This paper make an overview of the copula theory from a practical side. We consider different methods of copula estimation and different Goodness-of-Fit tests for model selection. In the GoF section we apply Kolmogorov-Smirnov and Cramer-von-Mises type tests and calculate power of these tests under different assumptions. Novating in this paper is that all the procedures are done in dimensions h...

We consider the class of polynomial optimization problems inf{f(x) : x ∈ K} for which the quadratic module generated by the polynomials that define K and the polynomial c − f (for some scalar c) is Archimedean. For such problems, the optimal value can be approximated as closely as desired by solving a hierarchy of semidefinite programs and the convergence is finite generically. Moreover, the Ar...

We study the non-archimedean counterpart to the complex amoeba of an algebraic variety, and show that it coincides with a polyhedral set defined by Bieri and Groves using valuations. For hypersurfaces this set is also the tropical variety of the defining polynomial. Using non-archimedean analysis and a recent result of Conrad we prove that the amoeba of an irreducible variety is connected. We i...

Let us first recall Lehmer’s conjecture [Le] on lower bounds for the height of an algebraic number which was stated in 1933. Let K be an algebraic number field of degree D over Q. For any valuation v we denote Dv = [Kv : Qv], where Kv,Qv are the completions of K,Q with respect to v. For archimedean v we normalise the valuation by |xv| = |x|Dv/D where |.| is the ordinary complex absolute value. ...

We propose a new test for the hypothesis that a bivariate copula is an Archimedean copula. The test statistic is based on a combination of two measures resulting from the characterization of Archimedean copulas by the property of associativity and by a strict upper bound on the diagonal by the Fréchet-upper bound. We prove weak convergence of this statistic and show that the critical values of ...

Archimedean tilings are periodic polygonal tessellations that are created by placing regular polygons edge-to-edge around a vertex to fill the plane. Here we show that three- and four-arm DNA junction tiles with specifically designed arm lengths and intertile sticky-end interactions can be used to form sophisticated two-dimensional (2D) and three-dimensional (3D) tessellation patterns. We demon...

In our previous work [8], we laid general foundations for motivic integration of constructible functions. One of the most salient features of motivic constructible functions is that they form a class which is stable by direct image and that motivic integrals of constructible functions depending on parameters are constructible as functions of the parameters. Though motivic constructible function...

Introduction Spiral coils have been used for various MRI applications as single-channel coils and array coils. Archimedes introduced a special type of spiral [1] consisting of two arms or more as shown in Fig. 1. The Archimedean spiral geometry has not been studied for MRI applications according to the literature reported. Computer simulations of the magnetic field for different Archimedean spi...

Discrete Lotka-Volterra equation over p-adic space was constructed since p-adic space is a prototype of spaces with the non-Archimedean valuations and the space given by taking ultra-discrete limit studied in soliton theory should be regarded as a space with the non-Archimedean valuations in the previous report (solv-int/9906011). In this article, using the natural projection from p-adic intege...

Copula models are often used to model the dependence structure in bivariate failure-time data. We consider a covariate effect regression method on the copula parameter for Archimedean copulas. The proposed method can handle three different data structures, namely typical bivariate data, semi-competing risks data and dependent truncation data. We derive large-sample properties of the proposed es...