Dynamic ham-sandwich cuts in the plane

We design efficient data structures for dynamically maintaining a ham-sandwich cut of two point sets in the plane subject to insertions and deletions of points in either set. A ham-sandwich cut is a line that simultaneously bisects the cardinality of both point sets. For general point sets, our first data structure supports each operation in O(n1/3+ε) amortized time and O(n4/3+ε) space. Our second data structure performs faster when each point set decomposes into a small number k of subsets in convex position: it supports insertions and deletions in O(logn) time and ham-sandwich queries in O(klog4n) time. In addition, if each point set has convex peeling depth k , then we can maintain the decomposition automatically using O(klogn) time per insertion and deletion. Alternatively, we can view each convex point set as a convex polygon, and we show how to find a ham-sandwich cut that bisects the total areas or total perimeters of these polygons in O(klog4n) time plus the O((kb)polylog(kb)) time required to approximate the root of a polynomial of degree O(k) up to b bits of precision. We also show how to maintain a partition of the plane by two lines into four regions each containing a quarter of the total point count, area, or perimeter in polylogarithmic time.Engineering and Applied Science

The structural plasticity of white matter networks following anterior temporal lobe resection

Anterior temporal lobe resection is an effective treatment for refractory temporal lobe epilepsy. The structural consequences of such surgery in the white matter, and how these relate to language function after surgery remain unknown. We carried out a longitudinal study with diffusion tensor imaging in 26 left and 20 right temporal lobe epilepsy patients before and a mean of 4.5 months after anterior temporal lobe resection. The whole-brain analysis technique tract-based spatial statistics was used to compare pre- and postoperative data in the left and right temporal lobe epilepsy groups separately. We observed widespread, significant, mean 7%, decreases in fractional anisotropy in white matter networks connected to the area of resection, following both left and right temporal lobe resections. However, we also observed a widespread, mean 8%, increase in fractional anisotropy after left anterior temporal lobe resection in the ipsilateral external capsule and posterior limb of the internal capsule, and corona radiata. These findings were confirmed on analysis of the native clusters and hand drawn regions of interest. Postoperative tractography seeded from this area suggests that this cluster is part of the ventro-medial language network. The mean pre- and postoperative fractional anisotropy and parallel diffusivity in this cluster were significantly correlated with postoperative verbal fluency and naming test scores. In addition, the percentage change in parallel diffusivity in this cluster was correlated with the percentage change in verbal fluency after anterior temporal lobe resection, such that the bigger the increase in parallel diffusivity, the smaller the fall in language proficiency after surgery. We suggest that the findings of increased fractional anisotropy in this ventro-medial language network represent structural reorganization in response to the anterior temporal lobe resection, which may damage the more susceptible dorso-lateral language pathway. These findings have important implications for our understanding of brain injury and rehabilitation, and may also prove useful in the prediction and minimization of postoperative language deficits

An Experimental Study of Old and New Depth Measures

Data depth is a statistical analysis method that assigns a numeric value to a point based on its centrality relative to a data set. Examples include the half-space depth (also known as Tukey depth), convex-hull peeling depth and L1 depth. Data depth has significant potential as a data analysis tool. The lack of efficient computational tools for depth based analysis of large high-dimensional data sets, however, prevents it from being in widespread use. We provide an experimental evaluation of several existing depth measures on different types of data sets, recognize problems with the existing measures and suggest modifications. Specifically, we show how the L1 depth contours are not indicative of shape and suggest a PCA-based scaling that handles this problem; we demonstrate how most existing depth measures are unable to cope with multimodal data sets and how the newly suggested proximity graph depth addresses this issue; and we explore how depth measures perform when the underlying distribution is not elliptic. Our experimental tool is of independent interest: it is an interactive software tool for the generation of data sets and visualization of the performance of multiple depth measures. The tool uses a hierarchical render-pipeline to allow for diverse data sets and fine control of the visual result. With this tool, new ideas in the field of data depth can be evaluated visually and quickly, allowing researchers to assess and adjust current depth functions

Vernal Keratoconjunctivitis in School Children in Rwanda and Its Association with Socio-Economic Status: A Population-Based Survey

Vernal keratoconjunctivitis (VKC) is an allergic eye disease and an important cause of hospital referral among children in Africa and Asia. Hospital-based studies have suggested a role for parasites in its pathogenesis. To determine the prevalence and risk factors for VKC in Central Africa, we conducted a nested population-based case control study in Rwanda, involving randomly selected primary schools from different environments (rural/urban) and climate. A prevalence of VKC of 4.0% (95% confidence interval 3.3-4.7%) was found among 3,041 children studied (participation rate 94.7%). The intestinal parasitic burden was not related to VKC. Besides hot dry climate (odds ratio [OR] = 1.5, P = 0.05) and male gender (OR = 1.7, P = 0.005), multivariate analysis identified higher economic status as a risk for VKC (OR = 1.4, P = 0.005). The effect on VKC of higher economic status appears not to act through differences in parasitic intestinal load

Dynamic ham-sandwich cuts in the plane

We design efficient data structures for dynamically maintaining a ham-sandwich cut of two point sets in the plane subject to insertions and deletions of points in either set. A ham-sandwich cut is a line that simultaneously bisects the cardinality of both point sets. For general point sets, our first data structure supports each operation in O(n 1/3+ε) amortized time and O(n4/3+ε) space. Our second data structure performs faster when each point set decomposes into a small number k of subsets in convex position: it supports insertions and deletions in O (log n) time and ham-sandwich queries in O(k log4 n) time. In addition, if each point set has convex peeling depth k, then we can maintain the decomposition automatically using O (k log n) time per insertion and deletion. Alternatively, we can view each convex point set as a convex polygon, and we show how to find a ham-sandwich cut that bisects the total areas or total perimeters of these polygons in O (k log4 n) time plus the O ((kb) polylog(kb)) time required to approximate the root of a polynomial of degree O (k) up to b bits of precision. We also show how to maintain a partition of the plane by two lines into four regions each containing a quarter of the total point count, area, or perimeter in polylogarithmic time.SCOPUS: ar.jSCOPUS: cp.jinfo:eu-repo/semantics/publishe

A short-echo-time proton magnetic resonance spectroscopic imaging study of temporal lobe epilepsy

Purpose: We used short-echo-time proton magnetic resonance spectroscopy imaging (MRSI) to study metabolite concentration variation through the temporal lobe in patients with temporal lobe epilepsy (TLE) with and without abnormal MRI.Methods: MRSI was performed at TE = 30 ms to study 10 control subjects, 10 patients with TLE and unilateral hippocampal sclerosis, and 10 patients with TLE and unremarkable MRI (MRI negative). We measured the concentrations of N-acetyl aspartate + N-acetyl aspartyl-glutamate (NAAt), creatine (Cr), choline (Cho), glutamate + glutamine (Glx), and myoinositol, in the anterior, middle, and posterior medial temporal lobe (MTL), and in the posterior lateral temporal lobe. Segmented volumetric T-1-weighted MRIs gave the tissue composition of each MRSI voxel. Normal ranges were defined as the control mean 3 SD,Results: In the hippocampal sclerosis group, seven of 10 had abnormally low NAAt in the ipsilateral anterior MTL. In the MRI-negative group. four of 10 had low NAAt in the middle MTL voxel ipsilateral to seizure onset. Metabolite ratios were less sensitive to abnormality than was the NAAt concentration. Group analysis showed low NAAt, Cr, and Cho in the anterior MTL in hippocampal sclerosis, Glx was elevated in the anterior voxel contralateral to seizure onset in the MRI-negative group. Metabolite concentrations were influenced by voxel position and tissue composition.Conclusions: (a) Low NAAt, Cr, and Cho were features of the anterior sclerotic hippocampus, whereas low NAAt was observed in the MRI-negative group in the middle MTL region. The posterior temporal lobe regions were not associated with significant metabolite abnormality; (b) The two patient groups demonstrated different metabolite profiles across the temporal lobe, with elevated Glx a feature of the MRI-negative groups and (c) Voxel tissue composition and position influenced obtained metabolite concentrations