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Carlo A Trugenberger - One of the best experts on this subject based on the ideXlab platform.

  • Combinatorial Quantum Gravity: Emergence of Geometric Space from Random Graphs
    Journal of Physics: Conference Series, 2019
    Co-Authors: Christy Kelly, Carlo A Trugenberger
    Abstract:

    We review and extend the recently proposed model of combinatorial quantum gravity. Contrary to previous discrete approaches, this model is defined on (regular) random graphs and is driven by a purely combinatorial version of Ricci curvature, the Ollivier curvature, defined on generic metric Spaces equipped with a Markov chain. It dispenses thus of notions such as simplicial complexes and Regge calculus and is ideally suited to extend quantum gravity to combinatorial structures which have a priori nothing to do with geometry. Indeed, our results show that geometry and general relativity emerge from random structures in a second-order phase transition due to the condensation of cycles on random graphs, a critical point that defines quantum gravity non-perturbatively according to asymptotic safety. In combinatorial quantum gravity the entropy area law emerges naturally as a consequence of infinite-dimensional critical behaviour on networks rather than on lattices. We propose thus that the entropy area law is a signature of the random graph nature of Space-(time) on the smallest scales.

  • Self-Assembly of Geometric Space from Random Graphs
    arXiv: General Relativity and Quantum Cosmology, 2019
    Co-Authors: Christy Kelly, Carlo A Trugenberger, Fabio Biancalana
    Abstract:

    We present a Euclidean quantum gravity model in which random graphs dynamically self-assemble into discrete manifold structures. Concretely, we consider a statistical model driven by a discretisation of the Euclidean Einstein-Hilbert action; contrary to previous approaches based on simplicial complexes and Regge calculus our discretisation is based on the Ollivier curvature, a coarse analogue of the manifold Ricci curvature defined for generic graphs. The Ollivier curvature is generally difficult to evaluate due to its definition in terms of optimal transport theory, but we present a new exact expression for the Ollivier curvature in a wide class of relevant graphs purely in terms of the numbers of short cycles at an edge. This result should be of independent intrinsic interest to network theorists. Action minimising configurations prove to be cubic complexes up to defects; there are indications that such defects are dynamically suppressed in the macroscopic limit. Closer examination of a defect free model shows that certain classical configurations have a Geometric interpretation and discretely approximate vacuum solutions to the Euclidean Einstein-Hilbert action. Working in a configuration Space where the Geometric configurations are stable vacua of the theory, we obtain direct numerical evidence for the existence of a continuous phase transition; this makes the model a UV completion of Euclidean Einstein gravity. Notably, this phase transition implies an area-law for the entropy of emerging Geometric Space. Certain vacua of the theory can be interpreted as baby universes; we find that these configurations appear as stable vacua in a mean field approximation of our model, but are excluded dynamically whenever the action is exact indicating the dynamical stability of Geometric Space. The model is intended as a setting for subsequent studies of emergent time mechanisms.

  • Topological network entanglement as order parameter for the emergence of geometry
    New Journal of Physics, 2017
    Co-Authors: M. Cristina Diamantini, Carlo A Trugenberger
    Abstract:

    We show that, in discrete models of quantum gravity, emergent Geometric Space can be viewed as the entanglement pattern in a mixed quantum state of the "universe", characterized by a universal topological network entanglement. As a concrete example we analyze the recently proposed model in which geometry emerges due to the condensation of 4-cycles in random regular bipartite graphs, driven by the combinatorial Ollivier-Ricci curvature. Using this model we show that the emergence of Geometric order decreases the entanglement entropy of random configurations. The lowest Geometric entanglement entropy is realized in four dimensions.

  • Combinatorial quantum gravity: geometry from random bits
    Journal of High Energy Physics, 2017
    Co-Authors: Carlo A Trugenberger
    Abstract:

    I propose a quantum gravity model in which Geometric Space emerges from random bits in a quantum phase transition driven by the combinatorial Ollivier-Ricci curvature and corresponding to the condensation of short cycles in random graphs. This quantum critical point defines quantum gravity non-perturbatively. In the ordered Geometric phase at large distances the action reduces to the standard Einstein-Hilbert term.

Kun Guo - One of the best experts on this subject based on the ideXlab platform.

  • a hybrid packet classification algorithm based on hash table and Geometric Space partition
    IEEE International Conference on Data Science in Cyberspace, 2019
    Co-Authors: Jiamin Huang, Kun Guo
    Abstract:

    The emergence of integrated Space-ground network (ISGN), with more complex network conditions compared with tradition network, requires packet classification to achieve high performance. Packet classification plays an important role in the field of network security. Although several existing classification schemes have been proposed recently to improve classification performance, the performance of these schemes is unable to meet the high-speed packet classification requirement in ISGN. To tackle this problem, a hybrid packet classification algorithm based on hash table and Geometric Space partition (HGSP) is proposed in this paper. HGSP falls into two sections: Geometric Space partition and hash matching. To improve the classification speed under the same accuracy, a parallel structure of hash table is designed to match the huge packets for classifying. The experimental results demonstrate that the matching time of HGSP algorithm is reduced by 40%-70% compared with traditional Hicuts algorithm. Particularly, with the growth of ruleset, the advantage of HGSP algorithm will become more obvious.

  • DSC - A Hybrid Packet Classification Algorithm Based on Hash Table and Geometric Space Partition
    2019 IEEE Fourth International Conference on Data Science in Cyberspace (DSC), 2019
    Co-Authors: Jiamin Huang, Kun Guo
    Abstract:

    The emergence of integrated Space-ground network (ISGN), with more complex network conditions compared with tradition network, requires packet classification to achieve high performance. Packet classification plays an important role in the field of network security. Although several existing classification schemes have been proposed recently to improve classification performance, the performance of these schemes is unable to meet the high-speed packet classification requirement in ISGN. To tackle this problem, a hybrid packet classification algorithm based on hash table and Geometric Space partition (HGSP) is proposed in this paper. HGSP falls into two sections: Geometric Space partition and hash matching. To improve the classification speed under the same accuracy, a parallel structure of hash table is designed to match the huge packets for classifying. The experimental results demonstrate that the matching time of HGSP algorithm is reduced by 40%-70% compared with traditional Hicuts algorithm. Particularly, with the growth of ruleset, the advantage of HGSP algorithm will become more obvious.

Amnon Yariv - One of the best experts on this subject based on the ideXlab platform.

  • Algebraic and Geometric Space-time analogies in nonlinear optical pulse propagation
    Optics letters, 2002
    Co-Authors: Shayan Mookherjea, Amnon Yariv
    Abstract:

    We extend recently developed algebraic Space time analogies for the dispersive and nonlinear propagation of optical breathers. Geometrical arguments can explain the similarity of evolutionary behavior between spatial and temporal phenomena even when strict algebraic translation of solutions may not be possible. This explanation offers a new set of tools for understanding and predicting the evolutionary structure of self-consistent Gaussian breathers in nonlinear optical fibers.

Farrokh Mistree - One of the best experts on this subject based on the ideXlab platform.

  • Platform Design for Customizable Products as a Problem of Access in a Geometric Space
    Engineering Optimization, 2003
    Co-Authors: Gabriel Hernandez, Janet K. Allen, Farrokh Mistree
    Abstract:

    A product platform is a set of common components, modules or parts from which a stream of derivative products can be created. Product platform design is typically performed as redesign and consolidation of existing products to create more competitive product families by reducing part variety and standardizing components. The main disadvantage of such an approach is that the benefits of product platform design are achieved only after a number of parts have been designed and manufactured, with all the associated expenditure. A number of approaches, referred to as “top-down approaches”, have been proposed recently to design the platforms since the original design of the product families. However, current top-own approaches have two major limitations: (1) they do not enable multiple levels of commonality for different components and features, and (2) they have been applied to products that are variegated in one specification, whereas products are typically variegated in multiple specifications. This paper des...

  • AN APPLICATION OF CONSTRUCTAL THEORY IN THE MULTI-OBJECTIVE DESIGN OF PRODUCT PLATFORMS
    Volume 3b: 15th International Conference on Design Theory and Methodology, 2003
    Co-Authors: Michael J. Carone, Janet K. Allen, Christopher B. Williams, Farrokh Mistree
    Abstract:

    Designers develop product platforms when they wish to offer variety to the customer and simultaneously keep costs down to a reasonable level. It has been shown that it is feasible and useful to design hierarchic product platforms for customizable products as a problem of optimization of access in a Geometric Space, allowing the designer to thoroughly explore a product family’s market Space. However, the presence of risk, uncertainty, and tradeoffs, which are inevitable aspects of a real-world design problem, are not considered in this method. We have addressed these limitations through the infusion of utility theory into the multi-stage decision-making process. The proposed approach is illustrated with an example: the design of a product platform for a line of customizable pressure vessels.Copyright © 2003 by ASME

Jiamin Huang - One of the best experts on this subject based on the ideXlab platform.

  • a hybrid packet classification algorithm based on hash table and Geometric Space partition
    IEEE International Conference on Data Science in Cyberspace, 2019
    Co-Authors: Jiamin Huang, Kun Guo
    Abstract:

    The emergence of integrated Space-ground network (ISGN), with more complex network conditions compared with tradition network, requires packet classification to achieve high performance. Packet classification plays an important role in the field of network security. Although several existing classification schemes have been proposed recently to improve classification performance, the performance of these schemes is unable to meet the high-speed packet classification requirement in ISGN. To tackle this problem, a hybrid packet classification algorithm based on hash table and Geometric Space partition (HGSP) is proposed in this paper. HGSP falls into two sections: Geometric Space partition and hash matching. To improve the classification speed under the same accuracy, a parallel structure of hash table is designed to match the huge packets for classifying. The experimental results demonstrate that the matching time of HGSP algorithm is reduced by 40%-70% compared with traditional Hicuts algorithm. Particularly, with the growth of ruleset, the advantage of HGSP algorithm will become more obvious.

  • DSC - A Hybrid Packet Classification Algorithm Based on Hash Table and Geometric Space Partition
    2019 IEEE Fourth International Conference on Data Science in Cyberspace (DSC), 2019
    Co-Authors: Jiamin Huang, Kun Guo
    Abstract:

    The emergence of integrated Space-ground network (ISGN), with more complex network conditions compared with tradition network, requires packet classification to achieve high performance. Packet classification plays an important role in the field of network security. Although several existing classification schemes have been proposed recently to improve classification performance, the performance of these schemes is unable to meet the high-speed packet classification requirement in ISGN. To tackle this problem, a hybrid packet classification algorithm based on hash table and Geometric Space partition (HGSP) is proposed in this paper. HGSP falls into two sections: Geometric Space partition and hash matching. To improve the classification speed under the same accuracy, a parallel structure of hash table is designed to match the huge packets for classifying. The experimental results demonstrate that the matching time of HGSP algorithm is reduced by 40%-70% compared with traditional Hicuts algorithm. Particularly, with the growth of ruleset, the advantage of HGSP algorithm will become more obvious.