Complex network analysis and nonlinear dynamics

This chapter aims at reviewing complex network and nonlinear dynamical models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the field of complex networks, the present summary introduces some applications of complex networks to economics, finance, epidemic spreading of innovations, and regional trade and developments. The chapter also reviews results involving applications of complex networks to other relevant socioeconomic issue

Long run analysis of crude oil portfolios

This paper deals with the analysis of the long-run behavior of a set of mispricing portfolios generated by three crude oils, where one of the oils is the reference commodity and it is compared to a combination of the other two ones. To this aim, the long-term parameter related to the mispricing portfolio are estimated on empirical data. We pay particular attention to the cases of mispricing portfolios either of stationary type or following a Brownian motion: the former situation is associated to replication portfolios of a reference commodity; the latter one allows to implement forecasts. The theoretical setting is validated through empirical data on WTI, Brent and Dubai oils

Complex-valued information entropy measure for networks with directed links (digraphs). Application to citations by community agents with opposite opinions

The notion of complex-valued information entropy measure is presented. It applies in particular to directed networks (digraphs). The corresponding statistical physics notions are outlined. The studied network, serving as a case study, in view of illustrating the discussion, concerns citations by agents belonging to two distinct communities which have markedly different opinions: the Neocreationist and Intelligent Design Proponents, on one hand, and the Darwinian Evolution Defenders, on the other hand. The whole, intra- and inter-community adjacency matrices, resulting from quotations of published work by the community agents, are elaborated and eigenvalues calculated. Since eigenvalues can be complex numbers, the information entropy may become also complex-valued. It is calculated for the illustrating case. The role of the imaginary part finiteness is discussed in particular and given some physical sense interpretation through local interaction range consideration. It is concluded that such generalizations are not only interesting and necessary for discussing directed networks, but also may give new insight into conceptual ideas about directed or other networks. Notes on extending the above to Tsallis entropy measure are found in an Appendix.Comment: 26 pages, 5 figures, 4 Tables, 72 refs.; submitted to EPJ

Effectiveness of Measures of Performance During Speculative Bubbles

Statistical analysis of financial data most focused on testing the validity of Brownian motion (Bm). Analysis performed on several time series have shown deviation from the Bm hypothesis, that is at the base of the evaluation of many financial derivatives. We inquiry in the behavior of measures of performance based on maximum drawdown movements (MDD), testing their stability when the underlying process deviates from the Bm hypothesis. In particular we consider the fractional Brownian motion (fBm), and fluctuations estimated empirically on raw market data. The case study of the rising part of speculative bubbles is reported

Hurst exponent of very long birth time series in XX century Romania. Social and religious aspects

The Hurst exponent of very long birth time series in Romania has been extracted from official daily records, i.e. over 97 years between 1905 and 2001 included. The series result from distinguishing between families located in urban (U) or rural (R) areas, and belonging (Ox) or not (NOx) to the orthodox religion. Four time series combining both criteria, (U,R) and (Ox, NOx), are also examined. A statistical information is given on these sub-populations measuring their XX-th century state as a snapshot. However, the main goal is to investigate whether the "daily" production of babies is purely noisy or is fluctuating according to some non trivial fractional Brownian motion, - in the four types of populations, characterized by either their habitat or their religious attitude, yet living within the same political regime. One of the goals was also to find whether combined criteria implied a different behavior. Moreover, we wish to observe whether some seasonal periodicity exists. The detrended fluctuation analysis technique is used for finding the fractal correlation dimension of such (9) signals. It has been first necessary, due to two periodic tendencies, to define the range regime in which the Hurst exponent is meaningfully defined. It results that the birth of babies in all cases is a very strongly persistent signal. It is found that the signal fractal correlation dimension is weaker (i) for NOx than for Ox, and (ii) or U with respect to R. Moreover, it is observed that the combination of U or R with NOx or OX enhances the UNOx, UOx, and ROx fluctuations, but smoothens the RNOx signal, thereby suggesting a stronger conditioning on religiosity rituals or rules.Comment: 19 pages, 37 references, 6 figures, 2 tables, to be published in Physica

Complex networks analysis in socioeconomic models

This chapter aims at reviewing complex networks models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the field of complex networks, the present summary adds insights on the statistical mechanical approach, and on the most relevant computational aspects for the treatment of these systems. As the most frequently used model for interacting agent-based systems, a brief description of the statistical mechanics of the classical Ising model on regular lattices, together with recent extensions of the same model on small-world Watts-Strogatz and scale-free Albert-Barabasi complex networks is included. Other sections of the chapter are devoted to applications of complex networks to economics, finance, spreading of innovations, and regional trade and developments. The chapter also reviews results involving applications of complex networks to other relevant socioeconomic issues, including results for opinion and citation networks. Finally, some avenues for future research are introduced before summarizing the main conclusions of the chapter.Comment: 39 pages, 185 references, (not final version of) a chapter prepared for Complexity and Geographical Economics - Topics and Tools, P. Commendatore, S.S. Kayam and I. Kubin Eds. (Springer, to be published

Lessons on Eternal Traversable Wormholes in AdS

We attempt to construct eternal traversable wormholes connecting two asymptotically AdS regions by introducing a static coupling between their dual CFTs. We prove that there are no semiclassical traversable wormholes with Poincar\'e invariance in the boundary directions in higher than two spacetime dimensions. We critically examine the possibility of evading our result by coupling a large number of bulk fields. Static, traversable wormholes with less symmetry may be possible, and could be constructed using the ingredients we develop here.Comment: 22 pages, 4 figures. v2: minor additions, matches published versio

Memory property in heterogeneously populated markets

This paper focuses on the long memory of prices and returns of an asset traded in a financial market. We consider a microeconomic model of the market, and we prove theoretical conditions on the parameters of the model that give rise to long memory. In particular, the long memory property is detected in an agents' aggregation framework under some distributional hypotheses on the market's parameters

Tremor price dynamics in the world's network of stock exchanges

We use insight from a model of earth tectonic plate movement to obtain a new understanding of the build up and release of stress in the price dynamics of the worlds stock exchanges. Nonlinearity enters the model due to a behavioral attribute of humans reacting disproportionately to big changes. This nonlinear response allows us to classify price movements of a given stock index as either being generated due to specific economic news for the country in question, or by the ensemble of the worlds stock exchanges reacting together like a complex system. Similar in structure to the Capital Asset Pricing Model in Finance, the model predicts how an individual stock exchange should be priced in terms of the performance of the global market of exchanges, but with human behavioral characteristics included in the pricing. A number of the models assumptions are validated against empirical data for 24 of the worlds leading stock exchanges. We show how treshold effects can lead to synchronization in the global network of stock exchanges