Decremental All-Pairs ALL Shortest Paths and Betweenness Centrality

We consider the all pairs all shortest paths (APASP) problem, which maintains the shortest path dag rooted at every vertex in a directed graph G=(V,E) with positive edge weights. For this problem we present a decremental algorithm (that supports the deletion of a vertex, or weight increases on edges incident to a vertex). Our algorithm runs in amortized O(\vstar^2 \cdot \log n) time per update, where n=|V|, and \vstar bounds the number of edges that lie on shortest paths through any given vertex. Our APASP algorithm can be used for the decremental computation of betweenness centrality (BC), a graph parameter that is widely used in the analysis of large complex networks. No nontrivial decremental algorithm for either problem was known prior to our work. Our method is a generalization of the decremental algorithm of Demetrescu and Italiano [DI04] for unique shortest paths, and for graphs with \vstar =O(n), we match the bound in [DI04]. Thus for graphs with a constant number of shortest paths between any pair of vertices, our algorithm maintains APASP and BC scores in amortized time O(n^2 \log n) under decremental updates, regardless of the number of edges in the graph.Comment: An extended abstract of this paper will appear in Proc. ISAAC 201

Solar Cycle variations of ƒoF2 from IGY to 1990

Noontime monthly median values of F2-layer critical frequency ƒoF2 (m) for some ionospheric stations representing low- and mid-latitudes are examined for their dependence on solar activity for the years 1957 (IGY) to 1990. This is the period for which ionospheric data in digital form is available in two CD-ROMs at the World Data Center, Boulder. It is observed that at mid-latitudes, foF2 (m) shows nearly a linear relationship with R12 (the 12-month running average of the Zurich sunspot number), though this relation is nonlinear for low-latitudes. These results indicate some departures from the existing information often used in theoretical and applied areas of space research

The glass transition and crystallization kinetic studies on BaNaB9O15 glasses

Transparent glasses of BaNaB9O15 (BNBO) were fabricated via the conventional melt-quenching technique. The amorphous and the glassy nature of the as-quenched samples were respectively, confirmed by X-ray powder diffraction (XRD) and differential scanning calorimetry (DSC). The glass transition and crystallization parameters were evaluated under non-isothermal conditions using DSC. The correlation between the heating rate dependent glass transition and the crystallization temperatures was discussed and deduced the Kauzmann temperature for BNBO glass-plates and powdered samples. The values of the Kauzmann temperature for the plates and powdered samples were 776 K and 768 K, respectively. Approximation-free method was used to evaluate the crystallization kinetic parameters for the BNBO glass samples. The effect of the sample thickness on the crystallization kinetics of BNBO glasses was also investigated.Comment: 23 pages, 12 figure

Liver abscess caused by Serratia grimesii in an immunocompetent patient

In tropical and subtropical countries, the most common cause of liver abscess is Entamoeba histolytica. However, pyogenic infections are common due to bacteria like Kleibsella pneumonia followed by Escherichchia coli and enterococcus species. The possibility of atypical organisms should be considered especially with recurrent liver abscess. We report a case of recurrent liver abscess caused by Serratia grimesii in an immunocopetent individual. Early isolation of the organism along with drug susceptibility testing would make a marked difference in improving the management of the patient and associated prognosis

Biomechanics of Disc Degeneration

Disc degeneration and associated disorders are among the most debated topics in the orthopedic literature over the past few decades. These may be attributed to interrelated mechanical, biochemical, and environmental factors. The treatment options vary from conservative approaches to surgery, depending on the severity of degeneration and response to conservative therapies. Spinal fusion is considered to be the “gold standard” in surgical methods till date. However, the association of adjacent level degeneration has led to the evolution of motion preservation technologies like spinal arthroplasty and posterior dynamic stabilization systems. These new technologies are aimed to address pain and preserve motion while maintaining a proper load sharing among various spinal elements. This paper provides an elaborative biomechanical review of the technologies aimed to address the disc degeneration and reiterates the point that biomechanical efficacy followed by long-term clinical success will allow these nonfusion technologies as alternatives to fusion, at least in certain patient population