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Journal articles on the topic 'Lattice networks'

Author: Grafiati

Published: 4 June 2025

Last updated: 1 August 2025

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1

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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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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3

Chen, Yu, Jinguo You, Benyuan Zou, Guoyu Gan, Ting Zhang, and Lianyin Jia. "Exploring Structural Characteristics of Lattices in Real World." Complexity 2020 (January 21, 2020): 1–11. http://dx.doi.org/10.1155/2020/1250106.

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There are two important models for data analysis and knowledge system: data cube lattices and concept lattices. They both essentially have lattice structures, which are actually irregular in our real world. However, their structural characteristics and relationship are not yet clear. To the best of our knowledge, no work has paid enough attention to this challenging issue from the perspective of graph data, in spite of the importance of structures in lattice data. In this paper, we first tackle the structural statistics of lattice data from three aspects: the degree distribution, clustering co

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Owaidat, M. Q., J. H. Asad, and J. M. Khalifeh. "Resistance calculation of the decorated centered cubic networks: Applications of the Green's function." Modern Physics Letters B 28, no. 32 (2014): 1450252. http://dx.doi.org/10.1142/s0217984914502522.

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The effective resistance between any pair of vertices (sites) on the three-dimensional decorated centered cubic lattices is determined by using lattice Green's function method. Numerical results are presented for infinite decorated centered cubic networks. A mapping between the resistance of the edge-centered cubic lattice and that of the simple cubic lattice is shown.

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Norris, Andrew N. "Mechanics of elastic networks." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2172 (2014): 20140522. http://dx.doi.org/10.1098/rspa.2014.0522.

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We consider a periodic lattice structure in d =2 or 3 dimensions with unit cell comprising Z thin elastic members emanating from a similarly situated central node. A general theoretical approach provides an algebraic formula for the effective elasticity of such frameworks. The method yields the effective cubic elastic constants for three-dimensional space-filling lattices with Z =4, 6, 8, 12 and 14, the last being the ‘stiffest’ lattice proposed by Gurtner & Durand (Gurtner & Durand 2014 Proc. R. Soc. A 470 , 20130611. ( doi:10.1098/rspa.2013.0611 )). The analytical expressions provide

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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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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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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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9

Harris, Marcus, and Martin Zwick. "Graphical Models in Reconstructability Analysis and Bayesian Networks." Entropy 23, no. 8 (2021): 986. http://dx.doi.org/10.3390/e23080986.

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Reconstructability Analysis (RA) and Bayesian Networks (BN) are both probabilistic graphical modeling methodologies used in machine learning and artificial intelligence. There are RA models that are statistically equivalent to BN models and there are also models unique to RA and models unique to BN. The primary goal of this paper is to unify these two methodologies via a lattice of structures that offers an expanded set of models to represent complex systems more accurately or more simply. The conceptualization of this lattice also offers a framework for additional innovations beyond what is p

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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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11

Silvi, Pietro, Enrique Rico, Tommaso Calarco, and Simone Montangero. "Lattice gauge tensor networks." New Journal of Physics 16, no. 10 (2014): 103015. http://dx.doi.org/10.1088/1367-2630/16/10/103015.

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12

Shmatkov, V. D. "Lattice flows in networks." Problems of Information Transmission 52, no. 1 (2016): 24–38. http://dx.doi.org/10.1134/s003294601601004x.

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Wang, Zhigang, Liqin Tian, Lianhai Lin, and Yinghua Tong. "Lattice-Based 3-Dimensional Wireless Sensor Deployment." Journal of Sensors 2021 (August 17, 2021): 1–14. http://dx.doi.org/10.1155/2021/2441122.

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With the wide application of wireless sensor networks (WSNs) in real space, there are numerous studies on 3D sensor deployments. In this paper, the k -connectivity theoretical model of fixed and random nodes in regular lattice-based deployment was proposed to study the coverage and connectivity of sensor networks with regular lattice in 3D space. The full connectivity range and cost of the deployment with sensor nodes fixed in the centers of four regular lattices were quantitatively analyzed. The optimal single lattice coverage model and the ratio of the communication range to the sensing rang

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14

ASAD, J. H., R. S. HIJJAWI, A. J. SAKAJI, and J. M. KHALIFEH. "INFINITE NETWORKS OF IDENTICAL CAPACITORS." Modern Physics Letters B 24, no. 07 (2010): 695–705. http://dx.doi.org/10.1142/s0217984910022767.

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The capacitance between the origin and any other lattice site in an infinite square lattice of identical capacitors each of capacitance C is calculated. The method is generalized to infinite Simple Cubic (SC) lattice of identical capacitors each of capacitance C. We make use of the superposition principle and the symmetry of the infinite grid.

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Chen, Mo, Lei Jin, Xiangyang Gong, Xiaojuan Wang, and Wenhua Sun. "Analysis of the spatial cascading effect in networks." International Journal of Modern Physics C 31, no. 04 (2020): 2050055. http://dx.doi.org/10.1142/s0129183120500552.

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Reality networks such as power grids and social networks can be spatially embedded. In this paper, we focus on the spatial cascading effect in such networks. The spatial cascading effect is that the failure of one node may cause other nodes that are close to it in space to fail. The phenomenon is very common, such that a person is more likely to have an impact on his neighbors even if he is not connected with his neighbors via social networks. Based on this, we construct a spatial cascading model to simulate the spatial cascading effect. In addition, we apply the exponential distribution [Form

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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 (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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17

Lei, Hui, Tao Li, Yuede Ma, and Hua Wang. "Analyzing lattice networks through substructures." Applied Mathematics and Computation 329 (July 2018): 297–314. http://dx.doi.org/10.1016/j.amc.2018.02.012.

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18

Campuzano, J. M., J. P. Bagrow, and D. ben-Avraham. "Kleinberg Navigation on Anisotropic Lattices." Research Letters in Physics 2008 (November 16, 2008): 1–4. http://dx.doi.org/10.1155/2008/346543.

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We study the Kleinberg problem of navigation in small-world networks when the underlying lattice is stretched along a preferred direction. Extensive simulations confirm that maximally efficient navigation is attained when the length r of long-range links is taken from the distribution P(r)∼r−α, when the exponent α is equal to 2, the dimension of the underlying lattice, regardless of the amount of anisotropy, but only in the limit of infinite lattice size, L→∞. For finite size lattices we find an optimal α(L) that depends strongly on L. The convergence to α=2 as L→∞ shows interesting power-law

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19

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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20

Qin, Wentao, Haresh Siriwardane, and Phil Fraundorf. "The 3d Parameters Of A (Nano)Crystal From Lattice Images At Two Tilts." Microscopy and Microanalysis 5, S2 (1999): 188–89. http://dx.doi.org/10.1017/s1431927600014264.

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Various techniques have been developed to infer the 3D relationship of reciprocal lattice vectors from electron diffraction patterns taken at different specimen orientations. Such relationship is subsequently applied in crystallographic analyses. Due to the transmitted nature of the electron beam, TEM images present 3D information averaged throughout the thickness of the specimen on each micrograph. Techniques for acquiring 3D information from such images include stereomicroscopy for characterizing irregular dislocation networks, and 3D reconstruction of nonperiodic macromolecular assemblies.

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21

Favoni, Matteo, Andreas Ipp, David I. Müller, and Daniel Schuh. "Preserving gauge invariance in neural networks." EPJ Web of Conferences 258 (2022): 09004. http://dx.doi.org/10.1051/epjconf/202225809004.

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In these proceedings we present lattice gauge equivariant convolutional neural networks (L-CNNs) which are able to process data from lattice gauge theory simulations while exactly preserving gauge symmetry. We review aspects of the architecture and show how L-CNNs can represent a large class of gauge invariant and equivariant functions on the lattice. We compare the performance of L-CNNs and non-equivariant networks using a non-linear regression problem and demonstrate how gauge invariance is broken for non-equivariant models.

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22

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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23

N. Al-Rabadi, Anas. "Concurrent Ternary Galois-based Computation using Nano-apex Multiplexing Nibs of Regular Three-dimensional Networks, Part I: Basics." International Journal of VLSI Design & Communication Systems 11, no. 5 (2020): 1–24. http://dx.doi.org/10.5121/vlsic.2020.11501.

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New implementations within concurrent processing using three-dimensional lattice networks via nano carbon-based field emission controlled-switching is introduced in this article. The introduced nano-based three-dimensional networks utilize recent findings in nano-apex field emission to implement the concurrent functionality of lattice networks. The concurrent implementation of ternary Galois functions using nano threedimensional lattice networks is performed by using carbon field-emission switching devices via nano-apex carbon fibers and nanotubes. The presented work in this part of the articl

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24

Massey, William A. "Calculating exit times for series Jackson networks." Journal of Applied Probability 24, no. 1 (1987): 226–34. http://dx.doi.org/10.2307/3214073.

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We define a new family of special functions that we call lattice Bessel functions. They are indexed by the N-dimensional integer lattice such that they reduce to modified Bessel functions when N = 1, and the exponential function when N = 0. The transition probabilities for an M/M/1 queue going from one state to another before becoming idle (exiting at 0) can be solved in terms of modified Bessel functions. In this paper, we use lattice Bessel functions to solve the analogous problem involving the exit time from the interior of the positive orthant of the N-dimensional lattice for a series Jack

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Massey, William A. "Calculating exit times for series Jackson networks." Journal of Applied Probability 24, no. 01 (1987): 226–34. http://dx.doi.org/10.1017/s0021900200030758.

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We define a new family of special functions that we call lattice Bessel functions. They are indexed by the N-dimensional integer lattice such that they reduce to modified Bessel functions when N = 1, and the exponential function when N = 0. The transition probabilities for an M/M/1 queue going from one state to another before becoming idle (exiting at 0) can be solved in terms of modified Bessel functions. In this paper, we use lattice Bessel functions to solve the analogous problem involving the exit time from the interior of the positive orthant of the N-dimensional lattice for a series Jack

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26

Feng, Yarong, Hosam Mahmoud, and Ludger Rüschendorf. "DEGREE PROFILE OF HIERARCHICAL LATTICE NETWORKS." Probability in the Engineering and Informational Sciences 31, no. 1 (2016): 60–82. http://dx.doi.org/10.1017/s0269964816000310.

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We study the degree profile of random hierarchical lattice networks. At every step, each edge is either serialized (with probability p) or parallelized (with probability 1−p). We establish an asymptotic Gaussian law for the number of nodes of outdegree 1, and show how to extend the derivations to encompass asymptotic limit laws for higher outdegrees. The asymptotic joint distribution of the number of nodes of outdegrees 1 and 2 is shown to be bivariate normal. No phase transition with p is detected in these asymptotic laws.For the limit laws, we use ideas from the contraction method. The recur

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27

Song, Doohee, Keun-Ho Lee, and Kwangjin Park. "Bitmap lattice index in road networks." Journal of Central South University 21, no. 10 (2014): 3856–63. http://dx.doi.org/10.1007/s11771-014-2372-y.

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28

Tondeur, Daniel, Yilin Fan, Jean-Marc Commenge, and Lingai Luo. "Uniform flows in rectangular lattice networks." Chemical Engineering Science 66, no. 21 (2011): 5301–12. http://dx.doi.org/10.1016/j.ces.2011.07.027.

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29

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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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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31

Turuban, Régis, Daniel R. Lester, Joris Heyman, Tanguy Le Borgne, and Yves Méheust. "Chaotic mixing in crystalline granular media." Journal of Fluid Mechanics 871 (May 24, 2019): 562–94. http://dx.doi.org/10.1017/jfm.2019.245.

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We study the Lagrangian kinematics of steady three-dimensional Stokes flow over simple cubic (SC) and body-centred cubic (BCC) lattices of close-packed spheres, and uncover the mechanisms governing chaotic mixing in these crystalline structures. Due to the cusp-shaped sphere contacts, the topology of the skin friction field is fundamentally different to that of continuous (non-granular) media, such as open pore networks, with significant implications for fluid mixing. Weak symmetry breaking of the flow orientation with respect to the lattice symmetries imparts a transition from regular to stro

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32

Cheng, Cheng, Ning Dai, Weiping Gu, Bai Xu, and Jing Xu. "Hierarchical Lattice Modeling Method with Gradient Functions." Mobile Information Systems 2022 (June 1, 2022): 1–14. http://dx.doi.org/10.1155/2022/1359472.

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Lattice structure materials have great application potential in biomedical, aerospace, and other fields. In fact, designing multilevel structure parametrically to achieve excellent mechanical performance is a challenging task. In this paper, a hierarchical lattice modeling method with gradient functions is proposed on the basis of the multilevel structural characteristics of organisms to solve the problem of the coexistence of high hardness, high strength, and high toughness. The multilevel body space is filled with matching lattices in accordance with the given dynamic parameters, and the des

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33

Wang, Jiuling, Brian Hyun-jong Lee, and Gaurav Arya. "Kinetically assembled binary nanoparticle networks." Nanoscale 12, no. 8 (2020): 5091–102. http://dx.doi.org/10.1039/c9nr09900j.

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WANG, CHUN-YANG, and XIANG-MU KONG. "AN ATTEMPT TO INTRODUCE LONG-RANGE INTERACTIONS INTO SMALL-WORLD NETWORKS." Modern Physics Letters B 24, no. 07 (2010): 671–79. http://dx.doi.org/10.1142/s0217984910022743.

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Distinguishing the long-range bonds with the regular ones, the critical temperature of the spin-lattice Gaussian model built on two typical small-world networks is studied. The results show much difference from the classical case, and thus may induce some more accurate discussion on the critical properties of the spin-lattice systems combined with the small-world networks.

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35

Petrich, Mario. "Congruence networks for completely simple semigroups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 56, no. 2 (1994): 243–66. http://dx.doi.org/10.1017/s1446788700034868.

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AbstractThe operators K, k, T and t are defined on the lattice of congruences on a Rees matrix semigroup S as follows. For ρ ∈ (S), ρK and ρk (ρT and ρt) are the greatest and the least congruences with the same kernel (trace) as ρ, respectively. We determine the semigroup generated by the operators K, k, T and t as they act on all completely simple semigroups. We also determine the network of congruences associated with a congruence ρ ∈ (S) and the lattice generated by it. The latter is then represented by generators and relations.

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Bandara, Harshana, Yasitha Herath, Thushara Weerasundara, and Janaka Alawatugoda. "On Advances of Lattice-Based Cryptographic Schemes and Their Implementations." Cryptography 6, no. 4 (2022): 56. http://dx.doi.org/10.3390/cryptography6040056.

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Lattice-based cryptography is centered around the hardness of problems on lattices. A lattice is a grid of points that stretches to infinity. With the development of quantum computers, existing cryptographic schemes are at risk because the underlying mathematical problems can, in theory, be easily solved by quantum computers. Since lattice-based mathematical problems are hard to be solved even by quantum computers, lattice-based cryptography is a promising foundation for future cryptographic schemes. In this paper, we focus on lattice-based public-key encryption schemes. This survey presents t

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Shabbir, Ayesha, and Tudor Zamfirescu. "Fault-tolerant designs in triangular lattice networks." Applicable Analysis and Discrete Mathematics 10, no. 2 (2016): 447–56. http://dx.doi.org/10.2298/aadm161013027s.

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38

Chinen, Michael, Jan Skoglund, and Andrew Hines. "Speech quality estimation with deep lattice networks." Journal of the Acoustical Society of America 149, no. 6 (2021): 3851–61. http://dx.doi.org/10.1121/10.0005130.

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39

Giordano, Stefano. "Two-dimensional disordered lattice networks with substrate." Physica A: Statistical Mechanics and its Applications 375, no. 2 (2007): 726–40. http://dx.doi.org/10.1016/j.physa.2006.09.026.

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Luo, Yu-Pin, Hung-Yeh Lin, Ming-Chang Huang, and Tsong-Ming Liaw. "Conformation-networks of two-dimensional lattice homopolymers." Physics Letters A 359, no. 3 (2006): 211–17. http://dx.doi.org/10.1016/j.physleta.2006.06.023.

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Tauro, Carolina B., Francisco A. Tamarit, and Pablo M. Gleiser. "Synchronization in lattice-embedded scale-free networks." Physica A: Statistical Mechanics and its Applications 391, no. 3 (2012): 834–42. http://dx.doi.org/10.1016/j.physa.2011.08.012.

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Franz, M., and S. Teitel. "Vortex lattice melting in 2D superconducting networks." Physica B: Condensed Matter 222, no. 4 (1996): 287–92. http://dx.doi.org/10.1016/0921-4526(96)85056-3.

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KWAK, Wooseop, Sojeong PARK, and Meesoon HA*. "Generalized Conserved Lattice Gas on Random Networks." New Physics: Sae Mulli 66, no. 10 (2016): 1210–14. http://dx.doi.org/10.3938/npsm.66.1210.

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44

Ammann, Paul, and Sushil Jajodia. "Distributed timestamp generation in planar lattice networks." ACM Transactions on Computer Systems 11, no. 3 (1993): 205–25. http://dx.doi.org/10.1145/152864.152865.

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45

Giordano, Stefano. "Disordered lattice networks: general theory and simulations." International Journal of Circuit Theory and Applications 33, no. 6 (2005): 519–40. http://dx.doi.org/10.1002/cta.335.

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Chang, Yi-Fang. "Biological Lattice Gauge Theory as Modeling of Quantum Neural Networks." Journal of Modeling and Optimization 10, no. 1 (2018): 23. http://dx.doi.org/10.32732/jmo.2018.10.1.23.

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Based on quantum biology and biological gauge field theory, we propose the biological lattice gauge theory as modeling of quantum neural networks. This method applies completely the same lattice theory in quantum field, but, whose two anomaly problems may just describe the double helical structure of DNA and violated chiral symmetry in biology. Further, we discuss the model of Neural Networks (NN) and the quantum neutral networks, which are related with biological loop quantum theory. Finally, we research some possible developments on described methods of networks by the extensive graph theory

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Galina, H., and J. B. Lechowicz. "Monte-Carlo modeling of degradation of polymer networks: 3. Lattice networks." Polymer 41, no. 2 (2000): 615–19. http://dx.doi.org/10.1016/s0032-3861(99)00221-9.

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Alkentar, Rashwan, Sándor Manó, Dávid Huri, and Tamás Mankovits. "Development of Patient-Specific Lattice Structured Femoral Stems Based on Finite Element Analysis and Machine Learning." Crystals 15, no. 7 (2025): 650. https://doi.org/10.3390/cryst15070650.

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Hip implant optimization is increasingly receiving attention due to the development of manufacturing technology and artificial intelligence interaction in the current research. This study investigates the development of hip implant stem design with the application of lattice structures, and the utilization of the MATLAB regression learner app in finding the best predictive regression model to calculate the mechanical behavior of the implant’s stem based on some of the design parameters. Many cases of latticed hip implants (using 3D lattice infill type) were designed in the ANSYS software, and

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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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Bachtis, Dimitrios, Gert Aarts, and Biagio Lucini. "Quantum field theories, Markov random fields and machine learning." Journal of Physics: Conference Series 2207, no. 1 (2022): 012056. http://dx.doi.org/10.1088/1742-6596/2207/1/012056.

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Abstract The transition to Euclidean space and the discretization of quantum field theories on spatial or space-time lattices opens up the opportunity to investigate probabilistic machine learning within quantum field theory. Here, we will discuss how discretized Euclidean field theories, such as the ϕ 4 lattice field theory on a square lattice, are mathematically equivalent to Markov fields, a notable class of probabilistic graphical models with applications in a variety of research areas, including machine learning. The results are established based on the Hammersley-Clifford theorem. We wil

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