Learning about knowledge: A complex network approach

This article describes an approach to modeling knowledge acquisition in terms of walks along complex networks. Each subset of knowledge is represented as a node, and relations between such knowledge are expressed as edges. Two types of edges are considered, corresponding to free and conditional transitions. The latter case implies that a node can only be reached after visiting previously a set of nodes (the required conditions). The process of knowledge acquisition can then be simulated by considering the number of nodes visited as a single agent moves along the network, starting from its lowest layer. It is shown that hierarchical networks, i.e. networks composed of successive interconnected layers, arise naturally as a consequence of compositions of the prerequisite relationships between the nodes. In order to avoid deadlocks, i.e. unreachable nodes, the subnetwork in each layer is assumed to be a connected component. Several configurations of such hierarchical knowledge networks are simulated and the performance of the moving agent quantified in terms of the percentage of visited nodes after each movement. The Barab\'asi-Albert and random models are considered for the layer and interconnecting subnetworks. Although all subnetworks in each realization have the same number of nodes, several interconnectivities, defined by the average node degree of the interconnection networks, have been considered. Two visiting strategies are investigated: random choice among the existing edges and preferential choice to so far untracked edges. A series of interesting results are obtained, including the identification of a series of plateaux of knowledge stagnation in the case of the preferential movements strategy in presence of conditional edges.Comment: 18 pages, 19 figure

Average shape of fluctuations for subdiffusive walks

We study the average shape of fluctuations for subdiffusive processes, i.e., processes with uncorrelated increments but where the waiting time distribution has a broad power-law tail. This shape is obtained analytically by means of a fractional diffusion approach. We find that, in contrast with processes where the waiting time between increments has finite variance, the fluctuation shape is no longer a semicircle: it tends to adopt a table-like form as the subdiffusive character of the process increases. The theoretical predictions are compared with numerical simulation results.Comment: 4 pages, 6 figures. Accepted for publication Phys. Rev. E (Replaced for the latest version, in press.) Section II rewritte

Collaboration in sensor network research: an in-depth longitudinal analysis of assortative mixing patterns

Many investigations of scientific collaboration are based on statistical analyses of large networks constructed from bibliographic repositories. These investigations often rely on a wealth of bibliographic data, but very little or no other information about the individuals in the network, and thus, fail to illustrate the broader social and academic landscape in which collaboration takes place. In this article, we perform an in-depth longitudinal analysis of a relatively small network of scientific collaboration (N = 291) constructed from the bibliographic record of a research center involved in the development and application of sensor network and wireless technologies. We perform a preliminary analysis of selected structural properties of the network, computing its range, configuration and topology. We then support our preliminary statistical analysis with an in-depth temporal investigation of the assortative mixing of selected node characteristics, unveiling the researchers' propensity to collaborate preferentially with others with a similar academic profile. Our qualitative analysis of mixing patterns offers clues as to the nature of the scientific community being modeled in relation to its organizational, disciplinary, institutional, and international arrangements of collaboration.Comment: Scientometrics (In press

Anomalous accelerations in spacecraft flybys of the Earth

[EN] The flyby anomaly is a persistent riddle in astrodynamics. Orbital analysis in several flybys of the Earth since the Galileo spacecraft flyby of the Earth in 1990 have shown that the asymptotic post-encounter velocity exhibits a difference with the initial velocity that cannot be attributed to conventional effects. To elucidate its origin, we have developed an orbital program for analyzing the trajectory of the spacecraft in the vicinity of the perigee, including both the Sun and the Moon¿s tidal perturbations and the geopotential zonal, tesseral and sectorial harmonics provided by the EGM96 model. The magnitude and direction of the anomalous acceleration acting upon the spacecraft can be estimated from the orbital determination program by comparing with the trajectories fitted to telemetry data as provided by the mission teams. This acceleration amounts to a fraction of a mm/s2 and decays very fast with altitude. The possibility of some new physics of gravity in the altitude range for spacecraft flybys is discussed.Acedo Rodríguez, L. (2017). Anomalous accelerations in spacecraft flybys of the Earth. Astrophysics and Space Science. 362(12):1-15. doi:10.1007/s10509-017-3205-xS11536212Acedo, L.: Galaxies 3, 113 (2015)Acedo, L.: Mon. Not. R. Astron. Soc. 463(2), 2119 (2016)Acedo, L.: Adv. Space Res. 59(7), 1715 (2017). 1701.06939Acedo, L., Bel, L.: Astron. Nachr. 338(1), 117 (2017). 1602.03669Adler, S.L.: Int. J. Mod. Phys. A 25, 4577 (2010). 0908.2414 . doi: 10.1142/S0217751X10050706Adler, S.L.: In: Proceedings of the Conference in Honour of Murray Gellimann’s 80th Birthday, p. 352 (2011). doi: 10.1142/9789814335614_0032Anderson, J.D., Nieto, M.M.: In: Klioner, S.A., Seidelmann, P.K., Soffel, M.H. (eds.) Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis. IAU Symposium, vol. 261, p. 189 (2010). doi: 10.1017/S1743921309990378Anderson, J.D., Laing, P.A., Lau, E.L., Liu, A.S., Nieto, M.M., Turyshev, S.G.: Phys. Rev. Lett. 81(14), 2858 (1998). gr-qc/0104064 . doi: 10.1103/PhysRevLett.81.2858Anderson, J.D., Laing, P.A., Lau, E.L., Liu, A.S., Nieto, M.M., Turyshev, S.G.: Phys. Rev. D 65(8), 082004 (2002). gr-qc/0104064 . doi: 10.1103/PhysRevD.65.082004Anderson, J.D., Campbell, J.K., Ekelund, J.E., Ellis, J., Jordan, J.F.: Phys. Rev. Lett. 100(9), 091102 (2008). doi: 10.1103/PhysRevLett.100.091102Atchison, J.A., Peck, M.A.: J. Guid. Control Dyn. 33, 1115 (2010). doi: 10.2514/1.47413Bertolami, O., Francisco, F., Gil, P.J.S.: Class. Quantum Gravity 33(12), 125021 (2016). 1507.08457 . doi: 10.1088/0264-9381/33/12/125021Bolton, S.J., Adriani, A., Adumitroaie, V., Allison, M., Anderson, J., Atreya, S., Bloxham, J., Brown, S., Connerney, J.E.P., DeJong, E., Folkner, W., Gautier, D., Grassi, D., Gulkis, S., Guillot, T., Hansen, C., Hubbard, W.B., Iess, L., Ingersoll, A., Janssen, M., Jorgensen, J., Kaspi, Y., Levin, S.M., Li, C., Lunine, J., Miguel, Y., Mura, A., Orton, G., Owen, T., Ravine, M., Smith, E., Steffes, P., Stone, E., Stevenson, D., Thorne, R., Waite, J., Durante, D., Ebert, R.W., Greathouse, T.K., Hue, V., Parisi, M., Szalay, J.R., Wilson, R.: Science 356, 821 (2017). doi: 10.1126/science.aal2108Cahill, R.T.: ArXiv e-prints (2008). 0804.0039Chamberlin, A., Yeomans, D., Giorgini, J., Chodas, P.: Horizons Ephemeris System (2016). http://ssd.jpl.nasa.gov/horizons.cgi . Accessed: 2016-10-27Chao, B.F.: C. R. Géosci. 338, 1123 (2006). doi: 10.1016/j.crte.2006.09.014Coddington, E., Levinson, N.: McGraw-Hill, New York (1955)Debono, I., Smoot, G.F.: Universe 2(4), 23 (2016). doi: 10.3390/universe2040023Desai, S.D.: J. Geophys. Res., Oceans 107(C11), 7 (2002). 3186. doi: 10.1029/2001JC001224Dickey, J.O., Bender, P.L., Faller, J.E., Newhall, X.X., Ricklefs, R.L., Ries, J.G., Shelus, P.J., Veillet, C., Whipple, A.L., Wiant, J.R., Williams, J.G., Yoder, C.F.: Science 265, 482 (1994). doi: 10.1126/science.265.5171.482Dyson, F.W., Eddington, A.S., Davidson, C.: Philos. Trans. R. Soc. Lond., Ser. A 220, 291 (1920). doi: 10.1098/rsta.1920.0009Everitt, C.W.F., et al.: Phys. Rev. Lett. 221101(106) (2011)Feng, J.L., Fornal, B., Galon, I., Gardner, S., Smolinsky, J., Tait, T.M.P., Tanedo, P.: Phys. Rev. Lett. 117, 071803 (2016). 1604.07411 . doi: 10.1103/PhysRevLett.117.071803Folkner, W.M., Williams, J.G., Boggs, D.H., Park, R.S., Kuchynka, P.: IPN Prog. Rep. 42(196) (2014)Fornberg, B.: Math. Comput. 51(184), 699 (1988). doi: 10.1090/S0025-5718-1988-0935077-0Franklin, A., Fischback, E.: The Rise and Fall of the Fifth Force. Discovery, Pursuit, and Justification in Modern Physics, second edition. Springer, New York (2016)Giorgini, J.D.: Personal communication (2015)Hackmann, E., Laemmerzahl, C.: In: 38th COSPAR Scientific Assembly. COSPAR Meeting, vol. 38, p. 3 (2010)Hafele, J.C.: ArXiv e-prints (2009). 0904.0383ICGEM: International Center for Global Gravity Field Models. http://icgem.gfz-potsdam.de/tom_longtimeIERS: In: Petit, G., Luzum, B. (eds.) IERS Conventions (2010), p. 1. Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main (2010)Iess, L., Asmar, S.: Int. J. Mod. Phys. D 16, 2117 (2007). doi: 10.1142/S0218271807011449Iess, L., Asmar, S., Tortora, P.: Acta Astronaut. 65, 666 (2009). doi: 10.1016/j.actaastro.2009.01.049Iess, L., Di Benedetto, M., James, M., Mercolino, M., Simone, L., Tortora, P.: Acta Astronaut. 94, 699 (2014). doi: 10.1016/j.actaastro.2013.06.011Iorio, L.: Sch. Res. Exch. (2009). 0811.3924 . doi: 10.3814/2009/807695Iorio, L.: Astron. J. 142, 68 (2011a). 1102.4572 . doi: 10.1088/0004-6256/142/3/68Iorio, L.: Mon. Not. R. Astron. Soc. 415, 1266 (2011b). 1102.0212Iorio, L.: Europhys. Lett. (2011c). 1105.4145 . doi: 10.1209/0295-5075/96/30001Iorio, L.: Adv. Space Res. 54(11), 2441 (2014a). 1311.4218 . doi: 10.1016/j.asr.2014.06.035Iorio, L.: Galaxies 2, 259 (2014b). 1404.6537 . doi: 10.3390/galaxies2020259Iorio, L.: Universe 1(1), 38 (2015a). doi: 10.3390/universe1010038Iorio, L.: Int. J. Mod. Phys. D 24, 1530015 (2015b). 1412.7673Iorio, L., Giudice, G.: New Astron. 11, 600 (2006). gr-qc/0601055Iorio, L., Lichtenegger, H.I.M., Ruggiero, M.L., Corda, C.: Astrophys. Space Sci. 331, 351 (2011). 1009.3225 . doi: 10.1007/s10509-010-0489-5Jouannic, B., Noomen, R., van den IJSel, J.A.A.: In: Proceedings of the 25th International Symposium on Space Flight Dynamics ISSFD, Munich, Germany (2015)Kennefick, D.: Phys. Today 62, 37 (2009). doi: 10.1063/1.3099578King-Hele, D.: Satellite Orbits in an Atmosphere. Theory and Applications. Blackie and Son Ltd., Glasgow (1987)Lämmerzahl, C., Preuss, O., Dittus, H.: In: Dittus, H., Lammerzahl, C., Turyshev, S.G. (eds.) Lasers, Clocks and Drag-Free Control: Exploration of Relativistic Gravity in Space. Astrophysics and Space Science Library, vol. 349, p. 75 (2008). doi: 10.1007/978-3-540-34377-6_3Le Verrier, U.: C. R. Hebd. Acad. Sci. 49, 379 (1859)Lemoine, F.G.E.A.: NASA/TP-1998-206861 (1998)Lewis, R.A.: In: Robertson, G.A. (ed.) American Institute of Physics Conference Series. American Institute of Physics Conference Series, vol. 1103, p. 226 (2009). doi: 10.1063/1.3115499Longair, M.: Philos. Trans. R. Soc., Math. Phys. Eng. Sci. (2015). doi: 10.1098/rsta.2014.0287McCulloch, M.E.: Mon. Not. R. Astron. Soc. 389, 57 (2008). 0806.4159 . doi: 10.1111/j.1745-3933.2008.00523.xMoe, M.M., Wallace, S.D., Moe, K.: In: Washington DC American Geophysical Union Geophysical Monograph Series, vol. 87, p. 349 (1995). doi: 10.1029/GM087p0349Murphy, E.M.: Phys. Rev. Lett. 83, 1890 (1998). doi: 10.1103/PhysRevLett.83.1890Naval Observatory: Dept. of the Navy, USA (2009)Newcomb, S.: Tables of the Four Inner Planets. Government Printing Office, Washington (1895)Nyambuya, G.G.: ArXiv e-prints (2008). 0803.1370Nyambuya, G.G.: New Astron. 57, 22 (2017). doi: 10.1016/j.newast.2017.06.001Páramos, J., Hechenblaikner, G.: Adv. Space Res. 79–80(7), 76 (2013). 1210.7333v1Peskin, M.E., Schroeder, D.V.: An Introduction to Quantum Field Theory. Westview Press, Perseus Books Group, London (1995)Pinheiro, M.J.: Phys. Lett. A 378, 3007 (2014). 1404.1101Pinheiro, M.J.: Mon. Not. R. Astron. Soc. 461(4), 3948 (2016)Renzetti, G.: Cent. Eur. J. Phys. 11, 531 (2013). doi: 10.2478/s11534-013-0189-1Rievers, B., Lämmerzahl, C.: Ann. Phys. 523, 439 (2011). 1104.3985 . doi: 10.1002/andp.201100081Roseveare, N.T.: Mercury’s Perihelion, from Le Verrier to Einstein. Clarendon Press, Wotton-under-Edge (1982)Rubincam, D.P.: Icarus 148, 2 (2000). doi: 10.1006/icar.2000.6485Standish, E.M.: In: Macias, A., Lämmerzahl, C., Camacho, A. (eds.) Recent Developments in Gravitation and Cosmology. American Institute of Physics Conference Series, vol. 977, p. 254 (2008). doi: 10.1063/1.2902789Standish, E.M.: In: Klioner, S.A., Seidelmann, P.K., Soffel, M.H. (eds.) Relativity in Fundamental Astronomy: Dynamics, Reference Frames, and Data Analysis. IAU Symposium, vol. 261, p. 179 (2010). doi: 10.1017/S1743921309990354Thompson, P.F., Abrahamson, M., Ardalan, S., Bordi, J.: In: 24th AAS/AIAA Space Flight Mechanics Meeting, Santa Fe, New Mexico, January 26–30, 2014 (2014). http://hdl.handle.net/2014/45519Turyshev, S.G., Toth, V.T.: Living Rev. Relativ. (2010). 1001.3686 . doi: 10.12942/lrr-2010-4Turyshev, S.G., Toth, V.T., Kinsella, G., Lee, S.-C., Lok, S.M., Ellis, J.: Phys. Rev. Lett. 108(24), 241101 (2012). 1204.2507 . doi: 10.1103/PhysRevLett.108.241101Varieschi, G.U.: Gen. Relativ. Gravit. 46, 1741 (2014). 1401.6503 . doi: 10.1007/s10714-014-1741-zWilhelm, K., Dwivedi, B.N.: Astrophys. Space Sci. 358, 18 (2015). doi: 10.1007/s10509-015-2413-5Will, C.M.: Living Rev. Relativ. 3(9) (2006)Will, C.M.: Class. Quantum Gravity (2015). doi: 10.1098/rsta.2014.0287Will, C.M.: In: Peron, R., Colpi, M., Gorini, V., Moschella, U. (eds.) Gravity: Where Do We Stand? Astrophysics and Space Science Library, vol. 349, p. 9 (2016). doi: 10.1007/978-3-319-20224-2_2Williams, J.G., Boggs, D.H.: Celest. Mech. Dyn. Astron. 126, 89 (2016). doi: 10.1007/s10569-016-9702-3Williams, J.G., Dickey, J.O.: In: Noomen, R., Klosko, S., Noll, C., Pearlman, M. (eds.) Proceedings of 13th International Workshop on Laser Ranging, p. 75 (2003). http://cddisa.gsfc.nasa.gov/lw13/lw_proceedings.htmlWilliams, J.G., Newhall, X.X., Dickey, J.O.: Phys. Rev. D 53, 6730 (1996). doi: 10.1103/PhysRevD.53.6730Williams, J.G., Turyshev, S.G., Boggs, D.H.: Phys. Rev. Lett. 93(26), 261101 (2004). gr-qc/0411113 . doi: 10.1103/PhysRevLett.93.261101Williams, J.G., Turyshev, S.G., Boggs, D.H.: Planet. Sci. 3, 2 (2014). doi: 10.1186/s13535-014-0002-5Williams, J.G., Boggs, D.H., Yoder, C.F., Ratcliff, J.T., Dickey, J.O.: J. Geophys. Res. 106, 27933 (2001). doi: 10.1029/2000JE001396Wolfram, S.: The Mathematica Book, fifth edition. Wolfram Media, Champaign (2003

Order statistics of the trapping problem

When a large number N of independent diffusing particles are placed upon a site of a d-dimensional Euclidean lattice randomly occupied by a concentration c of traps, what is the m-th moment of the time t_{j,N} elapsed until the first j are trapped? An exact answer is given in terms of the probability Phi_M(t) that no particle of an initial set of M=N, N-1,..., N-j particles is trapped by time t. The Rosenstock approximation is used to evaluate Phi_M(t), and it is found that for a large range of trap concentracions the m-th moment of t_{j,N} goes as x^{-m} and its variance as x^{-2}, x being ln^{2/d} (1-c) ln N. A rigorous asymptotic expression (dominant and two corrective terms) is given for for the one-dimensional lattice.Comment: 11 pages, 7 figures, to be published in Phys. Rev.

Reaction Front in an A+B -> C Reaction-Subdiffusion Process

We study the reaction front for the process A+B -> C in which the reagents move subdiffusively. Our theoretical description is based on a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive character of the process. We design numerical simulations to check our theoretical results, describing the simulations in some detail because the rules necessarily differ in important respects from those used in diffusive processes. Comparisons between theory and simulations are on the whole favorable, with the most difficult quantities to capture being those that involve very small numbers of particles. In particular, we analyze the total number of product particles, the width of the depletion zone, the production profile of product and its width, as well as the reactant concentrations at the center of the reaction zone, all as a function of time. We also analyze the shape of the product profile as a function of time, in particular its unusual behavior at the center of the reaction zone

Random Convex Hulls and Extreme Value Statistics

In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy's formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of $n$ independent random walks. In the continuum time limit this reduces to $n$ independent planar Brownian trajectories for which we compute exactly, for all $n$, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].Comment: 61 pages (pedagogical review); invited contribution to the special issue of J. Stat. Phys. celebrating the 50 years of Yeshiba/Rutgers meeting