A network dynamics approach to chemical reaction networks
NASA Astrophysics Data System (ADS)
van der Schaft, A. J.; Rao, S.; Jayawardhana, B.
2016-04-01
A treatment of a chemical reaction network theory is given from the perspective of nonlinear network dynamics, in particular of consensus dynamics. By starting from the complex-balanced assumption, the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in the chemical reaction network theory, and which directly relates to the thermodynamics and port-Hamiltonian formulation of the system. Central in this formulation is the definition of a balanced Laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality. This immediately leads to the characterisation of the set of equilibria and their stability. Furthermore, the assumption of complex balancedness is revisited from the point of view of Kirchhoff's matrix tree theorem. Both the form of the dynamics and the deduced behaviour are very similar to consensus dynamics, and provide additional perspectives to the latter. Finally, using the classical idea of extending the graph of chemical complexes by a 'zero' complex, a complete steady-state stability analysis of mass action kinetics reaction networks with constant inflows and mass action kinetics outflows is given, and a unified framework is provided for structure-preserving model reduction of this important class of open reaction networks.
Identification of dynamical models of chemical reaction networks
NASA Astrophysics Data System (ADS)
Haber, Aleksandar
Current first-principles models of complex chemistry, such as combustion reaction networks, often give inaccurate predictions of the time variation of chemical species. Moreover, the high complexity and dimensionality of these models render them impractical for real-time prediction and control of chemical network processes. These limitations have motivated us to search for an alternative paradigm that is able to both identify the correct model from the observed dynamical data and reduce complexity while preserving the underlying network structure. In this talk, I will present one such modeling paradigm under the scenarios of complete and incomplete observability of the dynamics. The proposed approach is applicable to combustion chemistry and a range of other chemical reaction networks. Research supported by ARO Grant W911NF-14-1-0359.
Reduction of dynamical biochemical reactions networks in computational biology
Radulescu, O.; Gorban, A. N.; Zinovyev, A.; Noel, V.
2012-01-01
Biochemical networks are used in computational biology, to model mechanistic details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as combinatorial explosion are strong obstacles against analyzing the dynamics of large models of this type. Multiscaleness, an important property of these networks, can be used to get past some of these obstacles. Networks with many well separated time scales, can be reduced to simpler models, in a way that depends only on the orders of magnitude and not on the exact values of the kinetic parameters. The main idea used for such robust simplifications of networks is the concept of dominance among model elements, allowing hierarchical organization of these elements according to their effects on the network dynamics. This concept finds a natural formulation in tropical geometry. We revisit, in the light of these new ideas, the main approaches to model reduction of reaction networks, such as quasi-steady state (QSS) and quasi-equilibrium approximations (QE), and provide practical recipes for model reduction of linear and non-linear networks. We also discuss the application of model reduction to the problem of parameter identification, via backward pruning machine learning techniques. PMID:22833754
Programming chemical kinetics: engineering dynamic reaction networks with DNA strand displacement
NASA Astrophysics Data System (ADS)
Srinivas, Niranjan
Over the last century, the silicon revolution has enabled us to build faster, smaller and more sophisticated computers. Today, these computers control phones, cars, satellites, assembly lines, and other electromechanical devices. Just as electrical wiring controls electromechanical devices, living organisms employ "chemical wiring" to make decisions about their environment and control physical processes. Currently, the big difference between these two substrates is that while we have the abstractions, design principles, verification and fabrication techniques in place for programming with silicon, we have no comparable understanding or expertise for programming chemistry. In this thesis we take a small step towards the goal of learning how to systematically engineer prescribed non-equilibrium dynamical behaviors in chemical systems. We use the formalism of chemical reaction networks (CRNs), combined with mass-action kinetics, as our programming language for specifying dynamical behaviors. Leveraging the tools of nucleic acid nanotechnology (introduced in Chapter 1), we employ synthetic DNA molecules as our molecular architecture and toehold-mediated DNA strand displacement as our reaction primitive. Abstraction, modular design and systematic fabrication can work only with well-understood and quantitatively characterized tools. Therefore, we embark on a detailed study of the "device physics" of DNA strand displacement (Chapter 2). We present a unified view of strand displacement biophysics and kinetics by studying the process at multiple levels of detail, using an intuitive model of a random walk on a 1-dimensional energy landscape, a secondary structure kinetics model with single base-pair steps, and a coarse-grained molecular model that incorporates three-dimensional geometric and steric effects. Further, we experimentally investigate the thermodynamics of three-way branch migration. Our findings are consistent with previously measured or inferred rates for
Catalysis in reaction networks.
Gopalkrishnan, Manoj
2011-12-01
We define catalytic networks as chemical reaction networks with an essentially catalytic reaction pathway: one which is "on" in the presence of certain catalysts and "off" in their absence. We show that examples of catalytic networks include synthetic DNA molecular circuits that have been shown to perform signal amplification and molecular logic. Recall that a critical siphon is a subset of the species in a chemical reaction network whose absence is forward invariant and stoichiometrically compatible with a positive point. Our main theorem is that all weakly-reversible networks with critical siphons are catalytic. Consequently, we obtain new proofs for the persistence of atomic event-systems of Adleman et al., and normal networks of Gnacadja. We define autocatalytic networks, and conjecture that a weakly-reversible reaction network has critical siphons if and only if it is autocatalytic. PMID:21503834
Autocatalysis in reaction networks.
Deshpande, Abhishek; Gopalkrishnan, Manoj
2014-10-01
The persistence conjecture is a long-standing open problem in chemical reaction network theory. It concerns the behavior of solutions to coupled ODE systems that arise from applying mass-action kinetics to a network of chemical reactions. The idea is that if all reactions are reversible in a weak sense, then no species can go extinct. A notion that has been found useful in thinking about persistence is that of "critical siphon." We explore the combinatorics of critical siphons, with a view toward the persistence conjecture. We introduce the notions of "drainable" and "self-replicable" (or autocatalytic) siphons. We show that: Every minimal critical siphon is either drainable or self-replicable; reaction networks without drainable siphons are persistent; and nonautocatalytic weakly reversible networks are persistent. Our results clarify that the difficulties in proving the persistence conjecture are essentially due to competition between drainable and self-replicable siphons. PMID:25245394
Liang, Xiao; Wang, Linshan; Wang, Yangfan; Wang, Ruili
2016-09-01
In this paper, we focus on the long time behavior of the mild solution to delayed reaction-diffusion Hopfield neural networks (DRDHNNs) driven by infinite dimensional Wiener processes. We analyze the existence, uniqueness, and stability of this system under the local Lipschitz function by constructing an appropriate Lyapunov-Krasovskii function and utilizing the semigroup theory. Some easy-to-test criteria affecting the well-posedness and stability of the networks, such as infinite dimensional noise and diffusion effect, are obtained. The criteria can be used as theoretic guidance to stabilize DRDHNNs in practical applications when infinite dimensional noise is taken into consideration. Meanwhile, considering the fact that the standard Brownian motion is a special case of infinite dimensional Wiener process, we undertake an analysis of the local Lipschitz condition, which has a wider range than the global Lipschitz condition. Two samples are given to examine the availability of the results in this paper. Simulations are also given using the MATLAB. PMID:26259224
NASA Astrophysics Data System (ADS)
Agrawal, Paras M.; Samadh, Abdul N. A.; Raff, Lionel M.; Hagan, Martin T.; Bukkapatnam, Satish T.; Komanduri, Ranga
2005-12-01
A new approach involving neural networks combined with molecular dynamics has been used for the determination of reaction probabilities as a function of various input parameters for the reactions associated with the chemical-vapor deposition of carbon dimers on a diamond (100) surface. The data generated by the simulations have been used to train and test neural networks. The probabilities of chemisorption, scattering, and desorption as a function of input parameters, such as rotational energy, translational energy, and direction of the incident velocity vector of the carbon dimer, have been considered. The very good agreement obtained between the predictions of neural networks and those provided by molecular dynamics and the fact that, after training the network, the determination of the interpolated probabilities as a function of various input parameters involves only the evaluation of simple analytical expressions rather than computationally intensive algorithms show that neural networks are extremely powerful tools for interpolating the probabilities and rates of chemical reactions. We also find that a neural network fits the underlying trends in the data rather than the statistical variations present in the molecular-dynamics results. Consequently, neural networks can also provide a computationally convenient means of averaging the statistical variations inherent in molecular-dynamics calculations. In the present case the application of this method is found to reduce the statistical uncertainty in the molecular-dynamics results by about a factor of 3.5.
Photochemical reaction dynamics
Moore, B.C.
1993-12-01
The purpose of the program is to develop a fundamental understanding of unimolecular and bimolecular reaction dynamics with application in combustion and energy systems. The energy dependence in ketene isomerization, ketene dissociation dynamics, and carbonyl substitution on organometallic rhodium complexes in liquid xenon have been studied. Future studies concerning unimolecular processes in ketene as well as energy transfer and kinetic studies of methylene radicals are discussed.
Ubiquitous ``glassy'' relaxation in catalytic reaction networks
NASA Astrophysics Data System (ADS)
Awazu, Akinori; Kaneko, Kunihiko
2009-10-01
Study of reversible catalytic reaction networks is important not only as an issue for chemical thermodynamics but also for protocells. From extensive numerical simulations and theoretical analysis, slow relaxation dynamics to sustain nonequlibrium states are commonly observed. These dynamics show two types of salient behaviors that are reminiscent of glassy behavior: slow relaxation along with the logarithmic time dependence of the correlation function and the emergence of plateaus in the relaxation-time course. The former behavior is explained by the eigenvalue distribution of a Jacobian matrix around the equilibrium state that depends on the distribution of kinetic coefficients of reactions. The latter behavior is associated with kinetic constraints rather than metastable states and is due to the absence of catalysts for chemicals in excess and the negative correlation between two chemical species. Examples are given and generality is discussed with relevance to bottleneck-type dynamics in biochemical reactions as well.
Deciphering Time Scale Hierarchy in Reaction Networks.
Nagahata, Yutaka; Maeda, Satoshi; Teramoto, Hiroshi; Horiyama, Takashi; Taketsugu, Tetsuya; Komatsuzaki, Tamiki
2016-03-01
Markovian dynamics on complex reaction networks are one of the most intriguing subjects in a wide range of research fields including chemical reactions, biological physics, and ecology. To represent the global kinetics from one node (corresponding to a basin on an energy landscape) to another requires information on multiple pathways that directly or indirectly connect these two nodes through the entire network. In this paper we present a scheme to extract a hierarchical set of global transition states (TSs) over a discrete-time Markov chain derived from first-order rate equations. The TSs can naturally take into account the multiple pathways connecting any pair of nodes. We also propose a new type of disconnectivity graph (DG) to capture the hierarchical organization of different time scales of reactions that can capture changes in the network due to changes in the time scale of observation. The crux is the introduction of the minimum conductance cut (MCC) in graph clustering, corresponding to the dividing surface across the network having the "smallest" transition probability between two disjoint subnetworks (superbasins on the energy landscape) in the network. We present a new combinatorial search algorithm for finding this MCC. We apply our method to a reaction network of Claisen rearrangement of allyl vinyl ether that consists of 23 nodes and 66 links (saddles on the energy landscape) connecting them. We compare the kinetic properties of our DG to those of the transition matrix of the rate equations and show that our graph can properly reveal the hierarchical organization of time scales in a network. PMID:26641663
From Catalytic Reaction Networks to Protocells
NASA Astrophysics Data System (ADS)
Kaneko, Kunihiko
2013-12-01
In spite of recent advances, there still remains a large gape between a set of chemical reactions and a biological cell. Here we discuss several theoretical efforts to fill in the gap. The topics cover (i) slow relaxation to equilibrium due to glassy behavior in catalytic reaction networks (ii) consistency between molecule replication and cell growth, as well as energy metabolism (iii) control of a system by minority molecules in mutually catalytic system, which work as a carrier of genetic information, and leading to evolvability (iv) generation of a compartmentalized structure as a cluster of molecules centered around the minority molecule, and division of the cluster accompanied by the replication of minority molecule (v) sequential, logical process over several states from concurrent reaction dynamics, by taking advantage of discreteness in molecule number.
Programmability of Chemical Reaction Networks
NASA Astrophysics Data System (ADS)
Cook, Matthew; Soloveichik, David; Winfree, Erik; Bruck, Jehoshua
Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior.
Boolean constraint satisfaction problems for reaction networks
NASA Astrophysics Data System (ADS)
Seganti, A.; De Martino, A.; Ricci-Tersenghi, F.
2013-09-01
We define and study a class of (random) Boolean constraint satisfaction problems representing minimal feasibility constraints for networks of chemical reactions. The constraints we consider encode, respectively, for hard mass-balance conditions (where the consumption and production fluxes of each chemical species are matched) and for soft mass-balance conditions (where a net production of compounds is in principle allowed). We solve these constraint satisfaction problems under the Bethe approximation and derive the corresponding belief propagation equations, which involve eight different messages. The statistical properties of ensembles of random problems are studied via the population dynamics methods. By varying a chemical potential attached to the activity of reactions, we find first-order transitions and strong hysteresis, suggesting a non-trivial structure in the space of feasible solutions.
Some Concepts in Reaction Dynamics
NASA Astrophysics Data System (ADS)
Polanyi, John C.
1987-05-01
The objective in this work has been one which I have shared with the two other 1986 Nobel lecturers in chemistry, D. R. Herschbach and Y. T. Lee, as well as with a wide group of colleagues and co-workers who have been responsible for bringing this field to its current state. That state is summarized in the title; we now have some concepts relevant to the motions of atoms and molecules in simple reactions, and some examples of the application of these concepts. We are, however, richer in vocabulary than in literature. The great epics of reaction dynamics remain to be written. I shall confine myself to some simple stories.
Modeling the Dynamics of Compromised Networks
Soper, B; Merl, D M
2011-09-12
Accurate predictive models of compromised networks would contribute greatly to improving the effectiveness and efficiency of the detection and control of network attacks. Compartmental epidemiological models have been applied to modeling attack vectors such as viruses and worms. We extend the application of these models to capture a wider class of dynamics applicable to cyber security. By making basic assumptions regarding network topology we use multi-group epidemiological models and reaction rate kinetics to model the stochastic evolution of a compromised network. The Gillespie Algorithm is used to run simulations under a worst case scenario in which the intruder follows the basic connection rates of network traffic as a method of obfuscation.
A Networks Approach to Modeling Enzymatic Reactions.
Imhof, P
2016-01-01
Modeling enzymatic reactions is a demanding task due to the complexity of the system, the many degrees of freedom involved and the complex, chemical, and conformational transitions associated with the reaction. Consequently, enzymatic reactions are not determined by precisely one reaction pathway. Hence, it is beneficial to obtain a comprehensive picture of possible reaction paths and competing mechanisms. By combining individually generated intermediate states and chemical transition steps a network of such pathways can be constructed. Transition networks are a discretized representation of a potential energy landscape consisting of a multitude of reaction pathways connecting the end states of the reaction. The graph structure of the network allows an easy identification of the energetically most favorable pathways as well as a number of alternative routes. PMID:27497170
Combining molecular dynamics with mesoscopic Green's function reaction dynamics simulations
NASA Astrophysics Data System (ADS)
Vijaykumar, Adithya; Bolhuis, Peter G.; ten Wolde, Pieter Rein
2015-12-01
In many reaction-diffusion processes, ranging from biochemical networks, catalysis, to complex self-assembly, the spatial distribution of the reactants and the stochastic character of their interactions are crucial for the macroscopic behavior. The recently developed mesoscopic Green's Function Reaction Dynamics (GFRD) method enables efficient simulation at the particle level provided the microscopic dynamics can be integrated out. Yet, many processes exhibit non-trivial microscopic dynamics that can qualitatively change the macroscopic behavior, calling for an atomistic, microscopic description. We propose a novel approach that combines GFRD for simulating the system at the mesoscopic scale where particles are far apart, with a microscopic technique such as Langevin dynamics or Molecular Dynamics (MD), for simulating the system at the microscopic scale where reactants are in close proximity. This scheme defines the regions where the particles are close together and simulated with high microscopic resolution and those where they are far apart and simulated with lower mesoscopic resolution, adaptively on the fly. The new multi-scale scheme, called MD-GFRD, is generic and can be used to efficiently simulate reaction-diffusion systems at the particle level.
Minimal Increase Network Coding for Dynamic Networks
Wu, Yanxia
2016-01-01
Because of the mobility, computing power and changeable topology of dynamic networks, it is difficult for random linear network coding (RLNC) in static networks to satisfy the requirements of dynamic networks. To alleviate this problem, a minimal increase network coding (MINC) algorithm is proposed. By identifying the nonzero elements of an encoding vector, it selects blocks to be encoded on the basis of relationship between the nonzero elements that the controls changes in the degrees of the blocks; then, the encoding time is shortened in a dynamic network. The results of simulations show that, compared with existing encoding algorithms, the MINC algorithm provides reduced computational complexity of encoding and an increased probability of delivery. PMID:26867211
Minimal Increase Network Coding for Dynamic Networks.
Zhang, Guoyin; Fan, Xu; Wu, Yanxia
2016-01-01
Because of the mobility, computing power and changeable topology of dynamic networks, it is difficult for random linear network coding (RLNC) in static networks to satisfy the requirements of dynamic networks. To alleviate this problem, a minimal increase network coding (MINC) algorithm is proposed. By identifying the nonzero elements of an encoding vector, it selects blocks to be encoded on the basis of relationship between the nonzero elements that the controls changes in the degrees of the blocks; then, the encoding time is shortened in a dynamic network. The results of simulations show that, compared with existing encoding algorithms, the MINC algorithm provides reduced computational complexity of encoding and an increased probability of delivery. PMID:26867211
Adaptive Dynamic Bayesian Networks
Ng, B M
2007-10-26
A discrete-time Markov process can be compactly modeled as a dynamic Bayesian network (DBN)--a graphical model with nodes representing random variables and directed edges indicating causality between variables. Each node has a probability distribution, conditional on the variables represented by the parent nodes. A DBN's graphical structure encodes fixed conditional dependencies between variables. But in real-world systems, conditional dependencies between variables may be unknown a priori or may vary over time. Model errors can result if the DBN fails to capture all possible interactions between variables. Thus, we explore the representational framework of adaptive DBNs, whose structure and parameters can change from one time step to the next: a distribution's parameters and its set of conditional variables are dynamic. This work builds on recent work in nonparametric Bayesian modeling, such as hierarchical Dirichlet processes, infinite-state hidden Markov networks and structured priors for Bayes net learning. In this paper, we will explain the motivation for our interest in adaptive DBNs, show how popular nonparametric methods are combined to formulate the foundations for adaptive DBNs, and present preliminary results.
Stochastic flux analysis of chemical reaction networks
2013-01-01
Background Chemical reaction networks provide an abstraction scheme for a broad range of models in biology and ecology. The two common means for simulating these networks are the deterministic and the stochastic approaches. The traditional deterministic approach, based on differential equations, enjoys a rich set of analysis techniques, including a treatment of reaction fluxes. However, the discrete stochastic simulations, which provide advantages in some cases, lack a quantitative treatment of network fluxes. Results We describe a method for flux analysis of chemical reaction networks, where flux is given by the flow of species between reactions in stochastic simulations of the network. Extending discrete event simulation algorithms, our method constructs several data structures, and thereby reveals a variety of statistics about resource creation and consumption during the simulation. We use these structures to quantify the causal interdependence and relative importance of the reactions at arbitrary time intervals with respect to the network fluxes. This allows us to construct reduced networks that have the same flux-behavior, and compare these networks, also with respect to their time series. We demonstrate our approach on an extended example based on a published ODE model of the same network, that is, Rho GTP-binding proteins, and on other models from biology and ecology. Conclusions We provide a fully stochastic treatment of flux analysis. As in deterministic analysis, our method delivers the network behavior in terms of species transformations. Moreover, our stochastic analysis can be applied, not only at steady state, but at arbitrary time intervals, and used to identify the flow of specific species between specific reactions. Our cases study of Rho GTP-binding proteins reveals the role played by the cyclic reverse fluxes in tuning the behavior of this network. PMID:24314153
Multilayer Network Analysis of Nuclear Reactions.
Zhu, Liang; Ma, Yu-Gang; Chen, Qu; Han, Ding-Ding
2016-01-01
The nuclear reaction network is usually studied via precise calculation of differential equation sets, and much research interest has been focused on the characteristics of nuclides, such as half-life and size limit. In this paper, however, we adopt the methods from both multilayer and reaction networks, and obtain a distinctive view by mapping all the nuclear reactions in JINA REACLIB database into a directed network with 4 layers: neutron, proton, (4)He and the remainder. The layer names correspond to reaction types decided by the currency particles consumed. This combined approach reveals that, in the remainder layer, the β-stability has high correlation with node degree difference and overlapping coefficient. Moreover, when reaction rates are considered as node strength, we find that, at lower temperatures, nuclide half-life scales reciprocally with its out-strength. The connection between physical properties and topological characteristics may help to explore the boundary of the nuclide chart. PMID:27558995
Multilayer Network Analysis of Nuclear Reactions
Zhu, Liang; Ma, Yu-Gang; Chen, Qu; Han, Ding-Ding
2016-01-01
The nuclear reaction network is usually studied via precise calculation of differential equation sets, and much research interest has been focused on the characteristics of nuclides, such as half-life and size limit. In this paper, however, we adopt the methods from both multilayer and reaction networks, and obtain a distinctive view by mapping all the nuclear reactions in JINA REACLIB database into a directed network with 4 layers: neutron, proton, 4He and the remainder. The layer names correspond to reaction types decided by the currency particles consumed. This combined approach reveals that, in the remainder layer, the β-stability has high correlation with node degree difference and overlapping coefficient. Moreover, when reaction rates are considered as node strength, we find that, at lower temperatures, nuclide half-life scales reciprocally with its out-strength. The connection between physical properties and topological characteristics may help to explore the boundary of the nuclide chart. PMID:27558995
Law of Localization in Chemical Reaction Networks
NASA Astrophysics Data System (ADS)
Okada, Takashi; Mochizuki, Atsushi
2016-07-01
In living cells, chemical reactions are connected by sharing their products and substrates, and form complex networks, e.g., metabolic pathways. Here we developed a theory to predict the sensitivity, i.e., the responses of concentrations and fluxes to perturbations of enzymes, from network structure alone. Nonzero response patterns turn out to exhibit two characteristic features, localization and hierarchy. We present a general theorem connecting sensitivity with network topology that explains these characteristic patterns. Our results imply that network topology is an origin of biological robustness. Finally, we suggest a strategy to determine real networks from experimental measurements.
Disease dynamics in a dynamic social network
NASA Astrophysics Data System (ADS)
Christensen, Claire; Albert, István; Grenfell, Bryan; Albert, Réka
2010-07-01
We develop a framework for simulating a realistic, evolving social network (a city) into which a disease is introduced. We compare our results to prevaccine era measles data for England and Wales, and find that they capture the quantitative and qualitative features of epidemics in populations spanning two orders of magnitude. Our results provide unique insight into how and why the social topology of the contact network influences the propagation of the disease through the population. We argue that network simulation is suitable for concurrently probing contact network dynamics and disease dynamics in ways that prior modeling approaches cannot and it can be extended to the study of less well-documented diseases.
Computational functions in biochemical reaction networks.
Arkin, A; Ross, J
1994-01-01
In prior work we demonstrated the implementation of logic gates, sequential computers (universal Turing machines), and parallel computers by means of the kinetics of chemical reaction mechanisms. In the present article we develop this subject further by first investigating the computational properties of several enzymatic (single and multiple) reaction mechanisms: we show their steady states are analogous to either Boolean or fuzzy logic gates. Nearly perfect digital function is obtained only in the regime in which the enzymes are saturated with their substrates. With these enzymatic gates, we construct combinational chemical networks that execute a given truth-table. The dynamic range of a network's output is strongly affected by "input/output matching" conditions among the internal gate elements. We find a simple mechanism, similar to the interconversion of fructose-6-phosphate between its two bisphosphate forms (fructose-1,6-bisphosphate and fructose-2,6-bisphosphate), that functions analogously to an AND gate. When the simple model is supplanted with one in which the enzyme rate laws are derived from experimental data, the steady state of the mechanism functions as an asymmetric fuzzy aggregation operator with properties akin to a fuzzy AND gate. The qualitative behavior of the mechanism does not change when situated within a large model of glycolysis/gluconeogenesis and the TCA cycle. The mechanism, in this case, switches the pathway's mode from glycolysis to gluconeogenesis in response to chemical signals of low blood glucose (cAMP) and abundant fuel for the TCA cycle (acetyl coenzyme A). Images FIGURE 3 FIGURE 4 FIGURE 5 FIGURE 7 FIGURE 10 FIGURE 12 FIGURE 13 FIGURE 14 FIGURE 15 FIGURE 16 PMID:7948674
Li, Jun; Guo, Hua E-mail: hguo@unm.edu; Chen, Jun; Zhang, Dong H. E-mail: hguo@unm.edu
2014-01-28
A permutationally invariant global potential energy surface for the HOCO system is reported by fitting a larger number of high-level ab initio points using the newly proposed permutation invariant polynomial-neural network method. The small fitting error (∼5 meV) indicates a faithful representation of the potential energy surface over a large configuration space. Full-dimensional quantum and quasi-classical trajectory studies of the title reaction were performed on this potential energy surface. While the results suggest that the differences between this and an earlier neural network fits are small, discrepancies with state-to-state experimental data remain significant.
Timescale analysis of rule-based biochemical reaction networks
Klinke, David J.; Finley, Stacey D.
2012-01-01
The flow of information within a cell is governed by a series of protein-protein interactions that can be described as a reaction network. Mathematical models of biochemical reaction networks can be constructed by repetitively applying specific rules that define how reactants interact and what new species are formed upon reaction. To aid in understanding the underlying biochemistry, timescale analysis is one method developed to prune the size of the reaction network. In this work, we extend the methods associated with timescale analysis to reaction rules instead of the species contained within the network. To illustrate this approach, we applied timescale analysis to a simple receptor-ligand binding model and a rule-based model of Interleukin-12 (IL-12) signaling in näive CD4+ T cells. The IL-12 signaling pathway includes multiple protein-protein interactions that collectively transmit information; however, the level of mechanistic detail sufficient to capture the observed dynamics has not been justified based upon the available data. The analysis correctly predicted that reactions associated with JAK2 and TYK2 binding to their corresponding receptor exist at a pseudo-equilibrium. In contrast, reactions associated with ligand binding and receptor turnover regulate cellular response to IL-12. An empirical Bayesian approach was used to estimate the uncertainty in the timescales. This approach complements existing rank- and flux-based methods that can be used to interrogate complex reaction networks. Ultimately, timescale analysis of rule-based models is a computational tool that can be used to reveal the biochemical steps that regulate signaling dynamics. PMID:21954150
Orthogonal gradient networks via post polymerization reaction
NASA Astrophysics Data System (ADS)
Chinnayan Kannan, Pandiyarajan; Genzer, Jan
2015-03-01
We report a novel synthetic route to generate orthogonal gradient networks through post polymerization reaction using pentaflurophenylmethacrylate (PFPMAc) active ester chemistry. These chemoselective monomers were successfully copolymerized with 5 mole% of the photo (methacryloyloxybenzophenone) and thermal (styrenesulfonylazide) crosslinkers. Subsequently, the copolymers were modified by a series of amines having various alkyl chain lengths. The conversion of post polymerization reaction was monitored using Fourier Transform Infrared Spectroscopy (FT-IR) and noticed that almost all pentaflurophenyl moieties are substituted by amines within in an hour without affecting the crosslinkers. In addition, the incorporation of photo and thermal crosslinkers in the polymer enabled us to achieve stable and covalently surface-bound polymer gradient networks (PGN) in an orthogonal manner, i.e. complete control over the crosslink density of the network in two opposite directions (i.e. heat vs photo). The network properties such as wettability, swelling and tensile modulus of the gradient coatings are studied and revealed in the paper.
Entropy of dynamical social networks
NASA Astrophysics Data System (ADS)
Zhao, Kun; Karsai, Marton; Bianconi, Ginestra
2012-02-01
Dynamical social networks are evolving rapidly and are highly adaptive. Characterizing the information encoded in social networks is essential to gain insight into the structure, evolution, adaptability and dynamics. Recently entropy measures have been used to quantify the information in email correspondence, static networks and mobility patterns. Nevertheless, we still lack methods to quantify the information encoded in time-varying dynamical social networks. In this talk we present a model to quantify the entropy of dynamical social networks and use this model to analyze the data of phone-call communication. We show evidence that the entropy of the phone-call interaction network changes according to circadian rhythms. Moreover we show that social networks are extremely adaptive and are modified by the use of technologies such as mobile phone communication. Indeed the statistics of duration of phone-call is described by a Weibull distribution and is significantly different from the distribution of duration of face-to-face interactions in a conference. Finally we investigate how much the entropy of dynamical social networks changes in realistic models of phone-call or face-to face interactions characterizing in this way different type human social behavior.
Dynamic Reaction Figures: An Integrative Vehicle for Understanding Chemical Reactions
ERIC Educational Resources Information Center
Schultz, Emeric
2008-01-01
A highly flexible learning tool, referred to as a dynamic reaction figure, is described. Application of these figures can (i) yield the correct chemical equation by simply following a set of menu driven directions; (ii) present the underlying "mechanism" in chemical reactions; and (iii) help to solve quantitative problems in a number of different…
Nonlinear Dynamics on Interconnected Networks
NASA Astrophysics Data System (ADS)
Arenas, Alex; De Domenico, Manlio
2016-06-01
Networks of dynamical interacting units can represent many complex systems, from the human brain to transportation systems and societies. The study of these complex networks, when accounting for different types of interactions has become a subject of interest in the last few years, especially because its representational power in the description of users' interactions in diverse online social platforms (Facebook, Twitter, Instagram, etc.) [1], or in representing different transportation modes in urban networks [2,3]. The general name coined for these networks is multilayer networks, where each layer accounts for a type of interaction (see Fig. 1).
Structurally Dynamic Spin Market Networks
NASA Astrophysics Data System (ADS)
Horváth, Denis; Kuscsik, Zoltán
The agent-based model of stock price dynamics on a directed evolving complex network is suggested and studied by direct simulation. The stationary regime is maintained as a result of the balance between the extremal dynamics, adaptivity of strategic variables and reconnection rules. The inherent structure of node agent "brain" is modeled by a recursive neural network with local and global inputs and feedback connections. For specific parametric combination the complex network displays small-world phenomenon combined with scale-free behavior. The identification of a local leader (network hub, agent whose strategies are frequently adapted by its neighbors) is carried out by repeated random walk process through network. The simulations show empirically relevant dynamics of price returns and volatility clustering. The additional emerging aspects of stylized market statistics are Zipfian distributions of fitness.
Some Concepts in Reaction Dynamics
NASA Technical Reports Server (NTRS)
Polannyi, John C.
1972-01-01
In 1929 London 1 published a very approximate solution of the Schroedinger equation for a system of chemical interest: H3. To the extent that chemistry can be regarded as existing separately from physics, this was a landmark in the history of chemistry, comparable in importance to the landmark in the history of physics marked by the appearance of the Heitler-London equation for H2. The expression for H3, was, of necessity, even less accurate than that for H2, but chemists, like the habitual poor, were accustomed to this sort of misfortune. Together with the physicists they enjoyed the sensation of living in a renaissance. The physicists still could not calculate a great deal that was of interest to them, and the chemists could calculate less, but both could now dream. It would be too easy to say that their dreams were dreams of unlimited computer time. Their dreams were a lot more productive than that. Two years after London published his equation, H. Eyring and M. Polanyi obtained the first numerical energy surface for H3. They infused the London equation with a measure of empiricism to produce an energy surface which, whether or not it was correct in its details, provided a basis for further speculations of an important sort. The existence of a tangible energy surface in 1931 stimulated speculation along two different lines. The following year Pelzer and Wigner used this London-Eyring-Polanyi (LEP) energy surface for a thermodynamic treatment of the reaction rate in H + H2. This important development reached its full flowering a few years later. In these remarks I shall be concerned with another line of development. A second more-or-less distinct category of speculation that began with (and, indeed, in) the 1931 paper has to do with the dynamics of individual reactive encounters under the influence of specified interaction potentials.
Dynamic and interacting complex networks
NASA Astrophysics Data System (ADS)
Dickison, Mark E.
This thesis employs methods of statistical mechanics and numerical simulations to study some aspects of dynamic and interacting complex networks. The mapping of various social and physical phenomena to complex networks has been a rich field in the past few decades. Subjects as broad as petroleum engineering, scientific collaborations, and the structure of the internet have all been analyzed in a network physics context, with useful and universal results. In the first chapter we introduce basic concepts in networks, including the two types of network configurations that are studied and the statistical physics and epidemiological models that form the framework of the network research, as well as covering various previously-derived results in network theory that are used in the work in the following chapters. In the second chapter we introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the time evolution of the network. We show that the dynamic network undergoes a percolation phase transition at a critical concentration pc, that decreases with the rate r at which the network links are changed. The behavior near criticality is universal and independent of r. We find that for dynamic random networks fundamental laws are changed: i) The size of the giant component at criticality scales with the network size N for all values of r, rather than as N2/3 in static network, ii) In the presence of a broad distribution of disorder, the optimal path length between two nodes in a dynamic network scales as N1/2, compared to N1/3 in a static network. The third chapter consists of a study of the effect of quarantine on the propagation of epidemics on an adaptive network of social contacts. For this purpose, we analyze the susceptible-infected-recovered model in the presence of quarantine, where susceptible
Disease Dynamics in a Dynamic Social Network
Christensen, Claire; Albert, István; Grenfell, Bryan; Albert, Réka
2010-01-01
We develop a framework for simulating a realistic, evolving social network (a city) into which a disease is introduced. We compare our results to prevaccine era measles data for England and Wales, and find that they capture the quantitative and qualitative features of epidemics in populations spanning two orders of magnitude. Our results provide unique insight into how and why the social topology of the contact network influences the propagation of the disease through the population. We argue that network simulation is suitable for concurrently probing contact network dynamics and disease dynamics in ways that prior modeling approaches cannot and it can be extended to the study of less well-documented diseases. PMID:20563303
Infering Networks From Collective Dynamics
NASA Astrophysics Data System (ADS)
Timme, Marc
How can we infer direct physical interactions between pairs of units from only knowing the units' time series? Here we present a dynamical systems' view on collective network dynamics, and propose the concept of a dynamics' space to reveal interaction networks from time series. We present two examples: one, where the time series stem from standard ordinary differential equations, and a second, more abstract, where the time series exhibits only partial information about the units' states. We apply the latter to neural circuit dynamics where the observables are spike timing data, i.e. only a discrete, state-dependent outputs of the neurons. These results may help revealing network structure for systems where direct access to dynamics is simpler than to connectivity, cf.. This is work with Jose Casadiego, Srinivas Gorur Shandilya, Mor Nitzan, Hauke Haehne and Dimitra Maoutsa. Supported by Grants of the BMBF (Future Compliant Power Grids - CoNDyNet) and by the Max Planck Society to MT.
Anomalous subdiffusion with multispecies linear reaction dynamics.
Langlands, T A M; Henry, B I; Wearne, S L
2008-02-01
We have introduced a set of coupled fractional reaction-diffusion equations to model a multispecies system undergoing anomalous subdiffusion with linear reaction dynamics. The model equations are derived from a mesoscopic continuous time random walk formulation of anomalously diffusing species with linear mean field reaction kinetics. The effect of reactions is manifest in reaction modified spatiotemporal diffusion operators as well as in additive mean field reaction terms. One consequence of the nonseparability of reaction and subdiffusion terms is that the governing evolution equation for the concentration of one particular species may include both reactive and diffusive contributions from other species. The general solution is derived for the multispecies system and some particular special cases involving both irreversible and reversible reaction dynamics are analyzed in detail. We have carried out Monte Carlo simulations corresponding to these special cases and we find excellent agreement with theory. PMID:18351991
Realistic Control of Network Dynamics
Cornelius, Sean P.; Kath, William L.; Motter, Adilson E.
2014-01-01
The control of complex networks is of paramount importance in areas as diverse as ecosystem management, emergency response, and cell reprogramming. A fundamental property of networks is that perturbations to one node can affect other nodes, potentially causing the entire system to change behavior or fail. Here, we show that it is possible to exploit the same principle to control network behavior. Our approach accounts for the nonlinear dynamics inherent to real systems, and allows bringing the system to a desired target state even when this state is not directly accessible due to constraints that limit the allowed interventions. Applications show that this framework permits reprogramming a network to a desired task as well as rescuing networks from the brink of failure—which we illustrate through the mitigation of cascading failures in a power-grid network and the identification of potential drug targets in a signaling network of human cancer. PMID:23803966
Transient spatiotemporal chaos in reaction-diffusion networks
NASA Astrophysics Data System (ADS)
Wackerbauer, Renate
2010-03-01
Complex transient dynamics is reported in various extended systems, including transient turbulence in shear flows, transient spatiotemporal chaos in reaction- diffusion models, and non-chaotic irregular transient dynamics in neural networks. The asymptotic stability is difficult to determine since the transient lifetime typically increases exponentially with the system size. Our studies show that transient spatiotemporal chaos is extensive in various reaction- diffusion systems; the Lyapunov dimension increases linearly with the network size. A master stability analysis provides insight into the asymptotic stability in the Baer- Eiswirth and the Gray-Scott systems. The asymptotic state is characterized by negative transverse Lyapunov exponents on the attractor of the invariant synchronization manifold. The average lifetime depends on the number of transverse directions that are unstable along a typical excitation cycle.
Solution of Chemical Master Equations for Nonlinear Stochastic Reaction Networks
Smadbeck, Patrick; Kaznessis, Yiannis N.
2014-01-01
Stochasticity in the dynamics of small reacting systems requires discrete-probabilistic models of reaction kinetics instead of traditional continuous-deterministic ones. The master probability equation is a complete model of randomly evolving molecular populations. Because of its ambitious character, the master equation remained unsolved for all but the simplest of molecular interaction networks. With the first solution of chemical master equations, a wide range of experimental observations of small-system interactions may be mathematically conceptualized. PMID:25215268
Interfacial welding of dynamic covalent network polymers
NASA Astrophysics Data System (ADS)
Yu, Kai; Shi, Qian; Li, Hao; Jabour, John; Yang, Hua; Dunn, Martin L.; Wang, Tiejun; Qi, H. Jerry
2016-09-01
Dynamic covalent network (or covalent adaptable network) polymers can rearrange their macromolecular chain network by bond exchange reactions (BERs) where an active unit replaces a unit in an existing bond to form a new bond. Such macromolecular events, when they occur in large amounts, can attribute to unusual properties that are not seen in conventional covalent network polymers, such as shape reforming and surface welding; the latter further enables the important attributes of material malleability and powder-based reprocessing. In this paper, a multiscale modeling framework is developed to study the surface welding of thermally induced dynamic covalent network polymers. At the macromolecular network level, a lattice model is developed to describe the chain density evolution across the interface and its connection to bulk stress relaxation due to BERs. The chain density evolution rule is then fed into a continuum level interfacial model that takes into account surface roughness and applied pressure to predict the effective elastic modulus and interfacial fracture energy of welded polymers. The model yields particularly accessible results where the moduli and interfacial strength of the welded samples as a function of temperature and pressure can be predicted with four parameters, three of which can be measured directly. The model identifies the dependency of surface welding efficiency on the applied thermal and mechanical fields: the pressure will affect the real contact area under the consideration of surface roughness of dynamic covalent network polymers; the chain density increment on the real contact area of interface is only dependent on the welding time and temperature. The modeling approach shows good agreement with experiments and can be extended to other types of dynamic covalent network polymers using different stimuli for BERs, such as light and moisture etc.
A model reduction method for biochemical reaction networks
2014-01-01
Background In this paper we propose a model reduction method for biochemical reaction networks governed by a variety of reversible and irreversible enzyme kinetic rate laws, including reversible Michaelis-Menten and Hill kinetics. The method proceeds by a stepwise reduction in the number of complexes, defined as the left and right-hand sides of the reactions in the network. It is based on the Kron reduction of the weighted Laplacian matrix, which describes the graph structure of the complexes and reactions in the network. It does not rely on prior knowledge of the dynamic behaviour of the network and hence can be automated, as we demonstrate. The reduced network has fewer complexes, reactions, variables and parameters as compared to the original network, and yet the behaviour of a preselected set of significant metabolites in the reduced network resembles that of the original network. Moreover the reduced network largely retains the structure and kinetics of the original model. Results We apply our method to a yeast glycolysis model and a rat liver fatty acid beta-oxidation model. When the number of state variables in the yeast model is reduced from 12 to 7, the difference between metabolite concentrations in the reduced and the full model, averaged over time and species, is only 8%. Likewise, when the number of state variables in the rat-liver beta-oxidation model is reduced from 42 to 29, the difference between the reduced model and the full model is 7.5%. Conclusions The method has improved our understanding of the dynamics of the two networks. We found that, contrary to the general disposition, the first few metabolites which were deleted from the network during our stepwise reduction approach, are not those with the shortest convergence times. It shows that our reduction approach performs differently from other approaches that are based on time-scale separation. The method can be used to facilitate fitting of the parameters or to embed a detailed model of
Wong, Albert S Y; Postma, Sjoerd G J; Vialshin, Ilia N; Semenov, Sergey N; Huck, Wilhelm T S
2015-09-30
Our knowledge of the properties and dynamics of complex molecular reaction networks, for example those found in living systems, considerably lags behind the understanding of elementary chemical reactions. In part, this is because chemical reactions networks are nonlinear systems that operate under conditions far from equilibrium. Of particular interest is the role of individual reaction rates on the stability of the network output. In this research we use a rational approach combined with computational methods, to produce complex behavior (in our case oscillations) and show that small changes in molecular structure are sufficient to impart large changes in network behavior. PMID:26352485
Dynamical dipole mode in fusion reactions
Pierroutsakou, D.; Boiano, A.; Romoli, M.; Martin, B.; Inglima, G.; La Commara, M.; Sandoli, M.; Agodi, C.; Alba, R.; Coniglione, R.; Zoppo, A. Del; Maiolino, C.; Piattelli, P.; Santonocito, D.; Sapienza, P.; Baran, V.; Glodariu, T.; Cardella, G.; De Filippo, E.; Pagano, A.
2009-05-04
We investigated the dynamical dipole mode, related with entrance channel charge asymmetry effects, in the {sup 40}Ar+{sup 92}Zr and {sup 36}Ar+{sup 96}Zr fusion reactions at E{sub lab} = 15.1 A and 16 A MeV, respectively. These reactions populate, through entrance channels having different charge asymmetries, a compound nucleus in the A = 126 mass energy region, identical spin distribution at an average excitation energy of about 280 MeV. The compound nucleus average excitation energy and average mass were deduced by the analysis of the light charged particle energy spectra. By studying the {gamma}-ray energy spectra and the {gamma}-ray angular distributions of the considered reactions, the dynamical nature of the prompt radiation related to the dynamical dipole mode was evidenced. The data are compared with calculations based on a collective bremsstrahlung analysis of the reaction dynamics.
Dynamical detection of network communities
Quiles, Marcos G.; Macau, Elbert E. N.; Rubido, Nicolás
2016-01-01
A prominent feature of complex networks is the appearance of communities, also known as modular structures. Specifically, communities are groups of nodes that are densely connected among each other but connect sparsely with others. However, detecting communities in networks is so far a major challenge, in particular, when networks evolve in time. Here, we propose a change in the community detection approach. It underlies in defining an intrinsic dynamic for the nodes of the network as interacting particles (based on diffusive equations of motion and on the topological properties of the network) that results in a fast convergence of the particle system into clustered patterns. The resulting patterns correspond to the communities of the network. Since our detection of communities is constructed from a dynamical process, it is able to analyse time-varying networks straightforwardly. Moreover, for static networks, our numerical experiments show that our approach achieves similar results as the methodologies currently recognized as the most efficient ones. Also, since our approach defines an N-body problem, it allows for efficient numerical implementations using parallel computations that increase its speed performance. PMID:27158092
Dynamical detection of network communities.
Quiles, Marcos G; Macau, Elbert E N; Rubido, Nicolás
2016-01-01
A prominent feature of complex networks is the appearance of communities, also known as modular structures. Specifically, communities are groups of nodes that are densely connected among each other but connect sparsely with others. However, detecting communities in networks is so far a major challenge, in particular, when networks evolve in time. Here, we propose a change in the community detection approach. It underlies in defining an intrinsic dynamic for the nodes of the network as interacting particles (based on diffusive equations of motion and on the topological properties of the network) that results in a fast convergence of the particle system into clustered patterns. The resulting patterns correspond to the communities of the network. Since our detection of communities is constructed from a dynamical process, it is able to analyse time-varying networks straightforwardly. Moreover, for static networks, our numerical experiments show that our approach achieves similar results as the methodologies currently recognized as the most efficient ones. Also, since our approach defines an N-body problem, it allows for efficient numerical implementations using parallel computations that increase its speed performance. PMID:27158092
Dynamical detection of network communities
NASA Astrophysics Data System (ADS)
Quiles, Marcos G.; Macau, Elbert E. N.; Rubido, Nicolás
2016-05-01
A prominent feature of complex networks is the appearance of communities, also known as modular structures. Specifically, communities are groups of nodes that are densely connected among each other but connect sparsely with others. However, detecting communities in networks is so far a major challenge, in particular, when networks evolve in time. Here, we propose a change in the community detection approach. It underlies in defining an intrinsic dynamic for the nodes of the network as interacting particles (based on diffusive equations of motion and on the topological properties of the network) that results in a fast convergence of the particle system into clustered patterns. The resulting patterns correspond to the communities of the network. Since our detection of communities is constructed from a dynamical process, it is able to analyse time-varying networks straightforwardly. Moreover, for static networks, our numerical experiments show that our approach achieves similar results as the methodologies currently recognized as the most efficient ones. Also, since our approach defines an N-body problem, it allows for efficient numerical implementations using parallel computations that increase its speed performance.
Cellular automata modelling of biomolecular networks dynamics.
Bonchev, D; Thomas, S; Apte, A; Kier, L B
2010-01-01
The modelling of biological systems dynamics is traditionally performed by ordinary differential equations (ODEs). When dealing with intracellular networks of genes, proteins and metabolites, however, this approach is hindered by network complexity and the lack of experimental kinetic parameters. This opened the field for other modelling techniques, such as cellular automata (CA) and agent-based modelling (ABM). This article reviews this emerging field of studies on network dynamics in molecular biology. The basics of the CA technique are discussed along with an extensive list of related software and websites. The application of CA to networks of biochemical reactions is exemplified in detail by the case studies of the mitogen-activated protein kinase (MAPK) signalling pathway, the FAS-ligand (FASL)-induced and Bcl-2-related apoptosis. The potential of the CA method to model basic pathways patterns, to identify ways to control pathway dynamics and to help in generating strategies to fight with cancer is demonstrated. The different line of CA applications presented includes the search for the best-performing network motifs, an analysis of importance for effective intracellular signalling and pathway cross-talk. PMID:20373215
Stochastic dynamics of macromolecular-assembly networks.
NASA Astrophysics Data System (ADS)
Saiz, Leonor; Vilar, Jose
2006-03-01
The formation and regulation of macromolecular complexes provides the backbone of most cellular processes, including gene regulation and signal transduction. The inherent complexity of assembling macromolecular structures makes current computational methods strongly limited for understanding how the physical interactions between cellular components give rise to systemic properties of cells. Here we present a stochastic approach to study the dynamics of networks formed by macromolecular complexes in terms of the molecular interactions of their components [1]. Exploiting key thermodynamic concepts, this approach makes it possible to both estimate reaction rates and incorporate the resulting assembly dynamics into the stochastic kinetics of cellular networks. As prototype systems, we consider the lac operon and phage λ induction switches, which rely on the formation of DNA loops by proteins [2] and on the integration of these protein-DNA complexes into intracellular networks. This cross-scale approach offers an effective starting point to move forward from network diagrams, such as those of protein-protein and DNA-protein interaction networks, to the actual dynamics of cellular processes. [1] L. Saiz and J.M.G. Vilar, submitted (2005). [2] J.M.G. Vilar and L. Saiz, Current Opinion in Genetics & Development, 15, 136-144 (2005).
Dynamics of associating networks
NASA Astrophysics Data System (ADS)
Tang, Shengchang; Habicht, Axel; Wang, Muzhou; Li, Shuaili; Seiffert, Sebastian; Olsen, Bradley
Associating polymers offer important technological solutions to renewable and self-healing materials, conducting electrolytes for energy storage and transport, and vehicles for cell and protein deliveries. The interplay between polymer topologies and association chemistries warrants new interesting physics from associating networks, yet poses significant challenges to study these systems over a wide range of time and length scales. In a series of studies, we explored self-diffusion mechanisms of associating polymers above the percolation threshold, by combining experimental measurements using forced Rayleigh scattering and analytical insights from a two-state model. Despite the differences in molecular structures, a universal super-diffusion phenomenon is observed when diffusion of molecular species is hindered by dissociation kinetics. The molecular dissociation rate can be used to renormalize shear rheology data, which yields an unprecedented time-temperature-concentration superposition. The obtained shear rheology master curves provide experimental evidence of the relaxation hierarchy in associating networks.
Spontaneous recovery in dynamical networks
NASA Astrophysics Data System (ADS)
Majdandzic, Antonio; Podobnik, Boris; Buldyrev, Sergey V.; Kenett, Dror Y.; Havlin, Shlomo; Eugene Stanley, H.
2014-01-01
Much research has been carried out to explore the structural properties and vulnerability of complex networks. Of particular interest are abrupt dynamic events that cause networks to irreversibly fail. However, in many real-world phenomena, such as brain seizures in neuroscience or sudden market crashes in finance, after an inactive period of time a significant part of the damaged network is capable of spontaneously becoming active again. The process often occurs repeatedly. To model this marked network recovery, we examine the effect of local node recoveries and stochastic contiguous spreading, and find that they can lead to the spontaneous emergence of macroscopic `phase-flipping' phenomena. As the network is of finite size and is stochastic, the fraction of active nodes z switches back and forth between the two network collective modes characterized by high network activity and low network activity. Furthermore, the system exhibits a strong hysteresis behaviour analogous to phase transitions near a critical point. We present real-world network data exhibiting phase switching behaviour in accord with the predictions of the model.
Dynamic interactions in neural networks
Arbib, M.A. ); Amari, S. )
1989-01-01
The study of neural networks is enjoying a great renaissance, both in computational neuroscience, the development of information processing models of living brains, and in neural computing, the use of neurally inspired concepts in the construction of intelligent machines. This volume presents models and data on the dynamic interactions occurring in the brain, and exhibits the dynamic interactions between research in computational neuroscience and in neural computing. The authors present current research, future trends and open problems.
Recent advances in symmetric and network dynamics
NASA Astrophysics Data System (ADS)
Golubitsky, Martin; Stewart, Ian
2015-09-01
We summarize some of the main results discovered over the past three decades concerning symmetric dynamical systems and networks of dynamical systems, with a focus on pattern formation. In both of these contexts, extra constraints on the dynamical system are imposed, and the generic phenomena can change. The main areas discussed are time-periodic states, mode interactions, and non-compact symmetry groups such as the Euclidean group. We consider both dynamics and bifurcations. We summarize applications of these ideas to pattern formation in a variety of physical and biological systems, and explain how the methods were motivated by transferring to new contexts René Thom's general viewpoint, one version of which became known as "catastrophe theory." We emphasize the role of symmetry-breaking in the creation of patterns. Topics include equivariant Hopf bifurcation, which gives conditions for a periodic state to bifurcate from an equilibrium, and the H/K theorem, which classifies the pairs of setwise and pointwise symmetries of periodic states in equivariant dynamics. We discuss mode interactions, which organize multiple bifurcations into a single degenerate bifurcation, and systems with non-compact symmetry groups, where new technical issues arise. We transfer many of the ideas to the context of networks of coupled dynamical systems, and interpret synchrony and phase relations in network dynamics as a type of pattern, in which space is discretized into finitely many nodes, while time remains continuous. We also describe a variety of applications including animal locomotion, Couette-Taylor flow, flames, the Belousov-Zhabotinskii reaction, binocular rivalry, and a nonlinear filter based on anomalous growth rates for the amplitude of periodic oscillations in a feed-forward network.
Recent advances in symmetric and network dynamics.
Golubitsky, Martin; Stewart, Ian
2015-09-01
We summarize some of the main results discovered over the past three decades concerning symmetric dynamical systems and networks of dynamical systems, with a focus on pattern formation. In both of these contexts, extra constraints on the dynamical system are imposed, and the generic phenomena can change. The main areas discussed are time-periodic states, mode interactions, and non-compact symmetry groups such as the Euclidean group. We consider both dynamics and bifurcations. We summarize applications of these ideas to pattern formation in a variety of physical and biological systems, and explain how the methods were motivated by transferring to new contexts René Thom's general viewpoint, one version of which became known as "catastrophe theory." We emphasize the role of symmetry-breaking in the creation of patterns. Topics include equivariant Hopf bifurcation, which gives conditions for a periodic state to bifurcate from an equilibrium, and the H/K theorem, which classifies the pairs of setwise and pointwise symmetries of periodic states in equivariant dynamics. We discuss mode interactions, which organize multiple bifurcations into a single degenerate bifurcation, and systems with non-compact symmetry groups, where new technical issues arise. We transfer many of the ideas to the context of networks of coupled dynamical systems, and interpret synchrony and phase relations in network dynamics as a type of pattern, in which space is discretized into finitely many nodes, while time remains continuous. We also describe a variety of applications including animal locomotion, Couette-Taylor flow, flames, the Belousov-Zhabotinskii reaction, binocular rivalry, and a nonlinear filter based on anomalous growth rates for the amplitude of periodic oscillations in a feed-forward network. PMID:26428565
Time-Dependent Molecular Reaction Dynamics
Oehrn, Yngve
2007-11-29
This paper is a brief review of a time-dependent, direct, nonadiabatic theory of molecular processes called Electron Nuclear Dynamics (END). This approach to the study of molecular reaction dynamics is a hierarchical theory that can be applied at various levels of approximation. The simplest level of END uses classical nuclei and represents all electrons by a single, complex, determinantal wave function. The wave function parameters such as average nuclear positions and momenta, and molecular orbital coefcients carry the time dependence and serve as dynamical variables. Examples of application are given of the simplest level of END to ion-atom and ion-molecule reactions.
Adaptive hybrid simulations for multiscale stochastic reaction networks
Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa
2015-01-21
The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such a partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.
Adaptive hybrid simulations for multiscale stochastic reaction networks
NASA Astrophysics Data System (ADS)
Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa
2015-01-01
The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such a partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.
Competitive Dynamics on Complex Networks
NASA Astrophysics Data System (ADS)
Zhao, Jiuhua; Liu, Qipeng; Wang, Xiaofan
2014-07-01
We consider a dynamical network model in which two competitors have fixed and different states, and each normal agent adjusts its state according to a distributed consensus protocol. The state of each normal agent converges to a steady value which is a convex combination of the competitors' states, and is independent of the initial states of agents. This implies that the competition result is fully determined by the network structure and positions of competitors in the network. We compute an Influence Matrix (IM) in which each element characterizing the influence of an agent on another agent in the network. We use the IM to predict the bias of each normal agent and thus predict which competitor will win. Furthermore, we compare the IM criterion with seven node centrality measures to predict the winner. We find that the competitor with higher Katz Centrality in an undirected network or higher PageRank in a directed network is most likely to be the winner. These findings may shed new light on the role of network structure in competition and to what extent could competitors adjust network structure so as to win the competition.
Competitive dynamics on complex networks.
Zhao, Jiuhua; Liu, Qipeng; Wang, Xiaofan
2014-01-01
We consider a dynamical network model in which two competitors have fixed and different states, and each normal agent adjusts its state according to a distributed consensus protocol. The state of each normal agent converges to a steady value which is a convex combination of the competitors' states, and is independent of the initial states of agents. This implies that the competition result is fully determined by the network structure and positions of competitors in the network. We compute an Influence Matrix (IM) in which each element characterizing the influence of an agent on another agent in the network. We use the IM to predict the bias of each normal agent and thus predict which competitor will win. Furthermore, we compare the IM criterion with seven node centrality measures to predict the winner. We find that the competitor with higher Katz Centrality in an undirected network or higher PageRank in a directed network is most likely to be the winner. These findings may shed new light on the role of network structure in competition and to what extent could competitors adjust network structure so as to win the competition. PMID:25068622
A chemical reaction network solver for the astrophysics code NIRVANA
NASA Astrophysics Data System (ADS)
Ziegler, U.
2016-02-01
Context. Chemistry often plays an important role in astrophysical gases. It regulates thermal properties by changing species abundances and via ionization processes. This way, time-dependent cooling mechanisms and other chemistry-related energy sources can have a profound influence on the dynamical evolution of an astrophysical system. Modeling those effects with the underlying chemical kinetics in realistic magneto-gasdynamical simulations provide the basis for a better link to observations. Aims: The present work describes the implementation of a chemical reaction network solver into the magneto-gasdynamical code NIRVANA. For this purpose a multispecies structure is installed, and a new module for evolving the rate equations of chemical kinetics is developed and coupled to the dynamical part of the code. A small chemical network for a hydrogen-helium plasma was constructed including associated thermal processes which is used in test problems. Methods: Evolving a chemical network within time-dependent simulations requires the additional solution of a set of coupled advection-reaction equations for species and gas temperature. Second-order Strang-splitting is used to separate the advection part from the reaction part. The ordinary differential equation (ODE) system representing the reaction part is solved with a fourth-order generalized Runge-Kutta method applicable for stiff systems inherent to astrochemistry. Results: A series of tests was performed in order to check the correctness of numerical and technical implementation. Tests include well-known stiff ODE problems from the mathematical literature in order to confirm accuracy properties of the solver used as well as problems combining gasdynamics and chemistry. Overall, very satisfactory results are achieved. Conclusions: The NIRVANA code is now ready to handle astrochemical processes in time-dependent simulations. An easy-to-use interface allows implementation of complex networks including thermal processes
Mathematically Reduced Chemical Reaction Mechanism Using Neural Networks
Ziaul Huque
2007-08-31
This is the final technical report for the project titled 'Mathematically Reduced Chemical Reaction Mechanism Using Neural Networks'. The aim of the project was to develop an efficient chemistry model for combustion simulations. The reduced chemistry model was developed mathematically without the need of having extensive knowledge of the chemistry involved. To aid in the development of the model, Neural Networks (NN) was used via a new network topology known as Non-linear Principal Components Analysis (NPCA). A commonly used Multilayer Perceptron Neural Network (MLP-NN) was modified to implement NPCA-NN. The training rate of NPCA-NN was improved with the GEneralized Regression Neural Network (GRNN) based on kernel smoothing techniques. Kernel smoothing provides a simple way of finding structure in data set without the imposition of a parametric model. The trajectory data of the reaction mechanism was generated based on the optimization techniques of genetic algorithm (GA). The NPCA-NN algorithm was then used for the reduction of Dimethyl Ether (DME) mechanism. DME is a recently discovered fuel made from natural gas, (and other feedstock such as coal, biomass, and urban wastes) which can be used in compression ignition engines as a substitute for diesel. An in-house two-dimensional Computational Fluid Dynamics (CFD) code was developed based on Meshfree technique and time marching solution algorithm. The project also provided valuable research experience to two graduate students.
Morphisms of reaction networks that couple structure to function
2014-01-01
Background The mechanisms underlying complex biological systems are routinely represented as networks. Network kinetics is widely studied, and so is the connection between network structure and behavior. However, similarity of mechanism is better revealed by relationships between network structures. Results We define morphisms (mappings) between reaction networks that establish structural connections between them. Some morphisms imply kinetic similarity, and yet their properties can be checked statically on the structure of the networks. In particular we can determine statically that a complex network will emulate a simpler network: it will reproduce its kinetics for all corresponding choices of reaction rates and initial conditions. We use this property to relate the kinetics of many common biological networks of different sizes, also relating them to a fundamental population algorithm. Conclusions Structural similarity between reaction networks can be revealed by network morphisms, elucidating mechanistic and functional aspects of complex networks in terms of simpler networks. PMID:25128194
Stochastic analysis of complex reaction networks using binomial moment equations.
Barzel, Baruch; Biham, Ofer
2012-09-01
The stochastic analysis of complex reaction networks is a difficult problem because the number of microscopic states in such systems increases exponentially with the number of reactive species. Direct integration of the master equation is thus infeasible and is most often replaced by Monte Carlo simulations. While Monte Carlo simulations are a highly effective tool, equation-based formulations are more amenable to analytical treatment and may provide deeper insight into the dynamics of the network. Here, we present a highly efficient equation-based method for the analysis of stochastic reaction networks. The method is based on the recently introduced binomial moment equations [Barzel and Biham, Phys. Rev. Lett. 106, 150602 (2011)]. The binomial moments are linear combinations of the ordinary moments of the probability distribution function of the population sizes of the interacting species. They capture the essential combinatorics of the reaction processes reflecting their stoichiometric structure. This leads to a simple and transparent form of the equations, and allows a highly efficient and surprisingly simple truncation scheme. Unlike ordinary moment equations, in which the inclusion of high order moments is prohibitively complicated, the binomial moment equations can be easily constructed up to any desired order. The result is a set of equations that enables the stochastic analysis of complex reaction networks under a broad range of conditions. The number of equations is dramatically reduced from the exponential proliferation of the master equation to a polynomial (and often quadratic) dependence on the number of reactive species in the binomial moment equations. The aim of this paper is twofold: to present a complete derivation of the binomial moment equations; to demonstrate the applicability of the moment equations for a representative set of example networks, in which stochastic effects play an important role. PMID:23030885
Partition signed social networks via clustering dynamics
NASA Astrophysics Data System (ADS)
Wu, Jianshe; Zhang, Long; Li, Yong; Jiao, Yang
2016-02-01
Inspired by the dynamics phenomenon occurred in social networks, the WJJLGS model is modified to imitate the clustering dynamics of signed social networks. Analyses show that the clustering dynamics of the model can be applied to partition signed social networks. Traditionally, blockmodel is applied to partition signed networks. In this paper, a detailed dynamics-based algorithm for signed social networks (DBAS) is presented. Simulations on several typical real-world and illustrative networks that have been analyzed by the blockmodel verify the correctness of the proposed algorithm. The efficiency of the algorithm is verified on large scale synthetic networks.
Probing reaction dynamics with GDR decay
Beene, J.R.
1994-10-01
The giant dipole resonance (GDR) has been a prolific source of information on the physics of the nucleus. Mostly it has taught us about nuclear structure, but recently experiments have utilized the GDR as a probe of nuclear reaction dynamics. In this report two examples of such investigations are discussed involving very different reactions and probing time scales that differ by a factor of {approximately}10{sup 3}.
Reaction dynamics and the interstellar environment
NASA Technical Reports Server (NTRS)
Polanyi, J. C.
1973-01-01
Following a brief outline of the 'normal' equilibrium reaction rate laws, the theme of thermal disequilibrium in interstellar space and the related topic of detailed rate constants are more extensively discussed. Comment is made concerning the two principal techniques that are currently being used to explore the dynamical details of an increasing range of chemical reactions in the laboratory, since it is considered that these techniques suggest ways in which the understanding of the chemistry of interstellar space may be extended.
Clustering under the line graph transformation: application to reaction network
Nacher, Jose C; Ueda, Nobuhisa; Yamada, Takuji; Kanehisa, Minoru; Akutsu, Tatsuya
2004-01-01
Background Many real networks can be understood as two complementary networks with two kind of nodes. This is the case of metabolic networks where the first network has chemical compounds as nodes and the second one has nodes as reactions. In general, the second network may be related to the first one by a technique called line graph transformation (i.e., edges in an initial network are transformed into nodes). Recently, the main topological properties of the metabolic networks have been properly described by means of a hierarchical model. While the chemical compound network has been classified as hierarchical network, a detailed study of the chemical reaction network had not been carried out. Results We have applied the line graph transformation to a hierarchical network and the degree-dependent clustering coefficient C(k) is calculated for the transformed network. C(k) indicates the probability that two nearest neighbours of a vertex of degree k are connected to each other. While C(k) follows the scaling law C(k) ~ k-1.1 for the initial hierarchical network, C(k) scales weakly as k0.08 for the transformed network. This theoretical prediction was compared with the experimental data of chemical reactions from the KEGG database finding a good agreement. Conclusions The weak scaling found for the transformed network indicates that the reaction network can be identified as a degree-independent clustering network. By using this result, the hierarchical classification of the reaction network is discussed. PMID:15617578
Complex reaction networks in high temperature hydrocarbon chemistry.
Mutlay, İbrahim; Restrepo, Albeiro
2015-03-28
Complex chemical reaction mechanisms of high temperature hydrocarbon decomposition are represented as networks and their underlying graph topologies are analyzed as a dynamic system. As model reactants, 1,3-butadiene, acetylene, benzene, ethane, ethylene, methane, methyl isobutyl ketone (MIBK) and toluene are chosen in view of their importance for the global environment, energy technologies as well as their quantum chemical properties. Accurate kinetic mechanisms are computationally simulated and converted to bipartite graphs for the incremental conversion steps of the main reactant. Topological analysis of the resulting temporal networks reveals novel features unknown to classical chemical kinetics theory. The time-dependent percolation behavior of the chemical reaction networks shows infinite order phase transition and a unique correlation between the percolation thresholds and electron distribution of the reactants. These observations are expected to yield important applications in the development of a new theoretical perspective to chemical reactions and technological processes e.g. inhibition of greenhouse gases, efficient utilization of fossil fuels, and large scale carbon nanomaterial production. PMID:25720589
Bosonic reaction-diffusion processes on scale-free networks
NASA Astrophysics Data System (ADS)
Baronchelli, Andrea; Catanzaro, Michele; Pastor-Satorras, Romualdo
2008-07-01
Reaction-diffusion processes can be adopted to model a large number of dynamics on complex networks, such as transport processes or epidemic outbreaks. In most cases, however, they have been studied from a fermionic perspective, in which each vertex can be occupied by at most one particle. While still useful, this approach suffers from some drawbacks, the most important probably being the difficulty to implement reactions involving more than two particles simultaneously. Here we develop a general framework for the study of bosonic reaction-diffusion processes on complex networks, in which there is no restriction on the number of interacting particles that a vertex can host. We describe these processes theoretically by means of continuous-time heterogeneous mean-field theory and divide them into two main classes: steady-state and monotonously decaying processes. We analyze specific examples of both behaviors within the class of one-species processes, comparing the results (whenever possible) with the corresponding fermionic counterparts. We find that the time evolution and critical properties of the particle density are independent of the fermionic or bosonic nature of the process, while differences exist in the functional form of the density of occupied vertices in a given degree class k . We implement a continuous-time Monte Carlo algorithm, well suited for general bosonic simulations, which allows us to confirm the analytical predictions formulated within mean-field theory. Our results, at both the theoretical and numerical levels, can be easily generalized to tackle more complex, multispecies, reaction-diffusion processes and open a promising path for a general study and classification of this kind of dynamical systems on complex networks.
Nonlinear Opinion Dynamics on Networks
NASA Astrophysics Data System (ADS)
Gabbay, Michael; Das, Arindam
2013-03-01
A model which treats group decision making as nonlinear opinion dynamics occurring over a network is presented. The model makes predictions regarding the interaction of network structure and initial disagreement level upon decision outcomes and consensus formation. The model displays bifurcations at high disagreement levels which lead to behaviors that are qualitatively distinct from those at low disagreement. For example, at high disagreement, the model exhibits asymmetric, majority rule outcomes that arise even when the system is symmetric with respect to the distribution of initial opinions and network structure. Analytical approximations for the bifurcation boundaries agree well with numerically-determined boundaries. An ongoing experimental effort involving the use of online discussion groups to test the model predictions is briefly described. We acknowledge the support of the Defense Threat Reduction Agency and the Office of Naval Research under grant HDTRA1-10-1-0075
Data modeling of network dynamics
NASA Astrophysics Data System (ADS)
Jaenisch, Holger M.; Handley, James W.; Faucheux, Jeffery P.; Harris, Brad
2004-01-01
This paper highlights Data Modeling theory and its use for text data mining as a graphical network search engine. Data Modeling is then used to create a real-time filter capable of monitoring network traffic down to the port level for unusual dynamics and changes in business as usual. This is accomplished in an unsupervised fashion without a priori knowledge of abnormal characteristics. Two novel methods for converting streaming binary data into a form amenable to graphics based search and change detection are introduced. These techniques are then successfully applied to 1999 KDD Cup network attack data log-on sessions to demonstrate that Data Modeling can detect attacks without prior training on any form of attack behavior. Finally, two new methods for data encryption using these ideas are proposed.
Chemical Reaction Dynamics in Nanoscle Environments
Evelyn M. Goldfield
2006-09-26
The major focus of the research in this program is the study of the behavior of molecular systems confined in nanoscale environments. The goal is to develop a theoretical framework for predicting how chemical reactions occur in nanoscale environments. To achieve this goal we have employed ab initio quantum chemistry, classical dynamics and quantum dynamics methods. Much of the research has focused on the behavior of molecules confined within single-walled carbon nanotubes (SWCNTs). We have also studied interactions of small molecules with the exterior surface of SWCNTs. Nonequilibrium molecular dynamics of interfaces of sliding surface interfaces have also been performed.
Reaction dynamics in polyatomic molecular systems
Miller, W.H.
1993-12-01
The goal of this program is the development of theoretical methods and models for describing the dynamics of chemical reactions, with specific interest for application to polyatomic molecular systems of special interest and relevance. There is interest in developing the most rigorous possible theoretical approaches and also in more approximate treatments that are more readily applicable to complex systems.
Hierarchical Feedback Modules and Reaction Hubs in Cell Signaling Networks
Xu, Jianfeng; Lan, Yueheng
2015-01-01
Despite much effort, identification of modular structures and study of their organizing and functional roles remain a formidable challenge in molecular systems biology, which, however, is essential in reaching a systematic understanding of large-scale cell regulation networks and hence gaining capacity of exerting effective interference to cell activity. Combining graph theoretic methods with available dynamics information, we successfully retrieved multiple feedback modules of three important signaling networks. These feedbacks are structurally arranged in a hierarchical way and dynamically produce layered temporal profiles of output signals. We found that global and local feedbacks act in very different ways and on distinct features of the information flow conveyed by signal transduction but work highly coordinately to implement specific biological functions. The redundancy embodied with multiple signal-relaying channels and feedback controls bestow great robustness and the reaction hubs seated at junctions of different paths announce their paramount importance through exquisite parameter management. The current investigation reveals intriguing general features of the organization of cell signaling networks and their relevance to biological function, which may find interesting applications in analysis, design and control of bio-networks. PMID:25951347
Dynamics of the Ethanolamine Glycerophospholipid Remodeling Network
Hermansson, Martin; Somerharju, Pentti; Chuang, Jeffrey
2012-01-01
Acyl chain remodeling in lipids is a critical biochemical process that plays a central role in disease. However, remodeling remains poorly understood, despite massive increases in lipidomic data. In this work, we determine the dynamic network of ethanolamine glycerophospholipid (PE) remodeling, using data from pulse-chase experiments and a novel bioinformatic network inference approach. The model uses a set of ordinary differential equations based on the assumptions that (1) sn1 and sn2 acyl positions are independently remodeled; (2) remodeling reaction rates are constant over time; and (3) acyl donor concentrations are constant. We use a novel fast and accurate two-step algorithm to automatically infer model parameters and their values. This is the first such method applicable to dynamic phospholipid lipidomic data. Our inference procedure closely fits experimental measurements and shows strong cross-validation across six independent experiments with distinct deuterium-labeled PE precursors, demonstrating the validity of our assumptions. In constrast, fits of randomized data or fits using random model parameters are worse. A key outcome is that we are able to robustly distinguish deacylation and reacylation kinetics of individual acyl chain types at the sn1 and sn2 positions, explaining the established prevalence of saturated and unsaturated chains in the respective positions. The present study thus demonstrates that dynamic acyl chain remodeling processes can be reliably determined from dynamic lipidomic data. PMID:23251394
Anomaly Detection in Dynamic Networks
Turcotte, Melissa
2014-10-14
Anomaly detection in dynamic communication networks has many important security applications. These networks can be extremely large and so detecting any changes in their structure can be computationally challenging; hence, computationally fast, parallelisable methods for monitoring the network are paramount. For this reason the methods presented here use independent node and edge based models to detect locally anomalous substructures within communication networks. As a first stage, the aim is to detect changes in the data streams arising from node or edge communications. Throughout the thesis simple, conjugate Bayesian models for counting processes are used to model these data streams. A second stage of analysis can then be performed on a much reduced subset of the network comprising nodes and edges which have been identified as potentially anomalous in the first stage. The first method assumes communications in a network arise from an inhomogeneous Poisson process with piecewise constant intensity. Anomaly detection is then treated as a changepoint problem on the intensities. The changepoint model is extended to incorporate seasonal behavior inherent in communication networks. This seasonal behavior is also viewed as a changepoint problem acting on a piecewise constant Poisson process. In a static time frame, inference is made on this extended model via a Gibbs sampling strategy. In a sequential time frame, where the data arrive as a stream, a novel, fast Sequential Monte Carlo (SMC) algorithm is introduced to sample from the sequence of posterior distributions of the change points over time. A second method is considered for monitoring communications in a large scale computer network. The usage patterns in these types of networks are very bursty in nature and don’t fit a Poisson process model. For tractable inference, discrete time models are considered, where the data are aggregated into discrete time periods and probability models are fitted to the
Deconvolution of dynamic mechanical networks
Hinczewski, Michael; von Hansen, Yann; Netz, Roland R.
2010-01-01
Time-resolved single-molecule biophysical experiments yield data that contain a wealth of dynamic information, in addition to the equilibrium distributions derived from histograms of the time series. In typical force spectroscopic setups the molecule is connected via linkers to a readout device, forming a mechanically coupled dynamic network. Deconvolution of equilibrium distributions, filtering out the influence of the linkers, is a straightforward and common practice. We have developed an analogous dynamic deconvolution theory for the more challenging task of extracting kinetic properties of individual components in networks of arbitrary complexity and topology. Our method determines the intrinsic linear response functions of a given object in the network, describing the power spectrum of conformational fluctuations. The practicality of our approach is demonstrated for the particular case of a protein linked via DNA handles to two optically trapped beads at constant stretching force, which we mimic through Brownian dynamics simulations. Each well in the protein free energy landscape (corresponding to folded, unfolded, or possibly intermediate states) will have its own characteristic equilibrium fluctuations. The associated linear response function is rich in physical content, because it depends both on the shape of the well and its diffusivity—a measure of the internal friction arising from such processes as the transient breaking and reformation of bonds in the protein structure. Starting from the autocorrelation functions of the equilibrium bead fluctuations measured in this force clamp setup, we show how an experimentalist can accurately extract the state-dependent protein diffusivity using a straightforward two-step procedure. PMID:21118989
Modeling stochasticity in biochemical reaction networks
NASA Astrophysics Data System (ADS)
Constantino, P. H.; Vlysidis, M.; Smadbeck, P.; Kaznessis, Y. N.
2016-03-01
Small biomolecular systems are inherently stochastic. Indeed, fluctuations of molecular species are substantial in living organisms and may result in significant variation in cellular phenotypes. The chemical master equation (CME) is the most detailed mathematical model that can describe stochastic behaviors. However, because of its complexity the CME has been solved for only few, very small reaction networks. As a result, the contribution of CME-based approaches to biology has been very limited. In this review we discuss the approach of solving CME by a set of differential equations of probability moments, called moment equations. We present different approaches to produce and to solve these equations, emphasizing the use of factorial moments and the zero information entropy closure scheme. We also provide information on the stability analysis of stochastic systems. Finally, we speculate on the utility of CME-based modeling formalisms, especially in the context of synthetic biology efforts.
Unimolecular reaction dynamics of free radicals
Terry A. Miller
2006-09-01
Free radical reactions are of crucial importance in combustion and in atmospheric chemistry. Reliable theoretical models for predicting the rates and products of these reactions are required for modeling combustion and atmospheric chemistry systems. Unimolecular reactions frequently play a crucial role in determining final products. The dissociations of vinyl, CH2= CH, and methoxy, CH3O, have low barriers, about 13,000 cm-1 and 8,000 cm-1, respectively. Since barriers of this magnitude are typical of free radicals these molecules should serve as benchmarks for this important class of reactions. To achieve this goal, a detailed understanding of the vinyl and methoxy radicals is required. Results for dissociation dynamics of vinyl and selectively deuterated vinyl radical are reported. Significantly, H-atom scrambling is shown not to occur in this reaction. A large number of spectroscopic experiments for CH3O and CHD2O have been performed. Spectra recorded include laser induced fluorescence (LIF), laser excited dispersed fluorescence (LEDF), fluorescence dip infrared (FDIR) and stimulated emission pumping (SEP). Such results are critical for implementing dynamics experiments involving the dissociation of methoxy.
Network dynamics in nanofilled polymers
NASA Astrophysics Data System (ADS)
Baeza, Guilhem P.; Dessi, Claudia; Costanzo, Salvatore; Zhao, Dan; Gong, Shushan; Alegria, Angel; Colby, Ralph H.; Rubinstein, Michael; Vlassopoulos, Dimitris; Kumar, Sanat K.
2016-04-01
It is well accepted that adding nanoparticles (NPs) to polymer melts can result in significant property improvements. Here we focus on the causes of mechanical reinforcement and present rheological measurements on favourably interacting mixtures of spherical silica NPs and poly(2-vinylpyridine), complemented by several dynamic and structural probes. While the system dynamics are polymer-like with increased friction for low silica loadings, they turn network-like when the mean face-to-face separation between NPs becomes smaller than the entanglement tube diameter. Gel-like dynamics with a Williams-Landel-Ferry temperature dependence then result. This dependence turns particle dominated, that is, Arrhenius-like, when the silica loading increases to ~31 vol%, namely, when the average nearest distance between NP faces becomes comparable to the polymer's Kuhn length. Our results demonstrate that the flow properties of nanocomposites are complex and can be tuned via changes in filler loading, that is, the character of polymer bridges which `tie' NPs together into a network.
Network dynamics in nanofilled polymers
Baeza, Guilhem P.; Dessi, Claudia; Costanzo, Salvatore; Zhao, Dan; Gong, Shushan; Alegria, Angel; Colby, Ralph H.; Rubinstein, Michael; Vlassopoulos, Dimitris; Kumar, Sanat K.
2016-01-01
It is well accepted that adding nanoparticles (NPs) to polymer melts can result in significant property improvements. Here we focus on the causes of mechanical reinforcement and present rheological measurements on favourably interacting mixtures of spherical silica NPs and poly(2-vinylpyridine), complemented by several dynamic and structural probes. While the system dynamics are polymer-like with increased friction for low silica loadings, they turn network-like when the mean face-to-face separation between NPs becomes smaller than the entanglement tube diameter. Gel-like dynamics with a Williams–Landel–Ferry temperature dependence then result. This dependence turns particle dominated, that is, Arrhenius-like, when the silica loading increases to ∼31 vol%, namely, when the average nearest distance between NP faces becomes comparable to the polymer's Kuhn length. Our results demonstrate that the flow properties of nanocomposites are complex and can be tuned via changes in filler loading, that is, the character of polymer bridges which ‘tie' NPs together into a network. PMID:27109062
Network dynamics in nanofilled polymers.
Baeza, Guilhem P; Dessi, Claudia; Costanzo, Salvatore; Zhao, Dan; Gong, Shushan; Alegria, Angel; Colby, Ralph H; Rubinstein, Michael; Vlassopoulos, Dimitris; Kumar, Sanat K
2016-01-01
It is well accepted that adding nanoparticles (NPs) to polymer melts can result in significant property improvements. Here we focus on the causes of mechanical reinforcement and present rheological measurements on favourably interacting mixtures of spherical silica NPs and poly(2-vinylpyridine), complemented by several dynamic and structural probes. While the system dynamics are polymer-like with increased friction for low silica loadings, they turn network-like when the mean face-to-face separation between NPs becomes smaller than the entanglement tube diameter. Gel-like dynamics with a Williams-Landel-Ferry temperature dependence then result. This dependence turns particle dominated, that is, Arrhenius-like, when the silica loading increases to ∼31 vol%, namely, when the average nearest distance between NP faces becomes comparable to the polymer's Kuhn length. Our results demonstrate that the flow properties of nanocomposites are complex and can be tuned via changes in filler loading, that is, the character of polymer bridges which 'tie' NPs together into a network. PMID:27109062
Quantum effects in unimolecular reaction dynamics
Gezelter, J.D.
1995-12-01
This work is primarily concerned with the development of models for the quantum dynamics of unimolecular isomerization and photodissociation reactions. We apply the rigorous quantum methodology of a Discrete Variable Representation (DVR) with Absorbing Boundary Conditions (ABC) to these models in an attempt to explain some very surprising results from a series of experiments on vibrationally excited ketene. Within the framework of these models, we are able to identify the experimental signatures of tunneling and dynamical resonances in the energy dependence of the rate of ketene isomerization. Additionally, we investigate the step-like features in the energy dependence of the rate of dissociation of triplet ketene to form {sup 3}B{sub 1} CH{sub 2} + {sup 1}{sigma}{sup +} CO that have been observed experimentally. These calculations provide a link between ab initio calculations of the potential energy surfaces and the experimentally observed dynamics on these surfaces. Additionally, we develop an approximate model for the partitioning of energy in the products of photodissociation reactions of large molecules with appreciable barriers to recombination. In simple bond cleavage reactions like CH{sub 3}COCl {yields} CH{sub 3}CO + Cl, the model does considerably better than other impulsive and statistical models in predicting the energy distribution in the products. We also investigate ways of correcting classical mechanics to include the important quantum mechanical aspects of zero-point energy. The method we investigate is found to introduce a number of undesirable dynamical artifacts including a reduction in the above-threshold rates for simple reactions, and a strong mixing of the chaotic and regular energy domains for some model problems. We conclude by discussing some of the directions for future research in the field of theoretical chemical dynamics.
Dynamics of active actin networks
NASA Astrophysics Data System (ADS)
Koehler, Simone
2014-03-01
Local mechanical and structural properties of a eukaryotic cell are determined by its cytoskeleton. To adapt to their environment, cells rely on constant self-organized rearrangement processes of their actin cytoskeleton. To shed light on the principles underlying these dynamic self-organization processes we investigate a minimal reconstituted active system consisting of actin filaments, crosslinking molecules and molecular motor filaments. Using quantitative fluorescence microscopy and image analysis, we show, that these minimal model systems exhibit a generic structure formation mechanism. The competition between force generation by molecular motors and the stabilization of the network by crosslinking proteins results in a highly dynamic reorganization process which is characterized by anomalous transport dynamics with a superdiffusive behavior also found in intracellular dynamics. In vitro, these dynamics are governed by chemical and physical parameters that alter the balance of motor and crosslinking proteins, such as pH. These findings can be expected to have broad implications in our understanding of cytoskeletal regulation in vivo.
Theoretical studies of chemical reaction dynamics
Schatz, G.C.
1993-12-01
This collaborative program with the Theoretical Chemistry Group at Argonne involves theoretical studies of gas phase chemical reactions and related energy transfer and photodissociation processes. Many of the reactions studied are of direct relevance to combustion; others are selected they provide important examples of special dynamical processes, or are of relevance to experimental measurements. Both classical trajectory and quantum reactive scattering methods are used for these studies, and the types of information determined range from thermal rate constants to state to state differential cross sections.
Molecular beam studies of reaction dynamics
Lee, Y.T.
1987-03-01
Purpose of this research project is two-fold: (1) to elucidate detailed dynamics of simple elementary reactions which are theoretically important and to unravel the mechanism of complex chemical reactions or photo chemical processes which play an important role in many macroscopic processes and (2) to determine the energetics of polyatomic free radicals using microscopic experimental methods. Most of the information is derived from measurement of the product fragment translational energy and angular distributions using unique molecular beam apparati designed for these purposes.
Yildirim, Necmettin; Kazanci, Caner
2011-01-01
A brief introduction to mathematical modeling of biochemical regulatory reaction networks is presented. Both deterministic and stochastic modeling techniques are covered with examples from enzyme kinetics, coupled reaction networks with oscillatory dynamics and bistability. The Yildirim-Mackey model for lactose operon is used as an example to discuss and show how deterministic and stochastic methods can be used to investigate various aspects of this bacterial circuit. PMID:21187231
Spiralling dynamics near heteroclinic networks
NASA Astrophysics Data System (ADS)
Rodrigues, Alexandre A. P.; Labouriau, Isabel S.
2014-02-01
There are few explicit examples in the literature of vector fields exhibiting complex dynamics that may be proved analytically. We construct explicitly a two parameter family of vector fields on the three-dimensional sphere S, whose flow has a spiralling attractor containing the following: two hyperbolic equilibria, heteroclinic trajectories connecting them transversely and a non-trivial hyperbolic, invariant and transitive set. The spiralling set unfolds a heteroclinic network between two symmetric saddle-foci and contains a sequence of topological horseshoes semiconjugate to full shifts over an alphabet with more and more symbols, coexisting with Newhouse phenomena. The vector field is the restriction to S of a polynomial vector field in R. In this article, we also identify global bifurcations that induce chaotic dynamics of different types.
Dynamics and pattern formation in a cancer network with diffusion
NASA Astrophysics Data System (ADS)
Zheng, Qianqian; Shen, Jianwei
2015-10-01
Diffusion is ubiquitous inside cells, and it is capable of inducing spontaneous pattern formation in reaction-diffusion systems on a spatially homogeneous domain. In this paper, we investigate the dynamics of a diffusive cancer network regulated by microRNA and obtain the condition that the network undergoes a Hopf bifurcation and a Turing pattern bifurcation. In addition, we also develop the amplitude equation of the network model by using Taylor series expansion, multi-scaling and further expansion in powers of a small parameter. As a result of these analyses, we obtain the explicit condition on how the dynamics of the diffusive cancer network evolve. These results reveal that this system has rich dynamics, such as spotted stripe and hexagon patterns. The bifurcation diagram helps us understand the biological mechanism in the cancer network. Finally, numerical simulations confirm our analytical results.
Reduction of chemical reaction networks through delay distributions
NASA Astrophysics Data System (ADS)
Barrio, Manuel; Leier, André; Marquez-Lago, Tatiana T.
2013-03-01
Accurate modelling and simulation of dynamic cellular events require two main ingredients: an adequate description of key chemical reactions and simulation of such chemical events in reasonable time spans. Quite logically, posing the right model is a crucial step for any endeavour in Computational Biology. However, more often than not, it is the associated computational costs which actually limit our capabilities of representing complex cellular behaviour. In this paper, we propose a methodology aimed at representing chains of chemical reactions by much simpler, reduced models. The abridgement is achieved by generation of model-specific delay distribution functions, consecutively fed to a delay stochastic simulation algorithm. We show how such delay distributions can be analytically described whenever the system is solely composed of consecutive first-order reactions, with or without additional "backward" bypass reactions, yielding an exact reduction. For models including other types of monomolecular reactions (constitutive synthesis, degradation, or "forward" bypass reactions), we discuss why one must adopt a numerical approach for its accurate stochastic representation, and propose two alternatives for this. In these cases, the accuracy depends on the respective numerical sample size. Our model reduction methodology yields significantly lower computational costs while retaining accuracy. Quite naturally, computational costs increase alongside network size and separation of time scales. Thus, we expect our model reduction methodologies to significantly decrease computational costs in these instances. We anticipate the use of delays in model reduction will greatly alleviate some of the current restrictions in simulating large sets of chemical reactions, largely applicable in pharmaceutical and biological research.
Molecular beam studies of reaction dynamics
Lee, Yuan T.
1991-03-01
The major thrust of this research project is to elucidate detailed dynamics of simple elementary reactions that are theoretically important and to unravel the mechanism of complex chemical reactions or photochemical processes that play important roles in many macroscopic processes. Molecular beams of reactants are used to study individual reactive encounters between molecules or to monitor photodissociation events in a collision-free environment. Most of the information is derived from measurement of the product fragment energy, angular, and state distributions. Recent activities are centered on the mechanisms of elementary chemical reactions involving oxygen atoms with unsaturated hydrocarbons, the dynamics of endothermic substitution reactions, the dependence of the chemical reactivity of electronically excited atoms on the alignment of excited orbitals, the primary photochemical processes of polyatomic molecules, intramolecular energy transfer of chemically activated and locally excited molecules, the energetics of free radicals that are important to combustion processes, the infrared-absorption spectra of carbonium ions and hydrated hydronium ions, and bond-selective photodissociation through electric excitation.
Molecular beam studies of reaction dynamics
Lee, Y.T.
1993-12-01
The major thrust of this research project is to elucidate detailed dynamics of simple elementary reactions that are theoretically important and to unravel the mechanism of complex chemical reactions or photochemical processes that play important roles in many macroscopic processes. Molecular beams of reactants are used to study individual reactive encounters between molecules or to monitor photodissociation events in a collision-free environment. Most of the information is derived from measurement of the product fragment energy, angular, and state distributions. Recent activities are centered on the mechanisms of elementary chemical reactions involving oxygen atoms with unsaturated hydrocarbons, the dynamics of endothermic substitution reactions, the dependence of the chemical reactivity of electronically excited atoms on the alignment of excited orbitals, the primary photochemical processes of polyatomic molecules, intramolecular energy transfer of chemically activated and locally excited molecules, the energetics of free radicals that are important to combustion processes, the infrared-absorption spectra of carbonium ions and hydrated hydronium ions, and bond-selective photodissociation through electric excitation.
Deterministic Function Computation with Chemical Reaction Networks*
Chen, Ho-Lin; Doty, David; Soloveichik, David
2013-01-01
Chemical reaction networks (CRNs) formally model chemistry in a well-mixed solution. CRNs are widely used to describe information processing occurring in natural cellular regulatory networks, and with upcoming advances in synthetic biology, CRNs are a promising language for the design of artificial molecular control circuitry. Nonetheless, despite the widespread use of CRNs in the natural sciences, the range of computational behaviors exhibited by CRNs is not well understood. CRNs have been shown to be efficiently Turing-universal (i.e., able to simulate arbitrary algorithms) when allowing for a small probability of error. CRNs that are guaranteed to converge on a correct answer, on the other hand, have been shown to decide only the semilinear predicates (a multi-dimensional generalization of “eventually periodic” sets). We introduce the notion of function, rather than predicate, computation by representing the output of a function f : ℕk → ℕl by a count of some molecular species, i.e., if the CRN starts with x1, …, xk molecules of some “input” species X1, …, Xk, the CRN is guaranteed to converge to having f(x1, …, xk) molecules of the “output” species Y1, …, Yl. We show that a function f : ℕk → ℕl is deterministically computed by a CRN if and only if its graph {(x, y) ∈ ℕk × ℕl ∣ f(x) = y} is a semilinear set. Finally, we show that each semilinear function f (a function whose graph is a semilinear set) can be computed by a CRN on input x in expected time O(polylog ∥x∥1). PMID:25383068
Neural dynamics in superconducting networks
NASA Astrophysics Data System (ADS)
Segall, Kenneth; Schult, Dan; Crotty, Patrick; Miller, Max
2012-02-01
We discuss the use of Josephson junction networks as analog models for simulating neuron behaviors. A single unit called a ``Josephson Junction neuron'' composed of two Josephson junctions [1] displays behavior that shows characteristics of single neurons such as action potentials, thresholds and refractory periods. Synapses can be modeled as passive filters and can be used to connect neurons together. The sign of the bias current to the Josephson neuron can be used to determine if the neuron is excitatory or inhibitory. Due to the intrinsic speed of Josephson junctions and their scaling properties as analog models, a large network of Josephson neurons measured over typical lab times contains dynamics which would essentially be impossible to calculate on a computer We discuss the operating principle of the Josephson neuron, coupling Josephson neurons together to make large networks, and the Kuramoto-like synchronization of a system of disordered junctions.[4pt] [1] ``Josephson junction simulation of neurons,'' P. Crotty, D. Schult and K. Segall, Physical Review E 82, 011914 (2010).
Lattice based Kinetic Monte Carlo Simulations of a complex chemical reaction network
NASA Astrophysics Data System (ADS)
Danielson, Thomas; Savara, Aditya; Hin, Celine
Lattice Kinetic Monte Carlo (KMC) simulations offer a powerful alternative to using ordinary differential equations for the simulation of complex chemical reaction networks. Lattice KMC provides the ability to account for local spatial configurations of species in the reaction network, resulting in a more detailed description of the reaction pathway. In KMC simulations with a large number of reactions, the range of transition probabilities can span many orders of magnitude, creating subsets of processes that occur more frequently or more rarely. Consequently, processes that have a high probability of occurring may be selected repeatedly without actually progressing the system (i.e. the forward and reverse process for the same reaction). In order to avoid the repeated occurrence of fast frivolous processes, it is necessary to throttle the transition probabilities in such a way that avoids altering the overall selectivity. Likewise, as the reaction progresses, new frequently occurring species and reactions may be introduced, making a dynamic throttling algorithm a necessity. We present a dynamic steady-state detection scheme with the goal of accurately throttling rate constants in order to optimize the KMC run time without compromising the selectivity of the reaction network. The algorithm has been applied to a large catalytic chemical reaction network, specifically that of methanol oxidative dehydrogenation, as well as additional pathways on CeO2(111) resulting in formaldehyde, CO, methanol, CO2, H2 and H2O as gas products.
Dynamic information routing in complex networks.
Kirst, Christoph; Timme, Marc; Battaglia, Demian
2016-01-01
Flexible information routing fundamentally underlies the function of many biological and artificial networks. Yet, how such systems may specifically communicate and dynamically route information is not well understood. Here we identify a generic mechanism to route information on top of collective dynamical reference states in complex networks. Switching between collective dynamics induces flexible reorganization of information sharing and routing patterns, as quantified by delayed mutual information and transfer entropy measures between activities of a network's units. We demonstrate the power of this mechanism specifically for oscillatory dynamics and analyse how individual unit properties, the network topology and external inputs co-act to systematically organize information routing. For multi-scale, modular architectures, we resolve routing patterns at all levels. Interestingly, local interventions within one sub-network may remotely determine nonlocal network-wide communication. These results help understanding and designing information routing patterns across systems where collective dynamics co-occurs with a communication function. PMID:27067257
Dynamic information routing in complex networks
NASA Astrophysics Data System (ADS)
Kirst, Christoph; Timme, Marc; Battaglia, Demian
2016-04-01
Flexible information routing fundamentally underlies the function of many biological and artificial networks. Yet, how such systems may specifically communicate and dynamically route information is not well understood. Here we identify a generic mechanism to route information on top of collective dynamical reference states in complex networks. Switching between collective dynamics induces flexible reorganization of information sharing and routing patterns, as quantified by delayed mutual information and transfer entropy measures between activities of a network's units. We demonstrate the power of this mechanism specifically for oscillatory dynamics and analyse how individual unit properties, the network topology and external inputs co-act to systematically organize information routing. For multi-scale, modular architectures, we resolve routing patterns at all levels. Interestingly, local interventions within one sub-network may remotely determine nonlocal network-wide communication. These results help understanding and designing information routing patterns across systems where collective dynamics co-occurs with a communication function.
Dynamic information routing in complex networks
Kirst, Christoph; Timme, Marc; Battaglia, Demian
2016-01-01
Flexible information routing fundamentally underlies the function of many biological and artificial networks. Yet, how such systems may specifically communicate and dynamically route information is not well understood. Here we identify a generic mechanism to route information on top of collective dynamical reference states in complex networks. Switching between collective dynamics induces flexible reorganization of information sharing and routing patterns, as quantified by delayed mutual information and transfer entropy measures between activities of a network's units. We demonstrate the power of this mechanism specifically for oscillatory dynamics and analyse how individual unit properties, the network topology and external inputs co-act to systematically organize information routing. For multi-scale, modular architectures, we resolve routing patterns at all levels. Interestingly, local interventions within one sub-network may remotely determine nonlocal network-wide communication. These results help understanding and designing information routing patterns across systems where collective dynamics co-occurs with a communication function. PMID:27067257
Robustness Analysis and Behavior Discrimination in Enzymatic Reaction Networks
Donzé, Alexandre; Fanchon, Eric; Gattepaille, Lucie Martine; Maler, Oded; Tracqui, Philippe
2011-01-01
Characterizing the behavior and robustness of enzymatic networks with numerous variables and unknown parameter values is a major challenge in biology, especially when some enzymes have counter-intuitive properties or switch-like behavior between activation and inhibition. In this paper, we propose new methodological and tool-supported contributions, based on the intuitive formalism of temporal logic, to express in a rigorous manner arbitrarily complex dynamical properties. Our multi-step analysis allows efficient sampling of the parameter space in order to define feasible regions in which the model exhibits imposed or experimentally observed behaviors. In a first step, an algorithmic methodology involving sensitivity analysis is conducted to determine bifurcation thresholds for a limited number of model parameters or initial conditions. In a second step, this boundary detection is supplemented by a global robustness analysis, based on quasi-Monte Carlo approach that takes into account all model parameters. We apply this method to a well-documented enzymatic reaction network describing collagen proteolysis by matrix metalloproteinase MMP2 and membrane type 1 metalloproteinase (MT1-MMP) in the presence of tissue inhibitor of metalloproteinase TIMP2. For this model, our method provides an extended analysis and quantification of network robustness toward paradoxical TIMP2 switching activity between activation or inhibition of MMP2 production. Further implication of our approach is illustrated by demonstrating and analyzing the possible existence of oscillatory behaviors when considering an extended open configuration of the enzymatic network. Notably, we construct bifurcation diagrams that specify key parameters values controlling the co-existence of stable steady and non-steady oscillatory proteolytic dynamics. PMID:21980344
Robustness analysis and behavior discrimination in enzymatic reaction networks.
Donzé, Alexandre; Fanchon, Eric; Gattepaille, Lucie Martine; Maler, Oded; Tracqui, Philippe
2011-01-01
Characterizing the behavior and robustness of enzymatic networks with numerous variables and unknown parameter values is a major challenge in biology, especially when some enzymes have counter-intuitive properties or switch-like behavior between activation and inhibition. In this paper, we propose new methodological and tool-supported contributions, based on the intuitive formalism of temporal logic, to express in a rigorous manner arbitrarily complex dynamical properties. Our multi-step analysis allows efficient sampling of the parameter space in order to define feasible regions in which the model exhibits imposed or experimentally observed behaviors. In a first step, an algorithmic methodology involving sensitivity analysis is conducted to determine bifurcation thresholds for a limited number of model parameters or initial conditions. In a second step, this boundary detection is supplemented by a global robustness analysis, based on quasi-Monte Carlo approach that takes into account all model parameters. We apply this method to a well-documented enzymatic reaction network describing collagen proteolysis by matrix metalloproteinase MMP2 and membrane type 1 metalloproteinase (MT1-MMP) in the presence of tissue inhibitor of metalloproteinase TIMP2. For this model, our method provides an extended analysis and quantification of network robustness toward paradoxical TIMP2 switching activity between activation or inhibition of MMP2 production. Further implication of our approach is illustrated by demonstrating and analyzing the possible existence of oscillatory behaviors when considering an extended open configuration of the enzymatic network. Notably, we construct bifurcation diagrams that specify key parameters values controlling the co-existence of stable steady and non-steady oscillatory proteolytic dynamics. PMID:21980344
Flux-concentration duality in dynamic nonequilibrium biological networks.
Jamshidi, Neema; Palsson, Bernhard Ø
2009-09-01
The structure of dynamic states in biological networks is of fundamental importance in understanding their function. Considering the elementary reaction structure of reconstructed metabolic networks, we show how appreciation of a gradient matrix, G =dv/dx (where v is the vector of fluxes and x is the vector of concentrations), enables the formulation of dual Jacobian matrices. One is for concentrations, J(x) =S x G, and the other is for fluxes, J(v) =G x S. The fundamental properties of these two Jacobians and the underlying duality that relates them are delineated. We describe a generalized approach to decomposing reaction networks in terms of the thermodynamic and kinetic components in the context of the network structure. The thermodynamic and kinetic influences can be viewed in terms of direction-driver relationships in the network. PMID:19720010
Quantum dynamics of fast chemical reactions
Light, J.C.
1993-12-01
The aims of this research are to explore, develop, and apply theoretical methods for the evaluation of the dynamics of gas phase collision processes, primarily chemical reactions. The primary theoretical tools developed for this work have been quantum scattering theory, both in time dependent and time independent forms. Over the past several years, the authors have developed and applied methods for the direct quantum evaluation of thermal rate constants, applying these to the evaluation of the hydrogen isotopic exchange reactions, applied wave packet propagation techniques to the dissociation of Rydberg H{sub 3}, incorporated optical potentials into the evaluation of thermal rate constants, evaluated the use of optical potentials for state-to-state reaction probability evaluations, and, most recently, have developed quantum approaches for electronically non-adiabatic reactions which may be applied to simplify calculations of reactive, but electronically adiabatic systems. Evaluation of the thermal rate constants and the dissociation of H{sub 3} were reported last year, and have now been published.
Community dynamics in social networks
NASA Astrophysics Data System (ADS)
Palla, Gergely; Barabási, Albert-László; Vicsek, Tamás
2007-06-01
We study the statistical properties of community dynamics in large social networks, where the evolving communities are obtained from subsequent snapshots of the modular structure. Such cohesive groups of people can grow by recruiting new members, or contract by loosing members; two (or more) groups may merge into a single community, while a large enough social group can split into several smaller ones; new communities are born and old ones may disappear. We find significant difference between the behaviour of smaller collaborative or friendship circles and larger communities, eg. institutions. Social groups containing only a few members persist longer on average when the fluctuations of the members is small. In contrast, we find that the condition for stability for large communities is continuous changes in their membership, allowing for the possibility that after some time practically all members are exchanged.
Mode specificity in unimolecular reaction dynamics
Waite, B.A.
1982-07-01
Theoretical studies on mode specificity in unimolecular reaction dynamics are presented, based on essentially exact quantum mechanical methods, a semi-classical multichannel branching model, and classical trajectory methods. The principal aim is to discover the relevant factors governing whether a unimolecular system exhibits mode specificity in its individual state rate constants, i.e., whether quasi-degenerate metastable states decay with significantly different rates. Model studies of two nonlinearly coupled oscillators (one of which can dissociate) demonstrate the effects of various features of potential energy surfaces on the character of the rates (e.g., degeneracy of modes, reaction path curvature, frequency modulation, etc.). These results and those obtained for the Henon-Heiles potential energy surface indicate and apparent absence of correlation between the quasi-periodic/ergodic motion of classical mechanics and the mode specific/statistical behavior of the unimolecular rate constants.
New methods for quantum mechanical reaction dynamics
Thompson, W.H. |
1996-12-01
Quantum mechanical methods are developed to describe the dynamics of bimolecular chemical reactions. We focus on developing approaches for directly calculating the desired quantity of interest. Methods for the calculation of single matrix elements of the scattering matrix (S-matrix) and initial state-selected reaction probabilities are presented. This is accomplished by the use of absorbing boundary conditions (ABC) to obtain a localized (L{sup 2}) representation of the outgoing wave scattering Green`s function. This approach enables the efficient calculation of only a single column of the S-matrix with a proportionate savings in effort over the calculation of the entire S-matrix. Applying this method to the calculation of the initial (or final) state-selected reaction probability, a more averaged quantity, requires even less effort than the state-to-state S-matrix elements. It is shown how the same representation of the Green`s function can be effectively applied to the calculation of negative ion photodetachment intensities. Photodetachment spectroscopy of the anion ABC{sup -} can be a very useful method for obtaining detailed information about the neutral ABC potential energy surface, particularly if the ABC{sup -} geometry is similar to the transition state of the neutral ABC. Total and arrangement-selected photodetachment spectra are calculated for the H{sub 3}O{sup -} system, providing information about the potential energy surface for the OH + H{sub 2} reaction when compared with experimental results. Finally, we present methods for the direct calculation of the thermal rate constant from the flux-position and flux-flux correlation functions. The spirit of transition state theory is invoked by concentrating on the short time dynamics in the area around the transition state that determine reactivity. These methods are made efficient by evaluating the required quantum mechanical trace in the basis of eigenstates of the Boltzmannized flux operator.
Controlling the rates of biochemical reactions and signaling networks by shape and volume changes.
Lizana, L; Bauer, B; Orwar, O
2008-03-18
In biological systems, chemical activity takes place in micrometer- and nanometer-sized compartments that constantly change in shape and volume. These ever-changing cellular compartments embed chemical reactions, and we demonstrate that the rates of such incorporated reactions are directly affected by the ongoing shape reconfigurations. First, we show that the rate of product formation in an enzymatic reaction can be regulated by simple volume contraction-dilation transitions. The results suggest that mitochondria may regulate the dynamics of interior reaction pathways (e.g., the Krebs cycle) by volume changes. We then show the effect of shape changes on reactions occurring in more complex and structured systems by using biomimetic networks composed of micrometer-sized compartments joined together by nanotubes. Chemical activity was measured by implementing an enzymatic reaction-diffusion system. During ongoing reactions, the network connectivity is changed suddenly (similar to the dynamic tube formations found inside Golgi stacks, for example), and the effect on the reaction is registered. We show that spatiotemporal properties of the reaction-diffusion system are extremely sensitive to sudden changes in network topology and that chemical reactions can be initiated, or boosted, in certain nodes as a function of connectivity. PMID:18337513
NASA Astrophysics Data System (ADS)
Pal, Krishnendu; Das, Biswajit; Banerjee, Kinshuk; Gangopadhyay, Gautam
2015-09-01
We have introduced an approach to nonequilibrium thermodynamics of an open chemical reaction network in terms of the propensities of the individual elementary reactions and the corresponding reverse reactions. The method is a microscopic formulation of the dissipation function in terms of the relative entropy or Kullback-Leibler distance which is based on the analogy of phase space trajectory with the path of elementary reactions in a network of chemical process. We have introduced here a fluctuation theorem valid for each opposite pair of elementary reactions which is useful in determining the contribution of each sub-reaction on the nonequilibrium thermodynamics of overall reaction. The methodology is applied to an oligomeric enzyme kinetics at a chemiostatic condition that leads the reaction to a nonequilibrium steady state for which we have estimated how each step of the reaction is energy driven or entropy driven to contribute to the overall reaction.
Networked Dynamic Systems: Identification, Controllability, and Randomness
NASA Astrophysics Data System (ADS)
Nabi-Abdolyousefi, Marzieh
The presented dissertation aims to develop a graph-centric framework for the analysis and synthesis of networked dynamic systems (NDS) consisting of multiple dynamic units that interact via an interconnection topology. We examined three categories of network problems, namely, identification, controllability, and randomness. In network identification, as a subclass of inverse problems, we made an explicit relation between the input-output behavior of an NDS and the underlying interacting network. In network controllability, we provided structural and algebraic insights into features of the network that enable external signal(s) to control the state of the nodes in the network for certain classes of interconnections, namely, path, circulant, and Cartesian networks. We also examined the relation between network controllability and the symmetry structure of the graph. Motivated by the analysis results for the controllability and observability of deterministic networks, a natural question is whether randomness in the network layer or in the layer of inputs and outputs generically leads to favorable system theoretic properties. In this direction, we examined system theoretic properties of random networks including controllability, observability, and performance of optimal feedback controllers and estimators. We explored some of the ramifications of such an analysis framework in opinion dynamics over social networks and sensor networks in estimating the real-time position of a Seaglider from experimental data.
Toward cell circuitry: Topological analysis of enzyme reaction networks via reaction route graphs
NASA Astrophysics Data System (ADS)
Datta, Ravindra; Vilekar, Saurabh A.; Fishtik, Ilie; Dittami, James P.
2008-05-01
The first step toward developing complete cell circuitry is to build quantitative networks for enzyme reactions. The conventional King-Altman-Hill (KAH) algorithm for topological analysis of enzyme networks, adapted from electrical networks, is based on “Reaction Graphs” that, unlike electrical circuits, are not quantitative, being straightforward renderings of conventional schematics of reaction mechanisms. Therefore, we propose the use of “Reaction Route (RR) Graphs” instead, as a more suitable graph-theoretical representation for topological analysis of enzyme reaction networks. The RR Graphs are drawn such that they are not only useful for visualizing the various reaction routes or pathways, but unlike Reaction Graphs possess network properties consistent with requisite kinetic, mass balance, and thermodynamic constraints. Therefore, they are better than the conventional Reaction Graphs for topological representation and analysis of enzyme reactions, both via the KAH methodology as well as via numerical matrix inversion. The difference between the two is highlighted based on the example of a single enzyme reaction network for the conversion of 7,8-dihydrofolate and NADPH into 5,6,7,8-tetrahydrofolate and NADP +, catalyzed by the enzyme dihydrofolate reductase.
Model Of Neural Network With Creative Dynamics
NASA Technical Reports Server (NTRS)
Zak, Michail; Barhen, Jacob
1993-01-01
Paper presents analysis of mathematical model of one-neuron/one-synapse neural network featuring coupled activation and learning dynamics and parametrical periodic excitation. Demonstrates self-programming, partly random behavior of suitable designed neural network; believed to be related to spontaneity and creativity of biological neural networks.
Structure, dynamics, and surface reactions of bioactive glasses
NASA Astrophysics Data System (ADS)
Zeitler, Todd R.
Three bioactive glasses (45S5, 55S4.3, and 60S3.8) have been investigated using atomic-scale molecular dynamics simulations in attempt to explain differences in observed macroscopic bioactivity. Bulk and surface structures and bulk dynamics have been characterized. Ion exchange and hydrolysis reactions, the first two stages in Hench's model describing the reactions of bioactive glass surfaces in vivo, have been investigated in detail. The 45S5 composition shows a much greater network fragmentation: it is suggested that this fragmentation can play a role in at least the first two stages of Hench's model for HCA formation on the surfaces of bioactive glasses. In terms of dynamic behavior, long-range diffusion was only observed for sodium. Calcium showed only jumps between adjacent sites, while phosphorus showed only local vibrations. Surface simulations show the distinct accumulation of sodium at the immediate surface for each composition. Surface channels are also shown to exist and are most evident for 45S5 glass. Results for a single ion exchange showed that the ion-exchange reaction is preferred (more exothermic) for Na+ ions near Si, rather than P. A range of reaction energies were found, due to a range of local environments, as expected for a glass surface. The average reaction energies are not significantly different among the three glass compositions. The results for bond hydrolysis on as-created surfaces show no significant differences among the three compositions for simulations involving Si-O-Si or Si-O-P. All average values are greater than zero, indicating endothermic reactions that are not favorable by themselves. However, it is shown that the hydrolysis reactions became more favorable (in fact, exothermic for 45S5 and 55S4.3) when simulated on surfaces that had already been ion-exchanged. This is significant because it gives evidence supporting Hench's proposed reaction sequence. Perhaps even more significantly, the reaction energies for hydrolysis
Forced synchronization of autonomous dynamical Boolean networks
Rivera-Durón, R. R. Campos-Cantón, E.; Campos-Cantón, I.; Gauthier, Daniel J.
2015-08-15
We present the design of an autonomous time-delay Boolean network realized with readily available electronic components. Through simulations and experiments that account for the detailed nonlinear response of each circuit element, we demonstrate that a network with five Boolean nodes displays complex behavior. Furthermore, we show that the dynamics of two identical networks display near-instantaneous synchronization to a periodic state when forced by a common periodic Boolean signal. A theoretical analysis of the network reveals the conditions under which complex behavior is expected in an individual network and the occurrence of synchronization in the forced networks. This research will enable future experiments on autonomous time-delay networks using readily available electronic components with dynamics on a slow enough time-scale so that inexpensive data collection systems can faithfully record the dynamics.
Using Network Dynamical Influence to Drive Consensus
NASA Astrophysics Data System (ADS)
Punzo, Giuliano; Young, George F.; MacDonald, Malcolm; Leonard, Naomi E.
2016-05-01
Consensus and decision-making are often analysed in the context of networks, with many studies focusing attention on ranking the nodes of a network depending on their relative importance to information routing. Dynamical influence ranks the nodes with respect to their ability to influence the evolution of the associated network dynamical system. In this study it is shown that dynamical influence not only ranks the nodes, but also provides a naturally optimised distribution of effort to steer a network from one state to another. An example is provided where the “steering” refers to the physical change in velocity of self-propelled agents interacting through a network. Distinct from other works on this subject, this study looks at directed and hence more general graphs. The findings are presented with a theoretical angle, without targeting particular applications or networked systems; however, the framework and results offer parallels with biological flocks and swarms and opportunities for design of technological networks.
Using Network Dynamical Influence to Drive Consensus.
Punzo, Giuliano; Young, George F; Macdonald, Malcolm; Leonard, Naomi E
2016-01-01
Consensus and decision-making are often analysed in the context of networks, with many studies focusing attention on ranking the nodes of a network depending on their relative importance to information routing. Dynamical influence ranks the nodes with respect to their ability to influence the evolution of the associated network dynamical system. In this study it is shown that dynamical influence not only ranks the nodes, but also provides a naturally optimised distribution of effort to steer a network from one state to another. An example is provided where the "steering" refers to the physical change in velocity of self-propelled agents interacting through a network. Distinct from other works on this subject, this study looks at directed and hence more general graphs. The findings are presented with a theoretical angle, without targeting particular applications or networked systems; however, the framework and results offer parallels with biological flocks and swarms and opportunities for design of technological networks. PMID:27210291
Using Network Dynamical Influence to Drive Consensus
Punzo, Giuliano; Young, George F.; Macdonald, Malcolm; Leonard, Naomi E.
2016-01-01
Consensus and decision-making are often analysed in the context of networks, with many studies focusing attention on ranking the nodes of a network depending on their relative importance to information routing. Dynamical influence ranks the nodes with respect to their ability to influence the evolution of the associated network dynamical system. In this study it is shown that dynamical influence not only ranks the nodes, but also provides a naturally optimised distribution of effort to steer a network from one state to another. An example is provided where the “steering” refers to the physical change in velocity of self-propelled agents interacting through a network. Distinct from other works on this subject, this study looks at directed and hence more general graphs. The findings are presented with a theoretical angle, without targeting particular applications or networked systems; however, the framework and results offer parallels with biological flocks and swarms and opportunities for design of technological networks. PMID:27210291
Reaction dynamics and photochemistry of divalent systems
Davis, H.F.
1992-05-01
Results are presented of molecular beam studies of bimolecular and unimolecular reactions of Ba. Chapter 1 discusses the reaction Ba + NO{sub 2}. Formation of the dominant BaO({sup 1}{Sigma}) + NO products resulted primarily from decay of long-lived Ba{sup +}NO{sub 2}{sup {minus}} collision complexes. Secondary mechanisms led to formation of forward scattered, internally excited BaO, and BaNO + O. D{sub o}(Ba-NO) = 65{plus_minus}20 kcal/mol. Reactions of ground state and electronically excited Ba with water and alcohols are examined in Chapter 2. Reaction of Ba({sup 1}S) + H{sup 2}O led to BaO + H{sub 2}, whereas excited state Ba({sup 1}D) + H{sub 2}O reacted to form BaOH + H. Collisions between Ba and CH{sub 3}OH led to BaOCH{sub 3} + H. Radical channels involve H-atom migration and are promoted by excitation of the incident Ba atom. In Chapter 3, reactions of Ba({sup 1}S) with ClO{sub 2}2 and O{sub 3} are discussed. Again, direct and complex mechanisms were observed. Formation of BaCl + O{sub 2} from decomposition of Ba{sup +}ClO{sub 2}{sup {minus}} accounted for 10% of total reaction crass section. Although Ba + O{sub 3} {yields} BaO + 0{sub 2} occurs primarily by direct reaction mechanisms, the secondary channel Ba + 0{sub 3} {yields} BaO{sub 2} + 0 involved decay of long lived Ba{sup +}O{sub 3}{sup {minus}} intermediates. D{sub o}(Ba{minus}O{sub 2}) = 120 {plus_minus}20 kcal/mol. Photodissociation dynamics of NO{sub 3} is explored in chapter 4. Visible excitation leads to formation of NO + 0{sub 2} and NO{sub 2} + O. Wavelength dependence of branching ratios is investigated. D{sub o}(O-NO{sub 2}) = 48.55 kcal/mole ;and calculate {Delta}H{sub f}(NO{sub 3}) = 17.75 kcal/mole (298K). Chapter 5 discusses the photodissociation of OClO in a molecular beam. Although ClO({sup 2}II) + O({sup 3}P) is dominant, Cl({sup 2}P) + O{sub 2} also forms, with a max yield of 3.9{plus_minus}0.8% near 404nm.
Dynamics on Complex Networks and Applications
NASA Astrophysics Data System (ADS)
Motter, Adilson E.; Matías, Manuel A.; Kurths, Jürgen; Ott, Edward
2006-12-01
At the eight-year anniversary of Watts and Strogatz’s work on the collective dynamics of small-world networks and seven years after Barabási and Albert’s discovery of scale-free networks, the area of dynamical processes on complex networks is at the forefront of the current research on nonlinear dynamics and complex systems. This volume brings together a selection of original contributions in complementary topics of statistical physics, nonlinear dynamics and biological sciences, and is expected to provide the reader with a comprehensive up-to-date representation of this rapidly developing area.
Charge transport network dynamics in molecular aggregates.
Jackson, Nicholas E; Chen, Lin X; Ratner, Mark A
2016-08-01
Due to the nonperiodic nature of charge transport in disordered systems, generating insight into static charge transport networks, as well as analyzing the network dynamics, can be challenging. Here, we apply time-dependent network analysis to scrutinize the charge transport networks of two representative molecular semiconductors: a rigid n-type molecule, perylenediimide, and a flexible p-type molecule, [Formula: see text] Simulations reveal the relevant timescale for local transfer integral decorrelation to be [Formula: see text]100 fs, which is shown to be faster than that of a crystalline morphology of the same molecule. Using a simple graph metric, global network changes are observed over timescales competitive with charge carrier lifetimes. These insights demonstrate that static charge transport networks are qualitatively inadequate, whereas average networks often overestimate network connectivity. Finally, a simple methodology for tracking dynamic charge transport properties is proposed. PMID:27439871
Using Visualizations to Explore Network Dynamics
Chu, Kar-Hai; Wipfli, Heather; Valente, Thomas W.
2014-01-01
Network analysis has become a popular tool to examine data from online social networks to politics to ecological systems. As more computing power has become available, new technology-driven methods and tools are being developed that can support larger and richer network data, including dynamic network analysis. This timely merger of abundant data and cutting edge techniques affords researchers the ability to better understand networks over time, accurately show how they evolve, find patterns of growth, or study models such as the diffusion of innovation. We combine traditional methods in social network analysis with new innovative visualizations and methods in dynamic network studies to explore an online tobacco-control community called GLOBALink, using almost twenty years of longitudinal data. We describe the methods used for the study, and perform an exploratory network study that links empirical results to real-world events. PMID:25285051
Mélykúti, Bence; Hespanha, João P.; Khammash, Mustafa
2014-01-01
Many biochemical reaction networks are inherently multiscale in time and in the counts of participating molecular species. A standard technique to treat different time scales in the stochastic kinetics framework is averaging or quasi-steady-state analysis: it is assumed that the fast dynamics reaches its equilibrium (stationary) distribution on a time scale where the slowly varying molecular counts are unlikely to have changed. We derive analytic equilibrium distributions for various simple biochemical systems, such as enzymatic reactions and gene regulation models. These can be directly inserted into simulations of the slow time-scale dynamics. They also provide insight into the stimulus–response of these systems. An important model for which we derive the analytic equilibrium distribution is the binding of dimer transcription factors (TFs) that first have to form from monomers. This gene regulation mechanism is compared to the cases of the binding of simple monomer TFs to one gene or to multiple copies of a gene, and to the cases of the cooperative binding of two or multiple TFs to a gene. The results apply equally to ligands binding to enzyme molecules. PMID:24920118
Mélykúti, Bence; Hespanha, João P; Khammash, Mustafa
2014-08-01
Many biochemical reaction networks are inherently multiscale in time and in the counts of participating molecular species. A standard technique to treat different time scales in the stochastic kinetics framework is averaging or quasi-steady-state analysis: it is assumed that the fast dynamics reaches its equilibrium (stationary) distribution on a time scale where the slowly varying molecular counts are unlikely to have changed. We derive analytic equilibrium distributions for various simple biochemical systems, such as enzymatic reactions and gene regulation models. These can be directly inserted into simulations of the slow time-scale dynamics. They also provide insight into the stimulus-response of these systems. An important model for which we derive the analytic equilibrium distribution is the binding of dimer transcription factors (TFs) that first have to form from monomers. This gene regulation mechanism is compared to the cases of the binding of simple monomer TFs to one gene or to multiple copies of a gene, and to the cases of the cooperative binding of two or multiple TFs to a gene. The results apply equally to ligands binding to enzyme molecules. PMID:24920118
Mathematically Reduced Chemical Reaction Mechanism Using Neural Networks
Nelson Butuk
2006-09-21
This is an annual technical report for the work done over the last year (period ending 9/30/2005) on the project titled ''Mathematically Reduced Chemical Reaction Mechanism Using Neural Networks''. The aim of the project is to develop an efficient chemistry model for combustion simulations. The reduced chemistry model will be developed mathematically without the need of having extensive knowledge of the chemistry involved. To aid in the development of the model, Neural Networks (NN) will be used via a new network topology know as Non-linear Principal Components Analysis (NPCA). We report on the significant development made in developing a truly meshfree computational fluid dynamics (CFD) flow solver to be coupled to NPCA. First, the procedure of obtaining nearly analytic accurate first order derivatives using the complex step method (CSM) is extended to include computation of accurate meshfree second order derivatives via a theorem described in this report. Next, boosted generalized regression neural network (BGRNN), described in our previous report is combined with CSM and used to obtain complete solution of a hard to solve wave dominated sample second order partial differential equation (PDE): the cubic Schrodinger equation. The resulting algorithm is a significant improvement of the meshfree technique of smooth particle hydrodynamics method (SPH). It is suggested that the demonstrated meshfree technique be termed boosted smooth particle hydrodynamics method (BSPH). Some of the advantages of BSPH over other meshfree methods include; it is of higher order accuracy than SPH; compared to other meshfree methods, it is completely meshfree and does not require any background meshes; It does not involve any construction of shape function with their associated solution of possibly ill conditioned matrix equations; compared to some SPH techniques, no equation for the smoothing parameter is required; finally it is easy to program.
Psychology and social networks: a dynamic network theory perspective.
Westaby, James D; Pfaff, Danielle L; Redding, Nicholas
2014-04-01
Research on social networks has grown exponentially in recent years. However, despite its relevance, the field of psychology has been relatively slow to explain the underlying goal pursuit and resistance processes influencing social networks in the first place. In this vein, this article aims to demonstrate how a dynamic network theory perspective explains the way in which social networks influence these processes and related outcomes, such as goal achievement, performance, learning, and emotional contagion at the interpersonal level of analysis. The theory integrates goal pursuit, motivation, and conflict conceptualizations from psychology with social network concepts from sociology and organizational science to provide a taxonomy of social network role behaviors, such as goal striving, system supporting, goal preventing, system negating, and observing. This theoretical perspective provides psychologists with new tools to map social networks (e.g., dynamic network charts), which can help inform the development of change interventions. Implications for social, industrial-organizational, and counseling psychology as well as conflict resolution are discussed, and new opportunities for research are highlighted, such as those related to dynamic network intelligence (also known as cognitive accuracy), levels of analysis, methodological/ethical issues, and the need to theoretically broaden the study of social networking and social media behavior. (PsycINFO Database Record (c) 2014 APA, all rights reserved). PMID:24750076
Embedding dynamical networks into distributed models
NASA Astrophysics Data System (ADS)
Innocenti, Giacomo; Paoletti, Paolo
2015-07-01
Large networks of interacting dynamical systems are well-known for the complex behaviours they are able to display, even when each node features a quite simple dynamics. Despite examples of such networks being widespread both in nature and in technological applications, the interplay between the local and the macroscopic behaviour, through the interconnection topology, is still not completely understood. Moreover, traditional analytical methods for dynamical response analysis fail because of the intrinsically large dimension of the phase space of the network which makes the general problem intractable. Therefore, in this paper we develop an approach aiming to condense all the information in a compact description based on partial differential equations. By focusing on propagative phenomena, rigorous conditions under which the original network dynamical properties can be successfully analysed within the proposed framework are derived as well. A network of Fitzhugh-Nagumo systems is finally used to illustrate the effectiveness of the proposed method.
Temporal fidelity in dynamic social networks
NASA Astrophysics Data System (ADS)
Stopczynski, Arkadiusz; Sapiezynski, Piotr; Pentland, Alex `Sandy'; Lehmann, Sune
2015-10-01
It has recently become possible to record detailed social interactions in large social systems with high resolution. As we study these datasets, human social interactions display patterns that emerge at multiple time scales, from minutes to months. On a fundamental level, understanding of the network dynamics can be used to inform the process of measuring social networks. The details of measurement are of particular importance when considering dynamic processes where minute-to-minute details are important, because collection of physical proximity interactions with high temporal resolution is difficult and expensive. Here, we consider the dynamic network of proximity-interactions between approximately 500 individuals participating in the Copenhagen Networks Study. We show that in order to accurately model spreading processes in the network, the dynamic processes that occur on the order of minutes are essential and must be included in the analysis.
Reaction-Diffusion Processes on Random and Scale-Free Networks
NASA Astrophysics Data System (ADS)
Banerjee, Subhasis; Mallick, Shrestha Basu; Bose, Indrani
We study the discrete Gierer-Meinhardt model of reaction-diffusion on three different types of networks: regular, random and scale-free. The model dynamics lead to the formation of stationary Turing patterns in the steady state in certain parameter regions. Some general features of the patterns are studied through numerical simulation. The results for the random and scale-free networks show a marked difference from those in the case of the regular network. The difference may be ascribed to the small world character of the first two types of networks.
Combining molecular dynamics with mesoscopic Green’s function reaction dynamics simulations
Vijaykumar, Adithya; Bolhuis, Peter G.; Rein ten Wolde, Pieter
2015-12-07
In many reaction-diffusion processes, ranging from biochemical networks, catalysis, to complex self-assembly, the spatial distribution of the reactants and the stochastic character of their interactions are crucial for the macroscopic behavior. The recently developed mesoscopic Green’s Function Reaction Dynamics (GFRD) method enables efficient simulation at the particle level provided the microscopic dynamics can be integrated out. Yet, many processes exhibit non-trivial microscopic dynamics that can qualitatively change the macroscopic behavior, calling for an atomistic, microscopic description. We propose a novel approach that combines GFRD for simulating the system at the mesoscopic scale where particles are far apart, with a microscopic technique such as Langevin dynamics or Molecular Dynamics (MD), for simulating the system at the microscopic scale where reactants are in close proximity. This scheme defines the regions where the particles are close together and simulated with high microscopic resolution and those where they are far apart and simulated with lower mesoscopic resolution, adaptively on the fly. The new multi-scale scheme, called MD-GFRD, is generic and can be used to efficiently simulate reaction-diffusion systems at the particle level.
Computational fluid dynamics of reaction injection moulding
NASA Astrophysics Data System (ADS)
Mateus, Artur; Mitchell, Geoffrey; Bártolo, Paulo
2012-09-01
The modern approach to the development of moulds for injection moulding (Reaction Injection Moulding - RIM, Thermoplastic Injection Moulding - TIM and others) differs from the conventional approach based exclusively on the designer's experience and hypotheses. The increasingly complexityof moulds and the requirement by the clients for the improvement of their quality, shorter delivery times, and lower prices, demand the development of novel approaches to developed optimal moulds and moulded parts. The development of more accurate computational tools is fundamental to optimize both, the injection mouldingprocesses and the design, quality and durability of the moulds. This paper focuses on the RIM process proposing a novel thermo-rheo-kinetic model. The proposed model was implemented in generalpurpose Computational Fluid Dynamics (CFD) software. The model enables to accurately describe both flow and curing stages. Simulation results were validated against experimental results.
Reconstructing Directed Networks From Noisy Dynamics
NASA Astrophysics Data System (ADS)
Tam, Hiu Ching; Ching, Emily Sc
Complex systems can be fruitfully studied as networks of many elementary units, known as nodes, interacting with one another with the interactions being the links between the nodes. The overall behavior of the systems depends crucially on the network structure depicting how the nodes are linked with each other. It is usually possible to measure the dynamics of the individual nodes but difficult, if not impossible, to directly measure the interactions or links between the nodes. For most systems of interest, the links are directional in that one node affects the dynamics of the other but not vice versa. Moreover, the strength of interaction can vary for different links. Reconstructing directed and weighted networks from dynamics is one of the biggest challenges in network research. We have studied directed and weighted networks modelled by noisy dynamical systems with nonlinear dynamics and developed a method that reconstructs the links and their directions using only the dynamics of the nodes as input. Our method is motivated by a mathematical result derived for dynamical systems that approach a fixed point in the noise-free limit. We show that our method gives good reconstruction results for several directed and weighted networks with different nonlinear dynamics. Supported by Hong Kong Research Grants Council under Grant No. CUHK 14300914.
Dynamic network analysis of protein interactions
NASA Astrophysics Data System (ADS)
Almaas, Eivind; Deri, Joya
2007-03-01
Network approaches have recently become a popular tool to study complex systems such as cellular metabolism and protein interactions. A substantial number of analyses of the protein interaction network (PIN) of the yeast Saccharomyces cerevisiae have considered this network as a static entity, not taking the network's dynamic nature into account. Here, we examine the time-variation of gene regulation superimposed on the PIN by defining mRNA expression profiles throughout the cell cycle as node weights. To characterize these network dynamics, we have both developed a set of novel network measures as well as studied previously published measures for weighted networks. We expect that our approach will provide a deeper understanding of protein regulation during the cell cycle.
Dynamical robustness analysis of weighted complex networks
NASA Astrophysics Data System (ADS)
He, Zhiwei; Liu, Shuai; Zhan, Meng
2013-09-01
Robustness of weighted complex networks is analyzed from nonlinear dynamical point of view and with focus on different roles of high-degree and low-degree nodes. We find that the phenomenon for the low-degree nodes being the key nodes in the heterogeneous networks only appears in weakly weighted networks and for weak coupling. For all other parameters, the heterogeneous networks are always highly vulnerable to the failure of high-degree nodes; this point is the same as in the structural robustness analysis. We also find that with random inactivation, heterogeneous networks are always more robust than the corresponding homogeneous networks with the same average degree except for one special parameter. Thus our findings give an integrated picture for the dynamical robustness analysis on complex networks.
Impulsive synchronization of networked nonlinear dynamical systems
NASA Astrophysics Data System (ADS)
Jiang, Haibo; Bi, Qinsheng
2010-06-01
In this Letter, we investigate the problem of impulsive synchronization of networked multi-agent systems, where each agent can be modeled as an identical nonlinear dynamical system. Firstly, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the synchronization of the networked nonlinear dynamical system by using algebraic graph theory and impulsive control theory. Furthermore, how to select the discrete instants and impulsive constants is discussed. The case that the topologies of the networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.
Reaction dynamics of photochromic dithienylethene derivatives
NASA Astrophysics Data System (ADS)
Ern, J.; Bens, A. T.; Martin, H.-D.; Mukamel, S.; Schmid, D.; Tretiak, S.; Tsiper, E.; Kryschi, C.
1999-07-01
The reaction dynamics of the photochromic ring-opening reaction of 1,2-bis(5-formyl-2-methyl-thien-3-yl)perfluorocyclopentene (CHO-BMTFP) in dichloromethane solution was investigated using femtosecond transient absorption spectroscopy. The data were analyzed in terms of a model potential and single-electron density matrices, which were calculated using the collective electronic oscillator (CEO) approach and the INDO/S semiempirical Hamiltonian. The S 0-S 1 and S 0-S 2 transitions of the closed isomer were resonantly excited using 120 fs pump pulses at 610 and 410 nm, respectively. A temporally delayed white light continuum probe pulse monitors the decay of the S 1 or S 2 state as well as the recovery of the S 0 state. Within the first picosecond after excitation, CHO-BMTFP was observed to undergo a fast structural relaxation along the S 1 potential energy surface into a minimum constituting a precursor of the ring-opening process. The rather long lifetime of the precursor, τ2=13 ps, was consistent with the calculated potential barrier in front of the conical intersection with the S 0 potential energy surface, which may arise from stabilization of the nearly planar closed isomer by an efficiently delocalized π-electron system.
Exploring Collective Dynamics in Communication Networks
Yuan, Jian; Mills, Kevin
2002-01-01
A communication network, such as the Internet, comprises a complex system where cooperative phenomena may emerge from interactions among various traffic flows generated and forwarded by individual nodes. To identify and understand such phenomena, we model a network as a two-dimensional cellular automaton. We suspect such models can promote better understanding of the spatial-temporal evolution of network congestion, and other emergent phenomena in communication networks. To search the behavior space of the model, we study dynamic patterns arising from interactions among traffic flows routed across shared network nodes, as we employ various configurations of parameters and two different congestion-control algorithms. In this paper, we characterize correlation in congestion behavior within the model at different system sizes and time granularities. As expected, we find that long-range dependence (LRD) appears at some time granularities, and that for a given network size LRD decays as time granularity increases. As network size increases, we find that long-range dependence exists at larger time scales. To distinguish effects due to network size from effects due to collective phenomena, we compare congestion behavior within networks of selected sizes to congestion behavior within comparably sized sub-areas in a larger network. We find stronger long-range dependence for sub-areas within the larger network. This suggests the importance of modeling networks of sufficiently large size when studying the effects of collective dynamics.
Stochastic Generator of Chemical Structure. 3. Reaction Network Generation
FAULON,JEAN-LOUP; SAULT,ALLEN G.
2000-07-15
A new method to generate chemical reaction network is proposed. The particularity of the method is that network generation and mechanism reduction are performed simultaneously using sampling techniques. Our method is tested for hydrocarbon thermal cracking. Results and theoretical arguments demonstrate that our method scales in polynomial time while other deterministic network generator scale in exponential time. This finding offers the possibility to investigate complex reacting systems such as those studied in petroleum refining and combustion.
The Dynamics of Network Topology
NASA Astrophysics Data System (ADS)
Voicu, Ramiro; Legrand, Iosif; Newman, Harvey; Barczyk, Artur; Grigoras, Costin; Dobre, Ciprian
2011-12-01
Network monitoring is vital to ensure proper network operation over time, and is tightly integrated with all the data intensive processing tasks used by the LHC experiments. In order to build a coherent set of network management services it is very important to collect in near real-time information about the network topology, the main data flows, traffic volume and the quality of connectivity. A set of dedicated modules were developed in the MonALISA framework to periodically perform network measurements tests between all sites. We developed global services to present in near real-time the entire network topology used by a community. For any LHC experiment such a network topology includes several hundred of routers and tens of Autonomous Systems. Any changes in the global topology are recorded and this information is can be easily correlated with traffic patterns. The evolution in time of global network topology is shown a dedicated GUI. Changes in the global topology at this level occur quite frequently and even small modifications in the connectivity map may significantly affect the network performance. The global topology graphs are correlated with active end to end network performance measurements, done with the Fast Data Transfer application, between all sites. Access to both real-time and historical data, as provided by MonALISA, is also important for developing services able to predict the usage pattern, to aid in efficiently allocating resources globally.
Dynamical Adaptation in Terrorist Cells/Networks
NASA Astrophysics Data System (ADS)
Hussain, D. M. Akbar; Ahmed, Zaki
Typical terrorist cells/networks have dynamical structure as they evolve or adapt to changes which may occur due to capturing or killing of a member of the cell/network. Analytical measures in graph theory like degree centrality, betweenness and closeness centralities are very common and have long history of their successful use in revealing the importance of various members of the network. However, modeling of covert, terrorist or criminal networks through social graph dose not really provide the hierarchical structure which exist in these networks as these networks are composed of leaders and followers etc. In this research we analyze and predict the most likely role a particular node can adapt once a member of the network is either killed or caught. The adaptation is based on computing Bayes posteriori probability of each node and the level of the said node in the network structure.
Optimal dynamic bandwidth allocation for complex networks
NASA Astrophysics Data System (ADS)
Jiang, Zhong-Yuan; Liang, Man-Gui; Li, Qian; Guo, Dong-Chao
2013-03-01
Traffic capacity of one network strongly depends on the link’s bandwidth allocation strategy. In previous bandwidth allocation mechanisms, once one link’s bandwidth is allocated, it will be fixed throughout the overall traffic transmission process. However, the traffic load of every link changes from time to time. In this paper, with finite total bandwidth resource of the network, we propose to dynamically allocate the total bandwidth resource in which each link’s bandwidth is proportional to the queue length of the output buffer of the link per time step. With plenty of data packets in the network, the traffic handling ability of all links of the network achieves full utilization. The theoretical analysis and the extensive simulation results on complex networks are consistent. This work is valuable for network service providers to improve network performance or to do reasonable network design efficiently.
Functional Motifs in Biochemical Reaction Networks
Tyson, John J.; Novák, Béla
2013-01-01
The signal-response characteristics of a living cell are determined by complex networks of interacting genes, proteins, and metabolites. Understanding how cells respond to specific challenges, how these responses are contravened in diseased cells, and how to intervene pharmacologically in the decision-making processes of cells requires an accurate theory of the information-processing capabilities of macromolecular regulatory networks. Adopting an engineer’s approach to control systems, we ask whether realistic cellular control networks can be decomposed into simple regulatory motifs that carry out specific functions in a cell. We show that such functional motifs exist and review the experimental evidence that they control cellular responses as expected. PMID:20055671
Dynamics of comb-of-comb networks
NASA Astrophysics Data System (ADS)
Liu, Hongxiao; Lin, Yuan; Dolgushev, Maxim; Zhang, Zhongzhi
2016-03-01
The dynamics of complex networks, a current hot topic in many scientific fields, is often coded through the corresponding Laplacian matrix. The spectrum of this matrix carries the main features of the networks' dynamics. Here we consider the deterministic networks which can be viewed as "comb-of-comb" iterative structures. For their Laplacian spectra we find analytical equations involving Chebyshev polynomials whose properties allow one to analyze the spectra in deep. Here, in particular, we find that in the infinite size limit the corresponding spectral dimension goes as ds→2 . The ds leaves its fingerprint on many dynamical processes, as we exemplarily show by considering the dynamical properties of polymer networks, including single monomer displacement under a constant force, mechanical relaxation, and fluorescence depolarization.
Accelerated Sensitivity Analysis in High-Dimensional Stochastic Reaction Networks
Arampatzis, Georgios; Katsoulakis, Markos A.; Pantazis, Yannis
2015-01-01
Existing sensitivity analysis approaches are not able to handle efficiently stochastic reaction networks with a large number of parameters and species, which are typical in the modeling and simulation of complex biochemical phenomena. In this paper, a two-step strategy for parametric sensitivity analysis for such systems is proposed, exploiting advantages and synergies between two recently proposed sensitivity analysis methodologies for stochastic dynamics. The first method performs sensitivity analysis of the stochastic dynamics by means of the Fisher Information Matrix on the underlying distribution of the trajectories; the second method is a reduced-variance, finite-difference, gradient-type sensitivity approach relying on stochastic coupling techniques for variance reduction. Here we demonstrate that these two methods can be combined and deployed together by means of a new sensitivity bound which incorporates the variance of the quantity of interest as well as the Fisher Information Matrix estimated from the first method. The first step of the proposed strategy labels sensitivities using the bound and screens out the insensitive parameters in a controlled manner. In the second step of the proposed strategy, a finite-difference method is applied only for the sensitivity estimation of the (potentially) sensitive parameters that have not been screened out in the first step. Results on an epidermal growth factor network with fifty parameters and on a protein homeostasis with eighty parameters demonstrate that the proposed strategy is able to quickly discover and discard the insensitive parameters and in the remaining potentially sensitive parameters it accurately estimates the sensitivities. The new sensitivity strategy can be several times faster than current state-of-the-art approaches that test all parameters, especially in “sloppy” systems. In particular, the computational acceleration is quantified by the ratio between the total number of parameters over
Restoration of rhythmicity in diffusively coupled dynamical networks
Zou, Wei; Senthilkumar, D. V.; Nagao, Raphael; Kiss, István Z.; Tang, Yang; Koseska, Aneta; Duan, Jinqiao; Kurths, Jürgen
2015-01-01
Oscillatory behaviour is essential for proper functioning of various physical and biological processes. However, diffusive coupling is capable of suppressing intrinsic oscillations due to the manifestation of the phenomena of amplitude and oscillation deaths. Here we present a scheme to revoke these quenching states in diffusively coupled dynamical networks, and demonstrate the approach in experiments with an oscillatory chemical reaction. By introducing a simple feedback factor in the diffusive coupling, we show that the stable (in)homogeneous steady states can be effectively destabilized to restore dynamic behaviours of coupled systems. Even a feeble deviation from the normal diffusive coupling drastically shrinks the death regions in the parameter space. The generality of our method is corroborated in diverse non-linear systems of diffusively coupled paradigmatic models with various death scenarios. Our study provides a general framework to strengthen the robustness of dynamic activity in diffusively coupled dynamical networks. PMID:26173555
Restoration of rhythmicity in diffusively coupled dynamical networks.
Zou, Wei; Senthilkumar, D V; Nagao, Raphael; Kiss, István Z; Tang, Yang; Koseska, Aneta; Duan, Jinqiao; Kurths, Jürgen
2015-01-01
Oscillatory behaviour is essential for proper functioning of various physical and biological processes. However, diffusive coupling is capable of suppressing intrinsic oscillations due to the manifestation of the phenomena of amplitude and oscillation deaths. Here we present a scheme to revoke these quenching states in diffusively coupled dynamical networks, and demonstrate the approach in experiments with an oscillatory chemical reaction. By introducing a simple feedback factor in the diffusive coupling, we show that the stable (in)homogeneous steady states can be effectively destabilized to restore dynamic behaviours of coupled systems. Even a feeble deviation from the normal diffusive coupling drastically shrinks the death regions in the parameter space. The generality of our method is corroborated in diverse non-linear systems of diffusively coupled paradigmatic models with various death scenarios. Our study provides a general framework to strengthen the robustness of dynamic activity in diffusively coupled dynamical networks. PMID:26173555
Restoration of rhythmicity in diffusively coupled dynamical networks
NASA Astrophysics Data System (ADS)
Zou, Wei; Senthilkumar, D. V.; Nagao, Raphael; Kiss, István Z.; Tang, Yang; Koseska, Aneta; Duan, Jinqiao; Kurths, Jürgen
2015-07-01
Oscillatory behaviour is essential for proper functioning of various physical and biological processes. However, diffusive coupling is capable of suppressing intrinsic oscillations due to the manifestation of the phenomena of amplitude and oscillation deaths. Here we present a scheme to revoke these quenching states in diffusively coupled dynamical networks, and demonstrate the approach in experiments with an oscillatory chemical reaction. By introducing a simple feedback factor in the diffusive coupling, we show that the stable (in)homogeneous steady states can be effectively destabilized to restore dynamic behaviours of coupled systems. Even a feeble deviation from the normal diffusive coupling drastically shrinks the death regions in the parameter space. The generality of our method is corroborated in diverse non-linear systems of diffusively coupled paradigmatic models with various death scenarios. Our study provides a general framework to strengthen the robustness of dynamic activity in diffusively coupled dynamical networks.
A Dynamic Navigation Algorithm Considering Network Disruptions
NASA Astrophysics Data System (ADS)
Jiang, J.; Wu, L.
2014-04-01
In traffic network, link disruptions or recoveries caused by sudden accidents, bad weather and traffic congestion, lead to significant increase or decrease in travel times on some network links. Similar situation also occurs in real-time emergency evacuation plan in indoor areas. As the dynamic nature of real-time network information generates better navigation solutions than the static one, a real-time dynamic navigation algorithm for emergency evacuation with stochastic disruptions or recoveries in the network is presented in this paper. Compared with traditional existing algorithms, this new algorithm adjusts pre-existing path to a new optimal one according to the changing link travel time. With real-time network information, it can provide the optional path quickly to adapt to the rapid changing network properties. Theoretical analysis and experimental results demonstrate that this proposed algorithm performs a high time efficiency to get exact solution and indirect information can be calculated in spare time.
Krumholz, Elias W.; Libourel, Igor G. L.
2015-01-01
Genome-scale metabolic models are central in connecting genotypes to metabolic phenotypes. However, even for well studied organisms, such as Escherichia coli, draft networks do not contain a complete biochemical network. Missing reactions are referred to as gaps. These gaps need to be filled to enable functional analysis, and gap-filling choices influence model predictions. To investigate whether functional networks existed where all gap-filling reactions were supported by sequence similarity to annotated enzymes, four draft networks were supplemented with all reactions from the Model SEED database for which minimal sequence similarity was found in their genomes. Quadratic programming revealed that the number of reactions that could partake in a gap-filling solution was vast: 3,270 in the case of E. coli, where 72% of the metabolites in the draft network could connect a gap-filling solution. Nonetheless, no network could be completed without the inclusion of orphaned enzymes, suggesting that parts of the biochemistry integral to biomass precursor formation are uncharacterized. However, many gap-filling reactions were well determined, and the resulting networks showed improved prediction of gene essentiality compared with networks generated through canonical gap filling. In addition, gene essentiality predictions that were sensitive to poorly determined gap-filling reactions were of poor quality, suggesting that damage to the network structure resulting from the inclusion of erroneous gap-filling reactions may be predictable. PMID:26041773
Recent Advances in Quantum Dynamics of Bimolecular Reactions
NASA Astrophysics Data System (ADS)
Zhang, Dong H.; Guo, Hua
2016-05-01
In this review, we survey the latest advances in theoretical understanding of bimolecular reaction dynamics in the past decade. The remarkable recent progress in this field has been driven by more accurate and efficient ab initio electronic structure theory, effective potential-energy surface fitting techniques, and novel quantum scattering algorithms. Quantum mechanical characterization of bimolecular reactions continues to uncover interesting dynamical phenomena in atom-diatom reactions and beyond, reaching an unprecedented level of sophistication. In tandem with experimental explorations, these theoretical developments have greatly advanced our understanding of key issues in reaction dynamics, such as microscopic reaction mechanisms, mode specificity, product energy disposal, influence of reactive resonances, and nonadiabatic effects.
DNA reaction networks: Providing a panoramic view
NASA Astrophysics Data System (ADS)
Wang, Fei; Fan, Chunhai
2016-08-01
A quantitative understanding of the functional landscape of a biochemical circuit can reveal the design rules required to optimize the circuit. Now, a high-throughput droplet-based microfluidic platform has been developed which enables high-resolution mapping of bifurcation diagrams for two nonlinear DNA networks.
Network analysis of human heartbeat dynamics
NASA Astrophysics Data System (ADS)
Shao, Zhi-Gang
2010-02-01
We construct the complex networks of human heartbeat dynamics and investigate their statistical properties, using the visibility algorithm proposed by Lacasa and co-workers [Proc. Natl. Acad. Sci. U.S.A. 105, 4972 (2008)]. Our results show that the associated networks for the time series of heartbeat interval are always scale-free, high clustering, hierarchy, and assortative mixing. In particular, the assortative coefficient of associated networks could distinguish between healthy subjects and patients with congestive heart failure.
Amplitude dynamics favors synchronization in complex networks
Gambuzza, Lucia Valentina; Gómez-Gardeñes, Jesus; Frasca, Mattia
2016-01-01
In this paper we study phase synchronization in random complex networks of coupled periodic oscillators. In particular, we show that, when amplitude dynamics is not negligible, phase synchronization may be enhanced. To illustrate this, we compare the behavior of heterogeneous units with both amplitude and phase dynamics and pure (Kuramoto) phase oscillators. We find that in small network motifs the behavior crucially depends on the topology and on the node frequency distribution. Surprisingly, the microscopic structures for which the amplitude dynamics improves synchronization are those that are statistically more abundant in random complex networks. Thus, amplitude dynamics leads to a general lowering of the synchronization threshold in arbitrary random topologies. Finally, we show that this synchronization enhancement is generic of oscillators close to Hopf bifurcations. To this aim we consider coupled FitzHugh-Nagumo units modeling neuron dynamics. PMID:27108847
Network Physiology: How Organ Systems Dynamically Interact
Bartsch, Ronny P.; Liu, Kang K. L.; Bashan, Amir; Ivanov, Plamen Ch.
2015-01-01
We systematically study how diverse physiologic systems in the human organism dynamically interact and collectively behave to produce distinct physiologic states and functions. This is a fundamental question in the new interdisciplinary field of Network Physiology, and has not been previously explored. Introducing the novel concept of Time Delay Stability (TDS), we develop a computational approach to identify and quantify networks of physiologic interactions from long-term continuous, multi-channel physiological recordings. We also develop a physiologically-motivated visualization framework to map networks of dynamical organ interactions to graphical objects encoded with information about the coupling strength of network links quantified using the TDS measure. Applying a system-wide integrative approach, we identify distinct patterns in the network structure of organ interactions, as well as the frequency bands through which these interactions are mediated. We establish first maps representing physiologic organ network interactions and discover basic rules underlying the complex hierarchical reorganization in physiologic networks with transitions across physiologic states. Our findings demonstrate a direct association between network topology and physiologic function, and provide new insights into understanding how health and distinct physiologic states emerge from networked interactions among nonlinear multi-component complex systems. The presented here investigations are initial steps in building a first atlas of dynamic interactions among organ systems. PMID:26555073
Network Physiology: How Organ Systems Dynamically Interact.
Bartsch, Ronny P; Liu, Kang K L; Bashan, Amir; Ivanov, Plamen Ch
2015-01-01
We systematically study how diverse physiologic systems in the human organism dynamically interact and collectively behave to produce distinct physiologic states and functions. This is a fundamental question in the new interdisciplinary field of Network Physiology, and has not been previously explored. Introducing the novel concept of Time Delay Stability (TDS), we develop a computational approach to identify and quantify networks of physiologic interactions from long-term continuous, multi-channel physiological recordings. We also develop a physiologically-motivated visualization framework to map networks of dynamical organ interactions to graphical objects encoded with information about the coupling strength of network links quantified using the TDS measure. Applying a system-wide integrative approach, we identify distinct patterns in the network structure of organ interactions, as well as the frequency bands through which these interactions are mediated. We establish first maps representing physiologic organ network interactions and discover basic rules underlying the complex hierarchical reorganization in physiologic networks with transitions across physiologic states. Our findings demonstrate a direct association between network topology and physiologic function, and provide new insights into understanding how health and distinct physiologic states emerge from networked interactions among nonlinear multi-component complex systems. The presented here investigations are initial steps in building a first atlas of dynamic interactions among organ systems. PMID:26555073
Dynamic Random Networks in Dynamic Populations
NASA Astrophysics Data System (ADS)
Britton, Tom; Lindholm, Mathias
2010-05-01
We consider a random network evolving in continuous time in which new nodes are born and old may die, and where undirected edges between nodes are created randomly and may also disappear. The node population is Markovian and so is the creation and deletion of edges, given the node population. Each node is equipped with a random social index and the intensity at which a node creates new edges is proportional to the social index, and the neighbour is either chosen uniformly or proportional to its social index in a modification of the model. We derive properties of the network as time and the node population tends to infinity. In particular, the degree-distribution is shown to be a mixed Poisson distribution which may exhibit a heavy tail (e.g. power-law) if the social index distribution has a heavy tail. The limiting results are verified by means of simulations, and the model is fitted to a network of sexual contacts.
Cellular metabolic network analysis: discovering important reactions in Treponema pallidum.
Chen, Xueying; Zhao, Min; Qu, Hong
2015-01-01
T. pallidum, the syphilis-causing pathogen, performs very differently in metabolism compared with other bacterial pathogens. The desire for safe and effective vaccine of syphilis requests identification of important steps in T. pallidum's metabolism. Here, we apply Flux Balance Analysis to represent the reactions quantitatively. Thus, it is possible to cluster all reactions in T. pallidum. By calculating minimal cut sets and analyzing topological structure for the metabolic network of T. pallidum, critical reactions are identified. As a comparison, we also apply the analytical approaches to the metabolic network of H. pylori to find coregulated drug targets and unique drug targets for different microorganisms. Based on the clustering results, all reactions are further classified into various roles. Therefore, the general picture of their metabolic network is obtained and two types of reactions, both of which are involved in nucleic acid metabolism, are found to be essential for T. pallidum. It is also discovered that both hubs of reactions and the isolated reactions in purine and pyrimidine metabolisms play important roles in T. pallidum. These reactions could be potential drug targets for treating syphilis. PMID:26495292
Cellular Metabolic Network Analysis: Discovering Important Reactions in Treponema pallidum
Chen, Xueying; Zhao, Min; Qu, Hong
2015-01-01
T. pallidum, the syphilis-causing pathogen, performs very differently in metabolism compared with other bacterial pathogens. The desire for safe and effective vaccine of syphilis requests identification of important steps in T. pallidum's metabolism. Here, we apply Flux Balance Analysis to represent the reactions quantitatively. Thus, it is possible to cluster all reactions in T. pallidum. By calculating minimal cut sets and analyzing topological structure for the metabolic network of T. pallidum, critical reactions are identified. As a comparison, we also apply the analytical approaches to the metabolic network of H. pylori to find coregulated drug targets and unique drug targets for different microorganisms. Based on the clustering results, all reactions are further classified into various roles. Therefore, the general picture of their metabolic network is obtained and two types of reactions, both of which are involved in nucleic acid metabolism, are found to be essential for T. pallidum. It is also discovered that both hubs of reactions and the isolated reactions in purine and pyrimidine metabolisms play important roles in T. pallidum. These reactions could be potential drug targets for treating syphilis. PMID:26495292
Mapping dynamical systems onto complex networks
NASA Astrophysics Data System (ADS)
Borges, E. P.; Cajueiro, D. O.; Andrade, R. F. S.
2007-08-01
The objective of this study is to design a procedure to characterize chaotic dynamical systems, in which they are mapped onto a complex network. The nodes represent the regions of space visited by the system, while the edges represent the transitions between these regions. Parameters developed to quantify the properties of complex networks, including those related to higher order neighbourhoods, are used in the analysis. The methodology is tested on the logistic map, focusing on the onset of chaos and chaotic regimes. The corresponding networks were found to have distinct features that are associated with the particular type of dynamics that generated them.
Metric projection for dynamic multiplex networks.
Jurman, Giuseppe
2016-08-01
Evolving multiplex networks are a powerful model for representing the dynamics along time of different phenomena, such as social networks, power grids, biological pathways. However, exploring the structure of the multiplex network time series is still an open problem. Here we propose a two-step strategy to tackle this problem based on the concept of distance (metric) between networks. Given a multiplex graph, first a network of networks is built for each time step, and then a real valued time series is obtained by the sequence of (simple) networks by evaluating the distance from the first element of the series. The effectiveness of this approach in detecting the occurring changes along the original time series is shown on a synthetic example first, and then on the Gulf dataset of political events. PMID:27626089
Collective dynamics of `small-world' networks
NASA Astrophysics Data System (ADS)
Watts, Duncan J.; Strogatz, Steven H.
1998-06-01
Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays,, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks `rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them `small-world' networks, by analogy with the small-world phenomenon, (popularly known as six degrees of separation). The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.
The molecular dynamics of atmospheric reaction
NASA Technical Reports Server (NTRS)
Polanyi, J. C.
1971-01-01
Detailed information about the chemistry of the upper atmosphere took the form of quantitative data concerning the rate of reaction into specified states of product vibration, rotation and translation for exothermic reaction, as well as concerning the rate of reaction from specified states of reagent vibration, rotation and translation for endothermic reaction. The techniques used were variants on the infrared chemiluminescence method. Emphasis was placed on reactions that formed, and that removed, vibrationally-excited hydroxyl radicals. Fundamental studies were also performed on exothermic reactions involving hydrogen halides.
Memory Dynamics in Attractor Networks
Li, Guoqi; Ramanathan, Kiruthika; Ning, Ning; Shi, Luping; Wen, Changyun
2015-01-01
As can be represented by neurons and their synaptic connections, attractor networks are widely believed to underlie biological memory systems and have been used extensively in recent years to model the storage and retrieval process of memory. In this paper, we propose a new energy function, which is nonnegative and attains zero values only at the desired memory patterns. An attractor network is designed based on the proposed energy function. It is shown that the desired memory patterns are stored as the stable equilibrium points of the attractor network. To retrieve a memory pattern, an initial stimulus input is presented to the network, and its states converge to one of stable equilibrium points. Consequently, the existence of the spurious points, that is, local maxima, saddle points, or other local minima which are undesired memory patterns, can be avoided. The simulation results show the effectiveness of the proposed method. PMID:25960737
Memory dynamics in attractor networks.
Li, Guoqi; Ramanathan, Kiruthika; Ning, Ning; Shi, Luping; Wen, Changyun
2015-01-01
As can be represented by neurons and their synaptic connections, attractor networks are widely believed to underlie biological memory systems and have been used extensively in recent years to model the storage and retrieval process of memory. In this paper, we propose a new energy function, which is nonnegative and attains zero values only at the desired memory patterns. An attractor network is designed based on the proposed energy function. It is shown that the desired memory patterns are stored as the stable equilibrium points of the attractor network. To retrieve a memory pattern, an initial stimulus input is presented to the network, and its states converge to one of stable equilibrium points. Consequently, the existence of the spurious points, that is, local maxima, saddle points, or other local minima which are undesired memory patterns, can be avoided. The simulation results show the effectiveness of the proposed method. PMID:25960737
Competing dynamic phases of active polymer networks
NASA Astrophysics Data System (ADS)
Freedman, Simon; Banerjee, Shiladitya; Dinner, Aaron R.
Recent experiments on in-vitro reconstituted assemblies of F-actin, myosin-II motors, and cross-linking proteins show that tuning local network properties can changes the fundamental biomechanical behavior of the system. For example, by varying cross-linker density and actin bundle rigidity, one can switch between contractile networks useful for reshaping cells, polarity sorted networks ideal for directed molecular transport, and frustrated networks with robust structural properties. To efficiently investigate the dynamic phases of actomyosin networks, we developed a coarse grained non-equilibrium molecular dynamics simulation of model semiflexible filaments, molecular motors, and cross-linkers with phenomenologically defined interactions. The simulation's accuracy was verified by benchmarking the mechanical properties of its individual components and collective behavior against experimental results at the molecular and network scales. By adjusting the model's parameters, we can reproduce the qualitative phases observed in experiment and predict the protein characteristics where phase crossovers could occur in collective network dynamics. Our model provides a framework for understanding cells' multiple uses of actomyosin networks and their applicability in materials research. Supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.
Origin and Structure of Dynamic Cooperative Networks
Wardil, Lucas; Hauert, Christoph
2014-01-01
Societies are built on social interactions among individuals. Cooperation represents the simplest form of a social interaction: one individual provides a benefit to another one at a cost to itself. Social networks represent a dynamical abstraction of social interactions in a society. The behaviour of an individual towards others and of others towards the individual shape the individual's neighbourhood and hence the local structure of the social network. Here we propose a simple theoretical framework to model dynamic social networks by focussing on each individual's actions instead of interactions between individuals. This eliminates the traditional dichotomy between the strategy of individuals and the structure of the population and easily complements empirical studies. As a consequence, altruists, egoists and fair types are naturally determined by the local social structures, while globally egalitarian networks or stratified structures arise. Cooperative interactions drive the emergence and shape the structure of social networks. PMID:25030202
Origin and Structure of Dynamic Cooperative Networks
NASA Astrophysics Data System (ADS)
Wardil, Lucas; Hauert, Christoph
2014-07-01
Societies are built on social interactions among individuals. Cooperation represents the simplest form of a social interaction: one individual provides a benefit to another one at a cost to itself. Social networks represent a dynamical abstraction of social interactions in a society. The behaviour of an individual towards others and of others towards the individual shape the individual's neighbourhood and hence the local structure of the social network. Here we propose a simple theoretical framework to model dynamic social networks by focussing on each individual's actions instead of interactions between individuals. This eliminates the traditional dichotomy between the strategy of individuals and the structure of the population and easily complements empirical studies. As a consequence, altruists, egoists and fair types are naturally determined by the local social structures, while globally egalitarian networks or stratified structures arise. Cooperative interactions drive the emergence and shape the structure of social networks.
The structure and dynamics of multilayer networks
NASA Astrophysics Data System (ADS)
Boccaletti, S.; Bianconi, G.; Criado, R.; del Genio, C. I.; Gómez-Gardeñes, J.; Romance, M.; Sendiña-Nadal, I.; Wang, Z.; Zanin, M.
2014-11-01
In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all components were treated on equivalent footing, while neglecting all the extra information about the temporal- or context-related properties of the interactions under study. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of real-world systems, and explicitly considered the time-varying and multilayer nature of networks. We offer here a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.
Gupta, Ankit; Briat, Corentin; Khammash, Mustafa
2014-06-01
Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is now well-established that, for small population sizes, stochastic models for biochemical reaction networks are necessary to capture randomness in the interactions. The tools for analyzing such models, however, still lag far behind their deterministic counterparts. In this paper, we bridge this gap by developing a constructive framework for examining the long-term behavior and stability properties of the reaction dynamics in a stochastic setting. In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics. We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas from probability theory, linear algebra and optimization theory. We demonstrate that the stability properties of a wide class of biological networks can be assessed from our sufficient theoretical conditions that can be recast as efficient and scalable linear programs, well-known for their tractability. It is notably shown that the computational complexity is often linear in the number of species. We illustrate the validity, the efficiency and the wide applicability of our results on several reaction networks arising in biochemistry, systems biology, epidemiology and ecology. The biological implications of the results as well as an example of a non-ergodic biological network are also discussed. PMID:24968191
Khammash, Mustafa
2014-01-01
Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is now well-established that, for small population sizes, stochastic models for biochemical reaction networks are necessary to capture randomness in the interactions. The tools for analyzing such models, however, still lag far behind their deterministic counterparts. In this paper, we bridge this gap by developing a constructive framework for examining the long-term behavior and stability properties of the reaction dynamics in a stochastic setting. In particular, we address the problems of determining ergodicity of the reaction dynamics, which is analogous to having a globally attracting fixed point for deterministic dynamics. We also examine when the statistical moments of the underlying process remain bounded with time and when they converge to their steady state values. The framework we develop relies on a blend of ideas from probability theory, linear algebra and optimization theory. We demonstrate that the stability properties of a wide class of biological networks can be assessed from our sufficient theoretical conditions that can be recast as efficient and scalable linear programs, well-known for their tractability. It is notably shown that the computational complexity is often linear in the number of species. We illustrate the validity, the efficiency and the wide applicability of our results on several reaction networks arising in biochemistry, systems biology, epidemiology and ecology. The biological implications of the results as well as an example of a non-ergodic biological network are also discussed. PMID:24968191
Efficient stochastic simulations of complex reaction networks on surfaces.
Barzel, Baruch; Biham, Ofer
2007-10-14
Surfaces serve as highly efficient catalysts for a vast variety of chemical reactions. Typically, such surface reactions involve billions of molecules which diffuse and react over macroscopic areas. Therefore, stochastic fluctuations are negligible and the reaction rates can be evaluated using rate equations, which are based on the mean-field approximation. However, in case that the surface is partitioned into a large number of disconnected microscopic domains, the number of reactants in each domain becomes small and it strongly fluctuates. This is, in fact, the situation in the interstellar medium, where some crucial reactions take place on the surfaces of microscopic dust grains. In this case rate equations fail and the simulation of surface reactions requires stochastic methods such as the master equation. However, in the case of complex reaction networks, the master equation becomes infeasible because the number of equations proliferates exponentially. To solve this problem, we introduce a stochastic method based on moment equations. In this method the number of equations is dramatically reduced to just one equation for each reactive species and one equation for each reaction. Moreover, the equations can be easily constructed using a diagrammatic approach. We demonstrate the method for a set of astrophysically relevant networks of increasing complexity. It is expected to be applicable in many other contexts in which problems that exhibit analogous structure appear, such as surface catalysis in nanoscale systems, aerosol chemistry in stratospheric clouds, and genetic networks in cells. PMID:17935419
Turing instability in reaction-diffusion models on complex networks
NASA Astrophysics Data System (ADS)
Ide, Yusuke; Izuhara, Hirofumi; Machida, Takuya
2016-09-01
In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erdős-Rényi, the Watts-Strogatz, and the threshold network models. From analysis of the Laplacian matrices of graphs generated by these models, we numerically reveal that stable and unstable regions of a homogeneous steady state on the parameter space of two diffusion coefficients completely differ, depending on the network architecture. In addition, we theoretically discuss the stable and unstable regions in the cases of regular enhanced ring lattices which include regular circles, and networks generated by the threshold network model when the number of vertices is large enough.
Stochastic Simulation of Biomolecular Networks in Dynamic Environments
Voliotis, Margaritis; Thomas, Philipp; Grima, Ramon; Bowsher, Clive G.
2016-01-01
Simulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the dynamic environment of the cell and its surroundings. We thus sample trajectories of the stochastic process described by the chemical master equation with time-varying propensities. A comparative analysis shows that existing approaches can either fail dramatically, or else can impose impractical computational burdens due to numerical integration of reaction propensities, especially when cell ensembles are studied. Here we introduce the Extrande method which, given a simulated time course of dynamic network inputs, provides a conditionally exact and several orders-of-magnitude faster simulation solution. The new approach makes it feasible to demonstrate—using decision-making by a large population of quorum sensing bacteria—that robustness to fluctuations from upstream signaling places strong constraints on the design of networks determining cell fate. Our approach has the potential to significantly advance both understanding of molecular systems biology and design of synthetic circuits. PMID:27248512
Stochastic Simulation of Biomolecular Networks in Dynamic Environments.
Voliotis, Margaritis; Thomas, Philipp; Grima, Ramon; Bowsher, Clive G
2016-06-01
Simulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the dynamic environment of the cell and its surroundings. We thus sample trajectories of the stochastic process described by the chemical master equation with time-varying propensities. A comparative analysis shows that existing approaches can either fail dramatically, or else can impose impractical computational burdens due to numerical integration of reaction propensities, especially when cell ensembles are studied. Here we introduce the Extrande method which, given a simulated time course of dynamic network inputs, provides a conditionally exact and several orders-of-magnitude faster simulation solution. The new approach makes it feasible to demonstrate-using decision-making by a large population of quorum sensing bacteria-that robustness to fluctuations from upstream signaling places strong constraints on the design of networks determining cell fate. Our approach has the potential to significantly advance both understanding of molecular systems biology and design of synthetic circuits. PMID:27248512
Semiclassical methods in chemical reaction dynamics
Keshavamurthy, S.
1994-12-01
Semiclassical approximations, simple as well as rigorous, are formulated in order to be able to describe gas phase chemical reactions in large systems. We formulate a simple but accurate semiclassical model for incorporating multidimensional tunneling in classical trajectory simulations. This model is based on the existence of locally conserved actions around the saddle point region on a multidimensional potential energy surface. Using classical perturbation theory and monitoring the imaginary action as a function of time along a classical trajectory we calculate state-specific unimolecular decay rates for a model two dimensional potential with coupling. Results are in good comparison with exact quantum results for the potential over a wide range of coupling constants. We propose a new semiclassical hybrid method to calculate state-to-state S-matrix elements for bimolecular reactive scattering. The accuracy of the Van Vleck-Gutzwiller propagator and the short time dynamics of the system make this method self-consistent and accurate. We also go beyond the stationary phase approximation by doing the resulting integrals exactly (numerically). As a result, classically forbidden probabilties are calculated with purely real time classical trajectories within this approach. Application to the one dimensional Eckart barrier demonstrates the accuracy of this approach. Successful application of the semiclassical hybrid approach to collinear reactive scattering is prevented by the phenomenon of chaotic scattering. The modified Filinov approach to evaluating the integrals is discussed, but application to collinear systems requires a more careful analysis. In three and higher dimensional scattering systems, chaotic scattering is suppressed and hence the accuracy and usefulness of the semiclassical method should be tested for such systems.
Controlling statistical moments of stochastic dynamical networks
NASA Astrophysics Data System (ADS)
Bielievtsov, Dmytro; Ladenbauer, Josef; Obermayer, Klaus
2016-07-01
We consider a general class of stochastic networks and ask which network nodes need to be controlled, and how, to stabilize and switch between desired metastable (target) states in terms of the first and second statistical moments of the system. We first show that it is sufficient to directly interfere with a subset of nodes which can be identified using information about the graph of the network only. Then we develop a suitable method for feedback control which acts on that subset of nodes and preserves the covariance structure of the desired target state. Finally, we demonstrate our theoretical results using a stochastic Hopfield network and a global brain model. Our results are applicable to a variety of (model) networks and further our understanding of the relationship between network structure and collective dynamics for the benefit of effective control.
Controlling statistical moments of stochastic dynamical networks.
Bielievtsov, Dmytro; Ladenbauer, Josef; Obermayer, Klaus
2016-07-01
We consider a general class of stochastic networks and ask which network nodes need to be controlled, and how, to stabilize and switch between desired metastable (target) states in terms of the first and second statistical moments of the system. We first show that it is sufficient to directly interfere with a subset of nodes which can be identified using information about the graph of the network only. Then we develop a suitable method for feedback control which acts on that subset of nodes and preserves the covariance structure of the desired target state. Finally, we demonstrate our theoretical results using a stochastic Hopfield network and a global brain model. Our results are applicable to a variety of (model) networks and further our understanding of the relationship between network structure and collective dynamics for the benefit of effective control. PMID:27575147
Reaction-diffusion processes on interconnected scale-free networks
NASA Astrophysics Data System (ADS)
Garas, Antonios
2015-08-01
We study the two-particle annihilation reaction A +B →∅ on interconnected scale-free networks, using different interconnecting strategies. We explore how the mixing of particles and the process evolution are influenced by the number of interconnecting links, by their functional properties, and by the interconnectivity strategies in use. We show that the reaction rates on this system are faster than what was observed in other topologies, due to the better particle mixing that suppresses the segregation effect, in line with previous studies performed on single scale-free networks.
Dynamics of Bottlebrush Networks: A Computational Study
NASA Astrophysics Data System (ADS)
Dobrynin, Andrey; Cao, Zhen; Sheiko, Sergei
We study dynamics of deformation of bottlebrush networks using molecular dynamics simulations and theoretical calculations. Analysis of our simulation results show that the dynamics of bottlebrush network deformation can be described by a Rouse model for polydisperse networks with effective Rouse time of the bottlebrush network strand, τR =τ0Ns2 (Nsc + 1) where, Ns is the number-average degree of polymerization of the bottlebrush backbone strands between crosslinks, Nsc is the degree of polymerization of the side chains and τ0is a characteristic monomeric relaxation time. At time scales t smaller than the Rouse time, t <τR , the time dependent network shear modulus decays with time as G (t) ~ ρkB T(τ0 / t) 1 / 2 , where ρis the monomer number density. However, at the time scale t larger than the Rouse time of the bottlebrush strands between crosslinks, the network response is pure elastic with shear modulus G (t) =G0 , where G0 is the equilibrium shear modulus at small deformation. The stress evolution in the bottlebrush networks can be described by a universal function of t /τR . NSF DMR-1409710.
Dynamics-based centrality for directed networks
NASA Astrophysics Data System (ADS)
Masuda, Naoki; Kori, Hiroshi
2010-11-01
Determining the relative importance of nodes in directed networks is important in, for example, ranking websites, publications, and sports teams, and for understanding signal flows in systems biology. A prevailing centrality measure in this respect is the PageRank. In this work, we focus on another class of centrality derived from the Laplacian of the network. We extend the Laplacian-based centrality, which has mainly been applied to strongly connected networks, to the case of general directed networks such that we can quantitatively compare arbitrary nodes. Toward this end, we adopt the idea used in the PageRank to introduce global connectivity between all the pairs of nodes with a certain strength. Numerical simulations are carried out on some networks. We also offer interpretations of the Laplacian-based centrality for general directed networks in terms of various dynamical and structural properties of networks. Importantly, the Laplacian-based centrality defined as the stationary density of the continuous-time random walk with random jumps is shown to be equivalent to the absorption probability of the random walk with sinks at each node but without random jumps. Similarly, the proposed centrality represents the importance of nodes in dynamics on the original network supplied with sinks but not with random jumps.
Traffic Dynamics of Computer Networks
NASA Astrophysics Data System (ADS)
Fekete, Attila
2008-10-01
Two important aspects of the Internet, namely the properties of its topology and the characteristics of its data traffic, have attracted growing attention of the physics community. My thesis has considered problems of both aspects. First I studied the stochastic behavior of TCP, the primary algorithm governing traffic in the current Internet, in an elementary network scenario consisting of a standalone infinite-sized buffer and an access link. The effect of the fast recovery and fast retransmission (FR/FR) algorithms is also considered. I showed that my model can be extended further to involve the effect of link propagation delay, characteristic of WAN. I continued my thesis with the investigation of finite-sized semi-bottleneck buffers, where packets can be dropped not only at the link, but also at the buffer. I demonstrated that the behavior of the system depends only on a certain combination of the parameters. Moreover, an analytic formula was derived that gives the ratio of packet loss rate at the buffer to the total packet loss rate. This formula makes it possible to treat buffer-losses as if they were link-losses. Finally, I studied computer networks from a structural perspective. I demonstrated through fluid simulations that the distribution of resources, specifically the link bandwidth, has a serious impact on the global performance of the network. Then I analyzed the distribution of edge betweenness in a growing scale-free tree under the condition that a local property, the in-degree of the "younger" node of an arbitrary edge, is known in order to find an optimum distribution of link capacity. The derived formula is exact even for finite-sized networks. I also calculated the conditional expectation of edge betweenness, rescaled for infinite networks.
Mathematics of small stochastic reaction networks: A boundary layer theory for eigenstate analysis
Mjolsness, Eric; Prasad, Upendra
2013-01-01
We study and analyze the stochastic dynamics of a reversible bimolecular reaction A + B ↔ C called the “trivalent reaction.” This reaction is of a fundamental nature and is part of many biochemical reaction networks. The stochastic dynamics is given by the stochastic master equation, which is difficult to solve except when the equilibrium state solution is desired. We present a novel way of finding the eigenstates of this system of difference-differential equations, using perturbation analysis of ordinary differential equations arising from approximation of the difference equations. The time evolution of the state probabilities can then be expressed in terms of the eigenvalues and the eigenvectors. PMID:23514469
Communication Dynamics in Finite Capacity Social Networks
NASA Astrophysics Data System (ADS)
Haerter, Jan O.; Jamtveit, Bjørn; Mathiesen, Joachim
2012-10-01
In communication networks, structure and dynamics are tightly coupled. The structure controls the flow of information and is itself shaped by the dynamical process of information exchanged between nodes. In order to reconcile structure and dynamics, a generic model, based on the local interaction between nodes, is considered for the communication in large social networks. In agreement with data from a large human organization, we show that the flow is non-Markovian and controlled by the temporal limitations of individuals. We confirm the versatility of our model by predicting simultaneously the degree-dependent node activity, the balance between information input and output of nodes, and the degree distribution. Finally, we quantify the limitations to network analysis when it is based on data sampled over a finite period of time.
Dynamic fracture toughnesses of reaction-bonded silicon nitride
NASA Technical Reports Server (NTRS)
Kobayashi, A. S.; Emery, A. F.; Liaw, B. M.
1983-01-01
The room-temperature dynamic fracture response of reaction-bonded silicon nitride is investigated using a hybrid experimental-numerical procedure. In this procedure, experimentally determined crack velocities are utilized to drive a dynamic finite-element code or dynamic finite-difference code in its generation mode in order to extract numerically the dynamic stress intensity factor of the fracturing specimen. Results show that the dynamic fracture toughness vs crack velocity relations of the two reaction-bonded silicon nitrides do not follow the general trend in those relations of brittle polymers and steel. A definite slow crack velocity during the initial phase of dynamic crack propagation is observed in reaction-bonded silicon nitride, which results in a nonunique dynamic fracture toughness vs crack velocity relation. In addition, it is found that a propagating crack will continue to propagate under a static stress intensity factor substantially lower than K(IC).
Targeting the dynamics of complex networks
Gutiérrez, Ricardo; Sendiña-Nadal, Irene; Zanin, Massimiliano; Papo, David; Boccaletti, Stefano
2012-01-01
We report on a generic procedure to steer (target) a network's dynamics towards a given, desired evolution. The problem is here tackled through a Master Stability Function approach, assessing the stability of the aimed dynamics, and through a selection of nodes to be targeted. We show that the degree of a node is a crucial element in this selection process, and that the targeting mechanism is most effective in heterogeneous scale-free architectures. This makes the proposed approach applicable to the large majority of natural and man-made networked systems. PMID:22563525
The cost and capacity of signaling in the Escherichia coli protein reaction network
NASA Astrophysics Data System (ADS)
Axelsen, Jacob Bock; Krishna, Sandeep; Sneppen, Kim
2008-01-01
In systems biology new ways are required to analyze the large amount of existing data on regulation of cellular processes. Recent work can be roughly classified into either dynamical models of well-described subsystems, or coarse-grained descriptions of the topology of the molecular networks at the scale of the whole organism. In order to bridge these two disparate approaches one needs to develop simplified descriptions of dynamics and topological measures which address the propagation of signals in molecular networks. Transmission of a signal across a reaction node depends on the presence of other reactants. It will typically be more demanding to transmit a signal across a reaction node with more input links. Sending signals along a path with several subsequent reaction nodes also increases the constraints on the presence of other proteins in the overall network. Therefore counting in and out links along reactions of a potential pathway can give insight into the signaling properties of a particular molecular network. Here, we consider the directed network of protein regulation in E. coli, characterizing its modularity in terms of its potential to transmit signals. We demonstrate that the simplest measure based on identifying subnetworks of strong components, within which each node could send a signal to every other node, does indeed partition the network into functional modules. We suggest that the total number of reactants needed to send a signal between two nodes in the network can be considered as the cost associated with transmitting this signal. Similarly we define spread as the number of reaction products that could be influenced by transmission of a successful signal. Our considerations open for a new class of network measures that implicitly utilize the constrained repertoire of chemical modifications of any biological molecule. The counting of cost and spread connects the topology of networks to the specificity of signaling across the network. Thereby, we
Neural network with formed dynamics of activity
Dunin-Barkovskii, V.L.; Osovets, N.B.
1995-03-01
The problem of developing a neural network with a given pattern of the state sequence is considered. A neural network structure and an algorithm, of forming its bond matrix which lead to an approximate but robust solution of the problem are proposed and discussed. Limiting characteristics of the serviceability of the proposed structure are studied. Various methods of visualizing dynamic processes in a neural network are compared. Possible applications of the results obtained for interpretation of neurophysiological data and in neuroinformatics systems are discussed.
Dynamics of overlapping structures in modular networks.
Almendral, J A; Leyva, I; Li, D; Sendiña-Nadal, I; Havlin, S; Boccaletti, S
2010-07-01
Modularity is a fundamental feature of real networks, being intimately bounded to their functionality, i.e., to their capability of performing parallel tasks in a coordinated way. Although the modular structure of real graphs has been intensively studied, very little is known on the interactions between functional modules of a graph. Here, we present a general method based on synchronization of networking oscillators, that is able to detect overlapping structures in multimodular environments. We furthermore report the full analytical and theoretical description on the relationship between the overlapping dynamics and the underlying network topology. The method is illustrated by means of a series of applications. PMID:20866697
Cytoskeletal Network Morphology Regulates Intracellular Transport Dynamics.
Ando, David; Korabel, Nickolay; Huang, Kerwyn Casey; Gopinathan, Ajay
2015-10-20
Intracellular transport is essential for maintaining proper cellular function in most eukaryotic cells, with perturbations in active transport resulting in several types of disease. Efficient delivery of critical cargos to specific locations is accomplished through a combination of passive diffusion and active transport by molecular motors that ballistically move along a network of cytoskeletal filaments. Although motor-based transport is known to be necessary to overcome cytoplasmic crowding and the limited range of diffusion within reasonable timescales, the topological features of the cytoskeletal network that regulate transport efficiency and robustness have not been established. Using a continuum diffusion model, we observed that the time required for cellular transport was minimized when the network was localized near the nucleus. In simulations that explicitly incorporated network spatial architectures, total filament mass was the primary driver of network transit times. However, filament traps that redirect cargo back to the nucleus caused large variations in network transport. Filament polarity was more important than filament orientation in reducing average transit times, and transport properties were optimized in networks with intermediate motor on and off rates. Our results provide important insights into the functional constraints on intracellular transport under which cells have evolved cytoskeletal structures, and have potential applications for enhancing reactions in biomimetic systems through rational transport network design. PMID:26488648
NASA Astrophysics Data System (ADS)
Zañudo, Jorge G. T.; Albert, Réka
2013-06-01
Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches that can directly relate the network structure to its dynamics. Of special interest is identifying the stable patterns of activity, i.e., the attractors of the system. This is a problem for large networks, because the state space of the system increases exponentially with network size. In this work, we present a novel network reduction approach that is based on finding network motifs that stabilize in a fixed state. Notably, we use a topological criterion to identify these motifs. Specifically, we find certain types of strongly connected components in a suitably expanded representation of the network. To test our method, we apply it to a dynamic network model for a type of cytotoxic T cell cancer and to an ensemble of random Boolean networks of size up to 200. Our results show that our method goes beyond reducing the network and in most cases can actually predict the dynamical repertoire of the nodes (fixed states or oscillations) in the attractors of the system.
Structural and dynamical properties of complex networks
NASA Astrophysics Data System (ADS)
Ghoshal, Gourab
Recent years have witnessed a substantial amount of interest within the physics community in the properties of networks. Techniques from statistical physics coupled with the widespread availability of computing resources have facilitated studies ranging from large scale empirical analysis of the worldwide web, social networks, biological systems, to the development of theoretical models and tools to explore the various properties of these systems. Following these developments, in this dissertation, we present and solve for a diverse set of new problems, investigating the structural and dynamical properties of both model and real world networks. We start by defining a new metric to measure the stability of network structure to disruptions, and then using a combination of theory and simulation study its properties in detail on artificially generated networks; we then compare our results to a selection of networks from the real world and find good agreement in most cases. In the following chapter, we propose a mathematical model that mimics the structure of popular file-sharing websites such as Flickr and CiteULike and demonstrate that many of its properties can solved exactly in the limit of large network size. The remaining part of the dissertation primarily focuses on the dynamical properties of networks. We first formulate a model of a network that evolves under the addition and deletion of vertices and edges, and solve for the equilibrium degree distribution for a variety of cases of interest. We then consider networks whose structure can be manipulated by adjusting the rules by which vertices enter and leave the network. We focus in particular on degree distributions and show that, with some mild constraints, it is possible by a suitable choice of rules to arrange for the network to have any degree distribution we desire. In addition we define a simple local algorithm by which appropriate rules can be implemented in practice. Finally, we conclude our
Fundamental structures of dynamic social networks.
Sekara, Vedran; Stopczynski, Arkadiusz; Lehmann, Sune
2016-09-01
Social systems are in a constant state of flux, with dynamics spanning from minute-by-minute changes to patterns present on the timescale of years. Accurate models of social dynamics are important for understanding the spreading of influence or diseases, formation of friendships, and the productivity of teams. Although there has been much progress on understanding complex networks over the past decade, little is known about the regularities governing the microdynamics of social networks. Here, we explore the dynamic social network of a densely-connected population of ∼1,000 individuals and their interactions in the network of real-world person-to-person proximity measured via Bluetooth, as well as their telecommunication networks, online social media contacts, geolocation, and demographic data. These high-resolution data allow us to observe social groups directly, rendering community detection unnecessary. Starting from 5-min time slices, we uncover dynamic social structures expressed on multiple timescales. On the hourly timescale, we find that gatherings are fluid, with members coming and going, but organized via a stable core of individuals. Each core represents a social context. Cores exhibit a pattern of recurring meetings across weeks and months, each with varying degrees of regularity. Taken together, these findings provide a powerful simplification of the social network, where cores represent fundamental structures expressed with strong temporal and spatial regularity. Using this framework, we explore the complex interplay between social and geospatial behavior, documenting how the formation of cores is preceded by coordination behavior in the communication networks and demonstrating that social behavior can be predicted with high precision. PMID:27555584
NASA Astrophysics Data System (ADS)
Brennan, John K.; Lísal, Martin; Gubbins, Keith E.; Rice, Betsy M.
2004-12-01
A molecular simulation method to study the dynamics of chemically reacting mixtures is presented. The method uses a combination of stochastic and dynamic simulation steps, allowing for the simulation of both thermodynamic and transport properties. The method couples a molecular dynamics simulation cell (termed dynamic cell) to a reaction mixture simulation cell (termed control cell) that is formulated upon the reaction ensemble Monte Carlo (RxMC) method, hence the term reaction ensemble molecular dynamics. Thermodynamic and transport properties are calculated in the dynamic cell by using a constant-temperature molecular dynamics simulation method. RxMC forward and reverse reaction steps are performed in the control cell only, while molecular dynamics steps are performed in both the dynamic cell and the control cell. The control cell, which acts as a sink and source reservoir, is maintained at reaction equilibrium conditions via the RxMC algorithm. The reaction ensemble molecular dynamics method is analogous to the grand canonical ensemble molecular dynamics technique, while using some elements of the osmotic molecular dynamics method, and so simulates conditions that directly relate to real, open systems. The accuracy and stability of the method is assessed by considering the ammonia synthesis reaction N2+3H2⇔2NH3 . It is shown to be a viable method for predicting the effects of nonideal environments on the dynamic properties (particularly diffusion) as well as reaction equilibria for chemically reacting mixtures.
Spreading dynamics in complex networks
NASA Astrophysics Data System (ADS)
Pei, Sen; Makse, Hernán A.
2013-12-01
Searching for influential spreaders in complex networks is an issue of great significance for applications across various domains, ranging from epidemic control, innovation diffusion, viral marketing, and social movement to idea propagation. In this paper, we first display some of the most important theoretical models that describe spreading processes, and then discuss the problem of locating both the individual and multiple influential spreaders respectively. Recent approaches in these two topics are presented. For the identification of privileged single spreaders, we summarize several widely used centralities, such as degree, betweenness centrality, PageRank, k-shell, etc. We investigate the empirical diffusion data in a large scale online social community—LiveJournal. With this extensive dataset, we find that various measures can convey very distinct information of nodes. Of all the users in the LiveJournal social network, only a small fraction of them are involved in spreading. For the spreading processes in LiveJournal, while degree can locate nodes participating in information diffusion with higher probability, k-shell is more effective in finding nodes with a large influence. Our results should provide useful information for designing efficient spreading strategies in reality.
Dynamic regimes of random fuzzy logic networks
NASA Astrophysics Data System (ADS)
Wittmann, Dominik M.; Theis, Fabian J.
2011-01-01
Random multistate networks, generalizations of the Boolean Kauffman networks, are generic models for complex systems of interacting agents. Depending on their mean connectivity, these networks exhibit ordered as well as chaotic behavior with a critical boundary separating both regimes. Typically, the nodes of these networks are assigned single discrete states. Here, we describe nodes by fuzzy numbers, i.e. vectors of degree-of-membership (DOM) functions specifying the degree to which the nodes are in each of their discrete states. This allows our models to deal with imprecision and uncertainties. Compatible update rules are constructed by expressing the update rules of the multistate network in terms of Boolean operators and generalizing them to fuzzy logic (FL) operators. The standard choice for these generalizations is the Gödel FL, where AND and OR are replaced by the minimum and maximum of two DOMs, respectively. In mean-field approximations we are able to analytically describe the percolation and asymptotic distribution of DOMs in random Gödel FL networks. This allows us to characterize the different dynamic regimes of random multistate networks in terms of FL. In a low-dimensional example, we provide explicit computations and validate our mean-field results by showing that they agree well with network simulations.
On a theory of stability for nonlinear stochastic chemical reaction networks
NASA Astrophysics Data System (ADS)
Smadbeck, Patrick; Kaznessis, Yiannis N.
2015-05-01
We present elements of a stability theory for small, stochastic, nonlinear chemical reaction networks. Steady state probability distributions are computed with zero-information (ZI) closure, a closure algorithm that solves chemical master equations of small arbitrary nonlinear reactions. Stochastic models can be linearized around the steady state with ZI-closure, and the eigenvalues of the Jacobian matrix can be readily computed. Eigenvalues govern the relaxation of fluctuation autocorrelation functions at steady state. Autocorrelation functions reveal the time scales of phenomena underlying the dynamics of nonlinear reaction networks. In accord with the fluctuation-dissipation theorem, these functions are found to be congruent to response functions to small perturbations. Significant differences are observed in the stability of nonlinear reacting systems between deterministic and stochastic modeling formalisms.
On a theory of stability for nonlinear stochastic chemical reaction networks
Smadbeck, Patrick; Kaznessis, Yiannis N.
2015-05-14
We present elements of a stability theory for small, stochastic, nonlinear chemical reaction networks. Steady state probability distributions are computed with zero-information (ZI) closure, a closure algorithm that solves chemical master equations of small arbitrary nonlinear reactions. Stochastic models can be linearized around the steady state with ZI-closure, and the eigenvalues of the Jacobian matrix can be readily computed. Eigenvalues govern the relaxation of fluctuation autocorrelation functions at steady state. Autocorrelation functions reveal the time scales of phenomena underlying the dynamics of nonlinear reaction networks. In accord with the fluctuation-dissipation theorem, these functions are found to be congruent to response functions to small perturbations. Significant differences are observed in the stability of nonlinear reacting systems between deterministic and stochastic modeling formalisms.
Solvable non-Markovian dynamic network
NASA Astrophysics Data System (ADS)
Georgiou, Nicos; Kiss, Istvan Z.; Scalas, Enrico
2015-10-01
Non-Markovian processes are widespread in natural and human-made systems, yet explicit modeling and analysis of such systems is underdeveloped. We consider a non-Markovian dynamic network with random link activation and deletion (RLAD) and heavy-tailed Mittag-Leffler distribution for the interevent times. We derive an analytically and computationally tractable system of Kolmogorov-like forward equations utilizing the Caputo derivative for the probability of having a given number of active links in the network and solve them. Simulations for the RLAD are also studied for power-law interevent times and we show excellent agreement with the Mittag-Leffler model. This agreement holds even when the RLAD network dynamics is coupled with the susceptible-infected-susceptible spreading dynamics. Thus, the analytically solvable Mittag-Leffler model provides an excellent approximation to the case when the network dynamics is characterized by power-law-distributed interevent times. We further discuss possible generalizations of our result.
Dynamical networks with topological self-organization
NASA Technical Reports Server (NTRS)
Zak, M.
2001-01-01
Coupled evolution of state and topology of dynamical networks is introduced. Due to the well organized tensor structure, the governing equations are presented in a canonical form, and required attractors as well as their basins can be easily implanted and controlled.
Limit-cycle oscillations and chaos in reaction networks subject to conservation of mass.
Di Cera, E; Phillipson, P E; Wyman, J
1989-01-01
A cyclic network of autocatalytic reactions involving an unbuffered cofactor and a number of components subject to conservation of mass displays a surprising richness of dynamical behaviors. Limit-cycle oscillations are possible over a wide range of parameter values. Additionally, a cascade of period-doubling bifurcations leading to chaos can coexist with a multiplicity of stable steady states. These results draw attention to the role of unbuffering as a feedback in biochemical systems. PMID:2911564
Dynamic salt effect on intramolecular charge-transfer reactions
Zhu Jianjun; Ma Rong; Lu Yan; Stell, George
2005-12-08
The dynamic salt effect in charge-transfer reactions is investigated theoretically in this paper. Free-energy surfaces are derived based on a nonequilibrium free-energy functional. Reaction coordinates are clearly defined. The solution of the reaction-diffusion equation leads to a rate constant depending on the time correlation function of the reaction coordinates. The time correlation function of the ion-atmosphere coordinate is derived from the solution of the Debye-Falkenhagen equation. It is shown that the dynamic salt effect plays an important role in controlling the rate of charge-transfer reactions in the narrow-window limit but is balanced by the energetics and the dynamics of the polar-solvent coordinate. The simplest version of the theory is compared with an experiment, and the agreement is fairly good. The theory can also be extended to charge-transfer in the class of electrolytes that has come to be called 'ionic fluids'.
Recent Advances in Quantum Dynamics of Bimolecular Reactions.
Zhang, Dong H; Guo, Hua
2016-05-27
In this review, we survey the latest advances in theoretical understanding of bimolecular reaction dynamics in the past decade. The remarkable recent progress in this field has been driven by more accurate and efficient ab initio electronic structure theory, effective potential-energy surface fitting techniques, and novel quantum scattering algorithms. Quantum mechanical characterization of bimolecular reactions continues to uncover interesting dynamical phenomena in atom-diatom reactions and beyond, reaching an unprecedented level of sophistication. In tandem with experimental explorations, these theoretical developments have greatly advanced our understanding of key issues in reaction dynamics, such as microscopic reaction mechanisms, mode specificity, product energy disposal, influence of reactive resonances, and nonadiabatic effects. PMID:26980305
Chemical reaction network approaches to Biochemical Systems Theory.
Arceo, Carlene Perpetua P; Jose, Editha C; Marin-Sanguino, Alberto; Mendoza, Eduardo R
2015-11-01
This paper provides a framework to represent a Biochemical Systems Theory (BST) model (in either GMA or S-system form) as a chemical reaction network with power law kinetics. Using this representation, some basic properties and the application of recent results of Chemical Reaction Network Theory regarding steady states of such systems are shown. In particular, Injectivity Theory, including network concordance [36] and the Jacobian Determinant Criterion [43], a "Lifting Theorem" for steady states [26] and the comprehensive results of Müller and Regensburger [31] on complex balanced equilibria are discussed. A partial extension of a recent Emulation Theorem of Cardelli for mass action systems [3] is derived for a subclass of power law kinetic systems. However, it is also shown that the GMA and S-system models of human purine metabolism [10] do not display the reactant-determined kinetics assumed by Müller and Regensburger and hence only a subset of BST models can be handled with their approach. Moreover, since the reaction networks underlying many BST models are not weakly reversible, results for non-complex balanced equilibria are also needed. PMID:26363083
A dynamical systems view of network centrality.
Grindrod, Peter; Higham, Desmond J
2014-05-01
To gain insights about dynamic networks, the dominant paradigm is to study discrete snapshots, or timeslices, as the interactions evolve. Here, we develop and test a new mathematical framework where network evolution is handled over continuous time, giving an elegant dynamical systems representation for the important concept of node centrality. The resulting system allows us to track the relative influence of each individual. This new setting is natural in many digital applications, offering both conceptual and computational advantages. The novel differential equations approach is convenient for modelling and analysis of network evolution and gives rise to an interesting application of the matrix logarithm function. From a computational perspective, it avoids the awkward up-front compromises between accuracy, efficiency and redundancy required in the prevalent discrete-time setting. Instead, we can rely on state-of-the-art ODE software, where discretization takes place adaptively in response to the prevailing system dynamics. The new centrality system generalizes the widely used Katz measure, and allows us to identify and track, at any resolution, the most influential nodes in terms of broadcasting and receiving information through time-dependent links. In addition to the classical static network notion of attenuation across edges, the new ODE also allows for attenuation over time, as information becomes stale. This allows 'running measures' to be computed, so that networks can be monitored in real time over arbitrarily long intervals. With regard to computational efficiency, we explain why it is cheaper to track good receivers of information than good broadcasters. An important consequence is that the overall broadcast activity in the network can also be monitored efficiently. We use two synthetic examples to validate the relevance of the new measures. We then illustrate the ideas on a large-scale voice call network, where key features are discovered that are not
On correlated reaction sets and coupled reaction sets in metabolic networks.
Marashi, Sayed-Amir; Hosseini, Zhaleh
2015-08-01
Two reactions are in the same "correlated reaction set" (or "Co-Set") if their fluxes are linearly correlated. On the other hand, two reactions are "coupled" if nonzero flux through one reaction implies nonzero flux through the other reaction. Flux correlation analysis has been previously used in the analysis of enzyme dysregulation and enzymopathy, while flux coupling analysis has been used to predict co-expression of genes and to model network evolution. The goal of this paper is to emphasize, through a few examples, that these two concepts are inherently different. In other words, except for the case of full coupling, which implies perfect correlation between two fluxes (R(2) = 1), there are no constraints on Pearson correlation coefficients (CC) in case of any other type of (un)coupling relations. In other words, Pearson CC can take any value between 0 and 1 in other cases. Furthermore, by analyzing genome-scale metabolic networks, we confirm that there are some examples in real networks of bacteria, yeast and human, which approve that flux coupling and flux correlation cannot be used interchangeably. PMID:25747383
Dynamics on modular networks with heterogeneous correlations
Melnik, Sergey; Porter, Mason A.; Mucha, Peter J.; Gleeson, James P.
2014-06-15
We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module, and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model. The new network ensemble generalizes existing models (e.g., the well-known configuration model and Lancichinetti-Fortunato-Radicchi networks) by allowing a heterogeneous distribution of degree-degree correlations across modules, which is important for the consideration of nonidentical interacting networks.
Complex Dynamics in Information Sharing Networks
NASA Astrophysics Data System (ADS)
Cronin, Bruce
This study examines the roll-out of an electronic knowledge base in a medium-sized professional services firm over a six year period. The efficiency of such implementation is a key business problem in IT systems of this type. Data from usage logs provides the basis for analysis of the dynamic evolution of social networks around the depository during this time. The adoption pattern follows an "s-curve" and usage exhibits something of a power law distribution, both attributable to network effects, and network position is associated with organisational performance on a number of indicators. But periodicity in usage is evident and the usage distribution displays an exponential cut-off. Further analysis provides some evidence of mathematical complexity in the periodicity. Some implications of complex patterns in social network data for research and management are discussed. The study provides a case study demonstrating the utility of the broad methodological approach.
Coevolutionary dynamics on scale-free networks
NASA Astrophysics Data System (ADS)
Lee, Sungmin; Kim, Yup
2005-05-01
We investigate Bak-Sneppen coevolution models on scale-free networks with various degree exponents γ including random networks. For γ>3 , the critical fitness value fc approaches a nonzero finite value in the limit N→∞ , whereas fc approaches zero as 2<γ⩽3 . These results are explained by showing analytically fc(N)≃A/⟨(k+1)2⟩N on the networks with size N . The avalanche size distribution P(s) shows the normal power-law behavior for γ>3 . In contrast, P(s) for 2<γ⩽3 has two power-law regimes. One is a short regime for small s with a large exponent τ1 and the other is a long regime for large s with a small exponent τ2(τ1>τ2) . The origin of the two power regimes is explained by the dynamics on an artificially made star-linked network.
Roaming dynamics in radical addition-elimination reactions
NASA Astrophysics Data System (ADS)
Joalland, Baptiste; Shi, Yuanyuan; Kamasah, Alexander; Suits, Arthur G.; Mebel, Alexander M.
2014-06-01
Radical addition-elimination reactions are a major pathway for transformation of unsaturated hydrocarbons. In the gas phase, these reactions involve formation of a transient strongly bound intermediate. However, the detailed mechanism and dynamics for these reactions remain unclear. Here we show, for reaction of chlorine atoms with butenes, that the Cl addition-HCl elimination pathway occurs from an abstraction-like Cl-H-C geometry rather than a conventional three-centre or four-centre transition state. Furthermore, access to this geometry is attained by roaming excursions of the Cl atom from the initially formed adduct. In effect, the alkene π cloud serves to capture the Cl atom and hold it, allowing many subsequent opportunities for the energized intermediate to find a suitable approach to the abstraction geometry. These bimolecular roaming reactions are closely related to the roaming radical dynamics recently discovered to play an important role in unimolecular reactions.
Nonparametric inference of network structure and dynamics
NASA Astrophysics Data System (ADS)
Peixoto, Tiago P.
The network structure of complex systems determine their function and serve as evidence for the evolutionary mechanisms that lie behind them. Despite considerable effort in recent years, it remains an open challenge to formulate general descriptions of the large-scale structure of network systems, and how to reliably extract such information from data. Although many approaches have been proposed, few methods attempt to gauge the statistical significance of the uncovered structures, and hence the majority cannot reliably separate actual structure from stochastic fluctuations. Due to the sheer size and high-dimensionality of many networks, this represents a major limitation that prevents meaningful interpretations of the results obtained with such nonstatistical methods. In this talk, I will show how these issues can be tackled in a principled and efficient fashion by formulating appropriate generative models of network structure that can have their parameters inferred from data. By employing a Bayesian description of such models, the inference can be performed in a nonparametric fashion, that does not require any a priori knowledge or ad hoc assumptions about the data. I will show how this approach can be used to perform model comparison, and how hierarchical models yield the most appropriate trade-off between model complexity and quality of fit based on the statistical evidence present in the data. I will also show how this general approach can be elegantly extended to networks with edge attributes, that are embedded in latent spaces, and that change in time. The latter is obtained via a fully dynamic generative network model, based on arbitrary-order Markov chains, that can also be inferred in a nonparametric fashion. Throughout the talk I will illustrate the application of the methods with many empirical networks such as the internet at the autonomous systems level, the global airport network, the network of actors and films, social networks, citations among
Dynamic functional network connectivity using distance correlation
NASA Astrophysics Data System (ADS)
Rudas, Jorge; Guaje, Javier; Demertzi, Athena; Heine, Lizette; Tshibanda, Luaba; Soddu, Andrea; Laureys, Steven; Gómez, Francisco
2015-01-01
Investigations about the intrinsic brain organization in resting-state are critical for the understanding of healthy, pathological and pharmacological cerebral states. Recent studies on fMRI suggest that resting state activity is organized on large scale networks of coordinated activity, in the so called, Resting State Networks (RSNs). The assessment of the interactions among these functional networks plays an important role for the understanding of different brain pathologies. Current methods to quantify these interactions commonly assume that the underlying coordination mechanisms are stationary and linear through the whole recording of the resting state phenomena. Nevertheless, recent evidence suggests that rather than stationary, these mechanisms may exhibit a rich set of time-varying repertoires. In addition, these approaches do not consider possible non-linear relationships maybe linked to feed-back communication mechanisms between RSNs. In this work, we introduce a novel approach for dynamical functional network connectivity for functional magnetic resonance imaging (fMRI) resting activity, which accounts for non-linear dynamic relationships between RSNs. The proposed method is based on a windowed distance correlations computed on resting state time-courses extracted at single subject level. We showed that this strategy is complementary to the current approaches for dynamic functional connectivity and will help to enhance the discrimination capacity of patients with disorder of consciousness.
Dynamic protoneural networks in plants
Debono, Marc-Williams
2013-01-01
Taking as a basis of discussion Kalanchoe’s spontaneous and evoked extracellular activities recorded at the whole plant level, we put the challenging questions: do these low-voltage variations, together with endocellular events, reflect integrative properties and complex behavior in plants? Does it reflect common perceptive systems in animal and plant species? Is the ability of plants to treat short-term variations and information transfer without nervous system relevant? Is a protoneural construction of the world by lower organisms possible? More generally, the aim of this paper is to reevaluate the probably underestimated role of plant surface potentials in the plant relation life, carefully comparing the biogenesis of both animal and plant organisms in the era of plant neurobiology. Knowing that surface potentials participate at least to morphogenesis, cell to cell coupling, long distance transmission and transduction of stimuli, some hypothesis are given indicating that plants have to be studied as environmental biosensors and non linear dynamic systems able to detect transitional states between perception and response to stimuli. This study is conducted in the frame of the “plasticity paradigm,” which gives a theoretical model of evolutionary processes and suggests some hypothesis about the nature of complexity, information and behavior. PMID:23603975
Population Dynamics of Genetic Regulatory Networks
NASA Astrophysics Data System (ADS)
Braun, Erez
2005-03-01
Unlike common objects in physics, a biological cell processes information. The cell interprets its genome and transforms the genomic information content, through the action of genetic regulatory networks, into proteins which in turn dictate its metabolism, functionality and morphology. Understanding the dynamics of a population of biological cells presents a unique challenge. It requires to link the intracellular dynamics of gene regulation, through the mechanism of cell division, to the level of the population. We present experiments studying adaptive dynamics of populations of genetically homogeneous microorganisms (yeast), grown for long durations under steady conditions. We focus on population dynamics that do not involve random genetic mutations. Our experiments follow the long-term dynamics of the population distributions and allow to quantify the correlations among generations. We focus on three interconnected issues: adaptation of genetically homogeneous populations following environmental changes, selection processes on the population and population variability and expression distributions. We show that while the population exhibits specific short-term responses to environmental inputs, it eventually adapts to a robust steady-state, largely independent of external conditions. Cycles of medium-switch show that the adapted state is imprinted in the population and that this memory is maintained for many generations. To further study population adaptation, we utilize the process of gene recruitment whereby a gene naturally regulated by a specific promoter is placed under a different regulatory system. This naturally occurring process has been recognized as a major driving force in evolution. We have recruited an essential gene to a foreign regulatory network and followed the population long-term dynamics. Rewiring of the regulatory network allows us to expose their complex dynamics and phase space structure.
Dynamic motifs in socio-economic networks
NASA Astrophysics Data System (ADS)
Zhang, Xin; Shao, Shuai; Stanley, H. Eugene; Havlin, Shlomo
2014-12-01
Socio-economic networks are of central importance in economic life. We develop a method of identifying and studying motifs in socio-economic networks by focusing on “dynamic motifs,” i.e., evolutionary connection patterns that, because of “node acquaintances” in the network, occur much more frequently than random patterns. We examine two evolving bi-partite networks: i) the world-wide commercial ship chartering market and ii) the ship build-to-order market. We find similar dynamic motifs in both bipartite networks, even though they describe different economic activities. We also find that “influence” and “persistence” are strong factors in the interaction behavior of organizations. When two companies are doing business with the same customer, it is highly probable that another customer who currently only has business relationship with one of these two companies, will become customer of the second in the future. This is the effect of influence. Persistence means that companies with close business ties to customers tend to maintain their relationships over a long period of time.
Motion detection based on recurrent network dynamics
Joukes, Jeroen; Hartmann, Till S.; Krekelberg, Bart
2014-01-01
The detection of visual motion requires temporal delays to compare current with earlier visual input. Models of motion detection assume that these delays reside in separate classes of slow and fast thalamic cells, or slow and fast synaptic transmission. We used a data-driven modeling approach to generate a model that instead uses recurrent network dynamics with a single, fixed temporal integration window to implement the velocity computation. This model successfully reproduced the temporal response dynamics of a population of motion sensitive neurons in macaque middle temporal area (MT) and its constituent parts matched many of the properties found in the motion processing pathway (e.g., Gabor-like receptive fields (RFs), simple and complex cells, spatially asymmetric excitation and inhibition). Reverse correlation analysis revealed that a simplified network based on first and second order space-time correlations of the recurrent model behaved much like a feedforward motion energy (ME) model. The feedforward model, however, failed to capture the full speed tuning and direction selectivity properties based on higher than second order space-time correlations typically found in MT. These findings support the idea that recurrent network connectivity can create temporal delays to compute velocity. Moreover, the model explains why the motion detection system often behaves like a feedforward ME network, even though the anatomical evidence strongly suggests that this network should be dominated by recurrent feedback. PMID:25565992
Modeling Insurgent Network Structure and Dynamics
NASA Astrophysics Data System (ADS)
Gabbay, Michael; Thirkill-Mackelprang, Ashley
2010-03-01
We present a methodology for mapping insurgent network structure based on their public rhetoric. Indicators of cooperative links between insurgent groups at both the leadership and rank-and-file levels are used, such as joint policy statements or joint operations claims. In addition, a targeting policy measure is constructed on the basis of insurgent targeting claims. Network diagrams which integrate these measures of insurgent cooperation and ideology are generated for different periods of the Iraqi and Afghan insurgencies. The network diagrams exhibit meaningful changes which track the evolution of the strategic environment faced by insurgent groups. Correlations between targeting policy and network structure indicate that insurgent targeting claims are aimed at establishing a group identity among the spectrum of rank-and-file insurgency supporters. A dynamical systems model of insurgent alliance formation and factionalism is presented which evolves the relationship between insurgent group dyads as a function of their ideological differences and their current relationships. The ability of the model to qualitatively and quantitatively capture insurgent network dynamics observed in the data is discussed.
Testing string dynamics in lepton nucleus reactions
Gyulassy, M.; Pluemer, M.
1989-10-01
The sensitivity of nuclear attenuation of 10-100 GeV lepton nucleus ({ell}A) reactions to space-time aspects of hadronization is investigated within the context of the Lund string model. We consider two mechanisms for attenuation in a nucleus: final state cascading and string flip excitations. Implications for the evolution of the energy density in nuclear collisions are discussed. 16 refs., 10 figs.
Dynamic network mechanisms of relational integration.
Parkin, Beth L; Hellyer, Peter J; Leech, Robert; Hampshire, Adam
2015-05-20
A prominent hypothesis states that specialized neural modules within the human lateral frontopolar cortices (LFPCs) support "relational integration" (RI), the solving of complex problems using inter-related rules. However, it has been proposed that LFPC activity during RI could reflect the recruitment of additional "domain-general" resources when processing more difficult problems in general as opposed to RI specifically. Moreover, theoretical research with computational models has demonstrated that RI may be supported by dynamic processes that occur throughout distributed networks of brain regions as opposed to within a discrete computational module. Here, we present fMRI findings from a novel deductive reasoning paradigm that controls for general difficulty while manipulating RI demands. In accordance with the domain-general perspective, we observe an increase in frontoparietal activation during challenging problems in general as opposed to RI specifically. Nonetheless, when examining frontoparietal activity using analyses of phase synchrony and psychophysiological interactions, we observe increased network connectivity during RI alone. Moreover, dynamic causal modeling with Bayesian model selection identifies the LFPC as the effective connectivity source. Based on these results, we propose that during RI an increase in network connectivity and a decrease in network metastability allows rules that are coded throughout working memory systems to be dynamically bound. This change in connectivity state is top-down propagated via a hierarchical system of domain-general networks with the LFPC at the apex. In this manner, the functional network perspective reconciles key propositions of the globalist, modular, and computational accounts of RI within a single unified framework. PMID:25995457
Dynamic Network Mechanisms of Relational Integration
Parkin, Beth L.; Hellyer, Peter J.; Leech, Robert
2015-01-01
A prominent hypothesis states that specialized neural modules within the human lateral frontopolar cortices (LFPCs) support “relational integration” (RI), the solving of complex problems using inter-related rules. However, it has been proposed that LFPC activity during RI could reflect the recruitment of additional “domain-general” resources when processing more difficult problems in general as opposed to RI specifically. Moreover, theoretical research with computational models has demonstrated that RI may be supported by dynamic processes that occur throughout distributed networks of brain regions as opposed to within a discrete computational module. Here, we present fMRI findings from a novel deductive reasoning paradigm that controls for general difficulty while manipulating RI demands. In accordance with the domain-general perspective, we observe an increase in frontoparietal activation during challenging problems in general as opposed to RI specifically. Nonetheless, when examining frontoparietal activity using analyses of phase synchrony and psychophysiological interactions, we observe increased network connectivity during RI alone. Moreover, dynamic causal modeling with Bayesian model selection identifies the LFPC as the effective connectivity source. Based on these results, we propose that during RI an increase in network connectivity and a decrease in network metastability allows rules that are coded throughout working memory systems to be dynamically bound. This change in connectivity state is top-down propagated via a hierarchical system of domain-general networks with the LFPC at the apex. In this manner, the functional network perspective reconciles key propositions of the globalist, modular, and computational accounts of RI within a single unified framework. PMID:25995457
trans-Symmetric Dynamic Covalent Systems: Connected Transamination and Transimination Reactions
Schaufelberger, Fredrik; Hu, Lei; Ramström, Olof
2015-01-01
The development of chemical transaminations as a new type of dynamic covalent reaction is described. The key 1,3-proton shift is under complete catalytic control and can be conducted orthogonally to, or simultaneous with, transimination in the presence of an amine to rapidly yield two-dimensional dynamic systems with a high degree of complexity evolution. The transamination–transimination systems are proven to be fully reversible, stable over several days, compatible with a range of functional groups, and highly tunable. Kinetic studies show transamination to be the rate-limiting reaction in the network. Furthermore, it was discovered that readily available quinuclidine is a highly potent catalyst for aldimine transaminations. This study demonstrates how connected dynamic reactions give rise to significantly larger systems than the unconnected counterparts, and shows how reversible isomerizations can be utilized as an effective diversity-generating element. PMID:26044061
Nuclear Reactions and Stellar Evolution: Unified Dynamics
Bauer, W.; Strother, T.
2007-10-26
Motivated by the success of kinetic theory in the description of observables in intermediate and high energy heavy ion collisions, we use kinetic theory to model the dynamics of collapsing iron cores in type II supernova explosions. The algorithms employed to model the collapse, some preliminary results and predictions, and the future of the code are discussed.
NASA Astrophysics Data System (ADS)
Marchetti, Luca; Priami, Corrado; Thanh, Vo Hong
2016-07-01
This paper introduces HRSSA (Hybrid Rejection-based Stochastic Simulation Algorithm), a new efficient hybrid stochastic simulation algorithm for spatially homogeneous biochemical reaction networks. HRSSA is built on top of RSSA, an exact stochastic simulation algorithm which relies on propensity bounds to select next reaction firings and to reduce the average number of reaction propensity updates needed during the simulation. HRSSA exploits the computational advantage of propensity bounds to manage time-varying transition propensities and to apply dynamic partitioning of reactions, which constitute the two most significant bottlenecks of hybrid simulation. A comprehensive set of simulation benchmarks is provided for evaluating performance and accuracy of HRSSA against other state of the art algorithms.
MONOMIALS AND BASIN CYLINDERS FOR NETWORK DYNAMICS
AUSTIN, DANIEL; DINWOODIE, IAN H
2014-01-01
We describe methods to identify cylinder sets inside a basin of attraction for Boolean dynamics of biological networks. Such sets are used for designing regulatory interventions that make the system evolve towards a chosen attractor, for example initiating apoptosis in a cancer cell. We describe two algebraic methods for identifying cylinders inside a basin of attraction, one based on the Groebner fan that finds monomials that define cylinders and the other on primary decomposition. Both methods are applied to current examples of gene networks. PMID:25620893
Traffic chaotic dynamics modeling and analysis of deterministic network
NASA Astrophysics Data System (ADS)
Wu, Weiqiang; Huang, Ning; Wu, Zhitao
2016-07-01
Network traffic is an important and direct acting factor of network reliability and performance. To understand the behaviors of network traffic, chaotic dynamics models were proposed and helped to analyze nondeterministic network a lot. The previous research thought that the chaotic dynamics behavior was caused by random factors, and the deterministic networks would not exhibit chaotic dynamics behavior because of lacking of random factors. In this paper, we first adopted chaos theory to analyze traffic data collected from a typical deterministic network testbed — avionics full duplex switched Ethernet (AFDX, a typical deterministic network) testbed, and found that the chaotic dynamics behavior also existed in deterministic network. Then in order to explore the chaos generating mechanism, we applied the mean field theory to construct the traffic dynamics equation (TDE) for deterministic network traffic modeling without any network random factors. Through studying the derived TDE, we proposed that chaotic dynamics was one of the nature properties of network traffic, and it also could be looked as the action effect of TDE control parameters. A network simulation was performed and the results verified that the network congestion resulted in the chaotic dynamics for a deterministic network, which was identical with expectation of TDE. Our research will be helpful to analyze the traffic complicated dynamics behavior for deterministic network and contribute to network reliability designing and analysis.
Spreading out of perturbations in reversible reaction networks.
Maslov, Sergei; Sneppen, Kim; Ispolatov, I
2007-08-17
Using an example of physical interactions between proteins, we study how a perturbation propagates in the equilibrium of a network of reversible reactions governed by the law of mass action. We introduce a matrix formalism to describe the linear response of all equilibrium concentrations to shifts in total abundances of individual reactants, and reveal its heuristic analogy to the flow of electric current in a network of resistors. Our main conclusion is that, on average, the induced changes in equilibrium concentrations decay exponentially as a function of network distance from the source of perturbation. We analyze how this decay is influenced by such factors as the topology of a network, binding strength, and correlations between concentrations of neighboring nodes. We find that the minimal branching of the network, small values of dissociation constants, and low equilibrium free (unbound) concentrations of reacting substances all decrease the decay constant and thus increase the range of propagation. Exact analytic expressions for the decay constant are obtained for the case of equally strong interactions and uniform as well as oscillating concentrations on the Bethe lattice. Our general findings are illustrated using a real network of protein-protein interactions in baker's yeast with experimentally determined protein concentrations. PMID:18046464
Spreading out of perturbations in reversible reaction networks
NASA Astrophysics Data System (ADS)
Maslov, Sergei; Sneppen, Kim; Ispolatov, I.
2007-08-01
Using an example of physical interactions between proteins, we study how a perturbation propagates in the equilibrium of a network of reversible reactions governed by the law of mass action. We introduce a matrix formalism to describe the linear response of all equilibrium concentrations to shifts in total abundances of individual reactants, and reveal its heuristic analogy to the flow of electric current in a network of resistors. Our main conclusion is that, on average, the induced changes in equilibrium concentrations decay exponentially as a function of network distance from the source of perturbation. We analyze how this decay is influenced by such factors as the topology of a network, binding strength, and correlations between concentrations of neighboring nodes. We find that the minimal branching of the network, small values of dissociation constants, and low equilibrium free (unbound) concentrations of reacting substances all decrease the decay constant and thus increase the range of propagation. Exact analytic expressions for the decay constant are obtained for the case of equally strong interactions and uniform as well as oscillating concentrations on the Bethe lattice. Our general findings are illustrated using a real network of protein-protein interactions in baker's yeast with experimentally determined protein concentrations.
Dynamic Trust Management for Mobile Networks and Its Applications
ERIC Educational Resources Information Center
Bao, Fenye
2013-01-01
Trust management in mobile networks is challenging due to dynamically changing network environments and the lack of a centralized trusted authority. In this dissertation research, we "design" and "validate" a class of dynamic trust management protocols for mobile networks, and demonstrate the utility of dynamic trust management…
Dynamic Analysis of Integrated Signaling, Metabolic, and Regulatory Networks
Eddy, James A.; Papin, Jason A.
2008-01-01
Extracellular cues affect signaling, metabolic, and regulatory processes to elicit cellular responses. Although intracellular signaling, metabolic, and regulatory networks are highly integrated, previous analyses have largely focused on independent processes (e.g., metabolism) without considering the interplay that exists among them. However, there is evidence that many diseases arise from multifunctional components with roles throughout signaling, metabolic, and regulatory networks. Therefore, in this study, we propose a flux balance analysis (FBA)–based strategy, referred to as integrated dynamic FBA (idFBA), that dynamically simulates cellular phenotypes arising from integrated networks. The idFBA framework requires an integrated stoichiometric reconstruction of signaling, metabolic, and regulatory processes. It assumes quasi-steady-state conditions for “fast” reactions and incorporates “slow” reactions into the stoichiometric formalism in a time-delayed manner. To assess the efficacy of idFBA, we developed a prototypic integrated system comprising signaling, metabolic, and regulatory processes with network features characteristic of actual systems and incorporating kinetic parameters based on typical time scales observed in literature. idFBA was applied to the prototypic system, which was evaluated for different environments and gene regulatory rules. In addition, we applied the idFBA framework in a similar manner to a representative module of the single-cell eukaryotic organism Saccharomyces cerevisiae. Ultimately, idFBA facilitated quantitative, dynamic analysis of systemic effects of extracellular cues on cellular phenotypes and generated comparable time-course predictions when contrasted with an equivalent kinetic model. Since idFBA solves a linear programming problem and does not require an exhaustive list of detailed kinetic parameters, it may be efficiently scaled to integrated intracellular systems that incorporate signaling, metabolic, and
Transverse flow reactor studies of the dynamics of radical reactions
Macdonald, R.G.
1993-12-01
Radical reactions are in important in combustion chemistry; however, little state-specific information is available for these reactions. A new apparatus has been constructed to measure the dynamics of radical reactions. The unique feature of this apparatus is a transverse flow reactor in which an atom or radical of known concentration will be produced by pulsed laser photolysis of an appropriate precursor molecule. The time dependence of individual quantum states or products and/or reactants will be followed by rapid infrared laser absorption spectroscopy. The reaction H + O{sub 2} {yields} OH + O will be studied.
Hybrid discrete/continuum algorithms for stochastic reaction networks
NASA Astrophysics Data System (ADS)
Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; Najm, Habib N.
2015-01-01
Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. The performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.
Hybrid discrete/continuum algorithms for stochastic reaction networks
Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; Najm, Habib N.
2014-10-22
Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components to avoid negative probability values. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. As a result, the performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.
Hybrid discrete/continuum algorithms for stochastic reaction networks
Safta, Cosmin Sargsyan, Khachik Debusschere, Bert Najm, Habib N.
2015-01-15
Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker–Planck equation. The Fokker–Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. The performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.
Hybrid discrete/continuum algorithms for stochastic reaction networks
Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; Najm, Habib N.
2014-10-22
Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components to avoid negative probability values. The numerical construction at the interface between the discretemore » and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. As a result, the performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.« less
Nonlinear Network Dynamics on Earthquake Fault Systems
NASA Astrophysics Data System (ADS)
Rundle, P. B.; Rundle, J. B.; Tiampo, K. F.
2001-12-01
Understanding the physics of earthquakes is essential if large events are ever to be forecast. Real faults occur in topologically complex networks that exhibit cooperative, emergent space-time behavior that includes precursory quiescence or activation, and clustering of events. The purpose of this work is to investigate the sensitivity of emergent behavior of fault networks to changes in the physics on the scale of single faults or smaller. In order to investigate the effect of changes at small scales on the behavior of the network, we need to construct models of earthquake fault systems that contain the essential physics. A network topology is therefore defined in an elastic medium, the stress Green's functions (i.e. the stress transfer coefficients) are computed, frictional properties are defined and the system is driven via the slip deficit as defined below. The long-range elastic interactions produce mean-field dynamics in the simulations. We focus in this work on the major strike-slip faults in Southern California that produce the most frequent and largest magnitude events. To determine the topology and properties of the network, we used the tabulation of fault properties published in the literature. We have found that the statistical distribution of large earthquakes on a model of a topologically complex, strongly correlated real fault network is highly sensitive to the precise nature of the stress dissipation properties of the friction laws associated with individual faults. These emergent, self-organizing space-time modes of behavior are properties of the network as a whole, rather than of the individual fault segments of which the network is comprised (ref: PBR et al., Physical Review Letters, in press, 2001).
Eigenvector dynamics under perturbation of modular networks
NASA Astrophysics Data System (ADS)
Sarkar, Somwrita; Chawla, Sanjay; Robinson, P. A.; Fortunato, Santo
2016-06-01
Rotation dynamics of eigenvectors of modular network adjacency matrices under random perturbations are presented. In the presence of q communities, the number of eigenvectors corresponding to the q largest eigenvalues form a "community" eigenspace and rotate together, but separately from that of the "bulk" eigenspace spanned by all the other eigenvectors. Using this property, the number of modules or clusters in a network can be estimated in an algorithm-independent way. A general argument and derivation for the theoretical detectability limit for sparse modular networks with q communities is presented, beyond which modularity persists in the system but cannot be detected. It is shown that for detecting the clusters or modules using the adjacency matrix, there is a "band" in which it is hard to detect the clusters even before the theoretical detectability limit is reached, and for which the theoretically predicted detectability limit forms the sufficient upper bound. Analytic estimations of these bounds are presented and empirically demonstrated.
Failure dynamics of the global risk network.
Szymanski, Boleslaw K; Lin, Xin; Asztalos, Andrea; Sreenivasan, Sameet
2015-01-01
Risks threatening modern societies form an intricately interconnected network that often underlies crisis situations. Yet, little is known about how risk materializations in distinct domains influence each other. Here we present an approach in which expert assessments of likelihoods and influence of risks underlie a quantitative model of the global risk network dynamics. The modeled risks range from environmental to economic and technological, and include difficult to quantify risks, such as geo-political and social. Using the maximum likelihood estimation, we find the optimal model parameters and demonstrate that the model including network effects significantly outperforms the others, uncovering full value of the expert collected data. We analyze the model dynamics and study its resilience and stability. Our findings include such risk properties as contagion potential, persistence, roles in cascades of failures and the identity of risks most detrimental to system stability. The model provides quantitative means for measuring the adverse effects of risk interdependencies and the materialization of risks in the network. PMID:26087020
Failure dynamics of the global risk network
Szymanski, Boleslaw K.; Lin, Xin; Asztalos, Andrea; Sreenivasan, Sameet
2015-01-01
Risks threatening modern societies form an intricately interconnected network that often underlies crisis situations. Yet, little is known about how risk materializations in distinct domains influence each other. Here we present an approach in which expert assessments of likelihoods and influence of risks underlie a quantitative model of the global risk network dynamics. The modeled risks range from environmental to economic and technological, and include difficult to quantify risks, such as geo-political and social. Using the maximum likelihood estimation, we find the optimal model parameters and demonstrate that the model including network effects significantly outperforms the others, uncovering full value of the expert collected data. We analyze the model dynamics and study its resilience and stability. Our findings include such risk properties as contagion potential, persistence, roles in cascades of failures and the identity of risks most detrimental to system stability. The model provides quantitative means for measuring the adverse effects of risk interdependencies and the materialization of risks in the network. PMID:26087020
Failure dynamics of the global risk network
NASA Astrophysics Data System (ADS)
Szymanski, Boleslaw K.; Lin, Xin; Asztalos, Andrea; Sreenivasan, Sameet
2015-06-01
Risks threatening modern societies form an intricately interconnected network that often underlies crisis situations. Yet, little is known about how risk materializations in distinct domains influence each other. Here we present an approach in which expert assessments of likelihoods and influence of risks underlie a quantitative model of the global risk network dynamics. The modeled risks range from environmental to economic and technological, and include difficult to quantify risks, such as geo-political and social. Using the maximum likelihood estimation, we find the optimal model parameters and demonstrate that the model including network effects significantly outperforms the others, uncovering full value of the expert collected data. We analyze the model dynamics and study its resilience and stability. Our findings include such risk properties as contagion potential, persistence, roles in cascades of failures and the identity of risks most detrimental to system stability. The model provides quantitative means for measuring the adverse effects of risk interdependencies and the materialization of risks in the network.
Information spreading on dynamic social networks
NASA Astrophysics Data System (ADS)
Liu, Chuang; Zhang, Zi-Ke
2014-04-01
Nowadays, information spreading on social networks has triggered an explosive attention in various disciplines. Most of previous works in this area mainly focus on discussing the effects of spreading probability or immunization strategy on static networks. However, in real systems, the peer-to-peer network structure changes constantly according to frequently social activities of users. In order to capture this dynamical property and study its impact on information spreading, in this paper, a link rewiring strategy based on the Fermi function is introduced. In the present model, the informed individuals tend to break old links and reconnect to their second-order friends with more uninformed neighbors. Simulation results on the susceptible-infected-recovered (SIR) model with fixed recovery time T=1 indicate that the information would spread more faster and broader with the proposed rewiring strategy. Extensive analyses of the information cascade size distribution show that the spreading process of the initial steps plays a very important role, that is to say, the information will spread out if it is still survival at the beginning time. The proposed model may shed some light on the in-depth understanding of information spreading on dynamical social networks.
Dynamic congestion control mechanisms for MPLS networks
NASA Astrophysics Data System (ADS)
Holness, Felicia; Phillips, Chris I.
2001-02-01
Considerable interest has arisen in congestion control through traffic engineering from the knowledge that although sensible provisioning of the network infrastructure is needed, together with sufficient underlying capacity, these are not sufficient to deliver the Quality of Service required for new applications. This is due to dynamic variations in load. In operational Internet Protocol (IP) networks, it has been difficult to incorporate effective traffic engineering due to the limited capabilities of the IP technology. In principle, Multiprotocol Label Switching (MPLS), which is a connection-oriented label swapping technology, offers new possibilities in addressing the limitations by allowing the operator to use sophisticated traffic control mechanisms. This paper presents a novel scheme to dynamically manage traffic flows through the network by re-balancing streams during periods of congestion. It proposes management-based algorithms that will allow label switched routers within the network to utilize mechanisms within MPLS to indicate when flows are starting to experience frame/packet loss and then to react accordingly. Based upon knowledge of the customer's Service Level Agreement, together with instantaneous flow information, the label edge routers can then instigate changes to the LSP route and circumvent congestion that would hitherto violate the customer contacts.
Dynamics of domain wall networks with junctions
Avelino, P. P.; Oliveira, J. C. R. E.; Martins, C. J. A. P.; Menezes, J.; Menezes, R.
2008-11-15
We use a combination of analytic tools and an extensive set of the largest and most accurate three-dimensional field theory numerical simulations to study the dynamics of domain wall networks with junctions. We build upon our previous work and consider a class of models which, in the limit of large number N of coupled scalar fields, approaches the so-called ''ideal'' model (in terms of its potential to lead to network frustration). We consider values of N between N=2 and N=20, and a range of cosmological epochs, and we also compare this class of models with other toy models used in the past. In all cases we find compelling evidence for a gradual approach to scaling, strongly supporting our no-frustration conjecture. We also discuss the various possible types of junctions (including cases where there is a hierarchy of them) and their roles in the dynamics of the network. Finally, we provide a cosmological Zel'dovich-type bound on the energy scale of this kind of defect network: it must be lower than 10 keV.
Vehicle dynamic analysis using neuronal network algorithms
NASA Astrophysics Data System (ADS)
Oloeriu, Florin; Mocian, Oana
2014-06-01
Theoretical developments of certain engineering areas, the emergence of new investigation tools, which are better and more precise and their implementation on-board the everyday vehicles, all these represent main influence factors that impact the theoretical and experimental study of vehicle's dynamic behavior. Once the implementation of these new technologies onto the vehicle's construction had been achieved, it had led to more and more complex systems. Some of the most important, such as the electronic control of engine, transmission, suspension, steering, braking and traction had a positive impact onto the vehicle's dynamic behavior. The existence of CPU on-board vehicles allows data acquisition and storage and it leads to a more accurate and better experimental and theoretical study of vehicle dynamics. It uses the information offered directly by the already on-board built-in elements of electronic control systems. The technical literature that studies vehicle dynamics is entirely focused onto parametric analysis. This kind of approach adopts two simplifying assumptions. Functional parameters obey certain distribution laws, which are known in classical statistics theory. The second assumption states that the mathematical models are previously known and have coefficients that are not time-dependent. Both the mentioned assumptions are not confirmed in real situations: the functional parameters do not follow any known statistical repartition laws and the mathematical laws aren't previously known and contain families of parameters and are mostly time-dependent. The purpose of the paper is to present a more accurate analysis methodology that can be applied when studying vehicle's dynamic behavior. A method that provides the setting of non-parametrical mathematical models for vehicle's dynamic behavior is relying on neuronal networks. This method contains coefficients that are time-dependent. Neuronal networks are mostly used in various types' system controls, thus
State-to-state reaction dynamics: A selective review
NASA Astrophysics Data System (ADS)
Teslja, Alexey; Valentini, James J.
2006-10-01
A selective review of state-to-state reaction dynamics experiments is presented. The review focuses on three classes of reactions that exemplify the rich history and illustrate the current state of the art in such work. These three reactions are (1) the hydrogen exchange reaction, H +H2→H2+H and its isotopomers; (2) the H +RH→H2+R reactions, where RH is an alkane, beginning with H +CH4→H2+CH3 and extending to much larger alkanes; and (3) the Cl +RH→HCl+R reactions, principally Cl +CH4→HCl+CH3. We describe the experiments, discuss their results, present comparisons with theory, and introduce heuristic models.
Mathematically Reduced Chemical Reaction Mechanism Using Neural Networks
Nelson Butuk
2004-12-01
This is an annual technical report for the work done over the last year (period ending 9/30/2004) on the project titled ''Mathematically Reduced Chemical Reaction Mechanism Using Neural Networks''. The aim of the project is to develop an efficient chemistry model for combustion simulations. The reduced chemistry model will be developed mathematically without the need of having extensive knowledge of the chemistry involved. To aid in the development of the model, Neural Networks (NN) will be used via a new network topology know as Non-linear Principal Components Analysis (NPCA). We report on the development of a procedure to speed up the training of NPCA. The developed procedure is based on the non-parametric statistical technique of kernel smoothing. When this smoothing technique is implemented as a Neural Network, It is know as Generalized Regression Neural Network (GRNN). We present results of implementing GRNN on a test problem. In addition, we present results of an in house developed 2-D CFD code that will be used through out the project period.
Hybrid function projective synchronization in complex dynamical networks
Wei, Qiang; Wang, Xing-yuan Hu, Xiao-peng
2014-02-15
This paper investigates hybrid function projective synchronization in complex dynamical networks. When the complex dynamical networks could be synchronized up to an equilibrium or periodic orbit, a hybrid feedback controller is designed to realize the different component of vector of node could be synchronized up to different desired scaling function in complex dynamical networks with time delay. Hybrid function projective synchronization (HFPS) in complex dynamical networks with constant delay and HFPS in complex dynamical networks with time-varying coupling delay are researched, respectively. Finally, the numerical simulations show the effectiveness of theoretical analysis.
Interdisciplinary applications of network dynamics: From microscopic to Macroscopic
NASA Astrophysics Data System (ADS)
Jeong, Hawoong
``Everything touches everything.'' We are living in a connected world, which has been modeled successfully by complex networks. Ever since, network science becomes new paradigm for understanding our connected yet complex world. After investigating network structure itself, our focus naturally moved to dynamics of/on the network because our connected world is not static but dynamic. In this presentation, we will briefly review the historical development of network science and show some applications of network dynamics ranging from microscopic (metabolic engineering, PNAS, 104 13638) to macroscopic scale (price of anarchy in transportation network, Phys.Rev.Lett. 101 128701). Supported by National Research Foundation of Korea through Grant No. 2011-0028908.
NASA Astrophysics Data System (ADS)
Jablonski, Piotr; Poe, Gina; Zochowski, Michal
2007-03-01
The hippocampus has the capacity for reactivating recently acquired memories and it is hypothesized that one of the functions of sleep reactivation is the facilitation of consolidation of novel memory traces. The dynamic and network processes underlying such a reactivation remain, however, unknown. We show that such a reactivation characterized by local, self-sustained activity of a network region may be an inherent property of the recurrent excitatory-inhibitory network with a heterogeneous structure. The entry into the reactivation phase is mediated through a physiologically feasible regulation of global excitability and external input sources, while the reactivated component of the network is formed through induced network heterogeneities during learning. We show that structural changes needed for robust reactivation of a given network region are well within known physiological parameters.
NASA Astrophysics Data System (ADS)
Jablonski, Piotr; Poe, Gina R.; Zochowski, Michal
2007-01-01
The hippocampus has the capacity for reactivating recently acquired memories and it is hypothesized that one of the functions of sleep reactivation is the facilitation of consolidation of novel memory traces. The dynamic and network processes underlying such a reactivation remain, however, unknown. We show that such a reactivation characterized by local, self-sustained activity of a network region may be an inherent property of the recurrent excitatory-inhibitory network with a heterogeneous structure. The entry into the reactivation phase is mediated through a physiologically feasible regulation of global excitability and external input sources, while the reactivated component of the network is formed through induced network heterogeneities during learning. We show that structural changes needed for robust reactivation of a given network region are well within known physiological parameters.
Propagation dynamics on networks featuring complex topologies
NASA Astrophysics Data System (ADS)
Hébert-Dufresne, Laurent; Noël, Pierre-André; Marceau, Vincent; Allard, Antoine; Dubé, Louis J.
2010-09-01
Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently couple the dynamics of the network elements (such as nodes, vertices, individuals, etc.) on the one hand and their recurrent topological patterns (such as subgraphs, groups, etc.) on the other hand. In a susceptible-infectious-susceptible (SIS) model of epidemic spread on social networks with community structure, this approach yields a set of ordinary differential equations for the time evolution of the system, as well as analytical solutions for the epidemic threshold and equilibria. The results obtained are in good agreement with numerical simulations and reproduce the behavior of random networks in the appropriate limits which highlights the influence of topology on the processes. Finally, it is demonstrated that our model predicts higher epidemic thresholds for clustered structures than for equivalent random topologies in the case of networks with zero degree correlation.
Dynamic traffic grooming in survivable WDM networks
NASA Astrophysics Data System (ADS)
Zhu, Yonghua; Lin, Rujian
2005-11-01
This paper investigates the survivable traffic grooming problem for optical mesh networks employing wavelength-division multiplexing (WDM). While the transmission rate of a wavelength channel is high, the bandwidth requirement of a typical connection request can vary from the full wavelength capacity down to subwavelength. To efficiently utilize network resources, subwavelength-granularity connections can be groomed onto direct optical transmission channels, or lightpaths. Meanwhile, the failure of a network element can cause the failure of several lightpaths, thereby leading to large data and revenue loss. Fault-management schemes such as protection are essential to survive such failures. Different low-speed connections may request different bandwidth granularities as well as different protection schemes. How to efficiently groom such low-speed connections while satisfying their protection requirements is the main focus of our investigation. The paper tackles the dynamic survivable traffic grooming problems in multifiber wavelength-routed optical networks by representing the network as a layered graph model. This graph multi layers, where each layer represents a specific wavelength. Each link in the layered graph has more than one fibers and an associated cost. We use a modified Dijkstra algorithm that has a reduced complexity due to the structure of the layered graph. Heuristic algorithms for fiber selection based on a well-designed link-cost metrics are proposed. The performance of various routing algorithms is evaluated through simulation studies.
Cortical attractor network dynamics with diluted connectivity.
Rolls, Edmund T; Webb, Tristan J
2012-01-24
The connectivity of the cerebral cortex is diluted, with the probability of excitatory connections between even nearby pyramidal cells rarely more than 0.1, and in the hippocampus 0.04. To investigate the extent to which this diluted connectivity affects the dynamics of attractor networks in the cerebral cortex, we simulated an integrate-and-fire attractor network taking decisions between competing inputs with diluted connectivity of 0.25 or 0.1, and with the same number of synaptic connections per neuron for the recurrent collateral synapses within an attractor population as for full connectivity. The results indicated that there was less spiking-related noise with the diluted connectivity in that the stability of the network when in the spontaneous state of firing increased, and the accuracy of the correct decisions increased. The decision times were a little slower with diluted than with complete connectivity. Given that the capacity of the network is set by the number of recurrent collateral synaptic connections per neuron, on which there is a biological limit, the findings indicate that the stability of cortical networks, and the accuracy of their correct decisions or memory recall operations, can be increased by utilizing diluted connectivity and correspondingly increasing the number of neurons in the network, with little impact on the speed of processing of the cortex. Thus diluted connectivity can decrease cortical spiking-related noise. In addition, we show that the Fano factor for the trial-to-trial variability of the neuronal firing decreases from the spontaneous firing state value when the attractor network makes a decision. This article is part of a Special Issue entitled "Neural Coding". PMID:21875702