Computing and updating the process number in trees

The process number is the minimum number of requests that have to be simultaneously disturbed during a routing reconfiguration phase of a connection oriented network. From a graph theory point of view, it is similar to the node search number, and thus to the pathwidth, however they are not always equal. In general determining these parameters is NP-complete. We present a distributed algorithm to compute these parameters and the edge search number, in trees. It can be executed in an asynchronous environment, requires n steps, an overall computation time of O(n log n), and n messages of size log3 n + 2. Then, we propose a distributed algorithm to update these parameters on each component of a forest after addition or deletion of any tree edge. This second algorithm requires O(D) steps, an overall computation time of O(D log n), and O(D) messages of size log3 n + 3, where D is the diameter of the new connected component

Centrality Measures Based on Current Flow

We consider variations of two well-known centrality measures, betweenness and closeness, with a different model of information spread. Rather than along shortest paths only, it is assumed that information spreads efficiently like an electrical current. We prove that the current-flow variant of closeness centrality is identical with another known measure, information centrality, and give improved algorithms for computing both measures exactly. Since running times and space requirements are prohibitive for large networks, we also present a randomized approximation scheme for current-flow betweenness

Inapproximability of Treewidth, One-Shot Pebbling, and Related Layout Problems

We study the approximability of a number of graph problems: treewidth and pathwidth of graphs, one-shot black (and black-white) pebbling costs of directed acyclic graphs, and a variety of different graph layout problems such as minimum cut linear arrangement and interval graph completion. We show that, assuming the recently introduced Small Set Expansion Conjecture, all of these problems are hard to approximate within any constant factor. ∗Research supported by NSERC. ar X i

The Sensıtıvıty And Specıfıcıty Of The Balance Evaluatıon Systems Test (Bestest) To Determıne The Rısk Of Fall In Stroke Patıents

Çalışmamız, inmeli bireylerde Denge Değerlendirme Sistemler Testi nin (BESTest) düşme riskini belirlemedeki duyarlılık ve özgüllüğünü incelemek amacı ile planlandı. Çalışmaya 18-65 yaş aralığında kronik inmeli 50 hasta dahil edildi. Hastalar düşen ve düşmeyen inmeli hastalar olarak iki gruba ayrıldı. Çalışmaya katılan hastaları tanımlamak amacı ile; inme tipi ve lokalizasyonu Oxfordshire İnme Projesi Sınıflandırma Topluluğu testi ile, fonksiyonel ambulasyon ve özür düzeyi Modifiye Rankin Ölçeği ile, fonksiyonel hareket ve mobilite performansı İnme Rehabilitasyonu Hareket Değerlendirme Ölçeği (STREAM) ile değerlendirildi. Denge BESTest, Berg Denge Ölçeği, Aktiviteye Spesifik Denge Güvenilirlik Ölçeği (ABC) ve Biodex Biosway ile değerlendirildi. Biodex-BioSway cihazı ile postüral stabilite, stabilite limiti ve modifiye sensori organizasyon testleri (MSOT) yapıldı. BESTest in kapsam geçerliliğini incelemek üzere, BESTest ile diğer klinik ve laboratuvar denge değerlendirme yöntemleri arasındaki ilişki incelendi. BESTest in iç tutarlılık güvenirliğine Cronbach &#945; katsayısı ile bakıldı. BESTest in kesim noktası, duyarlılık ve özgüllüğünü belirlemek için alıcı işlem karakteristikleri analizi (receiver operating characteristic-ROC) yapıldı. Düşen inmeli hastaların BESTest, Berg Denge Ölçeği, ABC Ölçeği ve Biodex-BioSway cihazı ile yapılan denge test sonuçlarının düşmeyen hastalara göre daha kötü olduğu bulundu (p0.05). BESTest in iç tutarlılığı Cronbach &#945;=0.960 bulundu. BESTest in 0.844 AUC değeri ile kesim noktası %69.44, duyarlılığı %75 ve özgüllüğü %84.6 bulundu (p 0.05). The internal consistency of BESTest was found to be Cronbach &#945; = 0.960. The BESTest was 0.844 AUC value, with a cut-off point of 69.44%, a sensitivity of 75% and a specificity of 84.6% (p <0.01). It was concluded that BESTest was a battery with high sensitivity and specificity in determining the safety, validity and risk of falling in stroke patients. It is thought that BESTest's systems related to the balance disorder and the risk of falls in chronic stroke patients are thought to be beneficial for the purpose of establishing physiotherapy and rehabilitation program in this direction