Previous works suggest that musical networks often present the scale-free and the small-world properties. From a musician's perspective,the most important aspect missing in those studies was harmony. In addition to that,the previous works made use of outdated statistical methods. Traditionally,least-squares linear regression is utilised to fit a power law to a given data set. However,according to Clauset et al. such a traditional method can produce inaccurate estimates for the power law exponent. In this paper,we present an analysis of musical networks which considers the existence of chords (an essential element of harmony). Here we show that only 52.5% of music in our database presents the scale-free property,while 62.5% of those pieces present the small-world property. Previous works argue that music is highly scale-free; consequently,it sounds appealing and coherent. In contrast,our results show that not all pieces of music present the scale-free and the small-world properties. In summary,this research is focused on the relationship between musical notes (Do,Re,Mi,Fa,Sol,La,Si,and their sharps) and accompaniment in classical music compositions. More information about this research project is available at https://eden.dei.uc.pt/~vitorgr/MS.html.https://doi.org/10.1209/0295-5075/121/38005 相似文献
Subways are crucial in modern transportation systems of metropolises. To quantitatively evaluate the potential risks of subway networks suffered from natural disasters or deliberate attacks, real data from seven Chinese subway systems are collected and their population distributions and anti-risk capabilities are analyzed. Counterintuitively, it is found that transfer stations with large numbers of connections are not the most crucial, but the stations and lines with large betweenness centrality are essential, if subway networks are being attacked. It is also found that cycles reduce such correlations due to the existence of alternative paths. To simulate the data-based observations, a network model is proposed to characterize the dynamics of subway systems under various intensities of attacks on stations and lines. This study sheds some light onto risk assessment of subway networks in metropolitan cities.https://doi.org/10.1209/0295-5075/121/48004 相似文献
Networks are designed to satisfy given objectives under specific requirements. While the static connectivity of networks is normally analyzed and corresponding design principles for static robustness are proposed, the challenge still remains of how to design survivable networks that maintain the required level of connectivity during their whole lifespan, against component aging. We introduce network survivability as a new concept to evaluate the networks overall performance during their whole lifespan, considering both network connectivity and network duration. We develop a framework for designing a survivable network by allocating the expected lifetimes of its components, given a limited budget. Based on percolation theory and simulation, we find that the maximal network survivability can be achieved with a quantitative balance between network duration and connectivity. For different survivability requirements, we find that the optimal design can be separated into two categories: strong dependence of lifetime on node's degree leads to larger network lifetime, while weak dependence generates stronger network connectivity. Our findings could help network design, by providing a quantitative prediction of network survivability based on network topology.https://doi.org/10.1209/0295-5075/122/36003 相似文献
A new and simple method for fabrication of nanofiber scaffolds with gradations in fiber organization is reported. The nanofiber organization, achieved by deposition of random fibers on the uniaxially aligned nanofiber mat in a gradient manner, directed morphological changes of applied adipose‐derived stem cells. These morphological changes and resultant biochemical changes can help mimic the structural orientation of complex biomechanical structures like the collagen fiber structure at the tendon‐to‐bone insertion site. In addition, chemical gradients can be established through nanoencapsulation in this novel scaffold allowing for enhanced biomedical applications.
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