A simpler explanation of the reflective properties of conic sections, by following light rays along local isosceles paths

Ellipses, parabolas and hyperbolas all have beautiful reflective properties. However, an intuitive explanation for why they have those properties has been lacking. There exist many mathematical proofs, but they tend to involve several analytical steps or geometrical constructions, making them unintuitive and hard to understand. Here, a simpler explanation is presented which only requires following the paths of light rays, and examining local paths that move from one point on a conic to a nearby one. First, a light-ray is followed as it runs along one of the legs of an isosceles triangle, and then reflects off a mirror that is parallel to the triangle's base. It bounces back along the path of the triangle's other leg. Next, a path is examined, moving from an arbitrary point on a conic section curve to a nearby point on the same curve. This path consists of two equal-length straight line steps, with each step following one of the constraints that defines the curve. For example, on an ellipse, defined by the sum of the distances to the two foci remaining constant, the path starts at a point on the ellipse, moves a distance delta directly away from one focus, then makes a second equal-length step directly towards the second focus. These two steps form the legs of precisely the sort of isosceles triangle described above, with its base running along the path of the curve. A light ray following the legs of that triangle gets reflected directly from one focus to the other. As the triangle shrinks towards zero, the reflection point converges onto the actual curve. Exactly the same argument also explains the reflections of parabolas and hyperbolas. Surprisingly, this explanation does not seem to have appeared previously in the long history of writings about conics. It is hoped that it will help to make the reflective properties of conic sections easier to understand and to explain.Comment: Minor edits to previous version to improve clarity of text, and added mention of local isosceles paths to the titl

Chinese and English speakers’ neural representations of word meaning offer adifferent picture of cross-language semantics than corpus and behavioral measures

Speakers of Chinese and English share decodable neuralsemantic representations, which can be elicited by words ineach language. We explore various, common models ofsemantic representation and their correspondences to eachother and to these neural representations. Despite very strongcross-language similarity in the neural data, we find that twoversions of a corpus-based semantic model do not show thesame strong correlation between languages. Behavior-basedmodels better approximate cross-language similarity, butthese models also fail to explain the similarities observed inthe neural data. Although none of the examined modelsexplain cross-language neural similarity, we explore how theymight provide additional information over and above cross-language neural similarity. We find that native speakers’ratings of noun-noun similarity and one of the corpus modelsdo further correlate with neural data after accounting forcross-language similarities

Linking brain-wide multivoxel activation patterns to behaviour: Examples from language and math

A key goal of cognitive neuroscience is to find simple and direct connections between brain and behaviour. However, fMRI analysis typically involves choices between many possible options, with each choice potentially biasing any brain-behaviour correlations that emerge. Standard methods of fMRI analysis assess each voxel individually, but then face the problem of selection bias when combining those voxels into a region-of-interest, or ROI. Multivariate pattern-based fMRI analysis methods use classifiers to analyse multiple voxels together, but can also introduce selection bias via data-reduction steps as feature selection of voxels, pre-selecting activated regions, or principal components analysis. We show here that strong brain-behaviour links can be revealed without any voxel selection or data reduction, using just plain linear regression as a classifier applied to the whole brain at once, i.e. treating each entire brain volume as a single multi-voxel pattern. The brain-behaviour correlations emerged despite the fact that the classifier was not provided with any information at all about subjects\u27 behaviour, but instead was given only the neural data and its condition-labels. Surprisingly, more powerful classifiers such as a linear SVM and regularised logistic regression produce very similar results. We discuss some possible reasons why the very simple brain-wide linear regression model is able to find correlations with behaviour that are as strong as those obtained on the one hand from a specific ROI and on the other hand from more complex classifiers. In a manner which is unencumbered by arbitrary choices, our approach offers a method for investigating connections between brain and behaviour which is simple, rigorous and direct. © 2010 Elsevier Inc

HIV Seroprevalence among Tuberculosis Patients in India, 2006–2007

BACKGROUND: Little information exists regarding the burden of HIV among tuberculosis patients in India, and no population-based surveys have been previously reported. A community-based HIV prevalence survey was conducted among tuberculosis patients treated by the national tuberculosis control programme to evaluate the HIV prevalence among tuberculosis patients in India. METHODOLOGY/PRINCIPAL FINDINGS: Fifteen districts (total population: 40.2 million) across 8 states were stratified by HIV prevalence in antenatal clinic HIV surveillance sites and randomly selected. From December 2006 to May 2007, remnant serum was collected from patients' clinical specimens taken after 2 months of anti-tuberculosis treatment and subjected to anonymous, unlinked HIV testing. Specimens were obtained and successfully tested for 5,995 (73%) of 8,217 tuberculosis patients eligible for the survey. HIV prevalence ranged widely among the 15 surveyed districts, from 1% in Koch Bihar, West Bengal, to 13.8% in Guntur, Andhra Pradesh. HIV infection was 1.3 times more likely among male TB patients than among female patients. Relative to smear-positive tuberculosis, HIV infection was 1.4 times more likely among smear-negative patients and 1.3 times more likely among extrapulmonary patients. In 4 higher-HIV prevalence districts, which had been previously surveyed in 2005-2006, no significant change in HIV prevalence was detected. CONCLUSIONS: The burden of HIV among tuberculosis patients varies widely in India. Programme efforts to implement comprehensive TB-HIV services should be targeted to areas with the highest HIV burden. Surveillance through routine reporting or special surveys is necessary to detect areas requiring intensification of TB-HIV collaborative activities

Linking HIV-Infected TB Patients to Cotrimoxazole Prophylaxis and Antiretroviral Treatment in India

BACKGROUND:HIV-infected persons suffering from tuberculosis experience high mortality. No programmatic studies from India have documented the delivery of mortality-reducing interventions, such as cotrimoxazole prophylactic treatment (CPT) and antiretroviral treatment (ART). To guide TB-HIV policy in India we studied the effectiveness of delivering CPT and ART to HIV-infected persons treated for tuberculosis in three districts in Andhra Pradesh, India, and evaluated factors associated with death. METHODS AND FINDINGS:We retrospectively abstracted data for all HIV-infected tuberculosis patients diagnosed from March 2007 through August 2007 using standard treatment outcome definitions. 734 HIV-infected tuberculosis patients were identified; 493 (67%) were males and 569 (80%) were between the ages of 24-44 years. 710 (97%) initiated CPT, and 351 (50%) collected >60% of their monthly cotrimoxazole pouches provided throughout TB treatment. Access to ART was documented in 380 (51%) patients. Overall 130 (17%) patients died during TB treatment. Patients receiving ART were less likely to die (adjusted hazard ratio [HR] 0.4, 95% confidence interval [CI] 0.3-0.6), while males and those with pulmonary TB were more likely to die (HR 1.7, 95% CI 1.1-2.7, and HR 1.9, 95% CI 1.1-3.2 respectively). CONCLUSIONS:Among HIV-infected TB patients in India death was common despite the availability of free cotrimoxazole locally and ART from referral centres. Death was strongly associated with the absence of ART during TB treatment. To minimize death, programmes should promote high levels of ART uptake and closely monitor progress in implementation

Questionnaire study to gain an insight into the manufacturing and fitting process of artificial eyes in children: an ocularist perspective

Purpose To gain an insight into the manufacturing and fitting of artificial eyes in children and potential improvements to the process. Method An online qualitative survey was distributed to 39 ocularists/prosthetists in Europe and Canada. Participants were recruited through purposive sampling, specifically maximum variation sampling from the researcher’s contacts and an online search. Results The findings highlighted the current impression technique as being the most difficult yet most important part of the current process for both the ocularist and child patient. Negatively affecting obtaining a good impression, the child patients distress can be reduced by their parents by providing encouragement, reassurance, practicing the insertion and removal of the artificial eye and being matter of fact. Whilst improvements to the current process provided mixed views, the incorporation of current technology was perceived as not being able to meet the requirements to produce aesthetically pleasing artificial eyes. Conclusion The current artificial eye process can be seen as an interaction with its success being dependent on the child patient’s acceptance and adjustment which is dependent on the factors associated to the process. Investigation into the needs of the patient and whether technology can improve the process are the next steps in its advancement

A study of the dissociative recombination of CaO + with electrons: Implications for Ca chemistry in the upper atmosphere

The dissociative recombination of CaO+ ions with electrons has been studied in a flowing afterglow reactor. CaO+ was generated by the pulsed laser ablation of a Ca target, followed by entrainment in an Ar+ ion/electron plasma. A kinetic model describing the gas-phase chemistry and diffusion to the reactor walls was fitted to the experimental data, yielding a rate coefficient of (3.0 ± 1.0) × 10¯⁷ cm³ molecule¯¹ s¯¹ at 295 K. This result has two atmospheric implications. First, the surprising observation that the Ca+/Fe+ ratio is ~8 times larger than Ca/Fe between 90 and 100 km in the atmosphere can now be explained quantitatively by the known ion-molecule chemistry of these two metals. Second, the rate of neutralization of Ca+ ions in a descending sporadic E layer is fast enough to explain the often explosive growth of sporadic neutral Ca layers

What should a quantitative model of masking look like and why would we want it?

Quantitative models of backward masking appeared almost as soon as computing technology was available to simulate them; and continued interest in masking has lead to the development of new models. Despite this long history, the impact of the models on the field has been limited because they have fundamental shortcomings. This paper discusses these shortcomings and outlines what future quantitative models should look like. It also discusses several issues about modeling and how a model could be used by researchers to better explore masking and other aspects of cognition

Music Alters Visual Perception

Background: Visual perception is not a passive process: in order to efficiently process visual input, the brain actively uses previous knowledge (e.g., memory) and expectations about what the world should look like. However, perception is not only influenced by previous knowledge. Especially the perception of emotional stimuli is influenced by the emotional state of the observer. In other words, how we perceive the world does not only depend on what we know of the world, but also by how we feel. In this study, we further investigated the relation between mood and perception. Methods and Findings: We let observers do a difficult stimulus detection task, in which they had to detect schematic happy and sad faces embedded in noise. Mood was manipulated by means of music. We found that observers were more accurate in detecting faces congruent with their mood, corroborating earlier research. However, in trials in which no actual face was presented, observers made a significant number of false alarms. The content of these false alarms, or illusory percepts, was strongly influenced by the observers ’ mood. Conclusions: As illusory percepts are believed to reflect the content of internal representations that are employed by the brain during top-down processing of visual input, we conclude that top-down modulation of visual processing is not purely predictive in nature: mood, in this case manipulated by music, may also directly alter the way we perceive the world

The relationship between socioeconomic status and white matter microstructure in pre-reading children: A longitudinal investigation

Reading is a learned skill crucial for educational attainment. Children from families of lower socioeconomic status (SES) tend to have poorer reading performance and this gap widens across years of schooling. Reading relies on the orchestration of multiple neural systems integrated via specific white-matter pathways, but there is limited understanding about whether these pathways relate differentially to reading performance depending on SES background. Kindergarten white-matter FA and second-grade reading outcomes were investigated in an SES-diverse sample of 125 children. The three left-hemisphere white-matter tracts most associated with reading, and their right-hemisphere homologs, were examined: arcuate fasciculus (AF), superior longitudinal fasciculus (SLF), and inferior longitudinal fasciculus (ILF). There was a significant and positive association between SES and fractional anisotropy (FA) in the bilateral ILF in kindergarten. SES moderated the association between kindergarten ILF and second grade reading performance, such that it was positive in lower-SES children, but not significant in higher-SES children. These results have implications for understanding the role of the environment in the development of the neural pathways that support reading