Journal articles: 'Network Lattice'

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KAMEI, HIROKO. "CONSTRUCTION OF LATTICES OF BALANCED EQUIVALENCE RELATIONS FOR REGULAR HOMOGENEOUS NETWORKS USING LATTICE GENERATORS AND LATTICE INDICES." International Journal of Bifurcation and Chaos 19, no. 11 (November 2009): 3691–705. http://dx.doi.org/10.1142/s0218127409025067.

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Regular homogeneous networks are a class of coupled cell network, which comprises one type of cell (node) with one type of coupling (arrow), and each cell has the same number of input arrows (called the valency of the network). In coupled cell networks, robust synchrony (a flow-invariant polydiagonal) corresponds to a special kind of partition of cells, called a balanced equivalence relation. Balanced equivalence relations are determined solely by the network structure. It is well known that the set of balanced equivalence relations on a given finite network forms a complete lattice. In this paper, we consider regular homogeneous networks in which the internal dynamics of each cell is one-dimensional, and whose associated adjacency matrices have simple eigenvalues (real or complex). We construct explicit forms of lattices of balanced equivalence relations for such networks by introducing key building blocks, called lattice generators, along with integer numbers called lattice indices. The properties of lattice indices allow construction of all possible lattice structures for balanced equivalence relations of regular homogeneous networks of any number of cells with any valency. As an illustration, we show all 14 possible lattice structures of balanced equivalence relations for four-cell regular homogeneous networks.

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KENDZIORRA, ANDREAS, and STEFAN E. SCHMIDT. "NETWORK CODING WITH MODULAR LATTICES." Journal of Algebra and Its Applications 10, no. 06 (December 2011): 1319–42. http://dx.doi.org/10.1142/s0219498811005208.

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Kötter and Kschischang presented in 2008 a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this alphabet is the map d : (U, V) ↦ dim (U+V)- dim (U∩V). In this paper we generalize this model to arbitrary modular lattices, i.e. we consider codes, which are subsets of modular lattices. The used metric in this general case is the map d : (u, v) ↦ h(u ∨ v) - h(u ∧ v), where h is the height function of the lattice. We apply this model to submodule lattices. Moreover, we show a method to compute the size of spheres in certain modular lattices and present a sphere packing bound, a sphere covering bound, and a Singleton bound for codes, which are subsets of modular lattices.

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Joewondo, Nerine, Valeria Garbin, and Ronny Pini. "Nonuniform Collective Dissolution of Bubbles in Regular Pore Networks." Transport in Porous Media 141, no. 3 (January 12, 2022): 649–66. http://dx.doi.org/10.1007/s11242-021-01740-w.

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AbstractUnderstanding the evolution of solute concentration gradients underpins the prediction of porous media processes limited by mass transfer. Here, we present the development of a mathematical model that describes the dissolution of spherical bubbles in two-dimensional regular pore networks. The model is solved numerically for lattices with up to 169 bubbles by evaluating the role of pore network connectivity, vacant lattice sites and the initial bubble size distribution. In dense lattices, diffusive shielding prolongs the average dissolution time of the lattice, and the strength of the phenomenon depends on the network connectivity. The extension of the final dissolution time relative to the unbounded (bulk) case follows the power-law function, $${B^k/\ell }$$ B k / ℓ , where the constant $$\ell$$ ℓ is the inter-bubble spacing, B is the number of bubbles, and the exponent k depends on the network connectivity. The solute concentration field is both the consequence and a factor affecting bubble dissolution or growth. The geometry of the pore network perturbs the inward propagation of the dissolution front and can generate vacant sites within the bubble lattice. This effect is enhanced by increasing the lattice size and decreasing the network connectivity, yielding strongly nonuniform solute concentration fields. Sparse bubble lattices experience decreased collective effects, but they feature a more complex evolution, because the solute concentration field is nonuniform from the outset.

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Ostoja-Starzewski, Martin. "Lattice models in micromechanics." Applied Mechanics Reviews 55, no. 1 (January 1, 2002): 35–60. http://dx.doi.org/10.1115/1.1432990.

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This review presents the potential that lattice (or spring network) models hold for micromechanics applications. The models have their origin in the atomistic representations of matter on one hand, and in the truss-type systems in engineering on the other. The paper evolves by first giving a rather detailed presentation of one-dimensional and planar lattice models for classical continua. This is followed by a section on applications in mechanics of composites and key computational aspects. We then return to planar lattice models made of beams, which are a discrete counterpart of non-classical continua. The final two sections of the paper are devoted to issues of connectivity and rigidity of networks, and lattices of disordered (rather than periodic) topology. Spring network models offer an attractive alternative to finite element analyses of planar systems ranging from metals, composites, ceramics and polymers to functionally graded and granular materials, whereby a fiber network model of paper is treated in considerable detail. This review article contains 81 references.

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Favoni, Matteo, Andreas Ipp, and David I. Müller. "Applications of Lattice Gauge Equivariant Neural Networks." EPJ Web of Conferences 274 (2022): 09001. http://dx.doi.org/10.1051/epjconf/202227409001.

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The introduction of relevant physical information into neural network architectures has become a widely used and successful strategy for improving their performance. In lattice gauge theories, such information can be identified with gauge symmetries, which are incorporated into the network layers of our recently proposed Lattice Gauge Equivariant Convolutional Neural Networks (L-CNNs). L-CNNs can generalize better to differently sized lattices than traditional neural networks and are by construction equivariant under lattice gauge transformations. In these proceedings, we present our progress on possible applications of L-CNNs to Wilson flow or continuous normalizing flow. Our methods are based on neural ordinary differential equations which allow us to modify link configurations in a gauge equivariant manner. For simplicity, we focus on simple toy models to test these ideas in practice.

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KAMEI, HIROKO. "THE EXISTENCE AND CLASSIFICATION OF SYNCHRONY-BREAKING BIFURCATIONS IN REGULAR HOMOGENEOUS NETWORKS USING LATTICE STRUCTURES." International Journal of Bifurcation and Chaos 19, no. 11 (November 2009): 3707–32. http://dx.doi.org/10.1142/s0218127409025079.

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For regular homogeneous networks with simple eigenvalues (real or complex), all possible explicit forms of lattices of balanced equivalence relations can be constructed by introducing lattice generators and lattice indices [Kamei, 2009]. Balanced equivalence relations in the lattice correspond to clusters of partially synchronized cells in a network. In this paper, we restrict attention to regular homogeneous networks with simple real eigenvalues, and one-dimensional internal dynamics for each cell. We first show that lattice elements with nonzero indices indicate the existence of codimension-one synchrony-breaking steady-state bifurcations, and furthermore, the positions of such lattice elements give the number of partially synchronized clusters. Using four-cell regular homogeneous networks as an example, we then classify a large number of regular homogeneous networks into a small number of lattice structures, in which networks share an equivalent clustering type. Indeed, some of these networks even share the same generic bifurcation structure. This classification leads us to explore how regular homogeneous networks that share synchrony-breaking bifurcation structure are topologically related.

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Stewart, Ian. "Exotic Patterns of Synchrony in Planar Lattice Networks." International Journal of Bifurcation and Chaos 29, no. 02 (February 2019): 1930003. http://dx.doi.org/10.1142/s0218127419300039.

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Patterns of dynamical synchrony that can occur robustly in networks of coupled dynamical systems are associated with balanced colorings of the nodes of the network. In symmetric networks, the orbits of any group of symmetries automatically determine a balanced orbit coloring. Balanced colorings not of this kind are said to be exotic. Exotic colorings occur in infinite planar lattices, both square and hexagonal, with various short-range couplings. In some cases, a balanced two-coloring remains balanced when colors are swapped along suitable diagonals, giving rise to uncountably many distinct exotic colorings. We explain this phenomenon in terms of iterated orbit colorings, in which the quotient of the lattice by an orbit coloring has extra symmetries, allowing new orbit colorings on the quotient, which then lift back to the lattice. We apply the same construction to several other exotic lattice colorings. Two appendices discuss how to modify the notion of balance for networks with diffusive coupling, and how to formalize the differential equations in infinitely many variables that arise for lattices.

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Akιn, H. "Phase diagrams of lattice models on Cayley tree and chandelier network: a review." Condensed Matter Physics 25, no. 3 (2022): 32501. http://dx.doi.org/10.5488/cmp.25.32501.

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The main purpose of this review paper is to give systematically all the known results on phase diagrams corresponding to lattice models (Ising and Potts) on Cayley tree (or Bethe lattice) and chandelier networks. A detailed survey of various modelling applications of lattice models is reported. By using Vannimenus's approach, the recursive equations of Ising and Potts models associated to a given Hamiltonian on the Cayley tree are presented and analyzed. The corresponding phase diagrams with programming codes in different programming languages are plotted. To detect the phase transitions in the modulated phase, we investigate in detail the actual variation of the wave-vector q with temperature and the Lyapunov exponent associated with the trajectory of our current recursive system. We determine the transition between commensurate (C) and incommensurate (I) phases by means of the Lyapunov exponents, wave-vector, and strange attractor for a comprehensive comparison. We survey the dynamical behavior of the Ising model on the chandelier network. We examine the phase diagrams of the Ising model corresponding to a given Hamiltonian on a new type of "Cayley-tree-like lattice", such as triangular, rectangular, pentagonal chandelier networks (lattices). Moreover, several open problems are discussed.

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Dias, Ana Paula S., and Eliana Manuel Pinho. "Enumerating periodic patterns of synchrony via finite bidirectional networks." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2115 (November 16, 2009): 891–910. http://dx.doi.org/10.1098/rspa.2009.0404.

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Periodic patterns of synchrony are lattice networks whose cells are coloured according to a local rule, or balanced colouring, and such that the overall system has spatial periodicity. These patterns depict the finite-dimensional flow-invariant subspaces for all the lattice dynamical systems, in the given lattice network, that exhibit those periods. Previous results relate the existence of periodic patterns of synchrony, in n -dimensional Euclidean lattice networks with nearest neighbour coupling architecture, with that of finite coupled cell networks that follow the same colouring rule and have all the couplings bidirectional. This paper addresses the relation between periodic patterns of synchrony and finite bidirectional coloured networks. Given an n -dimensional Euclidean lattice network with nearest neighbour coupling architecture, and a colouring rule with k colours, we enumerate all the periodic patterns of synchrony generated by a given finite network, or graph. This enumeration is constructive and based on the automorphisms group of the graph.

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Bang, Wonbae, M. T. Kaffash, M. T. Hossain, A. Hoffmann, J. B. Ketterson, and M. B. Jungfleisch. "Spin dynamics in permalloy nano-ellipses for honeycomb and square lattices." AIP Advances 12, no. 3 (March 1, 2022): 035131. http://dx.doi.org/10.1063/9.0000307.

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We report experimental and theoretical studies of spin dynamics in lattice structures of permalloy (Ni80Fe20) nano-ellipses, with four different types of networks including honeycomb and square lattices. The lattices are patterned at the center line of the co-planar wave guide and consist of non-contacting or contacting ellipses. Micromagnetic simulations show excellent agreement with the broadband ferromagnetic resonance (FMR) experimental results. We find the existence of a spin-wave mode localized in the vertex region of the contacting nano-ellipse network. Our finding has important implications when designing an artificial spin ice (ASI) network for functional magnonics.

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Stewart, Ian, and Dinis Gökaydin. "Symmetries of Quotient Networks for Doubly Periodic Patterns on the Hexagonal Lattice." International Journal of Bifurcation and Chaos 30, no. 02 (February 2020): 2030004. http://dx.doi.org/10.1142/s0218127420300049.

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Pattern formation, dynamics and bifurcations for lattice models are strongly influenced by the symmetry of the lattice. However, network structure introduces additional constraints, which sometimes affect the resulting behavior. We compute the automorphism groups of all doubly periodic quotient networks of the hexagonal lattice with nearest-neighbor coupling, with emphasis on “exotic” cases where this quotient network has extra automorphisms not induced by automorphisms of the square lattice. These cases comprise three isolated networks and two infinite families with wreath product structure. We briefly discuss the implications for pattern formation, dynamics and bifurcations. This paper is a sequel to a similar analysis of the square lattice and uses similar methods.

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ASAD, J. H., R. S. HIJJAWI, A. J. SAKAJI, and J. M. KHALIFEH. "INFINITE NETWORK OF IDENTICAL CAPACITORS BY GREEN'S FUNCTION." International Journal of Modern Physics B 19, no. 24 (September 30, 2005): 3713–21. http://dx.doi.org/10.1142/s0217979205032401.

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The capacitance between arbitrary nodes in perfect infinite networks of identical capacitors is studied. We calculate the capacitance between the origin and the lattice site (l, m) for an infinite linear chain, and for an infinite square network consisting of identical capacitors using the Lattice Green's Function. The asymptotic behavior of the capacitance for an infinite square lattice is investigated for infinite separation between the origin and the site (l, m). We point out the relation between the capacitance of the lattice and the van Hove singularity of the tight-binding Hamiltonian. This method can be applied directly to other lattice structures.

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13

STEWART, IAN. "The lattice of balanced equivalence relations of a coupled cell network." Mathematical Proceedings of the Cambridge Philosophical Society 143, no. 1 (July 2007): 165–83. http://dx.doi.org/10.1017/s0305004107000345.

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AbstractA coupled cell system is a collection of dynamical systems, or ‘cells’, that are coupled together. The associated coupled cell network is a labelled directed graph that indicates how the cells are coupled, and which cells are equivalent. Golubitsky, Stewart, Pivato and Török have presented a framework for coupled cell systems that permits a classification of robust synchrony in terms of the concept of a ‘balanced equivalence relation’, which depends solely on the network architecture. In their approach the network is assumed to be finite. We prove that the set of all balanced equivalence relations on a network forms a lattice, in the sense of a partially ordered set in which any two elements have a meet and a join. The partial order is defined by refinement. Some aspects of the theory make use of infinite networks, so we work in the category of networks of ‘finite type’, a class that includes all locally finite networks. This context requires some modifications to the standard framework. As partial compensation, the lattice of balanced equivalence relations can then be proved complete. However, the intersection of two balanced equivalence relations need not be balanced, as we show by a simple example, so this lattice is not a sublattice of the lattice of all equivalence relations with its usual operations of meet and join. We discuss the structure of this lattice and computational issues associated with it. In particular, we describe how to determine whether the lattice contains more than the equality relation. As an example, we derive the form of the lattice for a linear chain of identical cells with feedback.

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OUYANG, QI, KAI SUN, and HONGLI WANG. "MICROSCOPIC SELF-ORGANIZATION IN NETWORKS AND REGULAR LATTICE." Modern Physics Letters B 16, no. 25 (October 30, 2002): 923–35. http://dx.doi.org/10.1142/s0217984902004391.

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We report our numerical studies on the microscopic self-organizations of a reaction system in three types of networks: a regular network, a small-world network, and a random network as well as on a regular lattice. Our simulation results show that the topology of the network has an important effect on the communication among reaction molecules, and plays an important role in microscopic self-organization. The correlation length among reacting molecules in a random or a small-world network is much shorter compared with that in the regular network. As a result, it is much easier to obtain a microscopic self-organization in a small-world or a random network. A phase transition from a stochastic state to a synchronized state was observed when the randomness of a small-world network was increased. We also demonstrate that good synchronization activities of enzymatic turnover cycles can be developed on a regular lattice when the correlation length created by the fast diffusion of regulatory particles is large enough.

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Español, Malena I., Dmitry Golovaty, and J. Patrick Wilber. "Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2209 (January 2018): 20170612. http://dx.doi.org/10.1098/rspa.2017.0612.

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In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

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Pretti, M., C. Buzano, and E. De Stefanis. "Revisiting waterlike network-forming lattice models." Journal of Chemical Physics 131, no. 22 (December 14, 2009): 224508. http://dx.doi.org/10.1063/1.3270000.

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Stewart, Ian, and Dinis Gökaydin. "Symmetries of Quotient Networks for Doubly Periodic Patterns on the Square Lattice." International Journal of Bifurcation and Chaos 29, no. 10 (September 2019): 1930026. http://dx.doi.org/10.1142/s021812741930026x.

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Patterns of synchrony in networks of coupled dynamical systems can be represented as colorings of the nodes, in which nodes of the same color are synchronous. Balanced colorings, where nodes of the same color have color-isomorphic input sets, correspond to dynamically invariant subspaces, which can have a significant effect on the typical bifurcations of network dynamical systems. Orbit colorings for subgroups of the automorphism (symmetry) group of the network are always balanced, although the converse is false. We compute the automorphism groups of all doubly periodic quotient networks of the square lattice with nearest-neighbor coupling, and classify the “exotic” cases where this quotient network has extra automorphisms not induced by automorphisms of the square lattice. These comprise five isolated exceptions and two infinite families with wreath product symmetry. We also comment briefly on implications for bifurcations to doubly periodic patterns in square lattice models.

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Zeng, Ziyan, Qin Li, and Minyu Feng. "Spatial evolution of cooperation with variable payoffs." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 7 (July 2022): 073118. http://dx.doi.org/10.1063/5.0099444.

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In the evolution of cooperation, the individuals’ payoffs are commonly random in real situations, e.g., the social networks and the economic regions, leading to unpredictable factors. Therefore, there are chances for each individual to obtain the exceeding payoff and risks to get the low payoff. In this paper, we consider that each individual’s payoff follows a specific probability distribution with a fixed expectation, where the normal distribution and the exponential distribution are employed in our model. In the simulations, we perform the models on the weak prisoner’s dilemmas (WPDs) and the snowdrift games (SDGs), and four types of networks, including the hexagon lattice, the square lattice, the small-world network, and the triangular lattice are considered. For the individuals’ normally distributed payoff, we find that the higher standard deviation usually inhibits the cooperation for the WPDs but promotes the cooperation for the SDGs. Besides, with a higher standard deviation, the cooperation clusters are usually split for the WPDs but constructed for the SDGs. For the individuals’ exponentially distributed payoff, we find that the small-world network provides the best condition for the emergence of cooperators in WPDs and SDGs. However, when playing SDGs, the small-world network allows the smallest space for the pure cooperative state while the hexagon lattice allows the largest.

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ZHAO, HUI, and ZIYOU GAO. "GENERALIZED SHORTEST PATH AND TRAFFIC EQUILIBRIUM IN COMPLEX TRANSPORTATION NETWORKS." Modern Physics Letters B 21, no. 20 (August 30, 2007): 1343–49. http://dx.doi.org/10.1142/s021798490701350x.

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Shortest path plays an important role in the study of complex networks. But in real transportation systems, choosing the shortest path may not be the best way for the drivers. Based on the traffic equilibrium theory, we generalize the concept of shortest path. Flux distribution is also investigated by using the generalized concept on various types of complex networks. We find that the flux differs little in all the edges of lattice while in small-world and scale-free networks, the flux distribution follows a power law, and in the random network, the flux distribution has an exponential tail. We consider lattice may be the optimal topology in design a transportation network.

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HIJJAWI, R. S., J. H. ASAD, A. J. SAKAJI, and J. M. KHALIFEH. "PERTURBATION OF AN INFINITE NETWORK OF IDENTICAL CAPACITORS." International Journal of Modern Physics B 21, no. 02 (January 20, 2007): 199–209. http://dx.doi.org/10.1142/s0217979207035972.

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The capacitance between any two arbitrary lattice sites in an infinite square lattice is studied when one bond is removed (i.e. perturbed). A connection is made between the capacitance and the lattice Green's function of the perturbed network, where they are expressed in terms of those of the perfect network. The asymptotic behavior of the perturbed capacitance is investigated as the separation between the two sites goes to infinity. Finally, numerical results are obtained along different directions and a comparison is made with the perfect capacitances.

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Himoto, Kazuhiro, Masakazu Matsumoto, and Hideki Tanaka. "Lattice- and network-structure in plastic ice." Physical Chemistry Chemical Physics 13, no. 44 (2011): 19876. http://dx.doi.org/10.1039/c1cp21871a.

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Tao, Shang, Pei Hengli, and Liu Jianwei. "Secure network coding based on lattice signature." China Communications 11, no. 1 (January 2014): 138–51. http://dx.doi.org/10.1109/cc.2014.6821316.

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Ebisuzaki, Toshikazu, Hidetoshi Katori, Jun’ichiro Makino, Atsushi Noda, Hisaaki Shinkai, and Toru Tamagawa. "INO: Interplanetary network of optical lattice clocks." International Journal of Modern Physics D 29, no. 04 (March 28, 2019): 1940002. http://dx.doi.org/10.1142/s0218271819400029.

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The new technique of measuring frequency by optical lattice clocks now approaches to the relative precision of [Formula: see text]. We propose to place such precise clocks in space and to use Doppler tracking method for detecting low-frequency gravitational wave below 1[Formula: see text]Hz. Our idea is to locate three spacecrafts at one A.U. distance (say at L1, L4 and L5 of the Sun–Earth orbit), and apply the Doppler tracking method by communicating “the time” each other. Applying the current available technologies, we obtain the sensitivity for gravitational wave with third- or fourth-order improvement ([Formula: see text] or [Formula: see text] level in [Formula: see text]–[Formula: see text][Formula: see text]Hz) than that of Cassini spacecraft in 2001. This sensitivity enables us to observe black hole (BH) mergers of their mass greater than [Formula: see text] in the cosmological scale. Based on the hierarchical growth model of BHs in galaxies, we estimate the event rate of detection will be 20–50 a year. We nickname “INO” (Interplanetary Network of Optical Lattice Clocks) for this system, named after Tadataka Ino (1745–1818), a Japanese astronomer, cartographer, and geodesist.

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Sun, Q. T., Jinhong Yuan, Tao Huang, and K. W. Shum. "Lattice Network Codes Based on Eisenstein Integers." IEEE Transactions on Communications 61, no. 7 (July 2013): 2713–25. http://dx.doi.org/10.1109/tcomm.2013.050813.120759.

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Ogino, Nagao. "Photonic lattice-type self-routing switching network." Electronics and Communications in Japan (Part I: Communications) 75, no. 8 (1992): 26–41. http://dx.doi.org/10.1002/ecja.4410750803.

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Nikzad, Mohammad, Aaron Nicolson, Yongsheng Gao, Jun Zhou, Kuldip K. Paliwal, and Fanhua Shang. "Deep Residual-Dense Lattice Network for Speech Enhancement." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 05 (April 3, 2020): 8552–59. http://dx.doi.org/10.1609/aaai.v34i05.6377.

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Convolutional neural networks (CNNs) with residual links (ResNets) and causal dilated convolutional units have been the network of choice for deep learning approaches to speech enhancement. While residual links improve gradient flow during training, feature diminution of shallow layer outputs can occur due to repetitive summations with deeper layer outputs. One strategy to improve feature re-usage is to fuse both ResNets and densely connected CNNs (DenseNets). DenseNets, however, over-allocate parameters for feature re-usage. Motivated by this, we propose the residual-dense lattice network (RDL-Net), which is a new CNN for speech enhancement that employs both residual and dense aggregations without over-allocating parameters for feature re-usage. This is managed through the topology of the RDL blocks, which limit the number of outputs used for dense aggregations. Our extensive experimental investigation shows that RDL-Nets are able to achieve a higher speech enhancement performance than CNNs that employ residual and/or dense aggregations. RDL-Nets also use substantially fewer parameters and have a lower computational requirement. Furthermore, we demonstrate that RDL-Nets outperform many state-of-the-art deep learning approaches to speech enhancement. Availability: https://github.com/nick-nikzad/RDL-SE.

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Grabisch, Michel, and Agnieszka Rusinowska. "Lattices in Social Networks with Influence." International Game Theory Review 17, no. 01 (March 2015): 1540004. http://dx.doi.org/10.1142/s0219198915400046.

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We present an application of lattice theory to the framework of influence in social networks. The contribution of the paper is not to derive new results, but to synthesize our existing results on lattices and influence. We consider a two-action model of influence in a social network in which agents have to make their yes–no decision on a certain issue. Every agent is preliminarily inclined to say either "yes" or "no", but due to influence by others, the agent's decision may be different from his original inclination. We discuss the relation between two central concepts of this model: Influence function and follower function. The structure of the set of all influence functions that lead to a given follower function appears to be a distributive lattice. We also consider a dynamic model of influence based on aggregation functions and present a general analysis of convergence in the model. Possible terminal classes to which the process of influence may converge are terminal states (the consensus states and nontrivial states), cyclic terminal classes and unions of Boolean lattices.

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Wu, Shaojie, Yan Zhu, Ning Li, Yizeng Wang, Xingju Wang, and Daniel Jian Sun. "Urban Rail Transit System Network Reliability Analysis Based on a Coupled Map Lattice Model." Journal of Advanced Transportation 2021 (April 10, 2021): 1–9. http://dx.doi.org/10.1155/2021/5548956.

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During the last twenty years, the complex network modeling approach has been introduced to assess the reliability of rail transit networks, in which the dynamic performance involving passenger flows have attracted more attentions during operation stages recently. This paper proposes the passenger-flow-weighted network reliability evaluation indexes, to assess the impact of passenger flows on network reliability. The reliability performances of the rail transit network and passenger-flow-weighted one are analyzed from the perspective of a complex network. The actual passenger flow weight of urban transit network nodes was obtained from the Shanghai Metro public transportation card data, which were used to assess the reliability of the passenger-flow-weighted network. Furthermore, the dynamic model of the Shanghai urban rail transit network was constructed based on the coupled map lattice (CML) model. Then, the processes of cascading failure caused by network nodes under different destructive situations were simulated, to measure the changes of passenger-flow-weighted network reliability during the processes. The results indicate that when the scale of network damage attains 50%, the reliability of the passenger-flow-weighted network approaches zero. Consequently, taking countermeasures during the initial stage of network cascading may effectively prevent the disturbances from spreading in the network. The results of the paper could provide guidelines for operation management, as well as identify the unreliable stations within passenger-flow-weighted networks.

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Pum, Dietmar, Andreas Breitwieser, and Uwe B. Sleytr. "Patterns in Nature—S-Layer Lattices of Bacterial and Archaeal Cells." Crystals 11, no. 8 (July 27, 2021): 869. http://dx.doi.org/10.3390/cryst11080869.

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Bacterial surface layers (S-layers) have been observed as the outermost cell envelope component in a wide range of bacteria and most archaea. S-layers are monomolecular lattices composed of a single protein or glycoprotein species and have either oblique, square or hexagonal lattice symmetry with unit cell dimensions ranging from 3 to 30 nm. They are generally 5 to 10 nm thick (up to 70 nm in archaea) and represent highly porous protein lattices (30–70% porosity) with pores of uniform size and morphology in the range of 2 to 8 nm. Since S-layers can be considered as one of the simplest protein lattices found in nature and the constituent units are probably the most abundantly expressed proteins on earth, it seems justified to briefly review the different S-layer lattice types, the need for lattice imperfections and the discussion of S-layers from the perspective of an isoporous protein network in the ultrafiltration region. Finally, basic research on S-layers laid the foundation for applications in biotechnology, synthetic biology, and biomimetics.

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Malishava, Merab, and Sergej Flach. "Thermalization dynamics of macroscopic weakly nonintegrable maps." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 6 (June 2022): 063113. http://dx.doi.org/10.1063/5.0092032.

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We study thermalization of weakly nonintegrable nonlinear unitary lattice dynamics. We identify two distinct thermalization regimes close to the integrable limits of either linear dynamics or disconnected lattice dynamics. For weak nonlinearity, the almost conserved actions correspond to extended observables which are coupled into a long-range network. For weakly connected lattices, the corresponding local observables are coupled into a short-range network. We compute the evolution of the variance [Formula: see text] of finite time average distributions for extended and local observables. We extract the ergodization time scale [Formula: see text] which marks the onset of thermalization, and determine the type of network through the subsequent decay of [Formula: see text]. We use the complementary analysis of Lyapunov spectra [M. Malishava and S. Flach, Phys. Rev. Lett. 128, 134102 (2022)] and compare the Lyapunov time [Formula: see text] with [Formula: see text]. We characterize the spatial properties of the tangent vector and arrive at a complete classification picture of weakly nonintegrable macroscopic thermalization dynamics.

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Zhao, Shan, Minghao Hu, Zhiping Cai, Haiwen Chen, and Fang Liu. "Dynamic Modeling Cross- and Self-Lattice Attention Network for Chinese NER." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 16 (May 18, 2021): 14515–23. http://dx.doi.org/10.1609/aaai.v35i16.17706.

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Word-character lattice models have been proved to be effective for Chinese named entity recognition (NER), in which word boundary information is fused into character sequences for enhancing character representations. However, prior approaches have only used simple methods such as feature concatenation or position encoding to integrate word-character lattice information, but fail to capture fine-grained correlations in word-character spaces. In this paper, we propose DCSAN, a Dynamic Cross- and Self-lattice Attention Network that aims to model dense interactions over word-character lattice structure for Chinese NER. By carefully combining cross-lattice and self-lattice attention modules with gated word-character semantic fusion unit, the network can explicitly capture fine-grained correlations across different spaces (e.g., word-to-character and character-to-character), thus significantly improving model performance. Experiments on four Chinese NER datasets show that DCSAN obtains stateof-the-art results as well as efficiency compared to several competitive approaches.

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GARREAU DE LOUBRESSE, NICOLE, GUY KERYER, BERNARD VIGUÈS, and JANINE BEISSON. "A contractile cytoskeletal network of Paramecium: the infraciliary lattice." Journal of Cell Science 90, no. 3 (July 1, 1988): 351–64. http://dx.doi.org/10.1242/jcs.90.3.351.

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Among the various cytoskeletal networks and structures that compose the highly organized cortex of Paramecium, the infraciliary lattice (ICL) is the inner most one and marks the cortical boundary. It is made up of filamentous bundles running around the proximal ends of basalbodies. Immunofluorescence studies, using two different antibodies specifically labelling the network, allowed us to describe the disorganization-reorganization cycle of the ICL during division, and observations by immuno electron microscopy provided new information on it sultra structure. A partial purification of large fragments of a contracted form of the network was obtained. Among the proteins from ICL-enriched fractions, two 23 to 24(x103) Mr polypeptides were shown to cross-react with a polyclonal antibody raised against 22 to 23(x103)Mr Ca2+-binding proteins from the microfibrillar ectoplasmic-endoplasmic boundary of Isotricha and to beselectively solubilized in the presence of EGTA. The possibility that the ICL may be a new example of a non-actin contractile system foundin lower eukaryotes is discussed.

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Chapman, Christian, and Daniel W. Bliss. "Upper Bound on the Joint Entropy of Correlated Sources Encoded by Good Lattices." Entropy 21, no. 10 (September 29, 2019): 957. http://dx.doi.org/10.3390/e21100957.

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Lattices provide useful structure for distributed coding of correlated sources. A common lattice encoder construction is to first round an observed sequence to a `fine’ lattice with dither, then produce the result’s modulo to a `coarse’ lattice as the encoding. However, such encodings may be jointly-dependent. A class of upper bounds is established on the conditional entropy-rates of such encodings when sources are correlated and Gaussian and the lattices involved are a from an asymptotically-well-behaved sequence. These upper bounds guarantee existence of a joint–compression stage which can increase encoder efficiency. The bounds exploit the property that the amount of possible values for one encoding collapses when conditioned on other sufficiently informative encodings. The bounds are applied to the scenario of communicating through a many-help-one network in the presence of strong correlated Gaussian interferers, and such a joint–compression stage is seen to compensate for some of the inefficiency in certain simple encoder designs.

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AHMED, E., H. A. ABDUSALAM, and E. S. FAHMY. "ON TELEGRAPH COUPLED MAP LATTICE AND ITS APPLICATIONS." International Journal of Modern Physics C 12, no. 10 (December 2001): 1525–35. http://dx.doi.org/10.1142/s0129183101002863.

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In the present paper, we will study the general telegraph coupled map lattice and finite amplitude instability will be discussed. The persistence in telegraph reaction diffusion equation (TRD) will be studied in two dimensional systems and we show the critical size effect where phenomena persist only if the domain is large enough. Some applications are introduced and we made a simulation on the small world network, which is more realistic than the ordinary lattices in many cases.

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Xie, Feng Jie, and Jing Shi. "The Evolution of Price Competition Game on Complex Networks." Complexity 2018 (July 9, 2018): 1–13. http://dx.doi.org/10.1155/2018/9649863.

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The well-known “Bertrand paradox” describes a price competition game in which two competing firms reach an outcome where both charge a price equal to the marginal cost. The fact that the Bertrand paradox often goes against empirical evidences has intrigued many researchers. In this work, we study the game from a new theoretical perspective—an evolutionary game on complex networks. Three classic network models, square lattice, WS small-world network, and BA scale-free network, are used to describe the competitive relations among the firms which are bounded rational. The analysis result shows that full price keeping is one of the evolutionary equilibriums in a well-mixed interaction situation. Detailed experiment results indicate that the price-keeping phenomenon emerges in a square lattice, small-world network and scale-free network much more frequently than in a complete network which represents the well-mixed interaction situation. While the square lattice has little advantage in achieving full price keeping, the small-world network and the scale-free network exhibit a stronger capability in full price keeping than the complete network. This means that a complex competitive relation is a crucial factor for maintaining the price in the real world. Moreover, competition scale, original price, degree of cutting price, and demand sensitivity to price show a significant influence on price evolution on a complex network. The payoff scheme, which describes how each firm’s payoff is calculated in each round game, only influences the price evolution on the scale-free network. These results provide new and important insights for understanding price competition in the real world.

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OWAIDAT, M. Q., R. S. HIJJAWI, J. H. ASAD, and J. M. KHALIFEH. "ELECTRICAL NETWORKS WITH INTERSTITIAL SINGLE CAPACITOR." Modern Physics Letters B 27, no. 16 (June 6, 2013): 1350123. http://dx.doi.org/10.1142/s0217984913501236.

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We investigate the equivalent capacitance between two arbitrary nodes in a perturbed network (i.e. an interstitial capacitor is introduced between two arbitrary points in the perfect lattice) based on the lattice Green's function approach. An explicit formula for the capacitance of the perturbed lattice is derived in terms of the capacitances of the perfect lattice by solving Dyson's equation exactly. Numerical results are presented for the infinite perturbed square network. Finally, the asymptotic behavior of the effective capacitance has been studied.

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Asif, Rameez. "Post-Quantum Cryptosystems for Internet-of-Things: A Survey on Lattice-Based Algorithms." IoT 2, no. 1 (February 5, 2021): 71–91. http://dx.doi.org/10.3390/iot2010005.

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The latest quantum computers have the ability to solve incredibly complex classical cryptography equations particularly to decode the secret encrypted keys and making the network vulnerable to hacking. They can solve complex mathematical problems almost instantaneously compared to the billions of years of computation needed by traditional computing machines. Researchers advocate the development of novel strategies to include data encryption in the post-quantum era. Lattices have been widely used in cryptography, somewhat peculiarly, and these algorithms have been used in both; (a) cryptoanalysis by using lattice approximation to break cryptosystems; and (b) cryptography by using computationally hard lattice problems (non-deterministic polynomial time hardness) to construct stable cryptographic functions. Most of the dominant features of lattice-based cryptography (LBC), which holds it ahead in the post-quantum league, include resistance to quantum attack vectors, high concurrent performance, parallelism, security under worst-case intractability assumptions, and solutions to long-standing open problems in cryptography. While these methods offer possible security for classical cryptosytems in theory and experimentation, their implementation in energy-restricted Internet-of-Things (IoT) devices requires careful study of regular lattice-based implantation and its simplification in lightweight lattice-based cryptography (LW-LBC). This streamlined post-quantum algorithm is ideal for levelled IoT device security. The key aim of this survey was to provide the scientific community with comprehensive information on elementary mathematical facts, as well as to address real-time implementation, hardware architecture, open problems, attack vectors, and the significance for the IoT networks.

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GUO, LONG, and XU CAI. "THE KEY ROLE OF SHORTCUTS OF SMALL-WORLD NETWORK IN OPINION FORMATION." International Journal of Modern Physics C 19, no. 06 (June 2008): 867–73. http://dx.doi.org/10.1142/s012918310801256x.

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In this paper, we analyze the average magnetization and spatial correlation of opinion formation in small-world network and in the regular lattice. We construct NW small-world network through adding shortcuts on the regular lattice. With computer simulation, we find that there exists short- and long-range spatial correlation of the average magnetization m(t) in NW small-world network and the evolution trend of opinion is dependent on the initial opinion condition by comparing with that in regular lattice. On the other hand, we analyze the average magnetization m(t) using the time series analysis, and find the Hurst exponent H ≃ 0.5 in NW small-world network and H = 0 in regular lattice. All the results show the important role of shortcuts in the NW small-world network, which reflects some interesting aspects in our real society indirectly.

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Prabhu. M, Mr Dinesh, and Dr Dinesh Senduraja. "MAC chastised Dynamism Efficient in Wireless Device Lattice Spending Mistralapproach." International Journal of Engineering and Computer Science 10, no. 12 (December 15, 2021): 25453–58. http://dx.doi.org/10.18535/ijecs/v10i12.4641.

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In Wireless sensor Network, several researchers have provided different routing protocol for sensor networks, particularly routing protocols depending on clusters protocols. Reliability of nodes is necessary parameter in effective sensor networks. We use MAC protocol for controlling the network packets. This is because the usage of cluster based routing has several merits like minimized control messages, re-usability of bandwidth and enhanced power control. Different cluster based routing protocol is proposed by many researchers for the purpose of reducing the consumption energy in wireless sensor networks. Those techniques reduces the energy consumption but with several disadvantages like lack of QoS, inefficient transmission, etc., To overcome those problems, modified QoS enhanced base station controlled in Mistrial Approach (flooding Technique) for wireless sensor networks is proposed in this work. Here we reduce the number of retransmission and detect the overlay packets in networks using proposed approach. Simulation results show the better energy consumption, Maximum Life time & Efficient Bandwidth is achieved by flooding management when compared to the conventional techniques

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ABAL, G., R. DONANGELO, F. L. MARQUEZINO, and R. PORTUGAL. "Spatial search on a honeycomb network." Mathematical Structures in Computer Science 20, no. 6 (November 8, 2010): 999–1009. http://dx.doi.org/10.1017/s0960129510000332.

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The spatial search problem consists of minimising the number of steps required to find a given site in a network under the restriction that only oracle queries or translations to neighbouring sites are allowed. We propose a quantum algorithm for the spatial search problem on a honeycomb lattice with N sites and torus-like boundary conditions. The search algorithm is based on a modified quantum walk on an hexagonal lattice and the general framework proposed by Ambainis, Kempe and Rivosh (Ambainis et al. 2005) is employed to show that the time complexity of this quantum search algorithm is $O(\sqrt{N \log N})$.

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CARTWRIGHT, EDWARD J. "CONTAGION AND THE SPEED OF ADJUSTMENT IN SMALL WORLDS." International Game Theory Review 09, no. 04 (December 2007): 689–704. http://dx.doi.org/10.1142/s0219198907001667.

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We model a simple dynamic process in which myopic agents are matched amongst each other to play a coordination game. The network of player interaction is varied between a regular lattice and a random network allowing us to model contagion in small world networks. Weighting times for an equilibrium shift from the risk dominated to risk dominant equilibrium are shown to be smallest in small world networks.

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Baradaran, Marzieh, and Pavel Exner. "Kagome network with vertex coupling of a preferred orientation." Journal of Mathematical Physics 63, no. 8 (August 1, 2022): 083502. http://dx.doi.org/10.1063/5.0093546.

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We investigate spectral properties of periodic quantum graphs in the form of a kagome or a triangular lattice in the situation when the condition matching the wave functions at lattice vertices is chosen of a particular form violating the time-reversal invariance. The positive spectrum consists of an infinite number of bands, some of which may be flat; the negative one has at most three and two bands, respectively. The kagome lattice example shows that even in graphs with such an uncommon vertex coupling, spectral universality may hold: if its edges are incommensurate, the probability that a randomly chosen positive number is contained in the spectrum is [Formula: see text].

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Liu, Yang, Yicheng Ye, Qihu Wang, and Xiaoyun Liu. "Stability Prediction Model of Roadway Surrounding Rock Based on Concept Lattice Reduction and a Symmetric Alpha Stable Distribution Probability Neural Network." Applied Sciences 8, no. 11 (November 5, 2018): 2164. http://dx.doi.org/10.3390/app8112164.

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To combat the uncertainty of the multiple factors affecting roadway surrounding rock stability, five initial indexes are selected for reduction according to concept lattice theory: rock quality designation (RQD), uniaxial compressive strength (Rc), the integrity coefficient of rock mass, groundwater seepage, and joint condition. The aim of this study is to compute correlation coefficients among various indexes and verify the effectiveness of lattice reduction. Alpha stable distribution is used to replace the commonly used Gauss distribution in probabilistic neural networks. A prediction model for the stability of roadway surrounding rock is then established based on a concept lattice and improved probabilistic neural network. 100 groups of training sample data are plugged into this model one by one to examine its rationality. The established model is employed for engineering application prediction with ten indiscriminate sample groups from the Jianlinshan mining area of the Daye iron mine, revealing accuracy of up to 90%. This demonstrates that our prediction model based on a concept lattice and improved probabilistic neural network has high reliability and applicability.

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Mačernytė, Kotryna, and Rasa Šmidtaitė. "Chimera state in coupled map lattice of matrices." Lietuvos matematikos rinkinys 62 (December 20, 2021): 57–63. http://dx.doi.org/10.15388/lmr.2021.25228.

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In recent years, a lot of research has focused on understanding the behavior of when synchronous and asynchronous phases occur, that is, the existence of chimera states in various networks. Chimera states have wide-range applications in many disciplines including biology, chemistry, physics, or engineering. The object of research in this paper is a coupled map lattice of matrices when each node is described by an iterative map of matrices of order two. A regular topology network of iterative maps of matrices was formed by replacing the scalar iterative map with the iterative map of matrices in each node. The coupled map of matrices is special in a way where we can observe the effect of divergence. This effect can be observed when the matrix of initial conditions is a nilpotent matrix. Also, the evolution of the derived network is investigated. It is found that the network of the supplementary variable $\mu$ can evolve into three different modes: the quiet state, the state of divergence, and the formation of divergence chimeras. The space of parameters of node coupling including coupling strength $\varepsilon$ and coupling range $r$ is also analyzed in this study. Image entropy is applied in order to identify chimera state parameter zones.

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Stolarek, J. "Adaptive synthesis of a wavelet transform using fast neural network." Bulletin of the Polish Academy of Sciences: Technical Sciences 59, no. 1 (March 1, 2011): 9–13. http://dx.doi.org/10.2478/v10175-011-0002-5.

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Adaptive synthesis of a wavelet transform using fast neural network This paper introduces a new method for an adaptive synthesis of a wavelet transform using a fast neural network with a topology based on the lattice structure. The lattice structure and the orthogonal lattice structure are presented and their properties are discussed. A novel method for unsupervised training of the neural network is introduced. The proposed approach is tested by synthesizing new wavelets with an expected energy distribution between low- and high-pass filters. Energy compaction of the proposed method and Daubechies wavelets is compared. Tests are performed using sound and image signals.

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Wiggins, Richard H. "Speech analysis circuits using an inverse lattice network." Journal of the Acoustical Society of America 83, no. 3 (March 1988): 1211. http://dx.doi.org/10.1121/1.395986.

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Song, Yiwei, Natasha Devroye, Huai-Rong Shao, and Chiu Y. Ngo. "Lattice Coding for the Two-Way Line Network." IEEE Journal on Selected Areas in Communications 32, no. 9 (September 2014): 1707–20. http://dx.doi.org/10.1109/jsac.2014.2330012.

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Bienstock, Daniel. "Some Lattice-Theoretic Tools for Network Reliability Analysis." Mathematics of Operations Research 13, no. 3 (August 1988): 467–78. http://dx.doi.org/10.1287/moor.13.3.467.

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Fujita, S., A. Garcia, D. O'leyar, S. Watanabe, and T. Burnett. "On the conductance of a lattice-like network." Journal of Physics and Chemistry of Solids 50, no. 1 (January 1989): 27–31. http://dx.doi.org/10.1016/0022-3697(89)90468-x.

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Li, Jin Ling. "The Memory of Fuzzy Neural Network Based on Lattice Point Distribution." Key Engineering Materials 467-469 (February 2011): 1416–20. http://dx.doi.org/10.4028/www.scientific.net/kem.467-469.1416.

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This paper deals with the condition for a fuzzy neural network to realize memory, gives the concept of lattice point and proves that if sample set is of lattice point distribution the sample set can be memorized by a fuzzy neural network, otherwise the fuzzy neural network will lost its memory. A theorem shows that Choice-memory method not only reduces computation but also ensures memory of fuzzy neural network.

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Journal articles on the topic 'Network Lattice'

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