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1

Zhang, Xin Li, Li Min Jia, and Jie Li. "Project Management Pattern Selection of Post-Disaster Reconstruction Projects Based on Multi-Dimensions Perspective." Applied Mechanics and Materials 501-504 (January 2014): 2659–63. http://dx.doi.org/10.4028/www.scientific.net/amm.501-504.2659.

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This study selects nine indicators impacting on project management pattern selection of post-disaster reconstruction projects. Questionnaire investigation is carried out based on the nine indicators and the needed data for this study is collected. Using factor analysis method, the nine indicators are classified into three main dimensions, which are internal factors, external factors and project goals. Correlation analysis between three main dimensions and six project management patterns is conducted to find the key dimension affecting each management pattern selection. According to the above analysis process, this study provides a selection flowchart of post-disaster reconstruction project management pattern, which may provide a new way for post-disaster reconstruction project pattern selection.
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KEVREKIDIS, P. G., and D. J. FRANTZESKAKIS. "PATTERN FORMING DYNAMICAL INSTABILITIES OF BOSE–EINSTEIN CONDENSATES." Modern Physics Letters B 18, no. 05n06 (March 12, 2004): 173–202. http://dx.doi.org/10.1142/s0217984904006809.

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In this short topical review, we revisit a number of works on the pattern-forming dynamical instabilities of Bose–Einstein condensates in one- and two-dimensional settings. In particular, we illustrate the trapping conditions that allow the reduction of the three-dimensional, mean field description of the condensates (through the Gross–Pitaevskii equation) to such lower dimensional settings, as well as to lattice settings. We then go on to study the modulational instability in one dimension and the snaking/transverse instability in two dimensions as typical examples of long-wavelength perturbations that can destabilize the condensates and lead to the formation of patterns of coherent structures in them. Trains of solitons in one dimension and vortex arrays in two dimensions are prototypical examples of the resulting nonlinear waveforms, upon which we briefly touch at the end of this review.
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Hurrelbrink, Jurgen, and Ulf Rehmann. "Splitting Patterns and Trace Forms." Canadian Mathematical Bulletin 41, no. 1 (March 1, 1998): 71–78. http://dx.doi.org/10.4153/cmb-1998-011-8.

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AbstractThe splitting pattern of a quadratic form q over a field k consists of all distinct Witt indices that occur for q over extension fields of k. In small dimensions, the complete list of splitting patterns of quadratic forms is known. We show that all splitting patterns of quadratic forms of dimension at most nine can be realized by trace forms.
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VON BRECHT, JAMES H., DAVID UMINSKY, THEODORE KOLOKOLNIKOV, and ANDREA L. BERTOZZI. "PREDICTING PATTERN FORMATION IN PARTICLE INTERACTIONS." Mathematical Models and Methods in Applied Sciences 22, supp01 (April 2012): 1140002. http://dx.doi.org/10.1142/s0218202511400021.

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Large systems of particles interacting pairwise in d dimensions give rise to extraordinarily rich patterns. These patterns generally occur in two types. On one hand, the particles may concentrate on a co-dimension one manifold such as a sphere (in 3D) or a ring (in 2D). Localized, space-filling, co-dimension zero patterns can occur as well. In this paper, we utilize a dynamical systems approach to predict such behaviors in a given system of particles. More specifically, we develop a nonlocal linear stability analysis for particles uniformly distributed on a d - 1 sphere. Remarkably, the linear theory accurately characterizes the patterns in the ground states from the instabilities in the pairwise potential. This aspect of the theory then allows us to address the issue of inverse statistical mechanics in self-assembly: given a ground state exhibiting certain instabilities, we construct a potential that corresponds to such a pattern.
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Gu, Bingfei, Guolian Liu, and Bugao Xu. "Individualizing women’s suit patterns using body measurements from two-dimensional images." Textile Research Journal 87, no. 6 (July 21, 2016): 669–81. http://dx.doi.org/10.1177/0040517516636001.

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The goal of this study was to develop an approach that could automatically generate the customized patterns for women’s suits based on the body measurements taken from two-dimensional (2D) frontal and side images of a subject. The 26 important pattern dimensions relevant to certain body dimensions were first chosen, and the mapping relationships between the body and pattern dimensions were then established for pattern alterations. For the body dimensions (e.g. girths) that could not be directly measured in the 2D images, prediction models were created based on the available width and depth measurements. The body measurements from the 2D images (auto-measurements) of 295 subjects were compared with the corresponding manual measurements, which showed a good correlation between the auto and manual measurements. The try-on test of five suits made with the altered patterns demonstrated the good fitting effects of the customized suits at important characteristic landmarks of five participating subjects through a visual evaluation. The subjective test also showed a satisfactory result of clothing fit under five different postures. Since this pattern-making method is originated from the relationship between the features of a human body and the elements of a pattern prototype, the generated patterns are individualized by unique body shapes to attain a good fit. This method can also accelerate the pattern-making process, reducing human efforts, costs, and production time.
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Vere-Jones, David. "On the fractal dimensions of point patterns." Advances in Applied Probability 31, no. 03 (September 1999): 643–63. http://dx.doi.org/10.1017/s0001867800009344.

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When fractal dimensions are estimated from an observed point pattern, there is some ambiguity as to the interpretation of the quantity being estimated. (The point pattern itself has dimension zero.) Two possible interpretations are described. In the first of these, the observation region is regarded as being held fixed, while observations accumulate with time. In this case, provided the process is stationary and ergodic in time, and the cumulants satisfy certain regularity constraints, the dimension estimates consistently estimate the Rényi moment dimensions of the marginal distribution in space. If the regularity constraints are not satisfied, then different limits can be obtained according to the manner in which the limits are taken. In the second case, the process is regarded as being stationary and ergodic in its spatial component, time being held fixed. In this case the estimates provide consistent estimates of the initial power-law rates of growth of the moment measures of the Palm distribution, the estimates for successively higher Rényi dimensions estimating the growth rates for successively higher-order moment measures of the Palm distribution. Several examples are given, to illustrate the different types of behaviour which may occur, including the case where the points are generated by a dynamical system.
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Vere-Jones, David. "On the fractal dimensions of point patterns." Advances in Applied Probability 31, no. 3 (September 1999): 643–63. http://dx.doi.org/10.1239/aap/1029955197.

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When fractal dimensions are estimated from an observed point pattern, there is some ambiguity as to the interpretation of the quantity being estimated. (The point pattern itself has dimension zero.) Two possible interpretations are described. In the first of these, the observation region is regarded as being held fixed, while observations accumulate with time. In this case, provided the process is stationary and ergodic in time, and the cumulants satisfy certain regularity constraints, the dimension estimates consistently estimate the Rényi moment dimensions of the marginal distribution in space. If the regularity constraints are not satisfied, then different limits can be obtained according to the manner in which the limits are taken.In the second case, the process is regarded as being stationary and ergodic in its spatial component, time being held fixed. In this case the estimates provide consistent estimates of the initial power-law rates of growth of the moment measures of the Palm distribution, the estimates for successively higher Rényi dimensions estimating the growth rates for successively higher-order moment measures of the Palm distribution.Several examples are given, to illustrate the different types of behaviour which may occur, including the case where the points are generated by a dynamical system.
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8

Day, Charles. "Chemical pattern formation in three dimensions." Physics Today 64, no. 4 (April 2011): 20. http://dx.doi.org/10.1063/1.3583700.

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de Rezende, P. J., and D. T. Lee. "Point Set pattern matching ind-dimensions." Algorithmica 13, no. 4 (April 1995): 387–404. http://dx.doi.org/10.1007/bf01293487.

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10

Will, Elizabeth, and James E. Faust. "Comparison of Container Placement Patterns for Maximizing Greenhouse Space Use." HortScience 32, no. 3 (June 1997): 479E—480. http://dx.doi.org/10.21273/hortsci.32.3.479e.

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A model was developed that will calculate the maximum number of containers that can be placed in a specified area. There are basically three patterns of container placement. First, “square” placement involves placing pots in parallel rows in both directions so that any four pots form a square. The other two methods involve staggered patterns in which any three containers form a triangle. In the “long staggered” pattern, the long rows are parallel to the long dimension of the bench or floor space, while in the “short staggered” pattern, long rows are parallel to the short dimension of the bench. Comparisons of spacing patterns were made using a range of greenhouse/bench dimensions and container sizes. In most cases, a staggered arrangement allowed a significant increase in the number of containers fitting on a bench as compared to square placement. For example, when 6-inch pots are placed pot-to-pot in an 8 × 50-foot greenhouse section or bench, “short staggered” or “long staggered” arrangement of containers permitted 10.4% to 11.9% more containers over that allowed by a square pattern. In general, the larger the bench or greenhouse section, the greater the benefit of staggered spacing. The difference between short and long staggered was usually less than 3%, and depended on the specific space dimensions. This model can be easily entered into a spreadsheet for growers to perform their own calculations.
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Himali Gupta, Vinay S Dua, and Mannu Khanna. "A Cephalometric Comparative Study for Upper Airway Dimensions in Different Craniofacial Growth Patterns." International Healthcare Research Journal 2, no. 6 (September 23, 2018): 150–56. http://dx.doi.org/10.26440/ihrj/02_06/200.

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AIM AND OBJECTIVES: To compare different craniofacial patterns with pharyngeal widths. In OSA (Obstructive Sleep Apnea) patients, a mutual association between the pharyngeal structures and the dentofacial patterns has been suggested. The present study was performed to compare the nasopharynx, oropharynx and hypopharynx dimensions of persons with hypodivergent, normodivegent and hyperdivergent facial types and to predict and to facilitate treatment for OSA patients.Hypothesis: The Null hypothesis for the study was that there is no difference between the upper airway for patients with different growth pattern.MATERIALS AND METHODS: The sample comprised 60 patients divided into three groups: hypodivergent (n=20), normodivergent (n=20), and hyperdivergent (n=20) according to Jarabak’s ratio and FH-MP angle, which were used to compare the soft tissue airway dimensions. The statistical analysis was performed using Student’s t-Test, one way ANOVA (analysis of variance) and LSD (Least significant difference) test.RESULT: Overall narrower anteroposterior pharyngeal dimension was found in the hyperdivergent group as compared to the normodivergent group. Whereas, the superior part of upper pharyngeal width in the subjects with hypodivergent growth pattern was significantly narrower than in normal growth pattern groups.CONCLUSION: In hyperdivergent patients, the narrower anterioposterior dimension of the airway may be due to the skeletal features common to such patients, i.e., posterior vertical maxillary excess, posterior position and decreased mandibular size. The variations of the upper airway may be attributed to the horizontal and vertical growth patterns. Upper airway obstruction and later on OSA may be predisposed by skeletal deficiency.
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Monahan, Caroline B., and Edward C. Carterette. "Pitch and Duration as Determinants of Musical Space." Music Perception 3, no. 1 (1985): 1–32. http://dx.doi.org/10.2307/40285320.

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In an experiment aimed at assessing dimensional properties of musical space, musicians rated the similarity of pairs of brief melodies on a 9-point scale. From our review of previous work, we hypothesized (1) that pitch variables would be considered more important than time or rhythmic variables by our subjects and (2) that the metrical consonance of pitch and duration patterns would generate a factor related to pattern regularity in listeners' musical space. Four melodies and their inversions were played in each of four rhythmic patterns (anapestic, dactylic, iambic, and trochaic) for a total of 1024 pattern pairs. Both multidimensional scaling and cluster analyses of similarity showed that at least five dimensions were needed for a good accounting of the perceptual space of these melodies. Surprisingly, the major dimensions found were rhythmic: (1) duple or triple rhythm, (2) accent first or last, and (3) iambic-dactylic versus trochaic-anapestic. Other dimensions were (4) rising or falling pitch and (5) the number of pitch—contour inflections. The tendency to rate patterns on the basis of time or rhythm (Dimensions I, II, and III) was negatively correlated with the tendency to rate patterns on the basis of pitch (Dimensions IV and V). It could not be determined whether this result depends on cognitive processing limitations, attention, or preferences. No factor was found that related to pattern regularity as we defined it.
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Gu, Bingfei, Xinhua Li, Yanhong Yan, and Junqiang Su. "Predicting human dimensions in body images for automatic generation of female pants patterns." Textile Research Journal 89, no. 18 (December 30, 2018): 3792–801. http://dx.doi.org/10.1177/0040517518821914.

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This study proposed a method on how to obtain and predict body measurements from frontal and side images of a subject for the individualized pattern generation of women's pants. According to the relationship between front and back patterns and a body torso, 32 important pattern dimensions relevant to certain body dimensions were determined by the graphic flattening method. For the body dimensions (such as perimeters) that could not be directly extracted from the body images, the prediction models were established based on the available width and depth measurements. The body measurements from the body images of 425 subjects were compared with the corresponding manual measurements, which showed a good correlation between the automated and manual measurements. The tried-on test showed that the pants made with the generated patterns demonstrated good fitting effect at the important characteristic landmarks of a participating subject. This method can accelerate the pattern-making process for women's pants based on body measurements, reducing human efforts, costs and production time.
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Fernández-Domínguez, Juan Carlos, Isabel Escobio-Prieto, Albert Sesé-Abad, Rafael Jiménez-López, Natalia Romero-Franco, and Ángel Oliva-Pascual-Vaca. "Health Sciences—Evidence Based Practice Questionnaire (HS-EBP): Normative Data and Differential Profiles in Spanish Osteopathic Professionals." International Journal of Environmental Research and Public Health 17, no. 22 (November 15, 2020): 8454. http://dx.doi.org/10.3390/ijerph17228454.

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The main goal of this study was to obtain normative data of the scores of the Health-Sciences Evidence Based Practice (HS-EBP) questionnaire, and to analyse evidence-based practice (EBP) among potential clusters of osteopathy professionals in Spain. An online descriptive cross-sectional study has been applied. A total number of 443 Spanish practicing osteopaths answered a survey including the 5 dimensions of the HS-EBP questionnaire and sociodemographic, training, and practice variables using the “LimeSurvey” online platform. Results point out that the median scores for each five HS-EBP questionnaire dimensions were 95.00, 86.00, 78.00, 84.00 and 62.00 considering that the range of possible scores in each of the dimensions was: from 12 to 120 in dimensions 1, 4 and 5; from 14–140 in dimension 2; and from 10–100 in dimension 3. A clustering algorithm extracted 6 different profiles across the five HS-EBP latent dimensions: low scores in all dimensions (cluster 1); low scores in all dimensions but with medium scores in dimension 1 (cluster 2); mixed pattern of scores, low in dimensions 2 and 5 and medium in the rest of the dimensions; medium scores in all dimensions (cluster 4); high scores in all dimensions and low scores in dimension 5 (cluster 5); and high scores in all dimensions (cluster 6). Significant relationship was found among the response patterns in the clusters and: academic degree level, EBP training and training level, and work time invested in healthcare activity, research and teaching activity. These results allow a description of the actual level of EBP and differential profiles of Osteopathy care practice in Spain. Knowledge of normative scores of the HS-EBP questionnaire and identification of different predictors of Spanish osteopaths’ EBP, e.g., academic degree, EBP training and training level, work time invested in healthcare activity, research, and teaching activity, and having a working relationship with an accredited educational centre, enable a comprehensive evaluation of the EBP of osteopathic professionals and can also be useful for developing and implementing formative intervention programs for improving EBP practice in osteopathic practice.
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Tewo, Robert K., Hilary L. Rutto, Walter Focke, Tumisang Seodigeng, and Lawrence K. Koech. "Formulations, development and characterization techniques of investment casting patterns." Reviews in Chemical Engineering 35, no. 3 (March 26, 2019): 335–49. http://dx.doi.org/10.1515/revce-2017-0068.

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Abstract Conventionally, unfilled wax has been used as a universal pattern material for the investment casting process. With increase in demand for accurate dimensions and complex shapes, various materials have been blended with wax to develop more suitable patterns for investment casting in order to overcome performance limitations exhibited by unfilled wax. The present article initially reviews various investigations on the development of investment casting patterns by exploring pattern materials, type of waxes and their limitations, the effect of filler materials and various additives on unfilled wax, wax blends for pattern materials, plastics and polymers for pattern materials and 3D-printed patterns. The superiority of filled and polymer patterns in terms of dimensional accuracy, pattern strength, surface and flow properties over unfilled wax is also discussed. The present use of 3D patterns following their versatility in the manufacturing sector to revolutionize the investment casting process is also emphasized. Various studies on wax characterization such as physical (surface and dimensions), thermal (thermogravimetric analysis and differential scanning calorimetry), mechanical (thermomechanical analysis, tensile stress testing, dynamic mechanical analysis) and rheological (viscosity and shearing properties) are also discussed.
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Azodo, Adinife Patrick, Olasunkanmi Salami Isamaila, and Sampson Chisa Owhor. "FITNESS AND COMFORT ASSESSMENT OF FOOTWEAR: AN ANTHROPOMETRIC APPRAISAL." Journal of Engineering Science 28, no. 3 (September 2021): 80–86. http://dx.doi.org/10.52326/jes.utm.2021.28(3).06.

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Suitability determination of any product designed for specific types of consumers is possible through the effective use of anthropometric information. This study assessed anthropometric data utilization in footwear designs and patterns as an indicator of fitness and comfort in footwear production. The data collected for analysis were the length and the breadth dimensions of footwear design pattern from eighteen footwear cottage shops and the foot anthropometric parameter from a total of four hundred and thirty-three (433) (males (226) and females (207)) subjects. The instrumentation design for the data collection was a digital vernier caliper (model Mitutoyo 500-506-10). The analysis of the foot anthropometry dimension and the design footwear pattern data obtained showed a lack of bilateral symmetry for the male and female gender. The fitness and comfortable foot support function of the footwear analyzed using a paired samples t-test between the footwear design pattern dimensions, and the foot anthropometric parameters disclosed p > 0.05 in all cases – not significant. This study concluded that tailoring a product design to the users’ population reduces the mismatch challenges, grants fitness, and comfort to the users.
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Ougaard, Morten. "Dimensions of Hegemony." Cooperation and Conflict 23, no. 4 (September 1988): 197–214. http://dx.doi.org/10.1177/001083678802300402.

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Ougaard, M. Dimensions of Hegemony. Cooperation and Conflict, XXIII, 1988, 197- 214. The first section of the article deals briefly with the history of the concept of inter national hegemony. The second section identifies several dimensions in various defi nitions of the concept. The first dimension is the distribution of resources implying that hegemony is defined as a preponderance of material power resources, while the second dimension is control over outcomes. In some definitions the hegemon has a greater control than other actors, no matter which outcomes are attained. In other definitions a specific kind of outcome is required, such as the provision of certain collective goods. A related question is whether the hegemon takes care of shared interests or is catering to its own interests, to the detriment of those of others. This points to what is arguably a somewhat neglected dimension of hegemony: the underlying pattern of interests. It is suggested that the concept of hegemony is relevant in situations with common basic interests and secondary but significant contradictory interests. In such a situation hegemony is defined as one actor's ability to provide for its own interests in conflicts of a secondary nature. The third section focuses on the patterns of interests underlying US hegemony. Three possible changes that can lead to declining hegemony are examined: increasing difficulties for the common interests, increasing incompatibility between the interests of the hegemon and its allies, and finally a growing disparity within the hegemon's own interests. The evidence is only suggestive and points in different directions, but on balance it tends to strengthen the case for declining hegemony.
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POTAPOV, ALEXEI B., and M. K. ALI. "PATTERN RECOGNITION WITH HAMILTONIAN DYNAMICS." International Journal of Modern Physics C 12, no. 05 (June 2001): 751–58. http://dx.doi.org/10.1142/s0129183101001948.

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We consider pattern recognition schemes that are based upon Hamiltonian dynamical system. Different oscillatory modes are used for storing and encoding patterns, and the effect of resonance is used for determining the most excited mode. We also propose a new technique for pattern orthogonalization resorting to hidden dimensions. Numerical experiments confirm high storage capacity and absence of false memories for the proposed system. Hamiltonian systems may be important as classical analogs of quantum computing systems or quantum neural networks.
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FIASCONARO, A., D. VALENTI, and B. SPAGNOLO. "NONMONOTONIC PATTERN FORMATION IN THREE SPECIES LOTKA–VOLTERRA SYSTEM WITH COLORED NOISE." Fluctuation and Noise Letters 05, no. 02 (June 2005): L305—L311. http://dx.doi.org/10.1142/s0219477505002690.

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A coupled map lattice of generalized Lotka–Volterra equations in the presence of colored multiplicative noise is used to analyze the spatiotemporal evolution of three interacting species: one predator and two preys symmetrically competing each other. The correlation of the species concentration over the grid as a function of time and of the noise intensity is investigated. The presence of noise induces pattern formation, whose dimensions show a nonmonotonic behavior as a function of the noise intensity. The colored noise induces a greater dimension of the patterns with respect to the white noise case and a shift of the maximum of its area towards higher values of the noise intensity.
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TAO, YU, ERNEST C. M. LAM, and YUAN Y. TANG. "A COMBINATION OF FRACTAL AND WAVELET FOR FEATURE EXTRACTION." International Journal of Pattern Recognition and Artificial Intelligence 15, no. 08 (December 2001): 1277–98. http://dx.doi.org/10.1142/s021800140100143x.

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In this paper, a novel approach to feature extraction with wavelet and fractal theories is presented as a powerful technique in pattern recognition. The motivation behind using fractal transformation is to develop a high-speed feature extraction technique. A multiresolution family of the wavelets is also used to compute information conserving micro-features. In this study, a new fractal feature is reported. We employed a central projection method to reduce the dimensionality of the original input pattern, and a wavelet transform technique to convert the derived pattern into a set of subpatterns, from which the fractal dimensions can readily be computed. The new feature is a measurement of the fractal dimension, which is an important characteristic that contains information about the geometrical structure. This new scheme includes utilizing the central projection transformation to describe the shape, the wavelet transformation to aid the boundary identification, and the fractal features to enhance image discrimination. The proposed method reduces the dimensionality of a 2-D pattern by way of a central projection approach, and thereafter, performs Daubechies' wavelet transform on the derived 1-D pattern to generate a set of wavelet transform subpatterns, namely, curves that are non-self-intersecting. Further from the resulting non-self-intersecting curves, the divider dimensions are computed with a modified box-counting approach. These divider dimensions constitute a new feature vector for the original 2-D pattern, defined over the curve's fractal dimensions. We have conducted several experiments in which a set of printed Chinese characters, English letters of varying fonts and other images were classified. Based on the formulation of our new feature vector, the experiments have satisfying results.
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Zhizhin, Gennadiy V. "Higher Dimensions of Clusters of Intermetallic Compounds." International Journal of Applied Nanotechnology Research 4, no. 1 (January 2019): 8–25. http://dx.doi.org/10.4018/ijanr.2019010102.

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The author has previously proven that diffraction pattern of intermetallic compounds (quasicrystals) have translational symmetry in the space of higher dimension. In this paper, it is proved that the metallic nanoclusters also have a higher dimension. The internal geometry of clusters was investigated. General expressions for calculating the dimension of clusters is obtained, from which it follows that the dimension of metallic nanoclusters increases linearly with increasing number of cluster shells. The dimensions of many experimentally known metallic nanoclusters are determined. It is shown that these clusters, which are usually considered to be three - dimensional, have a higher dimension. The Euler-Poincaré equation was used, the internal geometry of clusters was investigated.
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Xiao, Ying, Xiao Mei Liu, and Jian Can Chen. "Fault Diagnosis of the Relief Valve Based on Fractal Box Dimension of Autoregressive Bispectrum Slices." Applied Mechanics and Materials 274 (January 2013): 70–73. http://dx.doi.org/10.4028/www.scientific.net/amm.274.70.

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After data preprocessing,the autoregressive(AR) bispectrum diagonal slices were figured and fractal box dimensions were calculated. The results show that the box dimensions are different in evidence under different conditions. So the fault pattern recognitions of the relief valve are effective by the method of using fractal box dimension of AR bispectrum diagonal slices, it provides a simple and accurate method for fault diagnosis of the relief valve.
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Wang, Junpeng, Xiaotong Liu, and Han-Wei Shen. "High-dimensional data analysis with subspace comparison using matrix visualization." Information Visualization 18, no. 1 (October 14, 2017): 94–109. http://dx.doi.org/10.1177/1473871617733996.

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Due to the intricate relationship between different dimensions of high-dimensional data, subspace analysis is often conducted to decompose dimensions and give prominence to certain subsets of dimensions, i.e. subspaces. Exploring and comparing subspaces are important to reveal the underlying features of subspaces, as well as to portray the characteristics of individual dimensions. To date, most of the existing high-dimensional data exploration and analysis approaches rely on dimensionality reduction algorithms (e.g. principal component analysis and multi-dimensional scaling) to project high-dimensional data, or their subspaces, to two-dimensional space and employ scatterplots for visualization. However, the dimensionality reduction algorithms are sometimes difficult to fine-tune and scatterplots are not effective for comparative visualization, making subspace comparison hard to perform. In this article, we aggregate high-dimensional data or their subspaces by computing pair-wise distances between all data items and showing the distances with matrix visualizations to present the original high-dimensional data or subspaces. Our approach enables effective visual comparisons among subspaces, which allows users to further investigate the characteristics of individual dimensions by studying their behaviors in similar subspaces. Through subspace comparisons, we identify dominant, similar, and conforming dimensions in different subspace contexts of synthetic and real-world high-dimensional data sets. Additionally, we present a prototype that integrates parallel coordinates plot and matrix visualization for high-dimensional data exploration and incremental dimensionality analysis, which also allows users to further validate the dimension characterization results derived from the subspace comparisons.
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Pidcock, Elna, and W. D. Sam Motherwell. "Parameterization of the close packing of molecules in the unit cell." Acta Crystallographica Section B Structural Science 60, no. 6 (November 11, 2004): 725–33. http://dx.doi.org/10.1107/s0108768104022128.

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The box model of crystal packing describes unit cells in terms of a limited number of arrangements, or packing patterns, of molecular building blocks. Cell dimensions have been shown to relate to molecular dimensions in a systematic way. The distributions of pattern coefficients (cell length/molecular dimension) for thousands of structures belonging to P21/c, P\bar 1, P212121, P21 and C2/c are presented and are shown to be entirely consistent with the box model of crystal packing. Contributions to the form of the histograms from molecular orientation and molecular overlap are discussed. Gaussian fitting of the histograms has led to the parameterization of close packing within the unit cell and it is shown that molecular crystal structures are very similar to one another at a fundamental level.
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정성태 and 한규철. "RRP Loading Patterns and Standard Dimensions for Block Pattern in Membership Wholesale Clubs." Journal of Distribution Science 13, no. 7 (July 2015): 41–51. http://dx.doi.org/10.15722/jds.13.7.201507.41.

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Uneputty, Prulley A. "PATTERNS OF RELATIVE GROWTH IN TROPICAL NERITIDS, NERITA UNDATA, BASED ON OPERCULUM ANALYSIS." Marine Research in Indonesia 32, no. 1 (May 11, 2007): 41–47. http://dx.doi.org/10.14203/mri.v32i1.430.

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Growth is one of the important events in the life history of an organism beside reproduction. The objective of the present study was to evaluate the possibility of using the operculum to determine the growth pattern of tropical neritids (Nerita undata). Shell and operculum dimension were measured using a vernier caliper to the nearest 0.01mm. The results showed that there was a relationship between operculum dimensions (length and width) and shell, and it was also shown allometric growth pattern. The study also indicated the relationship between operculum dimension and the shell parameters.
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Zheng, Yu, Li Peng, and Teturo Kamae. "Characterization of noncorrelated pattern sequences and correlation dimensions." Discrete & Continuous Dynamical Systems - A 38, no. 10 (2018): 5085–103. http://dx.doi.org/10.3934/dcds.2018223.

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Libanov, M. V., and E. Ya Nugaev. "Hierarchical fermionic mass pattern and large extra dimensions." Surveys in High Energy Physics 17, no. 1-4 (January 2002): 165–71. http://dx.doi.org/10.1080/0142241021000054167.

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Kim, Sang-Yoon, and Bambi Hu. "Scaling pattern of period doubling in four dimensions." Physical Review A 41, no. 10 (May 1, 1990): 5431–40. http://dx.doi.org/10.1103/physreva.41.5431.

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30

Glick, Mark, and Gary M. Hieftje. "Stereoscopic data visualization: pattern recognition in three dimensions." Analytica Chimica Acta 259, no. 1 (April 1992): 79–87. http://dx.doi.org/10.1016/0003-2670(92)85078-k.

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31

Rojer, Alan, and Eric Schwartz. "A Multiple-Map Model for Pattern Classification." Neural Computation 1, no. 1 (March 1989): 104–15. http://dx.doi.org/10.1162/neco.1989.1.1.104.

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A characteristic feature of vertebrate sensory cortex (and midbrain) is the existence of multiple two-dimensional map representations. Some workers have considered single-map classification (e.g. Kohonen 1984) but little work has focused on the use of multiple maps. We have constructed a multiple-map classifier, which permits abstraction of the computational properties of a multiple-map architecture. We identify three problems which characterize a multiple-map classifier: classification in two dimensions, mapping from high dimensions to two dimensions, and combination of multiple maps. We demonstrate component solutions to each of the problems, using Parzen-window density estimation in two dimensions, a generalized Fisher discriminant function for dimensionality reduction, and split/merge methods to construct a “tree of maps” for the multiple-map representation. The combination of components is modular and each component could be improved or replaced without affecting the other components. The classifier training procedure requires time linear in the number of training examples; classification time is independent of the number of training examples and requires constant space. Performance of this classifier on Fisher's iris data, Gaussian clusters on a five-dimensional simplex, and digitized speech data is comparable to competing algorithms, such as nearest-neighbor, back-propagation and Gaussian classifiers. This work provides an example of the computational utility of multiple-map representations for classification. It is one step towards the goal of understanding why brain areas such as visual cortex utilize multiple map-like representations of the world.
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Repp, Bruno H. "Pattern Typicality and Dimensional Interactions in Pianists' Imitation of Expressive Timing and Dynamics." Music Perception 18, no. 2 (2000): 173–211. http://dx.doi.org/10.2307/40285908.

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Success in an imitation task may be defined in absolute terms (how well the reproduction matches the model) or in relative terms (how much better the reproduction matches the model than the imitator's spontaneous production matches the model). In the present study of expressive music performance, it was hypothesized that absolute imitation success would decrease but relative imitation success would increase as the model pattern diverges more and more from the typical pattern of spontaneous production, within reasonable limits. This hypothesis received support in Experiment 1, which required pianists first to play a musical excerpt spontaneously and then to imitate model performances instantiating different patterns of expressive timing or dynamics, with the other dimension held constant at a typical pattern. The typical expressive pattern for a given musical passage seems to function as a cognitive schema that biases perception, memory, and (re) production of expressive nuances. The results also suggested that imitation of different dynamic patterns affects expressive timing (louder tones were followed by longer interonset intervals), whereas imitation of different timing patterns had little effect on produced dynamics. The latter findings were replicated in Experiment 2, which presented models that differed in both timing and dynamics. Attention to both dimensions simultaneously also reduced imitation accuracy, especially for timing.
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Kuswandari, Inna, Fatmawati Fatmawati, and Mohammad Imam Utoyo. "The Metric Dimension and Local Metric Dimension of Relative Prime Graph." CAUCHY 6, no. 3 (November 19, 2020): 149–61. http://dx.doi.org/10.18860/ca.v6i3.10103.

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This study aims to determine the value of metric dimensions and local metric dimensions of relative prime graphs formed from modulo integer rings, namely . As a vertex set is and if and are relatively prime. By finding the pattern elements of resolving set and local resolving set, it can be shown the value of the metric dimension and the local metric dimension of graphs are and respectively, where is the number of vertices groups that formed multiple 2,3, … , and is the cardinality of set . This research can be developed by determining the value of the fractional metric dimension, local fractional metric dimension and studying the advanced properties of graphs related to their forming rings.Key Words : metric dimension; modulo ; relative prime graph; resolving set; rings.
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ZHANG, DONGSHENG, ASHOK SAMAL, and JAMES R. BRANDLE. "A METHOD FOR ESTIMATING FRACTAL DIMENSION OF TREE CROWNS FROM DIGITAL IMAGES." International Journal of Pattern Recognition and Artificial Intelligence 21, no. 03 (May 2007): 561–72. http://dx.doi.org/10.1142/s0218001407005090.

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A new method for estimating fractal dimension of tree crowns from digital images is presented. Three species of trees, Japanese yew (Taxus cuspidata Sieb & Zucc), Hicks yew (Taxus × media), and eastern white pine (Pinus strobus L.), were studied. Fractal dimensions of Japanese yew and Hicks yew range from 2.26 to 2.70. Fractal dimension of eastern white pine range from 2.14 to 2.43. The difference in fractal dimension between Japanese yew and eastern white pine was statistically significant at 0.05 significance level as was the difference in fractal dimension between Hicks yew and eastern white pine. On average, the greater fractal dimensions of Japanese yew and Hicks yew were possibly related to uniform foliage distribution within their tree crowns. Therefore, fractal dimension may be useful for tree crown structure classification and for indexing tree images.
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Wang, Zhujun, Jianping Wang, Yingmei Xing, Yalan Yang, and Kaixuan Liu. "Estimating Human Body Dimensions Using RBF Artificial Neural Networks Technology and Its Application in Activewear Pattern Making." Applied Sciences 9, no. 6 (March 18, 2019): 1140. http://dx.doi.org/10.3390/app9061140.

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Nowadays, the popularity of the internet has continuously increased. Predicting human body dimensions intelligently would be beneficial to improve the precision and efficiency of pattern making for enterprises in the apparel industry. In this study, a new predictive model for estimating body dimensions related to garment pattern making is put forward based on radial basis function (RBF) artificial neural networks (ANNs). The model presented in this study was trained and tested using the anthropometric data of 200 adult males between the ages 20 and 48. The detailed body dimensions related to pattern making could be obtained by inputting four easy-to-measure key dimensions into the RBF ANN model. From the simulation results, when spreading parameter σ and momentum factor α were set to 0.012 and 1, the three-layer model with 4, 72, and 8 neurons in the input, hidden, and output layers, respectively, showed maximum accuracy, after being trained by a dataset with 180 samples. Moreover, compared with a classic linear regression model and the back propagation (BP) ANN model according to mean squared error, the predictive performance of the RBF ANN model put forward in this study was better than the other two models. Therefore, it is feasible for the presented predictive model to design garment patterns, especially for tight-fitting garment patterns like activewear. The estimating accuracy of the proposed model would be further improved if trained by more appropriate datasets in the future.
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Dhahi, Th S., U. Hashim, M. E. Ali, N. M. Ahmed, and T. Nazwa. "Fabrication of Lateral Polysilicon Gap of Less than 50 nm Using Conventional Lithography." Journal of Nanomaterials 2011 (2011): 1–8. http://dx.doi.org/10.1155/2011/250350.

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We report a thermal oxidation process for the fabrication of nanogaps of less than 50 nm in dimension. Nanogaps of this dimension are necessary to eliminate contributions from double-layer capacitance in the dielectric detection of protein or nucleic acid. The method combines conventional photolithography and pattern-size reduction techniques. The gaps are fabricated on polysilicon-coated silicon substrate with gold electrodes. The dimensions of the structure are determined by scanning electron microscopy (SEM). An electrical characterization of the structures by dielectric analyzer (DA) shows an improved conductivity as well as enhanced permittivity and capacity with the reduction of gap size, suggesting its potential applications in the detection of biomolecule with very low level of power supply. Two chrome Masks are used to complete the work: the first Mask is for the nanogap pattern and the second one is for the electrodes. An improved resolution of pattern size is obtained by controlling the oxidation time. The method expected to enable fabrication of nanogaps with a wide ranging designs and dimensions on different substrates. It is a simple and cost-effective method and does not require complicated nanolithography process for fabricating desired nanogaps in a reproducible fashion.
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Hudson, Alexander, and Ivar Alberto Hartmann. "Can you bury ideology? An empirical analysis of the ideal points of the Ministers of Brazil’s Supremo Tribunal Federal." A&C - Revista de Direito Administrativo & Constitucional 17, no. 68 (June 25, 2017): 43–59. http://dx.doi.org/10.21056/aec.v17i68.802.

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Brazil's Supremo Tribunal Federal (STF) is an especially interesting case for scholars with an interest in judicial behavior. The justices of the STF rule in tens of thousands of cases per year, in a great variety of legal disputes. The ideological breakdown of the STF remains puzzling. Observers of the STF find that a single left-right dimension is entirely inadequate to describe the voting coalitions that form in the court. In this paper, we utilize a new dataset covering a representative sample of all cases decided by the STF between 1992 and 2013. The first important finding is that the voting patterns of the STF show that at least four dimensions are necessary to describe the justices' ideal points. We then estimate ideal points for 23 justices on each of four dimensions, and associate these dimensions with the dominant areas of law with which the STF deals. Finally, we seek to use these ideal point estimates to compare the votes of the justices in key cases with their broader voting pattern.
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38

Oishi, Akira, and Yuji Matsumoto. "Detecting the Organization of Semantic Subclasses of Japanese Verbs." International Journal of Corpus Linguistics 2, no. 1 (January 1, 1997): 65–89. http://dx.doi.org/10.1075/ijcl.2.1.05ois.

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This paper describes an approach to detect the organization of semantic subclasses of Japanese verbs. First, we classify verbs along two dimensions: thematic and aspectual. In the thematic dimension, we exploit the pattern of case marking particles which are attached to arguments of verbs. In the aspectual dimension, we exploit the classification of adverbs which modify verbs in a corpus. By combining the results of two classifications, we obtain an elaborate classification of verbs. We can incorporate the prototypicality of the members which constitute each semantic subclass by taking account of the frequency of case particles patterns and cooccurring adverbs. Moreover, the existence of close relationships among them enable us to detect the organization of these subclasses.
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39

Cai, Y., M. W. Wambsganss, and J. A. Jendrzejczyk. "Application of Chaos Theory in Identification of Two-Phase Flow Patterns and Transitions in a Small, Horizontal, Rectangular Channel." Journal of Fluids Engineering 118, no. 2 (June 1, 1996): 383–90. http://dx.doi.org/10.1115/1.2817390.

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Various measurement tools that are used in chaos theory were applied to analyze two-phase pressure signals with the objective of identifying and interpreting flow pattern transitions for two-phase flows in a small, horizontal rectangular channel. These measurement tools included power spectral density function, autocorrelation junction, pseudo-phase-plane trajectory, Lyapunov exponents, and fractal dimensions. It was demonstrated that the randomlike pressure fluctuations characteristic of two-phase flow in small rectangular channels are chaotic, and governed by a high-order deterministic system. The correlation dimension is potentially a new approach for identifying certain two-phase flow patterns and transitions.
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40

Milton, Graeme W., and Ornella Mattei. "Field patterns: a new mathematical object." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2198 (February 2017): 20160819. http://dx.doi.org/10.1098/rspa.2016.0819.

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Field patterns occur in space–time microstructures such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is the field pattern. In one spatial direction plus time, the field patterns occur when the slope of the characteristics is, in a sense, commensurate with the space–time microstructure. Field patterns with different spatial shifts do not generally interact, but rather evolve as if they live in separate dimensions, as many dimensions as the number of field patterns. Alternatively one can view a collection as a multi-component potential, with as many components as the number of field patterns. Presumably, if one added a tiny nonlinear term to the wave equation one would then see interactions between these field patterns in the multi-dimensional space that one can consider them to live, or between the different field components of the multi-component potential if one views them that way. As a result of P T -symmetry many of the complex eigenvalues of an appropriately defined transfer matrix have unit norm and hence the corresponding eigenvectors correspond to propagating modes. There are also modes that blow up exponentially with time.
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41

Hagerhall, Caroline M., Thorbjörn Laike, Richard P. Taylor, Marianne Küller, Rikard Küller, and Theodore P. Martin. "Investigations of Human EEG Response to Viewing Fractal Patterns." Perception 37, no. 10 (January 1, 2008): 1488–94. http://dx.doi.org/10.1068/p5918.

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Owing to the prevalence of fractal patterns in natural scenery and their growing impact on cultures around the world, fractals constitute a common feature of our daily visual experiences, raising an important question: what responses do fractals induce in the observer? We monitored subjects' EEG while they were viewing fractals with different fractal dimensions, and the results show that significant effects could be found in the EEG even by employing relatively simple silhouette images. Patterns with a fractal dimension of 1.3 elicited the most interesting EEG, with the highest alpha in the frontal lobes but also the highest beta in the parietal area, pointing to a complicated interplay between different parts of the brain when experiencing this pattern.
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42

Saito, K., and S. Ogawa. "FRACTAL DIMENSIONS FOR RADIOISOTOPE POLLUTION PATTERNS BY NUCLEAR POWER PLANT ACCIDENTS." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-7/W3 (April 30, 2015): 919–25. http://dx.doi.org/10.5194/isprsarchives-xl-7-w3-919-2015.

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The radioisotope pollution shows two types of patterns: dry and wet deposits for nuclear power plant accidents. Two surface pollution patterns were analysed by fractal. In Fukushima nuclear power plant accident, surface pollution by wet deposits was estimated to occur. However, actually it was no rain and white crystals were observed on the surface. Then, fractal analysis was carried out for the spatial distribution patterns of radio isotopes on the surface to judge the types of deposits. As a reference, Chernobyl nuclear power plant accident was checked for the spatial distribution patterns of radioisotopes on the surface. The objective patterns by fractal analysis were the surface pollution maps in Fukushima and Chernobyl, Abukuma river watershed map, and NOAA/AVHRR. The calculation of fractal dimensions was carried out with the box counting for binarized images. Fractal analysis results suggested the next conclusions. The radioisotope pollution in Fukushima might occur in both dry and wet deposits. The dry deposit might make the pollution pattern similar to the watershed, while the wet deposit might make the pollution pattern similar to cloud images. Moreover, most radioisotope contaminants might flow on the road in the forest valley and deposit on forest with and without rainfall in Fukushima.
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43

Zhang, Yu, Christopher R. Krausert, Michael P. Kelly, and Jack J. Jiang. "Typing Vocal Fold Vibratory Patterns in Excised Larynx Experiments Via Digital Kymography." Annals of Otology, Rhinology & Laryngology 118, no. 8 (August 2009): 598–605. http://dx.doi.org/10.1177/000348940911800812.

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Objectives Signal typing is central to the understanding of vocal fold vibratory patterns. Digital kymography (DKG) allows the direct observation of vocal fold vibratory patterns, and therefore, using DKG for vibratory signal typing may provide a useful complement to traditional signal typing techniques. Methods Video data collected from 20 larynges excised from mongrel dogs were observed with DKG in order to find examples of type 1 (nearly periodic), type 2 (subharmonic), and type 3 (aperiodic) vibratory patterns. The time series, frequency spectra, and correlation dimensions were calculated for each signal type. Results The type 1 pattern showed a periodic time series of glottal edges and a discrete frequency spectrum. The type 2 vibratory pattern displayed a time series of alternating high- and low-amplitude waves and a frequency spectrum that included a subharmonic (F0/2) frequency component. Regular and symmetric vibratory patterns were observed in the type 1 and type 2 patterns. The type 3 vibratory pattern was characterized by an aperiodic time series of glottal edges, a broadband frequency spectrum, and irregular and asymmetric vibratory patterns. The correlation dimension estimates increased from type 1 to type 2 to type 3. Conclusions Imaging with DKG demonstrated an ability to assign a signal type to various laryngeal vibrations. Signal typing techniques utilizing direct observation of the vocal folds could be useful in determining valid methods for the analysis of vocal fold vibrations.
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Marisa, Cindy, Evi Fitriyanti, and Sri Utami. "Hubungan Pola Asuh Orangtua dengan Motivasi Belajar Remaja." Jurnal Konseling dan Pendidikan 6, no. 1 (February 18, 2018): 25. http://dx.doi.org/10.29210/118700.

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This research is based on parents' thinking is an important learning motivator for children, including in adolescence, because the family is the first and main environment. Provision of appropriate parenting patterns should also follow a good child's learning motivation. This study aims to determine whether there is a significant positive relationship between the pattern of care with motivation in learning, and knowing where old parenting patterns have the motivation to learn. The research design used herein is correlative with the method. Data taken by using closed questionnaires. Data were analyzed using Spearman's rho test. With this method researchers collect as much data as possible about the dimensions of motivation to learn, then do the analysis of these dimensions to get the complete data and as objective as possible with the pattern of care and motivation to learn adolescents. Testing is done by t test. Based on the data analysis can be concluded there is a significant relationship between the pattern of care with adolescent learning motivation with a contribution of 18.8%, where again increased adolescent learning motivation caused by other factors.
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45

Otjes, Simon. "Distinguishing welfare state reform and income redistribution. A two-dimensional approach to the Dutch voter space on economic issues." Party Politics 24, no. 5 (September 23, 2016): 563–76. http://dx.doi.org/10.1177/1354068816663039.

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There is growing evidence that voter and party positions on economic items do not conform to a left–right dimension. This article proposes that in Northern Eurozone states voter policy positions on economic issues are characterized by two dimensions: A redistribution dimension that consists out of views on income equality and a reform dimension that divides those who favour reform of the welfare state to ensure its long-term sustainability and those who oppose such reforms because they would hurt those who need the welfare state now. It examines to what extent voters positions on economic issues conform this two-dimensional pattern, employing the 2012 Dutch Election Survey; to what extent positions on these dimensions reflects voters’ attitudes on other issues and demographic characteristics; and to what extent these two dimensions help to understand voting behaviour. It shows that indeed a multidimensional approach to economic issues is justified; that voters who oppose reforms are characterized by higher levels of Euroscepticism; and that this reform dimension helps to understand voting behaviour, in particular preferences for the socialist, social-democratic and social-liberal party.
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LENG, JINSONG, and ZHIHU HUANG. "OUTLIERS DETECTION WITH CORRELATED SUBSPACES FOR HIGH DIMENSIONAL DATASETS." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 02 (March 2011): 227–36. http://dx.doi.org/10.1142/s0219691311004067.

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Detecting outliers in high dimensional datasets is quite a difficult data mining task. Mining outliers in subspaces seems to be a promising solution, because outliers may be embedded in some interesting subspaces. Due to the existence of many irrelevant dimensions in high dimensional datasets, it is of great importance to eliminate the irrelevant or unimportant dimensions and identify outliers in interesting subspaces with strong correlation. Normally, the correlation among dimensions can be determined by traditional feature selection techniques and subspace-based clustering methods. The dimension-growth subspace clustering techniques find interesting subspaces in relatively lower possible dimension space, while dimension-growth approaches intend to find the maximum cliques in high dimensional datasets. This paper presents a novel approach by identifying outliers in correlated subspaces. The degree of correlation among dimensions is measured in terms of the mean squared residue. In doing so, we employ the frequent pattern algorithms to find the correlated subspaces. Based on the correlated subspaces obtained, outliers are distinguished from the projected subspaces by using classical outlier detection techniques. Empirical studies show that the proposed approach can identify outliers effectively in high dimensional datasets.
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Ali, Shahbaz, Muhammad Khalid Mahmood, Fairouz Tchier, and F. M. O. Tawfiq. "Classification of Upper Bound Sequences of Local Fractional Metric Dimension of Rotationally Symmetric Hexagonal Planar Networks." Journal of Mathematics 2021 (February 27, 2021): 1–24. http://dx.doi.org/10.1155/2021/6613033.

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The term metric or distance of a graph plays a vital role in the study to check the structural properties of the networks such as complexity, modularity, centrality, accessibility, connectivity, robustness, clustering, and vulnerability. In particular, various metrics or distance-based dimensions of different kinds of networks are used to resolve the problems in different strata such as in security to find a suitable place for fixing sensors for security purposes. In the field of computer science, metric dimensions are most useful in aspects such as image processing, navigation, pattern recognition, and integer programming problem. Also, metric dimensions play a vital role in the field of chemical engineering, for example, the problem of drug discovery and the formation of different chemical compounds are resolved by means of some suitable metric dimension algorithm. In this paper, we take rotationally symmetric and hexagonal planar networks with all possible faces. We find the sequences of the local fractional metric dimensions of proposed rotationally symmetric and planar networks. Also, we discuss the boundedness of sequences of local fractional metric dimensions. Moreover, we summarize the sequences of local fractional metric dimension by means of their graphs.
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48

AlShahrani, Ibrahim, Ali A. Dawasaz, Sadatullah Syed, Mohammed Ibrahim, and Rafi A. Togoo. "Three-dimensional palatal anatomic characteristics' correlation with dermatoglyphic heterogeneity in Angle malocclusions." Angle Orthodontist 89, no. 4 (March 6, 2019): 643–50. http://dx.doi.org/10.2319/091718-675.1.

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ABSTRACTObjectives:To assess correlation of dermatoglyphic (DG) pattern with quantitative palatal anatomic parameters measured using three-dimensional (3D) scanning of dental casts and to explore the possibility of utilizing these to predict future occurrence of malocclusion.Materials and Methods:Pretreatment casts of 477 Saudi Arabian patients were divided into Class I, II, and III malocclusion groups. Fingerprints were recorded for all hand digits using a digital biometric device. Maxillary arch analysis was accomplished including intercanine, intermolar distance, palatal height, and palatal area. The results were statistically analyzed.Results:The mean surface area of the palate was highest in Class II malocclusion. The DG pattern was not significantly associated with the type of malocclusion, except in the instance of the double loop characteristic (P = .05). There was a strong correlation, however, between DG characteristics like simple arch, loop, and double loop and palatal dimensions (intercanine, intermolar distance, and palatal height). Heterogeneity of DG pattern could be reliably used to predict palatal dimensions. Logistic regression revealed that only tented arch, symmetrical, spiral DG patterns and palatal area were significant but weak predictors of Angle malocclusion (P < .05).Conclusions:A novel correlation of DG pattern with 3D palatal anatomic characteristics was assessed in different Angle malocclusion classes. Few of the DG characteristics and palatal dimensions showed significant correlations. However, only some of these were significant predictors of Angle malocclusion.
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Mi, Gang. "An Analysis of Dimension Roundness of Machine Elements Survey." Applied Mechanics and Materials 419 (October 2013): 489–93. http://dx.doi.org/10.4028/www.scientific.net/amm.419.489.

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Machine element survey is a process by measuring, drawing, analysis, design according to existing elements, finally drawing the formal pattern of the element. The method that the operator used to deduce the original design dimensions based on measured value analysis is called dimension roundness. It includes the measured data processing, defining the basic dimensions, tolerances, limits and fits type. Base on years of teaching, experiment, analyzing and practical producing experiences, I found that the dimension roundness and the presentation or definition of related elements in all textbooks were inexact and unreasonable. It influenced the effectiveness of higher vocational education. This paper analyzed advantages and disadvantages of several dimension roundness methods, and then put forward the innovative practical roundness method. I revised the unconventional design dimension roundness; and pointed out that no matter using what roundness method, result diversity always exists.
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Argaman, N., O. Levy, and G. Makov. "Dislocation pattern formation – simulations of annealing in two dimensions." Le Journal de Physique IV 11, PR5 (September 2001): Pr5–61—Pr5–68. http://dx.doi.org/10.1051/jp4:2001508.

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