution of a probability density function (PDF), which describes the distribution of neurons over state-space. The population firing rate is given by the flux of probability across the threshold voltage for firing an action potential. In the case of fast synaptic conductances, the PDF was one-dimensional, as the state of a neuron was completely determined by its transmembrane voltage. An exact extension to slow inhibitory synapses increases the dimension of the PDF to two or three, as the state of a neuron now includes the state of its inhibitory synaptic conductance. However, by assuming that the expected value of a neuron's inhibitory conductance is independent of its voltage, we derive a reduction to a one-dimensional PDF and avoid increasing the computational complexity of the problem. We demonstrate that although this assumption is not strictly valid, the results of the reduced model are surprisingly accurate.

Community detection has become an increasingly popular tool for analyzing and researching complex networks. Many methods have been proposed for accurate community detection, and one of them is spectral clustering. Most spectral clustering algorithms have been implemented on artificial networks, and accuracy of the community detection is still unsatisfactory. Therefore, this paper proposes an agglomerative spectral clustering method with conductance and edge weights. In this method, the most similar nodes are agglomerated based on eigenvector space and edge weights. In addition, the conductance is used to identify densely connected clusters while agglomerating. The proposed method shows improved performance in related works and proves to be efficient for real life complex networks from experiments.

It has been shown that identifying the structural holes in social networks may help people analyze complex networks, which is crucial in community detection, diffusion control, viral marketing, and academic activities. Structural holes bridge different communities and gain access to multiple sources of information flow. In this paper, we devised a structural hole detection algorithm, known as the Conductance–Degree structural hole detection algorithm (CD-SHA), which computes the conductance and degree score of a vertex to identify the structural hole spanners in social networks. Next, we proposed an improved label propagation algorithm based on conductance (C-LPA) to filter the jamming nodes, which have a high conductance and degree score but are not structural holes. Finally, we evaluated the performance of the algorithm on different real-world networks, and we calculated several metrics for both structural holes and communities. The experimental results show that the algorithm can detect the structural holes and communities accurately and efficiently.

The tendency for flows in microfluidic systems to behave linearly poses challenges for designing integrated flow control schemes to carry out complex fluid processing tasks. This hindrance precipitated the use of numerous external control devices to manipulate flows, thereby thwarting the potential scalability and portability of lab-on-a-chip technology. Here, we devise a microfluidic network exhibiting nonlinear flow dynamics that enable new mechanisms for on-chip flow control. This network is shown to exhibit oscillatory output patterns, bistable flow states, hysteresis, signal amplification, and negative-conductance transitions, all without reliance on dedicated external control hardware, movable parts, flexible components, or oscillatory inputs. These dynamics arise from nonlinear fluid inertia effects in laminar flows that we amplify and harness through the design of the network geometry. These results, which are supported by theory and simulations, have the potential to inspire development of new built-in control capabilities, such as on-chip timing and synchronized flow patterns.

A low-dimensional, time-resolved and adapting model neuron is formulated and evaluated. The model is an extension of the integrate-and-fire type of model with respect to adaptation and of a recent adapting firing-rate model with respect to time-resolution. It is obtained from detailed conductance-based models by a separation of fast and slow ionic processes of action potential generation. The model explicitly includes firing-rate regulation via the slow afterhyperpolarization phase of action potentials, which is controlled by calcium-sensitive potassium channels. It is demonstrated that the model closely reproduces the firing pattern and excitability behaviour of a detailed multicompartment conductance-based model of a neocortical pyramidal cell. The inclusion of adaptation in a model neuron is important for its capability to generate complex dynamics of networks of interconnected neurons. The time-resolution is required for studies of systems in which the temporal aspects of neural coding are important. The simplicity of the model facilitates analytical studies, insight into neurocomputational mechanisms and simulations of large-scale systems. The capability to generate complex network computations may also make the model useful in practical applications of artificial neural networks.

Accurate population models are needed to build very large-scale neural models, but their derivation is difficult for realistic networks of neurons, in particular when nonlinear properties are involved, such as conductance-based interactions and spike-frequency adaptation. Here, we consider such models based on networks of adaptive exponential integrate-and-fire excitatory and inhibitory neurons. Using a master equation formalism, we derive a mean-field model of such networks and compare it to the full network dynamics. The mean-field model is capable of correctly predicting the average spontaneous activity levels in asynchronous irregular regimes similar to in vivo activity. It also captures the transient temporal response of the network to complex external inputs. Finally, the mean-field model is also able to quantitatively describe regimes where high- and low-activity states alternate (up-down state dynamics), leading to slow oscillations. We conclude that such mean-field models are biologically realistic in the sense that they can capture both spontaneous and evoked activity, and they naturally appear as candidates to build very large-scale models involving multiple brain areas.

In an alternating-current network, each edge has a complex conductance with positive real part. The response map is the linear map from the vector of voltages at a subset of boundary nodes to the vector of currents flowing into the network through these nodes. In this paper, it is proved that the known necessary conditions for a linear map to be a response map are sufficient, and we show how to construct an appropriate network for a given response map.

We study transport properties such as conductance and diffusion of complex networks such as scale-free and Erdős-Rényi networks. We consider the equivalent conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k) ~ k−⋋ and Erdős-Rényi networks in which each link has the same unit resistance. Our theoretical analysis for scale-free networks predicts a broad range of values of G (or the related diffusion constant D), with a power-law tail distribution ɸSF(G) ~ G−gG, where gG = 2⋋ − 1. We confirm our predictions by simulations of scale-free networks solving the Kirchhoff equations for the conductance between a pair of nodes. The power-law tail in ɸSF(G) leads to large values of G, thereby significantly improving the transport in scale-free networks, compared to Erdős-R´nyi networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical “transport backbone” picture we suggest that the conductances of scale-free and Erdős-Rényi networks can be approximated by ckAkB/(kA + kB) for any pair of nodes A and B with degrees kA and kB. Thus, a single parameter c characterizes transport on both scale-free and Erdős-Rényi networks.

We study transport properties such as conductance and diffusion of complex networks such as scale-free and Erdős-Rényi networks. We consider the equivalent conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k) ~ k−⋋ and Erdős-Rényi networks in which each link has the same unit resistance. Our theoretical analysis for scale-free networks predicts a broad range of values of G (or the related diffusion constant D), with a power-law tail distribution ɸSF(G) ~ G−gG, where gG = 2⋋ − 1. We confirm our predictions by simulations of scale-free networks solving the Kirchhoff equations for the conductance between a pair of nodes. The power-law tail in ɸSF(G) leads to large values of G, thereby significantly improving the transport in scale-free networks, compared to Erdős-R´nyi networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical “transport backbone” picture we suggest that the conductances of scale-free and Erdős-Rényi networks can be approximated by ckAkB/(kA + kB) for any pair of nodes A and B with degrees kA and kB. Thus, a single parameter c characterizes transport on both scale-free and Erdős-Rényi networks.

Doctor of Philosophy
Department of Electrical and Computer Engineering
Caterina Scoglio
Critical infrastructures are repeatedly attacked by external triggers causing tremendous amount of damages. Any infrastructure can be studied using the powerful theory of complex networks. A complex network is composed of extremely large number of different elements that exchange commodities providing significant services. The main functions of complex networks can be damaged by different types of attacks and failures that degrade the network performance. These attacks and failures are considered as disturbing dynamics, such as the spread of viruses in computer networks, the spread of epidemics in social networks, and the cascading failures in power grids. Depending on the network structure and the attack strength, every network differently suffers damages and performance degradation. Hence, quantifying the robustness of complex networks becomes an essential task. In this dissertation, new metrics are introduced to measure the robustness of technological and social networks with respect to the spread of epidemics, and the robustness of power grids with respect to cascading failures. First, we introduce a new metric called the Viral Conductance ($VC_{SIS}$) to assess the robustness of networks with respect to the spread of epidemics that are modeled through the susceptible/infected/susceptible ($SIS$) epidemic approach. In contrast to assessing the robustness of networks based on a classical metric, the epidemic threshold, the new metric integrates the fraction of infected nodes at steady state for all possible effective infection strengths. Through examples, $VC_{SIS}$ provides more insights about the robustness of networks than the epidemic threshold. In addition, both the paradoxical robustness of Barab\'si-Albert preferential attachment networks and the effect of the topology on the steady state infection are studied, to show the importance of quantifying the robustness of networks. Second, a new metric $VC_$ is introduced to assess the robustness of networks with respect to the spread of susceptible/infected/recovered ($SIR$) epidemics. To compute $VC_$, we propose a novel individual-based approach to model the spread of $SIR$ epidemics in networks, which captures the infection size for a given effective infection rate. Thus, $VC_$ quantitatively integrates the infection strength with the corresponding infection size. To optimize the $VC_$ metric, a new mitigation strategy is proposed, based on a temporary reduction of contacts in social networks. The social contact network is modeled as a weighted graph that describes the frequency of contacts among the individuals. Thus, we consider the spread of an epidemic as a dynamical system, and the total number of infection cases as the state of the system, while the weight reduction in the social network is the controller variable leading to slow/reduce the spread of epidemics. Using optimal control theory, the obtained solution represents an optimal adaptive weighted network defined over a finite time interval. Moreover, given the high complexity of the optimization problem, we propose two heuristics to find the near optimal solutions by reducing the contacts among the individuals in a decentralized way. Finally, the cascading failures that can take place in power grids and have recently caused several blackouts are studied. We propose a new metric to assess the robustness of the power grid with respect to the cascading failures. The power grid topology is modeled as a network, which consists of nodes and links representing power substations and transmission lines, respectively. We also propose an optimal islanding strategy to protect the power grid when a cascading failure event takes place in the grid. The robustness metrics are numerically evaluated using real and synthetic networks to quantify their robustness with respect to disturbing dynamics. We show that the proposed metrics outperform the classical metrics in quantifying the robustness of networks and the efficiency of the mitigation strategies. In summary, our work advances the network science field in assessing the robustness of complex networks with respect to various disturbing dynamics.

Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2009.
Committee Chair: Mihail, Milena; Committee Member: Lu, Linyuan; Committee Member: Sokol, Joel; Committee Member: Tetali, Prasad; Committee Member: Trotter, Tom; Committee Member: Yu, Xingxing. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Les argiles sont répandues dans la proche surface de la Terre, et ont un fort impact sur la perméabilité des formations géologiques. Leur très faible perméabilité fait des formations argileuses des "pièges géologiques" d’intérêt dans divers domaines d’étude des géosciences (notamment pour le pétrole et le gaz, la géothermie, le stockage des déchets nucléaires, entre autres). Les minéraux argileux présentent une charge de surface et une surface spécifique très importantes, ce qui génère le développement d’une double couche électrique particulièrement importante. La polarisation provoquée spectrale (PPS) est une méthode géoélectrique active qui permet d’obtenir de manière non-invasive la conductivité électrique complexe en fonction de la fréquence d’un géo-matériau du mHz au kHz. La conductivité complexe informe sur la capacité du matériau sondé à conduire un courant électrique et sur sa capacité à se polariser (à mobiliser de manière réversible des charges électriques). Cette thèse présente un protocole de laboratoire détaillé pour obtenir des mesures de PPS sur différents types d’argiles à des salinités variables, ainsi que des mélanges hétérogènes artificiels d’illite et demontmorillonite. Les résultats de la première étude montrent que la partie réelle de la conductivité électrique augmente avec la salinité, mais la partie imaginaire augmente jusqu’à un maximum et puis diminue. Cette diminution est due à la coagulation des argiles à hautes salinités. Cette coagulation potentielle des argiles altérerait l’espace poral puis modifierait les mécanismes de polarisation en jeu. Par ailleurs, en comparant le rapport de la conductivité de surface (imaginaire versus réelle) et d’autres données de la littérature, on remarque que ce rapport diminue avec la teneur en argile. Pour la deuxième étude, on observe que la montmorillonite domine la polarisation par rapport à l’illite. Cependant, les deux argiles ont un effet sur la conduction des mélanges. Les lois de mélanges sont une approche efficace pour modéliser ce type de mélange hétérogène d’argiles. Les modèles de réseaux de conductance complexes sont également utiles pour prédire la forme des spectres de polarisation. Les résultats de ce travail de thèse ouvrent de nouvelles perspectives pour la caractérisation des matériaux argileux avec la PPS
Clays are ubiquitously present in the Earth’s near surface and they have a high impact on the permeability of a system. Due to this property, clay formations are used in a variety of geology related applications (oil and gas, geothermal, nuclear waste storage, critical zone research, among others). Clays have a high surface charge and a high specific surface area, this property gives clays a particularly strong electrical double layer (EDL). Spectral induced polarization (SIP) is an active geo-electrical method thatmeasures in a non-invasive manner the frequency-dependent complex conductivity of a geo-material from themHz to the kHz. The complex conductivity informs about the ability the probed material has to conduct an electrical current and the ability to polarize (to reversibly store electrical charges). This thesis presents a detailed laboratory protocol to obtain SIP measurements of different types of clay at varying salinities, as well as an artificial heterogeneous mixture of illite and red montmorillonite with a salinity of around 10¡2 mol L¡1. The results of the first study show that the real part of the electrical conductivity increases with salinity, but the imaginary part increases until a maxima and then decreases. An interpretation of the decrease can come fromthe fact that clays coagulate at high salinities. The potential coagulation of clays would alter the pore space and then alter the polarization mechanisms in play. Furthermore, when comparing the ratio of the surface conductivity (imaginary versus real) of these resultswith other data in the literature, we notice that this ratio decreaseswith clay content. For the second study, we observe that red montmorillonite dominates the polarization with respect to illite. However, both clays effect the conduction of the mixtures. Mixing laws are an effective approach to model the complex conductivity of these heterogeneous mixtures. Complex conductance network models are better at predicting the shape of the polarization spectra. The results of this thesis work open new opportunities for clay characterization using SIP

In the previous thirteen chapters, we met and described, sometimes in excruciating detail, the constitutive elements making up the neuronal hardware: dendrites, synapses, voltagedependent conductances, axons, spines and calcium. We saw how, different from electronic circuits in which only very few levels of organization exist, the nervous systems has many tightly interlocking levels of organization that codepend on each other in crucial ways. It is now time to put some of these elements together into a functioning whole, a single nerve cell. With such a single nerve cell model in hand, we can ask functional questions, such as: at what time scale does it operate, what sort of operations can it carry out, and how good is it at encoding information. We begin this Herculean task by (1) completely neglecting the dendritic tree and (2) replacing the conductance-based description of the spiking process (e.g., the Hodgkin- Huxley equations) by one of two canonical descriptions. These two steps dramatically reduce the complexity of the problem of characterizing the electrical behavior of neurons. Instead of having to solve coupled, nonlinear partial differential equations, we are left with a single ordinary differential equation. Such simplifications allow us to formally treat networks of large numbers of interconnected neurons, as exemplified in the neural network literature, and to simulate their dynamics. Understanding any complex system always entails choosing a level of description that retains key properties of the system while removing those nonessential for the purpose at hand. The study of brains is no exception to this. Numerous simplified single-cell models have been proposed over the years, yet most of them can be reduced to just one of two forms. These can be distinguished by the form of their output: spike or pulse models generate discrete, all-or-none impulses.

The ability to fabricate networks of micro-channels that obey the biological properties of bifurcating structures found in nature suggests that it is possible to construct artificial vasculatures or bronchial structures. These devices could aid in the desirable objective of eliminating many forms of animal testing. In addition, the ability to precisely control hydraulic conductance could allow designers to create specific concentration gradients that would allow biologists to correlate the behavior of cells. In 1926, Murray found that there was an optimum branching ratio between the diameters of the parent and daughter vessels at a bifurcation. For biological vascular systems, this is referred to as Murray’s law and its basic principle has been found to be valid in many plant and mammalian organisms. An important consequence arises from this law: when the successive generations consist of regular dichotomies, the tangential shear stress at the wall remains constant throughout the network. This simple concept forms an elegant biomimetic design rule that will allow designers to create complex sections with the desired hydraulic conductance or resistance. The paper presents a theoretical analysis of how biomimetic networks of constant-depth rectangular channels can be fabricated using standard photolithographic techniques. In addition, the design rule developed from Murray’s law is extended to a simple power-law fluid to investigate whether it is feasible to design biomimetic networks for non-Newtonian liquids. Remarkably, Murray’s law is obeyed for power-law fluids in cylindrical pipes. Although highly promising, the extension of the analysis to rectangular or trapezoidal channels requires much further work. Moreover, it is unclear at this stage whether Murray’s law holds for other non-Newtonian models.

Bilayers are synthetically made cell membranes that are used to study cell membrane properties or make functional devices that use the properties of the cell membrane components. Lipids and proteins are two of the main components of a cell membrane. Lipids are amphiphilic molecules that can self assemble into organized structures in the presences of water and this self assembly property can be used to form bilayers. Because of the amphiphilic nature of the lipids, a bilayer is impermeable to ion flow. Proteins are the active structures of a cell membrane that opens pores through the membrane for ions and other molecules to pass. Proteins are made from amino acids and have varying properties that depend on its configuration. Some proteins are activated by reactions (chemical, thermal, etc) or gradients induced across the bilayer. One way of testing bilayers to find bilayer properties is to induce a potential gradient across a membrane that induces ion flow and this flow can be measured as an electrical current. But, these pores may be voltage gated or activated by some other stimuli and therefore cannot be modeled as a linear conductor. Usually the conductance of the protein is a nonlinear function of the input that activates the protein. A small system that consists of a single bilayer and protein with few changing components can be easily modeled, but as systems become larger with multiple bilayers, multiple variables, and multiple proteins, the models will become more complex. This paper looks at how to model a system of multiple bilayers and the peptide alamethicin. An analytical expression for this peptide is used to match experimental data and a short study on the sensitivity of the variables is performed.