Search

In this paper, we first define the pseudo-circular evolute of a lightcone framed curve in the Lorentz–Minkowski 3-space, and show that the pseudo-circular evolute of a lightcone framed curve can be seen as a generalization of the circular evolute of a framed curve without type changing. We also define an involute of a lightcone framed curve, and study the duality relations between involutes and pseudo-circular evolutes. Moreover, we study the pseudo-circular evolutes and involutes with respect to a lightcone circle frame, and investigate the relationship with respect to a projection map. Meanwhile, examples are given for explaining the objects we investigated, which also show a certain physical significance of our investigation. [ABSTRACT FROM AUTHOR]

This article develops the theory of the conformal mapping of the surface of constant height above the ellipsoid (ChS), which has implications for the design of low-distortion projections. This paper gives a development of the Mercator, polar stereographic, Lambert conformal conic (LCC) and transverse Mercator (TM) projections based on the ChS, a better Earth model than the reference ellipsoid (RE) for positions at height. This article provides new formulas for the LCC and TM inverse scale problems – when given a value for the local scale function, where does it occur? These formulas apply to both traditional mapping on the RE and novel mapping on the ChS. [ABSTRACT FROM AUTHOR]

We investigate weighted Lebesgue space estimates for the Bergman projection on a simply connected planar domain via the domain's Riemann map. We extend the bounds which follow from a standard change-of-variable argument in two ways. First, we provide a regularity condition on the Riemann map, which turns out to be necessary in the case of uniform domains, in order to obtain the full range of weighted estimates for the Bergman projection for weights in a Békollè-Bonami-type class. Second, by slightly strengthening our condition on the Riemann map, we obtain the weighted weak-type (1,1) estimate as well. Our proofs draw on techniques from both conformal mapping and dyadic harmonic analysis. [ABSTRACT FROM AUTHOR]

The aim of this paper is to give expressions for modular linear differential operators (MLDOs) of any order. In particular, we show that they can all be described in terms of Rankin-Cohen brackets and a modified Rankin-Cohen bracket found by Kaneko and Koike. We also give more uniform descriptions of MLDOs in terms of canonically defined higher Serre derivatives and an extension of Rankin-Cohen brackets, as well as in terms of quasimodular forms and almost holomorphic modular forms. The last of these descriptions involves the holomorphic projection map. The paper also includes some general results on the theory of quasimodular forms on both cocompact and non-cocompact subgroups of SL_2(\mathbb {R}), as well as a slight sharpening of a theorem of Martin and Royer on Rankin-Cohen brackets of quasimodular forms. [ABSTRACT FROM AUTHOR]

The paper theorises how a place can influence the emergence and evolution of an exchange field. Specifically, we examine the Society for Arts and Technology building in Montreal, focusing on its geographical location, material form, and meanings as their adaptations over time. Our findings identify three types of influence that the SAT building has on the field of projection mapping: supporting the community, fostering interorganisational relationships, and catalysing innovation. These influences manifest in distinct ways depending on the field's evolution phase. We contribute to the literature on field configuration by developing the concept of the field-configuring place and distinguishing it from the established concept of the field-configuring event. Additionally, we extend the institutional dynamics literature by showing how a place can support the configuration of a field from its emergence, based on its characteristics that can be adapted while providing stability. This study thus underlines the cross-fertilisation between the literature on field configuration and that on places. [ABSTRACT FROM AUTHOR]

Paleogeography is the merger of sediment and volcanic facies, depositional settings, tectonic plate movements, topography, climate patterns and ecosystems through time. The construction of paleogeographic maps on tectonic plate reconstruction models requires a team effort to compile databases, data sharing standards and map projection methods. Two goals of the Paleogeography Working Group of the International Union of Geological Sciences (IUGS) program for Deep‐Time Digital Earth (DDE) are: (1) to interlink online national lexicons for all sedimentary and volcanic formations, and develop online ones for nations that currently lack these; (2) to target specific regions and intervals for testing/showcasing paleogeography output from the merger of these databases. Following those goals, we developed and applied new cloud‐based lexicon data services and interactive visualization techniques to regions in East Asia. This has been a successful collaboration among computer engineers and plate modellers and has involved stratigraphers in India (ONGC), China (Chengdu Univ. Tech., and Chinese Acad. Geol. Sci.), United States (Paleomap Project, and Purdue Univ.), Australia (GPlates visualization team) and Vietnam (Vietnam Nat. Univ.). Independent online lexicons with map‐based and stratigraphy‐based user interfaces have been developed (as of the date of this submission in March 2022) for all Proterozoic to Quaternary formations on the Indian Plate (over 800) and Vietnam (over 200), the majority of the Devonian through Neogene of China (ca. 2000) and partially for Thailand. A multi‐database search system returns all geologic formations of a desired geologic time from these four independent databases. With one click, users can plot the regional extent of one or of all of those regional formations on different plate reconstruction models of that desired age, and these polygons are filled with the lithologic facies pattern. [ABSTRACT FROM AUTHOR]

The nuclei are the main output structures of the cerebellum. Each and every cerebellar cortical computation reaches several areas of the brain by means of cerebellar nuclei processing and integration. Nevertheless, our knowledge of these structures is still limited compared to the cerebellar cortex. Here, we present a mouse genetic inducible fate‐mapping study characterizing rhombic lip‐derived glutamatergic neurons of the nuclei, the most conspicuous family of long‐range cerebellar efferent neurons. Glutamatergic neurons mainly occupy dorsal and lateral territories of the lateral and interposed nuclei, as well as the entire medial nucleus. In mice, they are born starting from about embryonic day 9.5, with a peak between 10.5 and 12.5, and invade the nuclei with a lateral‐to‐medial progression. While some markers label a heterogeneous population of neurons sharing a common location (BRN2), others appear to be lineage specific (TBR1, LMX1a, and MEIS2). A comparative analysis of TBR1 and LMX1a distributions reveals an incomplete overlap in their expression domains, in keeping with the existence of separate efferent subpopulations. Finally, some tagged glutamatergic progenitors are not labeled by any of the markers used in this study, disclosing further complexity. Taken together, our results obtained in late embryonic nuclei shed light on the heterogeneity of the excitatory neuron pool, underlying the diversity in connectivity and functions of this largely unexplored cerebellar territory. Our findings contribute to laying the groundwork for a comprehensive functional analysis of nuclear neuron subpopulations. [ABSTRACT FROM AUTHOR]

Neurons in the cortex are heterogeneous, sending diverse axonal projections to multiple brain regions. Unraveling the logic of these projections requires single-neuron resolution. Although a growing number of techniques have enabled high-throughput reconstruction, these techniques are typically limited to dozens or at most hundreds of neurons per brain, requiring that statistical analyses combine data from different specimens. Here we present axonal BARseq, a high-throughput approach based on reading out nucleic acid barcodes using in situ RNA sequencing, which enables analysis of even densely labeled neurons. As a proof of principle, we have mapped the long-range projections of >8000 primary auditory cortex neurons from a single male mouse. We identified major cell types based on projection targets and axonal trajectory. The large sample size enabled us to systematically quantify the projections of intratelencephalic (IT) neurons, and revealed that individual IT neurons project to different layers in an area-dependent fashion. Axonal BARseq is a powerful technique for studying the heterogeneity of single neuronal projections at high throughput within individual brains. High-throughput mapping of neural projections at the single-cell level remains challenging. Here, the authors have developed axonal BARseq, a new technique that allows for mapping projections from thousands of neurons within a single brain. [ABSTRACT FROM AUTHOR]

AbstractProjecting global urban expansion is crucial for environmental assessment under climate change scenarios. However, existing global future urban land products are typically provided at coarse resolutions (1 km) due to data and computing limitations. This hinders the accurate assessment of the impacts of global urban development at finer scales. Thus, we develop the first Cellular Automata (CA) online tool for simulating future global urban expansion in Google Earth Engine (GEE-CA), which can simulate future urban land change at a 30 m resolution under different SSP scenarios. GEE-CA enables seamless simulations of future urban land at high resolution through a partitioned parallel strategy. Seven large urban agglomerations are simulated under shared socioeconomic pathways as representative regions to present our fine-scale results. Comparatively, our datasets preserve significantly more spatial details than existing global urban land products. The improvement in resolution from 1 km to 30 m reduces errors by a range from 7.11% to 21.27% in the estimation of future urban area. So far, the proposed GEE-CA tool allows users to generate urban land projection maps for any defined region with a resolution as high as 30 m. [ABSTRACT FROM AUTHOR]

A k × j -rough Heyting algebra is a Heyting algebra endowed with a finite family of unary operations known as projection maps. The purpose of this paper is to define and investigate a new (equational) class of algebras called k × j -rough pseudocomplemented distributive lattices as an abstraction from k × j -rough Heyting algebras. [ABSTRACT FROM AUTHOR]

New results on the behaviour of the fast motion in slow-fast systems of ODEs with dependence on the fast time are given in terms of tracking of nonautonomous attractors. Under quite general assumptions, including the uniform ultimate boundedness of the solutions of the layer problems, inflated pullback attractors are considered. In general, one cannot disregard the inflated version of the pullback attractor, but it is possible under the continuity of the fiber projection map of the attractor. The problem of the limit of the solutions of the slow-fast system at each fixed positive value of the slow time is also treated and in this formulation the critical set is given by the union of the fibers of the pullback attractors. The results can be seen as extensions of the classical Tikhonov theorem to the nonautonomous setting. [ABSTRACT FROM AUTHOR]

This paper introduces a hybrid spectral-conjugate gradient (SCG) method to solve nonlinear monotone operator equations efficiently. The proposed method incorporates a hybrid parameter that encompasses the Polak--Ribière--Polyak (PRP), Liu-Storey (LS), Fletcher-Reeves (FR), and conjugate descent (CD) methods as particular instances. Additionally, we derive the spectral parameter to ensure that the search direction adheres to the sufficient descent condition. The search direction is also designed to be bounded, and under specific conditions, we demonstrate that the sequence produced by our hybrid SCG algorithm converges toward a solution. Furthermore, to underscore the effectiveness of our proposed method, we conducted extensive numerical experiments comparing its performance against that of existing algorithms. These experiments were based on a selection of benchmark nonlinear monotone operator equations, highlighting our proposed algorithm's superior efficiency and potential in practical applications. [ABSTRACT FROM AUTHOR]

This study integrates map information projection methods with machine learning algorithms to analyze the distribution of rare earth mines in mainland China. The information obtained through the map information projection method includes the latitude and longitude of the deposits, deposit type labels, and deposit names. This approach helps to overcome challenges related to the sensitivity of geological information. The acquired information was organized into a simple dataset containing only latitude and longitude information and a complete dataset containing additional information. These datasets were used to simulate the early and later stages of the research project, respectively. The K-Means algorithm was applied to the simple dataset, and the results demonstrated good clustering performance through specific validation. The Support Vector Machine (SVM) algorithm was applied to the complete dataset, and the analysis showed excellent classification performance, with relevant metrics (Accuracy, Precision, Recall, F1 Score) all around 90%. The experiments demonstrate that K-Means and SVM are suitable for information analysis in earth sciences and that they complement each other in research projects, being particularly applicable to the early and later stages of the project, respectively.The findings contribute to a more nuanced understanding of rare earth mineral distributions and underscore the potential for machine learning techniques to revolutionize geological sciences. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method for efficiently obtaining an approximate solution for constrained nonlinear monotone operator equations. The search direction of the proposed method closely aligns with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) direction, known for its low storage requirement. Notably, the search direction is shown to be sufficiently descent and bounded without using the line search condition. Furthermore, under some standard assumptions, the proposed method converges globally. As an application, the proposed method is applied to solve image restoration problems. The efficiency and robustness of the method in comparison to other methods are tested by numerical experiments using some test problems. [ABSTRACT FROM AUTHOR]

Continuous and dense time series of satellite remote sensing data are needed for several land monitoring applications, including vegetation phenology, in-season crop assessments, and improving land use and land cover classification. Supporting such applications at medium to high spatial resolution may be challenging with a single optical satellite sensor, as the frequency of good-quality observations can be low. To optimize good-quality data availability, some studies propose harmonized databases. This work aims at developing an 'all-in-one' Google Earth Engine (GEE) web-based workflow to produce harmonized surface reflectance data from Landsat-7 (L7) ETM+, Landsat-8 (L8) OLI, and Sentinel-2 (S2) MSI top of atmosphere (TOA) reflectance data. Six major processing steps to generate a new source of near-daily Harmonized Landsat and Sentinel (HLS) reflectance observations at 30 m spatial resolution are proposed and described: band adjustment, atmospheric correction, cloud and cloud shadow masking, view and illumination angle adjustment, co-registration, and reprojection and resampling. The HLS is applied to six equivalent spectral bands, resulting in a surface nadir BRDF-adjusted reflectance (NBAR) time series gridded to a common pixel resolution, map projection, and spatial extent. The spectrally corresponding bands and derived Normalized Difference Vegetation Index (NDVI) were compared, and their sensor differences were quantified by regression analyses. Examples of HLS time series are presented for two potential applications: agricultural and forest phenology. The HLS product is also validated against ground measurements of NDVI, achieving very similar temporal trajectories and magnitude of values (R2 = 0.98). The workflow and script presented in this work may be useful for the scientific community aiming at taking advantage of multi-sensor harmonized time series of optical data. [ABSTRACT FROM AUTHOR]

Mapping is now thoroughly digital at all stages of production and maps are widely used in digital form. This digital turn has transformed the nature of mapping and maps. Maps need no longer be static representations, but rather constitute spatial media, providing an interactive, dynamic means for creating, discussing, and sharing spatial information and mediating spatial practices. This has included the development of 3D mapping, including nascent digital twins and digital deep maps. In this short paper, we reflect on our attempts to produce a 3D city information model for Dublin that acts as a basic digital twin, which we have also used to explore deep mapping, as well as map projecting data onto a printed 3D map model of the city. We consider what digital twins and deep maps mean for how we understand the nature of mapping, arguing that they produce a dyadic intertwining of map and territory; a literal, material expression of post‐representational, ontogenetic conceptions of mapping. [ABSTRACT FROM AUTHOR]

This study presents the development of a world map projection intended to minimize distortion of all continents. I begin by reviewing a very similar map projection developed by Canters (2002), and address its shortcomings by carefully fine-tuning the initial constraints and the method of optimization, while retaining the most useful ideas of this earlier map. Most notably, the method described in this paper puts a great emphasis on the outline of the map, so that its aesthetics make it more suitable for atlases; the method also exclusively uses reproducible, deterministic methods. Finally, I compare the resulting world map to the original one of Canters in terms of map distortions and practical usefulness. The method presented here should work without changes if a low-distortion map of any other global-scale area is needed. [ABSTRACT FROM AUTHOR]

The AutoCarto 2022 symposium centered around the theme of "Ethics in Mapping: Integrity, Inclusion, and Empathy." The conference brought together experts in cartography and geographic information science (GIScience) to explore the ethical responsibilities in these fields. The conference featured sessions on topics such as the power of maps for equity and social justice, uncertainty in geospatial data, and diversity, ethics, and equality. A special issue of the conference included papers on societal impacts and ethical issues, cartographic design and map production, and technical advancements in cartography. The document also discusses the future of the conference series and potential research directions in the field. [Extracted from the article]

This paper explores scholarly literature published since the 1960s that examines peoples' cognitive and perceptual understanding of map projections. Map projections present challenges to virtually everyone who uses them. Some of the challenges include selecting a projection, specifying projection parameters, and understanding distortion patterns. Broadly speaking, cartographic inquiry has addressed many topics in cognition and perception; yet, research focused on projections remains scarce. We surveyed the body of research studies incorporating projections or a projection-related topic (e.g. distortion) as a variable in the experimental design. Topics included asking participants to estimate areas, conceptualize travel paths, or identify preferred graticule aesthetics. Despite the conclusions reported by these studies, we noted three general concerns that may diminish the accuracy of results from research in this area. First, projection-specific terminology or properties critical to the studies and analysis that may be misunderstood by researchers and/or participants. Second, study participants were largely homogenous. Third, most of the studies were not designed for replication or reproducibility. Given our critique, we offer six suggestions for those who are interested in new cognitive and perceptual projection research. [ABSTRACT FROM AUTHOR]

Traditional map projections introduce distortions, especially for global data. Discrete Global Grid Systems (DGGS) offer an alternative by dividing the Earth into equal-area grid cells at different resolutions. This paper describes xdggs, a new Xarray extension that simplifies working with DGGS. Xdggs provides a unified API for various DGGS libraries and integrates seamlessly with the Pangeo ecosystem through extending the widely used Xarray library to use the DGGS-specific cell identifiers as an index. This development makes DGGS more accessible and will lead to facilitating data analysis on a planetary scale.Xdggs aims to provide a user-friendly API that hides the implementation complexities of different DGGS libraries. And because it integrates seamlessly with Xarray, a popular tool for geospatial data analysis, xdggs promotes FAIR data practices by simplifying data access and interoperability and can become a valuable tool for geospatial scientists and application developers working with global datasets. [ABSTRACT FROM AUTHOR]

Copyright of Virtual Archaeology Review is the property of Virtual Archaeology Review and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The purpose of this study is to show that some coordinate systems previously described as isometric are in fact not isometric, and as a consequence, map projections derived from them do not show the expected characteristics, especially conformality. Definitions and methods of the mathematical theory of surfaces are used. The article discusses two methods of specifying coordinate systems on the surface of the triaxial ellipsoid, erroneously called isometric. A consistent mathematical study of each of them based on the initial definition of isometric coordinates showed that in the first method, the corresponding coordinate system is not orthogonal, much less isometric. In the second method, the coordinates are determined using integration, and the result of the integration depends on the path of this integration. This ambiguity shows that this method is also incorrect. The considered coordinate systems allow the creation of new projections, but these projections are not conformal. As a result of the study, errors in determining isometric coordinates were shown and proven, which in earlier studies led to a violation of the properties of projections. This analysis should lead to the development of truly conformal projections of triaxial ellipsoids. For clarity maps and cartographic grids are presented. [ABSTRACT FROM AUTHOR]

This work shows the original projection of a 1:57,600 scale map of southern Germany at the end of the 18th century, produced under the direction of Karl-Heinrich von Schmitt (1743–1805). The sections of the map were scanned and georeferenced as part of the MAPIRE project, and the results are publicly available. In the present work, we use contemporary documents, in particular the books of César-Francois Cassini de Thury and manuscript sketches of the map found in the Military Archive of Vienna, to show that the overall projection of the map is identical to that used in Cassini's survey of France (first half of the 18th century). In the archive, we managed to find the overview sheet on which—in addition to the Paris Cassini coordinate system—the section grid of the Schmitt map was also constructed. This sketch served as the basis for the compilation and copying work, wherein the existing map works and survey sketches were inserted into 197 sections of the Schmitt map. Thus, the map coordinate system can be modeled in GIS systems using the Cassini (or Cassini-Soldner) projection, with the Paris Observatory as the projection origin. The georeferencing accuracy of using the pure Cassini projection is around 1–1.3 km (at the extremes, around 5 km), which is much more inaccurate than the one used in later topographic surveys. It is considered a combined result of the compilation of the different maps, presumably surveyed by graphic triangulation with measuring tables. [ABSTRACT FROM AUTHOR]

This article provides an overview of the Juno mission and its observations of Jupiter's Galilean moons. The Juno spacecraft continues to send high-quality images of Jupiter, with a focus on the South Temperate Belt (STB) and the evolution of cyclonic spots within it. The article discusses the valuable insights gained from the images captured by JunoCam, including the changing pattern of images as Juno's orbit evolves. The text also discusses the close flybys of Jupiter's moon, Io, and the high-resolution images of its surface, revealing volcanic calderas and mountains. The impact of Jupiter's radiation belts on the spacecraft's camera is mentioned, along with the successful resolution of image degradation issues. [Extracted from the article]

α-Latrotoxin (α-LTX) was found to form two-dimensional (2D) monolayer arrays in solution at relatively low concentrations (0.1 mg/mL), with the toxin tetramer constituting a unit cell. The crystals were imaged using cryogenic electron microscopy (cryoEM), and image analysis yielded a ~12 Å projection map. At this resolution, no major conformational changes between the crystalline and solution states of α-LTX tetramers were observed. Electrophysiological studies showed that, under the conditions of crystallization, α-LTX simultaneously formed multiple channels in biological membranes that displayed coordinated gating. Two types of channels with conductance levels of 120 and 208 pS were identified. Furthermore, we observed two distinct tetramer conformations of tetramers both when observed as monodisperse single particles and within the 2D crystals, with pore diameters of 11 and 13.5 Å, suggestive of a flickering pore in the middle of the tetramer, which may correspond to the two states of toxin channels with different conductance levels. We discuss the structural changes that occur in α-LTX tetramers in solution and propose a mechanism of α-LTX insertion into the membrane. The propensity of α-LTX tetramers to form 2D crystals may explain many features of α-LTX toxicology and suggest that other pore-forming toxins may also form arrays of channels to exert maximal toxic effect. [ABSTRACT FROM AUTHOR]

In the present paper, it has been obtained that the fundamental group of n -dimensional Minkowski space with the time topology contains uncountably many copies of the additive group of integers and is not abelian. The result has been first proved for n = 2. Thereafter, it is extended to n > 2 by proving that loops nonhomotopic in M 2 continue to be nonhomotopic in Mn using embedding of M 2 in Mn as a retract through the projection map. [ABSTRACT FROM AUTHOR]

The katsura tree at Dumbarton Oaks is among the oldest of the species in North America and pre-dates the design of the garden. Japanese master gardener Kurato Fujimoto was commissioned to inspect and lead the construction and installation of a series of branch supports, known as "hoozue" in Japan, to rejuvenate this venerable tree that was in decline. The assessment of the tree included the inspection of the branch structure with a projection toward post-installation growth over the next several decades. Materials such as rope, bark fabric, nails (kasugai), and the wooden hoozue themselves were fabricated and installed with indigenous knowledge and experience, which were described in the text and drawings and documented in a series of photographic sequences. This article narrates the process of this preservation work, demonstrating the significance of this indigenous Japanese technique. [ABSTRACT FROM AUTHOR]

This article discusses the interpretation of Emily Dickinson's poem that includes the word "Checks" in the last line. The word was later changed to "chart" in subsequent publications, but the meaning of "Checks" has remained unclear. The author suggests that the definition of "check" as "checkered cloth" or "to variegate with cross lines" may provide insight into the meaning of the word in the poem. The author also explores Dickinson's reliance on Noah Webster's dictionary and the connection between language, nature, and spirit in her work. The article concludes by discussing the concept of "belief" in Dickinson's poetry and its connection to creating fictive explanations of natural facts. [Extracted from the article]

The general solution of detection and tracking technology in panoramic videos is to detect and track moving objects after converting 360° video into two-dimensional video by projection. However, the fixed spherical projection will lead to discontinuous projection boundaries in panoramic videos. When a moving object is at a projection boundary, conventional spherical projection methods may divide the object into multiple parts, resulting in the missed or false detection. A multi-motion object detection and tracking method in panoramic video combining equi-rectangular projection (ERP) and cube map projection (CMP) is proposed. It uses suitable CMP stitching frames to reduce the polar distortion and compensate for the discontinuity of projection boundaries of ERP frames, solving the detection of objects at projection boundaries or polar distortion. Then, multi-motion object tracking is solved by fusing multiple features of perceptual hashing, spherical centroid and motion direction. Experimental results show that the proposed scheme can effectively alleviate the false detection caused by discontinuous projection boundaries and correctly track moving objects with occlusion, frame boundary shuttle or polar distortion. [ABSTRACT FROM AUTHOR]

This study assessed how global map projections affect perceptions of the importance of world regions and beliefs about geopolitical events. We tested whether the Mercator projection, which represents polar regions as being larger than their actual landmass, compared to the Gall-Peters projection, an equal-area map that represents landmass proportionately, alters evaluations of the U.S.' proposal to purchase Greenland. In a 2 (map projection: Mercator vs. Gall-Peters) × 2 (emphasis frame: economic vs. national security) experiment, we found that people attributed greater importance to Russia after viewing the Mercator projection only when the arguments paired with the map adopted a national security frame. This perception mediated effects of the experimental interaction on attitude toward, support for, and perceived ethics of the purchase. [ABSTRACT FROM AUTHOR]

In previous papers that have dealt with cylindrical map projections as limiting cases of conical projections, standard or equidistant parallels were used in the derivations. This paper shows that this is not necessary and that it is sufficient to use parallels that preserve length. In addition, unlike other approaches, in this article the limiting cases of conic projections are derived in the most natural way, by deriving the equations of cylindrical projections from the equations of conic projections in a rectangular system in the projection plane using a mathematical concept of limits. It is shown that such an approach is possible, but not always, so it should be used carefully, or even better, avoided in teaching and studying map projections. [ABSTRACT FROM AUTHOR]

Length measurements calculated from the geometry of vector geographic objects, called geometric measurements, are inherently imprecise. The imprecision of the measurements is due to the accumulation of causes of various origins, related to the production processes, and the rules of data representation. In order to reduce the overall imprecision of geometric length measurements, this article proposes to identify the causes of measurement error in the data, to model their respective impact, and finally to combine these different impacts. To do so, five causes of geometric measurement error have been modeled: map projection, terrain disregard, polygonal approximation of curves, digitizing error, and cartographic generalization. To estimate the overall measurement imprecision, three combination methods are proposed: selection of the maximum error, sum of the errors, and quadratic aggregation of the errors. An experiment conducted on a sample of roads represented at a medium scale demonstrates that quadratic error aggregation is the most effective combination method for reducing the imprecision of geometric length measurements. [ABSTRACT FROM AUTHOR]

Deep coal seam mining causes instability and collapse of coal seam roof frequently, which seriously affects the safety production and threatens the personal safety of underground personnel. In order to evaluate the stability of coal roof accurately, this paper select 6th coal seam in Kongduigou Coalfield of Jungar Coalfieldas research object, analyzes the geological and hydrogeological data, and study the lithology, rock combination, sandstone thickness, fault, fold, seam inclination, rock quality index, and rock compressive strength on the influence of the roof stability, drawing the main control factor 3D mapping projection surface maps. Select 58 borehole data points as the input samples (50 training sets and 8 test sets), use genetic algorithm (GA) to optimize the network random initial weights and threshold initial and sparrow search algorithm (SSA) for secondary optimization for the BP neural network training and learning, establishing GA-BP neural network based on SSA optimization (SSA-GA-BP neural network) coal roof stability evaluation model, which is used to predict and evaluate the 6th coal roof stability of the research area after the training error accuracy reached the requirements. The fuzzy comprehensive evaluation method, BP neural network, GA-BP neural network and SSA-GA-BP neural network are also used to predict and evaluate the 6th coal roof stability. Compare the evaluation results of each model with the actual value. The results show that the error of coal seam roof stability evaluation of SSA-GA-BP neural network is smallest, with the accuracy 88%, and the model is successfully applied to predict the roof stability of the 6th coal seam in Kongduigou Coalfield, which provides a scientific evaluation method and theoretical basis for the evaluation of coal seam roof stability. [ABSTRACT FROM AUTHOR]

How to identify the ear hole more accurately and more quickly are critical for the active noise reduction in the road vehicle. Obscurations, causing by the long hair, the earphone, and some kind of caps, make the spatial location and orientation of the driver's ears almost impossible. To solve these two problems, a new method was proposed to replace the original image scaling detection by combining the Haar-like algorithm with the scale size of the variable detection window in the recognition process. A depth positioning camera is added to the ear recognition, which may offer more accurate point vectors for the driver's two ear holes. A simplified spatial reconstruction model was developed to assist the search when the piercing was occluded. After calculating the image-camera-cab projection mapping relationship, only four feature points are enough for the model's data requirement. The test results show that the detection Frame Per Second (FPS) was improved to 8.8, and the ear hole's positioning error is less than 0.1 cm. The proposed system can locate ear holes even with 100% obscurations. The research may have potential application as a front-end subsystem for the active noise reduction and voice interaction systems, improving the quality of acoustic control in cars. [ABSTRACT FROM AUTHOR]

Copyright of Rundbrief Fotografie is the property of De Gruyter and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Depth estimation from monocular panoramic image is a crucial step in 3D reconstruction, which is a close relationship with virtual reality and metaverse technologies. In recent years, some methods, such as HRDFuse, BiFuse++, and UniFuse, have employed a two‐branch neural network leveraging two common projections: equirectangular and cubemap projections (CMPs). The equirectangular projection (ERP) provides a complete field of view but introduces distortion, while the CMP avoids distortion but introduces discontinuity at the boundary of the cube. In order to address the issue of distortion and discontinuity, the authors propose an efficient depth estimation fusion module to balance the feature mapping of the two projections. Moreover, for the ERP, the authors propose a novel inflated network architecture to extend the receptive field and effectively harness visual information. Extensive experiments show that the authors' method predicts more clear boundaries and accurate depth results while outperforming mainstream panoramic depth estimation algorithms. [ABSTRACT FROM AUTHOR]

Distortion deformation usually imposes a potential threat to bridge safety. In order to comprehensively understand the distortion effect on thin-walled ultra-high performance concrete (UHPC) box girders, an innovative approach encompassing the governing distortion differential equation is introduced in this study based on the general definition of distortion angle within the cross-section plane. The analytical results obtained from the proposed method are in accordance with those obtained from the energy method, and exhibit favorable agreement with experimental findings documented in the existing literature. Furthermore, a finite element model is developed on the ANSYS 2021 R1 software platform with the employment of a Shell 63 element. Numerical outcomes are also in good agreement with the experimental data, affirming the validity and reliability of the findings. In addition, parameter analysis results indicate that the distortion angle remains approximately constant at a location approximately 1/10 of the span from the mid-span cross-section of the box girder, regardless of changes in the span-to-depth ratio. Increasing the web thickness yields a notable reduction in the distortion effects, and decreasing the wall thickness can effectively mitigate the distortion-induced transverse bending moment. Compared with normal-strength concrete box girders, UHPC box girders can reduce the distortion angle within the span range, which is beneficial for maintaining the overall stability of the box girders. The outcomes obtained from this study yield engineers an enhanced understanding of distortion effect on the UHPC girder performance. [ABSTRACT FROM AUTHOR]

Deciphering patterns of connectivity between neurons in the brain is a critical step toward understanding brain function. Imaging-based neuroanatomical tracing identifies area-to-area or sparse neuron-to-neuron connectivity patterns, but with limited throughput. Barcode-based connectomics maps large numbers of single-neuron projections, but remains a challenge for jointly analyzing single-cell transcriptomics. Here, we established a rAAV2-retro barcode-based multiplexed tracing method that simultaneously characterizes the projectome and transcriptome at the single neuron level. We uncovered dedicated and collateral projection patterns of ventromedial prefrontal cortex (vmPFC) neurons to five downstream targets and found that projection-defined vmPFC neurons are molecularly heterogeneous. We identified transcriptional signatures of projection-specific vmPFC neurons, and verified Pou3f1 as a marker gene enriched in neurons projecting to the lateral hypothalamus, denoting a distinct subset with collateral projections to both dorsomedial striatum and lateral hypothalamus. In summary, we have developed a new multiplexed technique whose paired connectome and gene expression data can help reveal organizational principles that form neural circuits and process information. [ABSTRACT FROM AUTHOR]

Persistence modules stratify their underlying parameter space, a quality that makes persistence modules amenable to study via invariants of stratified spaces. In this article, we extend a result previously known only for one-parameter persistence modules to grid multiparameter persistence modules. Namely, we show the K-theory of grid multiparameter persistence modules is additive over strata. This is true for both standard monotone multi-parameter persistence as well as multiparameter notions of zig-zag persistence. We compare our calculations for the specific group K_0 with the recent work of Botnan, Oppermann, and Oudot, highlighting and explaining the differences between our results through an explicit projection map between computed groups. [ABSTRACT FROM AUTHOR]

In cartographic literature, map projections are usually interpreted as mapping to auxiliary development surfaces, and then these surfaces are developed into a plane. The so-called secant projections, i.e. projections in which the auxiliary surface intersects the Earth's sphere or ellipsoid are especially emphasized. It is stated and taken as a fact without proof that the parallels in which the auxiliary surface intersects the sphere are mapped without distortions. An example of such an approach is the publication Basic Cartography, published several years ago by the International Cartographic Association. This paper proves that standard parallels and secant parallels generally do not match. It turns out that the widely accepted facts about secant and standard parallels, which can also be found even in the most recent literature, are wrong and need to be revised. The paper concludes that explaining cylindrical projections as mapping on a cylindrical surface is not a good approach, because it leads to misunderstanding important properties of projection. [ABSTRACT FROM AUTHOR]

The uniqueness and detail in the depiction of Croatian regions gives Glavač's map exceptional importance as part of the Croatian cultural heritage. Since Glavač left behind as written evidence of map creation only its title and an exhaustive dedication, other information about the map remains unknown. The appearance of the cartographic network indicates that it is a normal aspect of cylindrical projection. From the relationship between the coordinates from the map, we concluded that Glavač used the equidistant cylindrical projection with the equator as a standard parallel. After that we have calculated that the ratio of the radius of the Earth's sphere to the scale of the map is 2292.7. The numerical scale of the map can be determined from a graphical scale and from the calculated ratio of the radius to the map scale. Since there were several attempts to determine the Earth's dimensions at the time of Glavač's map, there are several possible radii of the Earth's sphere. At the end of the paper, calculating the interval of the numerical scale of the map enabled us to refute and/or accept the theses of other authors who cited different scales of Glavač's map in their works. [ABSTRACT FROM AUTHOR]

The auxiliary latitudes are essential tools in cartography. This paper summarizes methods for converting between them with an emphasis on providing full double-precision accuracy. This includes series expansions in the third flattening, where the truncation error is precisely measured and where estimates of the radii of convergence are given. Also new formulas are given for computing the rectifying and authalic latitudes with minimal roundoff error. [ABSTRACT FROM AUTHOR]

The Earth's crust is exposed by tectonic processes and is not static over time. Modelling of the Earth's surface velocities is of utmost importance for research in geodesy, geophysics, structural geology, and other geosciences. It may support positioning, navigation, seismic risk, and volcano notification services, for example. Space geodetic techniques can be used to provide high-quality velocities in a network of geodetic sites. Velocity field modelling should, however, expand the velocities from a discrete set of points to any location in-between. This paper presents four new methods for the Earth's surface velocity interpolation. Contrary to the widely used approach dividing the velocity field to the horizontal and vertical components, a full 3D interpolation approach is proposed based on the Delaunay triangulation and the n-simplex interpolation. The use of a combination of all three components is advantageous for geophysical interpretation. The proposed interpolation approach is entirely local but enables global modelling, which does not suffer from map projection distortions and singularities at the poles. Various global and regional position/velocity datasets are used to evaluate the performance of the proposed velocity interpolation methods. The latter provide practically the same results when applied to regional velocity field modelling. However, the so-called continuous piecewise quasi-radial 3D velocity field interpolation method is recommended for its favourable properties. It introduces an ellipsoidal Earth model, appropriately considers vertical/up and horizontal velocity components, tends to radial symmetry, and provides continuity for the interpolated velocity components as well as for the estimated uncertainties. [ABSTRACT FROM AUTHOR]

In the literature on map projections, we regularly encounter the name standard parallel or standard parallels. However, it is obvious that a unique definition of a standard parallel is not universally accepted. To fully clarify the meaning of standard parallels, the author proposes the notion of equidistantly mapped parallels, which has not been common in the literature so far. Equidistantly mapped parallels can be in the direction of the parallel or in the direction of the meridian. Here, it is shown that every standard parallel is also an equidistantly mapped parallel, but that the reverse need not be true. If the parallel is mapped equidistantly in the direction of the parallel, then its length in the projection plane is equal to the length of that parallel on the sphere. The opposite does not have to be true, i.e., if the length of the image of the parallel in the projection plane is equal to the length of the parallel on the sphere, this does not mean that the parallel was mapped equidistantly. In addition to standard and equidistant parallels, the concept of parallels of true length also appears in the theory of map projections. They should also be distinguished from standard and equidistant parallels. [ABSTRACT FROM AUTHOR]

We introduce the effectual topological complexity (ETC) of a G -space X. This is a G -equivariant homotopy invariant sitting in between the effective topological complexity of the pair (X , G) and the (regular) topological complexity of the orbit space X / G. We study ETC for spheres and surfaces with antipodal involution, obtaining a full computation in the case of the torus. This allows us to prove the vanishing of twice the nontrivial obstruction responsible for the fact that the topological complexity of the Klein bottle is 4. In addition, this gives a counterexample to the possibility — suggested in Pavešić's work on the topological complexity of a map — that ETC of (X , G) would agree with Farber's TC (X) whenever the projection map X → X / G is finitely sheeted. We conjecture that ETC of spheres with antipodal action recasts the Hopf invariant one problem, and describe (conjecturally optimal) effectual motion planners. [ABSTRACT FROM AUTHOR]

Let 퓗 be a finite dimensional complex Hilbert space with dimension n ≥ 3 and 퓟(퓗) the set of projections on 퓗. Let φ : 퓟(퓗) → P(퓗) be a surjective map. We show that φ shrinks the joint spectrum of any two projections if and only if it is induced by a semilinear automorphism on ∈. In addition, φ shrinks the joint spectrum of I,P,Q for any two projections P, Q ∈퓟(퓗) if and only if it is induced by a unitary or an anti-unitary. Assume that φ is a surjective map on the Grassmann space of rank one projections. We show that φ is joint spectrum shrinking for any n rank one projections if and only if it is induced by a semilinear automorphism on 퓗. Moreover, for any k > n, φ is joint spectrum shrinking for any k rank one projections if and only if it is induced by a unitary or an anti-unitary. [ABSTRACT FROM AUTHOR]

Terrorism poses a significant threat to security, and the need for an accurate monitoring visualization tool is essential for effective counterterrorism. However, the unavailability of such a customized tool is still a challenge in Mindanao, Philippines. Therefore, a terrorism visualization tool was developed in this study, covering the years 1975 to 2017. The methodology involved intensive data collection from the Global Terrorism Database and other reliable sources and featured the design development of a visualization tool in the form of a dashboard using Python. Also, regions with high terrorism activities along with major perpetrators have been presented. Findings indicate that Maguindanao yields the highest death frequency, with New People's Army (NPA) as the leading perpetrator as verified by the spatial map projection and overall preliminary prediction. In conclusion, with proper data management and feature selection, the developed tool is found to be highly viable and sufficient for decision-making. [ABSTRACT FROM AUTHOR]

Mapping the connectivity of diverse neuronal types provides the foundation for understanding the structure and function of neural circuits. High-throughput and low-cost neuroanatomical techniques based on RNA barcode sequencing have the potential to map circuits at cellular resolution and a brain-wide scale, but existing Sindbis virus-based techniques can only map long-range projections using anterograde tracing approaches. Rabies virus can complement anterograde tracing approaches by enabling either retrograde labeling of projection neurons or monosynaptic tracing of direct inputs to genetically targeted postsynaptic neurons. However, barcoded rabies virus has so far been only used to map non-neuronal cellular interactions in vivo and synaptic connectivity of cultured neurons. Here we combine barcoded rabies virus with single-cell and in situ sequencing to perform retrograde labeling and transsynaptic labeling in the mouse brain. We sequenced 96 retrogradely labeled cells and 295 transsynaptically labeled cells using single-cell RNA-seq, and 4130 retrogradely labeled cells and 2914 transsynaptically labeled cells in situ. We found that the transcriptomic identities of rabies virus-infected cells can be robustly identified using both single-cell RNA-seq and in situ sequencing. By associating gene expression with connectivity inferred from barcode sequencing, we distinguished long-range projecting cortical cell types from multiple cortical areas and identified cell types with converging or diverging synaptic connectivity. Combining in situ sequencing with barcoded rabies virus complements existing sequencing-based neuroanatomical techniques and provides a potential path for mapping synaptic connectivity of neuronal types at scale. [ABSTRACT FROM AUTHOR]