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

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

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

Dynamics of financial time series in an inhomogeneous framework

In this paper we provide a microeconomic model to investigate the long term memory of financial time series of one share. In the framework we propose, each trader selects a volume of shares to trade and a strategy. Strategies differ for the proportion of fundamentalist/chartist evaluation of price. The share price is determined by the aggregate price. The analyses of volume distribution give an insight of imitative structure among traders. The main property of this model is t the functional relation between its parameters at the micro and macro level. This allows an immediate calibration of the model to the long memory degree of the time series under examination, therefore opening the way to the understanding the emergence of stylized facts of the market through opinion aggregation

Companies' decisions for profit maximization: a structural model

Huge analyses on firms data selected from public available databases accomplished the task to describe the size and growth of firms through interpolating functions. The structure and internal ¯rms organization that lead to the optimal pro¯t is a main matter of business studies and must take carefully into account internal work distribution and the subsequent productivity. Moreover factors external to ¯rms, like as the evolution of markets and the availability of new technologies show their immediate bias on the wealth of the firms. In this paper a model is developed for a set of firms producing a single commodity. The shape of the productivity that leads to profit optimization is drawn and discussed. Furthermore the optimal time for the firm to renew its technology is established and consequences on the productivity are examined

Options with underlying asset driven by a fractional brownian motion: crossing barriers estimates

Electronic version of an article published as New Mathematics and Natural Computation Vol. 06, No. 01, pp. 109-118 (2010) DOI: 10.1142/S1793005710001633 ©World Scientific Publishing Company https://www.worldscientific.com/doi/abs/10.1142/S1793005710001633 This paper aims at supplying a decision support system tool to investors having options written on an underlying asset driven by a fractional Brownian motion (fBm). The results presented here rely on the theory of nonlinear transformations of fBm and provide the calculus of the probability estimate that the underlying asset crosses nonlinear barriers. Recent results stating a Black and Scholes-like pricing formula for fBm monitor the expected behaviour of options on the basis of the dynamics of the underlying asset. We rely on the results drawn for plain vanilla options, leaving their extension to barrier options for future work. The theory of speculative bubbles due to endogenous causes provides a useful suggestion for the detection of periods in which these results should be used. The application of the above results is shown through the NASDAQ case study

The Problem of Nature in the Phenomenology of Merleau-Ponty

In my dissertation, I show that Merleau-Ponty’s idea of nature yields a double meaning: nature as ensemble of genetic and productive processes that are attainable in experience (phenomenal nature) and nature as that which enables this experience (transcendental nature). My thesis is that the two meanings of nature, when taken together, offer a guide to Merleau-Ponty’s final philosophical formulations about “flesh” and the “visible” and the “invisible.” The aim of the dissertation is to trace the salient conceptual and methodological complications entailed by this conception. I argue that the bivalence of the problem of nature in Merleau-Ponty receives a methodological clarification and proves coherent if we pay attention to the way Merleau-Ponty understands the thrust of radicalization in play in Husserl’s later work in phenomenology, especially regarding his expansion of the notion of intentionality