Periodic pattern formation in reaction-diffusion systems -an introduction for numerical simulation

The aim of the present review is to provide a comprehensive explanation of Turing reaction–diffusion systems in sufficient detail to allow readers to perform numerical calculations themselves. The reaction–diffusion model is widely studied in the field of mathematical biology, serves as a powerful paradigm model for self-organization and is beginning to be applied to actual experimental systems in developmental biology. Despite the increase in current interest, the model is not well understood among experimental biologists, partly because appropriate introductory texts are lacking. In the present review, we provide a detailed description of the definition of the Turing reaction–diffusion model that is comprehensible without a special mathematical background, then illustrate a method for reproducing numerical calculations with Microsoft Excel. We then show some examples of the patterns generated by the model. Finally, we discuss future prospects for the interdisciplinary field of research involving mathematical approaches in developmental biology

Impact of Investor's Varying Risk Aversion on the Dynamics of Asset Price Fluctuations

While the investors' responses to price changes and their price forecasts are well accepted major factors contributing to large price fluctuations in financial markets, our study shows that investors' heterogeneous and dynamic risk aversion (DRA) preferences may play a more critical role in the dynamics of asset price fluctuations. We propose and study a model of an artificial stock market consisting of heterogeneous agents with DRA, and we find that DRA is the main driving force for excess price fluctuations and the associated volatility clustering. We employ a popular power utility function, $U(c,\gamma)=\frac{c^{1-\gamma}-1}{1-\gamma}$ with agent specific and time-dependent risk aversion index, $\gamma_i(t)$, and we derive an approximate formula for the demand function and aggregate price setting equation. The dynamics of each agent's risk aversion index, $\gamma_i(t)$ (i=1,2,...,N), is modeled by a bounded random walk with a constant variance $\delta^2$. We show numerically that our model reproduces most of the ``stylized'' facts observed in the real data, suggesting that dynamic risk aversion is a key mechanism for the emergence of these stylized facts.Comment: 17 pages, 7 figure

Evolving network structure of academic institutions

Today’s colleges and universities consist of highly complex structures that dictate interactions between the administration, faculty, and student body. These structures can play a role in dictating the efficiency of policy enacted by the administration and determine the effect that curriculum changes in one department have on other departments. Despite the fact that the features of these complex structures have a strong impact on the institutions, they remain by-and-large unknown in many cases. In this paper we study the academic structure of our home institution of Trinity College in Hartford, CT using the major and minor patterns between graduating students to build a temporal multiplex network describing the interactions between different departments. Using recent network science techniques developed for such temporal networks we identify the evolving community structures that organize departments’ interactions, as well as quantify the interdisciplinary centrality of each department. We implement this framework for Trinity College, finding practical insights and applications, but also present it as a general framework for colleges and universities to better understand their own structural makeup in order to better inform academic and administrative policy

Feigenbaum graphs: a complex network perspective of chaos

The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos.Comment: Published in PLoS ONE (Sep 2011

Mining and analysis of audiology data to find significant factors associated with tinnitus masker

Objectives: The objective of this research is to find the factors associated with tinnitus masker from the literature, and by using the large amount of audiology data available from a large NHS (National Health Services, UK) hearing aid clinic. The factors evaluated were hearing impairment, age, gender, hearing aid type, mould and clinical comments. Design: The research includes literature survey for factors associated with tinnitus masker, and performs the analysis of audiology data using statistical and data mining techniques. Setting: This research uses a large audiology data but it also faced the problem of limited data for tinnitus. Participants: It uses 1,316 records for tinnitus and other diagnoses, and 10,437 records of clinical comments from a hearing aid clinic. Primary and secondary outcome measures: The research is looking for variables associated with tinnitus masker, and in future, these variables can be combined into a single model to develop a decision support system to predict about tinnitus masker for a patient. Results: The results demonstrated that tinnitus maskers are more likely to be fit to individuals with milder forms of hearing loss, and the factors age, gender, type of hearing aid and mould were all found significantly associated with tinnitus masker. In particular, those patients having Age<=55 years were more likely to wear a tinnitus masker, as well as those with milder forms of hearing loss. ITE (in the ear) hearing aids were also found associated with tinnitus masker. A feedback on the results of association of mould with tinnitus masker from a professional audiologist of a large NHS (National Health Services, UK) was also taken to better understand them. The results were obtained with different accuracy for different techniques. For example, the chi-squared test results were obtained with 95% accuracy, for Support and Confidence only those results were retained which had more than 1% Support and 80% Confidence. Conclusions: The variables audiograms, age, gender, hearing aid type and mould were found associated with the choice of tinnitus masker in the literature and by using statistical and data mining techniques. The further work in this research would lead to the development of a decision support system for tinnitus masker with an explanation that how that decision was obtained

The International-Trade Network: Gravity Equations and Topological Properties

This paper begins to explore the determinants of the topological properties of the international - trade network (ITN). We fit bilateral-trade flows using a standard gravity equation to build a "residual" ITN where trade-link weights are depurated from geographical distance, size, border effects, trade agreements, and so on. We then compare the topological properties of the original and residual ITNs. We find that the residual ITN displays, unlike the original one, marked signatures of a complex system, and is characterized by a very different topological architecture. Whereas the original ITN is geographically clustered and organized around a few large-sized hubs, the residual ITN displays many small-sized but trade-oriented countries that, independently of their geographical position, either play the role of local hubs or attract large and rich countries in relatively complex trade-interaction patterns

Studying Fake News via Network Analysis: Detection and Mitigation

Social media for news consumption is becoming increasingly popular due to its easy access, fast dissemination, and low cost. However, social media also enable the wide propagation of "fake news", i.e., news with intentionally false information. Fake news on social media poses significant negative societal effects, and also presents unique challenges. To tackle the challenges, many existing works exploit various features, from a network perspective, to detect and mitigate fake news. In essence, news dissemination ecosystem involves three dimensions on social media, i.e., a content dimension, a social dimension, and a temporal dimension. In this chapter, we will review network properties for studying fake news, introduce popular network types and how these networks can be used to detect and mitigation fake news on social media.Comment: Submitted as a invited book chapter in Lecture Notes in Social Networks, Springer Pres

Tag-Aware Recommender Systems: A State-of-the-art Survey

In the past decade, Social Tagging Systems have attracted increasing attention from both physical and computer science communities. Besides the underlying structure and dynamics of tagging systems, many efforts have been addressed to unify tagging information to reveal user behaviors and preferences, extract the latent semantic relations among items, make recommendations, and so on. Specifically, this article summarizes recent progress about tag-aware recommender systems, emphasizing on the contributions from three mainstream perspectives and approaches: network-based methods, tensor-based methods, and the topic-based methods. Finally, we outline some other tag-related works and future challenges of tag-aware recommendation algorithms.Comment: 19 pages, 3 figure