On the expected diameter, width, and complexity of a stochastic convex-hull

We investigate several computational problems related to the stochastic convex hull (SCH). Given a stochastic dataset consisting of $n$ points in $\mathbb{R}^d$ each of which has an existence probability, a SCH refers to the convex hull of a realization of the dataset, i.e., a random sample including each point with its existence probability. We are interested in computing certain expected statistics of a SCH, including diameter, width, and combinatorial complexity. For diameter, we establish the first deterministic 1.633-approximation algorithm with a time complexity polynomial in both $n$ and $d$. For width, two approximation algorithms are provided: a deterministic $O(1)$-approximation running in $O(n^{d+1} \log n)$ time, and a fully polynomial-time randomized approximation scheme (FPRAS). For combinatorial complexity, we propose an exact $O(n^d)$-time algorithm. Our solutions exploit many geometric insights in Euclidean space, some of which might be of independent interest

Approximate Minimum Diameter

We study the minimum diameter problem for a set of inexact points. By inexact, we mean that the precise location of the points is not known. Instead, the location of each point is restricted to a contineus region (\impre model) or a finite set of points (\indec model). Given a set of inexact points in one of \impre or \indec models, we wish to provide a lower-bound on the diameter of the real points. In the first part of the paper, we focus on \indec model. We present an $O(2^{\frac{1}{\epsilon^d}} \cdot \epsilon^{-2d} \cdot n^3 )$ time approximation algorithm of factor $(1+\epsilon)$ for finding minimum diameter of a set of points in $d$ dimensions. This improves the previously proposed algorithms for this problem substantially. Next, we consider the problem in \impre model. In $d$-dimensional space, we propose a polynomial time $\sqrt{d}$-approximation algorithm. In addition, for $d=2$, we define the notion of $\alpha$-separability and use our algorithm for \indec model to obtain $(1+\epsilon)$-approximation algorithm for a set of $\alpha$-separable regions in time $O(2^{\frac{1}{\epsilon^2}}\allowbreak . \frac{n^3}{\epsilon^{10} .\sin(\alpha/2)^3} )$

Finding Pairwise Intersections Inside a Query Range

We study the following problem: preprocess a set O of objects into a data structure that allows us to efficiently report all pairs of objects from O that intersect inside an axis-aligned query range Q. We present data structures of size $O(n({\rm polylog} n))$ and with query time $O((k+1)({\rm polylog} n))$ time, where k is the number of reported pairs, for two classes of objects in the plane: axis-aligned rectangles and objects with small union complexity. For the 3-dimensional case where the objects and the query range are axis-aligned boxes in R^3, we present a data structures of size $O(n\sqrt{n}({\rm polylog} n))$ and query time $O((\sqrt{n}+k)({\rm polylog} n))$. When the objects and query are fat, we obtain $O((k+1)({\rm polylog} n))$ query time using $O(n({\rm polylog} n))$ storage

An Algorithmic Framework for Labeling Network Maps

Drawing network maps automatically comprises two challenging steps, namely laying out the map and placing non-overlapping labels. In this paper we tackle the problem of labeling an already existing network map considering the application of metro maps. We present a flexible and versatile labeling model. Despite its simplicity, we prove that it is NP-complete to label a single line of the network. For a restricted variant of that model, we then introduce an efficient algorithm that optimally labels a single line with respect to a given weighting function. Based on that algorithm, we present a general and sophisticated workflow for multiple metro lines, which is experimentally evaluated on real-world metro maps.Comment: Full version of COCOON 2015 pape

The Complexity of Separating Points in the Plane

We study the following separation problem: given n connected curves and two points s and t in the plane, compute the minimum number of curves one needs to retain so that any path connecting s to t intersects some of the retained curves. We give the first polynomial (O(n3)) time algorithm for the problem, assuming that the curves have reasonable computational properties. The algorithm is based on considering the intersection graph of the curves, defining an appropriate family of closed walks in the intersection graph that satisfies the 3-path-condition, and arguing that a shortest cycle in the family gives an optimal solution. The 3-path-condition has been used mainly in topological graph theory, and thus its use here makes the connection to topology clear. We also show that the generalized version, where several input points are to be separated, is NP-hard for natural families of curves, like segments in two directions or unit circles

A Time-Space Tradeoff for Triangulations of Points in the Plane

In this paper, we consider time-space trade-offs for reporting a triangulation of points in the plane. The goal is to minimize the amount of working space while keeping the total running time small. We present the first multi-pass algorithm on the problem that returns the edges of a triangulation with their adjacency information. This even improves the previously best known random-access algorithm

Criteria for Inclusion of Newer Bariatric and Metabolic Procedures into the Mainstream: a Survey of 396 Bariatric Surgeons

BACKGROUND: There is currently no consensus on the criteria for inclusion of new bariatric procedures into routine clinical practice. This study canvasses bariatric surgeons in an attempt to define these criteria. METHODS: Bariatric Surgeons from around the world were invited to participate in a questionnaire-based survey on SurveyMonkey ®. RESULTS: 396 bariatric surgeons, 337 International Federation for the Surgery of Obesity and Metabolic Disorders (IFSO) members, took the survey. Five clinical studies conducted under the strict monitoring of an Institutional Review Board would satisfy most surgeons (67.7 %, n = 266). When asked regarding the number of patients in these studies, a cumulative number of 500 patients would satisfy 64.5 % (n = 255) of the surgeons. Most respondents regarded endorsement by their national society and IFSO as 'very important' or 'extremely important'. An overwhelming 74.4 % (n = 294) felt that every new procedure should undergo a randomized comparison against one of the established alternatives like Roux-en-Y Gastric Bypass or Sleeve Gastrectomy. CONCLUSION: Evaluation of a new bariatric procedure in at least 5 adequately supervised clinical studies (four of which must be randomized comparisons with one of the existing alternatives) reporting at least 5 years results on a minimum of 500 patients would satisfy majority of bariatric surgeons for the inclusion of a new bariatric procedure into clinical practice. The findings of this survey are simply aimed at starting a discussion on this topic and cannot be used to influence the ground reality until an international consensus can be reached amongst experts.info:eu-repo/semantics/publishedVersio

Solving kk-means on High-dimensional Big Data

In recent years, there have been major efforts to develop data stream algorithms that process inputs in one pass over the data with little memory requirement. For the $k$-means problem, this has led to the development of several $(1+\varepsilon)$-approximations (under the assumption that $k$ is a constant), but also to the design of algorithms that are extremely fast in practice and compute solutions of high accuracy. However, when not only the length of the stream is high but also the dimensionality of the input points, then current methods reach their limits. We propose two algorithms, piecy and piecy-mr that are based on the recently developed data stream algorithm BICO that can process high dimensional data in one pass and output a solution of high quality. While piecy is suited for high dimensional data with a medium number of points, piecy-mr is meant for high dimensional data that comes in a very long stream. We provide an extensive experimental study to evaluate piecy and piecy-mr that shows the strength of the new algorithms.Comment: 23 pages, 9 figures, published at the 14th International Symposium on Experimental Algorithms - SEA 201

Co-existence of nocardiosis with pulmonary aspergillosis in a single patient

AbstrAct Introduction: Nocardia and Aspergillus are important causes of opportunistic infections in immunocompromised individuals. An aggressive workup is essential since these infections are remediable but potentially mortal. case report: We describe a case of a 50-year-old diabetic female with pulmonary aspergillosis who presented with cough and breathlessness for one and ahalf months. she was given steroids and itraconazole for the same but there was no relief. Later on, bronchoalveolar lavage on Kinyoun stain showed Nocardia. conclusion: this case highlights the importance to look for other causes as well in patients with pulmonary aspergillosis not responding to treatment since delay in diagnosis can be fatal for the patient

Multiple cysticerci as an unusual cause of mesenteric lymph node enlargement: a case report

<p>Abstract</p> <p>Introduction</p> <p>Cysticercosis is a disease caused by infestation with the larval stage of the intestinal cestode <it>Taenia solium</it>. The parasite usually localizes to subcutaneous tissues and muscles causing palpable or visible nodules, to the brain leading to epileptic attacks, and to the eyes with visible nodules leading to blindness and atrophy.</p> <p>Case presentation</p> <p>Here we present the case of a 15-year-old girl who was incidentally detected as having mesenteric lymph node enlargement caused by multiple cysticerci. This is the second case report of lymph node enlargement due to cysticercus infestation.</p> <p>Conclusion</p> <p>This rare mode of presentation of cysticercus infestation highlights the importance of parasites as a cause of treatable lymph node enlargement.</p