A study of the non-uniform convergence of the inverse of a doubly-infinite matrix associated with a boundary value problem in a waveguide /

"Contract AF33(616)-6079 Project No. 9-(13-6278), Task No. 40572. Sponsored by: Aeronautical Systems Division"

Uniform Convergence of the Newton Method for Aubin Continuous Maps

* This work was supported by National Science Foundation grant DMS 9404431.

The Graves Theorem Revisited II: Robust Convergence of the Newton Method

AMS subject classification: 65J15, 47H04, 90C30.

Territorial and demographic aspects of the Networks of Protected Natural Areas of Castilla-La Mancha: 1978-2014

The Autonomous Region of Castilla-La Mancha develops from the approval of the Spanish Constitution a whole executive and legislative branch to implement its policies on environmental protection. The new legislation (Law 9/1999, of 26 May) has pursued the conservation and the integral protection of the natural elements of the territory demanding to new criteria as such the environmental quality of ecosystems or the exceptional landscape. The spread and the declaration of new natural spaces have caused a double geographical and territorial model. First, natural spaces located in rural mountainous areas with depopulation and aging problems. And second, natural spaces situated in areas densely populated

Connectivity and dynamics of neuronal networks as defined by the shape of individual neurons

Biological neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of neuron shape on the overall connectivity and dynamics of the emerging networks. The current work addresses this issue by considering simplified neuronal shapes consisting of circular regions (soma/axons) with spokes (dendrites). Networks are grown by placing these patterns randomly in the two-dimensional (2D) plane and establishing connections whenever a piece of dendrite falls inside an axon. Several topological and dynamical properties of the resulting graph are measured, including the degree distribution, clustering coefficients, symmetry of connections, size of the largest connected component, as well as three hierarchical measurements of the local topology. By varying the number of processes of the individual basic patterns, we can quantify relationships between the individual neuronal shape and the topological and dynamical features of the networks. Integrate-and-fire dynamics on these networks is also investigated with respect to transient activation from a source node, indicating that long-range connections play an important role in the propagation of avalanches.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Wavelet based detection of changes in the composition of RLC networks

The current work discusses the compositional analysis of spectra that may be related to amorphous materials that lack discernible Lorentzian, Debye or Drude responses. We propose to model such response using a 3-dimensional random RLC network using a descriptor formulation which is converted into an input-output transfer function representation. A wavelet identification study of these networks is performed to infer the composition of the networks. It was concluded that wavelet filter banks enable a parsimonious representation of the dynamics in excited randomly connected RLC networks. Furthermore, chemometric classification using the proposed technique enables the discrimination of dielectric samples with different composition. The methodology is promising for the classification of amorphous dielectrics.

Three-feature model to reproduce the topology of citation networks and the effects from authors' visibility on their h-index

Various factors are believed to govern the selection of references in citation networks, but a precise, quantitative determination of their importance has remained elusive. In this paper, we show that three factors can account for the referencing pattern of citation networks for two topics, namely "graphenes" and "complex networks", thus allowing one to reproduce the topological features of the networks built with papers being the nodes and the edges established by citations. The most relevant factor was content similarity, while the other two - in-degree (i.e. citation counts) and age of publication - had varying importance depending on the topic studied. This dependence indicates that additional factors could play a role. Indeed, by intuition one should expect the reputation (or visibility) of authors and/or institutions to affect the referencing pattern, and this is only indirectly considered via the in-degree that should correlate with such reputation. Because information on reputation is not readily available, we simulated its effect on artificial citation networks considering two communities with distinct fitness (visibility) parameters. One community was assumed to have twice the fitness value of the other, which amounts to a double probability for a paper being cited. While the h-index for authors in the community with larger fitness evolved with time with slightly higher values than for the control network (no fitness considered), a drastic effect was noted for the community with smaller fitness. (C) 2012 Elsevier Ltd. All rights reserved.

Analyzing convergence of Agricultural and Rural Areas in the Enlarged EU: The case of Hungary

The fall of the Berlin Wall opened the way for a reform path – the transition process – which accompanied ten former Socialist countries in Central and South Eastern Europe to knock at the EU doors. By the way, at the time of the EU membership several economic and structural weaknesses remained. A tendency towards convergence between the new Member States (NMS) and the EU average income level emerged, together with a spread of inequality at the sub-regional level, mainly driven by the backwardness of the agricultural and rural areas. Several progresses were made in evaluating the policies for rural areas, but a shared definition of rurality is still missing. Numerous indicators were calculated for assessing the effectiveness of the Common Agricultural Policy and Rural Development Policy. Previous analysis on the Central and Eastern European countries found that the characteristics of the most backward areas were insufficiently addressed by the policies enacted; the low data availability and accountability at a sub-regional level, and the deficiencies in institutional planning and implementation represented an obstacle for targeting policies and payments. The next pages aim at providing a basis for understanding the connections between the peculiarities of the transition process, the current development performance of NMS and the EU role, with particular attention to the agricultural and rural areas. Applying a mixed methodological approach (multivariate statistics, non-parametric methods, spatial econometrics), this study contributes to the identification of rural areas and to the analysis of the changes occurred during the EU membership in Hungary, assessing the effect of CAP introduction and its contribution to the convergence of the Hungarian agricultural and rural. The author believes that more targeted – and therefore efficient – policies for agricultural and rural areas require a deeper knowledge of their structural and dynamic characteristics.

Improving availability of mobile networks using a cluster routing protocol with redundant cluster head

We show a cluster based routing protocol in order to improve the convergence of the clusters and of the network it is proposed to use a backup cluster head. The use of a event discrete simulator is used for the implementation and the simulation of a hierarchical routing protocol called the Backup Cluster Head Protocol (BCHP). Finally it is shown that the BCHP protocol improves the convergence and availability of the network through a comparative analysis with the Ad Hoc On Demand Distance Vector (AODV)[1] routing protocol and Cluster Based Routing Protocol (CBRP)[2]

Phase transitions and memory effects in the dynamics of Boolean networks

The generating functional method is employed to investigate the synchronous dynamics of Boolean networks, providing an exact result for the system dynamics via a set of macroscopic order parameters. The topology of the networks studied and its constituent Boolean functions represent the system's quenched disorder and are sampled from a given distribution. The framework accommodates a variety of topologies and Boolean function distributions and can be used to study both the noisy and noiseless regimes; it enables one to calculate correlation functions at different times that are inaccessible via commonly used approximations. It is also used to determine conditions for the annealed approximation to be valid, explore phases of the system under different levels of noise and obtain results for models with strong memory effects, where existing approximations break down. Links between Boolean networks and general Boolean formulas are identified and results common to both system types are highlighted. © 2012 Copyright Taylor and Francis Group, LLC.

Theorems on the Convergence of Series in Generalized Lommel-Wright Functions

Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20

Assessment of the EEE-4 oral test: a discourse analysis based on complex networks.

With the development of information technology, the theory and methodology of complex network has been introduced to the language research, which transforms the system of language in a complex networks composed of nodes and edges for the quantitative analysis about the language structure. The development of dependency grammar provides theoretical support for the construction of a treebank corpus, making possible a statistic analysis of complex networks. This paper introduces the theory and methodology of the complex network and builds dependency syntactic networks based on the treebank of speeches from the EEE-4 oral test. According to the analysis of the overall characteristics of the networks, including the number of edges, the number of the nodes, the average degree, the average path length, the network centrality and the degree distribution, it aims to find in the networks potential difference and similarity between various grades of speaking performance. Through clustering analysis, this research intends to prove the network parameters’ discriminating feature and provide potential reference for scoring speaking performance.

Comparison of module detection algorithms in protein networks and investigation of the biological meaning of predicted modules

Background
It is generally acknowledged that a functional understanding of a biological system can only be obtained by an understanding of the collective of molecular interactions in form of biological networks. Protein networks are one particular network type of special importance, because proteins form the functional base units of every biological cell. On a mesoscopic level of protein networks, modules are of significant importance because these building blocks may be the next elementary functional level above individual proteins allowing to gain insight into fundamental organizational principles of biological cells.
Results
In this paper, we provide a comparative analysis of five popular and four novel module detection algorithms. We study these module prediction methods for simulated benchmark networks as well as 10 biological protein interaction networks (PINs). A particular focus of our analysis is placed on the biological meaning of the predicted modules by utilizing the Gene Ontology (GO) database as gold standard for the definition of biological processes. Furthermore, we investigate the robustness of the results by perturbing the PINs simulating in this way our incomplete knowledge of protein networks.
Conclusions
Overall, our study reveals that there is a large heterogeneity among the different module prediction algorithms if one zooms-in the biological level of biological processes in the form of GO terms and all methods are severely affected by a slight perturbation of the networks. However, we also find pathways that are enriched in multiple modules, which could provide important information about the hierarchical organization of the system