Analytical properties of horizontal visibility graphs in the Feigenbaum scenario

Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [B. Luque et al., PLoS ONE 6, 9 (2011)] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-doubling and band-splitting attractor cascades that characterize unimodal maps transform into families of graphs that turn out to be independent of map nonlinearity or other particulars. Here, we provide an in depth description of the HV treatment of the Feigenbaum scenario, together with analytical derivations that relate to the degree distributions, mean distances, clustering coefficients, etc., associated to the bifurcation cascades and their accumulation points. We describe how the resultant families of graphs can be framed into a renormalization group scheme in which fixed-point graphs reveal their scaling properties. These fixed points are then re-derived from an entropy optimization process defined for the graph sets, confirming a suggested connection between renormalization group and entropy optimization. Finally, we provide analytical and numerical results for the graph entropy and show that it emulates the Lyapunov exponent of the map independently of its sign.

Annotated record of the detailed examination of Mn deposits from the H.M.S. Sealark Percy Sladen Trust Expedition in the Indian ocean

In 1905, the Percy Sladen Trust Expedition, under the supervision of Stanley Gardiner in H.M.S. 'Sealark' made an extensive cruise in the Indian Ocean. The author received 79 samples from Mr. Gardiner which were thoroughly examined.

Annotated record of the detailed examination of Mn deposits from the H.M.S. Egeria, H.M.S. Fling Fish and H.M.S. Investigator expeditions in the Indian Ocean and Southern Seas

Captain Wharton, the Hydrographer of the Admiralty sent to the author a series of the deposit-samples collected in the Indian and Antarctic Oceans during the expeditions in 1887 of H.M.S. Flying Fish, H.M.S. Egeria and H.M.S. Investigator. These deposits were submitted to careful microscopical examination and chemical analysis.

Journal of a tour in the "Indian territory," : performed by order of the Domestic Committee of the Board of Missions of the Protestant Episcopal Church, in the spring of 1844, by their secretary and general agent.

Disbound Original Held in Oak Street Library Facility.

Recent developments concerning foreign agent harassment of people in the United States [microform] : hearing before the Subcommittee on Human Rights and International Organizations of the Committee on Foreign Affairs, House of Representatives, One Hundredth Congress, second session, April 21, 1988.

CIS Microfiche Accession Numbers: CIS 89 H381-53

Reports of decisions in the Supreme court of British Guiana ... and in the West Indian court of appeal

Editors: 19 -1921, L.C. Dalton; 1922, L.C. Dalton, S.J. Van Sertima; 1923, S.J. Van Sertima; 1924, E.M. Duke; 1925, E.M. Duke, S.J. Van Sertima; 1926-1930, S.J. Van Sertime; 1931, E.M. Duke

Second history of Charlestown, N.H., the Old Number Four; embracing a summary of the early history of the town from its settlement to 1876 and more particularly developments and events in the town from 1876 to 1954.

Bibliography: p. 430-433.

Manual of instruction in the use of dumb bells, indian clubs and other exercises

Mode of access: Internet.

Notes on Indian Diptera. 1. Diptera from the Khasia hills. 2. Tabanidae in the collection of the forest zoologist. 3. New species of Diptera from the Indian region,

Mode of access: Internet.