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Journal articles on the topic 'Network Lattice'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

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 (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 p

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KENDZIORRA, ANDREAS, and STEFAN E. SCHMIDT. "NETWORK CODING WITH MODULAR LATTICES." Journal of Algebra and Its Applications 10, no. 06 (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. Mo

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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 (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 p

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4

Ostoja-Starzewski, Martin. "Lattice models in micromechanics." Applied Mechanics Reviews 55, no. 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

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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

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6

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 (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-

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7

Stewart, Ian. "Exotic Patterns of Synchrony in Planar Lattice Networks." International Journal of Bifurcation and Chaos 29, no. 02 (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 ex

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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 (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 ha

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9

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 th

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10

van Montfort, Yves, Sébastian de Bone, and David Elkouss. "Fault-tolerant structures for measurement-based quantum computation on a network." Quantum 9 (May 5, 2025): 1723. https://doi.org/10.22331/q-2025-05-05-1723.

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In this work, we introduce a method to construct fault-tolerant measurement-based quantum computation (MBQC) architectures and numerically estimate their performance over various types of networks. A possible application of such a paradigm is distributed quantum computation, where separate computing nodes work together on a fault-tolerant computation through entanglement. We gauge error thresholds of the architectures with an efficient stabilizer simulator to investigate the resilience against both circuit-level and network noise. We show that, for both monolithic (i.e., non-distributed) and d

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11

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 (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.

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12

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 (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 implica

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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 (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. T

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14

STEWART, IAN. "The lattice of balanced equivalence relations of a coupled cell network." Mathematical Proceedings of the Cambridge Philosophical Society 143, no. 1 (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 equivalen

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15

Bai, Jiaxuan, Menglong Li, and Jianghua Shen. "Prediction of Mechanical Properties of Lattice Structures: An Application of Artificial Neural Networks Algorithms." Materials 17, no. 17 (2024): 4222. http://dx.doi.org/10.3390/ma17174222.

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The yield strength and Young’s modulus of lattice structures are essential mechanical parameters that influence the utilization of materials in the aerospace and medical fields. Currently, accurately determining the Young’s modulus and yield strength of lattice structures often requires conduction of a large number of experiments for prediction and validation purposes. To save time and effort to accurately predict the material yield strength and Young’s modulus, based on the existing experimental data, finite element analysis is employed to expand the dataset. An artificial neural network algo

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16

Lan, Tian, Chenxi Peng, Kate Fox, Truong Do, and Phuong Tran. "Triply periodic minimal surfaces lattice structures: Functional graded and hybrid designs for engineering applications." Materials Science in Additive Manufacturing 2, no. 3 (2023): 1753. http://dx.doi.org/10.36922/msam.1753.

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In this work, we propose the strategies for designing radial graded sheet-based gyroid lattice and the approach to hybridizing solid-network-based gyroid lattice and primitive lattice. The elastic property of triply periodic minimal surfaces (TPMS) sheet-based gyroid lattice structures was explored. We also conducted numerical analysis to investigate the effect of functionally graded sheet-based gyroid lattices on the implant application, and explored the elastic properties of the uniform gyroid lattice parametrically with different relative densities based on the representative volume element

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17

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 (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

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18

OUYANG, QI, KAI SUN, and HONGLI WANG. "MICROSCOPIC SELF-ORGANIZATION IN NETWORKS AND REGULAR LATTICE." Modern Physics Letters B 16, no. 25 (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 micr

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19

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 (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 th

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20

Zeng, Ziyan, Qin Li, and Minyu Feng. "Spatial evolution of cooperation with variable payoffs." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 7 (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 t

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21

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

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22

ZHAO, HUI, and ZIYOU GAO. "GENERALIZED SHORTEST PATH AND TRAFFIC EQUILIBRIUM IN COMPLEX TRANSPORTATION NETWORKS." Modern Physics Letters B 21, no. 20 (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. W

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23

Grabisch, Michel, and Agnieszka Rusinowska. "Lattices in Social Networks with Influence." International Game Theory Review 17, no. 01 (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

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24

Pum, Dietmar, Andreas Breitwieser, and Uwe B. Sleytr. "Patterns in Nature—S-Layer Lattices of Bacterial and Archaeal Cells." Crystals 11, no. 8 (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

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25

Malishava, Merab, and Sergej Flach. "Thermalization dynamics of macroscopic weakly nonintegrable maps." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 6 (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 e

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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 (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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27

Chapman, Christian, and Daniel W. Bliss. "Upper Bound on the Joint Entropy of Correlated Sources Encoded by Good Lattices." Entropy 21, no. 10 (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 i

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28

Huang, Da, Jibin Yang, Zhiyong Yu, and Cheng Hu. "On the Network Index of MAS with Layered Lattice-like Structures of Multiple Vertex-Related Parameters." Symmetry 16, no. 2 (2024): 243. http://dx.doi.org/10.3390/sym16020243.

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In this article, a robust index named first-order network coherence (FONC) for the multi-agent systems (MASs) with layered lattice-like structure is studied via the angle of the graph spectra theory. The union operation of graphs is utilized to construct two pairs of non-isomorphic layered lattice-like structures, and the expression of the index is acquired by the approach of Laplacian spectra, then the corresponding asymptotic results are obtained. It is found that when the cardinality of the node sets of coronary substructures with better connectedness tends to infinity, the FONC of the whol

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29

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 (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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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 (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 analys

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31

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 th

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32

Asif, Rameez. "Post-Quantum Cryptosystems for Internet-of-Things: A Survey on Lattice-Based Algorithms." IoT 2, no. 1 (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) cryptoanalys

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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 urb

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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 (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 stru

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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 (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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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 (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

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CARTWRIGHT, EDWARD J. "CONTAGION AND THE SPEED OF ADJUSTMENT IN SMALL WORLDS." International Game Theory Review 09, no. 04 (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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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 (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 (RD

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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 (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 (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

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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 (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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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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ABAL, G., R. DONANGELO, F. L. MARQUEZINO, and R. PORTUGAL. "Spatial search on a honeycomb network." Mathematical Structures in Computer Science 20, no. 6 (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(\s

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Khan, Ihtiram Raza, Neha Gupta, Sheela Hundekari, Ashish Bansal, and Rupali Atul Mahajan. "Efficient key revocation in WSN with lattice-based cryptography." Journal of Discrete Mathematical Sciences and Cryptography 27, no. 2 (2024): 339–48. http://dx.doi.org/10.47974/jdmsc-1887.

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Strong security is crucial as Wireless Sensor Network (WSN) become more common. Dynamic Lattice-Based Key Revocation (DLBKR) is a novel method for improving key revocation in WSN. Lattice-based cryptography helps DLBKR overcome compromised keys and evolving security threats in dynamic sensor networks. Key revocation mechanisms are examined in detail, with a focus on their limitations in WSN. Due to these networks limited resources and ever-changing structure, we propose DLBKR as a novel way to minimize the security risks of compromised keys. DLBKR is featured as a flexible and reactive solutio

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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 (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 r

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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 (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 se

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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 (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 Daubec

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Zhang, Lei, Jing Xin Chang, and Xue Zhi Xiang. "Different Evaluation Approaches of Confusion Network in Chinese Spoken Classification." Advanced Materials Research 142 (October 2010): 174–79. http://dx.doi.org/10.4028/www.scientific.net/amr.142.174.

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As kind of multiple results in speech recognition system, lattice and confusion network are widely applied in spoken document classification and spoken document retrieval. In this paper, the relation between lattice and confusion network is analyzed firstly. Then based on the confusion network by clustering algorithm, different evaluation approaches are applied here to test the performance of confusion network, which include accuracy, complexity and distortion of confusion network. For the experiments on speech recognition system, it can be drawn that compared with 1-best result, confusion net

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