Journal articles: 'Shape statistics'

1

Small, Christopher G. "Statistics of shape." Wiley Interdisciplinary Reviews: Computational Statistics 3, no. 5 (June 10, 2011): 428–33. http://dx.doi.org/10.1002/wics.173.

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Dumoulin, Serge O., and Robert F. Hess. "Modulation of V1 Activity by Shape: Image-Statistics or Shape-Based Perception?" Journal of Neurophysiology 95, no. 6 (June 2006): 3654–64. http://dx.doi.org/10.1152/jn.01156.2005.

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It is current dogma that neurons in primary visual cortex extract local edges from the scene from which later visual areas reconstruct more meaningful shapes. Recent neuroimaging studies, however, have shown V1 modulations by the degree of structure in the image (shape). These V1 modulations due to the level of shape coherence have been explained in one of two possible ways: due to changes in image statistics or shape-based perceptual influences from higher visual areas. Here we compare both hypotheses using stimuli composed of Gabor arrays constructed to form circular shapes that can be successively degraded by manipulating the orientations of individual Gabors while maintaining local and global statistics. In a first experiment, we confirm that V1 responses are inversely correlated with the degree of structure in the image. In a second experiment, stimulus predictions are compared based on the degree of circular shape or change in the image statistic varied (orientation variance) in the image. We find that these V1 modulations to shape change are correlated with low-level changes in orientation contrast rather than shape perception per se.

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Wilder, J., J. Feldman, and M. Singh. "Shape classification based on natural shape statistics." Journal of Vision 8, no. 6 (March 29, 2010): 717. http://dx.doi.org/10.1167/8.6.717.

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4

Wilder, John, Jacob Feldman, and Manish Singh. "Superordinate shape classification using natural shape statistics." Cognition 119, no. 3 (June 2011): 325–40. http://dx.doi.org/10.1016/j.cognition.2011.01.009.

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5

Wheeler, David L. "The Statistics of Shape." Math Horizons 3, no. 3 (February 1996): 26–28. http://dx.doi.org/10.1080/10724117.1996.11974966.

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Chindelevitch, Leonid, Maryam Hayati, Art F. Y. Poon, and Caroline Colijn. "Network science inspires novel tree shape statistics." PLOS ONE 16, no. 12 (December 23, 2021): e0259877. http://dx.doi.org/10.1371/journal.pone.0259877.

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The shape of phylogenetic trees can be used to gain evolutionary insights. A tree’s shape specifies the connectivity of a tree, while its branch lengths reflect either the time or genetic distance between branching events; well-known measures of tree shape include the Colless and Sackin imbalance, which describe the asymmetry of a tree. In other contexts, network science has become an important paradigm for describing structural features of networks and using them to understand complex systems, ranging from protein interactions to social systems. Network science is thus a potential source of many novel ways to characterize tree shape, as trees are also networks. Here, we tailor tools from network science, including diameter, average path length, and betweenness, closeness, and eigenvector centrality, to summarize phylogenetic tree shapes. We thereby propose tree shape summaries that are complementary to both asymmetry and the frequencies of small configurations. These new statistics can be computed in linear time and scale well to describe the shapes of large trees. We apply these statistics, alongside some conventional tree statistics, to phylogenetic trees from three very different viruses (HIV, dengue fever and measles), from the same virus in different epidemiological scenarios (influenza A and HIV) and from simulation models known to produce trees with different shapes. Using mutual information and supervised learning algorithms, we find that the statistics adapted from network science perform as well as or better than conventional statistics. We describe their distributions and prove some basic results about their extreme values in a tree. We conclude that network science-based tree shape summaries are a promising addition to the toolkit of tree shape features. All our shape summaries, as well as functions to select the most discriminating ones for two sets of trees, are freely available as an R package at http://github.com/Leonardini/treeCentrality.

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7

Sahni, Varun. "Analysis of Large Scale Structure using Percolation, Genus and Shape Statistics." Symposium - International Astronomical Union 183 (1999): 210–20. http://dx.doi.org/10.1017/s0074180900132541.

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We probe gravitational clustering in N-body simulations using geometrical descriptors sensitive to ‘connectedness’: the genus curve, percolation and shape statistics. As gravitational clustering advances, the density field in N-body simulations shows an increasingly pronounced departure from Gaussianity reflected in the changing shape of the percolation curve and the changing amplitude and shape of the genus curve. We feel that both genus and percolation curves provide complementary probes of large scale structure topology and could be used to discriminate between models of structure formation and the analysis of observational data such as galaxy catalogs and MBR maps. The filling factor in clusters & superclusters at percolation is small indicating that matter is more likely to lie in filaments and pancakes. An analysis of ‘shapes’ in N-body simulations has shown that filaments are more pronounced than pancakes. To probe shapes of clusters and superclusters more rigorously we propose a new shape statistic which does not fit isodensity surfaces by ellipsoids (as done earlier). Instead our shape statistic is derived from fundamental properties of a compact body such as its volume V, surface area S, integrated mean curvature C, and connectivity (characterized by the Genus). The new shape statistic gives sensible results for topologically simple surfaces such as the ellipsoid, and for more complicated surfaces such as the torus.

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8

Micheas, Athanasios C., and Dipak K. Dey. "Assessing shape differences in populations of shapes using the complex watson shape distribution." Journal of Applied Statistics 32, no. 2 (March 2005): 105–16. http://dx.doi.org/10.1080/02664760500054137.

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9

Luo, Shan, and Ethan Vishniac. "Three-dimensional shape statistics: Methodology." Astrophysical Journal Supplement Series 96 (February 1995): 429. http://dx.doi.org/10.1086/192126.

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Mardia, K. V. "Directional statistics and shape analysis." Journal of Applied Statistics 26, no. 8 (December 1999): 949–57. http://dx.doi.org/10.1080/02664769921954.

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11

Luo, Shan, Ethan T. Vishniac, and Hugo Martel. "Three-dimensional Shape Statistics: Applications." Astrophysical Journal 468 (September 1996): 62. http://dx.doi.org/10.1086/177669.

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12

Chen, Shi-Fan, and Nickolas Kokron. "A Lagrangian theory for galaxy shape statistics." Journal of Cosmology and Astroparticle Physics 2024, no. 01 (January 1, 2024): 027. http://dx.doi.org/10.1088/1475-7516/2024/01/027.

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Abstract We formulate the Lagrangian perturbation theory of galaxy intrinsic alignments and compute the resulting auto and cross power spectra of galaxy shapes, densities and matter to 1-loop order. Our model represents a consistent effective-theory description of galaxy shape including the resummation of long-wavelength displacements which damp baryon acoustic oscillations, and includes one linear, three quadratic and two cubic dimensionless bias coefficients at this order, along with counterterms and stochastic contributions whose structure we derive. We compare this Lagrangian model against the three-dimensional helicity spectra of halo shapes measured in N-body simulations by ref. [1] and find excellent agreement on perturbative scales while testing a number of more restrictive bias parametrizations. The calculations presented are immediately relevant to analyses of both cosmic shear surveys and spectroscopic shape measurements, and we make a fast FFTLog-based code spinosaurus publicly available at https://github.com/sfschen/spinosaurus.

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13

Porter, Tim. "SHAPE AND SHAPE THEORY (Wiley Series in Probability and Statistics)." Bulletin of the London Mathematical Society 32, no. 6 (November 2000): 757–58. http://dx.doi.org/10.1112/s0024609300287353.

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14

Charpiat, Guillaume, Olivier Faugeras, and Renaud Keriven. "Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics." Foundations of Computational Mathematics 5, no. 1 (July 6, 2004): 1–58. http://dx.doi.org/10.1007/s10208-003-0094-x.

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15

Anevski, Dragi, Christopher Genovese, Geurt Jongbloed, and Wolfgang Polonik. "Statistics for Shape and Geometric Features." Oberwolfach Reports 13, no. 3 (2016): 1821–74. http://dx.doi.org/10.4171/owr/2016/32.

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16

Fleming, R., Y. Li, and E. Adelson. "Image statistics for 3D shape estimation." Journal of Vision 8, no. 6 (March 29, 2010): 76. http://dx.doi.org/10.1167/8.6.76.

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17

Sá Junior, Jarbas Joaci de Mesquita, and André Ricardo Backes. "Shape classification using line segment statistics." Information Sciences 305 (June 2015): 349–56. http://dx.doi.org/10.1016/j.ins.2015.01.027.

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18

Hong, Byung-Woo, Stefano Soatto, and Luminita A. Vese. "Enforcing local context into shape statistics." Advances in Computational Mathematics 31, no. 1-3 (October 30, 2008): 185–213. http://dx.doi.org/10.1007/s10444-008-9104-5.

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19

Fleming, R. W., A. Torralba, R. O. Dror, and E. H. Adelson. "How image statistics drive shape-from-texture and shape-from-specularity." Journal of Vision 3, no. 9 (March 18, 2010): 73. http://dx.doi.org/10.1167/3.9.73.

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20

Lever, J. H., D. Sen, and D. Attwood. "The Influence of Shape on Iceberg Wave-Induced Velocity Statistics." Journal of Offshore Mechanics and Arctic Engineering 112, no. 3 (August 1, 1990): 263–69. http://dx.doi.org/10.1115/1.2919865.

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The motion response of small icebergs in waves has been the subject of recent investigation to provide information for the design of offshore structures resistant to glacial ice impact. Since sea state and iceberg size are random variables, probabilistic formulations have been developed for use in risk analysis-based design procedures. The present work discusses the influence of iceberg shape on its motion response in waves. Wave tank tests were conducted which show that model shape has a significant effect on wave-induced ice motion. For all models tested, however, response spectra in an irregular sea could be accurately estimated using the linear superposition of measured responses in regular waves and the measured wave energy spectra. This was true in spite of obvious nonlinear behavior exhibited in high model seas. The observed differences in wave-induced motion for differently shaped models with similar masses and characteristic lengths suggest that iceberg shape should also be treated as a random variable in probabilistic formulations. In this way, wave-induced ice motion may be represented as a function of sea state, iceberg mass or characteristic length, and iceberg shape, all random variables. An earlier risk analysis formulation is extended to incorporate the influence of randomly varying iceberg shape on ice/structure impact velocity statistics.

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21

Sakya, Pranay Ratna, Rinky Nyachhyon, Amita Pradhan, Ratina Tamrakar, and Sudeep Acharya. "MORPHOLOGY OF CONDYLE- A RADIOGRAPHIC STUDY." Journal of Chitwan Medical College 12, no. 1 (March 15, 2022): 17–20. http://dx.doi.org/10.54530/jcmc.636.

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Background: Mandibular condyle has a variety of morphology. The changes in their shape and size has been attributed to ageing process, developmental abnormalities, distinct diseases, trauma, endocrine shock, radio therapy etc. Panoramic radiographs remain the easiest, safest and most cost-effective screening modality for temporomandibular joint abnormalities. The study aimed to assess the different shapes of condyles using orthopantomograms from the archives of the hospital data. The variations among the sexes and between the right and left sides of an individual were also determined. Methods: This retrospective study was conducted at People’s Dental College and Hospital within the time period of 1 year (November 2019- November 2020). Orthopantomogram of patients falling within the inclusion criteria were studied. The different shapes of condylar process were traced using marker pencil for both right and left sides. Data collected was entered in Microsoft Office Excel sheet 2013-- and calculated in SPSS version 24 and analyzed using descriptive statistics. Results: Out of the 874 mandibular condyles of 437 patients, the most common was the oval shaped in both the right (275) and the left sides (277), followed by bird beak, diamond, flat and crooked finger respectively. The oval shaped condyle appeared to be predominant in both sexes. The flat shaped and diamond shaped condyle appeared to be a rarity. Conclusions: The most common shape of condyle was found to be oval shape bilaterally and in both genders. Least observed shapes of condyle were flat shape in female patients and diamond shape in male patients.

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22

Matsen, Frederick A. "A Geometric Approach to Tree Shape Statistics." Systematic Biology 55, no. 4 (August 1, 2006): 652–61. http://dx.doi.org/10.1080/10635150600889617.

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23

Rohlf, F. James. "Shape Statistics: Procrustes Superimpositions and Tangent Spaces." Journal of Classification 16, no. 2 (July 1999): 197–223. http://dx.doi.org/10.1007/s003579900054.

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24

Mardia, K. V., J. Kirkbride, and F. L. Bookstein. "Statistics of Shape, Direction and Cylindrical Variables." Journal of Applied Statistics 31, no. 4 (May 2004): 465–79. http://dx.doi.org/10.1080/02664760410001681756.

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25

Huitink, David, Subrata Kundu, Chiwoo Park, Bani Mallick, Jianhua Z. Huang, and Hong Liang. "Nanoparticle Shape Evolution Identified through Multivariate Statistics." Journal of Physical Chemistry A 114, no. 17 (May 6, 2010): 5596–600. http://dx.doi.org/10.1021/jp100421t.

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26

De Baene, Wouter, Elsie Premereur, and Rufin Vogels. "Properties of Shape Tuning of Macaque Inferior Temporal Neurons Examined Using Rapid Serial Visual Presentation." Journal of Neurophysiology 97, no. 4 (April 2007): 2900–2916. http://dx.doi.org/10.1152/jn.00741.2006.

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We used rapid serial visual presentation (RSVP) to examine the tuning of macaque inferior temporal cortical (IT) neurons to five sets of 25 shapes each that varied systematically along predefined shape dimensions. A comparison of the RSVP technique using 100-ms presentations with that using a longer duration showed that shape preference can be determined with RSVP. Using relatively complex shapes that vary along relatively simple shape dimensions, we found that the large majority of neurons preferred extremes of the shape configuration, extending the results of a previous study using simpler shapes and a standard testing paradigm. A population analysis of the neuronal responses demonstrated that, in general, IT neurons can represent the similarities among the shapes at an ordinal level, extending a previous study that used a smaller number of shapes and a categorization task. However, the same analysis showed that IT neurons do not faithfully represent the physical similarities among the shapes. The responses to the two-part shapes could be predicted, virtually perfectly, from the average of the responses to the respective two parts presented in isolation. We also showed that IT neurons adapt to the stimulus distribution statistics. The neural shape discrimination improved when a shape set with a narrower stimulus range was presented, suggesting that the tuning of IT neurons is not static but adapts to the stimulus distribution statistics, at least when stimulated at a high rate with a restricted set of stimuli.

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27

Du, Jiejun, Ian L. Dryden, and Xianzheng Huang. "Size and Shape Analysis of Error-Prone Shape Data." Journal of the American Statistical Association 110, no. 509 (January 2, 2015): 368–79. http://dx.doi.org/10.1080/01621459.2014.908779.

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28

Kraus, I., Ph A. Bourdin, J. Zender, M. Bergmann, and A. Hanslmeier. "Coronal bright point statistics." Astronomy & Astrophysics 678 (October 2023): A184. http://dx.doi.org/10.1051/0004-6361/202346312.

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Context. The corona of the Sun is the part of the solar atmosphere with temperatures of over one million Kelvin, which needs to be heated internally in order to exist. This heating mechanism remains a mystery; we see large magnetically active regions in the photosphere lead to strong extreme UV (EUV) emission in the corona. On much smaller scales (on the order of tens of Mm), there are bipolar and multipolar regions that can be associated with evenly sized coronal bright points (CBPs). Aims. Our aim was to study the properties of CBPs in a statistical sense and to use continuous data from the SDO spacecraft, which makes it possible to track CBPs over their whole lifetime. Furthermore, we tested various rotation-speed profiles for CBPs in order to find out if the lower corona is co-rotating with the photosphere. Then we compiled a database with about 346 CBPs together with information of their sizes, shapes, appearance and disappearance, and their visibility in the EUV channels of the AIA instrument. We want to verify our methods with similar previous studies. Methods. We used the high-cadence data of the largest continuous SDO observation interval in 2015 to employ an automated tracking algorithm for CBPs. Some of the information (e.g., the total lifetime, the characteristic shape, and the magnetic polarities below the CBPs) still requires human interaction. Results. In this work we present statistics on fundamental properties of CBPs along with some comparison tables that relate, for example, the CBP lifetime with their shape. CBPs that are visible in all AIA channels simultaneously seem to be brighter in total and also have a stronger heating, and hence a higher total radiation flux. We compared the EUV emission visibility in different AIA channels with the CBP’s shape and lifetime. From the tracking algorithm we confirm a strict co-rotation of the CBPs with the photospheric differential rotation. Conclusions. The tracked CBPs have a typical lifetime of about 1–6 h, while the hottest and brightest ones seem to exist for significantly longer time, up to 24 h. Furthermore, the merging of two CBPs seems not to have an influence on the overall size of the persisting CBP. Finally, fainter and cooler CBPs tend to have only weaker magnetic polarities, which clearly supports a coronal bright point heating mechanism based on magnetic energy dissipation.

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29

Cameron, Kirk M. D. "RCRA leapfrog: How statistics shape and in turn are shaped by regulatory mandates." Remediation Journal 7, no. 1 (December 1996): 15–25. http://dx.doi.org/10.1002/rem.3440070103.

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30

Micheas, Athanasios C., and Dipak K. Dey. "Modeling shape distributions and inferences for assessing differences in shapes." Journal of Multivariate Analysis 92, no. 2 (February 2005): 257–80. http://dx.doi.org/10.1016/j.jmva.2003.09.013.

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31

Dryden, Ian L., and Andras Zempleni. "Extreme shape analysis." Journal of the Royal Statistical Society: Series C (Applied Statistics) 55, no. 1 (January 2006): 103–21. http://dx.doi.org/10.1111/j.1467-9876.2005.00533.x.

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32

Mardia, K. V., I. L. Dryden, M. A. Hurn, Q. Li, P. A. Millner, and R. A. Dickson. "Familial spinal shape." Journal of Applied Statistics 21, no. 6 (January 1994): 623–41. http://dx.doi.org/10.1080/757584222.

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33

Mardia, K. V., A. N. Walder, E. Berry, D. Sharples, P. A. Millner, and R. A. Dickson. "Assessing spinal shape." Journal of Applied Statistics 26, no. 6 (August 1999): 735–45. http://dx.doi.org/10.1080/02664769922179.

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34

Kayid, Mohamed. "Some new results on bathtub-shaped hazard rate models." Mathematical Biosciences and Engineering 19, no. 2 (2021): 1239–50. http://dx.doi.org/10.3934/mbe.2022057.

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<abstract><p>The most common non-monotonic hazard rate situations in life sciences and engineering involves bathtub shapes. This paper focuses on the quantile residual life function in the class of lifetime distributions that have bathtub-shaped hazard rate functions. For this class of distributions, the shape of the $ \alpha $-quantile residual lifetime function was studied. Then, the change points of the $ \alpha $-quantile residual life function of a general weighted hazard rate model were compared with the corresponding change points of the basic model in terms of their location. As a special weighted model, the order statistics were considered and the change points related to the order statistics were compared with the change points of the baseline distribution. Moreover, some comparisons of the change points of two different order statistics were presented.</p></abstract>

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35

Vlah, Zvonimir, Nora Elisa Chisari, and Fabian Schmidt. "Galaxy shape statistics in the effective field theory." Journal of Cosmology and Astroparticle Physics 2021, no. 05 (May 1, 2021): 061. http://dx.doi.org/10.1088/1475-7516/2021/05/061.

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36

Basilakos, Spyros. "Shape statistics of Sloan Digital Sky Survey superclusters." Monthly Notices of the Royal Astronomical Society 344, no. 2 (September 2003): 602–6. http://dx.doi.org/10.1046/j.1365-8711.2003.06845.x.

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37

Matsen, F. A. "Optimization Over a Class of Tree Shape Statistics." IEEE/ACM Transactions on Computational Biology and Bioinformatics 4, no. 3 (July 2007): 506–12. http://dx.doi.org/10.1109/tcbb.2007.1020.

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38

Lund, E. "Shape optimization using Weibull statistics of brittle failure." Structural Optimization 15, no. 3-4 (June 1998): 208–14. http://dx.doi.org/10.1007/bf01203533.

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39

Torppa, J., V. P. Hentunen, P. Pääkkönen, P. Kehusmaa, and K. Muinonen. "Asteroid shape and spin statistics from convex models." Icarus 198, no. 1 (November 2008): 91–107. http://dx.doi.org/10.1016/j.icarus.2008.07.014.

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40

ALISTE, Angel Manuel Fidalgo, and Maria Laura QUINTANILLA COBIAN. "EFFECT OF THE ABILITY DISTRIBUTION SHAPE ON THE GENERALIZED MANTEL-HAENSZEL STATISTICS USED FOR DIF DETECTION." REVISTA BRASILEIRA DE BIOMETRIA 36, no. 2 (June 29, 2018): 439. http://dx.doi.org/10.28951/rbb.v36i2.211.

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The main objective of this simulation study was to explore the effect of shape of the θ distribution on the generalized nominal and ordinal Mantel-Haenszel statistics used for detecting DIF in polytomous items. The variables manipulated were: trait ( θ), distribution shape (normal, positively skewed, and platykurtic), θ distribution difference between the reference and the focal group (equal and unequal), sample size (500/ 500 and 500/250 examinees in the reference/focal group), and DIF conditions (No DIF, constant and shift-high DIF patterns). The generalized ordinal Mantel-Haenszel statistic was calculated using integer and log-rank scores. The results show: a) a little impact of the θ distribution shape on the performance of all the statistics, and b) the advantages of employing log-rank scores, especially when the items show a shift-high DIF pattern.

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41

Le, Huiling. "Brownian motions on shape and size-and-shape spaces." Journal of Applied Probability 31, no. 1 (March 1994): 101–13. http://dx.doi.org/10.2307/3215238.

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The diffusions on the shape and size-and-shape spaces induced by brownian motions on the pre-size-and-shape spaces have been investigated in several papers (cf.). We here address the dual problem: the character of the diffusions on the pre-shape and pre-size-and-shape spaces which induce brownian motions on the shape and size-and-shape spaces. In particular we show that the shape and size-and-shape spaces for k labelled points in ℝm are stochastically complete if k > m and obtain the heat kernels of certain diffusions which induce brownian motions on the size-and-shape spaces.

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42

Le, Hulling. "Mean size-and-shapes and mean shapes: a geometric point of view." Advances in Applied Probability 27, no. 1 (March 1995): 44–55. http://dx.doi.org/10.2307/1428094.

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Unlike the means of distributions on a euclidean space, it is not entirely clear how one should define the means of distributions on the size-and-shape or shape spaces of k labelled points in ℝm since these spaces are all curved. In this paper, we discuss, from a shape-theoretic point of view, some questions which arise in practice while using procrustean methods to define mean size-and-shapes or shapes. We obtain sufficient conditions for such means to be unique and for the corresponding generalized procrustean algorithms to converge to them. These conditions involve the curvature of the size-and-shape or shape spaces and are much less restrictive than asking for the data to be concentrated.

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Kume, Alfred, and Huiling Le. "On Fréchet means in simplex shape spaces." Advances in Applied Probability 35, no. 4 (December 2003): 885–97. http://dx.doi.org/10.1239/aap/1067436325.

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By making use of the geometric properties of simplex shape spaces, this paper investigates the problems relating to the estimation of the Fréchet means of the random shapes of simplices in Euclidean spaces and also, for the random shapes induced by certain normally distributed simplices, the problems relating to the location of these Fréchet means. In particular, we obtain an algorithm for computing sample mean shapes in simplex shape spaces which converges reasonably fast.

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Boccardo, Francesco, and Olivier Pierre-Louis. "Temperature transitions and degeneracy in the control of small clusters with a macroscopic field." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 10 (October 1, 2022): 103205. http://dx.doi.org/10.1088/1742-5468/ac9616.

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Abstract We present a numerical investigation of the control of few-particle fluctuating clusters with a macroscopic field. Our goal is to reach a given target cluster shape in minimum time. This question is formulated as a first passage problem in the space of cluster configurations. We find the optimal policy to set the macroscopic field as a function of the observed shape using dynamic programming. Our results show that the optimal policy is non-unique, and its degeneracy is mainly related to symmetries shared by the initial shape, the force and the target shape. The total fraction of shapes for which optimal choice of the force is non-unique vanishes as the cluster size increases. Furthermore, the optimal policy exhibits a discrete set of transitions when the temperature is varied. Each transition leads to a discontinuity in the derivative of the time to reach with target with respect to temperature. As the size of the cluster increases, the change in the policy due to temperature transitions grows like the total number of configurations and a continuum limit emerges.

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Le, Hulling. "On procrustean mean shapes and the shape of the means." Advances in Applied Probability 28, no. 2 (June 1996): 336–37. http://dx.doi.org/10.2307/1428049.

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Two sets of k labelled points, or configurations, in ℝm are defined to have the same shape if they differ only in translation, rotation and scaling. An important matter in practice is the estimation of the shape of the means; the shape determined by the means of data on the vertices of configurations. However, statistical models for vertices-based shapes always involve some unknown samplewise nuisance parameters associated with ambiguity of location, rotation and scaling. The use of procrustean mean shapes for a finite set of configurations, which are usually formulated directly in terms of their vertices, will enable one to eliminate these nuisance parameters.

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46

Le, Hulling. "On procrustean mean shapes and the shape of the means." Advances in Applied Probability 28, no. 02 (June 1996): 336–37. http://dx.doi.org/10.1017/s0001867800048333.

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Two sets of k labelled points, or configurations, in ℝ m are defined to have the same shape if they differ only in translation, rotation and scaling. An important matter in practice is the estimation of the shape of the means; the shape determined by the means of data on the vertices of configurations. However, statistical models for vertices-based shapes always involve some unknown samplewise nuisance parameters associated with ambiguity of location, rotation and scaling. The use of procrustean mean shapes for a finite set of configurations, which are usually formulated directly in terms of their vertices, will enable one to eliminate these nuisance parameters.

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47

Dogra, Harshita, Shengxian Ding, Miyeon Yeon, Rongjie Liu, and Chao Huang. "Confounder Adjustment in Shape-on-Scalar Regression Model: Corpus Callosum Shape Alterations in Alzheimer’s Disease." Stats 6, no. 4 (September 28, 2023): 980–89. http://dx.doi.org/10.3390/stats6040061.

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Large-scale imaging studies often face challenges stemming from heterogeneity arising from differences in geographic location, instrumental setups, image acquisition protocols, study design, and latent variables that remain undisclosed. While numerous regression models have been developed to elucidate the interplay between imaging responses and relevant covariates, limited attention has been devoted to cases where the imaging responses pertain to the domain of shape. This adds complexity to the problem of imaging heterogeneity, primarily due to the unique properties inherent to shape representations, including nonlinearity, high-dimensionality, and the intricacies of quotient space geometry. To tackle this intricate issue, we propose a novel approach: a shape-on-scalar regression model that incorporates confounder adjustment. In particular, we leverage the square root velocity function to extract elastic shape representations which are embedded within the linear Hilbert space of square integrable functions. Subsequently, we introduce a shape regression model aimed at characterizing the intricate relationship between elastic shapes and covariates of interest, all while effectively managing the challenges posed by imaging heterogeneity. We develop comprehensive procedures for estimating and making inferences about the unknown model parameters. Through real-data analysis, our method demonstrates its superiority in terms of estimation accuracy when compared to existing approaches.

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Hasegawa, Hideyuki, Takumi Akamatsu, Masaaki Omura, and Ryo Nagaoka. "Adaptive beamformer with echo statistics." Journal of the Acoustical Society of America 152, no. 4 (October 2022): A217. http://dx.doi.org/10.1121/10.0016060.

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Delay-and-sum (DAS) beamforming is commonly used in commercial scanners and computationally efficient for real-time imaging. However, the ability to suppress off-axis signals is limited. A minimum variance (MV) beamformer realizes a superior performance in suppression of off-axis signals and improves lateral resolution significantly. On the other hand, MV degrades the contrast-to-noise ratio (CNR) compared to DAS because it alters speckle statistics. In this study, we developed a method for improvement of CNR in MV beamforming by evaluating envelope statistics of echo signals. It is well known that the envelope statistic of speckle echoes from a random medium obeys the Rayleigh distribution. The echo envelope statistics were evaluated using the shape parameter of the Nakagami distribution. The proposed beamformer is worked as DAS for speckle echoes and MV for non-speckle echoes by referring to the Nakagami shape parameter. In the phantom experiment, the lateral resolution of MV was 0.18 mm, which was significantly better than 0.53 mm obtained by DAS. However, CNR was degraded from 6.73 dB to 4.05 dB by MV. The proposed beamformer realized a lateral resolution of 0.25 mm, which was significantly better than DAS, with a CNR value of 6.03 dB, which was comparable to DAS.

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Dujak, D., A. Karač, Z. M. Jakšić, S. B. Vrhovac, and Lj Budinski-Petković. "Percolation in random sequential adsorption of polydisperse mixtures of extended objects on a triangular lattice." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 8 (August 1, 2023): 083209. http://dx.doi.org/10.1088/1742-5468/acecfb.

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Abstract Percolation properties of an adsorbed polydisperse mixture of extended objects on a triangular lattice are studied by Monte Carlo simulations. The depositing objects of various shapes are formed by self-avoiding walks on the lattice. We study polydisperse mixtures in which the size ℓ of the shape making the mixture increases gradually with the number of components. This study examines the influence of the shape of the primary object defining a polydisperse mixture on its percolation and jamming properties. The dependence of the jamming density and percolation threshold on the number of components n making the mixture is analyzed. Determining the contribution of the individual components in the lattice covering allowed a better insight into the deposit structure of the n-component mixture at the percolation threshold. In addition, we studied mixtures of objects of various shapes but the same size.

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Anderson, Edward. "Six new mechanics corresponding to further shape theories." International Journal of Modern Physics D 25, no. 04 (March 10, 2016): 1650044. http://dx.doi.org/10.1142/s0218271816500449.

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In this paper, suite of relational notions of shape are presented at the level of configuration space geometry, with corresponding new theories of shape mechanics and shape statistics. These further generalize two quite well known examples: (i) Kendall’s (metric) shape space with his shape statistics and Barbour’s mechanics thereupon. (ii) Leibnizian relational space alias metric scale-and-shape space to which corresponds Barbour–Bertotti mechanics. This paper’s new theories include, using the invariant and group namings, (iii) Angle alias conformal shape mechanics. (iv) Area ratio alias e shape mechanics. (v) Area alias e scale-and-shape mechanics. (iii)–(v) rest respectively on angle space, area-ratio space, and area space configuration spaces. Probability and statistics applications are also pointed to in outline.(vi) Various supersymmetric counterparts of (i)–(v) are considered. Since supergravity differs considerably from GR-based conceptions of background independence, some of the new supersymmetric shape mechanics are compared with both. These reveal compatibility between supersymmetry and GR-based conceptions of background independence, at least within these simpler model arenas.

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Journal articles on the topic 'Shape statistics'

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