A quantitative characterization of some finite

The behavioral distribution the fraction of observations corresponding to each behavior is then determined. This is an incomplete characterization of behavior, and in some instances, mild injury is not reflected by statistically significant changes in the distribution even though a human observer can confidently and correctly assert that the animal is not behaving normally.

This contribution describes procedures derived from symbolic dynamics for quantifying the sequential structure of animal behavior.

a quantitative characterization of some finite

Normalization procedures for complexity estimates are presented, and the limitations of complexity measures are discussed. Animal behavior changes as the result of injury. Similarly, animal behavior changes as the result of the administration of drugs, particularly drugs of abuse. These are commonplace observations, and as observers of animal behavior we are often able to discriminate between injured and uninjured animals by direct observation with a high degree of confidence and accuracy.

Quantifying the degree of behavioral distortion, especially in response to mild or intermediate degrees of injury or drug intoxication, is surprisingly difficult.

The simplest classical approach to quantifying animal behavior begins by identifying a list of defined discrete behaviors. For example, in the case of rats in a free field observation environment, that list could include sleeping, eating, drinking, moving, rearing, and grooming.

The fraction of observations corresponding to each behavior is calculated. The distribution of fractions of observations in each behavior is denoted by. In the case of severe head injury, for example, the fraction of observations recorded as sleep will often increase. After the administration of amphetamines, the fraction of observations of moving, rearing, and grooming may increase. While this is a beginning of the characterization of animal behavior, it is often found to be inadequate.

In response to mild injury or low drug dosages, the distribution of behaviors in experimental animals may be statistically indistinguishable from the distributions observed with untreated control animals.

Nonetheless, in some of these cases a human observer can confidently and correctly assert that the treated animal is not behaving normally. A possible response to this problem is to examine the sequential structure of animal behavior by calculating its complexity. Consider again the hypothetical example constructed with five behaviors.

Suppose that two behavioral sequences are observed. An observer would state that the second sequence is more complex than the first even though the behavior distributions of both sequences are identical. Complexity measures are used to quantify these differences. As the term is used here, complexity is a measure of structure in a symbol sequence. There are several mathematical definitions of complexity. Different definitions emphasize different aspects of sequence sensitive structure.

The choice of definition is informed by its functional utility in discriminating between experimental groups. It should be noted that different measures of complexity can be highly correlated.

OD-Characterization of Some Simple Unitary Groups

A review of complexity measures is given in Rapp and Schmah A taxonomic classification of complexity measures appears in Rapp and Schmah Various systems, methods, and programs embodied in computer-readable mediums are provided for the global quantitative characterization of patterns. In one representative embodiment, a method is provided in which fractal analysis is performed on a pattern to generate a global quantitative characterization of the pattern in a computer system. The U. The identification and matching of various patterns can be difficult and time intensive.

For example, in the field of fingerprinting, the accuracy of the identification procedure relies on algorithms that perform direct feature comparisons.

Such algorithms are sensitive to position and variability in resolution between field data and file data. The time and data-processing infrastructure required for such identification is extensive as the operation is quite cumbersome. Also, the identification of patterns in contexts other than fingerprinting can be expensive and time consuming as well.

Many aspects of the invention can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present invention.

Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views. Given the difficulty in performing identification of patterns such as fingerprints as described above, disclosed are various embodiments of the present invention in which a quantitative characterization of patterns are generated.

The quantitative characterizations may then be used for such purposes as pattern matching such as is the case in fingerprint identification or pattern matching in other contexts. Although the example of fingerprinting is discussed herein, the principles of the present invention are far more general than fingerprinting and may be applied in many different contexts.

In this sense, any discussion herein relating to fingerprinting is mentioned herein solely to provide an example context to aid in the understanding of the various principles described. The principles described herein apply in other contexts, such as in connection with DNA analysis, face analysis, analysis of data transactions, and in the context of other fields. In the discussion that follows, we first describe the generation of a quantitative characterization of a pattern such as fingerprints.

Specifically, the quantitative characterization is a global quantitative characterization generated by generating one or more fractal images based upon the pattern as will be described. Thereafter, we describe various implementations of these principles in computer systems or other implementations. With reference to FIG. In particular, data is obtained from the pattern from which a fractal may be constructed.

In one embodiment, the fractal comprises, for example, a four sided shape such as a square, although fractals can be generated in the form of any other shape. Assuming that a fractal is to be generated in the form of a square, then the random walk generates a sequence of data sets, where each data set comprises four values. Each of the four values in the data sets is associated with a respective corner of a square in order to be able to play a chaos game as will be described.

The random walk can be said to generate an array of data sets that are four values deep or having four values per each consecutive integer of the array. The random walk is performed by selecting a random sequence of points within the image itself.

To accommodate the random walk through the image, a border may be imposed around the periphery of the image within which all random points are contained. Alternatively, a region within the pattern may be specified by imposing an appropriate border within which the random walk is performed.

As illustrated in FIG. Next, a random sequence of points is specified that fall within the pattern or region specified within the pattern For each of the pointsa pair of data points are specified.The signals recorded by diffusion-weighted magnetic resonance imaging DWI are dependent on the micro-structural properties of biological tissues, so it is possible to obtain quantitative structural information non-invasively from such measurements.

Oscillating gradient spin echo OGSE methods have the ability to probe the behavior of water diffusion over different time scales and the potential to detect variations in intracellular structure. To assist in the interpretation of OGSE data, analytical expressions have been derived for diffusion-weighted signals with OGSE methods for restricted diffusion in some typical structures, including parallel planes, cylinders and spheres, using the theory of temporal diffusion spectroscopy.

These analytical predictions have been confirmed with computer simulations. These expressions suggest how OGSE signals from biological tissues should be analyzed to characterize tissue microstructure, including how to estimate cell nuclear sizes.

This approach provides a model to interpret diffusion data obtained from OGSE measurements that can be used for applications such as monitoring tumor response to treatment in vivo.

Measurements of tissue structure over different distance scales may be important in both clinical and research applications. For example, the size of axons reflects structure in white matter and the conduction velocity of myelinated neurons varies roughly linearly with axon diameter [ 1 — 3 ].

a quantitative characterization of some finite

Similarly, it has been reported that rates of cell division may be closely related to cell size. For some cells, there is a mechanism by which cell division is not initiated until a cell has reached a certain size [ 4 ] while measurements of tumor cell nuclear size have been suggested as a biomarker for tumor detection and grading [ 5 ; 6 ]. Usually, histological information may be obtained only from invasive biopsies. However, diffusion-weighted DW magnetic resonance imaging is dependent on specific microstructural properties of biological tissues, so it may be possible to obtain quantitative structural information noninvasively from DWI measurements.

Diffusion in tissues is slower than in free solutions because tissue compartments hinder or restrict fluid motions, and the reduction in diffusion rates reflects the scale and nature of the tissue environment. Stejskal suggested the use of a conditional probability approach to describe restricted diffusion analytically [ 7 ] and this approach enables an averaged diffusion propagator to be used to reveal dynamic displacements of water molecules in a certain diffusion time in q-space [ 8 ].

Cory used this method to demonstrate that the size of a diffusion compartment can be obtained from appropriate diffusion NMR experiments [ 9 ]. Others have derived the analytical conditional probability functions and signal attenuation dependence of diffusion within some simple geometries, such as diffusion between two infinitely large impermeable planes, or inside an infinitely-long impermeable cylinder or an impermeable sphere [ 10 — 12 ].

Neuman modeled DW signals with a constant field gradient [ 13 ] and based on this analysis, Assaf et al. Similarly, Zhao et al. However, in practice, the finite duration of gradients may invalidate the short gradient approximation.

More importantly, conventional PGSE methods are insensitive to relatively short distance scales, such as those that characterize intracellular structures, because they incorporate relatively long diffusion times necessitated by hardware limitations.Solution of the inversion problem in quantitative eddy current NDE requires an adequate mathematical model to describe the complicated interactions of currents, fields and flaws in materials.

Existing analytical techniques are not capable of accommodating materials with nonlinear magnetic characteristics or awkward flaw shapes. This paper describes a finite element computation of the complex impedance of an eddy current sensor in axisymmetric testing configurations, some with defects and gives the corresponding magnetic flux distributions. The authors suggest that, because finite element analysis techniques are not limited by material nonlinearities and complex defect geometries, they can be applied to the development of computer based defect characterization schemes for realistic eddy current NDE applications.

Advanced Search. This repository is part of the Iowa Research Commons. Privacy Copyright. Description Solution of the inversion problem in quantitative eddy current NDE requires an adequate mathematical model to describe the complicated interactions of currents, fields and flaws in materials.

Search Enter search terms:. Digital Commons.We prove that each projective special unitary group G can be characterized using only the set of element orders of G and the order of G. This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Google Scholar.

Mazurov, V. Shi Wujie, The pure quantitative characterization of finite simple groups IProgress in Natural Science,4 3 : — An Jianbei, Shi Wujie, The characterization of finite simple groups with no elements of order six by their element orders, Comm. Shi Wujie, A characterization of U 3 2 n by their element orders, J.

Shi Wujie, On simple K 3 -groups, J. Williams, J. Algebra,69 2 : — Higman, G. London Math. Passman, D. Benjamin, Yunnan Educational College in Chinese, 1 1 : 2— Conway, J. Feit, W. Zsigmondy, K.

Curtis, C. Iiyora, N. Algebra,— Sinica in Chinese, 32 6 : — Weir, A. Download references. Reprints and Permissions. Cao, H. Pure quantitative characterization of finite projective special unitary groups.

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a quantitative characterization of some finite

Download citation. Received : 11 November Search SpringerLink Search. Abstract We prove that each projective special unitary group G can be characterized using only the set of element orders of G and the order of G.

References 1.Various systems, methods, and programs embodied in computer-readable mediums are provided for detecting a match in patterns. In one embodiment, a method is provided that comprises performing a fractal analysis on a first pattern in a computer system to generate a first global quantitative characterization of the first pattern.

a quantitative characterization of some finite

The method further comprises comparing the first global quantitative characterization with a second global quantitative characterization associated with a second pattern in the computer system to determine whether the first pattern matches the second pattern. The second global quantitative characterization is generated from the second pattern. The U. This application is related to U. The identification and matching of various patterns can be difficult and time intensive.

For example, in the field of fingerprinting, the accuracy of the identification procedure relies on algorithms that perform direct feature comparisons. Such algorithms are sensitive to position and variability in resolution between field data and file data.

The time and data-processing infrastructure required for such identification is extensive as the operation is quite cumbersome. Also, the identification of patterns in contexts other than fingerprinting can be expensive and time consuming as well. Many aspects of the invention can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present invention.

Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views. Given the difficulty in performing identification of patterns such as fingerprints as described above, disclosed are various embodiments of the present invention in which a quantitative characterization of patterns are generated. The quantitative characterizations may then be used for such purposes as pattern matching such as is the case in fingerprint identification or pattern matching in other contexts.

Although the example of fingerprinting is discussed herein, the principles of the present invention are far more general than fingerprinting and may be applied in many different contexts.

In this sense, any discussion herein relating to fingerprinting is mentioned herein solely to provide an example context to aid in the understanding of the various principles described. The principles described herein apply in other contexts, such as in connection with DNA analysis, face analysis, analysis of data transactions, and in the context of other fields. In the discussion that follows, we first describe the generation of a quantitative characterization of a pattern such as fingerprints.

Specifically, the quantitative characterization is a global quantitative characterization generated by generating one or more fractal images based upon the pattern as will be described. Thereafter, we describe various implementations of these principles in computer systems or other implementations.

With reference to FIG.

No document with DOI "10.1.1.983.4703"

In particular, data is obtained from the pattern from which a fractal may be constructed. In one embodiment, the fractal comprises, for example, a four sided shape such as a square, although fractals can be generated in the form of any other shape. Assuming that a fractal is to be generated in the form of a square, then the random walk generates a sequence of data sets, where each data set comprises four values. Each of the four values in the data sets is associated with a respective corner of a square in order to be able to play a chaos game as will be described.Berkeley, CA When models of quantitative genetic variation are built from population genetic first principles, several assumptions are often made.

Quantitative characterization of animal behavior following blast exposure

One of the most important assumptions is that traits are controlled by many genes of small effect. This leads to a prediction of a Gaussian trait distribution in the population, via the Central Limit Theorem. Since these biological assumptions are often unknown or untrue, we characterized how finite numbers of loci or large mutational effects can impact the sampling distribution of a quantitative trait.

To do so, we developed a neutral coalescent-based framework, allowing us to gain a detailed understanding of how number of loci and the underlying mutational model impacts the distribution of a quantitative trait. Through both analytical theory and simulation we found the normality assumption was highly sensitive to the details of the mutational process, with the greatest discrepancies arising when the number of loci was small or the mutational kernel was heavy-tailed.

In particular, skewed mutational effects will produced skewed trait distributions and fat-tailed mutational kernels result in multimodal sampling distributions, even for traits controlled by a large number of loci. Since selection models and robust neutral models may produce qualitatively similar sampling distributions, we advise extra caution should be taken when interpreting model-based results for poorly understood systems of quantitative traits.

Questions about the distribution of traits that vary continuously in populations were critical in motivating early evolutionary biologists. The earliest studies of quantitative trait variation relied on phenomenological models, because the underlying nature of heritable variation was not yet well understood Galton,; Pearson, These views were reconciled when Fisher showed that the observations of correlation and variation between phenotypes in natural populations could be explained by a model in which many genes made small contributions to the phenotype of an individual.

The insights of Fisher made it possible to build models of quantitative trait evolution from population genetic first principles. Early work focused primarily on the interplay between mutation and natural selection in the maintenance of quantitative genetic variation in natural populations, while typically ignoring the effects of genetic drift Fisher, ; Haldane, ; Latter, ; Kimura, However, genetic drift plays an important role in shaping variation in natural populations.

While earlier work assumed that a finite number of alleles control quantitative genetic variation e. LatterLande used the continuum-of-alleles model proposed by Kimura to model the impact of genetic drift on differentiation within and between populations.

Several later papers explored more detailed models to understand how genetic variance changes through time due to the joint effects of mutation and drift e.

Chakraborty and Nei Lynch and Hill undertook an extremely thorough analysis of the evolution of neutral quantitative traits. They analyzed the moments e. Much of this earlier work has made several simplifying assumptions about the distribution of mutational effects and the genetic architecture of the traits in question.

For instance, Lynch and Hilldespite analyzing quite general models of dominance and epistasis, ignored the impact of heavy tailed or skewed mutational effects.

Graphene Characterization Methods and Issues - Dr. Andrew Pollard National Physical Laboratory NPL.

While, in many cases, such properties of the mutational effect distribution are not expected to have an impact if a large number of genes determine the phenotype in question, it is unknown what impact they may have when only a small number of genes determine the genetic architecture of the trait.

Such deviations that stem from the violations of common modeling assumptions have the potential to influence our understanding of variation in natural populations. For instance, leptokurtic trait distributions may be a signal of some kind of diversifying selection Kopp and Hermisson, but are also possible under neutrality when the number of loci governing a trait is small.

Similarly, multimodal trait distributions may reflect some kind of underlying selective process Doebeli et al. We have two main goals in this work. Primarily, we want to assess the impact of violations of common assumptions on properties of the sampling distribution of a quantitative trait e. Secondly, we believe that the formalism that we present here can be useful in a variety of situations in quantitative trait evolution, particularly in the development of robust null models for detecting selection at microevolutionary time scales.

To this end, we introduce a novel framework for computing sampling distributions of quantitative traits. Our framework builds upon the coalescent approach of Whitlockbut allows us to recover the full sampling distribution, instead of merely its moments.

First, we outline the biological model and explain how we can compute quantities of interest using a formalism based on characteristic functions. We then use this approach to compute the sample central moments. While much previous work focuses on only the first two central moments mean and variancewe are able to compute arbitrarily high central moments, which are related to properties such as skewness and kurtosis. By doing so, we are able to determine the regime in which the details of the mutational effect distribution are visible in a sample from a natural population.