A Linear-time Algorithm for Sparsification of Unweighted Graphs

Given an undirected graph $G$ and an error parameter $\epsilon > 0$, the {\em graph sparsification} problem requires sampling edges in $G$ and giving the sampled edges appropriate weights to obtain a sparse graph $G_{\epsilon}$ with the following property: the weight of every cut in $G_{\epsilon}$ is within a factor of $(1\pm \epsilon)$ of the weight of the corresponding cut in $G$. If $G$ is unweighted, an $O(m\log n)$-time algorithm for constructing $G_{\epsilon}$ with $O(n\log n/\epsilon^2)$ edges in expectation, and an $O(m)$-time algorithm for constructing $G_{\epsilon}$ with $O(n\log^2 n/\epsilon^2)$ edges in expectation have recently been developed (Hariharan-Panigrahi, 2010). In this paper, we improve these results by giving an $O(m)$-time algorithm for constructing $G_{\epsilon}$ with $O(n\log n/\epsilon^2)$ edges in expectation, for unweighted graphs. Our algorithm is optimal in terms of its time complexity; further, no efficient algorithm is known for constructing a sparser $G_{\epsilon}$. Our algorithm is Monte-Carlo, i.e. it produces the correct output with high probability, as are all efficient graph sparsification algorithms

Optimal Parallel Construction of Minimal Suffix and Factor Automata

This paper gives optimal parallel algorithms for the construction of the smallest deterministic finite automata recognizing all the suffixes and the factors of a string. The algorithms use recently discovered optimal parallel suffix tree construction algorithms together with data structures for the efficient manipulation of trees, exploiting the well known relation between suffix and factor automata and suffix trees

2008 Abstracts Collection -- IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science

This volume contains the proceedings of the 28th international conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2008), organized under the auspices of the Indian Association for Research in Computing Science (IARCS)

A randomized algorithm for large scale support vector learning

We propose a randomized algorithm for large scale SVM learning which solves the problem by iterating over random subsets of the data. Crucial to the algorithm for scalability is the size of the subsets chosen. In the context of text classification we show that, by using ideas from random projections, a sample size of O(log n) can be used to obtain a solution which is close to the optimal with a high probability. Experiments done on synthetic and real life data sets demonstrate that the algorithm scales up SVM learners, without loss in accuracy

Treatment of Refractory Ventricular Tachycardia with Radiofrequency Ablation and Temporary Mechanical Circulatory Support

Catheter-based radiofrequency ablation has long been recognized as an effective treatment for refractory ventricular tachycardia (VT). A 57-year-old male with severe coronary artery disease underwent percutaneous mechanical circulatory support because of worsening cardiogenic shock after failed revascularization attempts. Despite aggressive medical management, the patient experienced refractory VT episodes, leading to the decision to proceed with radiofrequency catheter ablation. Notably, the Impella 5.5 device (Abiomed) provided critical left ventricular support during the ablation procedure. This case underscores the potential benefits of Impella support during radiofrequency ablation of complex ventricular arrhythmias

Nanoscale changes in chromatin organization represent the initial steps of tumorigenesis: a transmission electron microscopy study

BACKGROUND: Nuclear alterations are a well-known manifestation of cancer. However, little is known about the early, microscopically-undetectable stages of malignant transformation. Based on the phenomenon of field cancerization, the tissue in the field of a tumor can be used to identify and study the initiating events of carcinogenesis. Morphological changes in nuclear organization have been implicated in the field of colorectal cancer (CRC), and we hypothesize that characterization of chromatin alterations in the early stages of CRC will provide insight into cancer progression, as well as serve as a biomarker for early detection, risk stratification and prevention. METHODS: For this study we used transmission electron microscopy (TEM) images of nuclei harboring pre-neoplastic CRC alterations in two models: a carcinogen-treated animal model of early CRC, and microscopically normal-appearing tissue in the field of human CRC. We quantify the chromatin arrangement using approaches with two levels of complexity: 1) binary, where chromatin is separated into areas of dense heterochromatin and loose euchromatin, and 2) grey-scale, where the statistics of continuous mass-density distribution within the nucleus is quantified by its spatial correlation function. RESULTS: We established an increase in heterochromatin content and clump size, as well as a loss of its characteristic peripheral positioning in microscopically normal pre-neoplastic cell nuclei. Additionally, the analysis of chromatin density showed that its spatial distribution is altered from a fractal to a stretched exponential. CONCLUSIONS: We characterize quantitatively and qualitatively the nanoscale structural alterations preceding cancer development, which may allow for the establishment of promising new biomarkers for cancer risk stratification and diagnosis. The findings of this study confirm that ultrastructural changes of chromatin in field carcinogenesis represent early neoplastic events leading to the development of well-documented, microscopically detectable hallmarks of cancer