1,720,985 research outputs found
Matching in a family of piecewise affine maps
No full textWe consider a class of simple one parameter families of interval maps, and we study how metric (resp. topological) entropy changes as the parameter varies. We show that in many cases the entropy displays a semi-regular behaviour, i.e. it is smooth on an open and dense set. This feature is due to a combinatorial property called matching, which was first observed in the parametric family of α-continued fractions introduced by Nakada and Natsui (2008 Nonlinearity 21 1207–25)
Entropy and Efficiency of the ETF Market
Full text linkWe investigate the relative information efficiency of financial markets by measuring the entropy of the time series of high frequency data. Our tool to measure efficiency is the Shannon entropy, applied to 2-symbol and 3-symbol discretisations of the data. Analysing 1-min and 5-min price time series of 55 Exchange Traded Funds traded at the New York Stock Exchange, we develop a methodology to isolate residual inefficiencies from other sources of regularities, such as the intraday pattern, the volatility clustering and the microstructure effects. The first two are modelled as multiplicative factors, while the microstructure is modelled as an ARMA noise process. Following an analytical and empirical combined approach, we find a strong relationship between low entropy and high relative tick size and that volatility is responsible for the largest amount of regularity, averaging 62% of the total regularity against 18% of the intraday pattern regularity and 20% of the microstructure
Long hitting time for translation flows and L-shaped billiards
No full textWe consider the flow in direction θ on a translation surface and we study the asymptotic behavior for r→0 of the time needed by orbits to hit the r-neighborhood of a prescribed point, or more precisely the exponent of the corresponding power law, which is known as hitting time. For flat tori the limsup of hitting time is equal to the Diophantine type of the direction θ. In higher genus, we consider a generalized geometric notion of Diophantine type of a direction θ and we seek for relations with hitting time. For genus two surfaces with just one conical singularity we prove that the limsup of hitting time is always less or equal to the square of the Diophantine type. For any square-tiled surface with the same topology the Diophantine type itself is a lower bound, and any value between the two bounds can be realized, moreover this holds also for a larger class of origamis satisfying a specific topological assumption. Finally, for the so-called Eierlegende Wollmilchsau origami, the equality between limsup of hitting time and Diophantine type subsists. Our results apply to L-shaped billiards
On the semiclassical density of states of quasi-integrable mechanical systems
No full textFor a class of quasi-integrable mechanical systems, we show that in the semiclassical limit the Bohr-Sommerfeld quantization applied to successive truncations of the Birkhoff series and a power series expansion of Weyl's formula give the same asymptotic number of states below a given energy
On the regularity of Mather's β-function for standard-like twist maps
Full text linkWe consider the minimal average action (Mather's β function) for area preserving twist maps of the annulus. The regularity properties of this function share interesting relations with the dynamics of the system. We prove that the β-function associated to a standard-like twist map admits a unique C1-holomorphic (canonical) complex extension, which coincides with this function on the set of real diophantine frequencies. In particular, we deduce a uniqueness result for Mather's β function
Coupling the Yoccoz-Birkeland population model with price dynamics: Chaotic livestock commodities market cycles
Full text linkWe propose a new model for the time evolution of livestock commodities prices which exhibits endogenous deterministic stochastic behaviour. The model is based on the Yoccoz–Birkeland integral equation, a model first developed for studying the time-evolution of single species with high average fertility, a relatively short mating season and density-dependent reproduction rates. This equation is then coupled with a differential equation describing the price of a livestock commodity driven by the unbalance between its demand and supply. At its birth the cattle population is split into two parts: reproducing females and cattle for butchery. The relative amount of the two is determined by the spot price of the meat. We prove the existence of an attractor (theorem A) and of a non-trivial periodic solution (theorem B) and we investigate numerically the properties of the attractor: the strange attractor existing for the original Yoccoz–Birkeland model is persistent but its chaotic behaviour depends also on the time evolution of the price in an essential way
Kelly betting with quantum payoff: A continuous variable approach
Full text linkThe main purpose of this study is to introduce a semi-classical model describing betting scenarios in which, at variance with conventional approaches, the payoff of the gambler is encoded into the internal degrees of freedom of a quantum memory element. In our scheme, we assume that the invested capital is explicitly associated with the quantum analog of the free-energy (i.e. ergotropy functional by Allahverdyan, Balian, and Nieuwenhuizen) of a single mode of the electromagnetic radiation which, depending on the outcome of the betting, experiences attenuation or amplification processes which model losses and winning events. The resulting stochastic evolution of the quantum memory resembles the dynamics of random lasing which we characterize within the theoretical setting of Bosonic Gaussian channels. As in the classical Kelly Criterion for optimal betting, we define the asymptotic doubling rate of the model and identify the optimal gambling strategy for fixed odds and probabilities of winning. The performance of the model are hence studied as a function of the input capital state under the assumption that the latter belongs to the set of Gaussian density matrices (i.e. displaced, squeezed thermal Gibbs states) revealing that the best option for the gambler is to devote all their initial resources into coherent state amplitude
Development and assessment of a distribution network of hydro-methane, methanol, oxygen and carbon dioxide in Paraguay
No full textThis paper summarizes key results of the analysis of different transport modes of hydro-methane, methanol, carbon dioxide and oxygen in Paraguay, Brazil and Argentina. Hydro-methane is produced in Paraguay and can be used to fuel natural gas vehicles, substituting gasoline and diesel which are at the moment imported from foreign countries. Methanol, also produced in Paraguay, is delivered to Brazil, which is one of the Countries with the highest demand in the region. Oxygen can be sold to Argentina for medical and industrial use. Carbon dioxide is delivered throughout Paraguay. The aim of this study is to determine the best transportation technology from an economic and strategic point of view, minimizing costs associated to products distribution. Several scenarios are investigated; each scenario is associated with different delivery modes. A model is developed to estimate both capital and variable costs for different transportation technologies (pipeline, trucks, ships) in order to choose the lowest-cost delivery mode for each product, depending on distances and flow rates. Four different analysis are performed for each scenario, varying the number of vehicles which must be fueled by hydro-methane and considering its influence on the results. The methodology presented here has a general value, thus it can be easily employed for the economic analysis of different fuels and distribution networks, also placed in different scenarios. © 2013 Elsevier Ltd. All rights reserved
Causality as a unifying approach between activation and connectivity analysis of fMRI data
No full text
- …
