In current textbooks the use of Chebyshev nodes with Newton interpolation is advocated as the most efficient numerical interpolation method in terms of approximation accuracy and computational effort. However, we show numerically that the approximation quality obtained by Newton interpolation with Fast Leja (FL) points is competitive to the use of Chebyshev nodes, even for extremely high degree interpolation. This is an experimental account of the analytic result that the limit distribution of FL points and Chebyshev nodes is the same when letting the number of points go to infinity. Since the FL construction is easy to perform and allows to add interpolation nodes on the fly in contrast to the use of Chebyshev nodes, our study suggests that Newton interpolation with FL points is currently the most efficient numerical technique for polynomial interpolation. Moreover, we give numerical evidence that any reasonable function can be approximated up to machine accuracy by Newton interpolation with FL points if desired, which shows the potential of this method.
A new functional ANOVA test, with a graphical interpretation of the result, is presented. The test is an extension of the global envelope test introduced by Myllymäki et al. (2017, Global envelope tests for spatial processes, J. R. Statist. Soc. B 79, 381-404, doi: 10.1111/rssb.12172). The graphical interpretation is realized by a global envelope which is drawn jointly for all samples of functions. If a mean function computed from the empirical data is out of the given envelope, the null hypothesis is rejected with the predetermined significance level α. The advantages of the proposed one-way functional ANOVA are that it identifies the domains of the functions which are responsible for the potential rejection. We introduce two versions of this test: the first gives a graphical interpretation of the test results in the original space of the functions and the second immediately offers a post-hoc test by identifying the significant pair-wise differences between groups. The proposed tests rely on discretization of the functions, therefore the tests are also applicable in the multidimensional ANOVA problem. In the empirical part of the article, we demonstrate the use of the method by analyzing fiscal decentralization in European countries.
In this paper, we propose a novel hybrid metaheuristic algorithm, which integrates a Threshold Accepting algorithm (TA) with a traditional Particle Swarm Optimization (PSO) algorithm. We used the TA as a catalyst in speeding up convergence of PSO towards the optimal solution. In this hybrid, at the end of every iteration of PSO, the TA is invoked probabilistically to refine the worst particle that lags in the race of finding the solution for that iteration. Consequently the worst particle will be refined in the next iteration. The robustness of the proposed approach has been tested on 34 unconstrained optimization problems taken from the literature. The proposed hybrid demonstrates superior preference in terms of functional evaluations and success rate for 30 simulations conducted.
A myxosporean producing actinospores of the tetractinomyxon type in Hydroides norvegicus Gunnerus (Serpulidae) in Denmark was identified as a member of the family Parvicapsulidae based on small-subunit ribosomal DNA (SSU rDNA) sequences. Myxosporean samples from various Danish and Norwegian marine fishes were examined with primers that detect the novel myxosporean. Sprattus sprattus (Linnaeus) and Clupea harengus Linnaeus (Teleostei, Clupeidae) were found to be infected. The sequences of this parvicapsulid from these hosts were consistently slightly different (0.8% divergence), but both these genotypes were found in H. norvegicus. Disporic trophozoites and minute spores of a novel myxosporean type were observed in the renal tubules of some of the hosts found infected through PCR. The spores appear most similar to those of species of Gadimyxa Køie, Karlsbakk et Nylund, 2007, but are much smaller. The actinospores of the tetractinomyxon type from H. norvegicus have been described previously. In GenBank, the SSU rDNA sequences of Parvicapsulidae gen. sp. show highest identity (82%) with Parvicapsula minibicornis Kent, Whitaker et Dawe, 1997 infecting salmonids (Oncorhynchus spp.) in fresh water in the western North America. A phylogenetic analysis places P. minibicornis and Parvicapsulidae gen. sp. in a sister clade to the other parvicapsulids (Parvicapsula spp. and Gadimyxa spp.).
Autologous vein grafts used as aortocoronary bypasses are often prone to intimal hyperplasia, which results in stenosis and occlusion of the vein. The aim of this study was to prevent intimal hyperplasia using a newly developed perivascular system with sustained release of sirolimus. This system of controlled drug release consists of a polyester mesh coated with a copolymer of L-lactic acid and ε -caprolactone that releases sirolimus. The mesh is intended for wrapping around the vein graft during surgery. The mesh releasing sirolimus was implanted in periadventitial position onto arteria carotis communis of rabbits, and neointimal hyperplasia was then assessed. We found that implanted sirolimus-releasing meshes reduced intima thickness by 47±10 % compared to a vein graft after 3 weeks. The pure polyester mesh decreased vein intima thickness by 35±9 %. Thus, our periadventitial system for controlled release of sirolimus prevented the develo pment of intimal hyperplasia in autologous vein grafts in vivo in rabbits. A perivascularly applied mesh releasing sirolimus is a promising device for preventing stenosis of autologous vein grafts., I. Skalský ... [et al.]., and Obsahuje bibliografii a bibliografické odkazy
We mainly prove: Assume that each output function of DCNN is bounded on R and satisfies the Lipschitz condition, if is a periodic function with period ω each i, then DCNN has a unique ω-period solution and all other solutions of DCNN converge exponentially to it, where is a Lipschitz constant of for i=1,2,...,n.
The present paper studies the \textit{approximate value iteration} (AVI) algorithm for the average cost criterion with bounded costs and Borel spaces. It is shown the convergence of the algorithm and provided a performance bound assuming that the model satisfies a standard continuity-compactness assumption and a uniform ergodicity condition. This is done for the class of approximation procedures that can be represented by linear positive operators which give exact representation of constant functions and also satisfy certain continuity property. The main point is that these operators define transition probabilities on the state space of the controlled system. This has the following important consequences: (a) the approximating function is the average value of the target function with respect to the induced transition probability; (b) the approximation step in the AVI algorithm can be seen as a perturbation of the original Markov model; (c) the perturbed model inherits the ergodicity properties imposed on the original Markov model. These facts allow to bound the AVI algorithm performance in terms of the accuracy of the approximations given by this kind of operators for the primitive data model, namely, the one-step reward function and the system transition law. The bounds are given in terms of the supremum norm of bounded functions and the total variation norm of finite-signed measures. The results are illustrated with numerical approximations for a class of single item inventory systems with linear order cost, no set-up cost and no back-orders.
Motivated by applications to transition semigroups, we introduce the notion of a norming dual pair and study a Pettis-type integral on such pairs. In particular, we establish a sufficient condition for integrability. We also introduce and study a class of semigroups on such dual pairs which are an abstract version of transition semigroups. Using our results, we give conditions ensuring that a semigroup consisting of kernel operators has a Laplace transform which also consists of kernel operators. We also provide conditions under which a semigroup is uniquely determined by its Laplace transform.
The parasitic caterpillars of Maculinea (Lepidoptera: Lycaenidae) need to be adopted and nursed by ants of the genus Myrmica (Hymenoptera: Formicidae). Each Maculinea species is locally associated with one or a few main and often several secondary host species. To determine whether the parasite-host associations bear marks of cophylogenetic constraints, we reconstructed phylogenies of Maculinea and Myrmica using DNA sequence data. We searched for evidence of cospeciation with a tree-independent (ParaFit) and tree-based (TreeFitter) method. This did not reveal any indication of phylogenetic host tracking in Maculinea. This agrees with earlier insights, which emphasise that as most of the potential host ant populations are never infested by Maculinea, the selective pressure of the butterflies on Myrmica is likely to be slight. Each Maculinea species also specialises on one or a few host plant species before adoption by ants. We suggest that Maculinea species have a substantial potential to accommodate evolutionarily to geographically changing ranges of potential Myrmica hosts, available at the oviposition sites of the butterflies. We use recently published evidence on geographically varying host ant species to discuss a suite of plausible scenarios of adaptive shifts to new Myrmica host species. and Gunther Jansen, Kari Vepsäläinen, Riitta Savolainen.