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The hidden nature of causality is a puzzling, yet critical notion for effective decision-making. Financial markets are characterized by fluctuating interdependencies which seldom give rise to emergent phenomena such as bubbles or crashes. In this paper, we propose a method based on symbolic dynamics, which probes beneath the surface of abstract causality and unveils the nature of causal interactions. Our method allows distinction between positive and negative interdependencies as well as a hybrid form that we refer to as “dark causality.” We propose an algorithm which is validated by models of a priori defined causal interaction. Then, we test our method on asset pairs and on a network of sovereign credit default swaps (CDS). Our findings suggest that dark causality dominates the sovereign CDS network, indicating interdependencies which require caution from an investor’s perspective.

Uncertainty theory is an area in axiomatic mathematics recently proposed by Professor Baoding Liu and aiming to deal with belief degrees. Retrieving 1004 journal articles from the Web of Science database between 2008 and 2019, and utilizing CiteSpace and Pajek software, we analyze the publications per year and by geographical distribution, productive scholars and their cooperation, key journals, highly cited articles and main paths of the field. In this way, seven key sub-fields of uncertainty theory and their research potential are derived. The results show the following: (1) The literature on uncertainty theory follows a linear growth trend, involves an extensive network of 1000 scholars worldwide and is published in 300 journals, indicating thus that uncertainty theory has become increasingly attractive, and its academic influence is gradually expanding. (2) Seven key sub-fields of uncertainty theory have clearly been identified, including the axiomatic system, uncertain programming, uncertain sets, uncertain logic, uncertain differential equations, uncertain risk analysis, and uncertain processes. Among them, uncertain differential equations and programming are the two main sub-fields with the largest numbers of published papers. Furthermore, for evaluating the research potential of sub-fields, maturity and recent attention indicators are calculated using the citations, total number of publications, quantity of most cited literature and half-life. Based on these indicators, uncertain processes shows the greatest development potential, and has remained a hot topic in recent years, being mainly concentrated on the uncertain renewal reward process, optimal control of discrete-time uncertain systems, and uncertain linear quadratic optimal control. Additionally, uncertain risk analysis is ranked second, and focuses on the analysis of expected losses, investment risk, and structural reliability of uncertain systems.

Throughout time, operational laws and concepts from complex systems have been employed to quantitatively model important aspects and interactions in nature and society. Nevertheless, it remains enigmatic and challenging, yet inspiring, to predict the actual interdependencies that comprise the structure of such systems, particularly when the causal interactions observed in real-world phenomena might be persistently hidden. In this article,we propose a robust methodology for detecting the latent and elusive structure of dynamic complex systems. Our treatment utilizes short-term predictions from information embedded in reconstructed state space. In this regard, using a broad class of real-world applications from ecology, neurology, and finance, we explore and are able to demonstrate our method’s power and accuracy to reconstruct the fundamental structure of these complex systems, and simultaneously highlight their most fundamental operations.

In this study, we assess the dynamic evolution of short-term correlation, long-term cointegration and Error Correction Model (hereafter referred to as ECM)-based long-term Granger causality between each pair of US, UK, and Eurozone stock markets from 1980 to 2015 using the rolling-window technique. A comparative analysis of pairwise dynamic integration and causality of stock markets, measured in common and domestic currency terms, is conducted to evaluate comprehensively how exchange rate fluctuations affect the time-varying integration among the S&P 500, FTSE 100 and EURO STOXX 50 indices. The results obtained show that the dynamic correlation, cointegration and ECM-based long-run Granger causality vary significantly over the whole sample period. The degree of dynamic correlation and cointegration between pairs of stock markets rises in periods of high volatility and uncertainty, especially under the influence of economic, financial and political shocks. Meanwhile, we observe the weaker and decreasing correlation and cointegration among the three developed stock markets during the recovery periods. Interestingly, the most persistent and significant cointegration among the three developed stock markets exists during the 2007-09 global financial crisis. Finally, the exchange rate fluctuations, also influence the dynamic integration and causality between all pairs of stock indices, with that influence increasing under the local currency terms. Our results suggest that the potential for diversifying risk by investing in the US, UK and Eurozone stock markets is limited during the periods of economic, financial and political shocks.

The house prices in China have been growing nearly twice as fast as national income over the last decade. Such an irrational soaring of house prices, not only puts the Chinese economy in danger, but also the country’s social interconnectedness and stability are at risk. Under this background, assuming that the affordable level of house prices from a consumer perspective is an uncertain parameter, which can be modelled, respectively, as symmetric and asymmetric triangular fuzzy number, several types of fuzzy linear regression models are introduced. A survey for the city of Shanghai was conducted, where three major policy and an equal number of non-policy variables have been selected to facilitate the analysis. The results derived show that the real estate tax policy had a key role for retaining the house prices in Shanghai in short run, whereas the two non-policies variables, annual household income and housing size, have even greater influence on consumers than policy variables. Additionally, it was observed that the family population and the affordable level of house prices are correlated negatively.

In this paper, we consider three methods for filtering pertinent information from a series of complex networks modelling the correlations between stock price returns of the DAX 30 stocks for the time period 2001–2012 using the Thomson Reuters Datastream database and also the FNA platform to create the visualizations of the correlation-based networks. These methods reduce the complete 30 × 30 correlation coefficient matrix to a simpler network structure consisting only of the most relevant edges. The chosen network structures include the minimum spanning tree, asset graph and the planar maximally filtered graph. The resulting networks and the extracted information are analysed and compared, looking at the clusters, cliques and connectivity. Finally, we consider some specific time periods (a) a period of crisis (October–December 2008) and (b) a period of recovery (May–August 2010) where we discuss the possible underlying economic reasoning for some aspects of the network structures produced. Overall, we find that network based representations of correlations within a broad market index are useful in providing insights about the growth dynamics of an economy.

In the literature of control and system theory, several explicit formulae appeared for solving square Vandermonde systems and computing the inverse of it. In the present paper, we will discuss and present analytically the generalized inverses of the rectangular and square Vandermonde matrix. These matrices have been appeared recently in an interesting control and system theory problem, where the change of the initial state of a linear descriptor system in (almost) zero time is required.

Green logistics is an emerging area in supply chain management, which has been shown to have tremendous impacts in recent years to face the serious climate changes risks. In this paper, the fuel consumption and fuzzy travel time have been delineated in developing and solving the green-fuzzy vehicle routing problem as an extension of the celebrated VRP in which routes are performed to reduce the total expenditure. Different from the existing solution manners, we transform the original fuzzy chance constrained programming model into an equivalent deterministic model, and then revise the original hybrid intelligent algorithm by replacing the embedded fuzzy simulation with analytical function calculation. Finally, a comparative study with the corresponding literature is performed, which shows that the revised algorithm can not only improve the solution accuracy but also shorten the runtime greatly.

An approximate analytical technique is developed for determining, in closed form, the transition probability density function (PDF) of a general class of first-order stochastic differential equations (SDEs) with nonlinearities both in the drift and in the diffusion coefficients. Specifically, first, resorting to the Wiener path integral most probable path approximation and utilizing the Cauchy–Schwarz inequality yields a closed-form expression for the system response PDF, at practically zero computational cost. Next, the accuracy of this approximation is enhanced by proposing a more general PDF form with additional parameters to be determined. This is done by relying on the associated Fokker–Planck operator to formulate and solve an error minimization problem. Besides the mathematical merit of the derived closed-form approximate PDFs, an additional significant advantage of the technique relates to the fact that it can be readily coupled with a stochastic averaging treatment of second-order SDEs governing the dynamics of diverse stochastically excited nonlinear/hysteretic oscillators. In this regard, it is shown that the technique is capable of determining approximately the response amplitude transition PDF of a wide range of nonlinear oscillators, including hysteretic systems following the Preisach versatile modeling. Several numerical examples are considered for demonstrating the reliability and computational efficiency of the technique. Comparisons with pertinent Monte Carlo simulation data are provided as well.