Scale Free Cluster Distributions from Conserving Merging-Fragmentation Processes

We propose a dynamical scheme for the combined processes of fragmentation and merging as a model system for cluster dynamics in nature and society displaying scale invariant properties. The clusters merge and fragment with rates proportional to their sizes, conserving the total mass. The total number of clusters grows continuously but the full time-dependent distribution can be rescaled over at least 15 decades onto a universal curve which we derive analytically. This curve includes a scale free solution with a scaling exponent of -3/2 for the cluster sizes.Comment: 4 pages, 3 figure

A General Framework for Sound and Complete Floyd-Hoare Logics

This paper presents an abstraction of Hoare logic to traced symmetric monoidal categories, a very general framework for the theory of systems. Our abstraction is based on a traced monoidal functor from an arbitrary traced monoidal category into the category of pre-orders and monotone relations. We give several examples of how our theory generalises usual Hoare logics (partial correctness of while programs, partial correctness of pointer programs), and provide some case studies on how it can be used to develop new Hoare logics (run-time analysis of while programs and stream circuits).Comment: 27 page

Diffusion, Fragmentation and Coagulation Processes: Analytical and Numerical Results

We formulate dynamical rate equations for physical processes driven by a combination of diffusive growth, size fragmentation and fragment coagulation. Initially, we consider processes where coagulation is absent. In this case we solve the rate equation exactly leading to size distributions of Bessel type which fall off as $\exp(-x^{3/2})$ for large $x$-values. Moreover, we provide explicit formulas for the expansion coefficients in terms of Airy functions. Introducing the coagulation term, the full non-linear model is mapped exactly onto a Riccati equation that enables us to derive various asymptotic solutions for the distribution function. In particular, we find a standard exponential decay, $\exp(-x)$, for large $x$, and observe a crossover from the Bessel function for intermediate values of $x$. These findings are checked by numerical simulations and we find perfect agreement between the theoretical predictions and numerical results.Comment: (28 pages, 6 figures, v2+v3 minor corrections

Nonsymbiotic hemoglobins in rice are synthesized during germination and in differentiating cell types

Nonsymbiotic hemoglobins (ns-Hbs) previously have been found in monocots and dicots; however, very little is known about the tissue and cell type localization as well as the physiological function(s) of these oxygen-binding proteins. We report the immunodetection and immunolocalization of ns-Hbs in rice (Oryza sativa L.) by Western blotting and in situ confocal laser scanning techniques. Ns-Hbs were detected in soluble extracts of different tissues from the developing rice seedling by immunoblotting. Levels of ns-Hbs increased in the germinating seed for the first six days following imbibition and remained relatively constant thereafter. In contrast, ns-Hb levels decreased during leaf maturation. Roots and mesocotyls contained detectable, but low levels of ns-Hbs. Split-seed experiments revealed that ns-Hbs are synthesized de novo during seed germination and are expressed in the absence of any signal originating from the embryo. Immunolocalization of ns-Hbs by con- focal microscopy indicated the presence of ns-Hbs primarily in differentiated and differentiating cell types of the developing seedling, such as the aleurone, scutellum, root cap cells, sclerenchyma, and tracheary elements. To our knowledge, this is the first report of the specific cellular localization of these proteins during seedling development

Nonsymbiotic hemoglobins in rice are synthesized during germination and in differentiating cell types

Nonsymbiotic hemoglobins (ns-Hbs) previously have been found in monocots and dicots; however, very little is known about the tissue and cell type localization as well as the physiological function(s) of these oxygen-binding proteins. We report the immunodetection and immunolocalization of ns-Hbs in rice (Oryza sativa L.) by Western blotting and in situ confocal laser scanning techniques. Ns-Hbs were detected in soluble extracts of different tissues from the developing rice seedling by immunoblotting. Levels of ns-Hbs increased in the germinating seed for the first six days following imbibition and remained relatively constant thereafter. In contrast, ns-Hb levels decreased during leaf maturation. Roots and mesocotyls contained detectable, but low levels of ns-Hbs. Split-seed experiments revealed that ns-Hbs are synthesized de novo during seed germination and are expressed in the absence of any signal originating from the embryo. Immunolocalization of ns-Hbs by con- focal microscopy indicated the presence of ns-Hbs primarily in differentiated and differentiating cell types of the developing seedling, such as the aleurone, scutellum, root cap cells, sclerenchyma, and tracheary elements. To our knowledge, this is the first report of the specific cellular localization of these proteins during seedling development

Digestion of timothy silage and hay in reindeer

Leafy timothy (Phleum pratense) silage (S), silage mixed with molasses (SM) and hay (H) were fed to nine male reindeer (Rangifer tarandus tarandus) calves in winter to investigate rumen function and digestion. Three calves were given S with 18.5% dry matter (DM), three were given SM (21.9% DM) and three were given H (85.0% DM). The content of water soluble carbohydrates (in % of DM) was 8.2% in S, 16.0% in SM and 8.5% in H. Median (range) daily DM food intake per kg BM was 12.9 (9-2-14.4) g in calves fed S, 19.0 (19-0-21.9) g in calves fed SM and 21.0 (19.2¬21.1) g in calves fed H. In vivo digestion of S and SM DM ranged from 78.5-83.1% compared to only 69-9-72.9% in calves fed H. In vitro DM digestion (IVDMD) of cellulose (median) incubated for 48 hours in rumen fluid was, however, significantly (F = 0.05) lower in calves fed S (24.4%) compared to calves fed SM (42.2%). Median IVDMD of cellulose (48 hours) in calves fed H was 36.4%. Total concentration of VFA (range) in the rumen fluid from reindeer fed H (99.7-113.6 mM) and was significantly (P<0.05) higher compared to animals fed S (57.7-85.9 mM) or SM (51.4-72.0 mM). Likewise, the pH of the rumen fluid (range) was significantly (P<0.05) lower in reindeer fed H (6.40-6.78) compared to animals fed S (6.97-7.30) or SM (6.79-7.27). Based on this study it is concluded that leafy timothy preserved as hay seems to be more suitable as emergency feed compared to silage. Supplementation of molasses to silage seems to stimulate food intake and ruminal cellulose digestion in reindeer. The lower intake of S compared to SM or H by reindeer may be explained by ruminal energy deficiency

Chandra Cluster Cosmology Project II: Samples and X-ray Data Reduction

We discuss the measurements of the galaxy cluster mass functions at z=~0.05 and z=~0.5 using high-quality Chandra observations of samples derived from the ROSAT PSPC All-Sky and 400deg^2 surveys. We provide a full reference for the data analysis procedures, present updated calibration of relations between the total cluster mass and its X-ray indicators (T_X, Mgas, and Y_X) based on a subsample of low-z relaxed clusters, and present a first measurement of the evolving L_X-Mtot relation (with Mtot estimated from Y_X) obtained from a well-defined statistically complete cluster sample and with appropriate corrections for the Malmquist bias applied. Finally, we present the derived cluster mass functions, estimate the systematic uncertainties in this measurement, and discuss the calculation of the likelihood function. We confidently measure the evolution in the cluster comoving number density at a fixed mass threshold, e.g., by a factor of 5.0 +- 1.2 at M_500=2.5e14 h^-1 Msun between z=0 and 0.5. This evolution reflects the growth of density perturbations and can be used for the cosmological constraints complementing those from the distance-redshift relation.Comment: ApJ in press (Feb 10, 2009 issue); replacement to match accepted version, includes revisions in response to referee's and community comment

Twitter-based analysis of the dynamics of collective attention to political parties

Large-scale data from social media have a significant potential to describe complex phenomena in real world and to anticipate collective behaviors such as information spreading and social trends. One specific case of study is represented by the collective attention to the action of political parties. Not surprisingly, researchers and stakeholders tried to correlate parties' presence on social media with their performances in elections. Despite the many efforts, results are still inconclusive since this kind of data is often very noisy and significant signals could be covered by (largely unknown) statistical fluctuations. In this paper we consider the number of tweets (tweet volume) of a party as a proxy of collective attention to the party, identify the dynamics of the volume, and show that this quantity has some information on the elections outcome. We find that the distribution of the tweet volume for each party follows a log-normal distribution with a positive autocorrelation of the volume over short terms, which indicates the volume has large fluctuations of the log-normal distribution yet with a short-term tendency. Furthermore, by measuring the ratio of two consecutive daily tweet volumes, we find that the evolution of the daily volume of a party can be described by means of a geometric Brownian motion (i.e., the logarithm of the volume moves randomly with a trend). Finally, we determine the optimal period of averaging tweet volume for reducing fluctuations and extracting short-term tendencies. We conclude that the tweet volume is a good indicator of parties' success in the elections when considered over an optimal time window. Our study identifies the statistical nature of collective attention to political issues and sheds light on how to model the dynamics of collective attention in social media.Comment: 16 pages, 7 figures, 3 tables. Published in PLoS ON