Heavy-tailed statistics in short-message communication

Short-message (SM) is one of the most frequently used communication channels in the modern society. In this Brief Report, based on the SM communication records provided by some volunteers, we investigate the statistics of SM communication pattern, including the interevent time distributions between two consecutive short messages and two conversations, and the distribution of message number contained by a complete conversation. In the individual level, the current empirical data raises a strong evidence that the human activity pattern, exhibiting a heavy-tailed interevent time distribution, is driven by a non-Poisson nature.Comment: 4 pages, 4 figures and 1 tabl

Priority queues with bursty arrivals of incoming tasks

Recently increased accessibility of large-scale digital records enables one to monitor human activities such as the interevent time distributions between two consecutive visits to a web portal by a single user, two consecutive emails sent out by a user, two consecutive library loans made by a single individual, etc. Interestingly, those distributions exhibit a universal behavior, $D(\tau)\sim \tau^{-\delta}$, where $\tau$ is the interevent time, and $\delta \simeq 1$ or 3/2. The universal behaviors have been modeled via the waiting-time distribution of a task in the queue operating based on priority; the waiting time follows a power law distribution $P_{\rm w}(\tau)\sim \tau^{-\alpha}$ with either $\alpha=1$ or 3/2 depending on the detail of queuing dynamics. In these models, the number of incoming tasks in a unit time interval has been assumed to follow a Poisson-type distribution. For an email system, however, the number of emails delivered to a mail box in a unit time we measured follows a powerlaw distribution with general exponent $\gamma$. For this case, we obtain analytically the exponent $\alpha$, which is not necessarily 1 or 3/2 and takes nonuniversal values depending on $\gamma$. We develop the generating function formalism to obtain the exponent $\alpha$, which is distinct from the continuous time approximation used in the previous studies.Comment: 19 pages, 5 figure

Analysis of spatial and temporal evolution of regularity maps during ventricular fibrillation

The analysis of cardiac mapping allows investigating the structure of ventricular fibrillation (VF). This work analyzes regions of interest (ROI) on cardiac maps obtained from the regularity analysis of VF records, providing information about signal regularity at each time instant and its spatial distribution. Cardiac registers were obtained using a 240- electrodes matrix located on left ventricle of isolated rabbit heart. A Langendorff system was used to maintain the heart perfusion. VF was induced by increased frequencies. Two groups of records were considered: control (G1: without physical training, N=10), and trained (G2, N=9). Records were processed in consecutive 4-second segments. Regularity index (RI) was obtained for every segment and channel. RI is a measure of similarity degree among local activation waves for every channel. A map with the RI value of each channel was computed for the 82 register segments. To analyze the spatial distribution of RI, a threshold value was determined experimentally and applied to the map in order to obtain the ROI. Two parameters were calculated: ROI spatial number (ROIsn, a measure of spatial fragmentation), and ROI spatial area (ROIsa, the percentage of area map occupied by ROI). In case of the time course of ROI, two additional parameters were computed: the number of electrodes which value had changed respect to the threshold in two consecutive maps (ROIen, which is related with the change size), and the cumulative absolute differences of RI values for the electrodes which are changed (ROIed). Obtained results for spatial analysis show that the number of ROI is lower for trained rabbits (ROIsn; G1: 4.465±1.120; G2: 2.,227±0.623; p<0.001), but ROI spatial area is greater than the control group (ROIsa; G1: 76.235±5.355%; G2: 88.163±2.885%; p<0.001). Time-course analysis shows that more electrodes change between consecutive maps in the control group (ROIen, G1: 22.455±6.702; G2: 13.877±2.485; p<0.001). No significant differences were found for ROIed (G1: 18.509±6.932; G2: 18.619±4.196; n.s.). To conclude, ROI analysis on RI maps applied to trained and no trained rabbits groups shows that VF cardiac response is more irregular and spatially fragmented in no trained group. In addition, regularity maps are more stable with time in trained group

New records of smallscale codlet, Bregmaceros nectabanus Whitley, 1941 (Gadiformes: Bregmacerotidae), in the Adriatic Sea

Six specimens of Bregmaceros nectabanus were collected during the acoustic survey MEDIAS in two consecutive years, off Termoli (Italy) in 2020 and in Albanian waters in 2021, during two night shallow hauls. We report the northernmost record of the alien species in the Mediterranean Sea (Northern Adriatic Sea, FAO fishing area 37.2.1) and one of the highest number of individuals caught in a single haul. This finding testifies a recent geographical spread to the eastern Mediterranean Sea from its distribution area in the Indo-Pacific Ocean and Red Sea, reaching the Adriatic Sea during the 2019. Our records support the hypothesis of a possible establishment of B. nectabanus in this basin

Lacunarity, predictability and predictive instability of the daily pluviometric regime in the Iberian Peninsula

The complexity of the daily pluviometric regime of the Iberian Peninsula is analysed from the point of view of its lacunarity, predictability and predictive instability. The database consists of daily pluviometric records obtained from 43 rain gauges in Spain and Portugal for the period 1950&ndash;1990. Five different series are generated for every rain gauge. The first series is constituted by the consecutive daily amounts. The other four consist of dry spell lengths with respect to daily amount thresholds of 0.1, 1.0, 5.0 and 10.0 mm/day. A dry spell length is defined as the number of consecutive days with rainfall amounts below one of these thresholds. The empirical lacunarity for every rain gauge is well reproduced by two power laws, the exponents varying notably from one gauge to another. The spatial distribution of the lacunarity is characterised by a north to south or southeast gradient, thus suggesting that this parameter can be a useful tool to distinguish between different pluviometric regimes. The predictability of the five series is quantified by means of the rescaled analysis and the interpretation of the Hurst exponent. Its patterns reveal that most part of the Iberian Peninsula shows signs of persistence for the daily rainfall and the dry spell series, although persistence is only clearly manifested in some small domains. The instability of possible predictive algorithms is analysed through the Lyapunov exponents. They are only computed for the series of daily amounts and for dry lengths respect to the threshold level of 0.1 mm/day due to the short number of dry spells for larger threshold levels. The series of daily amounts depict the highest instability along the Mediterranean coast. The series of dry spells show an increasing instability from NE to SW Spain, with a relevant nucleus of high Lyapunov values in the south-western Atlantic coast. As a summary, lacunarity and Hurst and Lyapunov exponents depict a relevant spatial variation, which is in agreement with well known patterns of the pluviometric regime, such as annual amount spatial distribution and return periods of dry spells

Universal survival probability for a correlated random walk and applications to records

We consider a model of space-continuous one-dimensional random walk with simple correlation between the steps: the probability that two consecutive steps have same sign is $q$ with $0\leq q\leq 1$. The parameter $q$ allows thus to control the persistence of the random walk. We compute analytically the survival probability of a walk of $n$ steps, showing that it is independent of the jump distribution for any finite $n$. This universality is a consequence of the Sparre-Andersen theorem for random walks with uncorrelated and symmetric steps. We then apply this result to derive the distribution of the step at which the random walk reaches its maximum and the record statistics of the walk, which show the same universality. In particular, we show that the distribution of the number of records for a walk of $n\gg 1$ steps is the same as for a random walk with $n_{\rm eff}(q)=n/(2(1-q))$ uncorrelated and symmetrically distributed steps. We also show that in the regime where $n\to \infty$ and $q\to 1$ with $y=n(1-q)$, this model converges to the run-and-tumble particle, a persistent random walk often used to model the motion of bacteria. Our theoretical results are confirmed by numerical simulations.Comment: 28 pages, 10 figure

Modeling record-breaking stock prices

We study the statistics of record-breaking events in daily stock prices of 366 stocks from the Standard and Poors 500 stock index. Both the record events in the daily stock prices themselves and the records in the daily returns are discussed. In both cases we try to describe the record statistics of the stock data with simple theoretical models. The daily returns are compared to i.i.d. RV's and the stock prices are modeled using a biased random walk, for which the record statistics are known. These models agree partly with the behavior of the stock data, but we also identify several interesting deviations. Most importantly, the number of records in the stocks appears to be systematically decreased in comparison with the random walk model. Considering the autoregressive AR(1) process, we can predict the record statistics of the daily stock prices more accurately. We also compare the stock data with simulations of the record statistics of the more complicated GARCH(1,1) model, which, in combination with the AR(1) model, gives the best agreement with the observational data. To better understand our findings, we discuss the survival and first-passage times of stock prices on certain intervals and analyze the correlations between the individual record events. After recapitulating some recent results for the record statistics of ensembles of N stocks, we also present some new observations for the weekly distributions of record events.Comment: 20 pages, 28 figure