121 research outputs found
Vanishing largest Lyapunov exponent and Tsallis entropy
We present a geometric argument that explains why some systems having
vanishing largest Lyapunov exponent have underlying dynamics aspects of which
can be effectively described by the Tsallis entropy. We rely on a comparison of
the generalised additivity of the Tsallis entropy versus the ordinary
additivity of the BGS entropy. We translate this comparison in metric terms by
using an effective hyperbolic metric on the configuration/phase space for the
Tsallis entropy versus the Euclidean one in the case of the BGS entropy.
Solving the Jacobi equation for such hyperbolic metrics effectively sets the
largest Lyapunov exponent computed with respect to the corresponding Euclidean
metric to zero. This conclusion is in agreement with all currently known
results about systems that have a simple asymptotic behaviour and are described
by the Tsallis entropy.Comment: 15 pages, No figures. LaTex2e. Some overlap with arXiv:1104.4869
Additional references and clarifications in this version. To be published in
QScience Connec
New distance measures for classifying X-ray astronomy data into stellar classes
The classification of the X-ray sources into classes (such as extragalactic
sources, background stars, ...) is an essential task in astronomy. Typically,
one of the classes corresponds to extragalactic radiation, whose photon
emission behaviour is well characterized by a homogeneous Poisson process. We
propose to use normalized versions of the Wasserstein and Zolotarev distances
to quantify the deviation of the distribution of photon interarrival times from
the exponential class. Our main motivation is the analysis of a massive dataset
from X-ray astronomy obtained by the Chandra Orion Ultradeep Project (COUP).
This project yielded a large catalog of 1616 X-ray cosmic sources in the Orion
Nebula region, with their series of photon arrival times and associated
energies. We consider the plug-in estimators of these metrics, determine their
asymptotic distributions, and illustrate their finite-sample performance with a
Monte Carlo study. We estimate these metrics for each COUP source from three
different classes. We conclude that our proposal provides a striking amount of
information on the nature of the photon emitting sources. Further, these
variables have the ability to identify X-ray sources wrongly catalogued before.
As an appealing conclusion, we show that some sources, previously classified as
extragalactic emissions, have a much higher probability of being young stars in
Orion Nebula.Comment: 29 page
Goodness-of-Fit Tests for Symmetric Stable Distributions -- Empirical Characteristic Function Approach
We consider goodness-of-fit tests of symmetric stable distributions based on
weighted integrals of the squared distance between the empirical characteristic
function of the standardized data and the characteristic function of the
standard symmetric stable distribution with the characteristic exponent
estimated from the data. We treat as an unknown parameter,
but for theoretical simplicity we also consider the case that is
fixed. For estimation of parameters and the standardization of data we use
maximum likelihood estimator (MLE) and an equivariant integrated squared error
estimator (EISE) which minimizes the weighted integral. We derive the
asymptotic covariance function of the characteristic function process with
parameters estimated by MLE and EISE. For the case of MLE, the eigenvalues of
the covariance function are numerically evaluated and asymptotic distribution
of the test statistic is obtained using complex integration. Simulation studies
show that the asymptotic distribution of the test statistics is very accurate.
We also present a formula of the asymptotic covariance function of the
characteristic function process with parameters estimated by an efficient
estimator for general distributions
Geometrical Insights for Implicit Generative Modeling
Learning algorithms for implicit generative models can optimize a variety of
criteria that measure how the data distribution differs from the implicit model
distribution, including the Wasserstein distance, the Energy distance, and the
Maximum Mean Discrepancy criterion. A careful look at the geometries induced by
these distances on the space of probability measures reveals interesting
differences. In particular, we can establish surprising approximate global
convergence guarantees for the -Wasserstein distance,even when the
parametric generator has a nonconvex parametrization.Comment: this version fixes a typo in a definitio
Portfolio selection problems in practice: a comparison between linear and quadratic optimization models
Several portfolio selection models take into account practical limitations on
the number of assets to include and on their weights in the portfolio. We
present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset
Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional
Value-at-Risk (LACVaR) models, where the assets are limited with the
introduction of quantity and cardinality constraints. We propose a completely
new approach for solving the LAM model, based on reformulation as a Standard
Quadratic Program and on some recent theoretical results. With this approach we
obtain optimal solutions both for some well-known financial data sets used by
several other authors, and for some unsolved large size portfolio problems. We
also test our method on five new data sets involving real-world capital market
indices from major stock markets. Our computational experience shows that,
rather unexpectedly, it is easier to solve the quadratic LAM model with our
algorithm, than to solve the linear LACVaR and LAMAD models with CPLEX, one of
the best commercial codes for mixed integer linear programming (MILP) problems.
Finally, on the new data sets we have also compared, using out-of-sample
analysis, the performance of the portfolios obtained by the Limited Asset
models with the performance provided by the unconstrained models and with that
of the official capital market indices
Entropies of Negative Incomes, Pareto-Distributed Loss, and Financial Crises
Health monitoring of world economy is an important issue, especially in a time of profound economic difficulty world-wide. The most important aspect of health monitoring is to accurately predict economic downturns. To gain insights into how economic crises develop, we present two metrics, positive and negative income entropy and distribution analysis, to analyze the collective “spatial” and temporal dynamics of companies in nine sectors of the world economy over a 19 year period from 1990–2008. These metrics provide accurate predictive skill with a very low false-positive rate in predicting downturns. The new metrics also provide evidence of phase transition-like behavior prior to the onset of recessions. Such a transition occurs when negative pretax incomes prior to or during economic recessions transition from a thin-tailed exponential distribution to the higher entropy Pareto distribution, and develop even heavier tails than those of the positive pretax incomes. These features propagate from the crisis initiating sector of the economy to other sectors
Research on regularized mean–variance portfolio selection strategy with modified Roy safety-first principle
The Central Limit Theorem for Random Dynamical Systems
We consider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. The Central Limit Theorem for random dynamical systems is established
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