Excitable human dynamics driven by extrinsic events in massive communities

Using empirical data from a social media site (Twitter) and on trading volumes of financial securities, we analyze the correlated human activity in massive social organizations. The activity, typically excited by real-world events and measured by the occurrence rate of international brand names and trading volumes, is characterized by intermittent fluctuations with bursts of high activity separated by quiescent periods. These fluctuations are broadly distributed with an inverse cubic tail and have long-range temporal correlations with a $1/f$ power spectrum. We describe the activity by a stochastic point process and derive the distribution of activity levels from the corresponding stochastic differential equation. The distribution and the corresponding power spectrum are fully consistent with the empirical observations.Comment: 9 pages, 3 figure

Dimensions, Maximal Growth Sites and Optimization in the Dielectric Breakdown Model

We study the growth of fractal clusters in the Dielectric Breakdown Model (DBM) by means of iterated conformal mappings. In particular we investigate the fractal dimension and the maximal growth site (measured by the Hoelder exponent $\alpha_{min}$) as a function of the growth exponent $\eta$ of the DBM model. We do not find evidence for a phase transition from fractal to non-fractal growth for a finite $\eta$-value. Simultaneously, we observe that the limit of non-fractal growth ($D\to 1$) is consistent with $\alpha_{min} \to 1/2$. Finally, using an optimization principle, we give a recipe on how to estimate the effective value of $\eta$ from temporal growth data of fractal aggregates.Comment: 5 pages, 7 figures; v2: extra figures and new data adde

Thermodynamic Formalism of the Harmonic Measure of Diffusion Limited Aggregates: Phase Transition and Converged f(α)f(\alpha)

We study the nature of the phase transition in the multifractal formalism of the harmonic measure of Diffusion Limited Aggregates (DLA). Contrary to previous work that relied on random walk simulations or ad-hoc models to estimate the low probability events of deep fjord penetration, we employ the method of iterated conformal maps to obtain an accurate computation of the probability of the rarest events. We resolve probabilities as small as $10^{-70}$. We show that the generalized dimensions $D_q$ are infinite for $q<q^*$, where $q^*= -0.17\pm 0.02$. In the language of $f(\alpha)$ this means that $\alpha_{max}$ is finite. We present a converged $f(\alpha)$ curve.Comment: accepted for Physical Review Letter

Measure of Node Similarity in Multilayer Networks

The weight of links in a network is often related to the similarity of the nodes. Here, we introduce a simple tunable measure for analysing the similarity of nodes across different link weights. In particular, we use the measure to analyze homophily in a group of 659 freshman students at a large university. Our analysis is based on data obtained using smartphones equipped with custom data collection software, complemented by questionnaire-based data. The network of social contacts is represented as a weighted multilayer network constructed from different channels of telecommunication as well as data on face-to-face contacts. We find that even strongly connected individuals are not more similar with respect to basic personality traits than randomly chosen pairs of individuals. In contrast, several socio-demographics variables have a significant degree of similarity. We further observe that similarity might be present in one layer of the multilayer network and simultaneously be absent in the other layers. For a variable such as gender, our measure reveals a transition from similarity between nodes connected with links of relatively low weight to dis-similarity for the nodes connected by the strongest links. We finally analyze the overlap between layers in the network for different levels of acquaintanceships.Comment: 12 pages, 4 figure

Branching Instabilities in Rapid Fracture: Dynamics and Geometry

We propose a theoretical model for branching instabilities in 2-dimensional fracture, offering predictions for when crack branching occurs, how multiple cracks develop, and what is the geometry of multiple branches. The model is based on equations of motion for crack tips which depend only on the time dependent stress intensity factors. The latter are obtained by invoking an approximate relation between static and dynamic stress intensity factors, together with an essentially exact calculation of the static ones. The results of this model are in good agreement with a sizeable quantity of experimental data.Comment: 9 pages, 11 figure

Gross anatomy of the gastrointestinal tract in reindeer, free-living and fed baled timothy silage in summer and winter

The gross anatomy of the gastrointestinal (GI) tract was investigated in reindeer calves (Rangtfer tarandus tarandus), free-living and fed two different qualities of timothy silage in September 1992 (summer) and April 1993 (winter) and related to the body condition. At both seasons nine male reindeer calves were taken from a natural pasture. Three animals were slaughtered directly (NP reindeer), three offered first cut (FC) silage and three regrowth (RG) silage ad lib., for 46 days. The FC silage contained 27% leaves and 57.8% dry matter (DM) cell wall content (CWC) and the RG silage 89 % leaves, and 38.7% DM CWC. The reticulo-rumen (RR) digesta wet weight in the NP reindeer in summer was 6.7-7.7% of body mass (BM), compared to 25.1-32.8% and 9.6-12.9% of BM, respectively, in the animals fed FC and RG silage. In winter the RR digesta wet weight relative to BM in the NP reindeer and in the animals fed FC and RG silages were 9-5-11.5%, 25.4-33.3% and 10.4-18.3%, respectively. The distal fermentation chamber (DFC) digesta wet weight in the NP animals in summer was 0.48-0.80% of BM, compared to 0.77-1.26% and 0.57&not;0.65% of BM, respectively, in the animals fed FC and RG silage. In winter the DFC digesta wet weight relative to BM in the animals fed FC and RG silage did not differ significantly from the summer values (P&gt;0.05), while in the NP reindeer it was 1.0-1.2% of BM which is significantly greater than in summer (P&lt;0.05). The differences in relative weight of the fermentation chambers between the animals fed FC and RG silage both summer and winter were not reflected in total BM, which was similar in all groups fed silage. This is explained by a significantly lower carcass weight in the animals fed FC silage compared to the animals fed RG silage. Thus, the GI-tract gross anatomy in the silage fed animals seem to be highly affected by the plant structure and composition, and not by the season

Round baled grass silage as food for reindeer in winter

Round baled silage of mixed grasses was tested as emergency food for reindeer in winter. The silage was made of leaf rich regrowth of Phleum pratense, Agrostis tenuis and Poa spp. It contained 33-3% dry matter (DM), and 14.8 % crude protein, 24.5% cellulose and 26.7% hemicellulose on a DM basis. Palatability, food intake, digestion, rumen fermentation, body mass (BM), carcass weight and gastrointestinal (GI) anatomy were investigated. A group of adult female reindeer (n = 38), were taken from natural winter pasture and fed grass silage ad libitum. The majority (78%) of the animals were eating silage after two days and 95% of the animals ate silage after five days. Five reindeer calves were taken from natural winter pasture and fed lichens ad libitum for 14 days after which they were starved for two days before being offered silage adlibitum. The median daily DM food intake was 370 g (range 250-610 g) on the first day increasing to 810 g (range 530-1100 g) at days 16 to 20. Median apparent digestibility coefficient (DC) of DM was 64.3% (range 62.4-66.2%). The median in vitro DM digestibility (IVDMD) of the silage after 72 h of microbial digestion was 68.3 % (range 66.6-71.3 %) (Ws=30, n,=5, n2=4, P&lt;0.01). Median ruminal VFA concentration and pH were 48.2 mM (range 38.4-52.5 mM) and 7.0 (range 6.95-7.17), respectively, in the reindeer calves (n=5). BM initially increased when the reindeer calves were fed silage, but stabilised after 11 days. The increased BM may have been due to an increased recticulo-rumen digesta load, which amounted to 19.6-23.7 % of BM (n=3). The carcass weight of the reindeer calves was 42.6-44.2% of the BM (n=3) after 47 days of silage feeding. The results indicate that although the round bale silage of mixed grasses of medium quality was highly palatable to reindeer it was apparantly of only limited value as an emergency food for the reindeer calves, as indicated by low DC of DM and low ruminal VFA concentration

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