536 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
Audio reader of electronic music as a means of teaching high school seniors the subject «World art culture»
The article considers the problems of formation of musical culture of high school seniors and shows the educational potential of an audio reader as a learning toolВ статье рассмотрены проблемы формирования музыкальной культуры старшеклассников, показан образовательный потенциал аудио-хрестоматии как средства обучени
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
Multivariate Copula Analysis Toolbox (MvCAT): Describing Dependence and Underlying Uncertainty Using a Bayesian Framework
We present a newly developed Multivariate Copula Analysis Toolbox (MvCAT) which includes a wide range of copula families with different levels of complexity. MvCAT employs a Bayesian framework with a residual-based Gaussian likelihood function for inferring copula parameters and estimating the underlying uncertainties. The contribution of this paper is threefold: (a) providing a Bayesian framework to approximate the predictive uncertainties of fitted copulas, (b) introducing a hybrid-evolution Markov Chain Monte Carlo (MCMC) approach designed for numerical estimation of the posterior distribution of copula parameters, and (c) enabling the community to explore a wide range of copulas and evaluate them relative to the fitting uncertainties. We show that the commonly used local optimization methods for copula parameter estimation often get trapped in local minima. The proposed method, however, addresses this limitation and improves describing the dependence structure. MvCAT also enables evaluation of uncertainties relative to the length of record, which is fundamental to a wide range of applications such as multivariate frequency analysis
Statistical Consequences of Devroye Inequality for Processes. Applications to a Class of Non-Uniformly Hyperbolic Dynamical Systems
In this paper, we apply Devroye inequality to study various statistical
estimators and fluctuations of observables for processes. Most of these
observables are suggested by dynamical systems. These applications concern the
co-variance function, the integrated periodogram, the correlation dimension,
the kernel density estimator, the speed of convergence of empirical measure,
the shadowing property and the almost-sure central limit theorem. We proved in
\cite{CCS} that Devroye inequality holds for a class of non-uniformly
hyperbolic dynamical systems introduced in \cite{young}. In the second appendix
we prove that, if the decay of correlations holds with a common rate for all
pairs of functions, then it holds uniformly in the function spaces. In the last
appendix we prove that for the subclass of one-dimensional systems studied in
\cite{young} the density of the absolutely continuous invariant measure belongs
to a Besov space.Comment: 33 pages; companion of the paper math.DS/0412166; corrected version;
to appear in Nonlinearit
Budget projections and clinical impact of an immuno-oncology class of treatments: Experience in four EU markets
Background
Immunotherapies have revolutionized oncology, but their rapid expansion may potentially put healthcare budgets under strain. We developed an approach to reduce demand uncertainty and inform decision makers and payers of the potential health outcomes and budget impact of the anti-PD-1/PD-L1 class of immuno-oncology (IO) treatments.
Methods
We used partitioned survival modelling and budget impact analysis to estimate overall survival, progression-free survival, life years gained (LYG), and number of adverse events (AEs), comparing “worlds with and without” anti-PD-1/PD-L1s over five years. The cancer types initially included melanoma, first and second line non-small cell lung cancer (NSCLC), bladder, head and neck, renal cell carcinoma, and triple negative breast cancer [1]. Inputs were based on publicly available data, literature, and expert advice.
Results
The model [2] estimated budget and health impact of the anti-PD-1/PD-L1s and projected that between 2018−2022 the class [3] would have a manageable economic impact per year, compared to the current standard of care (SOC).
The first country adaptations showed that for that period Belgium would save around 11,100 additional life years and avoid 6,100 AEs. Slovenia - 1,470 LYGs and 870 AEs avoided; Austria - respectively 4,200, 3,000; Italy – 19,800, 6,800. For Austria, the class had a projected share of about 4.5 % of the cancer care budget and 0.4 % of the total 2020 healthcare budget. For Belgium, Slovenia, and Italy - respectively 15.1 % and 1.1 %, 12.6 %, 0.6 %, and 6.5 %, 0.5 %.
Conclusion
The Health Impact Projection (HIP) is a horizon scanning model designed to estimate the potential budget and health impact of the PD-(L)1 inhibitor class at a country level for the next five years. It provides valuable data to payers which they can use to support their reimbursement plans
Monge Distance between Quantum States
We define a metric in the space of quantum states taking the Monge distance
between corresponding Husimi distributions (Q--functions). This quantity
fulfills the axioms of a metric and satisfies the following semiclassical
property: the distance between two coherent states is equal to the Euclidean
distance between corresponding points in the classical phase space. We compute
analytically distances between certain states (coherent, squeezed, Fock and
thermal) and discuss a scheme for numerical computation of Monge distance for
two arbitrary quantum states.Comment: 9 pages in LaTex - RevTex + 2 figures in ps. submitted to Phys. Rev.
Evolutionary multi-stage financial scenario tree generation
Multi-stage financial decision optimization under uncertainty depends on a
careful numerical approximation of the underlying stochastic process, which
describes the future returns of the selected assets or asset categories.
Various approaches towards an optimal generation of discrete-time,
discrete-state approximations (represented as scenario trees) have been
suggested in the literature. In this paper, a new evolutionary algorithm to
create scenario trees for multi-stage financial optimization models will be
presented. Numerical results and implementation details conclude the paper
Tail Parameters of Stable Distributions Using One Million Observations of Real Estate Returns from Five Continents
The structures of Hausdorff metric in non-Archimedean spaces
For non-Archimedean spaces and let and be the
ballean of (the family of the balls in ), the space of mappings from
to and the space of mappings from the ballen of to
respectively. By studying explicitly the Hausdorff metric structures related to
these spaces, we construct several families of new metric structures (e.g., ) on the corresponding spaces, and study their convergence,
structural relation, law of variation in the variable including
some normed algebra structure. To some extent, the class is a counterpart of the usual Levy-Prohorov metric in the
probability measure spaces, but it behaves very differently, and is interesting
in itself. Moreover, when is compact and is a complete
non-Archimedean field, we construct and study a Dudly type metric of the space
of valued measures on Comment: 43 pages; this is the final version. Thanks to the anonymous
referee's helpful comments, the original Theorem 2.10 is removed, Proposition
2.10 is stated now in a stronger form, the abstact is rewritten, the
Monna-Springer is used in Section 5, and Theorem 5.2 is written in a more
general for
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