The aim of the paper is to derive for the neg 599 ative correlation function with a time parameter an asymptotic disjunction of the numerical generalized least-squares estimator of an unknown constant mean of random field in fact the correct classic generalized least-squares estimator of an unknown constant mean of the field.

We 7e4 extend the formalism of Random Boolean Networks with canalizing rules to multilevel complex networks. The formalism allows to model genetic networks in which each gene might take part in more than one signaling pathway. We use a semi-annealed approach to study the stability of this class of models when coupled in a multiplex network and show that the analytical results are in good agreement with numerical simulations. Our main finding is that the multiplex structure provides a mechanism for the stabilization of the system and of chaotic regimes of individual layers. Our results help understanding why some genetic networks that are theoretically expected to operate in the chaotic regime can actually display dynamical stability.

The existence of imitative behavior among consumers is a well-known phenomenon in the field of Economics. This behavior is especially common in markets determined by a high degree of innovation, asymmetric information and/or price-inelastic demand, features that exist in the pharmaceutical market. This paper presents evidence of the existence of imitative behavior among primary care physicians in Galicia (Spain) when choosing treatments for their patients. From this and other evidence, we propose a dynamic model for determining the entry of new drugs into the market. To do this, we introduce the structure of the organization of primary health care centers and the presence of groups of doctors who are specially interrelated, as well as the existence of commercial pressure on doctors. For modeling purposes, physicians are treated as spins connected in an exponentially distributed complex network of the Watts-Strogatz type. The proposed model provides an explanation for the differences observed in the patterns of the introduction of technological innovations in different regions. The main cause of these differences is the different structure of relationships among consumers, where the existence of small groups that show a higher degree of coordination over the average is particularly influential. The evidence presented, together with the proposed model, might be useful for the design of optimal strategies for the introduction of new drugs, as well as for planning policies to manage pharmaceutical expenditure.

This paper extends the solution space for decision theory by introducing a behavioural operator that (1) transforms probability domains, and (2) generates sample paths for confidence from catalytic fuzzy or ambiguous sources. First, we prove that average sample paths for confidence/sentiment, generated from within and across source sets, differ. So conjugate priors should be used to mitigate the difference. Second, we identify loss aversion as the source of Langevin type friction that explains the popularity of Ornstein-Uhlenbeck processes for modeling mean reversion of sample paths for behaviour. However, in large markets, ergodic confidence levels, imbued by Lichtenstein and Slovic (1973) and Yaari (1987) type preference reversal operations, predict bubbles and crashes almost surely. Third, simulation of the model confirms that the distribution of priors, on Gilboa and Schmeilder (1989) source sets, controls confidence momentum and term structure of fields of confidence. For example, it explains the asset pricing ''anomaly" of sensitivity of momentum trading strategies to starting dates in Moskowitz, Ooi, Pedersen (2012}). Fourth, we provide several applications including but not limited to a sentiment based computer trading algorithm. For instance, our computer generated field of confidence mimics trends in CBOE VIX daily sentiment index, and survey driven Gallup Economic Confidence Index (GEDCI) sounding in Tversky and Wakker (1995) type impact events. We show how GEDCI splits VIX into source sets that depict term structures of confidence for relative hope and fear. A simple statistical test for relative confidence beta upholds our theory that the average sample path for confidence/sentiment differs within and across source sets. And we identify a VIX source set confidence beta arbitrage strategy.

Data confidentiality policies at major social network providers have severely limited researchers' access to large-scale datasets. The biggest impact has been on the study of network dynamics, where researchers have studied citation graphs and content-sharing networks, but few have analyzed detailed dynamics in the massive social networks that dominate the web today. In this paper, we present results of analyzing detailed dynamics in the Renren social network, covering a period of 2 years when the network grew from 1 user to 19 million users and 199 million edges. Rather than validate a single model of network dynamics, we analyze dynamics at different granularities (user-, community- and network- wide) to determine how much, if any, users are influenced by dynamics processes at different scales. We observe in- dependent predictable processes at each level, and find that while the growth of communities has moderate and sustained impact on users, significant events such as network merge events have a strong but short-lived impact that is quickly dominated by the continuous arrival of new users.