Geometric Morphometrics
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Geometric Morphometrics
Morphometrics (from Greek μορϕή ''morphe'', "shape, form", and -μετρία ''metria'', "measurement") or morphometry refers to the quantitative analysis of ''form'', a concept that encompasses size and shape. Morphometric analyses are commonly performed on organisms, and are useful in analyzing their fossil record, the impact of mutations on shape, developmental changes in form, covariances between ecological factors and shape, as well for estimating quantitative-genetic parameters of shape. Morphometrics can be used to quantify a trait of evolutionary significance, and by detecting changes in the shape, deduce something of their ontogeny, function or evolutionary relationships. A major objective of morphometrics is to statistically test hypotheses about the factors that affect shape. "Morphometrics", in the broader sense, is also used to precisely locate certain areas of organs such as the brain, and in describing the shapes of other things. Forms Three general app ...
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Confuciusornithidae Sizes
Confuciusornithidae is an extinct family of pygostylian avialans known from the Early Cretaceous, found in northern China. They are commonly placed as a sister group to Ornithothoraces, a group that contains all extant birds along with their closest extinct relatives. Confuciusornithidae contains four genera, possessing both shafted and non-shafted (downy) feathers. They are also noted for their distinctive pair of ribbon-like tail feathers of disputed function. The wing anatomy of confuciusornithids suggests an unusual flight behavior, due to anatomy that implies conflicting abilities. They possessed feathers similar to those of fast-flapping birds, which rely on quick flapping of their wings to stay aloft. At the same time, their wing anatomy also suggests a lack of flapping ability. Confuciusornithids are also noted for their beak and lack of teeth, similar to modern birds. Both predators and prey, confuciusornithid fossils have been observed with fish remains in their digestive ...
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Surface-based Morphometry
Brain morphometry is a subfield of both morphometry and the brain sciences, concerned with the measurement of brain structures and changes thereof during development, aging, learning, disease and evolution. Since autopsy-like dissection is generally impossible on living brains, brain morphometry starts with noninvasive neuroimaging data, typically obtained from magnetic resonance imaging (MRI). These data are born digital, which allows researchers to analyze the brain images further by using advanced mathematical and statistical methods such as shape quantification or multivariate analysis. This allows researchers to quantify anatomical features of the brain in terms of shape, mass, volume (e.g. of the hippocampus, or of the primary versus secondary visual cortex), and to derive more specific information, such as the encephalization quotient, grey matter density and white matter connectivity, gyrification, cortical thickness, or the amount of cerebrospinal fluid. These variables can ...
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Voxel-based Morphometry
Voxel-based morphometry is a computational approach to neuroanatomy that measures differences in local concentrations of brain tissue, through a voxel-wise comparison of multiple brain images. In traditional morphometry, volume of the whole brain or its subparts is measured by drawing regions of interest (ROIs) on images from brain scanning and calculating the volume enclosed. However, this is time consuming and can only provide measures of rather large areas. Smaller differences in volume may be overlooked. The value of VBM is that it allows for comprehensive measurement of differences, not just in specific structures, but throughout the entire brain. VBM registers every brain to a template, which gets rid of most of the large differences in brain anatomy among people. Then the brain images are smoothed so that each voxel represents the average of itself and its neighbors. Finally, the image volume is compared across brains at every voxel. However, VBM can be sensitive to vari ...
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Neuroimaging
Neuroimaging is the use of quantitative (computational) techniques to study the structure and function of the central nervous system, developed as an objective way of scientifically studying the healthy human brain in a non-invasive manner. Increasingly it is also being used for quantitative studies of brain disease and psychiatric illness. Neuroimaging is a highly multidisciplinary research field and is not a medical specialty. Neuroimaging differs from neuroradiology which is a medical specialty and uses brain imaging in a clinical setting. Neuroradiology is practiced by radiologists who are medical practitioners. Neuroradiology primarily focuses on identifying brain lesions, such as vascular disease, strokes, tumors and inflammatory disease. In contrast to neuroimaging, neuroradiology is qualitative (based on subjective impressions and extensive clinical training) but sometimes uses basic quantitative methods. Functional brain imaging techniques, such as functional magnet ...
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D'Arcy Wentworth Thompson
Sir D'Arcy Wentworth Thompson CB FRS FRSE (2 May 1860 – 21 June 1948) was a Scottish biologist, mathematician and classics scholar. He was a pioneer of mathematical and theoretical biology, travelled on expeditions to the Bering Strait and held the position of Professor of Natural History at University College, Dundee for 32 years, then at St Andrews for 31 years. He was elected a Fellow of the Royal Society, was knighted, and received the Darwin Medal and the Daniel Giraud Elliot Medal. Thompson is remembered as the author of the 1917 book ''On Growth and Form'', which led the way for the scientific explanation of morphogenesis, the process by which patterns and body structures are formed in plants and animals. Thompson's description of the mathematical beauty of nature, and the mathematical basis of the forms of animals and plants, stimulated thinkers as diverse as Julian Huxley, C. H. Waddington, Alan Turing, René Thom, Claude Lévi-Strauss, Eduardo Paolozzi, Le Co ...
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Thin Plate Splines
Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing. They were introduced to geometric design by Duchon. They are an important special case of a polyharmonic spline. Robust Point Matching (RPM) is a common extension and shortly known as the TPS-RPM algorithm. Physical analogy The name ''thin plate spline'' refers to a physical analogy involving the bending of a thin sheet of metal. Just as the metal has rigidity, the TPS fit resists bending also, implying a penalty involving the smoothness of the fitted surface. In the physical setting, the deflection is in the z direction, orthogonal to the plane. In order to apply this idea to the problem of coordinate transformation, one interprets the lifting of the plate as a displacement of the x or y coordinates within the plane. In 2D cases, given a set of K corresponding points, the TPS warp is described by 2(K+3) parameters which include 6 global affine motion parameters and 2K coefficients for corre ...
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Phylogenetic Relationship
In biology, phylogenetics (; from Greek φυλή/ φῦλον [] "tribe, clan, race", and wikt:γενετικός, γενετικός [] "origin, source, birth") is the study of the evolutionary history and relationships among or within groups of organisms. These relationships are determined by Computational phylogenetics, phylogenetic inference methods that focus on observed heritable traits, such as DNA sequences, protein amino acid sequences, or morphology. The result of such an analysis is a phylogenetic tree—a diagram containing a hypothesis of relationships that reflects the evolutionary history of a group of organisms. The tips of a phylogenetic tree can be living taxa or fossils, and represent the "end" or the present time in an evolutionary lineage. A phylogenetic diagram can be rooted or unrooted. A rooted tree diagram indicates the hypothetical common ancestor of the tree. An unrooted tree diagram (a network) makes no assumption about the ancestral line, and does n ...
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Eigenvector
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by \lambda, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated. Formal definition If is a linear transformation from a vector space over a field into itself and is a nonzero vector in , then is an eigenvector of if is a scalar multiple of . This can be written as T(\mathbf) = \lambda \mathbf, where is a scalar in , known as the eigenvalue, characteristic value, or characteristic root ass ...
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Principal Component Analysis
Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and enabling the visualization of multidimensional data. Formally, PCA is a statistical technique for reducing the dimensionality of a dataset. This is accomplished by linearly transforming the data into a new coordinate system where (most of) the variation in the data can be described with fewer dimensions than the initial data. Many studies use the first two principal components in order to plot the data in two dimensions and to visually identify clusters of closely related data points. Principal component analysis has applications in many fields such as population genetics, microbiome studies, and atmospheric science. The principal components of a collection of points in a real coordinate space are a sequence of p unit vectors, where th ...
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Paleobiology (journal)
Paleobiology is a scientific journal promoting the integration of biology and conventional paleontology Paleontology (), also spelled palaeontology or palæontology, is the scientific study of life that existed prior to, and sometimes including, the start of the Holocene epoch (roughly 11,700 years before present). It includes the study of fossi ..., with emphasis placed on biological or paleobiological processes and patterns. It attracts papers of interest to more than one discipline, and occasionally publishes research on recent organisms when this is of interest to paleontologists. Paleontology journals Academic journals published by learned and professional societies Publications established in 1975 Quarterly journals English-language journals Paleobiology Cambridge University Press academic journals {{paleontology-journal-stub ...
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