A complete framework of predicting the attributes of sea clutter under different operational conditions, specified by wind speed, wind direction, grazing angle, and polarization, is proposed for the first time. This framework is composed of empirical spectra to characterize sea-surface profiles under different wind speeds, the Monte Carlo method to generate realizations of sea-surface profiles, the physical-optics method to compute the normalized radar cross-sections (NRCSs) from individual sea-surface realizations, and regression of NRCS data (sea clutter) with an empirical probability density function (PDF) characterized by a few statistical parameters. JONSWAP and Hwang ocean-wave spectra are adopted to generate realizations of sea-surface profiles at low and high wind speeds, respectively. The probability density functions of NRCSs are regressed with K and Weibull distributions, each characterized by two parameters. The probability density functions in the outlier regions of weak and strong signals are regressed with a power-law distribution, each characterized by an index. The statistical parameters and power-law indices of the K and Weibull distributions are derived for the first time under different operational conditions. The study reveals succinct information of sea clutter that can be used to improve the radar performance in a wide variety of complicated ocean environments. The proposed framework can be used as a reference or guidelines for designing future measurement tasks to enhance the existing empirical models on ocean-wave spectra, normalized radar cross-sections, and so on.

Dunbar\'s number is the cognitive limit of an individual to maintain stable relationships with others in his network. It is based on the size of the neocortex of the human brain. On the other hand, trust is one of the major issues for one while selecting members for his social network and the evolution of his social network with time. Trust and Dunbar\'s number are interconnected in the case of one\'s stable social network. Trust needs time to be built after several social interactions, intimacy, etc. In this paper, we try to provide answers to the following important questions related to social networks: (i) Do trust levels remain the same for individuals from one\'s perspective in his social network when the network size increases? (ii) What is the relation between the power-law exponent α and the trust cutoff? (iii) Do trust levels help to diffuse information quickly or vice versa to reach Dunbar\'s number 150 along with hierarchy layers of 5, 15, and 50 individuals in networks of different sizes? We find that there is a requirement for trust levels to increase among the same individuals in one\'s social network if the size of the network increases. As a relation between the power-law exponent α and the trust cutoff, it is found that α∝ 1/(trust cutoff). Moreover, we also find that trust levels never help to diffuse information quickly or vice versa to reach Dunbar\'s number 150, along with hierarchy layers of 5, 15, and 50 individuals in networks of different sizes.

To reduce the impact of rating bias and popularity bias in recommender system, and make the recommender system reach a balance between recommendation utility and debias effect at the same time, we propose a bi-process debiasing recommendation model based on matrix factorization. Firstly, considering the problem that the user\'s ratings are affected by the herd mentality, which leads to a consistency between the rating and the selection of rating items, resulting in the power-law distribution, the k-times parabolic fuzzy distribution was used to fuse the user\'s age to redistribute the ratings. Secondly, the loss function is optimized by the continuously increasing flow and popularity of items. Finally, user emotion and item popularity are combined to construct user psychological tendency, which is divided into three levels: strong, medium and weak, and different levels are given different weights. To verify the performance of the model, the experimental results on real datasets show that the model proposed in this paper not only effectively reduces the recommendation bias but also ensures the recommendation utility.

The Weber-Fechner law proposes that our perceived sensory input increases with physical input on a logarithmic scale. Hippocampal \'time cells\' carry a record of recent experience by firing sequentially during a circumscribed period of time after a triggering stimulus. Different cells have \'time fields\' at different delays up to at least tens of seconds. Past studies suggest that time cells represent a compressed timeline by demonstrating that fewer time cells fire late in the delay and their time fields are wider. This paper asks whether the compression of time cells obeys the Weber-Fechner Law. Time cells were studied with a hierarchical Bayesian model that simultaneously accounts for the firing pattern at the trial level, cell level, and population level. This procedure allows separate estimates of the within-trial receptive field width and the across-trial variability. After isolating across-trial variability, time field width increased linearly with delay. Further, the time cell population was distributed evenly along a logarithmic time axis. These findings provide strong quantitative evidence that the neural temporal representation in rodent hippocampus is logarithmically compressed and obeys a neural Weber-Fechner Law.

Road network studies attracted unprecedented and overwhelming interest in recent years due to the clear relationship between human existence and city evolution. Current studies cover many aspects of a road network, for example, road feature extraction from video/image data, road map generalisation, traffic simulation, optimisation of optimal route finding problems, and traffic state prediction. However, analysing road networks as a complex graph is a field to explore. This study presents comparative studies on the Porto, in Portugal, road network sections, mainly of Matosinhos, Paranhos, and Maia municipalities, regarding degree distributions, clustering coefficients, centrality measures, connected components, k-nearest neighbours, and shortest paths. Further insights into the networks took into account the community structures, page rank, and small-world analysis. The results show that the information exchange efficiency of Matosinhos is 0.8, which is 10 and 12.8% more significant than that of the Maia and Paranhos networks, respectively. Other findings stated are: (1) the studied road networks are very accessible and densely linked; (2) they are small-world in nature, with an average length of the shortest pathways between any two roads of 29.17 units, which as found in the scenario of the Maia road network; and (3) the most critical intersections of the studied network are \'Avenida da Boavista, 4100-119 Porto (latitude: 41.157944, longitude: - 8.629105)\', and \'Autoestrada do Norte, Porto (latitude: 41.1687869, longitude: - 8.6400656)\', based on the analysis of centrality measures.

One of the main problems in scientometrics is to explore the factors that affect the growth of citations in publications to identify best practices of research policy to increase the diffusion of scientific research and knowledge in science and society. The principal purpose of this study is to analyze how research funding affects the citation-based performance of scientific output in vital research fields of life science, which is a critical province (area of knowledge) in science to improve the wellbeing of people. This study uses data from the Scopus database in 2015 (to assess the impact on citations in 2021, after more than 5 years) concerning different disciplines of life science, given by \"agricultural and biological sciences\", \"biochemistry, genetics, and molecular biology\", \"Immunology and microbiology\", \"neuroscience\" and \"pharmacology, toxicology and pharmaceutics\". Results demonstrate that although journals publish un-funded articles more than funded publications in all disciplines of life science, the fraction of total citations in funded papers is higher than the share in the total number of publications. In short, funded documents receive more citations than un-funded papers in all research fields of life science under study. Findings also support that citations of total (funded + un-funded), funded, and un-funded published papers have a power-law distribution in all five research fields of life science. Original results here reveal a general property in scientific development: funded research has a higher scaling potential than un-funded publications. Critical implications of research policy, systematized in a decision-making matrix, suggest that R&D investments in \"Neuroscience\" can generate a positive impact of scientific results in science and society-in terms of citations-higher than other research fields in medicine. Overall, then, results here can explain some characteristics driving scientific change and help policymakers and scholars to allocate resources towards research fields that facilitate the development and diffusion of scientific research and knowledge in life science for positive societal impact.

k-mer counts are important features used by many bioinformatics pipelines. Existing k-mer counting methods focus on optimizing either time or memory usage, producing in output very large count tables explicitly representing k-mers together with their counts. Storing k-mers is not needed if the set of k-mers is known, making it possible to only keep counters and their association to k-mers. Solutions avoiding explicit representation of k-mers include Minimal Perfect Hash Functions (MPHFs) and Count-Min sketches. We introduce Set-Min sketch-a sketching technique for representing associative maps inspired from Count-Min-and apply it to the problem of representing k-mer count tables. Set-Min is provably more accurate than both Count-Min and Max-Min-an improved variant of Count-Min for static datasets that we define here. We show that Set-Min sketch provides a very low error rate, in terms of both the probability and the size of errors, at the expense of a very moderate memory increase. On the other hand, Set-Min sketches are shown to take up to an order of magnitude less space than MPHF-based solutions, for fully assembled genomes and large k. Space-efficiency of Set-Min in this case takes advantage of the power-law distribution of k-mer counts in genomic datasets.

In this study, we propose a novel model-free feature screening method for ultrahigh dimensional binary features of binary classification, called weighted mean squared deviation (WMSD). Compared to Chi-square statistic and mutual information, WMSD provides more opportunities to the binary features with probabilities near 0.5. In addition, the asymptotic properties of the proposed method are theoretically investigated under the assumption log p = o ( n ) . The number of features is practically selected by a Pearson correlation coefficient method according to the property of power-law distribution. Lastly, an empirical study of Chinese text classification illustrates that the proposed method performs well when the dimension of selected features is relatively small.

Whether real-world complex networks are scale free or not has long been controversial. Recently, in Broido and Clauset [A. D. Broido, A. Clauset, Nat. Commun. 10, 1017 (2019)], it was claimed that the degree distributions of real-world networks are rarely power law under statistical tests. Here, we attempt to address this issue by defining a fundamental property possessed by each link, the degree-degree distance, the distribution of which also shows signs of being power law by our empirical study. Surprisingly, although full-range statistical tests show that degree distributions are not often power law in real-world networks, we find that in more than half of the cases the degree-degree distance distributions can still be described by power laws. To explain these findings, we introduce a bidirectional preferential selection model where the link configuration is a randomly weighted, two-way selection process. The model does not always produce solid power-law distributions but predicts that the degree-degree distance distribution exhibits stronger power-law behavior than the degree distribution of a finite-size network, especially when the network is dense. We test the strength of our model and its predictive power by examining how real-world networks evolve into an overly dense stage and how the corresponding distributions change. We propose that being scale free is a property of a complex network that should be determined by its underlying mechanism (e.g., preferential attachment) rather than by apparent distribution statistics of finite size. We thus conclude that the degree-degree distance distribution better represents the scale-free property of a complex network.

Inter-event times of various human behaviour are apparently non-Poissonian and obey long-tailed distributions as opposed to exponential distributions, which correspond to Poisson processes. It has been suggested that human individuals may switch between different states, in each of which they are regarded to generate events obeying a Poisson process. If this is the case, inter-event times should approximately obey a mixture of exponential distributions with different parameter values. In the present study, we introduce the minimum description length principle to compare mixtures of exponential distributions with different numbers of components (i.e. constituent exponential distributions). Because these distributions violate the identifiability property, one is mathematically not allowed to apply the Akaike or Bayes information criteria to their maximum-likelihood estimator to carry out model selection. We overcome this theoretical barrier by applying a minimum description principle to joint likelihoods of the data and latent variables. We show that mixtures of exponential distributions with a few components are selected, as opposed to more complex mixtures in various datasets, and that the fitting accuracy is comparable to that of state-of-the-art algorithms to fit power-law distributions to data. Our results lend support to Poissonian explanations of apparently non-Poissonian human behaviour.