Large Network Models Research Articles

Multiorder Arnoldi Approach for Model Order Reduction of PEEC Models With Retardation

This paper presents an efficient algorithm to create reduced-order models of large linear networks that contain delay elements. The proposed algorithm is based on a multiorder Arnoldi algorithm used to implicitly calculate the moments with respect to frequency. This procedure generates reduced-order models that preserve the structure of the original system, without having to introduce any extra state variables to calculate the moments. In addition, it is shown that the orthonormal subspace of the system, built by introducing extra state variables, is embedded in the subspace constructed by the multiorder Arnoldi approach. Numerical examples of distributed interconnects modeled by partial element equivalent circuits that include retardation effects are described to illustrate the validity of the proposed reduction technique.

IP/MPLS-over-OTN-over-DWDM Multilayer Networks: An Integrated Three-Layer Capacity Optimization Model, a Heuristic, and a Study

Multilayer network design has received significant attention in current literature. Despite this, the explicit modeling of IP/MPLS over OTN over DWDM in which the OTN layer is specifically considered has not been addressed before. This architecture has been identified as promising that bridges integration and interaction between the IP and optical layers. In this paper, we present an integrated capacity optimization model for network planning of such multilayer networks that consider the OTN layer as a distinct layer with its unique technological sublayer constraints. We develop a heuristic algorithm to solve this model for large networks. Finally, we provide a detailed numeric study that considers various cost parameter values of each layer in the network. We analyze the impact of each layer's cost parameter values on neighboring layers and overall network cost.

Analysis of routing protocols and interference-limited communication in large wireless networks via continuum modeling

The evaluation and assessment of the design of large wireless networks is an important problem in numerous applications. Direct simulation is a traditional approach for studying such networks but is severely limited in its utility as the size of the network increases. This necessitates other means for studying large networks, one of which is the modeling of large networks with continuum models. In this paper, we introduce nonlinear partial differential equations whose solutions approximate the expected behavior of large networks governed by probabilistic communication rules. The relative speed at which solutions can be obtained from the continuum models allows for the investigation of routing protocols and communication limitations due to interference—a feat that is not feasible via simulation methods. Specifically, we investigate the effects of a directed diffusion routing protocol and explore communication limitations in an interference-sensitive network. Network design studies using the approximating continuum models are then presented.

Abstract PR12: A model of HGF and EGF dual ligand stimulation in ACHN cells constructed with the aid of a novel model merging heuristic

Abstract The investigation of context-specific perturbations of cell signaling pathways requires the construction of large scale network models of multiple interacting pathways. A key issue in the production of these models is the process of model calibration, sometimes referred to as regression or optimization, during which parameters of a model are systematically adjusted to improve the model's predictions on a set of training data. We have developed a novel heuristic, termed “model merging,” to exploit parameter information from simpler models in the construction of new complex models. Using this merging heuristic, we developed a model of HGF and EGF stimulation of the MAP kinase cascade in ACHN cells, a renal cancer cell line. We constructed the model of HGF and EGF stimulation by first constructing smaller models of stimulation by each separate ligand. We use the single ligand models to inform the training of the dual ligand model by applying the model merging heuristic. Our model accurately reflects the time courses of pMET, pEGFR, and pMAPK under single ligand and dual ligand stimulation over two-hour time courses. It also captures several previously unmodeled features of MET and EGFR pathway crosstalk. The goal of model merging is to resolve parameter differences while maintaining the predictive quality of the previously known models. By the nature of model calibration, there are discrepancies between parameter estimates of the single ligand models whenever a parameter appears in both models. We design a scoring system for model predictions that takes into account the discrepancies between the parameter estimates. To resolve these discrepancies, our model merging heuristic iteratively adjusts the scoring system to create a series of optimization problems. The solutions to the series of problems converge to a resolved parametrization for the general model while maintaining the high quality of predictions of the component models. A key advantage of our heuristic over other model calibration algorithms is its ability to identify context-specific differences in parametrizations during model calibration. This is possible because the heuristic does not enforce any context-specific or context-free assumptions. Rather, it tries to resolve differences between multiple parameter sets by searching for a single consensus parameter set. If the training data precludes such a consensus for some of the parameters, then the heuristic can identify these parameters and simultaneously resolve the other parameters for which there is a consensus. In this way, the heuristic identifies parameters that are context-specific. This major advantage of our model merging method was integral to our construction of a model of HGF and EGF stimulation of the MAP Kinase cascade in ACHN cells. We identify context-specific parameters that describe a previously known, receptor-specific difference in phospho-MAPK negative feedback to the adapter protein GAB1. Identification of context-specific parametrizations also demonstrated that a prior model of EGF stimulated MAP kinase signaling employed an overly simplified mechanism of phospho-MAPK negative feedback to the protein SOS. Using this more detailed mechanism, we are now able to better interrogate the role of MAPK negative feedback in the more general multipathway setting. We also investigated the generalizability of our model merging heuristic by applying it repeatedly to a simplified version of our dual ligand model. We demonstrate that applying model merging in combination with Nelder-Mead calibration generates a significantly more robust estimation of parameters than Nelder-Mead calibration alone. Model merging thus produces a higher likelihood of finding a global best model parametrization instead of a local best parametrization. These results highlight the potential for our model merging technique to enable the creation of multipathway models with high mechanistic detail with reduced computational cost. This proffered talk is also presented as Poster A10. Citation Format: Andrew L. Matteson. A model of HGF and EGF dual ligand stimulation in ACHN cells constructed with the aid of a novel model merging heuristic [abstract]. In: Proceedings of the AACR Special Conference on Chemical Systems Biology: Assembling and Interrogating Computational Models of the Cancer Cell by Chemical Perturbations; 2012 Jun 27-30; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2012;72(13 Suppl):Abstract nr PR12.

Analysis on life model of large sensor networks

A large sensor network needs multiple base stations (BSs) to collect data efficiently. The design effort often aims at maximizing the network lifetime. The lifetime of a network depends on, besides battery capacity, factors such as node density, sampling period and the partitioning of the network for the multiple base stations. In this paper, we propose a stochastic approach to finding the lifetime of large sensor networks with multiple BSs and randomly scattered nodes. We begin by partitioning the network into regions by the Voronoi diagram method, one for each base station. We then propose a method to find the minimum transmission range needed for guaranteeing network connectivity. With nodes connected, we derive the traffic rate of nodes at specific distance from the base station. Based on the traffic rate and energy consumption model, the lifetime distribution of a region is calculated. Combining the results of individual regions, the network lifetime distribution is obtained. Case studies are presented and verified by computer simulation.

Parameter Estimation, Analysis, and Design of Synthetic Gene Switching Models: System Behavior- and Performance-based Approaches

This paper studies the parameter-dependent characteristics of a gene switching model that consists of dual positive feedback loops. Developing a predictive mathematical model for large regulatory networks in biological systems would be useful for their analysis and design. A parameter estimation scheme is proposed based on the observation of the steady-states for a gene switching model. Deterministic and stochastic stability are studied for this model, as well as other important system behaviors such as convergence rate to a stable equilibrium point, hysteresis induced by two time scales of the system model, and noise sensitivity with respect to the system parameters. Sensitivity of system performance indices with respect to the system parameters are analyzed in terms of H∞- and H2-norms of the linearized system model with their closed-form solutions. The presented qualitative and quantitative studies of the system characteristics enable the synthesis of a robust gene regulatory network that achieves desired static and dynamic responses.

Connectivity and Coverage in Hybrid Wireless Sensor Networks using Dynamic Random Geometric Graph Model

Random Geometric Graphs have been a very influential and well-studied model of large networks, such as sensor networks, where the network nodes are represented by the vertices of the RGG, and the direct connectivity between nodes is represented by the edges. This assumes homogeneous wireless nodes with uniform transmission ranges. In real life, there exist heterogeneous wireless networks in which devices have dramatically different capabilities. The connectivity of a WSN is related to the positions of nodes, and those positions are heavily affected by the method of sensor deployment. As sensors may be spread in an arbitrary manner, one of the fundamental issues in a wireless sensor network is the coverage problem. In this paper, I study connectivity and coverage in hybrid WSN based on dynamic random geometric graph.

Neural coding in graphs of bidirectional associative memories

In the last years we have developed large neural network models for the realization of complex cognitive tasks in a neural network architecture that resembles the network of the cerebral cortex. We have used networks of several cortical modules that contain two populations of neurons (one excitatory, one inhibitory). The excitatory populations in these so-called “cortical networks” are organized as a graph of Bidirectional Associative Memories (BAMs), where edges of the graph correspond to BAMs connecting two neural modules and nodes of the graph correspond to excitatory populations with associative feedback connections (and inhibitory interneurons). The neural code in each of these modules consists essentially of the firing pattern of the excitatory population, where mainly it is the subset of active neurons that codes the contents to be represented. The overall activity can be used to distinguish different properties of the patterns that are represented which we need to distinguish and control when performing complex tasks like language understanding with these cortical networks. The most important pattern properties or situations are: exactly fitting or matching input, incomplete information or partially matching pattern, superposition of several patterns, conflicting information, and new information that is to be learned. We show simple simulations of these situations in one area or module and discuss how to distinguish these situations based on the overall internal activation of the module.This article is part of a Special Issue entitled “Neural Coding”.

Weighted lasso in graphical Gaussian modeling for large gene network estimation based on microarray data.

We propose a statistical method based on graphical Gaussian models for estimating large gene networks from DNA microarray data. In estimating large gene networks, the number of genes is larger than the number of samples, we need to consider some restrictions for model building. We propose weighted lasso estimation for the graphical Gaussian models as a model of large gene networks. In the proposed method, the structural learning for gene networks is equivalent to the selection of the regularization parameters included in the weighted lasso estimation. We investigate this problem from a Bayes approach and derive an empirical Bayesian information criterion for choosing them. Unlike Bayesian network approach, our method can find the optimal network structure and does not require to use heuristic structural learning algorithm. We conduct Monte Carlo simulation to show the effectiveness of the proposed method. We also analyze Arabidopsis thaliana microarray data and estimate gene networks.

Building a dynamic electro‐mechanical model for the Pacific AC intertie using distributed synchrophasor measurements

AbstractIn this paper, we present a novel algorithm for constructing simplified interarea models of large power networks by using dynamic measurements available from phasor measurement units (PMUs) installed at specific points on the transmission line. Our example of study in this paper is a widely encountered realistic system, namely the Pacific AC intertie, which closely resembles a star‐connected three‐area power system. We derive analytical results showing how the voltage, phase angle, and frequency oscillations at different buses on the transfer path of this intertie can be used to estimate the essential parameters of the three‐machine equivalent model of this three‐area system. We illustrate the results with actual disturbance event data from the Western Electricity Coordinating Council. Copyright © 2011 John Wiley & Sons, Ltd.

A Measurement-Based Framework for Dynamic Equivalencing of Large Power Systems Using Wide-Area Phasor Measurements

Wide-area analysis and control of large-scale electric power systems are highly dependent on the idea of aggregation. For example, one often hears power system operators mentioning how northern Washington oscillates against southern California in response to various disturbance events. The main question here is whether we can analytically construct dynamic electromechanical models for these conceptual, aggregated generators representing Washington and California, which in reality are some hypothetical combinations of thousands of actual generators. In this paper we address this problem, and present a concise overview of several new results on how to construct simplified interarea models of large power networks by using dynamic measurements available from phasor measurement units (PMUs) installed at specific points on the transmission line. Our examples of study are motivated by widely encountered power transfer paths in the Western Electricity Coordinating Council (WECC), namely, a two-area radial system representing the WA-MT flow, and a star-connected three-area system resembling the Pacific AC Intertie.

The need to combine different traffic modelling levels for effectively tackling large-scale projects adding a hybrid meso/micro approach

The evaluation of ATMS requires a network-wide assessment of their impact as opposed to an isolated analysis of key intersections. Microscopic traffic simulation models emulate the dynamics of individual vehicles in a detailed network representation, based on car-following, lane changing, etc; include route choice models to implement dynamic traffic assignment. Microscopic models are usually appropriate for operational analysis due the detail of information provided by the simulator. However, they are data intensive and have a significant computational cost. Mesoscopic models combine simplified flow dynamics with explicit treatment of interrupted flows at intersections and allow modeling of large networks with high computational efficiency. However, the loss of realism implied by a mesoscopic model makes it necessary to emulate detailed outputs (detector measurements, instantaneous emissions). The above give rise to the need to combine meso and micro approaches into new hybrid traffic simulators where very large-scale networks are modeled mesoscopically and areas of complex interactions benefit from the finer detail of microscopic simulation.This paper presents the new system architecture implemented in Aimsun of the hybrid model with special emphasis on the consistency of the transition between the mesoscopic and the microscopic models, and vice versa and aims to demonstrate how consistency is complemented using computational results in a large-size network.

The development of large traffic network model

Our article examines speed and acceleration processes, describing the motion of unique vehicles crossing the large network. We take the real traffic into consideration by obtaining the driving cycle from our macroscopic network model. We grant the traffic changes in the entire network with this model. The unique motion process derived from the model is compared to the real - measured - speed and acceleration processes. In this article we validate our model by getting unique speed and acceleration processes. Based on the acceleration values calculated by the model, we redefine the condition set of the model. Comparing the modeled and measured values, it is clear that there are only some momentary differences. But even these small differences should not be neglected, rather they should be used in the model development, as described in this paper.

Averaged kinetic models for flows on unstructured networks

We derive a kinetic equation for flows on general, unstructured networks with applications to production, social and transportation networks. This model allows for a homogenization procedure, yielding a macroscopic transport model for large networks on large time scales.

Parameter Balancing in Kinetic Models of Cell Metabolism

Kinetic modeling of metabolic pathways has become a major field of systems biology. It combines structural information about metabolic pathways with quantitative enzymatic rate laws. Some of the kinetic constants needed for a model could be collected from ever-growing literature and public web resources, but they are often incomplete, incompatible, or simply not available. We address this lack of information by parameter balancing, a method to complete given sets of kinetic constants. Based on Bayesian parameter estimation, it exploits the thermodynamic dependencies among different biochemical quantities to guess realistic model parameters from available kinetic data. Our algorithm accounts for varying measurement conditions in the input data (pH value and temperature). It can process kinetic constants and state-dependent quantities such as metabolite concentrations or chemical potentials, and uses prior distributions and data augmentation to keep the estimated quantities within plausible ranges. An online service and free software for parameter balancing with models provided in SBML format (Systems Biology Markup Language) is accessible at www.semanticsbml.org. We demonstrate its practical use with a small model of the phosphofructokinase reaction and discuss its possible applications and limitations. In the future, parameter balancing could become an important routine step in the kinetic modeling of large metabolic networks.

Transient Modeling of a Full-Scale Distribution System: Comparison with Field Data

The usefulness of transient models depends on their predictive ability. Consequently, their results should ideally be validated with field data. Despite numerous theoretical developments in the area of surge analysis, comparisons between field and modeled data for large distribution systems (DSs) are scarce. Transient low-pressure events at a water treatment plant (WTP) resulted in negative pressures at nu- merous locations in the DS. Three distinct surge events were measured in a full-scale DS and modeled with transient analysis software. The simulated pressure profiles were compared with field data collected from 9-12 sites within the DS. The objective was to apply a commercial transient analysis algorithm to a large and detailed network model (≈15;000 nodes=pipes) to estimate transient pressure variations within the network. Results showed similar trends for the three low-pressure events analyzed: the modeled pressures matched reasonably well with the measured pressures, as long as they remained positive. Whenever the pressures reached negative values, the simulated amplitude was larger than that of the recorded pressures. Modeling parameters and factors that might explain such results were tentatively investigated. The importance of field data in understanding and confirming the model outputs is highlighted. DOI: 10.1061/(ASCE)WR.1943-5452 .0000109. © 2011 American Society of Civil Engineers. CE Database subject headings: Water distribution systems; Hydraulic transients; Computer models; Water pressure; Monitoring. Author keywords: Water distribution systems; Hydraulic transients; Computer models; Pressure monitoring.

Large Network Model of Complex Systems

We proposed a random network model to describe complex systems. The model is solved exactly by mean-field method and differential equation. We demonstrated the triangle distribution firstly to calculate the clustering coefficient. When the size of the network tends to infinity, the model has high clustering coefficient.

The origins of time-delay in template biopolymerization processes.

Time-delays are common in many physical and biological systems and they give rise to complex dynamic phenomena. The elementary processes involved in template biopolymerization, such as mRNA and protein synthesis, introduce significant time delays. However, there is not currently a systematic mapping between the individual mechanistic parameters and the time delays in these networks. We present here the development of mathematical, time-delay models for protein translation, based on PDE models, which in turn are derived through systematic approximations of first-principles mechanistic models. Theoretical analysis suggests that the key features that determine the time-delays and the agreement between the time-delay and the mechanistic models are ribosome density and distribution, i.e., the number of ribosomes on the mRNA chain relative to their maximum and their distribution along the mRNA chain. Based on analytical considerations and on computational studies, we show that the steady-state and dynamic responses of the time-delay models are in excellent agreement with the detailed mechanistic models, under physiological conditions that correspond to uniform ribosome distribution and for ribosome density up to 70%. The methodology presented here can be used for the development of reduced time-delay models of mRNA synthesis and large genetic networks. The good agreement between the time-delay and the mechanistic models will allow us to use the reduced model and advanced computational methods from nonlinear dynamics in order to perform studies that are not practical using the large-scale mechanistic models.

Transition Features from Simplicity-Universality to Complexity-Diversification Under UHNTF

A large unified hybrid network model with a variable speed growth (LUHNM-VSG) is proposed as third model of the unified hybrid network theoretical framework (UHNTF). A hybrid growth ratio vg of deterministic linking number to random linking number and variable speed growth index α are introduced in it. The main effects of vg and α on topological transition features of the LUHNM-VSG are revealed. For comparison with the other models, we construct a type of the network complexity pyramid with seven levels, in which from the bottom level-1 to the top level-7 of the pyramid simplicity-universality is increasing but complexity-diversity is decreasing. The transition relations between them depend on matching of four hybrid ratios (dr, fd, gr, vg). Thus the most of network models can be investigated in the unification way via four hybrid ratios (dr, fd, gr, vg). The LUHNM-VSG as the level-1 of the pyramid is much better and closer to description of real-world networks as well as has potential application.

Combining Mesoscopic and Microscopic Simulation in an Integrated Environment as a Hybrid Solution

The evaluation of advanced Intelligent Transportation Systems, and particularly those which involve real-time traffic management, requires a network-wide assessment of their impact as opposed to an isolated analysis of key intersections. To support such assessments, an integrated simulation environment that allows the use of different modeling levels (e.g., macro-meso-micro) offers undeniable advantages. One of the advantages is that traffic assignment results produced by any type of network loading modeling can be stored and reused for another simulation run. But even in an integrated environment with separate models, deciding between microscopic or mesoscopic was until recently a necessary and difficult choice. On the one hand, microscopic traffic simulation models emulate the dynamics of individual vehicles in a detailed network representation based on car-following, lane changing, and gap acceptance models. They also account explicitly for traffic control. As such, they are very appropriate for operational analysis due to the detail of information provided by the simulator. However, they have a significant calibration and computational cost. On the other hand, mesoscopic models combine simplified flow dynamics with explicit treatment of interrupted flows at intersections and allow modeling of large networks with high computational efficiency. However, the loss of realism implied by a mesoscopic model makes it necessary to emulate detailed outputs; for instance, detector measurements or instantaneous emissions. Some outputs, such as the number of start-stops or the exact location of congestion within a section elude even the most detailed mesoscopic simulators. This analysis gives rise to the need to combine meso and micro approaches into new concurrent hybrid traffic simulators where very large-scale networks are modeled mesoscopically and areas of complex interactions benefit from the finer detail of microscopic simulation. Combining an event-based mesoscopic model with a more detailed, time-sliced microsimulator raises consistency problems within the network representation and the meso-micro-meso transitions. This paper discusses these problems, proposes solutions and illustrates how they work in practice.