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- ItemAssessment of Stability in Partitional Clustering Using Resampling Techniques(Karlsruhe : KIT Scientific Publishing, 2016) Mucha, Hans-JoachimThe assessment of stability in cluster analysis is strongly related to the main difficult problem of determining the number of clusters present in the data. The latter is subject of many investigations and papers considering different resampling techniques as practical tools. In this paper, we consider non-parametric resampling from the empirical distribution of a given dataset in order to investigate the stability of results of partitional clustering. In detail, we investigate here only the very popular K-means method. The estimation of the sampling distribution of the adjusted Rand index (ARI) and the averaged Jaccard index seems to be the most general way to do this. In addition, we compare bootstrapping with different subsampling schemes (i.e., with different cardinality of the drawn samples) with respect to their performance in finding the true number of clusters for both synthetic and real data.
- ItemA boundary control problem for the pure Cahn–Hilliard equation with dynamic boundary conditions(Berlin ; Boston, Mass. : de Gruyter, 2015) Colli, Pierluigi; Gilardi, Gianni; Sprekels, JürgenA boundary control problem for the pure Cahn–Hilliard equations with possibly singular potentialsand dynamic boundary conditions is studied and rst-order necessary conditions for optimality are proved.
- ItemDistributed optimal control of a nonstandard nonlocal phase field system(Springfield, MO : AIMS Press, 2016) Colli, Pierluigi; Gilardi, Gianni; Sprekels, JürgenWe investigate a distributed optimal control problem for a nonlocal phase field model of viscous Cahn-Hilliard type. The model constitutes a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion that has been studied in a series of papers by P. Podio-Guidugli and the present authors. The model consists of a highly nonlinear parabolic equation coupled to an ordinary differential equation. The latter equation contains both nonlocal and singular terms that render the analysis difficult. Standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the first-order necessary conditions of optimality.
- ItemPrevention and trust evaluation scheme based on interpersonal relationships for large-scale peer-to-peer networks(New York, NY : Hindawi Publishing Corporation, 2014) Li, L.; Kurths, J.; Yang, Y.; Liu, G.In recent years, the complex network as the frontier of complex system has received more and more attention. Peer-to-peer (P2P) networks with openness, anonymity, and dynamic nature are vulnerable and are easily attacked by peers with malicious behaviors. Building trusted relationships among peers in a large-scale distributed P2P system is a fundamental and challenging research topic. Based on interpersonal relationships among peers of large-scale P2P networks, we present prevention and trust evaluation scheme, called IRTrust. The framework incorporates a strategy of identity authentication and a global trust of peers to improve the ability of resisting the malicious behaviors. It uses the quality of service (QoS), quality of recommendation (QoR), and comprehensive risk factor to evaluate the trustworthiness of a peer, which is applicable for large-scale unstructured P2P networks. The proposed IRTrust can defend against several kinds of malicious attacks, such as simple malicious attacks, collusive attacks, strategic attacks, and sybil attacks. Our simulation results show that the proposed scheme provides greater accuracy and stronger resistance compared with existing global trust schemes. The proposed scheme has potential application in secure P2P network coding.
- ItemLarge Deviations of Continuous Regular Conditional Probabilities(New York, NY [u.a.] : Springer Science + Business Media B.V., 2016) van Zuijlen, W.We study product regular conditional probabilities under measures of two coordinates with respect to the second coordinate that are weakly continuous on the support of the marginal of the second coordinate. Assuming that there exists a sequence of probability measures on the product space that satisfies a large deviation principle, we present necessary and sufficient conditions for the conditional probabilities under these measures to satisfy a large deviation principle. The arguments of these conditional probabilities are assumed to converge. A way to view regular conditional probabilities as a special case of product regular conditional probabilities is presented. This is used to derive conditions for large deviations of regular conditional probabilities. In addition, we derive a Sanov-type theorem for large deviations of the empirical distribution of the first coordinate conditioned on fixing the empirical distribution of the second coordinate.
- ItemAnalysis, simulation and prediction of multivariate random fields with package randomfields(Los Angeles, Calif. : UCLA, Dept. of Statistics, 2015) Schlather, Martin; Malinowski, Alexander; Menck, Peter J.; Oesting, Marco; Strokorb, KirstinModeling of and inference on multivariate data that have been measured in space, such as temperature and pressure, are challenging tasks in environmental sciences, physics and materials science. We give an overview over and some background on modeling with crosscovariance models. The R package RandomFields supports the simulation, the parameter estimation and the prediction in particular for the linear model of coregionalization, the multivariate Matérn models, the delay model, and a spectrum of physically motivated vector valued models. An example on weather data is considered, illustrating the use of RandomFields for parameter estimation and prediction.
- ItemThe effect of gender in the publication patterns in mathematics(San Francisco, CA : Public Library of Science, 2016) Mihaljević-Brandt, Helena; Santamaría, Lucía; Tullney, MarcoDespite the increasing number of women graduating in mathematics, a systemic gender imbalance persists and is signified by a pronounced gender gap in the distribution of active researchers and professors. Especially at the level of university faculty, women mathematicians continue being drastically underrepresented, decades after the first affirmative action measures have been put into place. A solid publication record is of paramount importance for securing permanent positions. Thus, the question arises whether the publication patterns of men and women mathematicians differ in a significant way. Making use of the zbMATH database, one of the most comprehensive metadata sources on mathematical publications, we analyze the scholarly output of ∼150,000 mathematicians from the past four decades whose gender we algorithmically inferred. We focus on development over time, collaboration through coautorships, presumed journal quality and distribution of research topics—factors known to have a strong impact on job perspectives. We report significant differences between genders which may put women at a disadvantage when pursuing an academic career in mathematics.
- ItemBochner integrals in ordered vector spaces(Cham (ZG) : Springer International Publishing AG, 2016) van Rooij, A.C.M.; van Zuijlen, W.B.We present a natural way to cover an Archimedean directed ordered vector space E by Banach spaces and extend the notion of Bochner integrability to functions with values in E. The resulting set of integrable functions is an Archimedean directed ordered vector space and the integral is an order preserving map.
- ItemTopology identification of complex network via chaotic ant swarm algorithm(New York, NY : Hindawi Publishing Corporation, 2013) Peng, H.; Li, L.; Kurths, J.; Li, S.; Yang, Y.Nowadays, the topology of complex networks is essential in various fields as engineering, biology, physics, and other scientific fields. We know in some general cases that there may be some unknown structure parameters in a complex network. In order to identify those unknown structure parameters, a topology identification method is proposed based on a chaotic ant swarm algorithm in this paper. The problem of topology identification is converted into that of parameter optimization which can be solved by a chaotic ant algorithm. The proposed method enables us to identify the topology of the synchronization network effectively. Numerical simulations are also provided to show the effectiveness and feasibility of the proposed method.
- ItemAdvances in Time Series Analysis and Its Applications(New York, NY : Hindawi Publishing Corporation, 2016) Gao, Z.-K.; Small, M.; Donner, R.; Meng, D.; Ghaffari, H.O.