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This work is concerned with a nonlinear Galerkin method for solving the incompressible Navier-Stokes equation on the sphere. It extends the work of Debussche, Marion,Shen, Temam et al. from one-dimensional or toroidal domains to the spherical geometry. In the first part, the method based on type 3 vector spherical harmonics is introduced and convergence is indicated. Further it is shown that the occurring coupling terms involving three vector spherical harmonics can be expressed algebraically in terms of Wigner-3j coefficients. To improve the numerical efficiency and economy we introduce an FFT based pseudo spectral algorithm for computing the Fourier coefficients of the nonlinear advection term. The resulting method scales with O(N^3), if N denotes the maximal spherical harmonic degree. The latter is demonstrated in an extensive numerical example.
In this paper a modified version of dynamic network
ows is discussed. Whereas dynamic network flows are widely analyzed already, we consider a dynamic flow problem with aggregate arc capacities called Bridge
Problem which was introduced by Melkonian [Mel07]. We extend his research to integer flows and show that this problem is strongly NP-hard. For practical relevance we also introduce and analyze the hybrid bridge problem, i.e. with underlying networks whose arc capacity can limit aggregate flow (bridge problem) or the flow entering an arc at each time (general dynamic flow). For this kind of problem we present efficient procedures for
special cases that run in polynomial time. Moreover, we present a heuristic for general hybrid graphs with restriction on the number of bridge arcs.
Computational experiments show that the heuristic works well, both on random graphs and on graphs modeling also on realistic scenarios.
Noughts and Crosses
(2008)
The Comparative Manifesto Project (CMP) dataset is the only dataset providing information about the positions of parties for comparative researchers across time and countries. This article evaluates its structure and finds a peculiarity: A high number of zeros and their unequal distribution across items, countries and time. They influence the results of any procedure to build a scale, but especially those using factor analyses. The article shows that zeroes have different meanings: Firstly, there are substantial zeroes in line with saliency theory. Secondly, zeroes exist for non-substantial reasons: The length of a manifesto and the percentage of uncoded sentences, both strongly varying across time and country. We quantify the problem and propose a procedure to identify data points containing non-substantial zeroes. For the future comparative use of the dataset we plead for a theoretical selection of items combined with the information about the likelihood that zeroes are substantially meaningful.
In retail, assortment planning refers to selecting a subset of products to offer that maximizes profit. Assortments can be planned for a single store or a retailer with multiple chain stores where demand varies between stores. In this paper, we assume that a retailer with a multitude of stores wants to specify her offered assortment. To suit all local preferences, regionalization and store-level assortment optimization are widely used in practice and lead to competitive advantages. When selecting regionalized assortments, a tradeoff between expensive, customized assortments in every store and inexpensive, identical assortments in all stores that neglect demand variation is preferable.
We formulate a stylized model for the regionalized assortment planning problem (APP) with capacity constraints and given demand. In our approach, a 'common assortment' that is supplemented by regionalized products is selected. While products in the common assortment are offered in all stores, products in the local assortments are customized and vary from store to store.
Concerning the computational complexity, we show that the APP is strongly NP-complete. The core of this hardness result lies in the selection of the common assortment. We formulate the APP as an integer program and provide algorithms and methods for obtaining approximate solutions and solving large-scale instances.
Lastly, we perform computational experiments to analyze the benefits of regionalized assortment planning depending on the variation in customer demands between stores.
In this paper we introduce a binary autoregressive model. In contrast to the typical autoregression framework, we allow the conditional distribution of the observed process to depend on past values of the time series and some exogenous variables. Such processes have
potential applications in econometrics, medicine and environmental sciences. In this
paper, we establish stationarity and geometric ergodicity of these
processes under suitable conditions on the parameters of the model. Such properties are
important for understanding the stability properties of the model as well as for deriving the
asymptotic behavior of the parameter estimators.
Superselection rules induced by the interaction with a mass zero Boson field are investigated for a class of exactly soluble Hamiltonian models. The calculations apply as well to discrete as to continuous superselection rules. The initial state (reference state) of the Boson field is either a normal state or a KMS state. The superselection sectors emerge if and only if the Boson field is infrared divergent, i. e. the bare photon number diverges and the ground state of the Boson field disappears in the continuum. The time scale of the decoherence depends on the strength of the infrared contributions of the interaction and on properties of the initial state of the Boson system. These results are first derived for a Hamiltonian with conservation laws. But in the most general case the Hamiltonian includes an additional scattering potential, and the only conserved quantity is the energy of the total system. The superselection sectors remain stable against the perturbation by the scattering processes.
The symplectic group of homogeneous canonical transformations is represented in the bosonic Fock space by the action of the group on the ultracoherent vectors, which are generalizations of the coherent states. The intertwining relations between this representation and the algebra of Weyl operators are derived. They confirm the identification of this representation with Bogoliubov transformations.
Botrytis cinerea is a major plant pathogen infecting more than 1400 plant species. During invasion, the fungus rapidly kills host cells, which is believed to be supported by induction of programmed plant cell death. To comprehensively evaluate the contributions of most of the currently known plant cell death inducing proteins (CDIPs) and metabolites for necrotrophic infection, an optimized CRISPR/Cas9 protocol was established which allowed to perform serial marker-free mutagenesis to generate multiple deletion mutants lacking up to 12 CDIPs. Whole genome sequencing of a 6x and 12x deletion mutant revealed a low number of off-target mutations which were unrelated to Cas9-mediated cleavage. Secretome analyses confirmed the loss of secreted proteins encoded by the deleted genes. Infection tests with the mutants revealed a successive decrease in virulence with increasing numbers of mutated genes, and varying effects of the knockouts on different host plants. Comparative analysis of mutants confirmed significant roles of two polygalacturonases (PG1, PG2) and the phytotoxic metabolites botrydial and botcinins for infection, but revealed no or only weak effects of deletion of the other CDIPs. Nicotiana benthamiana plants with mutated or silenced coreceptors of pattern recognition receptors, SOBIR1 and BAK1, showed similar susceptibility as control plants to infection by B. cinerea wild type and a 12x deletion mutant. These results raise doubts about a major role of manipulation of these plant defence regulators for B. cinerea infection. Despite the loss of most of the known phytotoxic compounds, the on planta secretomes of the multiple mutants retained substantial phytotoxic activity, proving that further, as yet unknown CDIPs contribute to necrosis and virulence. Our study has addressed for the first time systematically the functional redundancy of fungal virulence factors, and demonstrates that B. cinerea releases a highly redundant cocktail of proteins to achieve necrotrophic infection of a wide variety of host plants.
This paper presents a method for classifying traffic participants based on high-resolution automotive radar sensors for autonomous driving applications. The major classes of traffic participants addressed in this work are pedestrians, bicyclists and passenger cars. The preprocessed radar detections are first segmented into distinct clusters using density-based spatial clustering of applications with noise (DBSCAN) algorithm. Each cluster of detections would typically have different properties based on the respective characteristics of the object that they originated from. Therefore, sixteen distinct features based on radar detections, that are suitable for separating pedestrians, bicyclists and passenger car categories are selected and extracted for each of the cluster. A support vector machine (SVM) classifier is constructed, trained and parametrised for distinguishing the road users based on the extracted features. Experiments are conducted to analyse the classification performance of the proposed method on real data.
By mapping the boundaries of Kant’s categorical imperative to the point where it permits the committing of a crime against Hume’s three principles of justice, it shall be demonstrated how far the area is in which these two concepts persist alongside each other and how narrow the border zone is in which they do not. Indeed, the latter is a forbidden place that can only be accessed through destiny and never by choice. Whoever is witnessed to stay there, must wish for Justice to draw her sword against him, and whoever dares to try reaching it, will only wander about a deserted land where both justice and morality are left behind.