Permuting and Batched Geometric Lower Bounds in the I/O Model

We study permuting and batched orthogonal geometric reporting problems in the External Memory Model (EM), assuming indivisibility of the input records. Our main results are twofold. First, we prove a general simulation result that essentially shows that any permutation algorithm (resp. duplicate removal algorithm) that does alpha*N/B I/Os (resp. to remove a fraction of the existing duplicates) can be simulated with an algorithm that does alpha phases where each phase reads and writes each element once, but using a factor alpha smaller block size. Second, we prove two lower bounds for batched rectangle stabbing and batched orthogonal range reporting queries. Assuming a short cache, we prove very high lower bounds that currently are not possible with the existing techniques under the tall cache assumption

Applications of incidence bounds in point covering problems

In the Line Cover problem a set of n points is given and the task is to cover the points using either the minimum number of lines or at most k lines. In Curve Cover, a generalization of Line Cover, the task is to cover the points using curves with d degrees of freedom. Another generalization is the Hyperplane Cover problem where points in d-dimensional space are to be covered by hyperplanes. All these problems have kernels of polynomial size, where the parameter is the minimum number of lines, curves, or hyperplanes needed. First we give a non-parameterized algorithm for both problems in O*(2^n) (where the O*(.) notation hides polynomial factors of n) time and polynomial space, beating a previous exponential-space result. Combining this with incidence bounds similar to the famous Szemeredi-Trotter bound, we present a Curve Cover algorithm with running time O*((Ck/log k)^((d-1)k)), where C is some constant. Our result improves the previous best times O*((k/1.35)^k) for Line Cover (where d=2), O*(k^(dk)) for general Curve Cover, as well as a few other bounds for covering points by parabolas or conics. We also present an algorithm for Hyperplane Cover in R^3 with running time O*((Ck^2/log^(1/5) k)^k), improving on the previous time of O*((k^2/1.3)^k).Comment: SoCG 201

Evaluation of presumably disease causing SCN1A variants in a cohort of common epilepsy syndromes

Objective: The SCN1A gene, coding for the voltage-gated Na+ channel alpha subunit NaV1.1, is the clinically most relevant epilepsy gene. With the advent of high-throughput next-generation sequencing, clinical laboratories are generating an ever-increasing catalogue of SCN1A variants. Variants are more likely to be classified as pathogenic if they have already been identified previously in a patient with epilepsy. Here, we critically re-evaluate the pathogenicity of this class of variants in a cohort of patients with common epilepsy syndromes and subsequently ask whether a significant fraction of benign variants have been misclassified as pathogenic. Methods: We screened a discovery cohort of 448 patients with a broad range of common genetic epilepsies and 734 controls for previously reported SCN1A mutations that were assumed to be disease causing. We re-evaluated the evidence for pathogenicity of the identified variants using in silico predictions, segregation, original reports, available functional data and assessment of allele frequencies in healthy individuals as well as in a follow up cohort of 777 patients. Results and Interpretation: We identified 8 known missense mutations, previously reported as path

Riging notations in two-electron atoms in a uniform magnetic field

SIGLEITItal

Faster algorithms for the minimum red-blue-purple spanning graph problem

Consider a set of n points in the plane, each one of which is colored either red, blue, or purple. A red-blue-purple spanning graph (RBP spanning graph) is a graph whose vertices are the points and whose edges connect the points such that the subgraph induced by the red and purple points is connected, and the subgraph induced by the blue and purple points is connected. The minimum RBP spanning graph problem is to find an RBP spanning graph with minimum total edge length. First we consider this problem for the case when the points are located on a circle. We present an algorithm that solves this problem in O(n2) time, improving upon the previous algorithm by a factor of Θ(n). Also, for the general case we present an algorithm that runs in O(n5) time, improving upon the previous algorithm by a factor of Θ(n)