A hybrid parallel framework for the cellular Potts model simulations
Jiang, Yi [Los Alamos National Laboratory; He, Kejing [SOUTH CHINA UNIV; Dong, Shoubin [SOUTH CHINA UNIV
2009-01-01
The Cellular Potts Model (CPM) has been widely used for biological simulations. However, most current implementations are either sequential or approximated, which can't be used for large scale complex 3D simulation. In this paper we present a hybrid parallel framework for CPM simulations. The time-consuming POE solving, cell division, and cell reaction operation are distributed to clusters using the Message Passing Interface (MPI). The Monte Carlo lattice update is parallelized on shared-memory SMP system using OpenMP. Because the Monte Carlo lattice update is much faster than the POE solving and SMP systems are more and more common, this hybrid approach achieves good performance and high accuracy at the same time. Based on the parallel Cellular Potts Model, we studied the avascular tumor growth using a multiscale model. The application and performance analysis show that the hybrid parallel framework is quite efficient. The hybrid parallel CPM can be used for the large scale simulation ({approx}10{sup 8} sites) of complex collective behavior of numerous cells ({approx}10{sup 6}).
Multiscale Model of Colorectal Cancer Using the Cellular Potts Framework
Osborne, James M
2015-01-01
Colorectal cancer (CRC) is one of the major causes of death in the developed world and forms a canonical example of tumorigenesis. CRC arises from a string of mutations of individual cells in the colorectal crypt, making it particularly suited for multiscale multicellular modeling, where mutations of individual cells can be clearly represented and their effects readily tracked. In this paper, we present a multicellular model of the onset of colorectal cancer, utilizing the cellular Potts model (CPM). We use the model to investigate how, through the modification of their mechanical properties, mutant cells colonize the crypt. Moreover, we study the influence of mutations on the shape of cells in the crypt, suggesting possible cell- and tissue-level indicators for identifying early-stage cancerous crypts. Crucially, we discuss the effect that the motility parameters of the model (key factors in the behavior of the CPM) have on the distribution of cells within a homeostatic crypt, resulting in an optimal parameter regime that accurately reflects biological assumptions. In summary, the key results of this paper are 1) how to couple the CPM with processes occurring on other spatial scales, using the example of the crypt to motivate suitable motility parameters; 2) modeling mutant cells with the CPM; 3) and investigating how mutations influence the shape of cells in the crypt. PMID:26461973
Reconstruction of symmetric Potts Models
Sly, Allan
2008-01-01
The reconstruction problem on the tree has been studied in numerous contexts including statistical physics, information theory and computational biology. However, rigorous reconstruction thresholds have only been established in a small number of models. We prove the first exact reconstruction threshold in a non-binary model establishing the Kesten-Stigum bound for the 3-state Potts model on regular trees of large degree. We further establish that the Kesten-Stigum bound is not tight for the $...
Nested sampling for Potts models
Murray, Iain; MacKay, David J. C.; Ghahramani, Zoubin; Skilling, John
2006-01-01
Nested sampling is a new Monte Carlo method by Skilling intended for general Bayesian computation. Nested sampling provides a robust alternative to annealing-based methods for computing normalizing constants. It can also generate estimates of other quantities such as posterior expectations. The key technical requirement is an ability to draw samples uniformly from the prior subject to a constraint on the likelihood. We provide a demonstration with the Potts model, an undirected graphical model.
BTF Potts compound texture model
Haindl, Michal; Remeš, Václav; Havlíček, Vojtěch
Bellingham: SPIE-IS&T, 2015, 939807-1-939807-11. (Proceedings of SPIE. 9398). ISBN 978-1-62841-488-2. ISSN 0277-786X. [Electronic Imaging 2015. San Francisco (US), 08.02.2015-12.02.2015] R&D Projects: GA ČR(CZ) GA14-10911S; GA ČR(CZ) GA14-02652S Keywords : Texture * texture synthesis * compound Markov random field model * CAR model * Potts MRF * Voronoi mosaic Subject RIV: BD - Theory of Information http://library.utia.cas.cz/separaty/21015/RO/haindl-0443580.pdf
Potts Compound Markovian Texture Model
Haindl, Michal; Remeš, Václav; Havlíček, Vojtěch
Piscataway : IEEE Press, 2012, s. 29-32. ISBN 978-1-4673-2216-4. [21st International Conference on Pattern Recognition (ICPR 2012). Tsukuba (JP), 11.11.2012-15.11.2012] R&D Projects: GA ČR GAP103/11/0335; GA ČR GA102/08/0593 Grant ostatní: CESNET(CZ) 409/2011 Institutional support: RVO:67985556 Keywords : texture * Markov random field Subject RIV: BD - Theory of Information http://library.utia.cas.cz/separaty/2012/RO/haindl-potts compound markov ian texture model.pdf
Dilute Potts model in two dimensions
Qian, Xiaofeng; Deng, Youjin; Blöte, Henk W. J.
2005-11-01
We study the two-dimensional dilute q -state Potts model by means of transfer-matrix and Monte Carlo methods. Using the random-cluster representation, we include noninteger values of q . We locate phase transitions in the three-dimensional parameter space of q , the Potts coupling K⩾0 , and the chemical potential of the vacancies. The critical plane is found to contain a line of fixed points that divides into a critical branch and a tricritical one, just as predicted by the renormalization scenario formulated by Nienhuis for the dilute Potts model. The universal properties along the line of fixed points agree with the theoretical predictions. We also determine the density of the vacancies along these branches. For q=2-2 we obtain the phase diagram in a three-dimensional parameter space that also includes a coupling V⩾0 between the vacancies. For q=2 , the latter space contains the Blume-Capel model as a special case. We include a determination of the tricritical point of this model, as well as an analysis of percolation clusters constructed on tricritical Potts configurations for noninteger q . This percolation study is based on Monte Carlo algorithms that include local updates flipping between Potts sites and vacancies. The bond updates are performed locally for q1 . The updates for q>1 use a number of operations per site independent of the system size.
Phase Transitions in Delaunay Potts Models
Adams, Stefan; Eyers, Michael
2016-01-01
We establish phase transitions for certain classes of continuum Delaunay multi-type particle systems (continuum Potts models) with infinite range repulsive interaction between particles of different type. In one class of the Delaunay Potts models studied the repulsive interaction is a triangle (multi-body) interaction whereas in the second class the interaction is between pairs (edges) of the Delaunay graph. The result for the edge model is an extension of finite range results in Bertin et al. (J Stat Phys 114(1-2):79-100, 2004) for the Delaunay graph and in Georgii and Häggström (Commun Math Phys 181:507-528, 1996) for continuum Potts models to an infinite range repulsion decaying with the edge length. This is a proof of an old conjecture of Lebowitz and Lieb. The repulsive triangle interactions have infinite range as well and depend on the underlying geometry and thus are a first step towards studying phase transitions for geometry-dependent multi-body systems. Our approach involves a Delaunay random-cluster representation analogous to the Fortuin-Kasteleyn representation of the Potts model. The phase transitions manifest themselves in the percolation of the corresponding random-cluster model. Our proofs rely on recent studies (Dereudre et al. in Probab Theory Relat Fields 153:643-670, 2012) of Gibbs measures for geometry-dependent interactions.
Non compact continuum limit of two coupled Potts models
Vernier, Éric; Lykke Jacobsen, Jesper; Saleur, Hubert
2014-10-01
We study two Q-state Potts models coupled by the product of their energy operators, in the regime 2 discrete states emerging from the continuum at appropriate twists. The non compact boson entails strong logarithmic corrections to the finite-size behaviour of the scaling levels, an understanding of which allows us to correct an earlier proposal for some of the critical exponents. In particular, we infer the full set of magnetic scaling dimensions (watermelon operators) of the Potts model.
High-temperature series expansions for random Potts models
M.Hellmund
2005-01-01
Full Text Available We discuss recently generated high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices. Using the star-graph expansion technique, quenched disorder averages can be calculated exactly for arbitrary uncorrelated coupling distributions while keeping the disorder strength p as well as the dimension d as symbolic parameters. We present analyses of the new series for the susceptibility of the Ising (q=2 and 4-state Potts model in three dimensions up to the order 19 and 18, respectively, and compare our findings with results from field-theoretical renormalization group studies and Monte Carlo simulations.
The Many Faces of the Chiral Potts Model
Au-Yang, H; Au-Yang, Helen; Perk, Jacques H.H.
1996-01-01
In this talk, we give a brief overview of several aspects of the theory of the chiral Potts model, including higher-genus solutions of the star-triangle and tetrahedron equations, cyclic representations of affine quantum groups, basic hypergeometric functions at root of unity, and possible applications.
Phase transition in Potts model with invisible states
We study phase transition in the ferromagnetic Potts model with invisible states that are added as redundant states by mean-field calculation and Monte Carlo simulation. Invisible states affect the entropy and free energy, although they do not contribute to the internal energy. A second-order phase transition takes place at finite temperature in the standard q-state ferromagnetic Potts model on two-dimensional lattice for q=2,3, and 4. However, our present model on two-dimensional lattice undergoes a first-order phase transition with spontaneous q-fold symmetry breaking (q=2,3, and 4) due to entropy effect of invisible states. The model is fundamental for the analysis of a first-order phase transition with spontaneous discrete symmetry breaking. (author)
Potts models with invisible states on general Bethe lattices
The number of so-called invisible states which need to be added to the q-state Potts model to transmute its phase transition from continuous to first order has attracted recent attention. In the q = 2 case, a Bragg–Williams (mean-field) approach necessitates four such invisible states while a 3-regular random graph formalism requires seventeen. In both of these cases, the changeover from second- to first-order behaviour induced by the invisible states is identified through the tricritical point of an equivalent Blume–Emery–Griffiths model. Here we investigate the generalized Potts model on a Bethe lattice with z neighbours. We show that, in the q = 2 case, invisible states are required to manifest the equivalent Blume–Emery–Griffiths tricriticality. When z = 3, the 3-regular random graph result is recovered, while z → ∞ delivers the Bragg–Williams (mean-field) result. (paper)
Application of nested sampling in statistical physics: the Potts model
Pfeifenberger, Manuel J
2016-01-01
We present a systematic benchmark study of the nested sampling algorithm on the basis of the Potts model. This model exhibits a first order phase transition for $q>4$ at the critical temperature. The numerical evaluation of the partition function and thermodynamic observables, which involves high dimensional sums of sharply structured multi-modal density functions, represents a major challenge to most standard numerical techniques, such as Markov Chain Monte Carlo. Nested sampling, on the other hand, is particularly suited for such problems. In this paper we will employ both, nested sampling and thermodynamic integration to evaluate the partition function of the Potts model. In both cases individual moves are based on Swendsen-Wang updates. A autocorrelation time analysis of both algorithms shows that the severe slowing down of thermodynamic integration around the critical temperature does not occur in nested sampling. In addition we show, how thermodynamic variables can be computed with high accuracy from th...
Gibbs properties of the fuzzy Potts model on trees and in mean field
Haeggstroem, Olle; Kuelske, Christof
2003-01-01
We study Gibbs properties of the fuzzy Potts model in the mean field case (i.e on a complete graph) and on trees. For the mean field case, a complete characterization of the set of temperatures for which non-Gibbsianness happens is given. The results for trees are somewhat less explicit, but we do show for general trees that non-Gibbsianness of the fuzzy Potts model happens exactly for those temperatures where the underlying Potts model has multiple Gibbs measures.
Gibbs Properties of the Fuzzy Potts Model on Trees and in Mean Field
Häggström, O.; Külske, C.
2004-01-01
We study Gibbs properties of the fuzzy Potts model in the mean field case (i.e. on a complete graph) and on trees. For the mean field case, a complete characterization of the set of temperatures for which non-Gibbsianness happens is given. The results for trees are somewhat less explicit, but we do show for general trees that non-Gibbsianness of the fuzzy Potts model happens exactly for those temperatures where the underlying Potts model has multiple Gibbs measures.
Potts models with (17) invisible states on thin graphs
The order of a phase transition is usually determined by the nature of the symmetry breaking at the phase transition point and the dimension of the model under consideration. For instance, q-state Potts models in two dimensions display a second order, continuous transition for q = 2, 3, 4 and first order for higher q. Tamura et al recently introduced Potts models with ‘invisible’ states which contribute to the entropy but not the internal energy and noted that adding such invisible states could transmute continuous transitions into first order transitions (Tamura et al 2010 Prog. Theor. Phys. 124 381; 2011 J. Phys: Conf. Ser. 297 012022; 2012 Interface Between Quantum Information and Statistical Physics; Tanaka and Tamura 2011 J. Phys.: Conf. Ser. 320 012025). This was observed both in a Bragg–Williams type mean-field calculation and 2D Monte-Carlo simulations. It was suggested that the invisible state mechanism for transmuting the order of a transition might play a role where transition orders inconsistent with the usual scheme had been observed. In this paper we note that an alternative mean-field approach employing 3-regular random (‘thin’) graphs also displays this change in the order of the transition as the number of invisible states is varied, although the number of states required to effect the transmutation, 17 invisible states when there are 2 visible states, is much higher than in the Bragg–Williams case. The calculation proceeds by using the equivalence of the Potts model with two visible and r invisible states to the Blume–Emery–Griffiths (BEG) model, so a by-product is the solution of the BEG model on thin random graphs. (paper)
Parallel family trees for transfer matrices in the Potts model
Navarro, Cristobal A; Kahler, Nancy Hitschfeld; Navarro, Gonzalo
2013-01-01
The computational cost of transfer matrix methods for the Potts model is directly related to the problem of \\textit{into how many ways can two adjacent blocks of a lattice be connected}. Answering this question leads to the generation of a combinatorial set of lattice configurations. This set defines the \\textit{configuration space} of the problem, and the smaller it is, the faster the transfer matrix method can be. The configuration space of generic transfer matrix methods for strip lattices in the Potts model is in the order of the Catalan numbers, leading to an asymptotic cost of $O(4^m)$ with $m$ being the width of the strip. Transfer matrix methods with a smaller configuration space indeed exist but they make assumptions on the temperature, number of spin states, or restrict the topology of the lattice in order to work. In this paper we propose a general and parallel transfer matrix method, based on family trees, that uses a sub-Catalan configuration space of size $O(3^m)$. The improvement is achieved by...
Dynamical Properties of Potts Model with Invisible States
We study dynamic behavior of Potts model with invisible states near the first-order phase transition temperature. This model is regarded as a standard model to analyse nature of phase transition. We can control the energy barrier between the ordered state and disordered state without changing the symmetry which breaks at the transition point. We focus on melting process starting from the perfect ordered state. We calculate time-dependency of the order parameter, density of invisible state, and internal energy. All of them show two-step relaxation behavior. We also analyze the relationship between the characteristic melting time and characteristic scale of the energy barrier by changing the number of invisible states. We find that characteristic melting time increases as the energy barrier enlarges in this model. This model is regarded as a fundamental model to analyze dynamic behavior near the first-order phase transition point.
Coupled Potts models: Self-duality and fixed point structure
We consider q-state Potts models coupled by their energy operators. Restricting our study to self-dual couplings, numerical simulations demonstrate the existence of non-trivial fixed points for 2 ≤ q ≤ 4. These fixed points were first predicted by perturbative renormalisation group calculations. Accurate values for the central charge and the multiscaling exponents of the spin and energy operators are calculated using a series of novel transfer matrix algorithms employing clusters and loops. These results compare well with those of the perturbative expansion, in the range of parameter values where the latter is valid. The criticality of the fixed-point models is independently verified by examining higher eigenvalues in the even sector, and by demonstrating the existence of scaling laws from Monte Carlo simulations. This might be a first step towards the identification of the conformal field theories describing the critical behaviour of this class of models
Evolution of scale-free random graphs: Potts model formulation
We study the bond percolation problem in random graphs of N weighted vertices, where each vertex i has a prescribed weight Pi and an edge can connect vertices i and j with rate PiPj. The problem is solved by the q→1 limit of the q-state Potts model with inhomogeneous interactions for all pairs of spins. We apply this approach to the static model having Pi∝i-μ (03 and 2<λ<3. While for the former, the giant cluster forms abruptly at the percolation transition, for the latter, however, the formation of the giant cluster is gradual and the mean cluster size for finite N shows double peaks
Generalized Potts-Models and their Relevance for Gauge Theories
Andreas Wipf
2007-01-01
Full Text Available We study the Polyakov loop dynamics originating from finite-temperature Yang-Mills theory. The effective actions contain center-symmetric terms involving powers of the Polyakov loop, each with its own coupling. For a subclass with two couplings we perform a detailed analysis of the statistical mechanics involved. To this end we employ a modified mean field approximation and Monte Carlo simulations based on a novel cluster algorithm. We find excellent agreement of both approaches. The phase diagram exhibits both first and second order transitions between symmetric, ferromagnetic and antiferromagnetic phases with phase boundaries merging at three tricritical points. The critical exponents ν and γ at the continuous transition between symmetric and antiferromagnetic phases are the same as for the 3-state spin Potts model.
Glauber Dynamics for the mean-field Potts Model
Cuff, Paul; Louidor, Oren; Lubetzky, Eyal; Peres, Yuval; Sly, Allan
2012-01-01
We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with $q\\geq 3$ states and show that it undergoes a critical slowdown at an inverse-temperature $\\beta_s(q)$ strictly lower than the critical $\\beta_c(q)$ for uniqueness of the thermodynamic limit. The dynamical critical $\\beta_s(q)$ is the spinodal point marking the onset of metastability. We prove that when $\\beta\\beta_s(q)$ the mixing time is exponentially large in $n$. Furthermore, as $\\beta \\uparrow \\beta_s$ with $n$, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of $O(n^{-2/3})$ around $\\beta_s$. These results form the first complete analysis of the critical slowdown of a dynamics with a first order phase transition.
Interplay between sign problem and Z_3 symmetry in three-dimensional Potts model
Hirakida, Takehiro; Takahashi, Junichi; Yahiro, Masanobu
2016-01-01
We construct four kinds of Z3-symmetric three-dimentional (3-d) Potts models, each with different number of states at each site on a 3-d lattice, by extending the 3-d three-state Potts model. Comparing the ordinary Potts model with the four Z3-symmetric Potts models, we investigate how Z3 symmetry affects the sign problem and see how the deconfinement transition line changes in the $\\mu-\\kappa$ plane as the number of states increases, where $\\mu$ $(\\kappa)$ plays a role of chemical potential (temperature) in the models. We find that the sign problem is almost cured by imposing Z3 symmetry. This mechanism may happen in Z3-symmetric QCD-like theory. We also show that the deconfinement transition line has stronger $\\mu$-dependence with respect to increasing the number of states.
Nishimori point in random-bond Ising and Potts models in 2D
A. Honecker; Jacobsen, J. L.; Picco, M.; Pujol, P.
2001-01-01
We study the universality class of the fixed points of the 2D random bond q-state Potts model by means of numerical transfer matrix methods. In particular, we determine the critical exponents associated with the fixed point on the Nishimori line. Precise measurements show that the universality class of this fixed point is inconsistent with percolation on Potts clusters for q=2, corresponding to the Ising model, and q=3
Double Potts chain and exact results for some two-dimensional models
A closed-form exact analytical solution for the q-state Potts model on a ladder 2x∞ with arbitrary two-, three-, and four-site interactions in a unit cell is presented. Using the obtained solution it is shown that the finite-size internal energy equation [J. Wosiek, Phys. Rev. B 49, 15 023 (1994)] yields an accurate value of the critical temperature for the triangular Potts lattice with three-site interactions in alternate triangular faces. (author)
Ising and Potts models: binding disorder-and dimension effects
Within the real space renormalization group framework, some thermal equilibrium properties of pure and disordered insulating systems are calculated. In the pure hypercubic lattice system, the Ising model surface tension and the correlation length of the q-state Potts model, which generalizes the former are analyzed. Several asymptotic behaviors are obtained (for the first time as far as we know) for both functions and the influence of dimension over them can be observed. Accurate numerical proposals for the surface tension are made in several dimensions, and the effect of the number of states (q) on the correlation lenght is shown. In disordered systems, attention is focused essentiall on those which can be theoretically represented by pure sistem Hamiltonians where probability distributions are assumed for the coupling constants (disorder in the bonds). It is obtained with high precision several approximate critical surfaces for the quenched square-lattice Ising model, whose probability distribution can assume two positive values (hence there is no frustration). These aproximate surfaces contain all the exact known points. In the cases where the coupling constant probability distribution can also assume negative values (allowing disordered and frustrated systems), a theoretical treatment which distinguishes the frustration effect from the dilution one is proposed. This distinction can be seen by the different ways in which the bonds of any series-parallel topological array combine. (Author)
Roughness exponent in two-dimensional percolation, Potts model, and clock model
We present a numerical study of the self-affine profiles obtained from configurations of the q-state Potts (with q=2,3, and 7) and p=10 clock models as well as from the occupation states for site percolation on the square lattice. The first and second order static phase transitions of the Potts model are located by a sharp change in the value of the roughness exponent α characterizing those profiles. The low temperature phase of the Potts model corresponds to flat (α≅1) profiles, whereas its high temperature phase is associated with rough (α≅0.5) ones. For the p=10 clock model, in addition to the flat (ferromagnetic) and rough (paramagnetic) profiles, an intermediate rough (0.5<α<1) phase-associated with a soft spin-wave one-is observed. Our results for the transition temperatures in the Potts and clock models are in agreement with the static values, showing that this approach is able to detect the phase transitions in these models directly from the spin configurations, without any reference to thermodynamical potentials, order parameters, or response functions. Finally, we show that the roughness exponent α is insensitive to geometric critical phenomena
Scale-free random graphs and Potts model
D-S Lee; K-I Goh; B Kahng; D Kim
2005-06-01
We introduce a simple algorithm that constructs scale-free random graphs efficiently: each vertex has a prescribed weight − (0 < < 1) and an edge can connect vertices and with rate . Corresponding equilibrium ensemble is identified and the problem is solved by the → 1 limit of the -state Potts model with inhomogeneous interactions for all pairs of spins. The number of loops as well as the giant cluster size and the mean cluster size are obtained in the thermodynamic limit as a function of the edge density. Various critical exponents associated with the percolation transition are also obtained together with finite-size scaling forms. The process of forming the giant cluster is qualitatively different between the cases of > 3 and 2 < < 3, where = 1 + -1 is the degree distribution exponent. While for the former, the giant cluster forms abruptly at the percolation transition, for the latter, however, the formation of the giant cluster is gradual and the mean cluster size for finite shows double peaks.
Potts models with magnetic field: Arithmetic, geometry, and computation
Dasu, Shival; Marcolli, Matilde
2015-11-01
We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.
Optimal region of latching activity in an adaptive Potts model for networks of neurons
In statistical mechanics, the Potts model is a model for interacting spins with more than two discrete states. Neural networks which exhibit features of learning and associative memory can also be modeled by a system of Potts spins. A spontaneous behavior of hopping from one discrete attractor state to another (referred to as latching) has been proposed to be associated with higher cognitive functions. Here we propose a model in which both the stochastic dynamics of Potts models and an adaptive potential function are present. A latching dynamics is observed in a limited region of the noise(temperature)–adaptation parameter space. We hence suggest noise as a fundamental factor in such alternations alongside adaptation. From a dynamical systems point of view, the noise–adaptation alternations may be the underlying mechanism for multi-stability in attractor-based models. An optimality criterion for realistic models is finally inferred
Marginal dimensions of the Potts model with invisible states
Krasnytska, M.; Sarkanych, P.; Berche, B.; Holovatch, Yu; Kenna, R.
2016-06-01
We reconsider the mean-field Potts model with q interacting and r non-interacting (invisible) states. The model was recently introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems where the Z q -symmetry is spontaneously broken. We analyse the marginal dimensions of the model, i.e., the value of r at which the order of the phase transition changes. In the q = 2 case, we determine that value to be {r}{{c}}=3.65(5); there is a second-order phase transition there when r\\lt {r}{{c}} and a first-order one at r\\gt {r}{{c}}. We also analyse the region 1≤slant q\\lt 2 and show that the change from second to first order there is manifest through a new mechanism involving two marginal values of r. The q = 1 limit gives bond percolation. Above the lower value r c1, the order parameters exhibit discontinuities at temperature \\tilde{t} below a critical value t c. The larger value r c2 marks the point at which the phase transition at t c changes from second to first order. Thus, for {r}{{c}1}\\lt r\\lt {r}{{c}2}, the transition at t c remains second order while at \\tilde{t} the system undergoes a first order phase transition. As r increases further, \\tilde{t} increases, bringing the discontinuity closer to t c. Finally, when r exceeds r c2 \\tilde{t} coincides with t c and the phase transition becomes first order. This new mechanism indicates how the discontinuity characteristic of first order phase transitions emerges.
Dotsenko, V S; Pujol, P; Dotsenko, Vladimir; Picco, Marco; Pujol, Pierre
1995-01-01
We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series around the conformal field theories representing the pure models. We obtain a crossover in the amplitude for the correlation function for the Ising model which doesn't change the critical exponent, and a shift in the critical exponent produced by randomness in the case of the Potts model. A comparison with numerical data is discussed briefly.
Phase Transition of Generalized Ferromagnetic Potts Model - Effect of Invisible States -
We investigate the nature of the phase transition of the ferromagnetic Potts model with invisible states. The ferromagnetic Potts model with invisible states can be regarded as a straightforward extension of the standard ferromagnetic Potts model. The invisible states contribute the entropy, however they do not affect the internal energy. They also do not change the symmetry which breaks at the transition temperature. The invisible states stimulate a first-order phase transition. We confirm that the first-order phase transition with spontaneous q-fold symmetry breaking for q = 2,3, and 4 takes place even on two-dimensional lattice by Monte Carlo simulation. We also find that the transition temperature decreases and the latent heat increases as the number of invisible states increases.
Potts Model on Maple Leaf Lattice with Pure Three-Site Interaction
WANG Zhou-Fei; CHEN Li
2005-01-01
We use Monte Carlo method to study three-state Potts model on maple leaf lattice with pure three-site interaction. The critical behavior of both ferromagnetic and antiferromagnetic cases is studied. Our results confirm that the critical behavior of the ferromagnetic model is independent of the lattice details and lies in the universality class of the three-state ferromagnetic Potts model. For the antiferromagnetic case the transition is of the first order. We have calculated the energy jump and critical temperature in this area. We find there is a tricritical point separating the first order and second order phases for this system.
Potts model on directed small-world Voronoi-Delaunay lattices
Marques, R. M.; Lima, F. W. S.; Costa Filho, Raimundo N.
2016-06-01
The critical properties of the Potts model with q = 3 and 4 states in two-dimensions on directed small-world Voronoi-Delaunay random lattices with quenched connectivity disorder are investigated. This disordered system is simulated by applying the Monte Carlo update heat bath algorithm. The Potts model on these directed small-world random lattices presents in fact a second-order phase transition with new critical exponents for q = 3 and value of the rewiring probability p = 0.01, but for q = 4 the system exhibits only a first-order phase transition independent of p (0 < p < 1).
We employ the second renormalization group method of tensor-network states to investigate thermodynamic properties of the ferromagnetic and antiferromagnetic Potts model on triangular lattices. From the temperature dependence of the internal energy and the specific heat, both the critical temperatures and critical exponents are evaluated. For the q = 3 antiferromagnetic Potts model, the critical temperature is found to be Tc = 0.627163±0.000003, which is at least one order of magnitude more accurate than that obtained by other methods. (condensed matter: structure, mechanical and thermal properties)
Random matrix theory and higher genus integrability: the quantum chiral Potts model
We perform a random matrix theory (RMT) analysis of the quantum four-state chiral Potts chain for different sizes of the chain up to size L 8. Our analysis gives clear evidence of a Gaussian orthogonal ensemble (GOE) statistics, suggesting the existence of a generalized time-reversal invariance. Furthermore, a change from the (generic) GOE distribution to a Poisson distribution occurs when the integrability conditions are met. The chiral Potts model is known to correspond to a (star-triangle) integrability associated with curves of genus higher than zero or one. Therefore, the RMT analysis can also be seen as a detector of 'higher genus integrability'. (author)
Softening of Phase Transition in 2D Potts Model Under Quenched Bond Randomness
Yaşar, Fatih; Gündüç, Yiğit; Çelik, Tarık
1997-01-01
We have simulated, by using cluster algorithm, the $q=8$ state Potts model in two-dimension with varying amount of quenched bond randomness. We have shown that there exist a finite size dependent threshold value of the introduced quenched bond randomness for rounding the first-order phase transition and this threshold value becomes smaller as the system size increased.
Susceptibility of the Potts model in an hierarchical lattice: renormalisation group approach
Using a real space renormalization group method, the thermal dependence of the susceptibility of the q-state Potts model (ferro-and antiferromagnet) on self-dual Wheatstone-bridge-like hierarchical lattices is calculated. The influence of external fields on the antiferromagnetic phase diagram is discussed as well. (author)
An improvement of extremality regions for Gibbs measures of the Potts model on a Cayley tree
Haydarov, Farhod; Khakimov, Rustam
2016-03-01
We give a condition of extemelity for translation-invariant Gibbs measures of q—state Potts model on a Cayley tree. We'll improve the regions of extremality for some measures considered in [14]. Moreover, some results in [14] are generalized.
Positive association in the fractional fuzzy Potts model
Kahn, Jeff; Weininger, Nicholas
2007-01-01
A fractional fuzzy Potts measure is a probability distribution on spin configurations of a finite graph $G$ obtained in two steps: first a subgraph of $G$ is chosen according to a random cluster measure $\\phi_{p,q}$, and then a spin ($\\pm1$) is chosen independently for each component of the subgraph and assigned to all vertices of that component. We show that whenever $q\\geq1$, such a measure is positively associated, meaning that any two increasing events are positively correlated. This gene...
Joint Image Reconstruction and Segmentation Using the Potts Model
Storath, Martin; Frikel, Jürgen; Unser, Michael
2014-01-01
We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation from limited data in x-ray and photoacoustic tomography. For instance, our method is able to reconstruct the Shepp-Logan phantom from $7$ angular views only. We demonstrate the practical applicability in an experiment with real PET data.
Dotsenko, V S; Picco, M; Pujol, P; Dotsenko, Viktor; Dotsenko, Vladimir; Picco, Marco; Pujol, Pierre
1995-01-01
We find a new solution of the renormalization group for the Potts model with ferromagnetic random valued coupling constants. The solution exhibits universality and broken replica symmetry. It is argued that the model reaches this universality class if the replica symmetry is broken initially. Otherwise the model stays with the replica symmetric renormalization group flow and reaches the fixed point which has been considered before.
The number of link and cluster states: the core of the 2D q state Potts model
Due to Fortuin and Kastelyin the q state Potts model has a representation as a sum over random graphs, generalizing the Potts model to arbitrary q is based on this representation. A key element of the random cluster representation is the combinatorial factor Γg(C,E), which is the number of ways to form C distinct clusters, consisting of totally E edges. We have devised a method to calculate Γg(C,E) from Monte Carlo simulations
Critical dynamics of the Potts model: short-time Monte Carlo simulations
We calculate the new dynamic exponent θ of the 4-state Potts model, using short-time simulations. Our estimates θ1=-0.0471(33) and θ2=-0.0429(11) obtained by following the behavior of the magnetization or measuring the evolution of the time correlation function of the magnetization corroborate the conjecture by Okano et al. [Nucl. Phys. B 485 (1997) 727]. In addition, these values agree with previous estimate of the same dynamic exponent for the two-dimensional Ising model with three-spin interactions in one direction, that is known to belong to the same universality class as the 4-state Potts model. The anomalous dimension of initial magnetization x0=zθ+β/ν is calculated by an alternative way that mixes two different initial conditions. We have also estimated the values of the static exponents β and ν. They are in complete agreement with the pertinent results of the literature
Uniqueness of Gibbs measure for Potts model with countable set of spin values
We consider a nearest-neighbor Potts model with countable spin values 0,1,..., and non zero external field, on a Cayley tree of order k (with k+1 neighbors). We study translation-invariant 'splitting' Gibbs measures. We reduce the problem to the description of the solutions of some infinite system of equations. For any k≥1 and any fixed probability measure ν with ν(i)>0 on the set of all non negative integer numbers Φ={0,1,...} we show that the set of translation-invariant splitting Gibbs measures contains at most one point, independently on parameters of the Potts model with countable set of spin values on Cayley tree. Also we give a full description of the class of measures ν on Φ such that wit respect to each element of this class our infinite system of equations has unique solution {ai=1,2,...}, where a is an element of (0,1). (author)
FERRIMAGNETIC PHASES OF THE BLUME-EMERY-GRIFFITHS MODEL AND THE POTTS MODEL ON THE DIAMOND LATTICE
Ni Jun; Gu Bing-lin
2000-01-01
The phase transitions in the Blume-Emery-Griffiths (BEG) model andantiferromagnetic Potts model on the diamond lattice are investigatedusing the cluster-variation method in the pair approximation. Theferrimagnetic phases are found to be different from those on thesimple-cubic lattice. The phase diagrams of the BEG model are alsocalculated. In the vicinity of the parameter line where the BEG modelreduces to the three-state antiferromagnetic Potts model, new types ofphase diagram are obtained. The results are different from those of themean-field theory, which is a good approximation only for largecoordination number of the lattice.
Topological aspects of Potts gauge models and their 1/Q expansion
In the d-dimensional Potts gauge model the summation over field variables in the partition function is replaced by that over hyper graphs where the topological invariants (Betty numbers) are essentially used, that take into account both oriented and non oriented surfaces. 1/Q expansion in three - and four - dimensions is carried out. A critical temperature and latent heat are obtained by the Pade approximation
Entropy-driven phase transition in low-temperature antiferromagnetic Potts models
Kotecký, R.; Sokal, A.D.; Swart, Jan M.
2014-01-01
Roč. 330, č. 3 (2014), s. 1339-1394. ISSN 0010-3616 R&D Projects: GA ČR GA201/09/1931; GA ČR GAP201/12/2613 Institutional support: RVO:67985556 Keywords : Antiferromagnetic Potts model * proper coloring * plane quadrangulation * phase transition * diced lattice Subject RIV: BA - General Mathematics Impact factor: 2.086, year: 2014 http://library.utia.cas.cz/separaty/2014/SI/swart-0429507.pdf
Dynamic Scaling and Universality of the Two-Dimensional Random-Bond Potts Model
YING He-Ping; BIAN Bao-Jun; JI Da-Ren; Lothar Schiilke
2001-01-01
Short-time dynamics and universality are investigated for the random-bond Potts model with a trinary distribu tion of quenched randomness on a two-dimensional triangular lattice. The universal power-law scaling behaviour is applied to estimate the exponents z and β/v. Emphasis is placed on dynamic Monte Carlo evolutions for different multi-disorder amplitudes. Our results indicate that the quenched impurities cause a change of the critical universality.
Julia sets and complex singularities in diamond-like hierarchical Potts models
QIAO; Jianyong
2005-01-01
We study the phase transition of the Potts model on diamond-like hierarchical lattices. It is shown that the set of the complex singularities is the Julia set of a rational mapping. An interesting problem is how are these singularities continued to the complex plane. In this paper, by the method of complex dynamics, we give a complete description about the connectivity of the set of the complex singularities.
Efficient Monte Carlo Methods for the Potts Model at Low Temperature
Molkaraie, Mehdi
2015-01-01
We consider the problem of estimating the partition function of the ferromagnetic $q$-state Potts model. We propose an importance sampling algorithm in the dual of the normal factor graph representing the model. The algorithm can efficiently compute an estimate of the partition function in a wide range of parameters; in particular, when the coupling parameters of the model are strong (corresponding to models at low temperature) or when the model contains a mixture of strong and weak couplings. We show that, in this setting, the proposed algorithm significantly outperforms the state of the art methods in the primal and in the dual domains.
CSOS models descending from chiral Potts models: degeneracy of the eigenspace and loop algebra
Au-Yang, Helen; Perk, Jacques H. H.
2016-04-01
Monodromy matrices of the {{\\boldsymbol{τ }}}2\\phantom{^{\\prime }} model are known to satisfy a Yang-Baxter equation with a six-vertex R-matrix as the intertwiner. The commutation relations of the elements of the monodromy matrices are completely determined by this R-matrix. We show the reason why in the superintegrable case the eigenspace is degenerate, but not in the general case. We then show that the eigenspaces of special CSOS models descending from the chiral Potts model are also degenerate. The existence of an L({{sl}}2) quantum loop algebra (or subalgebra) in these models is established by showing that the Serre relations hold for the generators. The highest weight polynomial (or the Drinfeld polynomial) of the representation is obtained by using the method of Baxter for the superintegrable case. As a byproduct, the eigenvalues of all such CSOS models are given explicitly.
Shaken, but not stirred—Potts model coupled to quantum gravity
Ambjørn, J. A.; Anagnostopoulos, K. N.; Loll, R.; Pushkina, I.
2009-01-01
We investigate the critical behaviour of both matter and geometry of the three-state Potts model coupled to two-dimensional Lorentzian quantum gravity in the framework of causal dynamical triangulations. Contrary to what general arguments on the effects of disorder suggest, we find strong numerical evidence that the critical exponents of the matter are not changed under the influence of quantum fluctuations in the geometry, compared to their values on fixed, regular lattices. This lends further support to previous findings that quantum gravity models based on causal dynamical triangulations are in many ways better behaved than their Euclidean counterparts.
Nogawa, Tomoaki
2011-12-05
The evaporation-condensation transition of the Potts model on a square lattice is numerically investigated by the Wang-Landau sampling method. An intrinsically system-size-dependent discrete transition between supersaturation state and phase-separation state is observed in the microcanonical ensemble by changing constrained internal energy. We calculate the microcanonical temperature, as a derivative of microcanonical entropy, and condensation ratio, and perform a finite-size scaling of them to indicate the clear tendency of numerical data to converge to the infinite-size limit predicted by phenomenological theory for the isotherm lattice gas model. © 2011 American Physical Society.
The early history of the integrable chiral Potts model and the odd-even problem
Perk, Jacques H. H.
2016-04-01
In the first part of this paper I shall discuss the round-about way of how the integrable chiral Potts model was discovered about 30 years ago. As there should be more higher-genus models to be discovered, this might be of interest. In the second part I shall discuss some quantum group aspects, especially issues of odd versus even N related to the Serre relations conjecture in our quantum loop subalgebra paper of 5 years ago and how we can make good use of coproducts, also borrowing ideas of Drinfeld, Jimbo, Deguchi, Fabricius, McCoy and Nishino.
Spin-spin critical point correlation functions for the 2D random bond Ising and Potts models
Dotsenko, V S; Pujol, P; Vladimir Dotsenko; Marco Picco; Pierre Pujol
1994-01-01
We compute the combined two and three loop order correction to the spin-spin correlation functions for the 2D Ising and q-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation group approach for the perturbation series around the conformal field theories representing the pure models. We obtain corrections for the correlations functions which produce crossover in the amplitude but don't change the critical exponent in the case of the Ising model and which produce a shift in the critical exponent, due to randomness, in the case of the Potts model. Comparison with numerical data is discussed briefly.
First order phase transition of the q-state Potts model in two dimensions
Arisue, H
2000-01-01
We have calculated the large-$q$ series of the energy cumulants, the magnetization cumulants and the correlation length at the first order phase transition point both in the ordered and disordered phases for the $q$-state Potts model in two dimensions. The series enables us to estimate the numerical values of the quantities more precisely by a factor of $10^2 - 10^4$ than the Monte Carlo simulations. From the large-$q$ series of the eigenvalues of the transfer matrix, we also find that the excited states form a continuum spectrum and there is no particle state at the first order phase transition point.
High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials
Jacobsen, Jesper Lykke
2014-01-01
The critical curves of the q-state Potts model can be determined exactly for regular two-dimensional lattices G that are of the three-terminal type. Jacobsen and Scullard have defined a graph polynomial P_B(q,v) that gives access to the critical manifold for general lattices. It depends on a finite repeating part of the lattice, called the basis B, and its real roots in the temperature variable v = e^K - 1 provide increasingly accurate approximations to the critical manifolds upon increasing ...
Potts Model Partition Functions for Self-Dual Families of Strip Graphs
Chang, Shu-Chiuan; Shrock, Robert
2001-01-01
We consider the $q$-state Potts model on families of self-dual strip graphs $G_D$ of the square lattice of width $L_y$ and arbitrarily great length $L_x$, with periodic longitudinal boundary conditions. The general partition function $Z$ and the T=0 antiferromagnetic special case $P$ (chromatic polynomial) have the respective forms $\\sum_{j=1}^{N_{F,L_y,\\lambda}} c_{F,L_y,j} (\\lambda_{F,L_y,j})^{L_x}$, with $F=Z,P$. For arbitrary $L_y$, we determine (i) the general coefficient $c_{F,L_y,j}$ i...
Chang, Shu-Chiuan; Shrock, Robert
2000-01-01
partial abstract: The $q$-state Potts model partition function (equivalent to the Tutte polynomial) for a lattice strip of fixed width $L_y$ and arbitrary length $L_x$ has the form $Z(G,q,v)=\\sum_{j=1}^{N_{Z,G,\\lambda}}c_{Z,G,j}(\\lambda_{Z,G,j})^{L_x}$, where $v$ is a temperature-dependent variable. The special case of the zero-temperature antiferromagnet ($v=-1$) is the chromatic polynomial $P(G,q)$. Using coloring and transfer matrix methods, we give general formulas for $C_{X,G}=\\sum_{j=1}...
Interface tension of the 3d 4-state Potts model using the Wang-Landau algorithm
Hietanen, A
2011-01-01
We study the interface tension of the 4-state Potts model in three dimensions using the Wang- Landau algorithm. The interface tension is given by the ratio of the partition function with a twisted boundary condition in one direction and periodic boundary conditions in all other directions over the partition function with periodic boundary conditions in all directions. With the Wang-Landau algorithm we can explicitly calculate both partition functions and obtain the result for all temperatures. We find solid numerical evidence for perfect wetting. Our algorithm is tested by calculating thermodynamic quantities at the phase transition point.
High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials
The critical curves of the q-state Potts model can be determined exactly for regular two-dimensional lattices G that are of the three-terminal type. This comprises the square, triangular, hexagonal and bow–tie lattices. Jacobsen and Scullard have defined a graph polynomial PB(q, v) that gives access to the critical manifold for general lattices. It depends on a finite repeating part of the lattice, called the basis B, and its real roots in the temperature variable v = eK − 1 provide increasingly accurate approximations to the critical manifolds upon increasing the size of B. Using transfer matrix techniques, these authors computed PB(q, v) for large bases (up to 243 edges), obtaining determinations of the ferromagnetic critical point vc > 0 for the (4, 82), kagome, and (3, 122) lattices to a precision (of the order 10−8) slightly superior to that of the best available Monte Carlo simulations. In this paper we describe a more efficient transfer matrix approach to the computation of PB(q, v) that relies on a formulation within the periodic Temperley–Lieb algebra. This makes possible computations for substantially larger bases (up to 882 edges), and the precision on vc is hence taken to the range 10−13. We further show that a large variety of regular lattices can be cast in a form suitable for this approach. This includes all Archimedean lattices, their duals and their medials. For all these lattices we tabulate high-precision estimates of the bond percolation thresholds pc and Potts critical points vc. We also trace and discuss the full Potts critical manifold in the (q, v) plane, paying special attention to the antiferromagnetic region v B(p) for certain Archimedean and dual lattices (those having only cubic and quartic vertices), using very large bases (up to 243 vertices). This produces the site percolation thresholds pc to a precision of the order of 10−9. (paper)
Dynamics of Phase Transitions: The 3D 3-state Potts model
Berg, B A; Velytsky, A; Berg, Bernd A.; Meyer-Ortmanns, Hildegard; Velytsky, Alexander
2004-01-01
In studies of the QCD deconfining phase transition or cross-over by means of heavy ion experiments, one ought to be concerned about non-equilibrium effects due to heating and cooling of the system. In this paper we extend our previous study of Glauber dynamics of 2D Potts models to the 3D 3-state Potts model, which serves as an effective model for some QCD properties. We investigate the linear theory of spinodal decomposition in some detail. It describes the early time evolution of the 3D model under a quench from the disordered into the ordered phase well, but fails in 2D. Further, the quench leads to competing vacuum domains, which are difficult to equilibrate, even in the presence of a small external magnetic field. From our hysteresis study we find, as before, a dynamics dominated by spinodal decomposition. There is evidence that some effects survive in the case of a cross-over. But the infinite volume extrapolation is difficult to control, even with lattices as large as 120^3.
Critical behaviour of the dynamical Potts model, subjected to vivid turbulent mixing, is studied by means of the renormalization group. The advecting velocity field is modelled by Kraichnan’s rapid-change ensemble: Gaussian statistics with a given pair correlator 〈vv〉∝δ(t − t′) k−d−ξ, where k is the wave number, d is the dimension of space and 0 < ξ < 2 is an arbitrary exponent. The system exhibits different types of infrared scaling behaviour, associated with four infrared attractors of the renormalization group equations. In addition to the known asymptotic regimes (equilibrium Potts model and passive scalar field), the existence of a new, strongly non-equilibrium type of critical behaviour (universality class) is established, where the self-interaction of the order parameter and the turbulent mixing are equally important. The corresponding critical dimensions and the regions of stability for all the regimes are calculated in the leading order of the double expansion in ξ and ε = 6 − d. Special attention is paid to the effects of compressibility of the fluid, because they lead to interesting crossover phenomena. (paper)
Hu, Zhan-Ning
In this letter, the connection is found between the "star-square" relation in the Baxter-Bazhanov model and the "star-triangle" relation in the chiral Potts model, which means that the tetrahedron equation of the Baxter-Bazhanov model is a consequence of the latter. The four additional constraints in the tetrahedron equation given by Kashaev et al. hold naturally in respect to the spherical trigonometry parametrizations.
Cumulants of the three-state Potts model and of nonequilibrium models with C{sub 3v} symmetry
Tome, Tania [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, SP (Brazil); Petri, Alberto [Istituto di Acustica O M Corbino, Consiglio Nazionale delle Ricerche, Via del Fosso del Cavaliere, Rome (Italy)
2002-07-05
The critical behaviour of two-dimensional stochastic lattice gas models with C{sub 3v} symmetry is analysed. We study the cumulants of the order parameter for the three-state (equilibrium) Potts model and for two irreversible models whose dynamic rules are invariant under the symmetry operations of the point group C{sub 3v}. By means of extensive numerical analysis of the phase transition we show that irreversibility does not affect the critical behaviour of the systems. In particular, we find that the Binder reduced fourth-order cumulant takes a universal value U* which is the same for the three-state Potts model and for the irreversible models. The same universal behaviour is observed for the reduced third-order cumulant. (author)
Application of simulated tempering and magnetizing to a two-dimensional Potts model
We apply the simulated tempering and magnetizing (STM) method to the two-dimensional three-state Potts model in an external magnetic field in order to investigate STM’s applicability further. The temperature and the external field are treated as dynamical variables updated during the STM simulations. On the basis of adequate information obtained by STM for several lattice sizes L × L (up to 160×160), we also perform a number of conventional canonical simulations of larger lattices in order to illustrate the crossover behavior of the Potts model in an external field with increasing L. The temperature and external field for the larger lattice size simulations are chosen by extrapolation of the detailed information obtained by STM. We present a careful analysis of the crossover-scaling behavior at the phase transitions with respect to the lattice size as well as the temperature and external field. The crossover behavior is clearly observed in the simulations in agreement with theoretical predictions. (paper)
Integrable aspects of the scaling q-state Potts models II: finite-size effects
We continue our discussion of the q-state Potts models for q≤4, in the scaling regimes close to their critical and tricritical points. In a previous paper, the spectrum and full S-matrix of the models on an infinite line were elucidated; here, we consider finite-size behaviour. TBA equations are proposed for all cases related to phi21 and phi12 perturbations of unitary minimal models. These are subjected to a variety of checks in the ultraviolet and infrared limits, and compared with results from a recently-proposed non-linear integral equation. A non-linear integral equation is also used to study the flows from tricritical to critical models, over the full range of q. Our results should also be of relevance to the study of the off-critical dilute A models in regimes 1 and 2
Exact S-matrices for supersymmetric sigma models and the Potts model
We study the algebraic formulation of exact factorizable S-matrices for integrable two-dimensional field theories. We show that different formulations of the S-matrices for the Potts field theory are essentially equivalent, in the sense that they can be expressed in the same way as elements of the Temperley-Lieb algebra, in various representations. This enables us to construct the S-matrices for certain nonlinear sigma models that are invariant under the Lie 'supersymmetry' algebras sl(m+n|n) (m=1, 2, n>0), both for the bulk and for the boundary, simply by using another representation of the same algebra. These S-matrices represent the perturbation of the conformal theory at θ=π by a small change in the topological angle θ. The m=1, n=1 theory has applications to the spin quantum Hall transition in disordered fermion systems. We also find S-matrices describing the flow from weak to strong coupling, both for θ=0 and θ=π, in certain other supersymmetric sigma models
Fermat Surface and Group Theory in Symmetry of Rapidity Family in Chiral Potts Model
Roan, Shi-shyr
2013-01-01
The present paper discusses various mathematical aspects about the rapidity symmetry in chiral Potts model (CPM) in the context of algebraic geometry and group theory . We re-analyze the symmetry group of a rapidity curve in $N$-state CPM, explore the universal group structure for all $N$, and further enlarge it to modular symmetries of the complete rapidity family in CPM. As will be shown in the article that all rapidity curves in $N$-state CPM constitute a Fermat hypersurface in $\\PZ^3$ of degree 2N as the natural generalization of the Fermat K3 elliptic surface $(N=2)$, we conduct a thorough algebraic geometry study about the rapidity fibration of Fermat surface and its reduced hyperelliptic fibration via techniques in algebraic surface theory. Symmetries of rapidity family in CPM and hyperelliptic family in $\\tau^{(2)}$-model are exhibited through the geometrical representation of the universal structural group in mathematics.
Yang-Lee zeros for a Potts model of helix-coil transition with nontrivial topology
The Yang-Lee partition function zeros of the Q-state Potts model on a zigzag ladder are studied by a transfer-matrix approach. This Q-state model has a non-trivial topology induced by three-site interactions on a zigzag ladder and is proposed as a description of helix-coil transition in homo-polymers. The Yang-Lee zeros are associated to complex values of the solvent-related coupling constant K (magnetic field) and they are exactly derived for arbitrary values of the system parameters: Q, J (coupling constant of hydrogen binding) and temperature. It is shown that there is only a quasi-phase transition for all temperatures. The densities of the Yang-Lee zeros are singular at the edge singularity points and the critical exponent σ = -1/2. (author)
Au-Yang, Helen; Perk, Jacques H. H.
2016-01-01
In this paper we discuss the integrable chiral Potts model, as it clearly relates to how we got befriended with Vaughan Jones, whose birthday we celebrated at the Qinhuangdao meeting. Remarkably we can also celebrate the birthday of the model, as it has been introduced about 30 years ago as the first solution of the star-triangle equations parametrized in terms of higher genus functions. After introducing the most general checkerboard Yang--Baxter equation, we specialize to the star-triangle ...
Random-field Potts model for the polar domains of lead magnesium niobate and lead scandium tantalate
Qian, H.; Bursill, L.A
1997-06-01
A random filed Potts model is used to establish the spatial relationship between the nanoscale distribution of charges chemical defects and nanoscale polar domains for the perovskite-based relaxor materials lead magnesium niobate (PMN) and lead scandium tantalate (PST). The random fields are not set stochastically but are determined initially by the distribution of B-site cations (Mg, Nb) or (Sc, Ta) generated by Monte Carlo NNNI-model simulations for the chemical defects. An appropriate random field Potts model is derived and algorithms developed for a 2D lattice. It is shown that the local fields are strongly correlated with the chemical domain walls and that polar domains as a function of decreasing temperature is simulated for the two cases of PMN and PST. The dynamics of the polar clusters is also discussed. 33 refs., 9 figs.
Random-field Potts model for the polar domains of lead magnesium niobate and lead scandium tantalate
A random filed Potts model is used to establish the spatial relationship between the nanoscale distribution of charges chemical defects and nanoscale polar domains for the perovskite-based relaxor materials lead magnesium niobate (PMN) and lead scandium tantalate (PST). The random fields are not set stochastically but are determined initially by the distribution of B-site cations (Mg, Nb) or (Sc, Ta) generated by Monte Carlo NNNI-model simulations for the chemical defects. An appropriate random field Potts model is derived and algorithms developed for a 2D lattice. It is shown that the local fields are strongly correlated with the chemical domain walls and that polar domains as a function of decreasing temperature is simulated for the two cases of PMN and PST. The dynamics of the polar clusters is also discussed. 33 refs., 9 figs
We have recently developed methods for obtaining exact two-point resistance of the complete graph minus N edges. We use these methods to obtain closed formulas of certain trigonometrical sums that arise in connection with one-dimensional lattice, in proving Scott’s conjecture on permanent of Cauchy matrix, and in the perturbative chiral Potts model. The generalized trigonometrical sums of the chiral Potts model are shown to satisfy recursion formulas that are transparent and direct, and differ from those of Gervois and Mehta. By making a change of variables in these recursion formulas, the dimension of the space of conformal blocks of SU(2) and SO(3) WZW models may be computed recursively. Our methods are then extended to compute the corner-to-corner resistance, and the Kirchhoff index of the first non-trivial two-dimensional resistor network, 2×N. Finally, we obtain new closed formulas for variant of trigonometrical sums, some of which appear in connection with number theory. -- Highlights: • Alternative derivation of certain trigonometrical sums of the chiral Potts model are given. • Generalization of these trigonometrical sums satisfy recursion formulas. • The dimension of the space of conformal blocks may be computed from these recursions. • Exact corner-to-corner resistance, the Kirchhoff index of 2×N are given
Cluster-size distribution and the magnetic property of a Potts model
Hu, Chin-Kun
1986-11-01
Based on the connection between a q-state Potts model (QPM) and a q-state bond-correlated percolation model (QBCPM), we propose that in the calculation of the free energy and a physical quantity, e.g., the magnetic susceptibility, we need only to retain the terms of the most probable cluster-size distribution (MPCSD) defined in the text. For the one-dimensional model, the MPCSD may be calculated exactly. The free energy and the magnetic susceptibility determined by such MPCSD are the same as those calculated exactly by the transfer-matrix method. For the QPM on the lattice with dimensions d>=2, the above assumption about the MPCSD implies that the magnetic susceptibility of the QPM is proportional to the mean cluster sizes of the QBCPM for both T>Tc and T
Nature of phase transitions in Axelrod-like coupled Potts models in two dimensions
Gandica, Yerali; Chiacchiera, Silvia
2016-03-01
We study F coupled q -state Potts models in a two-dimensional square lattice. The interaction between the different layers is attractive to favor a simultaneous alignment in all of them, and its strength is fixed. The nature of the phase transition for zero field is numerically determined for F =2 ,3 . Using the Lee-Kosterlitz method, we find that it is continuous for F =2 and q =2 , whereas it is abrupt for higher values of q and/or F . When a continuous or a weakly first-order phase transition takes place, we also analyze the properties of the geometrical clusters. This allows us to determine the fractal dimension D of the incipient infinite cluster and to examine the finite-size scaling of the cluster number density via data collapse. A mean-field approximation of the model, from which some general trends can be determined, is presented too. Finally, since this lattice model has been recently considered as a thermodynamic counterpart of the Axelrod model of social dynamics, we discuss our results in connection with this one.
Chang, Shu-Chiuan; Shrock, Robert
2001-07-01
The q-state Potts model partition function (equivalent to the Tutte polynomial) for a lattice strip of fixed width Ly and arbitrary length Lx has the form Z(G,q,v)=∑ j=1N Z,G,λ c Z,G,j(λ Z,G,j) L x, where v is a temperature-dependent variable. The special case of the zero-temperature antiferromagnet ( v=-1) is the chromatic polynomial P( G, q). Using coloring and transfer matrix methods, we give general formulas for C X,G=∑ j=1N X,G,λ c X,G,j for X= Z, P on cyclic and Möbius strip graphs of the square and triangular lattice. Combining these with a general expression for the (unique) coefficient cZ, G, j of degree d in q: c (d)=U 2d( q/2) , where Un( x) is the Chebyshev polynomial of the second kind, we determine the number of λZ, G, j's with coefficient c( d) in Z( G, q, v) for these cyclic strips of width Ly to be n Z(L y,d)=(2d+1)(L y+d+1) -1{2L y}/{L y-d } for 0⩽ d⩽ Ly and zero otherwise. For both cyclic and Möbius strips of these lattices, the total number of distinct eigenvalues λZ, G, j is calculated to be N Z,L y,λ = {2L y}/{L y}. Results are also presented for the analogous numbers nP( Ly, d) and NP, Ly, λ for P( G, q). We find that nP( Ly,0)= nP( Ly-1,1)= MLy-1 (Motzkin number), nZ( Ly,0)= CLy (the Catalan number), and give an exact expression for NP, Ly, λ. Our results for NZ, Ly, λ and NP, Ly, λ apply for both the cyclic and Möbius strips of both the square and triangular lattices; we also point out the interesting relations NZ, Ly, λ=2 NDA, tri, Ly and NP, Ly, λ=2 NDA, sq, Ly, where NDA, Λ, n denotes the number of directed lattice animals on the lattice Λ. We find the asymptotic growths NZ, Ly, λ∼ Ly-1/24 Ly and NP, Ly, λ∼ Ly-1/23 Ly as Ly→∞. Some general geometric identities for Potts model partition functions are also presented.
Improved contact prediction in proteins: Using pseudolikelihoods to infer Potts models
Ekeberg, Magnus; Lövkvist, Cecilia; Lan, Yueheng; Weigt, Martin; Aurell, Erik
2013-01-01
Spatially proximate amino acids in a protein tend to coevolve. A protein's three-dimensional (3D) structure hence leaves an echo of correlations in the evolutionary record. Reverse engineering 3D structures from such correlations is an open problem in structural biology, pursued with increasing vigor as more and more protein sequences continue to fill the data banks. Within this task lies a statistical inference problem, rooted in the following: correlation between two sites in a protein sequence can arise from firsthand interaction but can also be network-propagated via intermediate sites; observed correlation is not enough to guarantee proximity. To separate direct from indirect interactions is an instance of the general problem of inverse statistical mechanics, where the task is to learn model parameters (fields, couplings) from observables (magnetizations, correlations, samples) in large systems. In the context of protein sequences, the approach has been referred to as direct-coupling analysis. Here we show that the pseudolikelihood method, applied to 21-state Potts models describing the statistical properties of families of evolutionarily related proteins, significantly outperforms existing approaches to the direct-coupling analysis, the latter being based on standard mean-field techniques. This improved performance also relies on a modified score for the coupling strength. The results are verified using known crystal structures of specific sequence instances of various protein families. Code implementing the new method can be found at http://plmdca.csc.kth.se/.
Reconstruction of a real world social network using the Potts model and Loopy Belief Propagation
Cristian eBisconti
2015-11-01
Full Text Available The scope of this paper is to test the adoption of a statistical model derived from Condensed Matter Physics, aiming at the reconstruction of a networked structure from observations of the states of the nodes in the network.The inverse Potts model, normally applied to observations of quantum states, is here addressed to observations of the node states in a network and their (anticorrelations, thus inferring interactions as links connecting the nodes. Adopting the Bethe approximation, such an inverse problem is known to be tractable.Within this operational framework, we discuss and apply this network-reconstruction method to a small real-world social network, where it is easy to track statuses of its members: the Italian parliament, adopted as a case study. The dataset is made of (cosponsorships of law proposals by parliament members. In previous studies of similar activity-based networks, the graph structure was inferred directly from activity co-occurrences: here we compare our statistical reconstruction with standard methods, outlining discrepancies and advantages.
Phase transitions for p-adic Potts model on the Cayley tree of order three
In the present paper, we study a phase transition problem for the q-state p-adic Potts model over the Cayley tree of order three. We consider a more general notion of p-adic Gibbs measure which depends on parameter ρ∈Qp. Such a measure is called generalized p-adic quasi Gibbs measure. When ρ equals the p-adic exponent, then it coincides with the p-adic Gibbs measure. When ρ = p, then it coincides with the p-adic quasi Gibbs measure. Therefore, we investigate two regimes with respect to the value of |ρ|p. Namely, in the first regime, one takes ρ = expp(J) for some J∈Qp, in the second one |ρ|p p,|q|p ≤ p−2 we prove the existence of a quasi phase transition. It turns out that if |ρ|pp2p, then one finds the existence of the strong phase transition. (paper)
The surface expoents of the Quantum XXZ, Ashkin-Teller, and Potts models
The eigen-spectrum of both the quantum Ashkin-Teller and Potts chains with free boundaries can be respectively obtained from that of the XXZ chain with free boundaries and a complex surface field. By solving numerically the recently introduced Bethe ansatz equations for such boundaries, eigen-energies are obtained for chains of up to L=256. The conformal anomaly and surface exponents of the quantum XXZ, Ashkin-Teller, and Potts chains are calculated by exploiting their relations with the mass gap amplitudes predicted by conformal invariance. (Author)
Chang, Shu-Chiuan; Shrock, Robert
2015-11-01
We calculate the partition function of the q-state Potts model on arbitrary-length cyclic ladder graphs of the square and triangular lattices, with a generalized external magnetic field that favors or disfavors a subset of spin values {1,ldots ,s} with s ≤ q. For the case of antiferromagnet spin-spin coupling, these provide exactly solved models that exhibit an onset of frustration and competing interactions in the context of a novel type of tensor-product S_s ⊗ S_{q-s} global symmetry, where S_s is the permutation group on s objects.
Ding, Chengxiang; Fu, Zhe; Guo, Wenan; Wu, F Y
2010-01-01
In a recent paper (arXiv:0911.2514), one of us (FYW) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangular-type and kagome-type lattices, and obtained closed-form expressions for the critical frontier with applications to various lattice models. For the triangular-type lattices Wu's result is exact, and for the kagome-type lattices Wu's expression is under a homogeneity assumption. The purpose of the present paper is two-fo...
Potts model partition functions for self-dual families of strip graphs
Chang, Shu-Chiuan; Shrock, Robert
2001-12-01
We consider the q-state Potts model on families of self-dual strip graphs GD of the square lattice of width Ly and arbitrarily great length Lx, with periodic longitudinal boundary conditions. The general partition function Z and the T=0 antiferromagnetic special case P (chromatic polynomial) have the respective forms ∑ j=1 NF, Ly, λcF, Ly, j( λF, Ly, j) Lx, with F= Z, P. For arbitrary Ly, we determine (i) the general coefficient cF, Ly, j in terms of Chebyshev polynomials, (ii) the number nF( Ly, d) of terms with each type of coefficient, and (iii) the total number of terms NF, Ly, λ. We point out interesting connections between the nZ( Ly, d) and Temperley-Lieb algebras, and between the NF, Ly, λ and enumerations of directed lattice animals. Exact calculations of P are presented for 2⩽ Ly⩽4. In the limit of infinite length, we calculate the ground state degeneracy per site (exponent of the ground state entropy), W( q). Generalizing q from Z+ to C, we determine the continuous locus B in the complex q plane where W( q) is singular. We find the interesting result that for all Ly values considered, the maximal point at which B crosses the real q-axis, denoted qc, is the same, and is equal to the value for the infinite square lattice, qc=3. This is the first family of strip graphs of which we are aware that exhibits this type of universality of qc.
Large-$q$ expansion of the two-dimensional $q$-state Potts model by the finite lattice method
Arisue, H
1999-01-01
We have calculated the large-$q$ expansion for the energy and magnetization cumulants at the first order phase transition point in the two-dimensional $q$-state Potts model to the 21st or 23rd order in $1/\\sqrt{q}$ using the finite lattice method. The obtained series allow us to give highly convergent estimates of the cumulants for $q>4$. The results confirm us the correctness of the conjecture by Bhattacharya {\\em et al.} on the asymptotic behavior of the energy cumulants for $q \\to 4_+$ and a similar new conjecture on the magnetization cumulants.
Arisue, H
1999-01-01
We have calculated the large-$q$ expansion for the energy cumulants and the magnetization cumulants at the phase transition point in the two-dimensional $q$-state Potts model to the 21st or 23rd order in $1/\\sqrt{q}$ using the finite lattice method. The obtained series allow us to give very precise estimates of the cumulants for $q>4$ on the first order transition point. The result confirms us the correctness of the conjecture by Bhattacharya et al. on the asymptotic behavior not only of the energy cumulants but also of the magnetization cumulants for $q \\to 4_+$.
Large-$q$ expansion of the specific heat for the two-dimensional $q$-state Potts model
Arisue, H
1999-01-01
We have calculated the large-$q$ expansion for the specific heat at the phase transition point in the two-dimensional $q$-state Potts model to the 23rd order in $1/\\sqrt{q}$ using the finite lattice method. The obtained series allows us to give highly convergent estimates of the specific heat for $q>4$ on the first order transition point. The result confirm us the correctness of the conjecture by Bhattacharya et al. on the asymptotic behavior of the specific heat for $q
Large-$q$ expansion of the energy cumulants for the two-dimensional $q$-state Potts model
Arisue, H
1998-01-01
We have calculated the large-q expansion for the energy cumulants at the phase transition point in the two-dimensional q-state Potts model to the 23rd order in $1/\\sqrt{q}$ using the finite lattice method. The obtained series allow us to give very precise estimates of the cumulants for $q>4$ on the first order transition point. The result confirm us the correctness of the conjecture by Bhattacharya et al. on the asymptotic behavior of the cumulants for $q \\to 4_+$.
Jacobsen, Jesper Lykke
2015-01-01
In previous work with Scullard, we defined a graph polynomial P_B(q,T) that gives access to the critical temperature T_c of the q-state Potts model on a general two-dimensional lattice L. It depends on a basis B, containing n x m unit cells of L, and the relevant root of P_B(q,T) was observed to converge quickly to T_c in the limit n,m to infinity. Moreover, in exactly solvable cases there is no finite-size dependence at all. We reformulate this method as an eigenvalue problem within the peri...
Non-trivial exponents in the zero temperature dynamics of the 1D Ising and Potts models
Derrida, B.; Bray, A. J.; Godrèche, C.
1994-01-01
We consider the Glauber dynamics of the $ q $-state Potts model in one dimension at zero temperature. Starting with a random initial configuration, we measure the density $ r_t $ of spins which have never flipped from the beginning of the simulation until time $ t. $ We find that for large $ t, $ the density $ r_t $ has a power law decay $ \\left(r_t \\sim t^{-\\theta} \\right) $ where the exponent $ \\theta $ varies with $ q. $ Our simulations lead to $ \\theta \\simeq .37 $ for $ q=2, $ $ \\theta \\...
The renormalization and the critical and tricritical behavior of the three-state Potts model with broken symmetry between the state vectors and with a external field is studied in a field theory. As an extension of Landau phase-transition theory, renormalization group transformations, to first order in ε =dc-d, are applyied, generating recursion relations. These differential equations are solved in two cases: (a) dc = 6 the φ3-field critical dimension; (b) dc = 4 the φ4-field (XY model) critical dimension. In both cases, non-universal ratios of temperaturestt/tc, magnetizationsmt/ mc and external fieldsht/ hc tricritical and critical are obtained. Such results are applyied to the structural phase transition of SrTiO3 stressed along p->//[1+δ, 1+δ, 1-2δ] yielding a non-universal ratioδt/ δc. Finally, the susceptibility, the magnetization and the singular part of the free energy are calculated in d = 4 - ε dimension at the critical region, showing the crossover from XY model to Potts model behavior. Universal ratio of susceptibilities calculated above and bellow the critical point is obtained too. (author)
The Potts glass on the Bethe lattice
It is considered the nearest-neighbor p-state random Potts model on a Cayley tree of infinite coordination. The problem is formulated as a discrete mapping whose fixed points correspond to solutions deep inside the tree. The introduction of an ansatz which allows for the breaking of the Potts symmetry leads to an instability of the spin glass fixed point for p > 4. (author)
We obtain long series expansions for the bulk, surface and corner free energies for several two-dimensional statistical models, by combining Enting’s finite lattice method (FLM) with exact transfer matrix enumerations. The models encompass all integrable curves of the Q-state Potts model on the square and triangular lattices, including the antiferromagnetic transition curves and the Ising model (Q = 2) at temperature T, as well as a fully packed O(n) type loop model on the square lattice. The expansions are around the trivial fixed points at infinite Q, n or 1/T. By using a carefully chosen expansion parameter, q ≪ 1, all expansions turn out to be of the form Πk=1∞(1-qk)αk+kβk, where the coefficients αk and βk are periodic functions of k. Thanks to this periodicity property, we can conjecture the form of the expansions to all orders (except in a few cases where the periodicity is too large). These expressions are then valid for all 0 ⩽ q − limit in which the models become critical. In this limit the divergence of the corner free energy defines a universal term which can be compared with the conformal field theory (CFT) predictions of Cardy and Peschel. This allows us to deduce the asymptotic expressions for the correlation length in several cases. Finally we work out the FLM formulae for the case where some of the system’s boundaries are endowed with particular (non-free) boundary conditions. We apply this in particular to the square-lattice Potts model with Jacobsen–Saleur boundary conditions, conjecturing the expansions of the surface and corner free energies to arbitrary order for any integer value of the boundary interaction parameter r. These results are in turn compared with CFT predictions. (paper)
Large-q expansion of the correlation length in the two-dimensional q-state Potts model
Arisue, H
2000-01-01
The large-q expansions of the exponential correlation length and the second moment correlation length for the q-state Potts model in two dimensions are calculated at the first order phase transition point both in the ordered and disordered phases. The expansion coefficients in the ordered and disordered phases coincide in lower orders for both of the two types of the correlation lengths, but they differ a little from each other in higher orders for the second moment correlation length. The second largest eigenvalues of the transfer matrix have the continuum spectrum both in the ordered and disordered phases in the large-q region, which is suggested to be maintained even in the limit of $q\\to 4$ from the analysis of the expansion series.
Arisue, H
2000-01-01
We calculate the large-q expansion of the second moment correlation length at the first order phase transition point of the q-state Potts model in two dimensions both in the ordered and disordered phases to order 21 in $1/\\sqrt{q}$. They coincide with each other to the third term of the series but differ a little in higher orders. Numerically the ratio of the second moment correlation length in the two phases is not far from unity in all region of q>4. The ratio of the second moment correlation length to the standard correlation length in the disordered phase is far from unity, which suggests that the second largest and smaller eigenvalues of the transfer matrix form a continuum spectrum not only in the large-q region but also in all the region of q>4.
Saburov, Mansoor; Khameini Ahmad, Mohd Ali
2015-12-01
Unlike the real number field, a set of p-adic Gibbs measures of p-adic lattice models of statistical mechanics has a complex structure in a sense that it is strongly tied up with a Diophantine problem over p-adic fields. Recently, all translation-invariant p-adic Gibbs measures of the p-adic Potts model on the Cayley tree of order two were described by means of roots of a certain quadratic equation over some domain of the p-adic field. In this paper, we consider the same problem on the Cayley tree of order three. In this case, we show that all translation-invariant p-adic Gibbs measures of the p-adic Potts model can be described in terms of roots of some cubic equation over Zpsetminus Zp^{*}. In own its turn, we also provide a solvability criterion of a general cubic equation over Zpsetminus Zp^{*} for p > 3.
Ding, Chengxiang; Fu, Zhe; Guo, Wenan; Wu, F. Y.
2010-06-01
In the preceding paper, one of us (F. Y. Wu) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangular-type and kagome-type lattices, and obtained closed-form expressions for the critical frontier with applications to various lattice models. For the triangular-type lattices Wu’s result is exact, and for the kagome-type lattices Wu’s expression is under a homogeneity assumption. The purpose of the present paper is twofold: First, an essential step in Wu’s analysis is the derivation of lattice-dependent constants A,B,C for various lattice models, a process which can be tedious. We present here a derivation of these constants for subnet networks using a computer algorithm. Second, by means of a finite-size scaling analysis based on numerical transfer matrix calculations, we deduce critical properties and critical thresholds of various models and assess the accuracy of the homogeneity assumption. Specifically, we analyze the q -state Potts model and the bond percolation on the 3-12 and kagome-type subnet lattices (n×n):(n×n) , n≤4 , for which the exact solution is not known. Our numerical determination of critical properties such as conformal anomaly and magnetic correlation length verifies that the universality principle holds. To calibrate the accuracy of the finite-size procedure, we apply the same numerical analysis to models for which the exact critical frontiers are known. The comparison of numerical and exact results shows that our numerical values are correct within errors of our finite-size analysis, which correspond to 7 or 8 significant digits. This in turn infers that the homogeneity assumption determines critical frontiers with an accuracy of 5 decimal places or higher. Finally, we also obtained the exact percolation thresholds for site percolation on kagome-type subnet lattices (1×1):(n×n) for 1≤n≤6 .
Testing the applicability of mathematical models with carefully designed experiments is a powerful tool in the investigations of the effects of ionizing radiation on cells. The modeling and cellular studies complement each other, for modeling provides guidance for designing critical experiments which must provide definitive results, while the experiments themselves provide new input to the model. Based on previous experimental results the model for the accumulation of damage in Chlamydomonas reinhardi has been extended to include various multiple two-event combinations. Split dose survival experiments have shown that models tested to date predict most but not all the observed behavior. Stationary-phase mammalian cells, required for tests of other aspects of the model, have been shown to be at different points in the cell cycle depending on how they were forced to stop proliferating. These cultures also demonstrate different capacities for repair of sublethal radiation damage
Liberty, Joshua W.
This dissertation uses the hierarchical q-state Potts model at the critical point to develop a new random number generator test. We start with an exposition of renormalization group approach by means of which one can numerically exactly compute the free energy, specific heat and susceptibility of large, but finite lattices. We then show that generalization of these standard techniques allows one to also compute probability distributions related to the energy and the order parameter. The various computed quantities can be compared with Monte Carlo estimates of the same quantities. We demonstrate that the structure of the hierarchical lattices used allows one to perform the Monte Carlo calculations by direct sampling. This avoids the usual critical slowing down that plagues Monte Carlo calculations at the critical point. As is well known, critical behavior is highly susceptible to perturbations. We expect that flaws of the pseudo random number generator, such as correlations, will cause statistically significant discrepancies between the results of the simulations and the numerically exactly computed results. Details of the computer code generated for these tests are included.
The geometrical critical behaviour of the two-dimensional Q-state Potts model is usually studied in terms of the Fortuin–Kasteleyn (FK) clusters, or their surrounding loops. In this paper we study a quite different geometrical object: the spin clusters, defined as connected domains where the spin takes a constant value. Unlike the usual loops, the domain walls separating different spin clusters can cross and branch. Moreover, they come in two versions, 'thin' or 'thick', depending on whether they separate spin clusters of different or identical colours. For these reasons their critical behaviour is different from, and richer than, those of FK clusters. We develop a transfer matrix technique enabling the formulation and numerical study of spin clusters even when Q is not an integer. We further identify geometrically the crossing events which give rise to conformal correlation functions. We study the critical behaviour both in the bulk, and at a boundary with free, fixed, or mixed boundary conditions. This leads to infinite series of fundamental critical exponents, hl1-l2,2l1 in the bulk and h1+2(l1-l2),1+4l1 at the boundary, valid for 0 ≤ Q ≤ 4, that describe the insertion of l1 thin and l2 thick domain walls. We argue that these exponents imply that the domain walls are 'thin' and 'thick' also in the continuum limit. A special case of the bulk exponents is derived analytically from a massless scattering approach
Statics and dynamics of the ten-state mean-field Potts glass model: a Monte Carlo study
We investigate by means of Monte Carlo simulations the fully connected p-state Potts model for different system sizes in order to see how the static and dynamic properties of a finite model compare with the, exactly known, behaviour of the system in the thermodynamic limit. Using p=10 we are able to study the equilibrium dynamics for system sizes as large as N=2560. We find that the static quantities, such as the energy, the entropy, the spin glass susceptibility as well as the distribution of the order parameter P(q) show very strong finite-size effects. From P(q) we calculate the fourth-order cumulant g4(N,T) and the Guerra parameter G(N,T) and show that these quantities cannot be used to locate the static transition temperature for the system sizes investigated. Also the spin-autocorrelation function C(t) shows strong finite-size effects in that it does not show a plateau even for temperatures around the dynamical critical temperature TD. We show that the dependence on N and T of the -relaxation time can be understood by means of a dynamical finite-size scaling ansatz. C(t) does not obey the time-temperature superposition principle for temperatures around TD, but does so for significantly lower T. Finally we study the relaxation dynamics of the individual spins and show that their dependence on time depends strongly on the chosen spin, i.e. that the system is dynamically very heterogeneous, which explains the non-exponentiality of C(t). (author)
Endy, Drew; Brent, Roger
2001-01-01
Representations of cellular processes that can be used to compute their future behaviour would be of general scientific and practical value. But past attempts to construct such representations have been disappointing. This is now changing. Increases in biological understanding combined with advances in computational methods and in computer power make it possible to foresee construction of useful and predictive simulations of cellular processes.
Modelling the phase diagram of Ni-Mn-X(X=In,Sn,Sb) alloys: A q-state Potts model monte Carlo study
On the basis of Monte Carlo simulations using Heisenberg and Potts model Hamiltonians, we investigate the complex temperature dependence of the phase diagram of Ni-Mn-X (X=In,Sn,Sb) Heusler alloys. For Mn excess concentration, we find Mn atoms on the X sites, whose magnetic moments interact antiferromagnetically with the Mn spin moments on the Mn sublattice. Using ab initio data for the magnetic exchange interactions, it is shown that this antiferromagnetic exchange is responsible for metamagnetic behavior and a series of magnetic phase transitions, which compete or act in favor of the martensitic transformation being present in the Heusler alloys. This scenario is finally responsible for the occurrence of magneto-structural phase transitions in this class of ferromagnetic Heusler alloys.
Andrade, Pedro H.A. de; Cabral, Manuela O.M., E-mail: andrade.pha@gmail.com [Universidade Federal de Pernambuco (DEN/UFPE), Recife, PE (Brazil). Departamento de Engenharia Nuclear; Vieira, Jose W.; Correia, Filipe L. de B., E-mail: jose.wilson59@uol.com.br [Instituto Federal de Educacao, Ciencia e Tecnologia de Pernambuco (IFPE), Recife, PE (Brazil); Lima, Fernando R. De A., E-mail: falima@cnen.gov.br [Centro Regional de Ciencias Nucleares do Nordeste (CRCN-NE/CNEN-PE), Recife, PE (brazil)
2015-07-01
Exposure Computational Models are composed basically of an anthropomorphic phantom, a Monte Carlo (MC) code, and an algorithm simulator of the radioactive source. Tomographic phantoms are developed from medical images and must be pre-processed and segmented before being coupled to a MC code (which simulates the interaction of radiation with matter). This work presents a methodology used for treatment of micro-CT images stack of a femur, obtained from a 30 year old female skeleton provided by the Imaging Laboratory for Anthropology of the University of Bristol, UK. These images contain resolution of 60 micrometers and from these a block containing only 160 x 60 x 160 pixels of trabecular tissues and bone marrow was cut and saved as ⁎.sgi file (header + ⁎.raw file). The Grupo de Dosimetria Numerica (Recife-PE, Brazil) developed a software named Digital Image Processing (DIP), in which a method for segmentation based on a physical model for particle interaction known as Potts Model (or q-Ising) was implemented. This model analyzes the statistical dependence between sites in a network. In Potts Model, when the values of spin variables at neighboring sites are identical, it is assigned an 'energy of interaction' between them. Otherwise, it is said that the sites do not interact. Making an analogy between network sites and the pixels of a digital image and, moreover, between the spins variables and the intensity of the gray scale, it was possible to apply this model to obtain texture descriptors and segment the image. (author)
Exposure Computational Models are composed basically of an anthropomorphic phantom, a Monte Carlo (MC) code, and an algorithm simulator of the radioactive source. Tomographic phantoms are developed from medical images and must be pre-processed and segmented before being coupled to a MC code (which simulates the interaction of radiation with matter). This work presents a methodology used for treatment of micro-CT images stack of a femur, obtained from a 30 year old female skeleton provided by the Imaging Laboratory for Anthropology of the University of Bristol, UK. These images contain resolution of 60 micrometers and from these a block containing only 160 x 60 x 160 pixels of trabecular tissues and bone marrow was cut and saved as ⁎.sgi file (header + ⁎.raw file). The Grupo de Dosimetria Numerica (Recife-PE, Brazil) developed a software named Digital Image Processing (DIP), in which a method for segmentation based on a physical model for particle interaction known as Potts Model (or q-Ising) was implemented. This model analyzes the statistical dependence between sites in a network. In Potts Model, when the values of spin variables at neighboring sites are identical, it is assigned an 'energy of interaction' between them. Otherwise, it is said that the sites do not interact. Making an analogy between network sites and the pixels of a digital image and, moreover, between the spins variables and the intensity of the gray scale, it was possible to apply this model to obtain texture descriptors and segment the image. (author)
Predictive Modelling of Cellular Load
Carolan, Emmett; McLoone, Seamus; Farrell, Ronan
2015-01-01
This work examines the temporal dynamics of cellular load in four Irish regions. Large scale underutilisation of network resources is identified both at the regional level and at the level of individual cells. Cellular load is modeled and prediction intervals are generated. These prediction intervals are used to put an upper bound on usage in a particular cell at a particular time. Opportunities for improvements in network utilization by incorporating these upper bounds on usage are identifie...
Xtoys cellular automata on xwindows
Creutz, M
1995-01-01
Xtoys is a collection of xwindow programs for demonstrating simulations of various statistical models. Included are xising, for the two dimensional Ising model, xpotts, for the q-state Potts model, xautomalab, for a fairly general class of totalistic cellular automata, xsand, for the Bak-Tang-Wiesenfield model of self organized criticality, and xfires, a simple forest fire simulation. The programs should compile on any machine supporting xwindows.
Vernier, Eric
2011-01-01
We obtain long series expansions for the bulk, surface and corner free energies for several two-dimensional statistical models, by combining Enting's finite lattice method (FLM) with exact transfer matrix enumerations. The models encompass all integrable curves of the Q-state Potts model on the square and triangular lattices, including the antiferromagnetic transition curves and the Ising model (Q=2) at temperature T, as well as a fully-packed O(n) type loop model on the square lattice. The expansions are around the trivial fixed points at infinite Q, n or 1/T. By using a carefully chosen expansion parameter, q << 1, all expansions turn out to be of the form \\prod_{k=1}^\\infty (1-q^k)^{\\alpha_k + k \\beta_k}, where the coefficients \\alpha_k and \\beta_k are periodic functions of k. Thanks to this periodicity property we can conjecture the form of the expansions to all orders (except in a few cases where the periodicity is too large). These expressions are then valid for all 0 <= q < 1. We analyse in...
Pott's disease: radioisotope scanning findings
The study is aim was to describe findings in bone scan in patients with Pott's disease. Eight patients had a bone scan with 99mTc . The findings included: a spindle image due to increased uptake in vertebrae and intervertebral uptake in three cases, increased uptake in vertebrae in three cases, paravertebral uptake in one case and vertebral compression with diminished uptake in one case. Bone scan is a useful tool in evaluating spinal tuberculosis (Pott's disease) as an indicator of activity within the lesion. (authors)
Cellular automata a parallel model
Mazoyer, J
1999-01-01
Cellular automata can be viewed both as computational models and modelling systems of real processes. This volume emphasises the first aspect. In articles written by leading researchers, sophisticated massive parallel algorithms (firing squad, life, Fischer's primes recognition) are treated. Their computational power and the specific complexity classes they determine are surveyed, while some recent results in relation to chaos from a new dynamic systems point of view are also presented. Audience: This book will be of interest to specialists of theoretical computer science and the parallelism challenge.
The potts chain in a random field: an exact solution
An exact solution is presented for the one-dimensional q-state Potts model in a quenched random field. The ferromagnetic phase is unstable against any small random field perturbation. The correlation function and the Edwards-Anderson order parameter Q are discussed. For finite q only the phase with Q ≠ 0 is present. (Author)
Potts critical frontiers of inhomogeneous and asymmetric bow-tie lattices
Scullard, Christian R.; Jacobsen, Jesper Lykke
2012-01-01
We study the critical frontiers of the Potts model on two-dimensional bow-tie lattices with fully inhomogeneous coupling constants. Generally, for the Potts critical frontier to be found exactly, the underlying lattice must be a 3-uniform hypergraph. A more general class of lattices are the 4-uniform ones, with unit cells contained within four boundary vertices. We demonstrate that in some cases, such lattices can be decomposed into triangular cells, and solved using a modification of standar...
Influence of lattice defects on criticality of Potts ferromagnet
The critical properties of the q-state Potts ferromagnet and the anisotropic Heisenberg model on hypercubic lattices (d = 2,3); emphasis is given to the free surface and the interface effects, the Real Space Renormalization Group approach. The criticality of the quenched bond-mixed q-state Potts ferromagnet on square lattice is discussed. It is shown that, the crossover from the pure fixed point to the random one occurs, while q increases, through a pitchfork bifurcation; the relation-ship with the Harris criterion is analyzed. High precision numerical values for the critical temperatures corresponding to arbitrary concentrations of the coupling constants J sub(1) and J sub(2), and arbitrary ratios J sub(1)/J sub(2) are presented.(author)
Understanding cisplatin resistance using cellular models.
STORDAL, BRITTA KRISTINA
2007-01-01
PUBLISHED Many mechanisms of cisplatin resistance have been proposed from studies of cellular models of resistance including changes in cellular drug accumulation, detoxification of the drug, inhibition of apoptosis and repair of the DNA adducts. A series of resistant models were developed from CCRF-CEM leukaemia cells with increasing doses of cisplatin from 100 ng/ml. This produced increasing resistance up to 7-fold with a treatment dose of 1.6 ?g/ml. Cisplatin resistance i...
Understanding cisplatin resistance using cellular models
Stordal, Britta; Davey, Mary
2007-01-01
Many mechanisms of cisplatin resistance have been proposed from studies of cellular models of resistance including changes in cellular drug accumulation, detoxification of the drug, inhibition of apoptosis and repair of the DNA adducts. A series of resistant models were developed from CCRF-CEM leukaemia cells with increasing doses of cisplatin from 100 ng/ml. This produced increasing resistance up to 7-fold with a treatment dose of 1.6 microg/ml. Cisplatin resistance in these cells correlated...
Animal and cellular models of human disease
Arends, Mark; White, Eric; Whitelaw, Christopher
2016-01-01
In this eighteenth (2016) Annual Review Issue of The Journal of Pathology, we present a collection of 19 invited review articles that cover different aspects of cellular and animal models of disease. These include genetically-engineered models, chemically-induced models, naturally-occurring models, and combinations thereof, with the focus on recent methodological and conceptual developments across a wide range of human diseases.
A Modified Sensitive Driving Cellular Automaton Model
GE Hong-Xia; DAI Shi-Qiang; DONG Li-Yun; LEI Li
2005-01-01
A modified cellular automaton model for traffic flow on highway is proposed with a novel concept about the variable security gap. The concept is first introduced into the original Nagel-Schreckenberg model, which is called the non-sensitive driving cellular automaton model. And then it is incorporated with a sensitive driving NaSch model,in which the randomization brake is arranged before the deterministic deceleration. A parameter related to the variable security gap is determined through simulation. Comparison of the simulation results indicates that the variable security gap has different influence on the two models. The fundamental diagram obtained by simulation with the modified sensitive driving NaSch model shows that the maximumflow are in good agreement with the observed data, indicating that the presented model is more reasonable and realistic.
Potts disease: Diagnosis with magnetic resonance imaging
The eponymously named Potts disease is a relatively rare form of Tuberculosis (TB) which affects the spine. TB of the spine is one of the earliest diseases known to man and in the 20th century was thought to be a disease which had been defeated by the advent of antitubercular drugs. Over the last two decades there have been several reports which indicate a revival of TB in both the developing and developed world. Factors which may be contributing to this are the spread of the HIV virus, increased immigration and the emergence of drug resistant strains of the TB bacteria. Potts disease has an insidious onset and often the radiographic findings are far advanced when a diagnosis is finally reached. MRI is able to detect changes to the vertebrae in Potts disease earlier than radiographs. This case report outlines the clinical presentation of a young male with Potts disease who was HIV negative, and the important role that MRI plays in diagnosis and therefore in appropriate and timely intervention. The typical magnetic resonance (MR) imaging features and the radiographic hallmarks of the disease will also be discussed.
Potts disease: Diagnosis with magnetic resonance imaging
Pursey, Jacqueline [MRI Department, Gartnavel General Hospitial, 1053 Great Western road, Glasgow G12 0YN (United Kingdom)], E-mail: Jacqueline.pursey@ggc.scot.nhs.uk; Stewart, Sharon [School of Health and Social Care, Caledonian University, Glasgow (United Kingdom)
2010-02-15
The eponymously named Potts disease is a relatively rare form of Tuberculosis (TB) which affects the spine. TB of the spine is one of the earliest diseases known to man and in the 20th century was thought to be a disease which had been defeated by the advent of antitubercular drugs. Over the last two decades there have been several reports which indicate a revival of TB in both the developing and developed world. Factors which may be contributing to this are the spread of the HIV virus, increased immigration and the emergence of drug resistant strains of the TB bacteria. Potts disease has an insidious onset and often the radiographic findings are far advanced when a diagnosis is finally reached. MRI is able to detect changes to the vertebrae in Potts disease earlier than radiographs. This case report outlines the clinical presentation of a young male with Potts disease who was HIV negative, and the important role that MRI plays in diagnosis and therefore in appropriate and timely intervention. The typical magnetic resonance (MR) imaging features and the radiographic hallmarks of the disease will also be discussed.
Segmenting images into four classes of magnetism: A linear-time Potts method
Bentrem, Frank W
2009-01-01
A computational method is presented which efficiently segments digital grayscale images by directly applying the Potts (or Q-state Ising) model. Since the Potts model was first proposed in 1952, physicists have studied lattice models to gain deep insights into magnetism and other disordered systems. For some time, researchers have realized that digital images may be modeled in much the same way as these physical systems (i.e., as a square lattice of numerical values). A major drawback in using Potts model methods for image segmentation is that, with conventional methods, it processes in exponential time. Advances have been made via certain approximations to reduce the segmentation process to power-law time. However, in many applications (such as for sonar imagery), real-time processing requires much greater efficiency. This article contains a description of an energy minimization technique that applies four Potts (Q-Ising) models directly to the image and processes in linear time. The result is analogous to p...
A Mathematical Model for Cisplatin Cellular Pharmacodynamics
Ardith W. El-Kareh
2003-03-01
Full Text Available A simple theoretical model for the cellular pharmacodynamics of cisplatin is presented. The model, which takes into account the kinetics of cisplatin uptake by cells and the intracellular binding of the drug, can be used to predict the dependence of survival (relative to controls on the time course of extracellular exposure. Cellular pharmacokinetic parameters are derived from uptake data for human ovarian and head and neck cancer cell lines. Survival relative to controls is assumed to depend on the peak concentration of DNA-bound intracellular platinum. Model predictions agree well with published data on cisplatin cytotoxicity for three different cancer cell lines, over a wide range of exposure times. In comparison with previously published mathematical models for anticancer drug pharmacodynamics, the present model provides a better fit to experimental data sets including long exposure times (∼100 hours. The model provides a possible explanation for the fact that cell kill correlates well with area under the extracellular concentration-time curve in some data sets, but not in others. The model may be useful for optimizing delivery schedules and for the dosing of cisplatin for cancer therapy.
Cellular automata modelling of hantarvirus infection
Hantaviruses are a group of viruses which have been identified as being responsible for the outbreak of diseases such as the hantavirus pulmonary syndrome. In an effort to understand the characteristics and dynamics of hantavirus infection, mathematical models based on differential equations have been developed and widely studied. However, such models neglect the local characteristics of the spreading process and do not include variable susceptibility of individuals. In this paper, we develop an alternative approach based on cellular automata to analyze and study the spatiotemporal patterns of hantavirus infection.
Cellular automata modelling of hantarvirus infection
Abdul Karim, Mohamad Faisal [School of Distance Education, Universiti Sains Malaysia, Minden 11800, Penang (Malaysia)], E-mail: faisal@usm.my; Md Ismail, Ahmad Izani [School of Mathematical Sciences, Universiti Sains Malaysia, Minden 11800, Penang (Malaysia)], E-mail: izani@cs.usm.my; Ching, Hoe Bee [School of Mathematical Sciences, Universiti Sains Malaysia, Minden 11800, Penang (Malaysia)], E-mail: Bee_Ching_Janice_Hoe@dell.com
2009-09-15
Hantaviruses are a group of viruses which have been identified as being responsible for the outbreak of diseases such as the hantavirus pulmonary syndrome. In an effort to understand the characteristics and dynamics of hantavirus infection, mathematical models based on differential equations have been developed and widely studied. However, such models neglect the local characteristics of the spreading process and do not include variable susceptibility of individuals. In this paper, we develop an alternative approach based on cellular automata to analyze and study the spatiotemporal patterns of hantavirus infection.
Spatial game in cellular automaton evacuation model
von Schantz, Anton; Ehtamo, Harri
2015-11-01
For numerical simulations of crowd dynamics in an evacuation we need a computationally light environment, such as the cellular automaton model (CA). By choosing the right model parameters, different types of crowd behavior and collective effects can be produced. But the CA does not answer why, when, and how these different behaviors and collective effects occur. In this article, we present a model, where we couple a spatial evacuation game to the CA. In the game, an agent chooses its strategy by observing its neighbors' strategies. The game matrix changes with the distance to the exit as the evacuation conditions develop. In the resulting model, an agent's strategy choice alters the parameters that govern its behavior in the CA. Thus, with our model, we are able to simulate how evacuation conditions affect the behavior of the crowd. Also, we show that some of the collective effects observed in evacuations are a result of the simple game the agents play.
John Potts, The New Time and Space
Jean-Christophe MURAT
2016-01-01
John Potts, Professor of Media at Macquarie University, Australia, is no newcomer to the domain of media studies. Some of his outstanding publications, like Radio in Australia (New South Wales University Press, 1989), Culture and Technology (with Andrew Murphie, Palgrave Macmillan, 2002) and Technologies of Magic (co-edited with Edward Scheer, Sydney: Power Publications, 2011), have established his credentials and revealed the versatility of his knowledge in the field. The New Time and Space,...
A cellular automata model for ant trails
Sibel Gokce; Ozhan Kayacan
2013-05-01
In this study, the unidirectional ant traffic flow with U-turn in an ant trail was investigated using one-dimensional cellular automata model. It is known that ants communicate with each other by dropping a chemical, called pheromone, on the substrate. Apart from the studies in the literature, it was considered in the model that (i) ant colony consists of two kinds of ants, goodand poor-smelling ants, (ii) ants might make U-turn for some special reasons. For some values of densities of good- and poor-smelling ants, the flux and mean velocity of the colony were studied as a function of density and evaporation rate of pheromone.
Modeling the topological organization of cellular processes.
Giavitto, Jean-Louis; Michel, Olivier
2003-07-01
The cell as a dynamical system presents the characteristics of having a dynamical structure. That is, the exact phase space of the system cannot be fixed before the evolution and integrative cell models must state the evolution of the structure jointly with the evolution of the cell state. This kind of dynamical systems is very challenging to model and simulate. New programming concepts must be developed to ease their modeling and simulation. In this context, the goal of the MGS project is to develop an experimental programming language dedicated to the simulation of this kind of systems. MGS proposes a unified view on several computational mechanisms (CHAM, Lindenmayer systems, Paun systems, cellular automata) enabling the specification of spatially localized computations on heterogeneous entities. The evolution of a dynamical structure is handled through the concept of transformation which relies on the topological organization of the system components. An example based on the modeling of spatially distributed biochemical networks is used to illustrate how these notions can be used to model the spatial and temporal organization of intracellular processes. PMID:12915272
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
Cellular automata modeling of cooperative eutectic growth
E. Olejnik
2010-01-01
Full Text Available The model and results of the 2D simulation of the cooperative growth of two phases in the lamellar eutectic are presented. The pro-posed model takes into account heat transfer, components diffusion and nonstationary concentration distribution in the liquid and solid phases, non-equlibrium nature of the phase transformation and kinetics of the growth, influence of the surface energy and interface curva-ture on the conditions of the thermodynamic equilibrium. For the determination of the phase interface shape the Cellular Automata tech-nique (CA was used. For the calculation of temperature and concentration distribution the numerical solution of the Fourier equation was used. The partial differential equations were solved by Finite Differences Method (FDM. The spatial position and cell sizes of CA lattice and FDM mesh are equal.Proposed model can predict the steady state growth with a constant interlamellar spacing in the regular plate eutectic, as well as some transient processes that bring to the changes of that parameters. Obtained simulation data show the solid-liquid interface changes result in the termination of lamella and enlargement of interlamellar spacing. Another simulation results illustrate a pocket formation in the center of one phase that forestalls nucleation (or intergrowth of the new lamellae of another phase. The data of the solidification study of the transparent material (CBr4 – 8,4% C2Cl6 obtained in the thin layer demonstrate the qualita-tive agreement of the simulation.
Modeling cellular effects of coal pollutants
The goal of this project is to develop and test models for the dose and dose-rate dependence of biological effects of coal pollutants on mammalian cells in tissue culture. Particular attention is given to the interaction of pollutants with the genetic material (deoxyribonucleic acid, or NDA) in the cell. Unlike radiation, which can interact directly with chromatin, chemical pollutants undergo numerous changes before the ultimate carcinogen becomes covalently bound to the DNA. Synthetic vesicles formed from a phospholipid bilayer are being used to investigate chemical transformations that may occur during the transport of pollutants across cellular membranes. The initial damage to DNA is rapidly modified by enzymatic repair systems in most living organisms. A model has been developed for predicting the effects of excision repair on the survival of human cells exposed to chemical carcinogens. In addition to the excision system, normal human cells also have tolerance mechanisms that permit continued growth and division of cells without removal of the damage. We are investigating the biological effect of damage passed to daughter cells by these tolerance mechanisms
Analytical Modeling of Uplink Cellular Networks
Novlan, Thomas D; Andrews, Jeffrey G
2012-01-01
Cellular uplink analysis has typically been undertaken by either a simple approach that lumps all interference into a single deterministic or random parameter in a Wyner-type model, or via complex system level simulations that often do not provide insight into why various trends are observed. This paper proposes a novel middle way that is both accurate and also results in easy-to-evaluate integral expressions based on the Laplace transform of the interference. We assume mobiles and base stations are randomly placed in the network with each mobile pairing up to its closest base station. The model requires two important changes compared to related recent work on the downlink. First, dependence is introduced between the user and base station point processes to make sure each base station serves a single mobile in the given resource block. Second, per-mobile power control is included, which further couples the locations of the mobiles and their receiving base stations. Nevertheless, we succeed in deriving the cov...
Short-Time Dynamics of Random-Bond Potts Ferromagnet with Continuous Self-Dual Quenched Disorders
PAN ZhengQuan; YING HePing; CHEN MeL; GU DeWei
2002-01-01
We present our Monte Carlo results of the random-bond Potts ferromagnet with the Olson-Young self-dual distribution of quenched disorders in two dimensions. By exploring the short-time scaling dynamics, we find the universal power-law critical behavior of the magnetization and Binder cumulant at the critical point, and thus obtain estimates of the dynamic exponent z and magnetic exponent η, as well as the exponent θ. Our special attention is paid to the dynamic process for the q = 8 Potts model.
Local Autoencoding for Parameter Estimation in a Hidden Potts-Markov Random Field.
Song, Sanming; Si, Bailu; Herrmann, J Michael; Feng, Xisheng
2016-05-01
A local-autoencoding (LAE) method is proposed for the parameter estimation in a Hidden Potts-Markov random field model. Due to sampling cost, Markov chain Monte Carlo methods are rarely used in real-time applications. Like other heuristic methods, LAE is based on a conditional independence assumption. It adapts, however, the parameters in a block-by-block style with a simple Hebbian learning rule. Experiments with given label fields show that the LAE is able to converge in far less time than required for a scan. It is also possible to derive an estimate for LAE based on a Cramer–Rao bound that is similar to the classical maximum pseudolikelihood method. As a general algorithm, LAE can be used to estimate the parameters in anisotropic label fields. Furthermore, LAE is not limited to the classical Potts model and can be applied to other types of Potts models by simple label field transformations and straightforward learning rule extensions. Experimental results on image segmentations demonstrate the efficiency and generality of the LAE algorithm. PMID:27019491
Typhoid fever as cellular microbiological model
Andrade Dahir Ramos de; Andrade Júnior Dahir Ramos de
2003-01-01
The knowledge about typhoid fever pathogenesis is growing in the last years, mainly about the cellular and molecular phenomena that are responsible by clinical manifestations of this disease. In this article are discussed several recent discoveries, as follows: a) Bacterial type III protein secretion system; b) The five virulence genes of Salmonella spp. that encoding Sips (Salmonella invasion protein) A, B, C, D and E, which are capable of induce apoptosis in macrophages; c) The function of ...
Typhoid fever as cellular microbiological model
Andrade Dahir Ramos de
2003-01-01
Full Text Available The knowledge about typhoid fever pathogenesis is growing in the last years, mainly about the cellular and molecular phenomena that are responsible by clinical manifestations of this disease. In this article are discussed several recent discoveries, as follows: a Bacterial type III protein secretion system; b The five virulence genes of Salmonella spp. that encoding Sips (Salmonella invasion protein A, B, C, D and E, which are capable of induce apoptosis in macrophages; c The function of Toll R2 and Toll R4 receptors present in the macrophage surface (discovered in the Drosophila. The Toll family receptors are critical in the signalizing mediated by LPS in macrophages in association with LBP and CD14; d The lines of immune defense between intestinal lumen and internal organs; e The fundamental role of the endothelial cells in the inflammatory deviation from bloodstream into infected tissues by bacteria. In addition to above subjects, the authors comment the correlation between the clinical features of typhoid fever and the cellular and molecular phenomena of this disease, as well as the therapeutic consequences of this knowledge.
Typhoid fever as cellular microbiological model.
de Andrade, Dahir Ramos; de Andrade Júnior, Dahir Ramos
2003-01-01
The knowledge about typhoid fever pathogenesis is growing in the last years, mainly about the cellular and molecular phenomena that are responsible by clinical manifestations of this disease. In this article are discussed several recent discoveries, as follows: a) Bacterial type III protein secretion system; b) The five virulence genes of Salmonella spp. that encoding Sips (Salmonella invasion protein) A, B, C, D and E, which are capable of induce apoptosis in macrophages; c) The function of Toll R2 and Toll R4 receptors present in the macrophage surface (discovered in the Drosophila). The Toll family receptors are critical in the signalizing mediated by LPS in macrophages in association with LBP and CD14; d) The lines of immune defense between intestinal lumen and internal organs; e) The fundamental role of the endothelial cells in the inflammatory deviation from bloodstream into infected tissues by bacteria. In addition to above subjects, the authors comment the correlation between the clinical features of typhoid fever and the cellular and molecular phenomena of this disease, as well as the therapeutic consequences of this knowledge. PMID:14502344
Modeling In Vitro Cellular Responses to Silver Nanoparticles
Dwaipayan Mukherjee
2014-01-01
Full Text Available Engineered nanoparticles (NPs have been widely demonstrated to induce toxic effects to various cell types. In vitro cell exposure systems have high potential for reliable, high throughput screening of nanoparticle toxicity, allowing focusing on particular pathways while excluding unwanted effects due to other cells or tissue dosimetry. The work presented here involves a detailed biologically based computational model of cellular interactions with NPs; it utilizes measurements performed in human cell culture systems in vitro, to develop a mechanistic mathematical model that can support analysis and prediction of in vivo effects of NPs. The model considers basic cellular mechanisms including proliferation, apoptosis, and production of cytokines in response to NPs. This new model is implemented for macrophages and parameterized using in vitro measurements of changes in cellular viability and mRNA levels of cytokines: TNF, IL-1b, IL-6, IL-8, and IL-10. The model includes in vitro cellular dosimetry due to nanoparticle transport and transformation. Furthermore, the model developed here optimizes the essential cellular parameters based on in vitro measurements, and provides a “stepping stone” for the development of more advanced in vivo models that will incorporate additional cellular and NP interactions.
TRAFFIC FLOW MODEL BASED ON CELLULAR AUTOMATION WITH ADAPTIVE DECELERATION
Shinkarev, A. A.
2016-01-01
This paper describes continuation of the authors’ work in the field of traffic flow mathematical models based on the cellular automata theory. The refactored representation of the multifactorial traffic flow model based on the cellular automata theory is used for a representation of an adaptive deceleration step implementation. The adaptive deceleration step in the case of a leader deceleration allows slowing down smoothly but not instantly. Concepts of the number of time steps without confli...
Oh, Eung Seok; Heo, Chaejeong; Kim, Ji Seon; Lee, Young Hee; Kim, Jong Min
2013-05-01
Parkinson's disease (PD) is characterized by progressive dopaminergic cell loss in the substantianigra (SN) and elevated iron levels demonstrated by autopsy and with 7-Tesla magnetic resonance imaging. Direct visualization of iron with live imaging techniques has not yet been successful. The aim of this study is to visualize and quantify the distribution of cellular iron using an intrinsic iron hyperspectral fluorescence signal. The 1-methyl-4-phenylpyridinium (MPP+)-induced cellular model of PD was established in SHSY5Y cells. The cells were exposed to iron by treatment with ferric ammonium citrate (FAC, 100 μM) for up to 6 hours. The hyperspectral fluorescence imaging signal of iron was examined usinga high- resolution dark-field optical microscope system with signal absorption for the visible/ near infrared (VNIR) spectral range. The 6-hour group showed heavy cellular iron deposition compared with the small amount of iron accumulation in the 1-hour group. The cellular iron was dispersed in a small, particulate form, whereas extracellular iron was detected in an aggregated form. In addition, iron particles were found to be concentrated on the cell membrane/edge of shrunken cells. The cellular iron accumulation readily occurred in MPP+-induced cells, which is consistent with previous studies demonstrating elevated iron levels in the SN in PD. This direct iron imaging methodology could be applied to analyze the physiological role of iron in PD, and its application might be expanded to various neurological disorders involving other metals, such as copper, manganese or zinc.
Cellular automaton for realistic modelling of landslides
E. Segre
1995-01-01
Full Text Available A numerical model is developed for the simulation of debris flow in landslides over a complex three dimensional topography. The model is then validated by comparing a simulation with reported field data. Our model is in fact a realistic elaboration of simpler "sandpile automata", which have in recent years been studied as supposedly paradigmatic of "self-organized criticality". Statistics and scaling properties of the simulation are examined, and show that the model has an intermittent behaviour.
Body composition analysis: Cellular level modeling of body component ratios
Z. Wang; Heymsfield, S. B.; PI-SUNYER, F.X.; Gallagher, D.; PIERSON, R.N.
2008-01-01
During the past two decades, a major outgrowth of efforts by our research group at St. Luke’s-Roosevelt Hospital is the development of body composition models that include cellular level models, models based on body component ratios, total body potassium models, multi-component models, and resting energy expenditure-body composition models. This review summarizes these models with emphasis on component ratios that we believe are fundamental to understanding human body composition during growt...
Modeling cellular deformations using the level set formalism
Yang Liu
2008-07-01
Full Text Available Abstract Background Many cellular processes involve substantial shape changes. Traditional simulations of these cell shape changes require that grids and boundaries be moved as the cell's shape evolves. Here we demonstrate that accurate cell shape changes can be recreated using level set methods (LSM, in which the cellular shape is defined implicitly, thereby eschewing the need for updating boundaries. Results We obtain a viscoelastic model of Dictyostelium cells using micropipette aspiration and show how this viscoelastic model can be incorporated into LSM simulations to recreate the observed protrusion of cells into the micropipette faithfully. We also demonstrate the use of our techniques by simulating the cell shape changes elicited by the chemotactic response to an external chemoattractant gradient. Conclusion Our results provide a simple but effective means of incorporating cellular deformations into mathematical simulations of cell signaling. Such methods will be useful for simulating important cellular events such as chemotaxis and cytokinesis.
Computational model of cellular metabolic dynamics
Li, Yanjun; Solomon, Thomas; Haus, Jacob M;
2010-01-01
Identifying the mechanisms by which insulin regulates glucose metabolism in skeletal muscle is critical to understanding the etiology of insulin resistance and type 2 diabetes. Our knowledge of these mechanisms is limited by the difficulty of obtaining in vivo intracellular data. To quantitatively...... cytosol and mitochondria. The model simulated skeletal muscle metabolic responses to insulin corresponding to human hyperinsulinemic-euglycemic clamp studies. Insulin-mediated rate of glucose disposal was the primary model input. For model validation, simulations were compared with experimental data...... type 2 diabetes....
Modeling cellular deformations using the level set formalism
Yang Liu; Effler Janet C; Kutscher Brett L; Sullivan Sarah E; Robinson Douglas N; Iglesias Pablo A
2008-01-01
Abstract Background Many cellular processes involve substantial shape changes. Traditional simulations of these cell shape changes require that grids and boundaries be moved as the cell's shape evolves. Here we demonstrate that accurate cell shape changes can be recreated using level set methods (LSM), in which the cellular shape is defined implicitly, thereby eschewing the need for updating boundaries. Results We obtain a viscoelastic model of Dictyostelium cells using micropipette aspiratio...
Cellular automata modeling of cooperative eutectic growth
E. Olejnik; E. Fraś; D. Gurgul; A. Burbelko
2010-01-01
The model and results of the 2D simulation of the cooperative growth of two phases in the lamellar eutectic are presented. The pro-posed model takes into account heat transfer, components diffusion and nonstationary concentration distribution in the liquid and solid phases, non-equlibrium nature of the phase transformation and kinetics of the growth, influence of the surface energy and interface curva-ture on the conditions of the thermodynamic equilibrium. For the determination of the phase ...
Palachanis, Dimitrios; Szabó, András; Merks, Roeland M. H.
2015-12-01
Computational modeling is helpful for elucidating the cellular mechanisms driving biological morphogenesis. Previous simulation studies of blood vessel growth based on the cellular Potts model proposed that elongated, adhesive or mutually attractive endothelial cells suffice for the formation of blood vessel sprouts and vascular networks. Because each mathematical representation of a model introduces potential artifacts, it is important that model results are reproduced using alternative modeling paradigms. Here, we present a lattice-free, particle-based simulation of the cell elongation model of vasculogenesis. The new, particle-based simulations confirm the results obtained from the previous cellular Potts simulations. Furthermore, our current findings suggest that the emergence of order is possible with the application of a high enough attractive force or, alternatively, a longer attraction radius. The methodology will be applicable to a range of problems in morphogenesis and noisy particle aggregation in which cell shape is a key determining factor.
The Pott's puffy tumor: a dangerous sign for intracranial complications.
Ketenci, Ibrahim; Unlü, Yaşar; Tucer, Bülent; Vural, Alperen
2011-12-01
The Pott's puffy tumor is a subperiosteal abscess of the frontal bone associated with osteomyelitis. The purpose of this article is to alert the physician to the severe complications of this entity. The records of six patients were reviewed retrospectively. There were four adults and two adolescents. Nasal endoscopy showed edematous, polypoid mucosa in middle meatus in three and nasal polyps in the rest. At initial admission, two had orbital subperiosteal abscess, but normal cranial CT findings. During hospitalization, three experienced frontal lobe abscess and one frontal cerebritis. Endoscopic sinus surgery was performed in all with external drainage of Pott's puffy tumor in addition to antibiotherapy. Three patients underwent craniotomy/craniectomy for removal of frontal lobe abscesses. One patient with frontal lobe abscess died. Pott's puffy tumor may result in potentially dangerous intracranial complications. Early diagnosis and treatment are essential to reduce morbidity and mortality. PMID:21660452
Development and validation of computational models of cellular interaction
Smallwood, R H; Holcombe, W.M.L.; Walker, D C
2004-01-01
In this paper we take the view that computational models of biological systems should satisfy two conditions – they should be able to predict function at a systems biology level, and robust techniques of validation against biological models must be available. A modelling paradigm for developing a predictive computational model of cellular interaction is described, and methods of providing robust validation against biological models are explored, followed by a consideration of soft...
Cellular Automaton Model for Immunology of Tumor Growth
Voitikova, M
1998-01-01
The stochastic discrete space-time model of an immune response on tumor spreading in a two-dimensional square lattice has been developed. The immunity-tumor interactions are described at the cellular level and then transferred into the setting of cellular automata (CA). The multistate CA model for system, in which all statesoflattice sites, composing of both immune and tumor cells populations, are the functions of the states of the 12 nearest neighbors. The CA model incorporates the essential featuresof the immunity-tumor system. Three regimes of neoplastic evolution including metastatic tumor growth and screen effect by inactive immune cells surrounding a tumor have been predicted.
A cellular automata evacuation model considering friction and repulsion
SONG Weiguo; YU Yanfei; FAN Weicheng; Zhang Heping
2005-01-01
There exist interactions among pedestrians and between pedestrian and environment in evacuation. These interactions include attraction, repulsion and friction that play key roles in human evacuation behaviors, speed and efficiency. Most former evacuation models focus on the attraction force, while repulsion and friction are not well modeled. As a kind of multi-particle self-driven model, the social force model introduced in recent years can represent those three forces but with low simulation efficiency because it is a continuous model with complex rules. Discrete models such as the cellular automata model and the lattice gas model have simple rules and high simulation efficiency, but are not quite suitable for interactions' simulation. In this paper, a new cellular automata model based on traditional models is introduced in which repulsion and friction are modeled quantitatively. It is indicated that the model can simulate some basic behaviors, e.g.arching and the "faster-is-slower" phenomenon, in evacuation as multi-particle self-driven models, but with high efficiency as the normal cellular automata model and the lattice gas model.
Modeling diffusion of innovations with probabilistic cellular automata
Boccara, Nino; Fuks, Henryk
1997-01-01
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a second-order phase transition. We show that the number of individuals who eventually keep adopting the innovation strongly depends on connectivity between individuals.
Modeling integrated cellular machinery using hybrid Petri-Boolean networks.
Natalie Berestovsky
Full Text Available The behavior and phenotypic changes of cells are governed by a cellular circuitry that represents a set of biochemical reactions. Based on biological functions, this circuitry is divided into three types of networks, each encoding for a major biological process: signal transduction, transcription regulation, and metabolism. This division has generally enabled taming computational complexity dealing with the entire system, allowed for using modeling techniques that are specific to each of the components, and achieved separation of the different time scales at which reactions in each of the three networks occur. Nonetheless, with this division comes loss of information and power needed to elucidate certain cellular phenomena. Within the cell, these three types of networks work in tandem, and each produces signals and/or substances that are used by the others to process information and operate normally. Therefore, computational techniques for modeling integrated cellular machinery are needed. In this work, we propose an integrated hybrid model (IHM that combines Petri nets and Boolean networks to model integrated cellular networks. Coupled with a stochastic simulation mechanism, the model simulates the dynamics of the integrated network, and can be perturbed to generate testable hypotheses. Our model is qualitative and is mostly built upon knowledge from the literature and requires fine-tuning of very few parameters. We validated our model on two systems: the transcriptional regulation of glucose metabolism in human cells, and cellular osmoregulation in S. cerevisiae. The model produced results that are in very good agreement with experimental data, and produces valid hypotheses. The abstract nature of our model and the ease of its construction makes it a very good candidate for modeling integrated networks from qualitative data. The results it produces can guide the practitioner to zoom into components and interconnections and investigate them
WWW Business Applications Based on the Cellular Model
Toshio Kodama; Tosiyasu L. Kunii; Yoichi Seki
2008-01-01
A cellular model based on the Incrementally Modular Abstraction Hierarchy (IMAH) is a novel model that can represent the architecture of and changes in cyberworlds, preserving invariants from a general level to a specific one. We have developed a data processing system called the Cellular Data System (CDS). In the development of business applications, you can prevent combinatorial explosion in the process of business design and testing by using CDS. In this paper, we have first designed and implemented wide-use algebra on the presentation level. Next, we have developed and verified the effectiveness of two general business applications using CDS: 1) a customer information management system, and 2) an estimate system.
Lattice gas cellular automata and lattice Boltzmann models an introduction
Wolf-Gladrow, Dieter A
2000-01-01
Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.
Modeling evolution and immune system by cellular automata
Bezzi, M. [Scuola Internazionale Superiore di Studi Avanzati, Trieste (Italy); Istituto Nazionale di Fisica della Materia, Florence (Italy)
2001-07-01
In this review the behavior of two different biological systems is investigated using cellular automata. Starting from this spatially extended approach it is also tried, in some cases, to reduce the complexity of the system introducing mean-field approximation, and solving (or trying to solve) these simplified systems. It is discussed the biological meaning of the results, the comparison with experimental data (if available) and the different features between spatially extended and mean-field versions. The biological systems considered in this review are the following: Darwinian evolution in simple ecosystems and immune system response. In the first section the main features of molecular evolution are introduced, giving a short survey of genetics for physicists and discussing some models for prebiotic systems and simple ecosystems. It is also introduced a cellular automaton model for studying a set of evolving individuals in a general fitness landscape, considering also the effects of co-evolution. In particular the process of species formation (speciation) is described in sect. 5. The second part deals with immune system modeling. The biological features of immune response are discussed, as well as it is introduced the concept of shape space and of idiotypic network. More detailed reviews which deal with immune system models (mainly focused on idiotypic network models) can be found. Other themes here discussed: the applications of CA to immune system modeling, two complex cellular automata for humoral and cellular immune response. Finally, it is discussed the biological data and the general conclusions are drawn in the last section.
Modeling evolution and immune system by cellular automata
In this review the behavior of two different biological systems is investigated using cellular automata. Starting from this spatially extended approach it is also tried, in some cases, to reduce the complexity of the system introducing mean-field approximation, and solving (or trying to solve) these simplified systems. It is discussed the biological meaning of the results, the comparison with experimental data (if available) and the different features between spatially extended and mean-field versions. The biological systems considered in this review are the following: Darwinian evolution in simple ecosystems and immune system response. In the first section the main features of molecular evolution are introduced, giving a short survey of genetics for physicists and discussing some models for prebiotic systems and simple ecosystems. It is also introduced a cellular automaton model for studying a set of evolving individuals in a general fitness landscape, considering also the effects of co-evolution. In particular the process of species formation (speciation) is described in sect. 5. The second part deals with immune system modeling. The biological features of immune response are discussed, as well as it is introduced the concept of shape space and of idiotypic network. More detailed reviews which deal with immune system models (mainly focused on idiotypic network models) can be found. Other themes here discussed: the applications of CA to immune system modeling, two complex cellular automata for humoral and cellular immune response. Finally, it is discussed the biological data and the general conclusions are drawn in the last section
A sub-cellular viscoelastic model for cell population mechanics.
Yousef Jamali
Full Text Available Understanding the biomechanical properties and the effect of biomechanical force on epithelial cells is key to understanding how epithelial cells form uniquely shaped structures in two or three-dimensional space. Nevertheless, with the limitations and challenges posed by biological experiments at this scale, it becomes advantageous to use mathematical and 'in silico' (computational models as an alternate solution. This paper introduces a single-cell-based model representing the cross section of a typical tissue. Each cell in this model is an individual unit containing several sub-cellular elements, such as the elastic plasma membrane, enclosed viscoelastic elements that play the role of cytoskeleton, and the viscoelastic elements of the cell nucleus. The cell membrane is divided into segments where each segment (or point incorporates the cell's interaction and communication with other cells and its environment. The model is capable of simulating how cells cooperate and contribute to the overall structure and function of a particular tissue; it mimics many aspects of cellular behavior such as cell growth, division, apoptosis and polarization. The model allows for investigation of the biomechanical properties of cells, cell-cell interactions, effect of environment on cellular clusters, and how individual cells work together and contribute to the structure and function of a particular tissue. To evaluate the current approach in modeling different topologies of growing tissues in distinct biochemical conditions of the surrounding media, we model several key cellular phenomena, namely monolayer cell culture, effects of adhesion intensity, growth of epithelial cell through interaction with extra-cellular matrix (ECM, effects of a gap in the ECM, tensegrity and tissue morphogenesis and formation of hollow epithelial acini. The proposed computational model enables one to isolate the effects of biomechanical properties of individual cells and the
Station Model for Rail Transit System Using Cellular Automata
XUN Jing; NING Bin; LI Ke-Ping
2009-01-01
In this paper, we propose a new cellular automata model to simulate the railway traffic at station.Based on NaSch model, the proposed station model is composed of the main track and the siding track.Two different schemes for trains passing through station are considered.One is the scheme of "pass by the main track, start and stop by the siding track".The other is the scheme of "two tracks play the same role".We simulate the train movement using the proposed model and analyze the traffic flow at station.The simulation results demonstrate that the proposed cellular automata model can be successfully used for the simulations of railway traffic.Some characteristic behaviors of railway traffic flow can be reproduced.Moreover, the simulation values of the minimum headway are close to the theoretical values.This result demonstrates the dependability and availability of the proposed model.
Cellular worlds: a framework for modeling micro - macro dynamics
H Couclelis
1985-01-01
Cellular spaces have recently received a lot of attention in computer science and elsewhere as models capable of bridging the gap between disaggregate and aggregate description. Despite their obvious spatial interpretation, standard cell-space models are too constrained by their background conventions to be useful in realistic geographic applications. In this paper, a generalization of the cell-space principle is presented, based on discrete model theory, and then applied to a hypothetical bu...
A Modified Cellular Automaton Model for Traffic Flow
葛红霞; 董力耘; 雷丽; 戴世强
2004-01-01
A modified cellular automaton model for traffic flow was proposed. A novel concept about the changeable security gap was introduced and a parameter related to the variable security gap was determined. The fundamental diagram obtained by simulation shows that the maximum flow more approaches to the observed data than that of the NaSch model, indicating that the presented model is more reasonable and realistic.
The brittleness model of complex system based on cellular automata
LIN De-ming; JIN Hong-zhang; LI Qi; WU Hong-mei
2004-01-01
Now the research on the complex system is a hot spot. Brittleness is one of the basic characteristics of a complex system. In a complex system, after one of subsystems is struck to be collapsed, the whole system will collapse. Meanwhile, cellular automata is a discrete dynamic system. When the rule is given, the cellular automata could be defined. Then it can imitate the complex action. Cellular automata is used to simulate the brittleness action in this study. Entropy was used to analyze the action and get the rule. Then,three normal brittleness models were given. The result shows that the brittleness of complex system is existent and in addition some important behavior mode of complex system brittleness has been achieved.
Modeling evolutionary dynamics of epigenetic mutations in hierarchically organized tumors.
Andrea Sottoriva; Louis Vermeulen; Simon Tavaré
2011-01-01
The cancer stem cell (CSC) concept is a highly debated topic in cancer research. While experimental evidence in favor of the cancer stem cell theory is apparently abundant, the results are often criticized as being difficult to interpret. An important reason for this is that most experimental data that support this model rely on transplantation studies. In this study we use a novel cellular Potts model to elucidate the dynamics of established malignancies that are driven by a small subset of ...
Modeling Evolutionary Dynamics of Epigenetic Mutations in Hierarchically Organized Tumors
Sottoriva, A.; Vermeulen, L; Tavare, S
2011-01-01
The cancer stem cell (CSC) concept is a highly debated topic in cancer research. While experimental evidence in favor of the cancer stem cell theory is apparently abundant, the results are often criticized as being difficult to interpret. An important reason for this is that most experimental data that support this model rely on transplantation studies. In this study we use a novel cellular Potts model to elucidate the dynamics of established malignancies that are driven by a small subset of ...
Fire Spread Model for Old Towns Based on Cellular Automaton
GAO Nan; WENG Wenguo; MA Wei; NI Shunjiang; HUANG Quanyi; YUAN Hongyong
2008-01-01
Old towns like Lijiang have enormous historic,artistic,and architectural value.The buildings in such old towns are usually made of highly combustible materials,such as wood and grass.If a fire breaks out,it will spread to multiple buildings,so fire spreading and controlling in old towns need to be studied.This paper presents a fire spread model for old towns based on cellular automaton.The cellular automaton rules were set according to historical fire data in empirical formulas.The model also considered the effects of climate.The simulation results were visualized in a geography information system.An example of a fire spread in Lijiang was investigated with the results showing that this model provides a realistic tool for predicting fire spread in old towns.Fire brigades can use this tool to predict when and how a fire spreads to minimize the losses.
An intelligent floor field cellular automata model for pedestrian dynamics
Kirik, Ekaterina; Krouglov, Dmitriy
2009-01-01
A stochastic cellular automata (CA) model for pedestrian dynamics is presented. Our goal is to simulate different types of pedestrian movement, from regular to panic. But here we emphasize regular situations which imply that pedestrians analyze environment and choose their route more carefully. And transition probabilities have to depict such effect. The potentials of floor fields and environment analysis are combined in the model obtained. People patience is included in the model. This makes simulation of pedestrians movement more realistic. Some simulation results are presented and comparison with basic FF-model is made.
A cellular automata model of Ebola virus dynamics
Burkhead, Emily; Hawkins, Jane
2015-11-01
We construct a stochastic cellular automaton (SCA) model for the spread of the Ebola virus (EBOV). We make substantial modifications to an existing SCA model used for HIV, introduced by others and studied by the authors. We give a rigorous analysis of the similarities between models due to the spread of virus and the typical immune response to it, and the differences which reflect the drastically different timing of the course of EBOV. We demonstrate output from the model and compare it with clinical data.
Car Deceleration Considering Its Own Velocity in Cellular Automata Model
LI Ke-Ping
2006-01-01
In this paper, we propose a new cellular automaton model, which is based on NaSch traffic model. In our method, when a car has a larger velocity, if the gap between the car and its leading car is not enough large, it will decrease. The aim is that the following car has a buffer space to decrease its velocity at the next time, and then avoid to decelerate too high. The simulation results show that using our model, the car deceleration is realistic, and is closer to thefield measure than that of NaSch model.
Simulations of Living Cell Origins Using a Cellular Automata Model
Ishida, Takeshi
2014-04-01
Understanding the generalized mechanisms of cell self-assembly is fundamental for applications in various fields, such as mass producing molecular machines in nanotechnology. Thus, the details of real cellular reaction networks and the necessary conditions for self-organized cells must be elucidated. We constructed a 2-dimensional cellular automata model to investigate the emergence of biological cell formation, which incorporated a looped membrane and a membrane-bound information system (akin to a genetic code and gene expression system). In particular, with an artificial reaction system coupled with a thermal system, the simultaneous formation of a looped membrane and an inner reaction process resulted in a more stable structure. These double structures inspired the primitive biological cell formation process from chemical evolution stage. With a model to simulate cellular self-organization in a 2-dimensional cellular automata model, 3 phenomena could be realized: (1) an inner reaction system developed as an information carrier precursor (akin to DNA); (2) a cell border emerged (akin to a cell membrane); and (3) these cell structures could divide into 2. This double-structured cell was considered to be a primary biological cell. The outer loop evolved toward a lipid bilayer membrane, and inner polymeric particles evolved toward precursor information carriers (evolved toward DNA). This model did not completely clarify all the necessary and sufficient conditions for biological cell self-organization. Further, our virtual cells remained unstable and fragile. However, the "garbage bag model" of Dyson proposed that the first living cells were deficient; thus, it would be reasonable that the earliest cells were more unstable and fragile than the simplest current unicellular organisms.
Mathematical model for flood routing based on cellular automaton
Xin CAI
2014-04-01
Full Text Available Increasing frequency and severity of flooding have caused tremendous damage in China, requiring more essential countermeasures to alleviate the damage. In this study, the dynamic simulation property of a cellular automaton was used to make further progress in flood routing. In consideration of terrain’s influence on flood routing, we regarded the terrain elevation as an auxiliary attribute of a two-dimensional cellular automaton in path selection for flood routing and developed a mathematical model based on a cellular automaton. A numerical case of propagation of an outburst flood in an area of the lower Yangtze River was analyzed with both the fixed-step and variable-step models. The results show that the flood does not spread simultaneously in all directions, but flows into the lower place first, and that the submerged area grows quickly at the beginning, but slowly later on. The final submerged areas obtained from the two different models are consistent, and the flood volume balance test shows that the flood volume meets the requirement of the total volume balance. The analysis of the case shows that the proposed model can be a valuable tool for flood routing.
Modeling self-organizing traffic lights with elementary cellular automata
Gershenson, Carlos
2009-01-01
There have been several highway traffic models proposed based on cellular automata. The simplest one is elementary cellular automaton rule 184. We extend this model to city traffic with cellular automata coupled at intersections using only rules 184, 252, and 136. The simplicity of the model offers a clear understanding of the main properties of city traffic and its phase transitions. We use the proposed model to compare two methods for coordinating traffic lights: a green-wave method that tries to optimize phases according to expected flows and a self-organizing method that adapts to the current traffic conditions. The self-organizing method delivers considerable improvements over the green-wave method. For low densities, the self-organizing method promotes the formation and coordination of platoons that flow freely in four directions, i.e. with a maximum velocity and no stops. For medium densities, the method allows a constant usage of the intersections, exploiting their maximum flux capacity. For high dens...
A Cellular Model for Screening Neuronal Nitric Oxide Synthase Inhibitors
Fang, Jianguo; Silverman, Richard B.
2009-01-01
Nitric oxide synthase (NOS) inhibitors are potential drug candidates because it has been well demonstrated that excessive production of NO critically contributes to a range of diseases. Most inhibitors have been screened in vitro using recombinant enzymes, leading to the discovery of a variety of potent compounds. To make inhibition studies more physiologically relevant and bridge the gap between the in vitro assay and in vivo studies, we report here a cellular model for screening NOS inhibit...
Cellular-Based Statistical Model for Mobile Dispersion
Abdulla, Mouhamed; Shayan, Yousef R.
2013-01-01
While analyzing mobile systems we often approximate the actual coverage surface and assume an ideal cell shape. In a multi-cellular network, because of its tessellating nature, a hexagon is more preferred than a circular geometry. Despite this reality, perhaps due to the inherent simplicity, only a model for circular based random spreading is available. However, if used, this results an unfair terminal distribution for non-circular contours. Therefore, in this paper we specifically derived an...
Pott's Puffy Tumor Arising from Frontal Sinusitis
Lim, Ji Yeon; Kang, Hyun Koo [Seoul Veterans Hospital, Seoul (Korea, Republic of)
2010-02-15
Pott's puffy tumor is an extremely rare and potentially life-threatening complication of frontal sinusitis. We report a case of a 64-year-old man who presented at our emergency department with mild tenderness on the glabellar area and diplopia. Computed Tomography (CT) revealed frontal sinusitis and osteomyelitis of the frontal bone. Following sinus trephination and long-term antibiotic therapy, the patient achieved a complete recovery.
Potts ferromagnet: Transformations and critical exponents in planar hierarchical lattices
Hauser, Paulo R.; Curado, Evaldo M. F.
1988-07-01
We prove that the duality transformation for a Potts ferromagnet on two-rooted planar hierarchical lattices (HL) preserves the thermal eigenvalue. This leads to a relation between the correlation length critical exponents υ of a HL and its corresponding dual lattice. Using hyperscaling, we show that their specific heat critical exponents α coincide. For a smaller class of HL—namely of diamond and tress types—we prove that another transformation also preserves υ and α.
Potts ferromagnet: transformations and critical exponents in planar hierarchial lattices
We prove that the duality transformation for a Potts ferromagnet on two-rooted planar hierachical lattices (HL) preserves the thermal eigenvalue. This leads to a relation between the correlation lenght critical exponents v of a HL and its corresponding dual lattice. Using hyperscaling we show that their specific heat critical exponents α coincide. For a smaller class of HL-namely of diamond and tress types-we prove that another transformation also preserves v and α. (author)
Modelling of detonation cellular structure in aluminium suspensions
Briand, A.; Veyssiere, B.; Khasainov, B. A.
2010-12-01
Heterogeneous detonations involving aluminium suspensions have been studied for many years for industrial safety policies, and for military and propulsion applications. Owing to their weak detonability and to the lack of available experimental results on the detonation cellular structure, numerical simulations provide a convenient way to improve the knowledge of such detonations. One major difficulty arising in numerical study of heterogeneous detonations involving suspensions of aluminium particles in oxidizing atmospheres is the modelling of aluminium combustion. Our previous two-step model provided results on the effect on the detonation cellular structure of particle diameter and characteristic chemical lengths. In this study, a hybrid model is incorporated in the numerical code EFAE, combining both kinetic and diffusion regimes in parallel. This more realistic model provides good agreement with the previous two-step model and confirms the correlations found between the detonation cell width, and particle diameter and characteristic lengths. Moreover, the linear dependence found between the detonation cell width and the induction length remains valid with the hybrid model.
A cellular automaton model for tumor growth in heterogeneous environment
Jiao, Yang; Torquato, Sal
2011-03-01
Cancer is not a single disease: it exhibits heterogeneity on different spatial and temporal scales and strongly interacts with its host environment. Most mathematical modeling of malignant tumor growth has assumed a homogeneous host environment. We have developed a cellular automaton model for tumor growth that explicitly incorporates the structural heterogeneity of the host environment such as tumor stroma. We show that these structural heterogeneities have non-trivial effects on the tumor growth dynamics and prognosis. Y. J. is supported by PSOC, NCI.
Cellular automata model of magnetospheric-ionospheric coupling
Kozelov, B. V.; Kozelova, T. V.
2003-01-01
We propose a cellular automata model (CAM) to describe the substorm activity of the magnetospheric-ionospheric system. The state of each cell in the model is described by two numbers that correspond to the energy content in a region of the current sheet in the magnetospheric tail and to the conductivity of the ionospheric domain that is magnetically connected with this region. The driving force of the system is supposed to be provided by the solar wind that is convected along the two b...
A Realistic Cellular Automaton Model for Synchronized Traffic Flow
ZHAO Bo-Han; HU Mao-Bin; JIANG Rui; WU Qing-Song
2009-01-01
A cellular automaton model is proposed to consider the anticipation effect in drivers' behavior. It is shown that the anticipation effect can be one of the origins of synchronized traffic flow. With anticipation effect, the congested traffic flow simulated by the model exhibits the features of synchronized flow. The spatiotemporal patterns induced by an on-ramp are also consistent with the three-phaee traffic theory. Since the origin of synchronized flow is still controversial, our work can shed some light on the mechanism of synchronized flow.
Cellular automata modelling of phase-change memories
Wanhua Yu; David Wright
2008-01-01
A novel approach to modelling phase-transition processes in phase change materials used for optical and electrical data storage applications is presented. The model is based on a cellular automaton (CA) approach to predict crystallization behaviour that is linked to thermal and electrical simulations to enable the study of the data writing and erasing processes. The CA approach is shown to be able to predict the evolution of the microstructure during the rapid heating and cooling cycles pertinent to data storage technology, and maps crystallization behaviour on the nanoscale. A simple example based on possible future nonvolatile phase-change random access solid-state memory is presented.
[Huge dorsolumbar cold abscess associated with Pott's disease].
Rakotoson, J L; Rakotomizao, J R; Andrianarisoa, A C F
2010-12-01
Pott's disease, or tuberculosis of the spine, is the most common osteoarticular tuberculosis. Among them, dorsolumbar impairment is predominant. The authors report the case of a patient with a huge cold lumbar abscess associated with Pott's disease. The patient is a 32-year-old man presenting dorsolumbar tumefaction associated with an alteration in his general condition and fever for three months. Treatment by "traditional healers" did not provide any improvement. He consulted for mild lumbar pain triggered by fatigue appearing one week before and after the failure of the traditional practitioner. The clinical examination found a temperature of 38.5°C, cachexia, mild lumber kyphosis and impressive, soft, painless and non inflammatory dorsolumbar bruised tumefaction, 40 cm high, 15 cm wide and 7 cm deep. He did not present any neurological signs. The dorsolumbar X-ray of the spine revealed a lesion associated with Pott's disease in the first and second lumbar vertebrae with pinching of the disc, punched-out lesions and osteocondensation. The ultrasound examination of the soft tissue revealed the presence of a laterovertebral collection of fluid diffusing in the subcutaneous region. The psoas major and the paravertebral muscles were not affected. A scan or MRI of the spine was not carried out. Examination of the tissue sample and drainage of the abscess confirmed the tubercular origin. Treatment with tuberculostatic drugs for 12 months associated with immobilisation resulted in a cure with sequelae of mild kyphoscoliosis vertebral statics. PMID:21167445
Modeling and simulation for train control system using cellular automata
LI; KePing; GAO; ZiYou; YANG; LiXing
2007-01-01
Train control system plays a key role in railway traffic. Its function is to manage and control the train movement on railway networks. In our previous works, based on the cellular automata (CA) model, we proposed several models and algorithms for simulating the train movement under different control system conditions. However, these models are only suitable for some simple traffic conditions. Some basic factors, which are important for train movement, are not considered. In this paper, we extend these models and algorithms and give a unified formula. Using the proposed method, we analyze and discuss the space-time diagram of railway traffic flow and the trajectories of the train movement. The numerical simulation and analytical results demonstrate that the unified CA model is an effective tool for simulating the train control system.
Cellular automaton model considering headway-distance effect
Hu, Shou-Xin; Gao, Kun; Wang, Bing-Hong; Lu, Yu-Feng
2008-05-01
This paper presents a cellular automaton model for single-lane traffic flow. On the basis of the Nagel-Schreckenberg (NS) model, it further considers the effect of headway-distance between two successive cars on the randomization of the latter one. In numerical simulations, this model shows the following characteristics. (1) With a simple structure, this model succeeds in reproducing the hysteresis effect, which is absent in the NS model. (2) Compared with the slow-to-start models, this model exhibits a local fundamental diagram which is more consistent to empirical observations. (3) This model has much higher efficiency in dissolving congestions compared with the so-called NS model with velocity-dependent randomization (VDR model). (4) This model is more robust when facing traffic obstructions. It can resist much longer shock times and has much shorter relaxation times on the other hand. To summarize, compared with the existing models, this model is quite simple in structure, but has good characteristics.
Structural modeling of sandwich structures with lightweight cellular cores
T. Liu; Z. C. Deng; T. J. Lu
2007-01-01
An effective single layered finite element (FE) computational model is proposed to predict the structural behavior of lightweight sandwich panels having two dimensional (2D) prismatic or three dimensional (3D) truss cores.Three different types of cellular core topology are considered: pyramidal truss core (3D), Kagome truss core (3D) and corrugated core (2D), representing three kinds of material anisotropy: orthotropic, monoclinic and general anisotropic. A homogenization technique is developed to obtain the homogenized macroscopic stiffness properties of the cellular core. In comparison with the results obtained by using detailed FE model, the single layered computational model cangive acceptable predictions for both the static and dynamic behaviors of orthotropic truss core sandwich panels. However, for non-orthotropic 3D truss cores, the predictions are not so well. For both static and dynamic behaviors of a 2D corrugated core sandwich panel, the predictions derived by the single layered computational model is generally acceptable when the size of the unit cell varies within a certain range, with the predictions for moderately strong or strong corrugated cores more accurate than those for weak cores.
A Fluid Model for Performance Analysis in Cellular Networks
Coupechoux Marceau
2010-01-01
Full Text Available We propose a new framework to study the performance of cellular networks using a fluid model and we derive from this model analytical formulas for interference, outage probability, and spatial outage probability. The key idea of the fluid model is to consider the discrete base station (BS entities as a continuum of transmitters that are spatially distributed in the network. This model allows us to obtain simple analytical expressions to reveal main characteristics of the network. In this paper, we focus on the downlink other-cell interference factor (OCIF, which is defined for a given user as the ratio of its outer cell received power to its inner cell received power. A closed-form formula of the OCIF is provided in this paper. From this formula, we are able to obtain the global outage probability as well as the spatial outage probability, which depends on the location of a mobile station (MS initiating a new call. Our analytical results are compared to Monte Carlo simulations performed in a traditional hexagonal network. Furthermore, we demonstrate an application of the outage probability related to cell breathing and densification of cellular networks.
Integrating cellular metabolism into a multiscale whole-body model.
Markus Krauss
Full Text Available Cellular metabolism continuously processes an enormous range of external compounds into endogenous metabolites and is as such a key element in human physiology. The multifaceted physiological role of the metabolic network fulfilling the catalytic conversions can only be fully understood from a whole-body perspective where the causal interplay of the metabolic states of individual cells, the surrounding tissue and the whole organism are simultaneously considered. We here present an approach relying on dynamic flux balance analysis that allows the integration of metabolic networks at the cellular scale into standardized physiologically-based pharmacokinetic models at the whole-body level. To evaluate our approach we integrated a genome-scale network reconstruction of a human hepatocyte into the liver tissue of a physiologically-based pharmacokinetic model of a human adult. The resulting multiscale model was used to investigate hyperuricemia therapy, ammonia detoxification and paracetamol-induced toxication at a systems level. The specific models simultaneously integrate multiple layers of biological organization and offer mechanistic insights into pathology and medication. The approach presented may in future support a mechanistic understanding in diagnostics and drug development.
Robustness of a Cellular Automata Model for the HIV Infection
Figueirêdo, P H; Santos, R M Zorzenon dos
2008-01-01
An investigation was conducted to study the robustness of the results obtained from the cellular automata model which describes the spread of the HIV infection within lymphoid tissues [R. M. Zorzenon dos Santos and S. Coutinho, Phys. Rev. Lett. 87, 168102 (2001)]. The analysis focussed on the dynamic behavior of the model when defined in lattices with different symmetries and dimensionalities. The results illustrated that the three-phase dynamics of the planar models suffered minor changes in relation to lattice symmetry variations and, while differences were observed regarding dimensionality changes, qualitative behavior was preserved. A further investigation was conducted into primary infection and sensitiveness of the latency period to variations of the model's stochastic parameters over wide ranging values. The variables characterizing primary infection and the latency period exhibited power-law behavior when the stochastic parameters varied over a few orders of magnitude. The power-law exponents were app...
Fluctuation in option pricing using cellular automata based market models
Gao, Yuying; Beni, Gerardo
2005-05-01
A new agent-based Cellular Automaton (CA) computational algorithm for option pricing is proposed. CAs have been extensively used in modeling complex dynamical systems but not in modeling option prices. Compared with traditional tools, which rely on guessing volatilities to calculate option prices, the CA model is directly addressing market mechanisms and simulates price fluctuation from aggregation of actions made by interacting individual market makers in a large population. This paper explores whether CA models can provide reasonable good answers to pricing European options. The Black-Scholes model and the Binomial Tree model are used for comparison. Comparison reveals that CA models perform reasonably well in pricing options, reproducing overall characteristics of random walk based model, while at the same time providing plausible results for the 'fat-tail' phenomenon observed in many markets. We also show that the binomial tree model can be obtained from a CA rule. Thus, CA models are suitable tools to generalize the standard theories of option pricing.
Simulation of root forms using cellular automata model
This research aims to produce a simulation program for root forms using cellular automata model. Stephen Wolfram in his book entitled “A New Kind of Science” discusses the formation rules based on the statistical analysis. In accordance with Stephen Wolfram’s investigation, the research will develop a basic idea of computer program using Delphi 7 programming language. To best of our knowledge, there is no previous research developing a simulation describing root forms using the cellular automata model compared to the natural root form with the presence of stone addition as the disturbance. The result shows that (1) the simulation used four rules comparing results of the program towards the natural photographs and each rule had shown different root forms; (2) the stone disturbances prevent the root growth and the multiplication of root forms had been successfully modeled. Therefore, this research had added some stones, which have size of 120 cells placed randomly in the soil. Like in nature, stones cannot be penetrated by plant roots. The result showed that it is very likely to further develop the program of simulating root forms by 50 variations
Simulation of root forms using cellular automata model
Winarno, Nanang; Prima, Eka Cahya; Afifah, Ratih Mega Ayu
2016-02-01
This research aims to produce a simulation program for root forms using cellular automata model. Stephen Wolfram in his book entitled "A New Kind of Science" discusses the formation rules based on the statistical analysis. In accordance with Stephen Wolfram's investigation, the research will develop a basic idea of computer program using Delphi 7 programming language. To best of our knowledge, there is no previous research developing a simulation describing root forms using the cellular automata model compared to the natural root form with the presence of stone addition as the disturbance. The result shows that (1) the simulation used four rules comparing results of the program towards the natural photographs and each rule had shown different root forms; (2) the stone disturbances prevent the root growth and the multiplication of root forms had been successfully modeled. Therefore, this research had added some stones, which have size of 120 cells placed randomly in the soil. Like in nature, stones cannot be penetrated by plant roots. The result showed that it is very likely to further develop the program of simulating root forms by 50 variations.
Simulation of root forms using cellular automata model
Winarno, Nanang, E-mail: nanang-winarno@upi.edu; Prima, Eka Cahya [International Program on Science Education, Universitas Pendidikan Indonesia, Jl. Dr. Setiabudi no 229, Bandung40154 (Indonesia); Afifah, Ratih Mega Ayu [Department of Physics Education, Post Graduate School, Universitas Pendidikan Indonesia, Jl. Dr. Setiabudi no 229, Bandung40154 (Indonesia)
2016-02-08
This research aims to produce a simulation program for root forms using cellular automata model. Stephen Wolfram in his book entitled “A New Kind of Science” discusses the formation rules based on the statistical analysis. In accordance with Stephen Wolfram’s investigation, the research will develop a basic idea of computer program using Delphi 7 programming language. To best of our knowledge, there is no previous research developing a simulation describing root forms using the cellular automata model compared to the natural root form with the presence of stone addition as the disturbance. The result shows that (1) the simulation used four rules comparing results of the program towards the natural photographs and each rule had shown different root forms; (2) the stone disturbances prevent the root growth and the multiplication of root forms had been successfully modeled. Therefore, this research had added some stones, which have size of 120 cells placed randomly in the soil. Like in nature, stones cannot be penetrated by plant roots. The result showed that it is very likely to further develop the program of simulating root forms by 50 variations.
National Oceanic and Atmospheric Administration, Department of Commerce — The purpose of this project is to adapt cellular in vitro assay systems of the rainbow trout pituitary, liver and ovary for high-throughput screening (HTS) of...
Cellular automaton model of cell response to targeted radiation
It has been shown that the response of cells to low doses of radiation is not linear and cannot be accurately extrapolated from the high dose response. To investigate possible mechanisms involved in the behaviour of cells under very low doses of radiation, a cellular automaton (CA) model was created. The diffusion and consumption of glucose in the culture dish were computed in parallel to the growth of cells. A new model for calculating survival probability was introduced; the communication between targeted and non-targeted cells was also included. Early results on the response of non-confluent cells to targeted irradiation showed the capability of the model to take account for the non-linear response in the low-dose domain
Cellular automaton model of coupled mass transport and chemical reactions
Mass transport, coupled with chemical reactions, is modelled as a cellular automaton in which solute molecules perform a random walk on a lattice and react according to a local probabilistic rule. Assuming molecular chaos and a smooth density function, we obtain the standard reaction-transport equations in the continuum limit. The model is applied to the reactions a + b ↔c and a + b →c, where we observe interesting macroscopic effects resulting from microscopic fluctuations and spatial correlations between molecules. We also simulate autocatalytic reaction schemes displaying spontaneous formation of spatial concentration patterns. Finally, we propose and discuss the limitations of a simple model for mineral-solute interaction. (author) 5 figs., 20 refs
Global Network Model based on Earth Grid and Cellular
Dongqi Lu
2014-06-01
Full Text Available We aim to understand the current health state of the Earth and find how human activities influence it. Based on the theory of Earth’s Grid and Cellular Automata, we define and test a global network model, analyze the mutual interactions and feedbacks of ecosystem, hydrologic circle and atmosphere. In addition, we consult a lot of data to find a benchmark for the “Earth Health Map”, with the ecosystem distribution on it, which can be helpful for making a strategic decision for policy makers and prediction. Our model can be extended to other similar fields. In the end, we discuss the sensitivity of parameters selection, and the superiorities and weaknesses of our model.
A cellular automata-based mathematical model for thymocyte development.
Hallan Souza-e-Silva
Full Text Available Intrathymic T cell development is an important process necessary for the normal formation of cell-mediated immune responses. Importantly, such a process depends on interactions of developing thymocytes with cellular and extracellular elements of the thymic microenvironment. Additionally, it includes a series of oriented and tunely regulated migration events, ultimately allowing mature cells to cross endothelial barriers and leave the organ. Herein we built a cellular automata-based mathematical model for thymocyte migration and development. The rules comprised in this model take into account the main stages of thymocyte development, two-dimensional sections of the normal thymic microenvironmental network, as well as the chemokines involved in intrathymic cell migration. Parameters of our computer simulations with further adjusted to results derived from previous experimental data using sub-lethally irradiated mice, in which thymus recovery can be evaluated. The model fitted with the increasing numbers of each CD4/CD8-defined thymocyte subset. It was further validated since it fitted with the times of permanence experimentally ascertained in each CD4/CD8-defined differentiation stage. Importantly, correlations using the whole mean volume of young normal adult mice revealed that the numbers of cells generated in silico with the mathematical model fall within the range of total thymocyte numbers seen in these animals. Furthermore, simulations made with a human thymic epithelial network using the same mathematical model generated similar profiles for temporal evolution of thymocyte developmental stages. Lastly, we provided in silico evidence that the thymus architecture is important in the thymocyte development, since changes in the epithelial network result in different theoretical profiles for T cell development/migration. This model likely can be used to predict thymocyte evolution following therapeutic strategies designed for recovery of the
Motor Schema-Based Cellular Automaton Model for Pedestrian Dynamics
Weng, Wenguo; Hasemi, Yuji; Fan, Weicheng
A new cellular automaton model for pedestrian dynamics based on motor schema is presented. Each pedestrian is treated as an intelligent mobile robot, and motor schemas including move-to-goal, avoid-away and avoid-around drive pedestrians to interact with their environment. We investigate the phenomenon of many pedestrians with different move velocities escaping from a room. The results show that the pedestrian with high velocity have predominance in competitive evacuation, if we only consider repulsion from or avoiding around other pedestrians, and interaction with each other leads to disordered evacuation, i.e., decreased evacuation efficiency. Extensions of the model using learning algorithms for controlling pedestrians, i.e., reinforcement learning, neural network and genetic algorithms, etc. are noted.
Critical Behavior in a Cellular Automata Animal Disease Transmission Model
Morley, P D; Chang, Julius
2003-01-01
Using a cellular automata model, we simulate the British Government Policy (BGP) in the 2001 foot and mouth epidemic in Great Britain. When clinical symptoms of the disease appeared on a farm, there is mandatory slaughter (culling) of all livestock on an infected premise (IP). Those farms that neighbor an IP (contiguous premise, CP), are also culled, aka nearest neighbor interaction. Farms where the disease may be prevalent from animal, human, vehicle or airborne transmission (dangerous contact, DC), are additionally culled, aka next-to-nearest neighbor iteractions and lightning factor. The resulting mathematical model possesses a phase transition, whereupon if the physical disease transmission kernel exceeds a critical value, catastrophic loss of animals ensues. The non-local disease transport probability can be as low as .01% per day and the disease can still be in the high mortality phase. We show that the fundamental equation for sustainable disease transport is the criticality equation for neutron fissio...
Computer Modeling of the Earliest Cellular Structures and Functions
Pohorille, Andrew
2000-03-01
In the absence of extinct or extant record of protocells (the earliest ancestors of contemporary cells), the most direct way to test ourunderstanding of the origin of cellular life is to construct laboratory models of protocells. Such efforts are currently underway in the NASA Astrobiology Program. They are accompanied by computational studies aimed at explaining self-organization of simple molecules into ordered structures and developing designs for molecules that perform protocellular functions. Many of these functions, such as import of nutrients, capture and storage of energy, and response to changes in the environment are carried out by proteins bound to membranes. We will discuss a series of large-scale, molecular-level computer simulations which demonstrate (a) how small proteins (peptides)organize themselves into ordered structures at water-membrane interfaces and insert into membranes, (b) how these peptides aggregate to form membrane-spanning structures (e.g. channels), and (c) by what mechanisms such aggregates perform essential protocellular functions, such as proton transport of protons across cell walls, a key step in cellular bioenergetics. The simulations were performed using the molecular dynamics method, in which Newton's equations of motion for each atom in the system are solved iteratively. The problems of interest required simulations on multi-nanosecond time scales, which corresponded to 10^6-10^8 time steps.
Pott's Disease in a Pediatric Patient. A Case Report
Lourdes Marimón Amador
2014-08-01
Full Text Available The case of a four-year old boy with Pott's disease diagnosed by clinical, radiological and laboratory study at the Guido Valladares National Hospital in East Timor is presented. Inquiries about the etiopathogenesis of the disease in relation to the family and personal history were conducted. This is a very complex and clinically important case since a rare and serious complication was observed in the child. It is concluded that early diagnosis of this condition is essential due to its poor prognosis once developed.
Credit Default Swaps and Insurance: Against the Potts Opinion
Juurikkala, Oskari
2011-01-01
Little attention has been given to the possibility that CDS transactions might be construed as insurance contracts in English law. This article challenges the widespread âPotts opinionâ, which states that CDSs are not insurance, because they do not require the protection buyer to sustain a loss or to have an insurable interest in the subject matter. CDSs often do provide protection against loss that the buyer is exposed to; loss indemnity is not a necessary characterisation of an insuranc...
Load-Aware Modeling and Analysis of Heterogeneous Cellular Networks
Dhillon, Harpreet S; Andrews, Jeffrey G
2012-01-01
Random spatial models are attractive for modeling heterogeneous cellular networks (HCNs) due to their realism, tractability, and scalability. A major limitation of such models to date in the context of HCNs is the neglect of network traffic and load: all base stations (BSs) have typically been assumed to always be transmitting. Small cells in particular will have a lighter load than macrocells, and so their contribution to the network interference may be significantly overstated in a fully loaded model. This paper incorporates a flexible notion of BS load by introducing a new idea of conditionally thinning the interference field. For a $K$-tier HCN where BSs across tiers differ in terms of transmit power, supported data rate, deployment density, and now load, we derive the coverage probability for a typical mobile, which connects to the strongest BS signal. Conditioned on this connection, the interfering BSs of the $i^{th}$ tier are assumed to transmit independently with probability $p_i$, which models the lo...
A Computational Model of Cellular Response to Modulated Radiation Fields
Purpose: To develop a model to describe the response of cell populations to spatially modulated radiation exposures of relevance to advanced radiotherapies. Materials and Methods: A Monte Carlo model of cellular radiation response was developed. This model incorporated damage from both direct radiation and intercellular communication including bystander signaling. The predictions of this model were compared to previously measured survival curves for a normal human fibroblast line (AGO1522) and prostate tumor cells (DU145) exposed to spatially modulated fields. Results: The model was found to be able to accurately reproduce cell survival both in populations which were directly exposed to radiation and those which were outside the primary treatment field. The model predicts that the bystander effect makes a significant contribution to cell killing even in uniformly irradiated cells. The bystander effect contribution varies strongly with dose, falling from a high of 80% at low doses to 25% and 50% at 4 Gy for AGO1522 and DU145 cells, respectively. This was verified using the inducible nitric oxide synthase inhibitor aminoguanidine to inhibit the bystander effect in cells exposed to different doses, which showed significantly larger reductions in cell killing at lower doses. Conclusions: The model presented in this work accurately reproduces cell survival following modulated radiation exposures, both in and out of the primary treatment field, by incorporating a bystander component. In addition, the model suggests that the bystander effect is responsible for a significant portion of cell killing in uniformly irradiated cells, 50% and 70% at doses of 2 Gy in AGO1522 and DU145 cells, respectively. This description is a significant departure from accepted radiobiological models and may have a significant impact on optimization of treatment planning approaches if proven to be applicable in vivo.
A cellular automaton model for neurogenesis in Drosophila
Luthi, Pascal O.; Chopard, Bastien; Preiss, Anette; Ramsden, Jeremy J.
1998-07-01
A cellular automaton (CA) is constructed for the formation of the central nervous system of the Drosophila embryo. This is an experimentally well-studied system in which complex interactions between neighbouring cells appear to drive their differentiation into different types. It appears that all the cells initially have the potential to become neuroblasts, and all strive to this end, but those which differentiate first block their as yet undifferentiated neighbours from doing so. The CA makes use of observational evidence for a lateral inhibition mechanism involving signalling products S of the ‘proneural’ or neuralizing genes. The key concept of the model is that cells are continuously producing S, but the production rate is lowered by inhibitory signals received from neighbouring cells which have advanced further along the developmental pathway. Comparison with experimental data shows that it well accounts for the observed proportion of neuroectodermal cells delaminating as neuroblasts.
Cellular automaton model of mass transport with chemical reactions
The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes advection and diffusion in a simple way, and as no restriction is placed on the number of particles at a lattice site, it is also able to describe a wide variety of chemical reactions. Assuming molecular chaos and a smooth density function, we obtain the standard reaction-transport equations in the continuum limit. Simulations on one-and two-dimensional lattices show that the discrete model can be used to approximate the solutions of the continuum equations. We discuss discrepancies which arise from correlations between molecules and how these discrepancies disappear as the continuum limit is approached. Of particular interest are simulations displaying long-time behaviour which depends on long-wavelength statistical fluctuations not accounted for by the standard equations. The model is applied to the reactions a + b ↔ c and a + b → c with homogeneous and inhomogeneous initial conditions as well as to systems subject to autocatalytic reactions and displaying spontaneous formation of spatial concentration patterns. (author) 9 figs., 34 refs
COMPARATIVE ANALYSIS OF CONGESTION CONTROL MODELS FOR CELLULAR WIRELESS NETWORK
Falade A. J
2015-08-01
Full Text Available Cellular wireless systems like GSM suffer from congestion resulting in overall system degradation and poor service delivery. When the traffic demand in a geographical area is high, the input traffic rate will exceed thecapacity of the output lines. This work focused on homogenous wireless network (the network traffic and resource dimensioning that are statistically identical such that the network performance evaluation can be reduced to a system with single cell and a single traffic type. Such system can employa queuing model to evaluate the performance metric of a cell in terms of blocking probability. Five congestion control models were compared in the work to ascertain their peculiarities, they are Erlang B, Erlang C, Engset (cleared, Engset (buffered, and Bernoulli. To analyze the system, an aggregate onedimensional Markov chain wasderived, such that it describes a call arrival process under the assumption that it is Poisson distributed. The models were simulated and their results show varying performances, however the Bernoulli model (Pb5 tends to show a situation that allows more users access to the system and the congestion level remain unaffected despite increase in the number of users and the offered traffic into the system.
Cellular automaton model of crowd evacuation inspired by slime mould
Kalogeiton, V. S.; Papadopoulos, D. P.; Georgilas, I. P.; Sirakoulis, G. Ch.; Adamatzky, A. I.
2015-04-01
In all the living organisms, the self-preservation behaviour is almost universal. Even the most simple of living organisms, like slime mould, is typically under intense selective pressure to evolve a response to ensure their evolution and safety in the best possible way. On the other hand, evacuation of a place can be easily characterized as one of the most stressful situations for the individuals taking part on it. Taking inspiration from the slime mould behaviour, we are introducing a computational bio-inspired model crowd evacuation model. Cellular Automata (CA) were selected as a fully parallel advanced computation tool able to mimic the Physarum's behaviour. In particular, the proposed CA model takes into account while mimicking the Physarum foraging process, the food diffusion, the organism's growth, the creation of tubes for each organism, the selection of optimum tube for each human in correspondence to the crowd evacuation under study and finally, the movement of all humans at each time step towards near exit. To test the model's efficiency and robustness, several simulation scenarios were proposed both in virtual and real-life indoor environments (namely, the first floor of office building B of the Department of Electrical and Computer Engineering of Democritus University of Thrace). The proposed model is further evaluated in a purely quantitative way by comparing the simulation results with the corresponding ones from the bibliography taken by real data. The examined fundamental diagrams of velocity-density and flow-density are found in full agreement with many of the already published corresponding results proving the adequacy, the fitness and the resulting dynamics of the model. Finally, several real Physarum experiments were conducted in an archetype of the aforementioned real-life environment proving at last that the proposed model succeeded in reproducing sufficiently the Physarum's recorded behaviour derived from observation of the aforementioned
Some properties of the floor field cellular automata evacuation model
Gwizdałła, Tomasz M.
2015-02-01
We study the process of evacuation of pedestrians from the room with the given arrangement of doors and obstacles by using the cellular automata technique. The technique which became quite popular is characterized by the discretization of time as well as space. For such a discretized space we use so-called floor field model which generally corresponds to the description of every cell by some monotonic function of distance between this cell and the closest exit. We study several types of effects. We start from some general features of model like the kind of a neighborhood or the factors disrupting the motion. Then we analyze the influence of asymmetry and size on the evacuation time. Finally we show characteristics concerning different arrangements of exits and include a particular approach to the proxemics effects. The scaling analyses help us to distinguish these cases which just reflect the geometry of the system and those which depend also on the simulation properties. All calculations are performed for a wide range of initial densities corresponding to different occupation rates as described by the typical crowd counting techniques.
From equilibrium spin models to probabilistic cellular automata
The general equivalence between D-dimensional probabilistic cellular automata (PCA) and (D + 1)-dimensional equilibrium spin models satisfying a disorder condition is first described in a pedagogical way and then used to analyze the phase diagrams, the critical behavior, and the universality classes of some automato. Diagrammatic representations of time-dependent correlation functions PCA are introduced. Two important classes of PCA are singled out for which these correlation functions simplify: (1) Quasi-Hamiltonian automata, which have a current-carrying steady state, and for which some correlation functions are those of a D-dimensional static model PCA satisfying the detailed balance condition appear as a particular case of these rules for which the current vanishes. (2) Linear (and more generally affine) PCA for which the diagrammatics reduces to a random walk problem closely related to (D + 1)-dimensional directed SAWs: both problems display a critical behavior with mean-field exponents in any dimension. The correlation length and effective velocity of propagation of excitations can be calculated for affine PCA, as is shown on an explicit D = 1 example. The authors conclude with some remarks on nonlinear PCA, for which the diagrammatics is related to reaction-diffusion processes, and which belong in some cases to the universality class of Reggeon field theory
Modeling chemical systems using cellular automata a textbook and laboratory manual
Kier, Lemont B; Cheng, Chao-Kun
2006-01-01
Provides a practical introduction to an exciting modeling paradigm for complex systems. This book discusses the nature of scientific inquiry using models and simulations, and describes the nature of cellular automata models. It gives descriptions of how cellular automata models can be used in the study of a variety of phenomena.
Relationship between cellular response models and biochemical mechanisms
In most cellular response experiments, survival reflects the kinetics of a variety of damage and repair processes. Unfortunately, biochemical studies of molecular repair deal with mechanisms which cannot be readily correlated with these kinetic observations. The difference in these approaches sometimes leads to confusion over terms such as potentially-lethal and sublethal damage. These terms were introduced with operation definitions, derived from kinetic studies of cell survival, but some researchers have since attempted to associate them with specific biochemical mechanisms. Consequently, the terms are often used in totally different ways be different investigators. The use of carefully constructed models originating either out of assumptions based on mechanisms, or on kinetics, can be used to design experiments to eliminate some alternative kinetic schemes. In turn, some mechanisms may also be eliminated, resulting in a reduction in the number of mechanisms which must be investigated biochemically. One must take advantage of a wide range of specialized radiation procedures in order to accomplish this. Examples of the use of such specialized experimental designs, which have led to a more detailed understanding of the kinetics of both algal and mammalian cell responses, are discussed
Modeling and Performance Analyses of Hybrid Cellular and Broadcasting Networks
Peter Unger
2009-01-01
Full Text Available Mobile communication services are getting more and more important and, in particular, multimedia services have attracted the interest of the users. Mobile TV is one of the most demanded candidates. Powerful and efficient communication systems are needed, which provide high capacities, especially at the downlink. Furthermore, interactivity is essential for supporting the user needs and to extend the service offering. As one possible solution to meet the mentioned requirements, we consider the combination of the cellular network UMTS and the mobile broadcast network DVB-H, which form a hybrid network. We investigate the performance of hybrid networks and develop a system model, which describes the hybrid network and the load switching between both networks. One of the contributions is the definition of the switching bound concept, which represents an efficient tool to assess the necessity and the feasibility of hybrid networks and the amount of load switching. The performance indicators cell load and grade of service are analyzed by using theoretical and realistic scenarios.
Chang-Hua Zou
2009-01-01
Full Text Available Problem statement: Cardiovascular Diseases (CVD continued to be the leading cause of death. Failure or abnormal cardiac cellular or sub-cellular vibrations (oscillations could lead failure or abnormal heart beats that could cause CVD. Understanding the mechanisms of the vibrations (oscillations could help to prevent or to treat the diseases. Scientists have studied the mechanisms for more than 100 years. To our knowledge, the mechanisms are still unclear today. In this investigation, based on published data or results, conservation laws of the momentum as well as the energy, in views of biology, biochemistry, informatics and physics (BioChemInfoPhysics, we proposed our models of cardiac cellular and sub-cellular vibrations (oscillations of biological components, such as free ions in Biological Fluids (BF, Biological Membranes (BM, Ca++H+ (Ca++ and Na+K+ ATPases, Na+Ca++ exchangers (NCX, Ca++ carriers and myosin heads. Approach: Our models were described with 4-D (x, y, z, t or r, ?, z, t momentum transfer equations in mathematical physics. Results: The momentum transfer equations were solved with free and forced, damped, un-damped and over-damped, vibrations (oscillations. The biological components could be modeled as resonators or vibrators (oscillators, such as liquid plasmas, membranes, active springs, passive springs and active swings. Conclusion: We systematically provided new insights of automation (ignition and maintain, transportation, propagation and orientation of the cardiac cellular and sub-cellular vibrations (oscillations and resonances, with our BioChemInfoPhysics models of 4-D momentum transfer equations. Our modeling results implied: Auto-rhythmic cells (Sinoatrial Node Cells (SANC, Atrioventricular Node Cells (AVNC, Purkinje fibers, non-Auto-rhythmic ventricular myocytes and their Sarcoplasmic Reticulums (SR work as Biological Liquid Plasma Resonators (BLPR. The resonators were
Cellular automata model of magnetospheric-ionospheric coupling
B. V. Kozelov
Full Text Available We propose a cellular automata model (CAM to describe the substorm activity of the magnetospheric-ionospheric system. The state of each cell in the model is described by two numbers that correspond to the energy content in a region of the current sheet in the magnetospheric tail and to the conductivity of the ionospheric domain that is magnetically connected with this region. The driving force of the system is supposed to be provided by the solar wind that is convected along the two boundaries of the system. The energy flux inside is ensured by the penetration of the energy from the solar wind into the array of cells (magnetospheric tail with a finite velocity. The third boundary (near to the Earth is closed and the fourth boundary is opened, thereby modeling the flux far away from the tail. The energy dissipation in the system is quite similar to other CAM models, when the energy in a particular cell exceeds some pre-defined threshold, and the part of the energy excess is redistributed between the neighbouring cells. The second number attributed to each cell mimics ionospheric conductivity that can allow for a part of the energy to be shed on field-aligned currents. The feedback between "ionosphere" and "magnetospheric tail" is provided by the change in a part of the energy, which is redistributed in the tail when the threshold is surpassed. The control parameter of the model is the z-component of the interplanetary magnetic field (Bz IMF, "frozen" into the solar wind. To study the internal dynamics of the system at the beginning, this control parameter is taken to be constant. The dynamics of the system undergoes several bifurcations, when the constant varies from - 0.6 to - 6.0. The Bz IMF input results in the periodic transients (activation regions and the inter-transient period decreases with the decrease of Bz. At the same time the onset of activations in the array shifts towards the "Earth". When the modulus of the Bz IMF exceeds some
Millimeter Wave Channel Modeling and Cellular Capacity Evaluation
Akdeniz, Mustafa Riza; Liu, Yuanpeng; Samimi, Mathew K.; Sun, Shu; Rangan, Sundeep; Rappaport, Theodore S.; Erkip, Elza
2013-01-01
With the severe spectrum shortage in conventional cellular bands, millimeter wave (mmW) frequencies between 30 and 300 GHz have been attracting growing attention as a possible candidate for next-generation micro- and picocellular wireless networks. The mmW bands offer orders of magnitude greater spectrum than current cellular allocations and enable very high-dimensional antenna arrays for further gains via beamforming and spatial multiplexing. This paper uses recent real-world measurements at...
A Cellular Automata Model for the Study of Landslides
Liucci, Luisa; Suteanu, Cristian; Melelli, Laura
2016-04-01
Power-law scaling has been observed in the frequency distribution of landslide sizes in many regions of the world, for landslides triggered by different factors, and in both multi-temporal and post-event datasets, thus indicating the universal character of this property of landslides and suggesting that the same mechanisms drive the dynamics of mass wasting processes. The reasons for the scaling behavior of landslide sizes are widely debated, since their understanding would improve our knowledge of the spatial and temporal evolution of this phenomenon. Self-Organized Critical (SOC) dynamics and the key role of topography have been suggested as possible explanations. The scaling exponent of the landslide size-frequency distribution defines the probability of landslide magnitudes and it thus represents an important parameter for hazard assessment. Therefore, another - still unanswered - important question concerns the factors on which its value depends. This paper investigates these issues using a Cellular Automata (CA) model. The CA uses a real topographic surface acquired from a Digital Elevation Model to represent the initial state of the system, where the states of cells are defined in terms of altitude. The stability criterion is based on the slope gradient. The system is driven to instability through a temporal decrease of the stability condition of cells, which may be thought of as representing the temporal weakening of soil caused by factors like rainfall. A transition rule defines the way in which instabilities lead to discharge from unstable cells to the neighboring cells, deciding upon the landslide direction and the quantity of mass involved. Both the direction and the transferred mass depend on the local topographic features. The scaling properties of the area-frequency distributions of the resulting landslide series are investigated for several rates of weakening and for different time windows, in order to explore the response of the system to model
Anisotropic square lattice Potts ferromagnet: renormalization group treatment
The choice of a convenient self-dual cell within a real space renormalization group framework enables a satisfactory treatment of the anisotropic square lattice q-state Potts ferromagnet criticality. The exact critical frontier and dimensionality crossover exponent PHI as well as the expected universality behaviour (renormalization flow sense) are recovered for any linear scaling factor b and all values of q(q -< 4). The b = 2 and b = 3 approximate correlation lenght critical exponent ν is calculated for all values of q and compared with den Nijs conjecture. The same calculation is performed, for all values of b, for the exponent ν(d=1) associated to the one-dimensional limit and the exact result ν (d=1) = 1 is recovered in the limit b → infinite. (Author)
Cellular Automata Models Applied to the Study of Landslide Dynamics
Liucci, Luisa; Melelli, Laura; Suteanu, Cristian
2015-04-01
Landslides are caused by complex processes controlled by the interaction of numerous factors. Increasing efforts are being made to understand the spatial and temporal evolution of this phenomenon, and the use of remote sensing data is making significant contributions in improving forecast. This paper studies landslides seen as complex dynamic systems, in order to investigate their potential Self Organized Critical (SOC) behavior, and in particular, scale-invariant aspects of processes governing the spatial development of landslides and their temporal evolution, as well as the mechanisms involved in driving the system and keeping it in a critical state. For this purpose, we build Cellular Automata Models, which have been shown to be capable of reproducing the complexity of real world features using a small number of variables and simple rules, thus allowing for the reduction of the number of input parameters commonly used in the study of processes governing landslide evolution, such as those linked to the geomechanical properties of soils. This type of models has already been successfully applied in studying the dynamics of other natural hazards, such as earthquakes and forest fires. The basic structure of the model is composed of three modules: (i) An initialization module, which defines the topographic surface at time zero as a grid of square cells, each described by an altitude value; the surface is acquired from real Digital Elevation Models (DEMs). (ii) A transition function, which defines the rules used by the model to update the state of the system at each iteration. The rules use a stability criterion based on the slope angle and introduce a variable describing the weakening of the material over time, caused for example by rainfall. The weakening brings some sites of the system out of equilibrium thus causing the triggering of landslides, which propagate within the system through local interactions between neighboring cells. By using different rates of
Genetic Algorithm Calibration of Probabilistic Cellular Automata for Modeling Mining Permit Activity
Louis, S.J.; Raines, G.L.
2003-01-01
We use a genetic algorithm to calibrate a spatially and temporally resolved cellular automata to model mining activity on public land in Idaho and western Montana. The genetic algorithm searches through a space of transition rule parameters of a two dimensional cellular automata model to find rule parameters that fit observed mining activity data. Previous work by one of the authors in calibrating the cellular automaton took weeks - the genetic algorithm takes a day and produces rules leading to about the same (or better) fit to observed data. These preliminary results indicate that genetic algorithms are a viable tool in calibrating cellular automata for this application. Experience gained during the calibration of this cellular automata suggests that mineral resource information is a critical factor in the quality of the results. With automated calibration, further refinements of how the mineral-resource information is provided to the cellular automaton will probably improve our model.
The similia principle: results obtained in a cellular model system.
Wiegant, Fred; Van Wijk, Roeland
2010-01-01
This paper describes the results of a research program focused on the beneficial effect of low dose stress conditions that were applied according to the similia principle to cells previously disturbed by more severe stress conditions. In first instance, we discuss criteria for research on the similia principle at the cellular level. Then, the homologous ('isopathic') approach is reviewed, in which the initial (high dose) stress used to disturb cellular physiology and the subsequent (low dose) stress are identical. Beneficial effects of low dose stress are described in terms of increased cellular survival capacity and at the molecular level as an increase in the synthesis of heat shock proteins (hsps). Both phenomena reflect a stimulation of the endogenous cellular self-recovery capacity. Low dose stress conditions applied in a homologous approach stimulate the synthesis of hsps and enhance survival in comparison with stressed cells that were incubated in the absence of low dose stress conditions. Thirdly, the specificity of the low dose stress condition is described where the initial (high dose) stress is different in nature from the subsequently applied (low dose) stress; the heterologous or 'heteropathic' approach. The results support the similia principle at the cellular level and add to understanding of how low dose stress conditions influence the regulatory processes underlying self-recovery. In addition, the phenomenon of 'symptom aggravation' which is also observed at the cellular level, is discussed in the context of self-recovery. Finally, the difference in efficiency between the homologous and the heterologous approach is discussed; a perspective is indicated for further research; and the relationship between studies on the similia principle and the recently introduced concept of 'postconditioning hormesis' is emphasized. PMID:20129172
Cellular-automata model of the dwarf shrubs populations and communities dynamics
A. S. Komarov; E. V. Zubkova; P. V. Frolov
2015-01-01
The probabilistic cellular-automata model of development and long-time dynamics of dwarf shrub populations and communities is developed. It is based on the concept of discrete description of the plant ontogenesis and joint model approaches in terms of probabilistic cellular automata and L-systems by Lindenmayer. Short representation of the basic model allows evaluation of the approach and software implementation. The main variables of the model are a number of partial bushes in clones or area...
Stochastic Models of Vesicular Sorting in Cellular Organelles
Vagne, Quentin
2016-01-01
The proper sorting of membrane components by regulated exchange between cellular organelles is crucial to intra-cellular organization. This process relies on the budding and fusion of transport vesicles, and should be strongly influenced by stochastic fluctuations considering the relatively small size of many organelles. We identify the perfect sorting of two membrane components initially mixed in a single compartment as a first passage process, and we show that the mean sorting time exhibits two distinct regimes as a function of the ratio of vesicle fusion to budding rates. Low ratio values leads to fast sorting, but results in a broad size distribution of sorted compartments dominated by small entities. High ratio values result in two well defined sorted compartments but is exponentially slow. Our results suggests an optimal balance between vesicle budding and fusion for the rapid and efficient sorting of membrane components, and highlight the importance of stochastic effects for the steady-state organizati...
Mathematical models and multiscale simulations of cellular secretion processes
González-Vélez, Virginia
2011-01-01
Exocytosis is the cellular process whereby a product such as a hormone or a neurotransmitter is released as a response to stimulation. There are a lot of exocytotic cells in mammals, and each cell type has their specific subcellular mechanisms, needed to achieve the final substance release. Therefore, unveiling the role of subcellular mechanisms in secretion processes is highly relevant to understand disease evolution and possible therapies. The efficiency of the coupling between stimulus...
A Large Deformation Model for the Elastic Moduli of Two-dimensional Cellular Materials
HU Guoming; WAN Hui; ZHANG Youlin; BAO Wujun
2006-01-01
We developed a large deformation model for predicting the elastic moduli of two-dimensional cellular materials. This large deformation model was based on the large deflection of the inclined members of the cells of cellular materials. The deflection of the inclined member, the strain of the representative structure and the elastic moduli of two-dimensional cellular materials were expressed using incomplete elliptic integrals. The experimental results show that these elastic moduli are no longer constant at large deformation, but vary significantly with the strain. A comparison was made between this large deformation model and the small deformation model proposed by Gibson and Ashby.
Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results
Van Liedekerke, P.; Palm, M. M.; Jagiella, N.; Drasdo, D.
2015-12-01
In this paper we present an overview of agent-based models that are used to simulate mechanical and physiological phenomena in cells and tissues, and we discuss underlying concepts, limitations, and future perspectives of these models. As the interest in cell and tissue mechanics increase, agent-based models are becoming more common the modeling community. We overview the physical aspects, complexity, shortcomings, and capabilities of the major agent-based model categories: lattice-based models (cellular automata, lattice gas cellular automata, cellular Potts models), off-lattice models (center-based models, deformable cell models, vertex models), and hybrid discrete-continuum models. In this way, we hope to assist future researchers in choosing a model for the phenomenon they want to model and understand. The article also contains some novel results.
A mathematical model of amphibian skin epithelium with two types of transporting cellular units
Larsen, Erik Hviid; Rasmussen, B E
1985-01-01
A computer model of ion transport across amphibian skin epithelium containing two types of cellular units, their relative number and sizes, and a paracellular pathway has been developed. The two cellular units are, a large Na+ transporting compartment representing the major epithelium from stratum...
Predictive model to describe water migration in cellular solid foods during storage
Voogt, J.A.; Hirte, A.; Meinders, M.B.J.
2011-01-01
BACKGROUND: Water migration in cellular solid foods during storage causes loss of crispness. To improve crispness retention, physical understanding of this process is needed. Mathematical models are suitable tools to gain this physical knowledge. RESULTS: Water migration in cellular solid foods invo
Excellent approach to modeling urban expansion by fuzzy cellular automata: agent base model
Khajavigodellou, Yousef; Alesheikh, Ali A.; Mohammed, Abdulrazak A. S.; Chapi, Kamran
2014-09-01
Recently, the interaction between humans and their environment is the one of important challenges in the world. Landuse/ cover change (LUCC) is a complex process that includes actors and factors at different social and spatial levels. The complexity and dynamics of urban systems make the applicable practice of urban modeling very difficult. With the increased computational power and the greater availability of spatial data, micro-simulation such as the agent based and cellular automata simulation methods, has been developed by geographers, planners, and scholars, and it has shown great potential for representing and simulating the complexity of the dynamic processes involved in urban growth and land use change. This paper presents Fuzzy Cellular Automata in Geospatial Information System and remote Sensing to simulated and predicted urban expansion pattern. These FCA-based dynamic spatial urban models provide an improved ability to forecast and assess future urban growth and to create planning scenarios, allowing us to explore the potential impacts of simulations that correspond to urban planning and management policies. A fuzzy inference guided cellular automata approach. Semantic or linguistic knowledge on Land use change is expressed as fuzzy rules, based on which fuzzy inference is applied to determine the urban development potential for each pixel. The model integrates an ABM (agent-based model) and FCA (Fuzzy Cellular Automata) to investigate a complex decision-making process and future urban dynamic processes. Based on this model rapid development and green land protection under the influences of the behaviors and decision modes of regional authority agents, real estate developer agents, resident agents and non- resident agents and their interactions have been applied to predict the future development patterns of the Erbil metropolitan region.
Dynamic modeling of cellular response to DNA damage based on p53 stress response networks
Jinpeng Qi; Yongsheng Ding; Shihuang Shao
2009-01-01
Under acute perturbations from the outside, cells can trigger self-defensive mechanisms to fight against genome stress. To investigate the cellular response to continuous ion radiation (IR), a dynamic model for p53 stress response networks at the cellular level is proposed. The model can successfully be used to simulate the dynamic processes of double-strand breaks (DSBs) generation and their repair, switch-like ataxia telangiectasia mutated (ATM) activation, oscillations occurring in the p53-MDM2 feedback loop, as well as toxins elimination triggered by p53 stress response networks. Especially, the model can predict the plausible outcomes of cellular response under different IR dose regimes.
Modeling and Analysis of Cellular Networks using Stochastic Geometry: A Tutorial
ElSawy, Hesham
2016-03-22
This paper presents a tutorial on stochastic geometry (SG) based analysis for cellular networks. This tutorial is distinguished by its depth with respect to wireless communication details and its focus on cellular networks. The paper starts by modeling and analyzing the baseband interference in a basic cellular network model. Then, it characterizes signal-tointerference- plus-noise-ratio (SINR) and its related performance metrics. In particular, a unified approach to conduct error probability, outage probability, and rate analysis is presented. Although the main focus of the paper is on cellular networks, the presented unified approach applies for other types of wireless networks that impose interference protection around receivers. The paper then extends the baseline unified approach to capture cellular network characteristics (e.g., frequency reuse, multiple antenna, power control, etc.). It also presents numerical examples associated with demonstrations and discussions. Finally, we point out future research directions.
Cellular Automation Model of Traffic Flow Based on the Car-Following Model
LI Ke-Ping; GAO Zi-You
2004-01-01
@@ We propose a new cellular automation (CA) traffic model that is based on the car-following model. A class of driving strategies is used in the car-following model instead of the acceleration in the NaSch traffic model. In our model, some realistic driver behaviour and detailed vehicle characteristics have been taken into account, such as distance-headway and safe distance, etc. The simulation results show that our model can exhibit some traffic flow states that have been observed in the real traffic, and both of the maximum flux and the critical density are very close to the real measurement. Moreover, it is easy to extend our method to multi-lane traffic.
Kapitanov, Georgi I.; Wang, Xiayi; Ayati, Bruce P; Brouillette, Marc J.; Martin, James A.
2016-01-01
A severe application of stress on articular cartilage can initiate a cascade of biochemical reactions that can lead to the development of osteoarthritis. We constructed a multiscale mathematical model of the process with three components: cellular, chemical, and mechanical. The cellular component describes the different chondrocyte states according to the chemicals these cells release. The chemical component models the change in concentrations of those chemicals. The mechanical component cont...
Excitation spectrum and correlation functions of the Z3 chiral Potts quantum spin chain
We study the excitation spectrum and the correlation functions of the Z3 chiral Potts model in the massive high-temperature phase using perturbation expansions and numerical diagonalization. We are mainly interested in results for general chiral angles but we consider also the superintegrable case. For the parameter values considered, we find that the band structure of the low-lying part of the excitation spectrum has the form expected from a quasiparticle picture with two fundamental particles. Studying the chain-size dependence of the spectrum, we find a remarkable stability of the second fundamental particle in a limited range of the momentum, even when its energy becomes so high that it lies very high up among the multiparticle scattering states. This is not a phenomenon restricted to the superintegrable line. Calculating a non-translationally invariant correlation function, we give evidence that it is oscillating. Within our numerical accuracy we find a relation between the oscillation length and the dip position of the momentum dispersion of the lightest particle which seems to be quite independent of the chiral angles. ((orig.))
Simulation Modeling by Classification of Problems: A Case of Cellular Manufacturing
Afiqah, K. N.; Mahayuddin, Z. R.
2016-02-01
Cellular manufacturing provides good solution approach to manufacturing area by applying Group Technology concept. The evolution of cellular manufacturing can enhance performance of the cell and to increase the quality of the product manufactured but it triggers other problem. Generally, this paper highlights factors and problems which emerge commonly in cellular manufacturing. The aim of the research is to develop a thorough understanding of common problems in cellular manufacturing. A part from that, in order to find a solution to the problems exist using simulation technique, this classification framework is very useful to be adapted during model building. Biology evolution tool was used in the research in order to classify the problems emerge. The result reveals 22 problems and 25 factors using cladistic technique. In this research, the expected result is the cladogram established based on the problems in cellular manufacturing gathered.
Cellular cardiac electrophysiology modeling with Chaste and CellML
Cooper, Jonathan; Spiteri, Raymond J.; Mirams, Gary R
2014-01-01
Chaste is an open-source C++ library for computational biology that has well-developed cardiac electrophysiology tissue simulation support. In this paper, we introduce the features available for performing cardiac electrophysiology action potential simulations using a wide range of models from the Physiome repository. The mathematics of the models are described in CellML, with units for all quantities. The primary idea is that the model is defined in one place (the CellML file), and all model...
Modelling lava flows by Cellular Nonlinear Networks (CNN: preliminary results
C. Del Negro
2005-01-01
Full Text Available The forecasting of lava flow paths is a complex problem in which temperature, rheology and flux-rate all vary with space and time. The problem is more difficult to solve when lava runs down a real topography, considering that the relations between characteristic parameters of flow are typically nonlinear. An alternative approach to this problem that does not use standard differential equation methods is Cellular Nonlinear Networks (CNNs. The CNN paradigm is a natural and flexible framework for describing locally interconnected, simple, dynamic systems that have a lattice-like structure. They consist of arrays of essentially simple, nonlinearly coupled dynamic circuits containing linear and non-linear elements able to process large amounts of information in real time. Two different approaches have been implemented in simulating some lava flows. Firstly, a typical technique of the CNNs to analyze spatio-temporal phenomena (as Autowaves in 2-D and in 3-D has been utilized. Secondly, the CNNs have been used as solvers of partial differential equations of the Navier-Stokes treatment of Newtonian flow.
Study of phase separation using liquid-gas model of lattice-gas cellular automata
This report describes the study of phase separation by the liquid gas model of lattice gas cellular automata. The lattice gas cellular automaton is one model for simulating fluid phenomena which was proposed by Frisch, Hasslacher and Pomeau in 1986. In 1990, Appert and Zaleski added a new long-range interaction to lattice gas cellular automata to construct a model, the liquid-gas model, which could simulate phase separation using lattice-gas cellular automata. Gerits et al formulated the liquid-gas model mathematically using the theory of statistical dynamics in 1993 and explained the mechanism of phase separation in the liquid-gas model using the equation of state. At first this report explains the FHP model of lattice gas cellular automata and derives fluid dynamics equations such as the equation of continuity and the Navier-Stokes equation. Then the equation of state for the liquid-gas model which was derived by Gerits et al is modified by adding the interactions which were proposed by Appert but not considered by Gerits et al. The modified equation of state is verified by the computer simulation using the liquid gas model. The relation between phase separation and the equation of state is discussed. (author)
ZHU Ming-fang; CAO Wei-sheng; CHEN Shuang-lin; XIE Fan-you; HONG Chunpyo; CHANG Y. Austin
2006-01-01
A modified cellular automaton (MCA) model has been extended to the ternary alloy system by coupling thermodynamic and phase equilibrium calculation engine PanEngine. In the present model the dendrite growth is driven by the difference between the local equilibrium liquidus temperature and local actual temperature, incorporating the effect of curvature. The local equilibrium liquidus temperature is calculated with PanEngine according to the local liquid concentrations of two solutes, which are determined by numerically solving the species transport equation in the domain. Model validation was carried out through the comparison of the simulated values to the prediction of the Scheil model for solute profiles in the primary dendrites. The simulated data with zero solid diffusivity and limited liquid diffusivity were increasingly close to the Scheil profiles as the solidification rate decreased. The simulated microstructure and microsegregation in an Al-Cu-Mg ternary alloy were compared with those obtained experimentally.
Jeans type instability for a chemotactic model of cellular aggregation
Chavanis, Pierre-Henri
2008-01-01
We consider an inertial model of chemotactic aggregation generalizing the Keller-Segel model and we study the linear dynamical stability of an infinite and homogeneous distribution of cells (bacteria, amoebae, endothelial cells,...) when inertial effects are accounted for. These inertial terms model cells directional persistance. We determine the condition of instability and the growth rate of the perturbation as a function of the cell density and the wavelength of the perturbation. We discuss the differences between overdamped (Keller-Segel) and inertial models. Finally, we show the analogy between the instability criterion for biological populations and the Jeans instability criterion in astrophysics.
From cellular to tissue scales by asymptotic limits of thermostatted kinetic models
Bianca, Carlo; Dogbe, Christian; Lemarchand, Annie
2016-02-01
Tumor growth strictly depends on the interactions occurring at the cellular scale. In order to obtain the linking between the dynamics described at tissue and cellular scales, asymptotic methods have been employed, consisting in deriving tissue equations by suitable limits of mesoscopic models. In this paper, the evolution at the cellular scale is described by thermostatted kinetic theory that include conservative, nonconservative (proliferation, destruction and mutations), stochastic terms, and the role of external agents. The dynamics at the tissue scale (cell-density evolution) is obtained by performing a low-field scaling and considering the related convergence of the rescaled framework when the scaling parameter goes to zero.
Cellular cardiac electrophysiology modeling with Chaste and CellML.
Cooper, Jonathan; Spiteri, Raymond J; Mirams, Gary R
2014-01-01
Chaste is an open-source C++ library for computational biology that has well-developed cardiac electrophysiology tissue simulation support. In this paper, we introduce the features available for performing cardiac electrophysiology action potential simulations using a wide range of models from the Physiome repository. The mathematics of the models are described in CellML, with units for all quantities. The primary idea is that the model is defined in one place (the CellML file), and all model code is auto-generated at compile or run time; it never has to be manually edited. We use ontological annotation to identify model variables describing certain biological quantities (membrane voltage, capacitance, etc.) to allow us to import any relevant CellML models into the Chaste framework in consistent units and to interact with them via consistent interfaces. This approach provides a great deal of flexibility for analysing different models of the same system. Chaste provides a wide choice of numerical methods for solving the ordinary differential equations that describe the models. Fixed-timestep explicit and implicit solvers are provided, as discussed in previous work. Here we introduce the Rush-Larsen and Generalized Rush-Larsen integration techniques, made available via symbolic manipulation of the model equations, which are automatically rearranged into the forms required by these approaches. We have also integrated the CVODE solvers, a 'gold standard' for stiff systems, and we have developed support for symbolic computation of the Jacobian matrix, yielding further increases in the performance and accuracy of CVODE. We discuss some of the technical details of this work and compare the performance of the available numerical methods. Finally, we discuss how this is generalized in our functional curation framework, which uses a domain-specific language for defining complex experiments as a basis for comparison of model behavior. PMID:25610400
A study of a main-road cellular automata traffic flow model
黄乒花; 孔令江; 刘慕仁
2002-01-01
A main-road cellular automata traffic flow model on two dimensions is presented based on the Biham-Middleton-Levine traffic model. Its evolution equations are given and the self-organization and organization cooperation phenomenain this model are also studied by using computer simulation.
Propagation Path Loss Models for 5G Urban Micro- and Macro-Cellular Scenarios
Sun, Shu; Rappaport, Theodore S.; Rangan, Sundeep;
2016-01-01
This paper presents and compares two candidate large-scale propagation path loss models, the alpha-beta-gamma (ABG) model and the close-in (CI) free space reference distance model, for the design of fifth generation (5G) wireless communication systems in urban micro- and macro-cellular scenarios...
Jokar Arsanjani, J.; Helbich, M.; Kainz, W.; Boloorani, A.
2013-01-01
This research analyses the suburban expansion in the metropolitan area of Tehran, Iran. A hybrid model consisting of logistic regression model, Markov chain (MC), and cellular automata (CA) was designed to improve the performance of the standard logistic regression model. Environmental and socio-eco
On Modeling Coverage and Rate of Random Cellular Networks under Generic Channel Fading
Al-Hourani, Akram; Kandeepan, Sithamparanathan
2016-01-01
In this paper we provide an analytic framework for computing the expected downlink coverage probability, and the associated data rate of cellular networks, where base stations are distributed in a random manner. The provided expressions are in computable integral forms that accommodate generic channel fading conditions. We develop these expressions by modelling the cellular interference using stochastic geometry analysis, then we employ them for comparing the coverage resulting from various c...
A cellular network model with Ginibre configured base stations
Miyoshi, Naoto; Shirai, Tomoyuki
2014-01-01
Stochastic geometry models for wireless communication networks have recently attracted much attention. This is because the performance of such networks critically depends on the spatial configuration of wireless nodes and the irregularity of the node configuration in a real network can be captured by a spatial point process. However, most analysis of such stochastic geometry models for wireless networks assumes, owing to its tractability, that the wireless nodes are deployed...
A cellular automata model for simulating fed-batch penicillin fermentation process
Yu Naigong; Ruan Xiaogang
2006-01-01
A cellular automata model to simulate penicillin fed-batch fermentation process(CAPFM)was established in this study,based on a morphologically structured dynamic penicillin production model,that is in turn based on the growth mechanism of penicillin producing microorganisms and the characteristics of penicillin fed-batch fermentation.CAPFM uses the three-dimensional cellular automata as a growth space,and a Moore-type neighborhood as the cellular neighborhood.The transition roles of CAPFM are designed based on mechanical and structural kinetic models of penicillin batch-fed fermentation processes.Every cell of CAPFM represents a single or specific number of penicillin producing microorganisms,and has various state.The simulation experimental results show that CAPFM replicates the evolutionary behavior of penicillin batch-fed fermentation processes described by the structured penicillin production kinetic model accordingly.