On Euclidean Norm Approximations

Euclidean norm calculations arise frequently in scientific and engineering applications. Several approximations for this norm with differing complexity and accuracy have been proposed in the literature. Earlier approaches were based on minimizing the maximum error. Recently, Seol and Cheun proposed an approximation based on minimizing the average error. In this paper, we first examine these approximations in detail, show that they fit into a single mathematical formulation, and compare their average and maximum errors. We then show that the maximum errors given by Seol and Cheun are significantly optimistic.Comment: 9 pages, 1 figure, Pattern Recognitio

Comments on "On Approximating Euclidean Metrics by Weighted t-Cost Distances in Arbitrary Dimension"

Mukherjee (Pattern Recognition Letters, vol. 32, pp. 824-831, 2011) recently introduced a class of distance functions called weighted t-cost distances that generalize m-neighbor, octagonal, and t-cost distances. He proved that weighted t-cost distances form a family of metrics and derived an approximation for the Euclidean norm in $\mathbb{Z}^n$. In this note we compare this approximation to two previously proposed Euclidean norm approximations and demonstrate that the empirical average errors given by Mukherjee are significantly optimistic in $\mathbb{R}^n$. We also propose a simple normalization scheme that improves the accuracy of his approximation substantially with respect to both average and maximum relative errors.Comment: 7 pages, 1 figure, 3 tables. arXiv admin note: substantial text overlap with arXiv:1008.487

Competition between species can stabilize public-goods cooperation within a species

Competition between species is a major ecological force that can drive evolution. Here, we test the effect of this force on the evolution of cooperation within a species. We use sucrose metabolism of budding yeast, Saccharomyces cerevisiae, as a model cooperative system that is subject to social parasitism by cheater strategies. We find that when cocultured with a bacterial competitor, Escherichia coli, the frequency of cooperator phenotypes in yeast populations increases dramatically as compared with isolated yeast populations. Bacterial competition stabilizes cooperation within yeast by limiting the yeast population density and also by depleting the public goods produced by cooperating yeast cells. Both of these changes induced by bacterial competition increase the cooperator frequency because cooperator yeast cells have a small preferential access to the public goods they produce; this preferential access becomes more important when the public good is scarce. Our results indicate that a thorough understanding of species interactions is crucial for explaining the maintenance and evolution of cooperation in nature.United States. National Institutes of Health (GM085279‐02)National Science Foundation (U.S.) (PHY‐1055154)Alfred P. Sloan Foundation (BR2011‐066

Abnormal LDIflare but Normal Quantitative Sensory Testing and Dermal Nerve Fiber Density in Patients with Painful Diabetic Neuropathy

OBJECTIVE—Abnormal small nerve fiber function may be an early feature of diabetic neuropathy and may also underlie painful symptoms. Methods for assessing small-fiber damage include quantitative sensory testing (QST) and determining intraepidermal nerve fiber density. We recently described a reproducible physiological technique, the LDIflare, which assesses small-fiber function and thus may reflect early dysfunction before structural damage. The value of this technique in painful neuropathy was assessed by comparing it with QST and dermal nerve fiber density (NFD)

Expansion microscopy of zebrafish for neuroscience and developmental biology studies

Expansion microscopy (ExM) allows scalable imaging of preserved 3D biological specimens with nanoscale resolution on fast diffraction-limited microscopes. Here, we explore the utility of ExM in the larval and embryonic zebrafish, an important model organism for the study of neuroscience and development. Regarding neuroscience, we found that ExM enabled the tracing of fine processes of radial glia, which are not resolvable with diffraction-limited microscopy. ExM further resolved putative synaptic connections, as well as molecular differences between densely packed synapses. Finally, ExM could resolve subsynaptic protein organization, such as ring-like structures composed of glycine receptors. Regarding development, we used ExM to characterize the shapes of nuclear invaginations and channels, and to visualize cytoskeletal proteins nearby. We detected nuclear invagination channels at late prophase and telophase, potentially suggesting roles for such channels in cell division. Thus, ExM of the larval and embryonic zebrafish may enable systematic studies of how molecular components are configured in multiple contexts of interest to neuroscience and developmental biology.National Institutes of Health (U.S.) (Grant 1R01EB024261)National Institutes of Health (U.S.) (Grant 1R01MH110932)National Institutes of Health (U.S.) (Grant 2R01DA029639)National Institutes of Health (U.S.) (Grant 1R01NS087950)National Institutes of Health (U.S.) (Grant 1U01MH106011

Clinical outcome of transcatheter closure of patent ductus arteriosus in small children weighing 10 kg or less

PurposeTranscatheter closure has become an effective therapy in most patients with patent ductus arteriosus (PDA). However, there are difficulties in transcatheter closure of PDA in small children. We reviewed clinical outcomes of transcatheter closure of PDA in children weighing less than 10 kg in a single center.MethodsBetween January 2003 and December 2009, 314 patients with PDA underwent transcatheter closure in our institute. Among them, 115 weighed less than 10 kg. All of these patients underwent transcatheter closure of PDA using either COOK Detachable Coil®, PFM Nit-Occlud®, or Amplatzer duct occluder®. A retrospective review of the treatment results and complications was performed.ResultsThe mean age of patients was 9.1±5.9 months (median, 8 months), and mean weight was 7.6±1.8 kg (median, 7.8 kg). The mean diameter of PDA was 3.2±1.4 mm (median, 3 mm). Complete occlusion occurred in 113 patients (98%). One patient was sent to surgery because of a failed attempt at device closure, and another patient had a small residual shunt after device placement. The average mean length of hospital stay was 3.0±3.3 days, and mean follow-up duration was 21.0±19.6 months. There were no major complications in any of the patients.ConclusionTranscatheter closure of PDA is considered safe and efficacious in infants weighing less than 10 kg. With sufficient experience and further effort, transcatheter closure of PDA can be accepted as the gold standard of treatment for this group of patients

When increasing population density can promote the evolution of metabolic cooperation.

This is the author accepted manuscript. The final version is available from Nature Publishing Group via the DOI in this record.Microbial cooperation drives ecological and epidemiological processes and is affected by the ecology and demography of populations. Population density influences the selection for cooperation, with spatial structure and the type of social dilemma, namely public-goods production or self-restraint, shaping the outcome. While existing theories predict that in spatially structured environments increasing population density can select either for or against cooperation, experimental studies with both public-goods production and self-restraint systems have only ever shown that increasing population density favours cheats. We suggest that the disparity between theory and empirical studies results from experimental procedures not capturing environmental conditions predicted by existing theories to influence the outcome. Our study resolves this issue and provides the first experimental evidence that high population density can favour cooperation in spatially structured environments for both self-restraint and public-goods production systems. Moreover, using a multi-trait mathematical model supported by laboratory experiments we extend this result to systems where the self-restraint and public-goods social dilemmas interact. We thus provide a systematic understanding of how the strength of interaction between the two social dilemmas and the degree of spatial structure within an environment affect selection for cooperation. These findings help to close the current gap between theory and experiments.RJL and IG: European Research Council No. 647292 MathModExp. BJP: Engineering and Physical Sciences Research Council Doctoral training grant studentship

Randomized clinical trial of surgery versus conservative therapy for carpal tunnel syndrome [ISRCTN84286481]

BACKGROUND: Conservative treatment remains the standard of care for treating mild to moderate carpal tunnel syndrome despite a small number of well-controlled studies and limited objective evidence to support current treatment options. There is an increasing interest in the usefulness of wrist magnetic resonance imaging could play in predicting who will benefit for various treatments. METHOD AND DESIGN: Two hundred patients with mild to moderate symptoms will be recruited over 3 1/2 years from neurological surgery, primary care, electrodiagnostic clinics. We will exclude patients with clinical or electrodiagnostic evidence of denervation or thenar muscle atrophy. We will randomly assign patients to either a well-defined conservative care protocol or surgery. The conservative care treatment will include visits with a hand therapist, exercises, a self-care booklet, work modification/ activity restriction, B6 therapy, ultrasound and possible steroid injections. The surgical care would be left up to the surgeon (endoscopic vs. open) with usual and customary follow-up. All patients will receive a wrist MRI at baseline. Patients will be contacted at 3, 6, 9 and 12 months after randomization to complete the Carpal Tunnel Syndrome Assessment Questionnaire (CTSAQ). In addition, we will compare disability (activity and work days lost) and general well being as measured by the SF-36 version II. We will control for demographics and use psychological measures (SCL-90 somatization and depression scales) as well as EDS and MRI predictors of outcomes. DISCUSSION: We have designed a randomized controlled trial which will assess the effectiveness of surgery for patients with mild to moderate carpal tunnel syndrome. An important secondary goal is to study the ability of MRI to predict patient outcomes