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1
Cecconello, Moiseis S., Jefferson Leite, Rodney C. Bassanezi, and Joao de Deus M. Silva. "About Projections of Solutions for Fuzzy Differential Equations." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/184950.
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In this paper we propose the concept offuzzy projectionson subspaces of , obtained from Zadeh's extension of canonical projections in , and we study some of the main properties of such projections. Furthermore, we will review some properties of fuzzy projection solution of fuzzy differential equations. As we will see, the concept of fuzzy projection can be interesting for the graphical representation of fuzzy solutions.
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Nyrtsov, Maxim V., Maria E. Fleis, Michael M. Borisov, and Philip J. Stooke. "Conic projections of the triaxial ellipsoid: the projections for regional mapping of celestial bodies." Proceedings of the ICA 1 (May 16, 2018): 1–3. http://dx.doi.org/10.5194/ica-proc-1-84-2018.
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Different distortion classes of the azimuthal and cylindrical projections of the triaxial ellipsoid have been considered in our previous works. These projections make it possible to construct maps of the celestial bodies in planetary scale. However, for regions in the middle latitudes it is advisable to use a conic projection which was not developed until now. In this investigation we describe the development of three conic projections of a triaxial ellipsoid: a conic projection with true scale along meridians, an equal-area conic projection and a quasi-conformal conic projection. In derivation of the projections we use an elliptical cone tangent to a triaxial ellipsoid. The projections are calculated and maps in these projections are created for the first time.
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KhaIiI Ibrahim Kadhim. "Principal Components Analysis as enhancement Operator and Compression factor." journal of the college of basic education 17, no. 72 (June 17, 2019): 25–33. http://dx.doi.org/10.35950/cbej.v17i72.4495.
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Principal components analysis (PCA) is effective at compressing information in multivariate data sets by computing orthogonal projections that maximize the amount of data variance. Unfortunately, information content in hyper spectral images does not always coincide with such projections. We propose an application of projection pursuit (pp), which seeks to find a set of projections that are "interesting" in the sense that they deviate from the Gaussian distribution assumption.
Once these projections are obtained, they can be used for image compression, segmentation, or enhancement for visual analysis. To find these projections, a two –step iterative process is followed where we first search for a projection that maximizes a projection index based on the information divergence of the projections estimated probability distribution from the Gaussian distribution and then reduce the rank by projections the data on to the subspace orthogonal to the previous projection . To calculate each projections, we use a simplified approach to maximizing the projection index, which does not require optimization algorithm. It searches for a solution by obtaining a set of candidate projections from the data and choosing the one with the highest projection index. The effectiveness of the method is demonstrated through simulated examples as well as data from the hyper spectral digital imagery collection experiment and the spatially enhanced broadband and array spectrograph system.
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Barrenechea, Ana Lucía, and Carlos Peña. "Invariance and normality of projections in the dual of Banach algebras." New Zealand Journal of Mathematics 51 (December 14, 2021): 115–18. http://dx.doi.org/10.53733/132.
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We study the classes of invariant and natural projections in the dual of a Banach algebra $A$. These type of projections are relevant by their connections with the existence problem of bounded approximate identities in closed ideals of Banach algebras. It is known that any invariant projection is a natural projection. In this article we consider the issue of when a natural projection is an invariant projection.
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Wilson, Tom, and Philip Rees. "A brief guide to producing a national population projection." Australian Population Studies 5, no. 1 (May 30, 2021): 77–100. http://dx.doi.org/10.37970/aps.v5i1.84.
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Background There are surprisingly few resources available which offer an introductory guide to preparing a national population projection using a cohort-component model. Many demography textbooks cover projections quite briefly, and many academic papers on projections focus on advanced technical issues.
Aims The aim of this paper is to provide a short and accessible guide to producing a national-scale population projection using the cohort-component model.
Data and methods The paper describes the cohort-component model from a population accounting perspective, presents all the necessary projection calculations, and covers the key steps which form part of the projections preparation process – from gathering input data to validating outputs. An accompanying Excel workbook implements the model and contains example projections for Australia.
Conclusions Calculating a national population projection using a cohort-component model involves fairly simple algebra, but the broader projections preparation process is more complex, and requires careful consideration and judgement.
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Lapaine, Miljenko, and Nedjeljko Frančula. "Polar and Equatorial Aspects of Map Projections?" Proceedings of the ICA 2 (July 10, 2019): 1–6. http://dx.doi.org/10.5194/ica-proc-2-71-2019.
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<p><strong>Abstract.</strong> There is no standard or generally accepted terminology of aspect in the theory of map projections. The term is probably derived from the concept that a graticule is produced by perspective projection of the meridians and parallels on a sphere onto a developable surface. Developable surfaces are widely accepted, and it is almost impossible to find a publication that deals with map projections in general and without developable surfaces story. If found, it usually classifies projections as cylindrical, conical and azimuthal, and applies developable surfaces to define the projection aspect. This paper explains why applying developable surfaces in the interpretation of map projections is not recommended, nor defining the aspect of all projections by the position of a midpoint as polar, equatorial, or oblique. In fact, defining a projection aspect this way is invalid in general, and obscures the fact that the aspect depends on the class to which a particular map projection belongs.</p>
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Lee, Jimmy, Ka Lun Leung, and Yi Wu. "Polynomially Decomposable Global Cost Functions in Weighted Constraint Satisfaction." Proceedings of the AAAI Conference on Artificial Intelligence 26, no. 1 (September 20, 2021): 507–13. http://dx.doi.org/10.1609/aaai.v26i1.8130.
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In maintaining consistencies, such as GAC*, FDGAC* and weak EDGAC*, for global cost functions, Weighted CSP (WCSP) solvers rely on the projection and extension operations, which entail the computation of the cost functions' minima. Tractability of this minimum computation is essential for efficient execution. Since projections/extensions modify the cost functions, an important issue is tractable projection-safety, concerning whether minimum cost computation remains tractable after projections/extensions. In this paper, we prove that tractable projection-safety is always possible for projections/extensions to/from the nullary cost function (W0), and always impossible for projections/extensions to/from n-ary cost functions for n > = 2. When n = 1, the answer is indefinite. We give a simple negative example, while Lee and Leung's flow-based projection-safe cost functions are also tractable projection-safe. We propose polynomially decomposable cost functions, which are amenable to tractable minimum computation. We further prove that the polynomial decomposability property is unaffected by projections/extensionsto/from unary cost functions. Thus, polynomially decomposable cost functions are tractable projection-safe. We show that the SOFT_AMONG, SOFT_REGULAR, SOFT_GRAMMAR and MAX_WEIGHT/MIN_WEIGHT are polynomially decomposable. They are embedded in a WCSP solver for extensive experiments to confirm the feasibility and efficiency of our proposal.
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Borisov, Mirko, Miro Govedarica, and Vladimir Petrovic. "Cartographic conic projections and their appliance in national cartography." Glasnik Srpskog geografskog drustva 91, no. 4 (2011): 183–204. http://dx.doi.org/10.2298/gsgd1104183b.
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This paper is dedicated to the mapping of conic projections and their appliance in producing maps of our state cartography. So far they were often applied, and will be used precisely coned, polyconed and modified polyconed projections for the official mapping (1:500 000, 1:750 000, 1:1000 000 and 1:1500 000). In particular, they cartographic conical projection at a scale of 1:1000 000 were taken into consideration. Those are the Lambert conformal conical projection with two standard parallels and the Modified polyconic projections. In addition to these cartographic conical projections, is described Boneo`s pseudoconic equivalent projections. This is one of the cartographic conical map projection that is commonly used in the preparation of thematic maps as well as for atlas editions of geographic maps both in Serbia and abroad.
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Horiguchi, Kirara, Ayaka Shimizu, Ryohei Watanabe, and Yoshiro Yaguchi. "Axis systems of link projections." Journal of Knot Theory and Its Ramifications 26, no. 08 (March 31, 2017): 1750043. http://dx.doi.org/10.1142/s0218216517500432.
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An axis of a link projection is a closed curve which lies symmetrically on each region of the link projection. In this paper we define axis systems of link projections and characterize axis systems of the standard projections of twist knots.
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Gibbs, Andrew, E. James Pearse, Jennifer A. Sheehan, Kathleen T. Meleady, Hirani Jayasinha, and Neill Jones. "Estimating and projecting subacute care demand: findings from a review of international methods." Australian Health Review 32, no. 4 (2008): 778. http://dx.doi.org/10.1071/ah080778.
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A review of projection methodologies used to project sub-acute inpatient activity in various international health care jurisdictions was undertaken as part of a project to develop subacute inpatient activity projections for the state with the largest population in Australia. The literature search identified nearly 200 articles and found three main groups of projection methodologies: projections with a focus on subacute care; projections with a focus on acute care, but which often included subacute activity in the overall projections; and projections of specific diseases/conditions influencing the demand for subacute care. In terms of the examples in the literature specifically regarding subacute care, the most common method of estimating current or future need was the use of normative benchmark ratios of beds to population. This was mainly to provide a policy basis to encourage development of subacute services, but also because of convenience. In the literature regarding acute activity projection methodologies, many incorporated subacute activity in the overall activity measures of the acute hospital unit. The most common method of acute care activity projection was use of current or trended utilisation rates applied to population projections. It appears that a significant amount of planning and demand projection being undertaken internationally on subacute care takes place within acute care methodologies. In regard to the potential use of specific diseases/ conditions that drive demand for subacute care, such as stroke or cancer, it is suggested that the best use of these disease-specific projections is in reality testing the results of other modelling. A number of conclusions are made and issues highlighted regarding projections of subacute inpatient activity.
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Arablouei, Reza, and Kutluyıl Doğançay. "Affine projection algorithm with selective projections." Signal Processing 92, no. 9 (September 2012): 2253–63. http://dx.doi.org/10.1016/j.sigpro.2012.02.018.
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HELEODORO, RAPHAEL AQUINO. "A new species of Mecomera Audinet-Serville earwig (Dermaptera: Spongiphoridae) from the Brazilian Atlantic Rainforest." Zootaxa 5047, no. 4 (October 1, 2021): 477–83. http://dx.doi.org/10.11646/zootaxa.5047.4.7.
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A new earwig species, Mecomera ze sp. nov. (Spongiphoridae: Sparattinae: Sparattini) from the Brazilian Atlantic Rainforest is described based on males and females from Piracicaba, São Paulo, Brazil. Mecomera ze sp. nov. has a pygidium shape similar to that of M. chacoensis (Borelli), and can be differentiated by the flattened projections of M. ze sp. nov., with emarginations between each projection, whilst in M. chacoensis the pygidium has cylindrical projections, with a single emargination between apical projections. Mecomera ze sp. nov. is also similar to M. reichardti in that both have cerci as long as the abdomen. However, M. reichardti has an inconspicuous basal projection and a more acute conspicuous projection at middle, whilst M. ze sp. nov. has a more conspicuous basal projection and less conspicuous middle projection. Comparisons are made with the male genitalia of all species.
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Ni, Chengcai, and Chunmei Liu. "Evaluating behaviors of factors affecting the site index estimate on the basis of a single stand using simulation approach." Canadian Journal of Forest Research 38, no. 11 (November 2008): 2762–70. http://dx.doi.org/10.1139/x08-095.
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Height observations H1and H2present on the right- and left-hand sides of site index models, respectively. The error terms associated with H1and H2, along with parameter estimate errors, affect the estimate of the site index. Projection error variance (PEV), in a projection from A1to A2, consisted of four components associated with H1, H2, the covariance of H1and H2, and the parameter estimate errors. In this study, behaviors of these components were investigated via simulations on the basis of six equations derived from the Lundqvist–Kerf and the Hossfeld IV functions. Simulation results showed that projection interval, projection direction, and selected site-dependent parameter influenced PEV and its components. PEVs of backward and forward projections with the same projection interval lengths were remarkably different if the underlying model was anamorphic. With increasing projection interval length, the PEV of forward projections monotonically increased to a certain value, whereas the PEV of backward projections decreased to zero after reaching a maximum.
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Fleis, M. E., M. V. Nyrtsov, and A. I. Sokolov. "Cylindrical projections of triaxial ellipsoid: precise formulae and elliptical integrals." Geodesy and Cartography 982, no. 4 (May 20, 2022): 26–38. http://dx.doi.org/10.22389/0016-7126-2022-982-4-26-38.
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Cylindrical projections of a triaxial ellipsoid are used for global mapping the surfaces of celestial bodies, the figures of which the International Astronomical Union recommends to approximate by the mathematical surface of the mentioned geometric body. Its reference surface and projections are not available in GIS packages. In this regard, we are facing the problem of representing projection formulae in finite elementary functions or reducing the integrals included in them to elliptic ones. This will simplify direct and inverse transformations of such map projections for inclusion in GIS software. The authors present formulae for obtaining coordinates for cylindrical projections of a triaxial ellipsoid. Determining the horizontal coordinate for all those projections is reduced to the calculation of an elliptic integral of the second kind, as well as determining the vertical coordinate of a cylindrical projection which preserves lengths along the meridians. To determine that coordinate in an equal-area cylindrical projection, original formulae were obtained that enables representing the corresponding integral in elementary functions. For the vertical coordinate in the cylindrical projection of the meridian section similar formulae deduced in previous studies are presented. The definition of a vertical coordinate in a projection preserving the angle between the meridian and the parallel is reduced to the calculation of elliptic integrals of the first, second, and third kind. Thus, the formulae derived in the article can be used when including cylindrical projections of a triaxial ellipsoid in geoinformation technologies.
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Kerkovits, Krisztián. "Polyazimuthal Map Projections." Kartografija i geoinformacije 18, no. 32 (December 15, 2019): 18–32. http://dx.doi.org/10.32909/kg.18.32.2.
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A polyazimuthal map projection is a mapping that represents parallels as non-concentric full circles on the plane. Polyazimuthal mappings are almost never mentioned in the literature dealing with map projections. However, these projections are flexible; their distortion characteristics are highly mutable. This paper expands the theory of polyazimuthal map projections. Furthermore, this study also shows the derivation for variants of this projection family (e. g. equal-area, orthogonal). The article concludes with some practical applications in the field of low-distortion map projections to demonstrate their advantages.
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Kessler, Fritz. "Map Projection Education in General Cartography Textbooks: A Content Analysis." Cartographic Perspectives, no. 90 (August 16, 2018): 6–30. http://dx.doi.org/10.14714/cp90.1449.
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As developments in the field of map projections occur (e.g., the deriving of a new map projection), it would be reasonable to expect that those developments that are important from a teaching standpoint would be included in cartography textbooks. However, researchers have not examined whether map projection material presented in cartography textbooks is keeping pace with developments in the field and whether that material is important for cartography students to learn. To provide such an assessment, I present the results of a content analysis of projection material discussed in 24 cartography textbooks published during the twentieth and early twenty-first centuries. Results suggest that some material, such as projection properties, was discussed in all textbooks across the study period. Other material, such as methods used to illustrate distortion patterns, and the importance of datums, was either inconsistently presented or rarely mentioned. Comparing recent developments in projections to the results of the content analysis, I offer three recommendations that future cartography textbooks should follow when considering what projection material is important. First, textbooks should discuss the importance that defining a coordinate system has in the digital environment. Second, textbooks should summarize the results from experimental studies that provide insights into how map readers understand projections and how to choose appropriate map projections. Third, textbooks should review the impacts of technology on projections, such as the web Mercator projection, programming languages, and the challenges of projecting raster data.
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Lapaine, М. "Secant Parallels in Azimuthal Projections." Geodesy and Cartography 946, no. 4 (May 20, 2019): 39–54. http://dx.doi.org/10.22389/0016-7126-2019-946-4-39-54.
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Map projections are commonly approached as mapping onto developable surfaces; cylindrical projections onto the lateral surface of a cylinder, conic projections onto the lateral surface of a cone, and azimuthal projections onto a plane. If an intermediate developable surface intersects the Earth’s sphere or ellipsoid, the projection is referred to as a secant projection. The intersection of a developable surface and the Earth’s sphere or ellipsoid, e.g. secant parallel is considered a standard parallel. In this paper the definitions of secant and standard parallel in azimuthal projections are given. The first conclusion is that the secant and standard parallels are two distinct notions. The second one is that a standard parallel, if such a parallel exists in an azimuthal projection, is a secant parallel, while the converse statement is not true in general. Furthermore, it is shown that there are azimuthal projections with only one secant parallel that is not standard, with only one standard parallel which is also secant one, with two different secant parallels, and with one standard and one secant parallel.
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Werschler, T., and F. Nault. "Projecting Interregional Migration Balances within a Multiregional Cohort—Component Framework." Environment and Planning A: Economy and Space 28, no. 5 (May 1996): 769–82. http://dx.doi.org/10.1068/a280769.
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An examination of the projection output derived from fixed-rate and variable-rate interregional migration assumptions reveals the difficulty with which an acceptable range of migration scenarios is developed for use in Canadian population projections. The development of acceptable migration assumptions is limited by the choice of projection methodology, the requirements of projections within the present context, and the demographic characteristics of Canada's regions. In order to overcome these limitations, a technique for controlling projected interregional migration balances within a cohort—component framework is proposed. This approach improves the utility of the interregional projection methodology and meets all the requirements for population projections in the present context.
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Indrati, Rini, Siti Daryati, Dewi Kartikasari, Sri Mulyati, and Marichatul Jannah. "RADIATION DOSE AND ANATOMICAL INFORMATION IN SACRUM BONE EXAMINATION WITH AP AND AXIAL AP PROJECTIONS." Jurnal Riset Kesehatan 10, no. 1 (May 28, 2021): 77–83. http://dx.doi.org/10.31983/jrk.v10i1.6777.
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The projections for the sacrum are axial anteroposterior with the beam 15 degrees toward the cephalad, and axial posteroanterior in the direction of the beam 15 degrees caudally. Some practitioners take steps to examine the sacrum with AP projections in a perpendicular beam direction. Around the sacrum are reproductive organs that are sensitive to radiation, so it is necessary to select the right projection to reduce the radiation dose and show clear anatomical information. This study aims to determine the projection of an examination that produces clear anatomical information at a minimal dose. This is an experimental study with one shot post-test only. Samples in the form of radiographs were obtained from perpendicular AP and axial AP projections assessed by radiologists regarding the clarity of anatomical information. The radiation dose was measured using TLD on the ovaries and gonads. Data were analyzed by t-test and Wilcoxon test with an error level of 5%. The AP axial projection shows better anatomical information than the perpendicular AP projection. The axial AP projection shows a smaller dose of the ovaries and gonads. There is a difference in anatomical information between AP and axial AP projections with a p-value = 0.017. There was a difference in radiation dose between AP and axial AP projections on the right ovary (p-value = 0.002), left ovary (p-value 0.001) and gonads (p-value = 0.008).
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Ball, Vaughn, Luis Tenorio, Christian Schiøtt, Michelle Thomas, and J. P. Blangy. "Three-term amplitude-variation-with-offset projections." GEOPHYSICS 83, no. 5 (September 1, 2018): N51—N65. http://dx.doi.org/10.1190/geo2017-0763.1.
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A three-term (3T) amplitude-variation-with-offset projection is a weighted sum of three elastic reflectivities. Parameterization of the weighting coefficients requires two angle parameters, which we denote by the pair [Formula: see text]. Visualization of this pair is accomplished using a globe-like cartographic representation, in which longitude is [Formula: see text], and latitude is [Formula: see text]. Although the formal extension of existing two-term (2T) projection methods to 3T methods is trivial, practical implementation requires a more comprehensive inversion framework than is required in 2T projections. We distinguish between projections of true elastic reflectivities computed from well logs and reflectivities estimated from seismic data. When elastic reflectivities are computed from well logs, their projection relationships are straightforward, and they are given in a form that depends only on elastic properties. In contrast, projection relationships between reflectivities estimated from seismic may also depend on the maximum angle of incidence and the specific reflectivity inversion method used. Such complications related to projections of seismic-estimated elastic reflectivities are systematized in a 3T projection framework by choosing an unbiased reflectivity triplet as the projection basis. Other biased inversion estimates are then given exactly as 3T projections of the unbiased basis. The 3T projections of elastic reflectivities are connected to Bayesian inversion of other subsurface properties through the statistical notion of Bayesian sufficiency. The triplet of basis reflectivities is computed so that it is Bayes sufficient for all rock properties in the hierarchical seismic rock-physics model; that is, the projection basis contains all information about rock properties that is contained in the original seismic.
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Liu, Qiang, Shao Feng Bian, and Zhong Mei Li. "Comparisons and Direct Transformation Formulae between Azimuthal Conformal and Gnomonic Projections." Advanced Materials Research 1065-1069 (December 2014): 2259–64. http://dx.doi.org/10.4028/www.scientific.net/amr.1065-1069.2259.
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Definitions of azimuthal conformal and gnomonic projections were introduced, and contrastive analyses of graticules shapes between these two projections were conducted. Based on theories of perspective azimuthal projection and space geometrical relationships, transformation between azimuthal conformal and gnomonic projections was carried out through series of derivation. Direct transformation formulae between coordinates of the two projections were established with respect to standard parallel. Finally, correctness and reliability of these formulae were tested and verified by numerical examples. The formulae could be widely used and enrich theories of projection transformation to a certain degree, which would offer reference value for charting in polar regions.
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DA ROCHA, RONALDO DOS SANTOS. "Definição de um Sistema de Projeção Cartográfica para Mapeamento Urbano no Estado do Rio Grande do Sul." Pesquisas em Geociências 23, no. 1-2 (December 31, 1996): 25. http://dx.doi.org/10.22456/1807-9806.21223.
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This work studies the use of map projections in large scale mapping to provide support for a Land Information System. For this purpose, evaluations of the map projections commonly used in France, Switzerland, USA and Brazil are presented. The adequate precision to record property lines in a cadastral survey is identified and then compared to the linear distortions inherent to the map projections used in Brazil. Based upon these discrepancies, an optimum projection was developed to be used in large scale cartography in the State of Rio Grande do SuI. The expressions to transform geographic coordinates into projection coordinates are also presented. Several tests have been performed and the results are portrayed on a comparative chart showing the values of geodectics, plane distance on the UTM projection and plane distance on the above mentioned projection. The identified projection presents linear distortions lower than the established precision for property delimitation, corroborating the validity of its use in a Land Information System.
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HE, YUN, XU CAO, FEI LIU, JIANWEN LUO, and JING BAI. "INFLUENCE OF LIMITED-PROJECTION ON FLUORESCENCE MOLECULAR TOMOGRAPHY." Journal of Innovative Optical Health Sciences 05, no. 03 (July 2012): 1250020. http://dx.doi.org/10.1142/s1793545812500204.
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Challenges remain in imaging fast biological processes in vivo with fluorescence molecular tomography (FMT) due to the long data acquisition time. Data acquisition with limited projections can greatly reduce the time consumption, but the influence of limited-projection on reconstruction quality is currently unclear. Both numerical simulations and a phantom experiment are conducted to analyze this problem. Through a systematic investigation of all the results reconstructed from different numbers of projections, we evaluate the influence of limited-projection data on FMT. A mouse experiment is also performed to validate our work. A general relationship between the number of projections and reconstruction quality is obtained which indicates that the projection number of three is preferred for fast FMT experiment.
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Gomi, Tsutomu, and Yukio Koibuchi. "Use of a Total Variation Minimization Iterative Reconstruction Algorithm to Evaluate Reduced Projections during Digital Breast Tomosynthesis." BioMed Research International 2018 (June 19, 2018): 1–14. http://dx.doi.org/10.1155/2018/5239082.
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Purpose. We evaluated the efficacies of the adaptive steepest descent projection onto convex sets (ASD-POCS), simultaneous algebraic reconstruction technique (SART), filtered back projection (FBP), and maximum likelihood expectation maximization (MLEM) total variation minimization iterative algorithms for reducing exposure doses during digital breast tomosynthesis for reduced projections. Methods. Reconstructions were evaluated using normal (15 projections) and half (i.e., thinned-out normal) projections (seven projections). The algorithms were assessed by determining the full width at half-maximum (FWHM), and the BR3D Phantom was used to evaluate the contrast-to-noise ratio (CNR) for the in-focus plane. A mean similarity measure of structural similarity (MSSIM) was also used to identify the preservation of contrast in clinical cases. Results. Spatial resolution tended to deteriorate in ASD-POCS algorithm reconstructions involving a reduced number of projections. However, the microcalcification size did not affect the rate of FWHM change. The ASD-POCS algorithm yielded a high CNR independently of the simulated mass lesion size and projection number. The ASD-POCS algorithm yielded a high MSSIM in reconstructions from reduced numbers of projections. Conclusions. The ASD-POCS algorithm can preserve contrast despite a reduced number of projections and could therefore be used to reduce radiation doses.
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Read, E. B., H. H. Okamura, and D. G. Drubin. "Actin- and tubulin-dependent functions during Saccharomyces cerevisiae mating projection formation." Molecular Biology of the Cell 3, no. 4 (April 1992): 429–44. http://dx.doi.org/10.1091/mbc.3.4.429.
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Several conditional-lethal mutant alleles of the single-copy Saccharomyces cerevisiae beta-tubulin and actin genes were used to evaluate the roles of microtubules and actin filaments in the pheromone-induced extension of mating projections. Mutants defective in tubulin assembly form projections indistinguishable in appearance from those formed by wild-type cells. However, the tubulin mutants are unable to move their nuclei into the projections and to orient the spindle pole body associated with each nucleus toward the projection tip. Actin mutants are defective in spatial orientation of cell-surface growth required for formation of normal mating projections. Migration of nuclei into mating projections and Spa2p segregation to projection tips are also defective in actin mutants. Studies with abp1 null mutants showed that the function of the Abp1p actin-binding protein is either not required for projection formation or there are other proteins in yeast with similar functions. Our findings demonstrate that actin is required to restrict cell-surface growth to a defined region for pheromone-induced morphogenesis and suggest that nuclear position and orientation in mating projections depend on direct or indirect interaction of microtubules with actin filaments.
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Panigrahi, Narayan, and Cyan Subhra Mishra. "A Generic Method for Azimuthal Map Projection." Defence Science Journal 65, no. 5 (September 11, 2015): 390. http://dx.doi.org/10.14429/dsj.65.8598.
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Map projections are mathematical methods for projecting spherical coordinates in the form of (φ, λ) to the map coordinates in the form of (X,Y) in Cartesian reference frame. Numerous methods for map projection have been derived and are being used for preparation of cartographic products. These map projections take into account specific position of the viewer on the datum surface for derivation of the map projections. A generic method for azimuthal map projection where the position of the viewer can be taken at an arbitrary point on the datum surface is derived. Using this generic method all the specific azimuthal map projections can be derived.
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Raymer, James, Nicholas Biddle, and Qing Guan. "A multiregional sources of growth model for school enrolment projections." Australian Population Studies 1, no. 1 (November 19, 2017): 26–40. http://dx.doi.org/10.37970/aps.v1i1.10.
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Background: Education planning requires accurate and efficient projection models. Current projection models either do not make use of all available information and are reliant on idiosyncratic expert judgement, or are too complex to be maintained and explained.
Aims: To test whether a multiregional projection model performs better than current methodology in explaining and projecting school enrolments in a school system with student mobility.
Data and methods: A multiregional cohort model was developed for projecting enrolments for multiple schools or districts simultaneously. For illustration, data were obtained for all government schools in the Australian Capital Territory (ACT) for the years 2008–2016. Multiregional projections were compared with a cohort transition model and the ACT Education Directorate’s own projections.
Results: (i) There is great diversity in the sources of school enrolment growth that need to be accommodated in enrolment projections; and (ii) multiregional projections perform slightly better than traditional methods with less effort and more transparency.
Conclusion: A sources of growth approach guides the understanding of enrolment change, which is critical for making informed projections.
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Strebe, Daniel. "Given the problem of projection, are heat maps an oxymoron?" Abstracts of the ICA 1 (July 15, 2019): 1–2. http://dx.doi.org/10.5194/ica-abs-1-352-2019.
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<p><strong>Abstract.</strong> With the proliferation of data analysis and visualization tools, we see more and more heat maps. But should we? Are such displays meaningful? At large scales, heat maps need not be controversial (though common tools can blight even simple cases). But what about small-scale maps? Is anyone thinking about the effects of projection on heat maps? How do map projections change the semantics of heat maps? What projections permit meaningful heat maps? How should heat maps be calculated in the presence of a map projection? We explore these problems and questions in this presentation to offer critique and advice.</p><p>For the purposes of this discussion, a heat map is a representation of the density or magnitude of a spatial phenomenon on two dimensions, treating the density or magnitude as a continuous measure whether or not the underlying phenomenon is continuous. If the data are too sparse in the presentation space, then the fiction of continuity ought to be avoided; a heat map would not be an appropriate visualization. While real world examples of heat maps that violate this principle are easy to find, we take the principle for granted and do not elaborate further here.</p><p>Unfortunately, there are several other ways to construct ineffective heat maps. One of the primary offenses is to ignore the effect of map projection on the presentation of density. It should be clear that a projection whose area measure varies widely across the presentation space necessarily distorts density. If the heat map is a presentation of density &ndash; which most are &ndash; then poor choice of projection would contradict the purpose of a heat map. The result would be a blatant fiction. Surprisingly, the Mercator projection often can be found in small scale heat maps, for the reason that the projection is common, is the default in many sets of tooling, and is sometimes the only projection available with the set of map construction tools. And yet, as far as density variation goes, a worse case than Mercator cannot be found among common projections.</p><p>Even if density remains constant across the map, a poor heat map could be generated if the analysis for the heat map mixes phenomenon space, which is geographic, with projected space, which is not. Common tools commit this fallacy. The result is that a phenomenon whose density diminishes radially (for example) from a hot point might show as concentric circles of decreasing intensity on the projected map, whereas we would expect elongations of the heat field in accordance with the projection’s distortion metric.</p><p>We conclude that, while it is possible to construct responsible heat maps of geographic data, there are several pitfalls. Among these pitfalls, we find that common tools conspire to assist in the presentation of fiction instead of fact.</p>
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Marois, Guillaume, Patrick Sabourin, and Alain Bélanger. "Forecasting human capital of EU member countries accounting for sociocultural determinants." Journal of Demographic Economics 85, no. 3 (August 22, 2019): 231–69. http://dx.doi.org/10.1017/dem.2019.4.
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AbstractInclusion of additional dimensions to population projections can lead to an improvement in the overall quality of the projections and to an enhanced analytical potential of derived projections such as literacy skills and labor force participation. This paper describes the modeling of educational attainment of a microsimulation projection model of the European Union countries. Using ordered logistic regressions on five waves of the European Social Survey, we estimate the impact of mother's education and other sociocultural characteristics on educational attainment and implement them into the microsimulation model. Results of the different projection scenarios are contrasted to understand how the education of the mother and sociocultural variables may affect projection outcomes. We show that a change in the impact of mother's education on children's educational attainment may have a big effect on future trends. Moreover, the proposed approach yields more consistent population projection outputs for specific subpopulations.
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Lapaine, Miljenko, and Nedjeljko Frančula. "Web Mercator Projection – One of Cylindrical Projections of an Ellipsoid to a Plane." Kartografija i geoinformacije 20, no. 35 (June 30, 2021): 30–47. http://dx.doi.org/10.32909/kg.20.35.2.
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The Web Mercator projection is a projection of a relatively recent date. There has been a lot of controversy about its application. Some believe that this projection is not a projection of either the sphere or the surface of the ellipsoid. Therefore, in this paper, several projections of the surface of a rotational ellipsoid into a plane are investigated and it is shown that the Web Mercator projection is one of such projections. Namely, although the equations of this projection are identical to the equations for the projection of the sphere, the basic difference is in the choice of the area of definition, i.e., the domain of the projection. Furthermore, we have shown that the Web Mercator projection can also be interpreted as double mapping: mapping an ellipsoid to a sphere according to the normals and then mapping the sphere to the plane according to the formulas of the Mercator projection for the sphere. The Web Mercator projection is not a conformal projection, but it is close in properties to the Mercator projection.
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Li, Yuan, Jiajia Niu, and Xiao-Ming Xu. "The minus order for projections." Filomat 35, no. 8 (2021): 2761–74. http://dx.doi.org/10.2298/fil2108761l.
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Let B(H)Id be the set of all projections on a Hilbert space H. The necessary and sufficient conditions are presented for the existence of the supremum, as well as the infimum, of two arbitrary projections in B(H)Id with respect to the minus order ?. For a projection Q in B(H)Id; the properties of the sets {P : P is an orthogonal projection on H and Q ? P} and {P : P is an orthogonal projection on H and P ? Q} are further explored.
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Tejada, Eduardo, Rosane Minghim, and Luis Gustavo Nonato. "On Improved Projection Techniques to Support Visual Exploration of Multi-Dimensional Data Sets." Information Visualization 2, no. 4 (December 2003): 218–31. http://dx.doi.org/10.1057/palgrave.ivs.9500054.
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Projection (or dimensionality reduction) techniques have been used as a means to handling the growing dimensionality of data sets as well as providing a way to visualize information coded into point relationships. Their role is essential in data interpretation and simultaneous use of different projections and their visualizations improve data understanding and increase the level of confidence in the result. For that purpose, projections should be fast to allow multiple views of the same data set. In this work we present a novel fast technique for projecting multi-dimensional data sets into bidimensional (2D) spaces that preserves neighborhood relationships. Additionally, a new technique for improving 2D projections from multi-dimensional data is presented, that helps reduce the inherent loss of information yielded by dimensionality reduction. The results are stimulating and are presented in the form of comparative visualizations against known and new 2D projection techniques. Based on the projection improvement approach presented here, a new metric for quality of projection is also given, that matches well the visual perception of quality. We discuss the implication of using improved projections in visual exploration of large data sets and the role of interaction in visualization of projected subspaces.
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Jenny, Bernhard, Tom Patterson, and Lorenz Hurni. "Flex Projector–Interactive Software for Designing World Map Projections." Cartographic Perspectives, no. 59 (March 1, 2008): 12–27. http://dx.doi.org/10.14714/cp59.245.
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Flex Projector is a free, open-source, and cross-platform software application that allows cartographers to interactively design custom projections for small-scale world maps. It specializes in cylindrical, and pseudocylindrical projections, as well as polyconical projections with curved parallels. Giving meridians non-uniform spacing is an option for all classes of projections. The interface of Flex Projector enables cartographers to shape the projection graticule, and provides visual and numerical feedback to judge its distortion properties. The intended users of Flex Projector are those without specialized mathematical expertise, including practicing mapmakers and cartography students. The pages that follow discuss why the authors developed Flex Projector, give an overview of its features, and introduce two new map projections created by the authors with this new software: the A4 and the Natural Earth projection.
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Dunstan, Kim, and Christopher Ball. "Demographic Projections: User and Producer Experiences of Adopting a Stochastic Approach." Journal of Official Statistics 32, no. 4 (December 1, 2016): 947–62. http://dx.doi.org/10.1515/jos-2016-0050.
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Abstract Statistics New Zealand is one of the few national statistical agencies to have applied a stochastic (probabilistic) approach to official demographic projections. This article discusses the experience and benefits of adopting this new approach, including the perspective of a key user of projections, the New Zealand Treasury. Our experience is that the change is less difficult to make than might be expected. Uncertainty in the different projection inputs (components) can be modelled simply or with more complexity, and progressively applied to different projection types. This means that not all the different demographic projections an agency produces need to adopt a stochastic approach simultaneously. At the same time, users of the projections are keen to better understand the relative certainty and uncertainty of projected outcomes, given the important uses of projections.
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Pędzich, Paweł. "Image of the World on polyhedral maps and globes." Polish Cartographical Review 48, no. 4 (December 1, 2016): 197–210. http://dx.doi.org/10.1515/pcr-2016-0014.
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Abstract Application of polyhedrons as image surface in cartographic projections has a tradition of more than 200 years. The first maps relying on polyhedrons appeared in the 19th century. One of the first maps which based on an original polyhedral projection using a regular octahedron was constructed by the Californian architect Bernard Cahill in 1909. Other well known polyhedral projections and maps included Buckminster Fuller’s projection and map into icosahedron from 1954 and S. Waterman’s projection into truncated octahedron from 1996, which resulted in the “butterfly” map. Polyhedrons as image surface have the advantage of allowing a continuous image of continents of the Earth with low projection distortion. Such maps can be used for many purposes, such as presentation of tectonic plates or geographic discoveries. The article presents most well known polyhedral maps, describes cartographic projections applied in their preparation, as well as contemporary examples of polyhedral maps. The method of preparation of a polyhedral map and a virtual polyhedral globe is also presented.
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Liu, Weiping, Jennifer Fung, Craig Abbey, John W. Sedat, and David A. Agard. "Automatic/interactive bead alignment in electron tomographic image processing." Proceedings, annual meeting, Electron Microscopy Society of America 52 (1994): 932–33. http://dx.doi.org/10.1017/s0424820100172395.
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In the electron tomographic (EM) reconstruction process the mutual alignment between projections of different view angles is a crucial step. The routinely used alignment method is based on fiducial markers': a single-axis tilt projection series is collected with gold particles distributed on the specimen, the positions of high density gold beads on the projections are found, and the relationship between the specimen and the digital projection coordinate systems is determined from least-square fitting these found bead positions. There are four alignment parameters for each projection: two in shifts, one in in-plane rotation, and one in magnification. In the threedimensional studies of subcellular biological structures, we routinely collect data sets of more than 100 projections in the tilt range of ±75 ° with our automated EM set-up. Normally around 10 bead positions are used on each projection to achieve the alignment. Bead alignment used to be a laborious task since approximately 1000 bead positions need to be hand-picked for each data set.
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Ene, Alina, Huy L. Nguyen, and Adrian Vladu. "Projection-Free Bandit Optimization with Privacy Guarantees." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 8 (May 18, 2021): 7322–30. http://dx.doi.org/10.1609/aaai.v35i8.16899.
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We design differentially private algorithms for the bandit convex optimization problem in the projection-free setting. This setting is important whenever the decision set has a complex geometry, and access to it is done efficiently only through a linear optimization oracle, hence Euclidean projections are unavailable (e.g. matroid polytope, submodular base polytope). This is the first differentially-private algorithm for projection-free bandit optimization, and in fact our bound matches the best known non-private projection-free algorithm and the best known private algorithm, even for the weaker setting when projections are available.
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Rivard, Denis, and Malcolm G. Foy. "An Analysis of Errors in Catch Projections for Canadian Atlantic Fish Stocks." Canadian Journal of Fisheries and Aquatic Sciences 44, no. 5 (May 1, 1987): 967–81. http://dx.doi.org/10.1139/f87-115.
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Two techniques were used to identify and evaluate the components of error inherent in the catch projection method used in the assessment of Canadian Atlantic fish stocks. Firstly, a retrospective analysis was used to evaluate, for the projections made in 1979 and 1981, the impact of the actual error made in input variables such as catch-at-age, mean weight-at-age, recruitment, and stock size. Secondly, the variance of projections was estimated from the variance of input variables. From the retrospective analysis, the principal causes of error in catch projections were identified as the estimation of stock size, as well as the estimation and forecast of fishing mortalities for the projection years. The difference between actual catch and assumed catch for the first year of a 2-yr projection did not appear to be a major source of bias for catch projections. The coefficients of variation of the catch projected at F0.1 were estimated as follows: 15–20% for the projections of Atlantic cod (Gadus morhua) catches; 25–50% for those of haddock (Melanogrammus aeglefinus); 28% for those of pollock (Pollachius virens); 16% for those of redfish (Sebastes sp.); and 35–42% for those of herring (Clupea harengus). The uncertainties associated with abundance estimates for prerecruited age-groups and estimates of stock size emerged as key factors in the projections. Also important was the effect of uncertainties associated with the forecast of reference fishing mortalities (partial recruitment coefficients × F0.1) for the projection period, e.g. uncertainties resulting from changes in fish catchability, in fleet behavior, and in fishing patterns.
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Ledermann, Florian. "Classifying Cartographic Projections Based on Dynamic Analysis of Program Code." Abstracts of the ICA 2 (October 9, 2020): 1. http://dx.doi.org/10.5194/ica-abs-2-38-2020.
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Abstract. Analyzing a given map to identify its projection and other geometrical properties has long been an important aspect of cartographic analysis. If explicit information about the projection used in a particular map is not available, the properties of the cartographic transformation can sometimes be reconstructed from the map image. However, such a process of projection analysis requires significant manual labor and oversight.For digital maps, we usually expect the projection from geographic space to map space to have been calculated by a computer program. Such a program can be expected to contain the implementation of the mathematical rules of the projection and subsequent coordinate transformations such as translation and scaling. The program code, therefore, contains information that would allow an analyst to reliably identify map projections and other geometrical transformations applied to the input data.In the case of interactive online maps, the code generating the map is in fact delivered to the map user and could be used for cartographic analysis. The core idea of our novel method proposed for map analysis is to apply reverse engineering techniques on the code implementing the cartographic transformations in order to retrieve the properties of the applied map projection. However, automatic reasoning about computer code by way of static analysis (analyzing the source code without running it) is provably limited – for example, the code delivered to the map user may contain a whole library of different map projections, of which only a specific one may be actually used at runtime. Instead, we propose a dynamic analysis approach to observe and monitor the operations performed by the code as the program runs, and to retrieve the mathematical operations that have been used to calculate the coordinates of every graphical element on the map.The presented method produces, for every graphical element of the map, a transformation graph consisting of low-level mathematical operations. Cartographic projections can be identified as distinctive patterns in the transformation graph, and can be distinguished in a fully automatic way by matching a set of predefined patterns against a particular graph.Projections vary widely in their arithmetic structure, and therefore by the structure of the corresponding transformation graphs extracted from program code. Some projections can be computed directly using continuous equations involving trigonometric functions. Other projections involve solving nonlinear equations, which need to be solved by approximation. Composite projections use different projections depending on some threshold value. Yet other projections, such as the Robinson projection, define a table of predefined values, between which interpolation is used etc.. In each of these cases, we expect to find the operations corresponding to the mathematical structure of the projection in the transformation graph extracted by the presented method.For verifying the method, we have implemented the patterns of several well-known cartographic projections based on the literature and have used it on the transformation graphs extracted from a variety of sample programs. To ensure a diversity of implementations, we have evaluated programs using different and independent JavaScript implementations of projections, including the open source libraries D3.js, proj4js, Leaflet, OpenLayers, and informal implementations of example programs found online. For these case studies, we could successfully identify many projections based on identifying patterns in the transformation graph in a fully automated, unsupervised manner.In the future, the proposed method may be further developed for many innovative application scenarios, such as building a “cartographic search engine” or constructing novel tools for semi-automatic cartographic analysis and review.
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Arroyo Ohori, Ken, Hugo Ledoux, and Jantien Stoter. "Visualising higher-dimensional space-time and space-scale objects as projections to ℝ3." PeerJ Computer Science 3 (July 3, 2017): e123. http://dx.doi.org/10.7717/peerj-cs.123.
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Objects of more than three dimensions can be used to model geographic phenomena that occur in space, time and scale. For instance, a single 4D object can be used to represent the changes in a 3D object’s shape across time or all its optimal representations at various levels of detail. In this paper, we look at how such higher-dimensional space-time and space-scale objects can be visualised as projections from ℝ4to ℝ3. We present three projections that we believe are particularly intuitive for this purpose: (i) a simple ‘long axis’ projection that puts 3D objects side by side; (ii) the well-known orthographic and perspective projections; and (iii) a projection to a 3-sphere (S3) followed by a stereographic projection to ℝ3, which results in an inwards-outwards fourth axis. Our focus is in using these projections from ℝ4to ℝ3, but they are formulated from ℝnto ℝn−1so as to be easily extensible and to incorporate other non-spatial characteristics. We present a prototype interactive visualiser that applies these projections from 4D to 3D in real-time using the programmable pipeline and compute shaders of the Metal graphics API.
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Heitzler, Magnus, Hans-Rudolf Bär, Roland Schenkel, and Lorenz Hurni. "The Light Source Metaphor Revisited—Bringing an Old Concept for Teaching Map Projections to the Modern Web." ISPRS International Journal of Geo-Information 8, no. 4 (March 28, 2019): 162. http://dx.doi.org/10.3390/ijgi8040162.
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Map projections are one of the foundations of geographic information science and cartography. An understanding of the different projection variants and properties is critical when creating maps or carrying out geospatial analyses. The common way of teaching map projections in text books makes use of the light source (or light bulb) metaphor, which draws a comparison between the construction of a map projection and the way light rays travel from the light source to the projection surface. Although conceptually plausible, such explanations were created for the static instructions in textbooks. Modern web technologies may provide a more comprehensive learning experience by allowing the student to interactively explore (in guided or unguided mode) the way map projections can be constructed following the light source metaphor. The implementation of this approach, however, is not trivial as it requires detailed knowledge of map projections and computer graphics. Therefore, this paper describes the underlying computational methods and presents a prototype as an example of how this concept can be applied in practice. The prototype will be integrated into the Geographic Information Technology Training Alliance (GITTA) platform to complement the lesson on map projections.
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Bickel, Peter J., Gil Kur, and Boaz Nadler. "Projection pursuit in high dimensions." Proceedings of the National Academy of Sciences 115, no. 37 (August 27, 2018): 9151–56. http://dx.doi.org/10.1073/pnas.1801177115.
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Projection pursuit is a classical exploratory data analysis method to detect interesting low-dimensional structures in multivariate data. Originally, projection pursuit was applied mostly to data of moderately low dimension. Motivated by contemporary applications, we here study its properties in high-dimensional settings. Specifically, we analyze the asymptotic properties of projection pursuit on structureless multivariate Gaussian data with an identity covariance, as both dimension p and sample size n tend to infinity, with p/n→γ∈[0,∞]. Our main results are that (i) if γ=∞, then there exist projections whose corresponding empirical cumulative distribution function can approximate any arbitrary distribution; and (ii) if γ∈(0,∞), not all limiting distributions are possible. However, depending on the value of γ, various non-Gaussian distributions may still be approximated. In contrast, if we restrict to sparse projections, involving only a few of the p variables, then asymptotically all empirical cumulative distribution functions are Gaussian. And (iii) if γ=0, then asymptotically all projections are Gaussian. Some of these results extend to mean-centered sub-Gaussian data and to projections into k dimensions. Hence, in the “small n, large p” setting, unless sparsity is enforced, and regardless of the chosen projection index, projection pursuit may detect an apparent structure that has no statistical significance. Furthermore, our work reveals fundamental limitations on the ability to detect non-Gaussian signals in high-dimensional data, in particular through independent component analysis and related non-Gaussian component analysis.
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Wilson, Tom. "Forecast Accuracy and Uncertainty of Australian Bureau of Statistics State and Territory Population Projections." International Journal of Population Research 2012 (November 8, 2012): 1–16. http://dx.doi.org/10.1155/2012/419824.
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Errors from past rounds of population projections can provide both diagnostic information to improve future projections as well as information for users on the likely uncertainty of current projections. This paper assesses the forecast accuracy of official Australian Bureau of Statistics (ABS) population projections for the states and territories of Australia and is the first major study to do so. For the states and territories, it is found that, after 10-year projection durations, absolute percentage errors lie between about 1% and 3% for the states and around 6% for the territories. Age-specific population projections are also assessed. It is shown that net interstate migration and net overseas migration are the demographic components of change which contributed most to forecast error. The paper also compares ABS projections of total population against simple linear extrapolation, finding that, overall, ABS projections just outperformed extrapolation. No identifiable trend in accuracy over time is detected. Under the assumption of temporal stability in the magnitude of error, empirical prediction intervals are created from past errors and applied to the current set of ABS projections. The paper concludes with a few ideas for future projection rounds.
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Ábrahámová, Andrea, and Margita Vajsáblová. "A Comparison of Variational Projection and Cartographic Projection by Ritz’s Method." Slovak Journal of Civil Engineering 30, no. 2 (June 1, 2022): 22–29. http://dx.doi.org/10.2478/sjce-2022-0011.
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Abstract The application of alternative mathematical methods in creating cartographic projections is an interesting factor, which affects the optimization of distortions and their distribution in the projected territory. This article presents the methodology for the creation and comparison of conformal cartographic projections formed by alternative mathematical methods of minimizing the integral criterion for scale distortion in Slovakia. The creation of the variational projection is based on the Airy-Kavraiskii criterion of evaluating the projection on the displayed area by solving Laplace's equation. The second projection is created by solving Poisson's equation using Ritz's method. Our analysis showed that the variational projection of Slovakia achieves more satisfactory distortion values than the cartographic projection created using Ritz's method. The advantage of Ritz's method is that it is possible to choose a boundary condition for a predefined undistorted convex closed curve. In this paper, we have also derived specific members of the map equations for cartographic projection based on solving Poisson's equation by Ritz's method.
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Paweł, Pędzich. "Conformal projections of a tri-axial ellipsoid based on isometric coordinates: history, methodology, and examples." Polish Cartographical Review 54, no. 1 (January 1, 2022): 35–53. http://dx.doi.org/10.2478/pcr-2022-0004.
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Abstract The paper presents a review of the conformal projections of a tri-axial ellipsoid and the methodology of creating these projections with the use of isometric coordinates. The concept is very simple and has been known for a long time; if isometric coordinates are introduced on the surface of the original and on the plane of the image, then any analytical function of the complex variable, i.e. a function that has a continuous derivative, creates a conformal projection. The introduction presents the history of conformal projections. Then, existing projections are presented, including the Bugayevskiy projection and several projections developed by the author that apply selected functions of the complex variable. Scripts were prepared in the Octave software with the use of the presented methodology. Programming in Octave offers a possibility of a simple implementation of complex variable functions, which is also briefly discussed in the paper. The developed scripts were then used to perform calculations and to draw cartographic grids and distortion isolines in the selected conformal projections. The test object was the tri-axial ellipsoid that represents Phobos.
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Tian, Zonglin, Xiaorui Zhai, Gijs van Steenpaal, Lingyun Yu, Evanthia Dimara, Mateus Espadoto, and Alexandru Telea. "Quantitative and Qualitative Comparison of 2D and 3D Projection Techniques for High-Dimensional Data." Information 12, no. 6 (June 3, 2021): 239. http://dx.doi.org/10.3390/info12060239.
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Projections are well-known techniques that help the visual exploration of high-dimensional data by creating depictions thereof in a low-dimensional space. While projections that target the 2D space have been studied in detail both quantitatively and qualitatively, 3D projections are far less well understood, with authors arguing both for and against the added-value of a third visual dimension. We fill this gap by first presenting a quantitative study that compares 2D and 3D projections along a rich selection of datasets, projection techniques, and quality metrics. To refine these insights, we conduct a qualitative study that compares the preference of users in exploring high-dimensional data using 2D vs. 3D projections, both without and with visual explanations. Our quantitative and qualitative findings indicate that, in general, 3D projections bring only limited added-value atop of the one provided by their 2D counterparts. However, certain 3D projection techniques can show more structure than their 2D counterparts, and can stimulate users to further exploration. All our datasets, source code, and measurements are made public for ease of replication and extension.
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Syuhada, Fahmi, Rarasmaya Indraswari, Agus Zainal Arifin, and Dini Adni Navastara. "Multi-Projection Segmentation on Dental Cone Beam Computed Tomography Images Using Level Set Method." Journal of Computer Science and Informatics Engineering (J-Cosine) 5, no. 2 (December 28, 2021): 130–39. http://dx.doi.org/10.29303/jcosine.v5i2.413.
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Segmentation of dental Cone-beam computed tomography (CBCT) images based on Boundary Tracking has been widely used in recent decades. Generally, the process only uses axial projection data of CBCT where the slices image that representing the tip of the tooth object have decreased in contrast which impact to difficult to distinguish with background or other elements. In this paper we propose the multi-projection segmentation method by combining the level set segmentation result on three projections to detect the tooth object more optimally. Multiprojection is performed by decomposing CBCT data which produces three projections called axial, sagittal and coronal projections. Then, the segmentation based on the set level method is implemented on the slices image in the three projections. The results of the three projections are combined to get the final result of this method. This proposed method obtains evaluation results of accuracy, sensitivity, specificity with values of 97.18%, 88.62%, and 97.61%, respectively.
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Walters, S. "Decomposable projections related to the Fourier and flip automorphisms." MATHEMATICA SCANDINAVICA 107, no. 2 (December 1, 2010): 174. http://dx.doi.org/10.7146/math.scand.a-15150.
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In this paper we classify Fourier invariant projections $g$ in the irrational rotation $C^*$-algebra that can be decomposed in the form 26741 g = f + \sigma(f) + \sigma^2(f) + \sigma^3(f) 26741 for some Fourier orthogonal projection $f$, where $\sigma$ is the Fourier transform automorphism. The analogous result is shown for the flip automorphism as well as the existence of flip-orthogonal projections. Both classifications are achieved by means of topological invariants (given by unbounded traces) and the canonical trace. We also show (in both the flip and Fourier cases) that invariant projections $h$ are subprojections of orthogonal decompositions $g$ for some projection $f$ such that $\tau(f) = \tau(h)$ (where $\tau$ is the canonical trace).
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LIM, JACQUELINE HUI CHERN, BIN ABDUL RAHIM AZMAN, ICHIRO TAKEUCHI, and BIN HAJI ROSS OTHMAN. "Pseudaeginella telukrimau sp. n., a new species of caprellid (Crustacea: Amphipoda) from Malaysia." Zootaxa 4282, no. 1 (June 23, 2017): 62. http://dx.doi.org/10.11646/zootaxa.4282.1.3.
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A new species of caprellid, Pseudaeginella telukrimau (Amphipoda: Senticaudata: Caprellidae) was discovered from Pulau Besar, Johor in Malaysia. This species was collected from a coral reef off Teluk Rimau. Species of Pseudaeginella are unique in terms of a very small/sometimes absent mandibular molar and the numerous projections on its pereonites. Pseudaeginella telukrimau is distinguishable by its paired mid-dorsal projections on pereonites 2 to 5, 1 ventrodistal triangular projection on pereonite 4, and gnathopod 2 ischium with 1 large trapezoid projection.
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García-Núñez, José María. "On the left periphery of Spanish indirect interrogatives." Probus 32, no. 1 (April 28, 2020): 55–92. http://dx.doi.org/10.1515/probus-2019-0005.
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AbstractSpanish doubly filled complementizer (DFComp) clauses differ from plain embedded questions in a number of respects (availability of discourse-related projections, islandhood, sequence of tenses, licensing of discourse particles). I argue that the contrast is caused by the presence in the left periphery of these clauses of an illocutionary projection (Haegeman 2004, 2006; Coniglio and Zegrean 2012; Woods 2016b) between the leftmost projection, here identified as Haegeman’s (2004) SubP, and the criterial interrogative projections (InterP and QembP). This illocutionary projection prevents syncretism of the clause-typing and the criterial projections, the default option in plain embedded clauses. This not only explains the range of structural phenomena differentiating DFComp clauses and embedded questions, but also a key semantic property of the former, namely their speech-act denotation. Finally, DFComp clauses are compared with plain embedded questions displaying root behavior under first-person matrix subjects and with English inverted embedded questions. Both are shown to pose minimal variants of the structural pattern proposed for DFComp clauses.