On a class of distributions stable under random summation

We investigate a family of distributions having a property of stability-under-addition, provided that the number $\nu$ of added-up random variables in the random sum is also a random variable. We call the corresponding property a \,$\nu$-stability and investigate the situation with the semigroup generated by the generating function of $\nu$ is commutative. Using results from the theory of iterations of analytic functions, we show that the characteristic function of such a $\nu$-stable distribution can be represented in terms of Chebyshev polynomials, and for the case of $\nu$-normal distribution, the resulting characteristic function corresponds to the hyperbolic secant distribution. We discuss some specific properties of the class and present particular examples.Comment: 12 pages, 1 figur

A Geospatial Semantic Enrichment and Query Service for Geotagged Photographs

With the increasing abundance of technologies and smart devices, equipped with a multitude of sensors for sensing the environment around them, information creation and consumption has now become effortless. This, in particular, is the case for photographs with vast amounts being created and shared every day. For example, at the time of this writing, Instagram users upload 70 million photographs a day. Nevertheless, it still remains a challenge to discover the “right” information for the appropriate purpose. This paper describes an approach to create semantic geospatial metadata for photographs, which can facilitate photograph search and discovery. To achieve this we have developed and implemented a semantic geospatial data model by which a photograph can be enrich with geospatial metadata extracted from several geospatial data sources based on the raw low-level geo-metadata from a smartphone photograph. We present the details of our method and implementation for searching and querying the semantic geospatial metadata repository to enable a user or third party system to find the information they are looking for

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

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

Structural results on convexity relative to cost functions

Mass transportation problems appear in various areas of mathematics, their solutions involving cost convex potentials. Fenchel duality also represents an important concept for a wide variety of optimization problems, both from the theoretical and the computational viewpoints. We drew a parallel to the classical theory of convex functions by investigating the cost convexity and its connections with the usual convexity. We give a generalization of Jensen's inequality for cost convex functions.Comment: 10 page

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

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.

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

The structures of Hausdorff metric in non-Archimedean spaces

For non-Archimedean spaces $X$ and $Y,$ let $\mathcal{M}_{\flat } (X), \mathfrak{M}(V \rightarrow W)$ and $\mathfrak{D}_{\flat }(X, Y)$ be the ballean of $X$ (the family of the balls in $X$), the space of mappings from $X$ to $Y,$ and the space of mappings from the ballen of $X$ to $Y,$ respectively. By studying explicitly the Hausdorff metric structures related to these spaces, we construct several families of new metric structures (e.g., $\widehat{\rho } _{u}, \widehat{\beta }_{X, Y}^{\lambda }, \widehat{\beta }_{X, Y}^{\ast \lambda }$) on the corresponding spaces, and study their convergence, structural relation, law of variation in the variable $\lambda,$ including some normed algebra structure. To some extent, the class $\widehat{\beta }_{X, Y}^{\lambda }$ 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 $X$ is compact and $Y = K$ is a complete non-Archimedean field, we construct and study a Dudly type metric of the space of $K-$valued measures on $X.$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