Plasticity facilitates sustainable growth in the commons

In the commons, communities whose growth depends on public goods, individuals often rely on surprisingly simple strategies, or heuristics, to decide whether to contribute to the common good (at risk of exploitation by free-riders). Although this appears a limitation, here we show how four heuristics lead to sustainable growth by exploiting specific environmental constraints. The two simplest ones --contribute permanently or switch stochastically between contributing or not-- are first shown to bring sustainability when the public good efficiently promotes growth. If efficiency declines and the commons is structured in small groups, the most effective strategy resides in contributing only when a majority of individuals are also contributors. In contrast, when group size becomes large, the most effective behavior follows a minimal-effort rule: contribute only when it is strictly necessary. Both plastic strategies are observed in natural systems what presents them as fundamental social motifs to successfully manage sustainability

Heterogeneity shapes groups growth in social online communities

Many complex systems are characterized by broad distributions capturing, for example, the size of firms, the population of cities or the degree distribution of complex networks. Typically this feature is explained by means of a preferential growth mechanism. Although heterogeneity is expected to play a role in the evolution it is usually not considered in the modeling probably due to a lack of empirical evidence on how it is distributed. We characterize the intrinsic heterogeneity of groups in an online community and then show that together with a simple linear growth and an inhomogeneous birth rate it explains the broad distribution of group members.Comment: 5 pages, 3 figure panel

Power Law of Customers' Expenditures in Convenience Stores

In a convenience store chain, a tail of the cumulative density function of the expenditure of a person during a single shopping trip follows a power law with an exponent of -2.5. The exponent is independent of the location of the store, the shopper's age, the day of week, and the time of day.Comment: 9 pages, 5 figures. Accepted for publication in Journal of the Physical Society of Japan Vol.77No.

Scaling Theory for Migration-Driven Aggregate Growth

We give a comprehensive rate equation description for the irreversible growth of aggregates by migration from small to large aggregates. For a homogeneous rate K(i;j) at which monomers migrate from aggregates of size i to those of size j, that is, K(ai;aj) ~ a^{lambda} K(i,j), the mean aggregate size grows with time as t^{1/(2-lambda)} for lambda<2. The aggregate size distribution exhibits distinct regimes of behavior which are controlled by the scaling properties of the migration rate from the smallest to the largest aggregates. Our theory applies to diverse phenomena, such as the distribution of city populations, late stage coarsening of non-symmetric binary systems, and models for wealth exchange.Comment: 4 pages, 2-column revtex format. Revision to appear in PRL. Various changes in response to referee comments. Figure from version 1 deleted but is available at http://physics.bu.edu/~redne

Dynamics on expanding spaces: modeling the emergence of novelties

Novelties are part of our daily lives. We constantly adopt new technologies, conceive new ideas, meet new people, experiment with new situations. Occasionally, we as individuals, in a complicated cognitive and sometimes fortuitous process, come up with something that is not only new to us, but to our entire society so that what is a personal novelty can turn into an innovation at a global level. Innovations occur throughout social, biological and technological systems and, though we perceive them as a very natural ingredient of our human experience, little is known about the processes determining their emergence. Still the statistical occurrence of innovations shows striking regularities that represent a starting point to get a deeper insight in the whole phenomenology. This paper represents a small step in that direction, focusing on reviewing the scientific attempts to effectively model the emergence of the new and its regularities, with an emphasis on more recent contributions: from the plain Simon's model tracing back to the 1950s, to the newest model of Polya's urn with triggering of one novelty by another. What seems to be key in the successful modelling schemes proposed so far is the idea of looking at evolution as a path in a complex space, physical, conceptual, biological, technological, whose structure and topology get continuously reshaped and expanded by the occurrence of the new. Mathematically it is very interesting to look at the consequences of the interplay between the "actual" and the "possible" and this is the aim of this short review.Comment: 25 pages, 10 figure

On Hilberg's Law and Its Links with Guiraud's Law

Hilberg (1990) supposed that finite-order excess entropy of a random human text is proportional to the square root of the text length. Assuming that Hilberg's hypothesis is true, we derive Guiraud's law, which states that the number of word types in a text is greater than proportional to the square root of the text length. Our derivation is based on some mathematical conjecture in coding theory and on several experiments suggesting that words can be defined approximately as the nonterminals of the shortest context-free grammar for the text. Such operational definition of words can be applied even to texts deprived of spaces, which do not allow for Mandelbrot's ``intermittent silence'' explanation of Zipf's and Guiraud's laws. In contrast to Mandelbrot's, our model assumes some probabilistic long-memory effects in human narration and might be capable of explaining Menzerath's law.Comment: To appear in Journal of Quantitative Linguistic

Positive words carry less information than negative words

We show that the frequency of word use is not only determined by the word length \cite{Zipf1935} and the average information content \cite{Piantadosi2011}, but also by its emotional content. We have analyzed three established lexica of affective word usage in English, German, and Spanish, to verify that these lexica have a neutral, unbiased, emotional content. Taking into account the frequency of word usage, we find that words with a positive emotional content are more frequently used. This lends support to Pollyanna hypothesis \cite{Boucher1969} that there should be a positive bias in human expression. We also find that negative words contain more information than positive words, as the informativeness of a word increases uniformly with its valence decrease. Our findings support earlier conjectures about (i) the relation between word frequency and information content, and (ii) the impact of positive emotions on communication and social links.Comment: 16 pages, 3 figures, 3 table

Imaging Spectroscopy for Extrasolar Planet Detection

Coronagraphic imaging in combination with moderate to high spectral resolution may prove more effective in both detecting extrasolar planets and characterizing them than a standard coronagraphic imaging approach. We envisage an integral-field spectrograph coupled to a coronagraph to produce a 3D datacube. For the idealised case where the spectrum of the star is well-known and unchanging across the field, we discuss the utility of cross-correlation to seek the extrasolar planet signal, and describe a mathematical approach to completely eliminate stray light from the host star (although not its Poisson noise). For the case where the PSF is dominated by diffraction and scattering effects, and comprises a multitude of speckles within an Airy pattern typical of a space-based observation, we turn the wavelength dependence of the PSF to advantage and present a general way to eliminate the contribution from the star while preserving both the flux and spectrum of the extrasolar planet. We call this method `spectral deconvolution'. We illustrate the dramatic gains by showing an idealized simulation that results in a 20-sigma detection of a Jovian planet at 2 pc with a 2-m coronagraphic space telescope, even though the planet's peak flux is only 1% that of the PSF wings of the host star. This scales to detection of a terrestrial extrasolar planet at 2 pc with an 8-m coronagraphic Terrestrial Planet Finder (TPF) in ~7 hr (or less with appropriate spatial filtering). Data on the spectral characteristics of the extrasolar planet and hence on its atmospheric constituents and possible biomarkers are obtained naturally as part of this process.Comment: 62 pages 27 figures accepted for publication in Ap

New stopping criteria for segmenting DNA sequences

We propose a solution on the stopping criterion in segmenting inhomogeneous DNA sequences with complex statistical patterns. This new stopping criterion is based on Bayesian Information Criterion (BIC) in the model selection framework. When this stopping criterion is applied to a left telomere sequence of yeast Saccharomyces cerevisiae and the complete genome sequence of bacterium Escherichia coli, borders of biologically meaningful units were identified (e.g. subtelomeric units, replication origin, and replication terminus), and a more reasonable number of domains was obtained. We also introduce a measure called segmentation strength which can be used to control the delineation of large domains. The relationship between the average domain size and the threshold of segmentation strength is determined for several genome sequences.Comment: 4 pages, 4 figures, Physical Review Letters, to appea

Electron impact excitation cross sections for allowed transitions in atoms

We present a semiempirical Gaunt factor for widely used Van Regemorter formula [Astrophys. J. 136, 906 (1962)] for the case of allowed transitions in atoms with the LS coupling scheme. Cross sections calculated using this Gaunt factor agree with measured cross sections to within the experimental error.Comment: RevTeX, 3 pages, 10 PS figures, 2 PS tables, submitted to Phys. Rev.