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In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center. Median income, for example, may be a better way to describe center of the income distribution because increases in the largest incomes alone have no effect on median. For this reason, the median is of central importance in robust statistics. Finite data set of numbers The median of a finite list of numbers is the "middle" number, when those numbers are listed in order from smallest to greatest. If the data set has an odd number of observations, the middle one is selected. For example, the fol

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The Gene Family-Free Median of Three

Metin Balaban

The gene family-free framework for comparative genomics aims at developing methods for gene order analysis that do not require prior gene family assignment, but work directly on a sequence similarity graph. We present a model for constructing a median of three genomes in this family-free setting, based on maximizing an objective function that generalizes the classical breakpoint distance by integrating sequence similarity in the score of a gene adjacency. We show that the corresponding computational problem is MAX SNP-hard and we present a 0-1 linear program for its exact solution. The result of this program is a median genome with median genes associated to extant genes, in which median adjacencies are assumed to define positional orthologs. We demonstrate through simulations and comparison with the OMA orthology database that the herein presented method is able compute accurate medians and positional orthologs for genomes comparable in size of bacterial genomes.

Springer AG2016

The gene family-free median of three

Metin Balaban

Background: The gene family-free framework for comparative genomics aims at providing methods for gene order analysis that do not require prior gene family assignment, but work directly on a sequence similarity graph. We study two problems related to the breakpoint median of three genomes, which asks for the construction of a fourth genome that minimizes the sum of breakpoint distances to the input genomes. Methods: We present a model for constructing a median of three genomes in this family-free setting, based on maximizing an objective function that generalizes the classical breakpoint distance by integrating sequence similarity in the score of a gene adjacency. We study its computational complexity and we describe an integer linear program (ILP) for its exact solution. We further discuss a related problem called family-free adjacencies for k genomes for the special case of k

2017

Trigeminal Neuralgia Related to Megadolichobasilar Artery Compression: A Prospective Series of Twenty-Nine Patients Treated with Gamma Knife Surgery, with More Than One Year of Follow-Up

Anne Donnet, Constantin Tuleasca

Background: Trigeminal neuralgia (TN) secondary to megadolichobasilar artery (MBA) compression is considerably difficult to manage surgically. Objective: This study aims to evaluate the safety/efficacy of Gamma Knife surgery (GKS) in this special group of patients. Methods: Between July 1992 and November 2010, 29 patients with >1 year of follow-up presenting with MBA compression were treated with GKS at Timone University Hospital. Radiosurgery was performed using a Gamma Knife (model B, C or Perfexion). A single 4-mm isocenter was positioned in the cisternal portion of the trigeminal nerve at a median distance of 9.1 mm (range: 6-18.2 mm) from the emergence. Results: The median follow-up period was 46.1 months (range: 12.9-157.9 months). Initially, all patients (100%) were pain free; the average time to complete pain relief was 13.5 days (range: 0-240 days). Their actuarial probability of remaining pain free without medication at 0.5, 1 and 2 years was 93.1, 79.3 and 75.7%, respectively, and remained stable until 13 years after treatment. The actuarial probability of hypoesthesia onset at 6 months was 4.3%; at 1 year it reached 13% and remained stable until 13 years after treatment. Conclusions: GKS proved to be reasonably safe and effective on a long-term basis as a first- and/or second-line surgical treatment for TN due to MBA compression. (C) 2014 S. Karger AG, Basel

Karger2014

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