We study the price dynamics of 65 stocks from the Dow Jones Composite Average from 1973 until 2014. We show that it is possible to define a Daily Market Volatility $sigma(t)$ which is directly observable from data. This quantity is usually indirectly defined by $r(t)=sigma(t) omega(t)$ where the $r(t)$ are the daily returns of the market index and the $omega(t)$ are i.i.d. random variables with vanishing average and unitary variance. The relation $r(t)=sigma(t) omega(t)$ alone is unable to give an operative definition of the index volatility, which remains unobservable. On the contrary, we show that using the whole information available in the market, the index volatility can be operatively defined and detected.
In a recent paper we proposed a non-Markovian random walk model with memory of the maximum distance ever reached from the starting point (home). The behavior of the walker is at variance with respect to the simple symmetric random walk (SSRW) only when she is at this maximum distance, where, having the choice to move either farther or closer, she decides with different probabilities. If the probability of a forward step is higher then the probability of a backward step, the walker is bold and her behavior turns out to be super-diffusive, otherwise she is timorous and her behavior turns out to be sub-diffusive. The scaling behavior vary continuously from sub-diffusive (timorous) to super-diffusive (bold) according to a single parameter $gamma in R$. We investigate here the asymptotic properties of the bold case in the non ballistic region $gamma in [0,1/2]$, a problem which was left partially unsolved in cite{S}. The exact results proved in this paper require new probabilistic tools which rely on the construction of appropriate martingales of the random walk and its hitting times.
We initially consider a single-particle tight-binding model on the Regularized Apollonian Network (RAN). The RAN is defined starting from a tetrahedral structure with four nodes all connected (generation 0). At any successive generations, new nodes are added and connected with the surrounding three nodes. As a result, a power-law cumulative distribution of connectivity $P(k)propto {1}/{k^{eta}}$ with $eta=ln(3)/ln(2) approx 1.585$ is obtained. The eigenvalues of the Hamiltonian are exactly computed by a recursive approach for any size of the network. In the infinite size limit, the density of states and the cumulative distribution of states (integrated density of states) are also exactly determined. The relevant scaling behavior of the cumulative distribution close to the band bottom is shown to be power law with an exponent depending on the spectral dimension and not on the embedding dimension. We then consider a gas made by an infinite number of non-interacting bosons each of them described by the tight-binding Hamiltonian on the RAN and we prove that, for sufficiently large bosonic density and sufficiently small temperature, a macroscopic fraction of the particles occupy the lowest single-particle energy state forming the Bose-Einstein condensate. We determine no only the transition temperature as a function of the bosonic density, but also the fraction of condensed particle, the fugacity, the energy and the specific heat for any temperature and bosonic density.
The compartmentalization of distinct templates in protocells and the exchange of templates between them (migration) are key elements of a modern scenario for prebiotic evolution. Here we use the diffusion approximation of population genetics to study analytically the steady-state properties of such prebiotic scenario. The coexistence of distinct template types inside a protocell is achieved by a selective pressure at the protocell level (group selection) favoring protocells with a mixed template composition. In the degenerate case, where the templates have the same replication rate, we find that a vanishingly small migration rate suffices to eliminate the segregation effect of random drift and so to promote coexistence. In the non-degenerate case, a small migration rate greatly boosts coexistence as compared with the situation where there is no migration. However, increase of the migration rate beyond a critical value leads to the complete dominance of the more efficient template type (homogeneous regime). In this case, we find a continuous phase transition separating the homogeneous and the coexistence regimes, with the order parameter vanishing linearly with the distance to the transition point.
We study a one-dimensional random walk with memory. The behavior of the walker is modified with respect to the simple symmetric random walk (SSRW) only when he is at the maximum distance ever reached from his starting point (home). In this case, having the choice to move farther or to move closer, he decides with different probabilities. If the probability of a forward step is higher then the probability of a backward step, the walker is bold, otherwise he is timorous. We investigate the asymptotic properties of this bold/timorous random walk (BTRW) showing that the scaling behavior vary continuously from subdiffusive (timorous) to superdiffusive (bold). The scaling exponents are fully determined with a new mathematical approach.
Establishing the conditions that guarantee the spreading or the sustenance of altruistic traits in a population is the main goal of intergroup selection models. Of particular interest is the balance of the parameters associated to group size, migration and group survival against the selective advantage of the non-altruistic individuals. Here we use Kimuras diffusion model of intergroup selection to determine those conditions in the case the group survival probability is a nonlinear non-decreasing function of the proportion of altruists in a group. In the case this function is linear, there are two possible steady states which correspond to the non-altruistic and the altruistic phases. At the discontinuous transition line separating these phases there is a non-ergodic coexistence phase. For a continuous concave survival function, we find an ergodic coexistence phase that occupies a finite region of the parameter space in between the altruistic and the non-altruistic phases, and is separated from these phases by continuous transition lines. For a convex survival function, the coexistence phase disappears altogether but a bistable phase appears for which the choice of the initial condition determines whether the evolutionary dynamics leads to the altruistic or the non-altruistic steady state.
The dialects of Madagascar belong to the Greater Barito East group of the Austronesian family and it is widely accepted that the Island was colonized by Indonesian sailors after a maritime trek which probably took place around 650 CE. The language most closely related to Malagasy dialects is Maanyan but also Malay is strongly related especially for what concerns navigation terms. Since the Maanyan Dayaks live along the Barito river in Kalimantan (Borneo) and they do not possess the necessary skill for long maritime navigation, probably they were brought as subordinates by Malay sailors. In a recent paper we compared 23 different Malagasy dialects in order to determine the time and the landing area of the first colonization. In this research we use new data and new methods to confirm that the landing took place on the south-east coast of the Island. Furthermore, we are able to state here that it is unlikely that there were multiple settlements and, therefore, colonization consisted in a single founding event. To reach our goal we find out the internal kinship relations among all the 23 Malagasy dialects and we also find out the different kinship degrees of the 23 dialects versus Malay and Maanyan. The method used is an automated version of the lexicostatistic approach. The data concerning Madagascar were collected by the author at the beginning of 2010 and consist of Swadesh lists of 200 items for 23 dialects covering all areas of the Island. The lists for Maanyan and Malay were obtained from published datasets integrated by authors interviews.
The idea that the distance among pairs of languages can be evaluated from lexical differences seems to have its roots in the work of the French explorer Dumont DUrville. He collected comparative words lists of various languages during his voyages aboard the Astrolabe from 1826 to 1829 and, in his work about the geographical division of the Pacific, he proposed a method to measure the degree of relation between languages. The method used by the modern lexicostatistics, developed by Morris Swadesh in the 1950s, measures distances from the percentage of shared cognates, which are words with a common historical origin. The weak point of this method is that subjective judgment plays a relevant role. Recently, we have proposed a new automated method which is motivated by the analogy with genetics. The new approach avoids any subjectivity and results can be easily replicated by other scholars. The distance between two languages is defined by considering a renormalized Levenshtein distance between pair of words with the same meaning and averaging on the words contained in a list. The renormalization, which takes into account the length of the words, plays a crucial role, and no sensible results can be found without it. In this paper we give a short review of our automated method and we illustrate it by considering the cluster of Malagasy dialects. We show that it sheds new light on their kinship relation and also that it furnishes a lot of new information concerning the modalities of the settlement of Madagascar.
