6,920 research outputs found

    Teleportation Topology

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    We discuss the structure of teleportation. By associating matrices to the preparation and measurement states, we show that for a unitary transformation M there is a full teleportation procedure for obtaining M|S> from a given state |S>. The key to this construction is a diagrammatic intepretation of matrix multiplication that applies equally well to a topological composition of a maximum and a minimum that underlies the structure of the teleportation. This paper is a preliminary report on joint work with H. Carteret and S. Lomonaco.Comment: LaTeX document, 16 pages, 8 figures, Talk delivered at the Xth International Conference on Quantum Optics, Minsk, Belaru

    Are Dark Energy and Dark Matter Different Aspects of the Same Physical Process?

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    It is suggested that the apparently disparate cosmological phenomena attributed to so-called 'dark matter' and 'dark energy' arise from the same fundamental physical process: the emergence, from the quantum level, of spacetime itself. This creation of spacetime results in metric expansion around mass points in addition to the usual curvature due to stress-energy sources of the gravitational field. A recent modification of Einstein's theory of general relativity by Chadwick, Hodgkinson, and McDonald incorporating spacetime expansion around mass points, which accounts well for the observed galactic rotation curves, is adduced in support of the proposal. Recent observational evidence corroborates a prediction of the model that the apparent amount of 'dark matter' increases with the age of the universe. In addition, the proposal leads to the same result for the small but nonvanishing cosmological constant, related to 'dark energy, as that of the causet model of Sorkin et al.Comment: Some typos corrected. Comments welcome, pro or co

    The computational complexity of Kauffman nets and the P versus NP problem

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    Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown that the parameters of a specific model can be adjusted so that the problem of finding its global energy minimum is extremely sensitive to small changes in the problem statement. This result has implications not only for studies of the physics of random systems but may also lead to new strategies for resolving the well-known P versus NP question in computational complexity theory.Comment: 4 pages, no figure

    Phase transition in a class of non-linear random networks

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    We discuss the complex dynamics of a non-linear random networks model, as a function of the connectivity k between the elements of the network. We show that this class of networks exhibit an order-chaos phase transition for a critical connectivity k = 2. Also, we show that both, pairwise correlation and complexity measures are maximized in dynamically critical networks. These results are in good agreement with the previously reported studies on random Boolean networks and random threshold networks, and show once again that critical networks provide an optimal coordination of diverse behavior.Comment: 9 pages, 3 figures, revised versio

    The Number of Different Binary Functions Generated by NK-Kauffman Networks and the Emergence of Genetic Robustness

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    We determine the average number ϑ(N,K) \vartheta (N, K) , of \textit{NK}-Kauffman networks that give rise to the same binary function. We show that, for N1 N \gg 1 , there exists a connectivity critical value Kc K_c such that ϑ(N,K)eϕN \vartheta(N,K) \approx e^{\phi N} (ϕ>0 \phi > 0 ) for K<Kc K < K_c and ϑ(N,K)1\vartheta(N,K) \approx 1 for K>Kc K > K_c . We find that Kc K_c is not a constant, but scales very slowly with N N , as Kclog2log2(2N/ln2) K_c \approx \log_2 \log_2 (2N / \ln 2) . The problem of genetic robustness emerges as a statistical property of the ensemble of \textit{NK}-Kauffman networks and impose tight constraints in the average number of epistatic interactions that the genotype-phenotype map can have.Comment: 4 figures 18 page

    On the number of attractors in random Boolean networks

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    The evaluation of the number of attractors in Kauffman networks by Samuelsson and Troein is generalized to critical networks with one input per node and to networks with two inputs per node and different probability distributions for update functions. A connection is made between the terms occurring in the calculation and between the more graphic concepts of frozen, nonfrozen and relevant nodes, and relevant components. Based on this understanding, a phenomenological argument is given that reproduces the dependence of the attractor numbers on system size.Comment: 6 page
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