SciCombinator

Discover the most talked about and latest scientific content & concepts.

Concept: Geometry

173

BACKGROUND: The whole-genome sequences of many non-model organisms have recently been determined. Using these genome sequences, next-generation sequencing based experiments such as RNA-seq and ChIP-seq have been performed and comparisons of the experiments between related species have provided new knowledge about evolution and biological processes. Although these comparisons require transformation of the genome coordinates of the reads between the species, current software tools are not suitable to convert the massive numbers of reads to the corresponding coordinates of other species' genomes. RESULTS: Here, we introduce a set of programs, called REad COordinate Transformer (RECOT), created to transform the coordinates of short reads obtained from the genome of a query species being studied to that of a comparison target species after aligning the query and target gene/genome sequences. RECOT generates output in SAM format that can be viewed using recent genome browsers capable of displaying next-generation sequencing data. CONCLUSIONS: We demonstrate the usefulness of RECOT in comparing ChIP-seq results between two closely-related fruit flies. The results indicate position changes of a transcription factor binding site caused sequence polymorphisms at the binding site.

Concepts: RNA, Geometry, Genetics, Organism, Molecular biology, Gene expression, Gene, DNA

142

This paper presents a vehicle autonomous localization method in local area of coal mine tunnel based on vision sensors and ultrasonic sensors. Barcode tags are deployed in pairs on both sides of the tunnel walls at certain intervals as artificial landmarks. The barcode coding is designed based on UPC-A code. The global coordinates of the upper left inner corner point of the feature frame of each barcode tag deployed in the tunnel are uniquely represented by the barcode. Two on-board vision sensors are used to recognize each pair of barcode tags on both sides of the tunnel walls. The distance between the upper left inner corner point of the feature frame of each barcode tag and the vehicle center point can be determined by using a visual distance projection model. The on-board ultrasonic sensors are used to measure the distance from the vehicle center point to the left side of the tunnel walls. Once the spatial geometric relationship between the barcode tags and the vehicle center point is established, the 3D coordinates of the vehicle center point in the tunnel’s global coordinate system can be calculated. Experiments on a straight corridor and an underground tunnel have shown that the proposed vehicle autonomous localization method is not only able to quickly recognize the barcode tags affixed to the tunnel walls, but also has relatively small average localization errors in the vehicle center point’s plane and vertical coordinates to meet autonomous unmanned vehicle positioning requirements in local area of coal mine tunnel.

Concepts: Frame of reference, Coordinate systems, Barcode, Polar coordinate system, Geometry, Geographic coordinate system, Analytic geometry, Coordinate system

88

Primates recognize complex objects such as faces with remarkable speed and reliability. Here, we reveal the brain’s code for facial identity. Experiments in macaques demonstrate an extraordinarily simple transformation between faces and responses of cells in face patches. By formatting faces as points in a high-dimensional linear space, we discovered that each face cell’s firing rate is proportional to the projection of an incoming face stimulus onto a single axis in this space, allowing a face cell ensemble to encode the location of any face in the space. Using this code, we could precisely decode faces from neural population responses and predict neural firing rates to faces. Furthermore, this code disavows the long-standing assumption that face cells encode specific facial identities, confirmed by engineering faces with drastically different appearance that elicited identical responses in single face cells. Our work suggests that other objects could be encoded by analogous metric coordinate systems. PAPERCLIP.

Concepts: Analytic geometry, Dimension, Brain, Face, Primate, Organism, Geometry, DNA

72

Imagine that you are blindfolded inside an unknown room. You snap your fingers and listen to the room’s response. Can you hear the shape of the room? Some people can do it naturally, but can we design computer algorithms that hear rooms? We show how to compute the shape of a convex polyhedral room from its response to a known sound, recorded by a few microphones. Geometric relationships between the arrival times of echoes enable us to “blindfoldedly” estimate the room geometry. This is achieved by exploiting the properties of Euclidean distance matrices. Furthermore, we show that under mild conditions, first-order echoes provide a unique description of convex polyhedral rooms. Our algorithm starts from the recorded impulse responses and proceeds by learning the correct assignment of echoes to walls. In contrast to earlier methods, the proposed algorithm reconstructs the full 3D geometry of the room from a single sound emission, and with an arbitrary geometry of the microphone array. As long as the microphones can hear the echoes, we can position them as we want. Besides answering a basic question about the inverse problem of room acoustics, our results find applications in areas such as architectural acoustics, indoor localization, virtual reality, and audio forensics.

Concepts: Room acoustics, Architectural acoustics, Geometry, Computational geometry, Algorithm, Sound, Acoustics, Computer

61

The substantial gender gap in the science, technology, engineering, and mathematics (STEM) workforce can be traced back to the underrepresentation of women at various milestones in the career pathway. Calculus is a necessary step in this pathway and has been shown to often dissuade people from pursuing STEM fields. We examine the characteristics of students who begin college interested in STEM and either persist or switch out of the calculus sequence after taking Calculus I, and hence either continue to pursue a STEM major or are dissuaded from STEM disciplines. The data come from a unique, national survey focused on mainstream college calculus. Our analyses show that, while controlling for academic preparedness, career intentions, and instruction, the odds of a woman being dissuaded from continuing in calculus is 1.5 times greater than that for a man. Furthermore, women report they do not understand the course material well enough to continue significantly more often than men. When comparing women and men with above-average mathematical abilities and preparedness, we find women start and end the term with significantly lower mathematical confidence than men. This suggests a lack of mathematical confidence, rather than a lack of mathematically ability, may be responsible for the high departure rate of women. While it would be ideal to increase interest and participation of women in STEM at all stages of their careers, our findings indicate that if women persisted in STEM at the same rate as men starting in Calculus I, the number of women entering the STEM workforce would increase by 75%.

Concepts: Physics, Geometry, Gender role, Science, Gender, Woman, Calculus, Mathematics

43

This paper applies topological methods to study complex high dimensional data sets by extracting shapes (patterns) and obtaining insights about them. Our method combines the best features of existing standard methodologies such as principal component and cluster analyses to provide a geometric representation of complex data sets. Through this hybrid method, we often find subgroups in data sets that traditional methodologies fail to find. Our method also permits the analysis of individual data sets as well as the analysis of relationships between related data sets. We illustrate the use of our method by applying it to three very different kinds of data, namely gene expression from breast tumors, voting data from the United States House of Representatives and player performance data from the NBA, in each case finding stratifications of the data which are more refined than those produced by standard methods.

Concepts: Leonhard Euler, Mathematics, Scientific method, Geometry, Cancer, Manifold, United States, United States House of Representatives

39

During language processing, humans form complex embedded representations from sequential inputs. Here, we ask whether a “geometrical language” with recursive embedding also underlies the human ability to encode sequences of spatial locations. We introduce a novel paradigm in which subjects are exposed to a sequence of spatial locations on an octagon, and are asked to predict future locations. The sequences vary in complexity according to a well-defined language comprising elementary primitives and recursive rules. A detailed analysis of error patterns indicates that primitives of symmetry and rotation are spontaneously detected and used by adults, preschoolers, and adult members of an indigene group in the Amazon, the Munduruku, who have a restricted numerical and geometrical lexicon and limited access to schooling. Furthermore, subjects readily combine these geometrical primitives into hierarchically organized expressions. By evaluating a large set of such combinations, we obtained a first view of the language needed to account for the representation of visuospatial sequences in humans, and conclude that they encode visuospatial sequences by minimizing the complexity of the structured expressions that capture them.

Concepts: Human, Set, Geometry, Series, Sequence, Topology, Group, Mathematics

38

Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using only the intrinsic pattern of neural correlations. Remarkably, we found similar results during nonspatial behaviors such as wheel running and rapid eye movement (REM) sleep. This suggests that the geometric structure of correlations is shaped by the underlying hippocampal circuits and is not merely a consequence of position coding. We propose that clique topology is a powerful new tool for matrix analysis in biological settings, where the relationship of observed quantities to more meaningful variables is often nonlinear and unknown.

Concepts: Geometry, Neuron, Manifold, Cerebral cortex, Brain, Rapid eye movement sleep, Pyramidal cell, Hippocampus

37

Interactions between individuals and the structure of their environment play a crucial role in shaping self-organized collective behaviors. Recent studies have shown that ants crossing asymmetrical bifurcations in a network of galleries tend to follow the branch that deviates the least from their incoming direction. At the collective level, the combination of this tendency and the pheromone-based recruitment results in a greater likelihood of selecting the shortest path between the colony’s nest and a food source in a network containing asymmetrical bifurcations. It was not clear however what the origin of this behavioral bias is. Here we propose that it results from a simple interaction between the behavior of the ants and the geometry of the network, and that it does not require the ability to measure the angle of the bifurcation. We tested this hypothesis using groups of ant-like robots whose perceptual and cognitive abilities can be fully specified. We programmed them only to lay down and follow light trails, avoid obstacles and move according to a correlated random walk, but not to use more sophisticated orientation methods. We recorded the behavior of the robots in networks of galleries presenting either only symmetrical bifurcations or a combination of symmetrical and asymmetrical bifurcations. Individual robots displayed the same pattern of branch choice as individual ants when crossing a bifurcation, suggesting that ants do not actually measure the geometry of the bifurcations when travelling along a pheromone trail. Finally at the collective level, the group of robots was more likely to select one of the possible shorter paths between two designated areas when moving in an asymmetrical network, as observed in ants. This study reveals the importance of the shape of trail networks for foraging in ants and emphasizes the underestimated role of the geometrical properties of transportation networks in general.

Concepts: Human behavior, Robot, Behaviorism, Geometry, Symmetry, Behavior, Cognition, Psychology

30

Self-assembly of block-copolymers provides a route to the fabrication of small (size, <50 nm) and dense (pitch, <100 nm) features with an accuracy that approaches even the demanding specifications for nanomanufacturing set by the semiconductor industry. A key requirement for practical applications, however, is a rapid, high-resolution method for patterning block-copolymers with different molecular weights and compositions across a wafer surface, with complex geometries and diverse feature sizes. Here we demonstrate that an ultrahigh-resolution jet printing technique that exploits electrohydrodynamic effects can pattern large areas with block-copolymers based on poly(styrene-block-methyl methacrylate) with various molecular weights and compositions. The printed geometries have diameters and linewidths in the sub-500 nm range, line edge roughness as small as ∼45 nm, and thickness uniformity and repeatability that can approach molecular length scales (∼2 nm). Upon thermal annealing on bare, or chemically or topographically structured substrates, such printed patterns yield nanodomains of block-copolymers with well-defined sizes, periodicities and morphologies, in overall layouts that span dimensions from the scale of nanometres (with sizes continuously tunable between 13 nm and 20 nm) to centimetres. As well as its engineering relevance, this methodology enables systematic studies of unusual behaviours of block-copolymers in geometrically confined films.

Concepts: Methodology, Annealing, Inkjet printer, Geometry, Semiconductor, Pattern, Printing