The Fractional Preferential Attachment Scale-Free Network Model

Many networks generated by nature have two generic properties: they are formed in the process of {preferential attachment} and they are scale-free. Considering these features, by interfering with mechanism of the {preferential attachment}, we propose a generalisation of the Barab\'asi--Albert model---the 'Fractional Preferential Attachment' (FPA) scale-free network model---that generates networks with time-independent degree distributions $p(k)\sim k^{-\gamma}$ with degree exponent $2<\gamma\leq3$ (where $\gamma=3$ corresponds to the typical value of the BA model). In the FPA model, the element controlling the network properties is the $f$ parameter, where $f \in (0,1\rangle$. Depending on the different values of $f$ parameter, we study the statistical properties of the numerically generated networks. We investigate the topological properties of FPA networks such as degree distribution, degree correlation (network assortativity), clustering coefficient, average node degree, network diameter, average shortest path length and features of fractality. We compare the obtained values with the results for various synthetic and real-world networks. It is found that, depending on $f$, the FPA model generates networks with parameters similar to the real-world networks. Furthermore, it is shown that $f$ parameter has a significant impact on, among others, degree distribution and degree correlation of generated networks. Therefore, the FPA scale-free network model can be an interesting alternative to existing network models. In addition, it turns out that, regardless of the value of $f$, FPA networks are not fractal.Comment: 16 pages, 6 figure

Route to chaos in generalized logistic map

Motivated by a possibility to optimize modelling of the population evolution we postulate a generalization of the well-know logistic map. Generalized difference equation reads: \begin{equation} x_{n+1}=rx^p_n(1-x^q_n), \end{equation} $x\in[0,1],\;(p,q)>0,\;n=0,1,2,...$, where the two new parameters $p$ and $q$ may assume any positive values. The standard logistic map thus corresponds to the case $p=q=1$. For such a generalized equation we illustrate the character of the transition from regularity to chaos as a function of $r$ for the whole spectrum of $p$ and $q$ parameters. As an example we consider the case for $p=1$ and $q=2$ both in the periodic and chaotic regime. We focus on the character of the corresponding bifurcation sequence and on the quantitative nature of the resulting attractor as well as its universal attribute (Feigenbaum constant).Comment: Accepted for publication in Acta Physica Polonica A, 12 pages, 6 figures, 1 tabl

Dynamical variety of shapes in financial multifractality

The concept of multifractality offers a powerful formal tool to filter out multitude of the most relevant characteristics of complex time series. The related studies thus far presented in the scientific literature typically limit themselves to evaluation of whether or not a time series is multifractal and width of the resulting singularity spectrum is considered a measure of the degree of complexity involved. However, the character of the complexity of time series generated by the natural processes usually appears much more intricate than such a bare statement can reflect. As an example, based on the long-term records of S&P500 and NASDAQ - the two world leading stock market indices - the present study shows that they indeed develop the multifractal features, but these features evolve through a variety of shapes, most often strongly asymmetric, whose changes typically are correlated with the historically most significant events experienced by the world economy. Relating at the same time the index multifractal singularity spectra to those of the component stocks that form this index reflects the varying degree of correlations involved among the stocks.Comment: 26 pages, 10 figure

2,6-diaminopurine promotes repair of DNA lesions under prebiotic conditions

High-yielding and selective prebiotic syntheses of RNA and DNA nucleotides involve UV irradiation to promote the key reaction steps and eradicate biologically irrelevant isomers. While these syntheses were likely enabled by UV-rich prebiotic environment, UV-induced formation of photodamages in polymeric nucleic acids, such as cyclobutane pyrimidine dimers (CPDs), remains the key unresolved issue for the origins of RNA and DNA on Earth. Here, we demonstrate that substitution of adenine with 2,6-diaminopurine enables repair of CPDs with yields reaching 92%. This substantial self-repairing activity originates from excellent electron donating properties of 2,6-diaminopurine in nucleic acid strands. We also show that the deoxyribonucleosides of 2,6-diaminopurine and adenine can be formed under the same prebiotic conditions. Considering that 2,6-diaminopurine was previously shown to increase the rate of nonenzymatic RNA replication, this nucleobase could have played critical roles in the formation of functional and photostable RNA/DNA oligomers in UV-rich prebiotic environments

The foreign exchange market: return distributions, multifractality, anomalous multifractality and Epps effect

We present a systematic study of various statistical characteristics of high-frequency returns from the foreign exchange market. This study is based on six exchange rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It is shown that the exchange rate return fluctuations for all the pairs considered are well described by the nonextensive statistics in terms of q-Gaussians. There exist some small quantitative variations in the nonextensivity q-parameter values for different exchange rates and this can be related to the importance of a given exchange rate in the world's currency trade. Temporal correlations organize the series of returns such that they develop the multifractal characteristics for all the exchange rates with a varying degree of symmetry of the singularity spectrum f(alpha) however. The most symmetric spectrum is identified for the GBP/USD. We also form time series of triangular residual returns and find that the distributions of their fluctuations develop disproportionately heavier tails as compared to small fluctuations which excludes description in terms of q-Gaussians. The multifractal characteristics for these residual returns reveal such anomalous properties like negative singularity exponents and even negative singularity spectra. Such anomalous multifractal measures have so far been considered in the literature in connection with the diffusion limited aggregation and with turbulence. We find that market inefficiency on short time scales leads to the occurrence of the Epps effect on much longer time scales. Although the currency market is much more liquid than the stock markets and it has much larger transaction frequency, the building-up of correlations takes up to several hours - time that does not differ much from what is observed in the stock markets. This may suggest that non-synchronicity of transactions is not the unique source of the observed effect

Differences in Perceived Occupational Stress by Demographic Characteristics, of European Emergency Medical Services Personnel during the COVID-19 Virus Pandemic-An International Study

Objectives: The outbreak of the COVID-19 pandemic has brought commercial, social, and economic consequences in every country that has experienced substantial SARS-CoV-2 infection rates. The complete change in the environment that took place due to the outbreak of the pandemic can lead to stressful situations, especially among healthcare personnel. Material and methods: The research were conducted during the COVID-19 pandemic between the 27 March 2020 and the 20 April 2020. The research included 1984 employees of emergency medical systems in seven European countries. An internet-based questionnaire format was adopted for the study (ΩMc-Donald > 0.7). Results: The highest level of stress was experienced by personnel in the United Kingdom M = 4.03, and the lowest by Norwegian employees M = 2.89. High levels of stress were also experienced by nurses from Spain and Poland. Women actively working in the healthcare system during the pandemic experienced higher stress levels than men. Conclusions: Women working in European emergency medical systems are more vulnerable to work-related stress, while carrying out emergency medical procedures during the pandemic. Differences in the level of stress experienced while carrying out duties in pre-hospital conditions were only found among Spanish emergency medical system personnel

Using Data Mining Techniques for Detecting Dependencies in the Outcoming Data of a Web-Based System

The increasing amount of data from web systems data is becoming one of the most valuable resources for information retrieval and knowledge discovery. The huge content of information makes it an important area for data mining research. To analyze the dependencies of the outcoming data, expressed as query scenarios, we present a new approach for evaluating the behavior of interactive web systems by applying different data mining techniques to solve the problem. We propose tools that take outcoming logs as input, analyze them, and provide information about web client actions. Qualitative and quantitative automatic evaluation of the data can explain the connections between the most significant parameters of the system in particular scenarios. In this paper, we propose a new method, which can be used to efficiently verify the type of client behavior of a web system or design of the system. The analysis of results demonstrates the possibility of efficient pattern search