Reply to Comment on ``Towards a large deviation theory for strongly correlated systems''

The computational study commented by Touchette opens the door to a desirable generalization of standard large deviation theory for special, though ubiquitous, correlations. We focus on three interrelated aspects: (i) numerical results strongly suggest that the standard exponential probability law is asymptotically replaced by a power-law dominant term; (ii) a subdominant term appears to reinforce the thermodynamically extensive entropic nature of q-generalized rate function; (iii) the correlations we discussed, correspond to Q -Gaussian distributions, differing from Lévy?s, except in the case of Cauchy?Lorentz distributions. Touchette has agreeably discussed point (i), but, unfortunately, points (ii) and (iii) escaped to his analysis. Claiming the absence of connection with q-exponentials is unjustified.

Electrodynamic Tethers For Planetary And De-orbiting Missions

Nuevas aplicaciones tecnológicas y científicas mediante amarras electrodinámicas son analizadas para misiones planetarias. i) Primero, se considera un conjunto de amarras cilíndricas en paralelo (veleros electrosolares) para una misión interplanetaria. Los iones provenientes del viento solar son repelidos por el alto potencial de dichas amarras generando empuje sobre el velero. Para conocer el intercambio de momento que provocan los iones sobre las amarras se ha considerado un modelo de potencial estacionario. Se ha analizado la transferencia orbital de la Tierra a Júpiter siguiendo un método de optimización de trayectoria indirecto. ii) Una vez que el velero se encuentra cerca de Júpiter, se ha considerado el despliegue de una amarra para diferentes objetivos científicos. iia) Una amarra podría ser utilizada para diagnóstico de plasmas, al ser una fuente efectiva de ondas, y también como un generador de auroras artificiales. Una amarra conductora que orbite en la magnetosfera jovial es capaz de producir ondas. Se han analizado las diferentes ondas radiadas por un conductor por el que circula una corriente constante que sigue una órbita polar de alta excentricidad y bajo apoápside, como ocurre en la misión Juno de la NASA. iib) Además, se ha estudiado una misión tentativa que sigue una órbita ecuatorial (LJO) por debajo de los intensos cinturones de radiación. Ambas misiones requiren potencia eléctrica para los sistemas de comunicación e instrumentos científicos. Las amarras pueden generar potencia de manera más eficiente que otros sistemas que utlizan paneles solares o sistemas de potencia de radioisótopos (RPS). La impedancia de radiación es necesaria para determinar la corriente que circula por todo el circuito de la amarra. En un modelo de plasma frío, la radiación ocurre principalmente en los modos de Alfven y magnetosónica rápida, mostrando un elevado índice de refracción. Se ha estudiado la impedancia de radiación en amarras con recubrimiento aislante para los dos modos de radiación y cada una de las misiones. A diferencia del caso ionosférico terrestre, la baja densidad y el intenso campo magnético que aparecen en el entorno de Júpiter consiguen que la girofrecuencia de los electrones sea mucho mayor que la frecuencia del plasma; esto hace que el espectro de potencia para cada modo se modifique substancialmente, aumentando la velocidad de Alfven. Se ha estimado también la impedancia de radiación para amarras sin aislante conductor. En la misión LJO, un vehículo espacial bajando lentamente la altitud de su órbita permitiría estudiar la estructura del campo magnético y composición atmosférica para entender la formación, evolución, y estructura de Júpiter. Adicionalmente, si el contactor (cátodo) se apaga, se dice que la amarra flota eléctricamente, permitiendo emisión de haz de electrones que generan auroras. El continuo apagado y encendido produce pulsos de corriente dando lugar a emisiones de señales, que pueden ser utilizadas para diagnóstico del plasma jovial. En Órbita Baja Jovial, los iones que impactan contra una amarra polarizada negativamente producen electrones secundarios, que, viajando helicoidalmente sobre las líneas de campo magnético de Júpiter, son capaces de alcanzar su atmósfera más alta, y, de esta manera, generar auroras. Se han identificado cuáles son las regiones donde la amarra sería más eficiente para producir auroras. iic) Otra aplicación científica sugerida para la misión LJO es la detección de granos cargados que orbitan cerca de Júpiter. Los electrones de alta energía en este ambiente pueden ser modelados por una distribucción no Maxwelliana conocida como distribución kappa. En escenarios con plasmas complejos, donde los campos eléctricos en Júpiter pueden acelerar las cargas hasta velocidades que superen la velocidad térmica, este tipo de distribuciones son muy útiles. En este caso las colas de las distribuciones de electrones siguen una ley de potencias. Se han estudiado las fluctuaciones de granos cargados para funciones de distribución kappa. iii) La tesis concluye con el análisis para deorbitar satélites con amarras electrodinámicas que siguen una Órbita Baja Terrestre (LEO). Una amarra debe presentar una baja probabilidad de corte por pequeño debris y además debe ser suficientemente ligero para que el cociente entre la masa de la amarra y el satélite sea muy pequeño. En este trabajo se estiman las medidas de la longitud, anchura y espesor que debe tener una amarra para minimizar el producto de la probabilidad de corte por el cociente entre las masas de la amarra y el satélite. Se presentan resultados preliminares del diseño de una amarra con forma de cinta para deorbitar satélites relativamente ligeros como Cryosat y pesados como Envisat. Las misiones espaciales a planetas exteriores y en el ámbito terrestre plantean importantes retos científico-tecnológicos que deben ser abordados y solucionados. Por ello, desde el inicio de la era espacial se han diseñando novedosos métodos propulsivos, sistemas de guiado, navegación y control más robustos, y nuevos materiales para mejorar el rendimiento de los vehículos espaciales (SC). En un gran número de misiones interplanetarias y en todas las misiones a planetas exteriores se han empleado sistemas de radioisótopos (RPS) para generar potencia eléctrica en los vehículos espaciales y en los rovers de exploración. Estos sistemas emplean como fuente de energía el escaso y costoso plutonio-238. La NASA, por medio de un informe de la National Academy of Science (5 de Mayo del 2009), expresó una profunda preocupación por la baja cantidad de plutonio almacenado, insuficiente para desarrollar todas las misiones de exploración planetaria planeadas en el futuro [81, 91]. Esta circustancia ha llevado a dicha Agencia tomar la decisión de limitar el uso de estos sistemas RPS en algunas misiones de especial interés científico y una recomendación de alta prioridad para que el Congreso de los EEUU apruebe el reestablecimiento de la producción de plutonio-238, -son necesarios cerca de 5 kg de este material radiactivo al año-, para salvaguardar las misiones que requieran dichos sistemas de potencia a partir del año 2018. Por otro lado, la Agencia estadounidense ha estado considerando el uso de fuentes de energía alternativa; como la fisión nuclear a través del ambicioso proyecto Prometheus, para llevar a cabo una misión de exploración en el sistema jovial (JIMO). Finalmente, dicha misión fue desestimada por su elevado coste. Recientemente se han estado desarrollando sistemas que consigan energía a través de los recursos naturales que nos aporta el Sol, mediante paneles solares -poco eficientes para misiones a planetas alejados de la luz solar-. En este contexto, la misión JUNO del programa Nuevas Fronteras de la NASA, cuyo lanzamiento fue realizado con éxito en Agosto de 2011, va a ser la primera misión equipada con paneles solares que sobrevolará Júpiter en el 2015 siguiendo una órbita polar. Anteriormente se habían empleado los antes mencionados RPS para las misiones Pioneer 10,11, Voyager 1,2, Ulysses, Cassini-Huygens y Galileo (todas sobrevuelos excepto Galileo). Dicha misión seguirá una órbita elíptica de alta excentricidad con un periápside muy cercano a Júpiter, y apoápside lejano, evitando que los intensos cinturones de radiación puedan dañar los instrumentos de navegación y científicos. Un tether o amarra electrodinámica es capaz de operar como sistema propulsivo o generador de potencia, pero también puede ser considerado como solución científicotecnológica en misiones espaciales tanto en LEO (Órbita Baja Terrestre) como en planetas exteriores. Siguiendo una perspectiva histórica, durante las misiones terrestres TSS-1 (1992) y TSS-1R (1996) se emplearon amarras estandard con recubrimiento aislante en toda su longitud, aplicando como terminal anódico pasivo un colector esférico para captar electrones. En una geometría alternativa, propuesta por J. R. Sanmartín et al. (1993) [93], se consideró dejar la amarra sin recubrimiento aislante (“bare tether”), y sin colector anódico esférico, de forma que recogiera electrones a lo largo del segmento que resulta polarizado positivo, como si se tratara de una sonda de Langmuir de gran longitud. A diferencia de la amarra estandard, el “bare tether” es capaz de recoger electrones a lo largo de una superficie grande ya que este segmento es de varios kilómetros de longitud. Como el radio de la amarra es del orden de la longitud de Debye y pequeño comparado con el radio de Larmor de los electrones, permite una recolección eficiente de electrones en el régimen OML (Orbital Motion Limited) de sondas de Langmuir. La corriente dada por la teoría OML varía en función del perímetro y la longitud. En el caso de una cinta delgada, el perímetro depende de la anchura, que debe ser suficientemente grande para evitar cortes producidos por debris y micrometeoritos, y suficientemente pequeño para que la amarra funcione en dicho régimen [95]. En el experimento espacial TSS-1R mencionado anteriormente, se identificó una recolección de corriente más elevada que la que predecía el modelo teórico de Parker- Murphy, debido posiblemente a que se utilizaba un colector esférico de radio bastante mayor que la longitud de Debye [79]. En el caso de una amarra “bare”, que recoge electrones a lo largo de gran parte de su longitud, se puede producir un fenómeno conocido como atrapamiento adiabático de electrones (adiabatic electron trapping) [25, 40, 60, 73, 74, 97]. En el caso terrestre (LEO) se da la condición mesotérmica en la que la amarra se mueve con una velocidad muy superior a la velocidad térmica de los iones del ambiente y muy inferior a la velocidad térmica de los electrones. J. Laframboise y L. Parker [57] mostraron que, para una función de distribución quasi-isotrópica, la densidad de electrones debe entonces ser necesariamente inferior a la densidad ambiente. Por otra parte, debido a su flujo hipersónico y a la alta polarización positiva de la amarra, la densidad de los iones es mayor que la densidad ambiente en una vasta región de la parte “ram” del flujo, violando la condición de cuasi-neutralidad,-en una región de dimensión mayor que la longitud de Debye-. La solución a esta paradoja podría basarse en el atrapamiento adiabático de electrones ambiente en órbitas acotadas entorno al tether. ABSTRACT New technological and scientific applications by electrodynamic tethers for planetary missions are analyzed: i) A set of cylindrical, parallel tethers (electric solar sail or e-sail) is considered for an interplanetary mission; ions from the solar wind are repelled by the high potential of the tether, providing momentum to the e-sail. An approximated model of a stationary potential for a high solar wind flow is considered. With the force provided by a negative biased tether, an indirect method for the optimization trajectory of an Earth-to-Jupiter orbit transfer is analyzed. ii) The deployment of a tether from the e-sail allows several scientific applications in Jupiter. iia) It might be used as a source of radiative waves for plasma diagnostics and artificial aurora generator. A conductive tether orbiting in the Jovian magnetosphere produces waves. Wave radiation by a conductor carrying a steady current in both a polar, highly eccentric, low perijove orbit, as in NASA’s Juno mission, and an equatorial low Jovian orbit (LJO) mission below the intense radiation belts, is considered. Both missions will need electric power generation for scientific instruments and communication systems. Tethers generate power more efficiently than solar panels or radioisotope power systems (RPS). The radiation impedance is required to determine the current in the overall tether circuit. In a cold plasma model, radiation occurs mainly in the Alfven and fast magnetosonic modes, exhibiting a large refraction index. The radiation impedance of insulated tethers is determined for both modes and either mission. Unlike the Earth ionospheric case, the low-density, highly magnetized Jovian plasma makes the electron gyrofrequency much larger than the plasma frequency; this substantially modifies the power spectrum for either mode by increasing the Alfven velocity. An estimation of the radiation impedance of bare tethers is also considered. iib) In LJO, a spacecraft orbiting in a slow downward spiral under the radiation belts would allow determining magnetic field structure and atmospheric composition for understanding the formation, evolution, and structure of Jupiter. Additionally, if the cathodic contactor is switched off, a tether floats electrically, allowing e-beam emission that generate auroras. On/off switching produces bias/current pulses and signal emission, which might be used for Jovian plasma diagnostics. In LJO, the ions impacting against the negative-biased tether do produce secondary electrons, which racing down Jupiter’s magnetic field lines, reach the upper atmosphere. The energetic electrons there generate auroral effects. Regions where the tether efficiently should produce secondary electrons are analyzed. iic) Other scientific application suggested in LJO is the in-situ detection of charged grains. Charged grains naturally orbit near Jupiter. High-energy electrons in the Jovian ambient may be modeled by the kappa distribution function. In complex plasma scenarios, where the Jovian high electric field may accelerate charges up superthermal velocities, the use of non-Maxwellian distributions should be considered. In these cases, the distribution tails fit well to a power-law dependence for electrons. Fluctuations of the charged grains for non-Mawellian distribution function are here studied. iii) The present thesis is concluded with the analysis for de-orbiting satellites at end of mission by electrodynamic tethers. A de-orbit tether system must present very small tether-to-satellite mass ratio and small probability of a tether cut by small debris too. The present work shows how to select tape dimensions so as to minimize the product of those two magnitudes. Preliminary results of tape-tether design are here discussed to minimize that function. Results for de-orbiting Cryosat and Envisat are also presented.

A universal scaling law between gray matter and white matter of cerebral cortex

Neocortex, a new and rapidly evolving brain structure in mammals, has a similar layered architecture in species over a wide range of brain sizes. Larger brains require longer fibers to communicate between distant cortical areas; the volume of the white matter that contains long axons increases disproportionally faster than the volume of the gray matter that contains cell bodies, dendrites, and axons for local information processing, according to a power law. The theoretical analysis presented here shows how this remarkable anatomical regularity might arise naturally as a consequence of the local uniformity of the cortex and the requirement for compact arrangement of long axonal fibers. The predicted power law with an exponent of 4/3 minus a small correction for the thickness of the cortex accurately accounts for empirical data spanning several orders of magnitude in brain sizes for various mammalian species, including human and nonhuman primates.

Deep observation of the NGC1275 region with MAGIC: search of diffuse gamma-ray emission from cosmic rays in the Perseus cluster

Clusters of galaxies are expected to be reservoirs of cosmic rays (CRs) that should produce diffuse γ-ray emission due to their hadronic interactions with the intra-cluster medium. The nearby Perseus cool-core cluster, identified as the most promising target to search for such an emission, has been observed with the MAGIC telescopes at very-high energies (VHE, E ≥ 100 GeV) for a total of 253 hr from 2009 to 2014. The active nuclei of NGC 1275, the central dominant galaxy of the cluster, and IC 310, lying at about 0.6º from the centre, have been detected as point-like VHE γ-ray emitters during the first phase of this campaign. We report an updated measurement of the NGC 1275 spectrum, which is described well by a power law with a photon index Γ = 3.6 ± 0.2_(stat) ± 0.2_(syst) between 90 GeV and 1200 GeV. We do not detect any diffuse γ-ray emission from the cluster and so set stringent constraints on its CR population. To bracket the uncertainties over the CR spatial and spectral distributions, we adopt different spatial templates and power-law spectral indexes α. For α = 2.2, the CR-to-thermal pressure within the cluster virial radius is constrained to be ≤ 1 − 2%, except if CRs can propagate out of the cluster core, generating a flatter radial distribution and releasing the CR-to-thermal pressure constraint to ≤ 20%. Assuming that the observed radio mini-halo of Perseus is generated by secondary electrons from CR hadronic interactions, we can derive lower limits on the central magnetic field, B_(0), that depend on the CR distribution. For α = 2.2, B_(0) ≥ 5 − 8 µG, which is below the ∼25 µG inferred from Faraday rotation measurements, whereas for α ≤ 2.1, the hadronic interpretation of the diffuse radio emission contrasts with our γ-ray flux upper limits independently of the magnetic field strength.

Law and the executive in Britain : a comparative study /

Bibliographical footnotes.

Modelling the growth of prion protein aggregates in the brain in variant Creutzfeldt-Jakob disease

Deposition of insoluble prion protein (PrP) in the brain in the form of protein aggregates or deposits is characteristic of the ‘transmissible spongiform encephalopathies’ (TSEs). Understanding the growth and development of these PrP aggregates is important both in attempting to the elucidate of the pathogenesis of prion disease and in the development of treatments designed to prevent or inhibit the spread of prion pathology within the brain. Aggregation and disaggregation of proteins and the diffusion of substances into the developing aggregates (surface diffusion) are important factors in the development of protein aggregates. Mathematical models suggest that if aggregation/disaggregation or surface diffusion is the predominant factor, the size frequency distribution of the resulting protein aggregates in the brain should be described by either a power-law or a log-normal model respectively. This study tested this hypothesis for two different types of PrP deposit, viz., the diffuse and florid-type PrP deposits in patients with variant Creutzfeldt-Jakob disease (vCJD). The size distributions of the florid and diffuse plaques were fitted by a power-law function in 100% and 42% of brain areas studied respectively. By contrast, the size distributions of both types of plaque deviated significantly from a log-normal model in all brain areas. Hence, protein aggregation and disaggregation may be the predominant factor in the development of the florid plaques. A more complex combination of factors appears to be involved in the pathogenesis of the diffuse plaques. These results may be useful in the design of treatments to inhibit the development of protein aggregates in vCJD.

Size frequency distribution of the β-amyloid (aβ) deposits in dementia with Lewy bodies with associated Alzheimer’s disease pathology

The objective is to study beta-amyloid (Abeta) deposition in dementia with Lewy bodies (DLB) with Alzheimer's disease (AD) pathology (DLB/AD). The size frequency distributions of the Abeta deposits were studied and fitted by log-normal and power-law models. Patients were ten clinically and pathologically diagnosed DLB/AD cases. Size distributions had a single peak and were positively skewed and similar to those described in AD and Down's syndrome. Size distributions had smaller means in DLB/AD than in AD. Log-normal and power-law models were fitted to the size distributions of the classic and diffuse deposits, respectively. Size distributions of Abeta deposits were similar in DLB/AD and AD. Size distributions of the diffuse deposits were fitted by a power-law model suggesting that aggregation/disaggregation of Abeta was the predominant factor, whereas the classic deposits were fitted by a log-normal distribution suggesting that surface diffusion was important in the pathogenesis of the classic deposits.

Modelling growth of prion protein aggregates in the brain in variant Creutzfeldt-Jakob disease

Deposition of insoluble prion protein (PrP) in the brain in the form of protein aggregates or deposits is characteristic of the ‘transmissible spongiform encephalopathies’ (TSEs). Understanding the growth and development of PrP aggregates is important both in attempting to elucidate the pathogenesis of prion disease and in the development of treatments designed to inhibit the spread of prion pathology within the brain. Aggregation and disaggregation of proteins and the diffusion of substances into the developing aggregates (surface diffusion) are important factors in the development of protein deposits. Mathematical models suggest that if either aggregation/disaggregation or surface diffusion is the predominant factor, then the size frequency distribution of the resulting protein aggregates will be described by either a power-law or a log-normal model respectively. This study tested this hypothesis for two different populations of PrP deposit, viz., the diffuse and florid-type PrP deposits characteristic of patients with variant Creutzfeldt-Jakob disease (vCJD). The size distributions of the florid and diffuse deposits were fitted by a power-law function in 100% and 42% of brain areas studied respectively. By contrast, the size distributions of both types of aggregate deviated significantly from a log-normal model in all areas. Hence, protein aggregation and disaggregation may be the predominant factor in the development of the florid deposits. A more complex combination of factors appears to be involved in the pathogenesis of the diffuse deposits. These results may be useful in the design of treatments to inhibit the development of PrP aggregates in vCJD.

Synchronization processes in nonlinear systems and their relation to cortical oscillatory dynamics

This thesis was focused on theoretical models of synchronization to cortical dynamics as measured by magnetoencephalography (MEG). Dynamical systems theory was used in both identifying relevant variables for brain coordination and also in devising methods for their quantification. We presented a method for studying interactions of linear and chaotic neuronal sources using MEG beamforming techniques. We showed that such sources can be accurately reconstructed in terms of their location, temporal dynamics and possible interactions. Synchronization in low-dimensional nonlinear systems was studied to explore specific correlates of functional integration and segregation. In the case of interacting dissimilar systems, relevant coordination phenomena involved generalized and phase synchronization, which were often intermittent. Spatially-extended systems were then studied. For locally-coupled dissimilar systems, as in the case of cortical columns, clustering behaviour occurred. Synchronized clusters emerged at different frequencies and their boundaries were marked through oscillation death. The macroscopic mean field revealed sharp spectral peaks at the frequencies of the clusters and broader spectral drops at their boundaries. These results question existing models of Event Related Synchronization and Desynchronization. We re-examined the concept of the steady-state evoked response following an AM stimulus. We showed that very little variability in the AM following response could be accounted by system noise. We presented a methodology for detecting local and global nonlinear interactions from MEG data in order to account for residual variability. We found crosshemispheric nonlinear interactions of ongoing cortical rhythms concurrent with the stimulus and interactions of these rhythms with the following AM responses. Finally, we hypothesized that holistic spatial stimuli would be accompanied by the emergence of clusters in primary visual cortex resulting in frequency-specific MEG oscillations. Indeed, we found different frequency distributions in induced gamma oscillations for different spatial stimuli, which was suggestive of temporal coding of these spatial stimuli. Further, we addressed the bursting character of these oscillations, which was suggestive of intermittent nonlinear dynamics. However, we did not observe the characteristic-3/2 power-law scaling in the distribution of interburst intervals. Further, this distribution was only seldom significantly different to the one obtained in surrogate data, where nonlinear structure was destroyed. In conclusion, the work presented in this thesis suggests that advances in dynamical systems theory in conjunction with developments in magnetoencephalography may facilitate a mapping between levels of description int he brain. this may potentially represent a major advancement in neuroscience.

Temporal correlations of local network losses

We introduce a continuum model describing data losses in a single node of a packet-switched network (like the Internet) which preserves the discrete nature of the data loss process. By construction, the model has critical behavior with a sharp transition from exponentially small to finite losses with increasing data arrival rate. We show that such a model exhibits strong fluctuations in the loss rate at the critical point and non-Markovian power-law correlations in time, in spite of the Markovian character of the data arrival process. The continuum model allows for rather general incoming data packet distributions and can be naturally generalized to consider the buffer server idleness statistics.

Development of areolae and growth of the peripheral prothallus in the crustose lichen Rhizocarpon geographicum:an image analysis study

Areolae of the crustose lichen Rhizocarpon geographicum (L.) DC., are present on the peripheral prothallus (marginal areolae) and also aggregate to form confluent masses in the centre of the thallus (central areolae). To determine the relationships between these areolae and whether growth of the peripheral prothallus is dependent on the marginal areolae, the density, morphology, and size frequency distributions of marginal areolae were measured in 23 thalli of R. geographicum in north Wales, UK using image analysis (Image J). Size and morphology of central areolae were also studied across the thallus. Marginal areolae were small, punctate, and occurred in clusters scattered over the peripheral prothallus while central areolae were larger and had a lobed structure. The size-class frequency distributions of the marginal and central areolae were fitted by power-law and log-normal models respectively. In 16 out of 23 thalli, central areolae close to the outer edge were larger and had a more complex lobed morphology than those towards the thallus centre. Neither mean width nor radial growth rate (RaGR) of the peripheral prothallus were correlated with density, diameter, or area fraction of marginal areolae. The data suggest central areolae may develop from marginal areolae as follows: (1) marginal areolae develop in clusters at the periphery and fuse to form central areolae, (2) central areolae grow exponentially, and (3) crowding of central areolae results in constriction and fragmentation. In addition, growth of the peripheral prothallus may be unrelated to the marginal areolae. © 2013 Springer Science+Business Media Dordrecht.

Coding together at scale:GitHub as a collaborative social network

GitHub is the most popular repository for open source code (Finley 2011). It has more than 3.5 million users, as the company declared in April 2013, and more than 10 million repositories, as of December 2013. It has a publicly accessible API and, since March 2012, it also publishes a stream of all the events occurring on public projects. Interactions among GitHub users are of a complex nature and take place in different forms. Developers create and fork repositories, push code, approve code pushed by others, bookmark their favorite projects and follow other developers to keep track of their activities. In this paper we present a characterization of GitHub, as both a social network and a collaborative platform. To the best of our knowledge, this is the first quantitative study about the interactions happening on GitHub. We analyze the logs from the service over 18 months (between March 11, 2012 and September 11, 2013), describing 183.54 million events and we obtain information about 2.19 million users and 5.68 million repositories, both growing linearly in time. We show that the distributions of the number of contributors per project, watchers per project and followers per user show a power-law-like shape. We analyze social ties and repository-mediated collaboration patterns, and we observe a remarkably low level of reciprocity of the social connections. We also measure the activity of each user in terms of authored events and we observe that very active users do not necessarily have a large number of followers. Finally, we provide a geographic characterization of the centers of activity and we investigate how distance influences collaboration.

Size-partitioned phytoplankton carbon concentrations retrieved from ocean color data, links to data in netCDF format

Owing to their important roles in biogeochemical cycles, phytoplankton functional types (PFTs) have been the aim of an increasing number of ocean color algorithms. Yet, none of the existing methods are based on phytoplankton carbon (C) biomass, which is a fundamental biogeochemical and ecological variable and the "unit of accounting" in Earth system models. We present a novel bio-optical algorithm to retrieve size-partitioned phytoplankton carbon from ocean color satellite data. The algorithm is based on existing methods to estimate particle volume from a power-law particle size distribution (PSD). Volume is converted to carbon concentrations using a compilation of allometric relationships. We quantify absolute and fractional biomass in three PFTs based on size - picophytoplankton (0.5-2 µm in diameter), nanophytoplankton (2-20 µm) and microphytoplankton (20-50 µm). The mean spatial distributions of total phytoplankton C biomass and individual PFTs, derived from global SeaWiFS monthly ocean color data, are consistent with current understanding of oceanic ecosystems, i.e., oligotrophic regions are characterized by low biomass and dominance of picoplankton, whereas eutrophic regions have high biomass to which nanoplankton and microplankton contribute relatively larger fractions. Global climatological, spatially integrated phytoplankton carbon biomass standing stock estimates using our PSD-based approach yield - 0.25 Gt of C, consistent with analogous estimates from two other ocean color algorithms and several state-of-the-art Earth system models. Satisfactory in situ closure observed between PSD and POC measurements lends support to the theoretical basis of the PSD-based algorithm. Uncertainty budget analyses indicate that absolute carbon concentration uncertainties are driven by the PSD parameter No which determines particle number concentration to first order, while uncertainties in PFTs' fractional contributions to total C biomass are mostly due to the allometric coefficients. The C algorithm presented here, which is not empirically constrained a priori, partitions biomass in size classes and introduces improvement over the assumptions of the other approaches. However, the range of phytoplankton C biomass spatial variability globally is larger than estimated by any other models considered here, which suggests an empirical correction to the No parameter is needed, based on PSD validation statistics. These corrected absolute carbon biomass concentrations validate well against in situ POC observations.

Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework

Understanding the exploration patterns of foragers in the wild provides fundamental insight into animal behavior. Recent experimental evidence has demonstrated that path lengths (distances between consecutive turns) taken by foragers are well fitted by a power law distribution. Numerous theoretical contributions have posited that “Lévy random walks”—which can produce power law path length distributions—are optimal for memoryless agents searching a sparse reward landscape. It is unclear, however, whether such a strategy is efficient for cognitively complex agents, from wild animals to humans. Here, we developed a model to explain the emergence of apparent power law path length distributions in animals that can learn about their environments. In our model, the agent’s goal during search is to build an internal model of the distribution of rewards in space that takes into account the cost of time to reach distant locations (i.e., temporally discounting rewards). For an agent with such a goal, we find that an optimal model of exploration in fact produces hyperbolic path lengths, which are well approximated by power laws. We then provide support for our model by showing that humans in a laboratory spatial exploration task search space systematically and modify their search patterns under a cost of time. In addition, we find that path length distributions in a large dataset obtained from free-ranging marine vertebrates are well described by our hyperbolic model. Thus, we provide a general theoretical framework for understanding spatial exploration patterns of cognitively complex foragers.

Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework

Understanding the exploration patterns of foragers in the wild provides fundamental insight into animal behavior. Recent experimental evidence has demonstrated that path lengths (distances between consecutive turns) taken by foragers are well fitted by a power law distribution. Numerous theoretical contributions have posited that “Lévy random walks”—which can produce power law path length distributions—are optimal for memoryless agents searching a sparse reward landscape. It is unclear, however, whether such a strategy is efficient for cognitively complex agents, from wild animals to humans. Here, we developed a model to explain the emergence of apparent power law path length distributions in animals that can learn about their environments. In our model, the agent’s goal during search is to build an internal model of the distribution of rewards in space that takes into account the cost of time to reach distant locations (i.e., temporally discounting rewards). For an agent with such a goal, we find that an optimal model of exploration in fact produces hyperbolic path lengths, which are well approximated by power laws. We then provide support for our model by showing that humans in a laboratory spatial exploration task search space systematically and modify their search patterns under a cost of time. In addition, we find that path length distributions in a large dataset obtained from free-ranging marine vertebrates are well described by our hyperbolic model. Thus, we provide a general theoretical framework for understanding spatial exploration patterns of cognitively complex foragers.