Vertex splitting and connectivity augmentation in hypergraphs

We consider problems of splitting and connectivity augmentation in hypergraphs. In a hypergraph G = (V +s, E), to split two edges su, sv, is to replace them with a single edge uv. We are interested in doing this in such a way as to preserve a defined level of connectivity in V . The splitting technique is often used as a way of adding new edges into a graph or hypergraph, so as to augment the connectivity to some prescribed level. We begin by providing a short history of work done in this area. Then several preliminary results are given in a general form so that they may be used to tackle several problems. We then analyse the hypergraphs G = (V + s, E) for which there is no split preserving the local-edge-connectivity present in V. We provide two structural theorems, one of which implies a slight extension to Mader’s classical splitting theorem. We also provide a characterisation of the hypergraphs for which there is no such “good” split and a splitting result concerned with a specialisation of the local-connectivity function. We then use our splitting results to provide an upper bound on the smallest number of size-two edges we must add to any given hypergraph to ensure that in the resulting hypergraph we have λ(x, y) ≥ r(x, y) for all x, y in V, where r is an integer valued, symmetric requirement function on V*V. This is the so called “local-edge-connectivity augmentation problem” for hypergraphs. We also provide an extension to a Theorem of Szigeti, about augmenting to satisfy a requirement r, but using hyperedges. Next, in a result born of collaborative work with Zoltán Király from Budapest, we show that the local-connectivity augmentation problem is NP-complete for hypergraphs. Lastly we concern ourselves with an augmentation problem that includes a locational constraint. The premise is that we are given a hypergraph H = (V,E) with a bipartition P = {P1, P2} of V and asked to augment it with size-two edges, so that the result is k-edge-connected, and has no new edge contained in some P(i). We consider the splitting technique and describe the obstacles that prevent us forming “good” splits. From this we deduce results about which hypergraphs have a complete Pk-split. This leads to a minimax result on the optimal number of edges required and a polynomial algorithm to provide an optimal augmentation.

A new frequency-uniform coercive boundary integral equation for acoustic scattering

A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this integral operator is coercive in L2(Γ) (where Γ is the surface of the scatterer) for all Lipschitz star-shaped domains. Moreover, the coercivity is uniform in the wavenumber k = ω/c, where ω is the frequency and c is the speed of sound. The new boundary integral operator, which we call the “star-combined” potential operator, is a slight modification of the standard combined potential operator, and is shown to be as easy to implement as the standard one. Additionally, to the authors' knowledge, it is the only second-kind integral operator for which convergence of the Galerkin method in L2(Γ) is proved without smoothness assumptions on Γ except that it is Lipschitz. The coercivity of the star-combined operator implies frequency-explicit error bounds for the Galerkin method for any approximation space. In particular, these error estimates apply to several hybrid asymptoticnumerical methods developed recently that provide robust approximations in the high-frequency case. The proof of coercivity of the star-combined operator critically relies on an identity first introduced by Morawetz and Ludwig in 1968, supplemented further by more recent harmonic analysis techniques for Lipschitz domains.

Non-uniform data distribution for communication-efficient parallel clustering

Global communicationrequirements andloadimbalanceof someparalleldataminingalgorithms arethe major obstacles to exploitthe computational power of large-scale systems. This work investigates how non-uniform data distributions can be exploited to remove the global communication requirement and to reduce the communication costin parallel data mining algorithms and, in particular, in the k-means algorithm for cluster analysis. In the straightforward parallel formulation of the k-means algorithm, data and computation loads are uniformly distributed over the processing nodes. This approach has excellent load balancing characteristics that may suggest it could scale up to large and extreme-scale parallel computing systems. However, at each iteration step the algorithm requires a global reduction operationwhichhinders thescalabilityoftheapproach.Thisworkstudiesadifferentparallelformulation of the algorithm where the requirement of global communication is removed, while maintaining the same deterministic nature ofthe centralised algorithm. The proposed approach exploits a non-uniform data distribution which can be either found in real-world distributed applications or can be induced by means ofmulti-dimensional binary searchtrees. The approachcanalso be extended to accommodate an approximation error which allows a further reduction ofthe communication costs. The effectiveness of the exact and approximate methods has been tested in a parallel computing system with 64 processors and in simulations with 1024 processing element

Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

The effect of non-uniform radiative damping on the zonal-mean dynamics of the extratropical middle atmosphere

The effect of spatial and temporal variations in the radiative damping rate on the response to an imposed forcing or diabatic heating is examined in a zonal-mean model of the middle atmosphere. Attention is restricted to the extratropics, where a linear approach is viable. It is found that regions with weak radiative damping rates are more sensitive in terms of temperature to the remote influence of the diabatic circulation. The delay in the response in such regions can mean that ‘downward’ control is not achieved on seasonal time-scales. A seasonal variation in the radiative damping rate modulates the evolution of the response and leaves a transient-like signature in the annual mean temperature field. Several idealized examples are considered, motivated by topical questions. It is found that wave drag outside the polar vortex can significantly affect the temperatures in its interior, so that high-latitude, high-altitude gravity-wave drag is not the only mechanism for warming the southern hemisphere polar vortex. Diabatic mass transport through the 100 hPa surface is found to lag the seasonal evolution of the wave drag that drives the transport, and thus cannot be considered to be in the downward control regime. On the other hand, the seasonal variation of the radiative damping rate is found to make only a weak contribution to the annual mean temperature increase that has been observed above the ozone hole. Copyright © 2002 Royal Meteorological Society.

Non-uniform sparsity in rapid compressive sensing MRI

Magnetic Resonance Imaging (MRI) is one of the prominent medical imaging techniques. This process is time-consuming and can take several minutes to acquire one image. The aim of this research is to reduce the imaging process time of MRI. This issue is addressed by reducing the number of acquired measurements using theory of Compressive Sensing (CS). Compressive Sensing exploits sparsity in MR images. Randomly under sampled k-space generates incoherent noise which can be handled using a nonlinear image reconstruction method. In this paper, a new framework is presented based on the idea to exploit non-uniform nature of sparsity in MR images, where local sparsity constrains were used instead of traditional global constraint, to further reduce the sample set. Experimental results and comparison with CS using global constraint are demonstrated.

Não vício assintótico, consistência forte e uniformemente forte de estimadores do tipo núcleo para dados direcionais sobre uma esfera unitária k-dimensional

In this work we studied the asymptotic unbiasedness, the strong and the uniform strong consistencies of a class of kernel estimators fn as an estimator of the density function f taking values on a k-dimensional sphere

(m,k)-Gur game: Exploiting message discards in order to increase the lifetime and spatial diversity in autonomic wireless sensor networks

The main concern in Wireless Sensor Networks (WSN) algorithms and protocols are the energy consumption. Thus, the WSN lifetime is one of the most important metric used to measure the performance of the WSN approaches. Another important metric is the WSN spatial coverage, where the main goal is to obtain sensed data in a uniform way. This paper has proposed an approach called (m,k)-Gur Game that aims a trade-off between quality of service and the increasement of spatial coverage diversity. Simulation results have shown the effectiveness of this approach. © 2012 IEEE.

Atypical scrapie isolates involve a uniform prion species with a complex molecular signature

The pathobiology of atypical scrapie, a prion disease affecting sheep and goats, is still poorly understood. In a previous study, we demonstrated that atypical scrapie affecting small ruminants in Switzerland differs in the neuroanatomical distribution of the pathological prion protein (PrP(d)). To investigate whether these differences depend on host-related vs. pathogen-related factors, we transmitted atypical scrapie to transgenic mice over-expressing the ovine prion protein (tg338). The clinical, neuropathological, and molecular phenotype of tg338 mice is similar between mice carrying the Swiss atypical scrapie isolates and the Nor98, an atypical scrapie isolate from Norway. Together with published data, our results suggest that atypical scrapie is caused by a uniform type of prion, and that the observed phenotypic differences in small ruminants are likely host-dependant. Strikingly, by using a refined SDS-PAGE technique, we established that the prominent proteinase K-resistant prion protein fragment in atypical scrapie consists of two separate, unglycosylated peptides with molecular masses of roughly 5 and 8 kDa. These findings show similarities to those for other prion diseases in animals and humans, and lay the groundwork for future comparative research.

Sudden cardiac arrest in sports - need for uniform registration: A Position Paper from the Sport Cardiology Section of the European Association for Cardiovascular Prevention and Rehabilitation

There are large variations in the incidence, registration methods and reported causes of sudden cardiac arrest/sudden cardiac death (SCA/SCD) in competitive and recreational athletes. A crucial question is to which degree these variations are genuine or partly due to methodological incongruities. This paper discusses the uncertainties about available data and provides comprehensive suggestions for standard definitions and a guide for uniform registration parameters of SCA/SCD. The parameters include a definition of what constitutes an 'athlete', incidence calculations, enrolment of cases, the importance of gender, ethnicity and age of the athlete, as well as the type and level of sporting activity. A precise instruction for autopsy practice in the case of a SCD of athletes is given, including the role of molecular samples and evaluation of possible doping. Rational decisions about cardiac preparticipation screening and cardiac safety at sport facilities requires increased data quality concerning incidence, aetiology and management of SCA/SCD in sports. Uniform standard registration of SCA/SCD in athletes and leisure sportsmen would be a first step towards this goal.

Tagsbefehl vom 24. Mai 1848: Die nachfolgenden Beschlüsse des Verwaltungsrathes der Nationalgarde werden behufs genauer Darnachachtung zur allgemeinen Kenntniß gebracht: Erstens. Daß die Nationalgarde-Uniform bei Ausübung schwerer Arbeiten nicht getragen werden soll ...

Welsch (Projektbearbeiter): Dienstreglements für die Nationalgarde das Tragen der Uniform, die Übergabe von Petitionen sowie die Zusammenberufung betreffend

K-Ar dating of magmatic rocks from the Urup Island, Kuril Island Chain

An isotope-geochronological study of Neogene-Quaternary igneous rocks from the Urup Island (Greater Kuril Ridge) was carried out. It was established that magmatic activity in the island developed during the last 10 my and it was not interrupted by long inactive periods. K-Ar data obtained along with results of diatomic analysis are in good agreement with the regional stratigraphic scheme of Paleogene and Neogene deposits and the intraregional correlation scheme of magmatic rocks in the Kuril Islands, which are developed for the State Geologic Map, scale 1:200 000 (Second edition). In the present-day territory of the Urup Island, the earliest Late Miocene - Early Pliocene (10.5-4.5 Ma) magmatic stage was associated with formation of the Rybakovsky andesite volcanic complex, which is represented by an effusive series (Rybakovskaya Suite) and subvolcanic rocks. Actually at the same time (6.6-4.7 Ma), but at a great depth, intrusive bodies of the Prasolovsky plagiogranite-diorite plutonic complex were intruded. The Pliocene stage of magmatism in the Urup Island is characterized by formation of rocks of the Kamuysky dacitic volcanic complex (4.0-2.1 Ma). This complex is locally represented only by subvolcanic acidic bodies, and its occurrence in the island is limited. During the Pliocene - Early Neopleistocene stage of magmatism (3.0-0.8 Ma) the Fregatsky andesibasalt volcanic complex was formed in the Urup Island. This complex includes effusive series (Fregatskaya unit) and subvolcanic bodies. Quaternary time in the Urup Island is characterized by eruptive activity in subaerial conditions with formation of effusive-pyroclastic intermediate-basic rocks of the Bogatyrsky Middle Neopleistocene - Holocene complex (<0.5 Ma). Rocks of this complex formed stratovolcano cones. Pyroclastic rocks of the Rokovsky dacitic volcanic complex were erupted simultaneously. The mentioned magmatic complexes of the Urup Island well correlate with the distinguished magmatic complexes within the bounds of contiguous insular blocks of the Greater Kuril Arc and confirm uniform geologic history of magmatic development of the region.