980 resultados para Invariants of Ulm-Kaplansky


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The probability distribution of the four-phase invariants in the case of single isomorphous replacement has been developed to estimate some individual phases. An example of its application to obtain the phases having special values of 0, pi or +/-pi /2 is given for a known protein structure in space group P2(1)2(1)2(1). The phasing procedure includes the determination of starting phases and an iterative calculation. The initial values of starting phases, which are required by the formula, can be obtained from the estimate of one-phase seminvariants and by specifying the origin and enantiomorph. In addition, the calculations lead to two sets of possible phases for each type of reflection by assigning arbitrarily an initial phase value. The present method provides a possibility for the multisolution technique to increase greatly the number of known phases while keeping the number of the trials quite small.

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Concise probabilistic formulae with definite crystallographic implications are obtained from the distribution for eight three-phase structure invariants (3PSIs) in the case of a native protein and a heavy-atom derivative [Hauptman (1982). Acta Cryst. A38, 289-294] and from the distribution for 27 3PSIs in the case of a native and two derivatives [Fortier, Weeks & Hauptman (1984). Acta Cryst. A40, 646-651]. The main results of the probabilistic formulae for the four-phase structure invariants are presented and compared with those for the 3PSIs. The analysis directly leads to a general formula of probabilistic estimation for the n-phase structure invariants in the case of a native and m derivatives. The factors affecting the estimated accuracy of the 3PSIs are examined using the diffraction data from a moderate-sized protein. A method to estimate a set of the large-modulus invariants, each corresponding to one of the eight 3PSIs, that has the largest \Delta\ values and relatively large structure-factor moduli between the native and derivative is suggested, which remarkably improves the accuracy, and thus a phasing procedure making full use of all eight 3PSIs is proposed.

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Structure from motion often refers to the computation of 3D structure from a matched sequence of images. However, a depth map of a surface is difficult to compute and may not be a good representation for storage and recognition. Given matched images, I will first show that the sign of the normal curvature in a given direction at a given point in the image can be computed from a simple difference of slopes of line-segments in one image. Using this result, local surface patches can be classified as convex, concave, parabolic (cylindrical), hyperbolic (saddle point) or planar. At the same time the translational component of the optical flow is obtained, from which the focus of expansion can be computed.

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A study is made of the recognition and transformation of figures by iterative arrays of finite state automata. A figure is a finite rectangular two-dimensional array of symbols. The iterative arrays considered are also finite, rectangular, and two-dimensional. The automata comprising any given array are called cells and are assumed to be isomorphic and to operate synchronously with the state of a cell at time t+1 being a function of the states of it and its four nearest neighbors at time t. At time t=0 each cell is placed in one of a fixed number of initial states. The pattern of initial states thus introduced represents the figure to be processed. The resulting sequence of array states represents a computation based on the input figure. If one waits for a specially designated cell to indicate acceptance or rejection of the figure, the array is said to be working on a recognition problem. If one waits for the array to come to a stable configuration representing an output figure, the array is said to be working on a transformation problem.

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Based only on the parallel-transport condition, we present a general method to compute Abelian or non-Abelian geometric phases acquired by the basis states of pure or mixed density operators, which also holds for nonadiabatic and noncyclic evolution. Two interesting features of the non-Abelian geometric phase obtained by our method stand out: i) it is a generalization of Wilczek and Zee`s non-Abelian holonomy, in that it describes nonadiabatic evolution where the basis states are parallelly transported between distinct degenerate subspaces, and ii) the non-Abelian character of our geometric phase relies on the transitional evolution of the basis states, even in the nondegenerate case. We apply our formalism to a two-level system evolving nonadiabatically under spontaneous decay to emphasize the non- Abelian nature of the geometric phase induced by the reservoir. We also show, through the generalized invariant theory, that our general approach encompasses previous results in the literature. Copyright (c) EPLA, 2008.

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Childhood obesity is one of the greatest public health challenges in Western countries. Abnormal eating behavior is thought to be a developmental trajectory to obesity. The Eating Pattern Inventory for Children (EPI-C) has not been used for children as young as eight years, and possible associations with body weight have not yet been established. Five hundred and twenty-one children of the Ulm Birth Cohort Study (UBCS; age eight) filled out the EPI-C and BMI was assessed. Adequacy of the scales was tested with confirmatory factor analysis and a MANOVA and cluster analysis established associations between eating patterns and BMI. The factor structure of the EPI-C was confirmed (GFI = .968) and abnormal eating behavior was associated with overweight (χ2(8) = 79.29, p<.001). The EPI-C is a valid assessment tool in this young age group. Overweight children consciously restrain their eating.

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Rational invariants on the space of all structures of algebras on a two-dimensional vector space

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Moment invariants have been thoroughly studied and repeatedly proposed as one of the most powerful tools for 2D shape identification. In this paper a set of such descriptors is proposed, being the basis functions discontinuous in a finite number of points. The goal of using discontinuous functions is to avoid the Gibbs phenomenon, and therefore to yield a better approximation capability for discontinuous signals, as images. Moreover, the proposed set of moments allows the definition of rotation invariants, being this the other main design concern. Translation and scale invariance are achieved by means of standard image normalization. Tests are conducted to evaluate the behavior of these descriptors in noisy environments, where images are corrupted with Gaussian noise up to different SNR values. Results are compared to those obtained using Zernike moments, showing that the proposed descriptor has the same performance in image retrieval tasks in noisy environments, but demanding much less computational power for every stage in the query chain.

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Published in 1896 under the title: A fair pioneer.