Flat Map Research Articles

Reduction of derived Hochschild functors over commutative algebras and schemes

We study functors underlying derived Hochschild cohomology, also called Shukla cohomology, of a commutative algebra S essentially of finite type and of finite flat dimension over a commutative noetherian ring K. We construct a complex of S-modules D, and natural reduction isomorphisms Ext S ⊗ K L S ∗ ( S | K ; M ⊗ K L N ) ≃ Ext S ∗ ( R Hom S ( M , D ) , N ) for all complexes of S-modules N and all complexes M of finite flat dimension over K whose homology H ( M ) is finitely generated over S; such isomorphisms determine D up to derived isomorphism. Using Grothendieck duality theory we establish analogous isomorphisms for any essentially finite-type flat map f : X → Y of noetherian schemes, with f ! O Y in place of D.

Preliminary studyon electronic map based on surface of ellipsoid

Map carrier not only decides the storage mode of map information, it also has important influence on mathematic foundation and expression mode of geographical information. Based on analysis of the limitations lying in the flat map, this paper introduces the concept of the digital map and electronic map on ellipsoid surface, elaborates on the superiority. The paper investigates the fundamental method of drawing, display and analysis of the digital map on ellipsoid surface farther. Compared with conventional map mode, the digital map on ellipsoid surface is a new concept, it fits the spatial data visual mode based on geographical features superlatively well and suits the people’s cognitive and thought habit who regards earth surface as a ellipsoid; it carries out a reform of expression mode of the existing digital map, and will explore the analysis function and application scope of electronic map and digital map effectively.

Advances in high-resolution imaging and computational unfolding of the human hippocampus

The hippocampus is often a difficult structure to visualize with magnetic resonance imaging (MRI) and functional MRI (fMRI) due to its convoluted nature and susceptibility to signal dropout. Improving our ability to pinpoint changes in neural activity using fMRI in this structure remains an important challenge. Current fMRI/MRI methods typically do not permit visualization of the hippocampus and surrounding cortex at a resolution less than 1 mm. We present here improvements to our previous methods for obtaining structural MR images of the hippocampus, which provided an in-plane resolution of 0.4 mm2 mm and two-dimensional “flat” maps of the hippocampus with an interpolated isotropic resolution of 0.4 mm3 (Engel, S.A., Glover, G.H., and Wandell, B.A., (1997). Retinotopic organization in human visual cortex and the spatial precision of functional MRI. Cereb. Cortex 7, 181–192.; Zeineh, M.M., Engel, S.A., and Bookheimer, S.Y., (2000). Application of cortical unfolding techniques to functional MRI of the human hippocampal region. NeuroImage 11, 668–683.). We present changes to existing structural imaging sequences that now augment the resolution of previous scans, permitting visualization of the anterior portion of CA1, parts of the dentate gyrus, and CA23. These imaging improvements are of relevance generally to the field of imaging because they permit higher overall resolution imaging of the hippocampus than previously possible (at 3 T). We also introduce a novel application of a computational interpolation method that improves our ability to capture the convoluted three-dimensional shape of the hippocampus. Furthermore, we have developed a quantitative method for obtaining group activation patterns based on producing averaged flat maps using vector field warping techniques, allowing localization of activations to specific hippocampal subregions across groups of subjects. Together, these methods provide a means to improve imaging of neural activity in the human hippocampus and surrounding cortex during cognitive tasks.

Cosmic imagery: key images in the history of science

We live in a visual age, an age of images-iconic, instant, and influential-that have crystallized our conception of the large, the small, and the complex, of both inner and outer space. Some, like Robert Hooke's first microscopic views of the natural world, arose because of new technical capabilities. Others, like the first graphs, were breathtakingly simple but perennially useful. The first stunning picture of Earth from space stimulated an environmental consciousness that has grown ever since; the mushroom clouds from atomic and nuclear explosions became the ultimate symbol of death and destruction; Mercator's flat map of the Earth cemented an entire worldview. John D. Barrow's collection encompasses the frontiers of modern science and its most memorable historic moments. But this is much more than a picture book. Entertaining and informative essays accompany the powerful display of images that have illuminated concepts of far-reaching significance.

Radial orientation and direction biases in the response of human visual cortex to kinetic contours

Event Abstract Back to Event Radial orientation and direction biases in the response of human visual cortex to kinetic contours It has recently been observed using fMRI that radial orientations produce higher activity in retinotopic regions of visual cortex (Sasaki, Y. et al. (2006) Neuron 51, 661-670). Here, we report analogous biases for: (1) the axis of motion (horizontal or vertical) of unoriented textures; (2) the orientation of ‘kinetic’ contours defined solely by the borders between strips of texture moving in opposite directions. fMRI at 3T was used to measure the BOLD signal (1.5mm cubic voxels; TR = 3s.) in the visual cortex of six human subjects viewing kinetic contour stimuli presented in 15-second blocks. Stimuli were composed of 0.6° strips of spatial white noise texture presented in an annulus 1-6° in radius. The texture in alternate strips moved in opposite directions (left-right or up-down) at 3°. The strips themselves were static and tilted 45°either left or right from vertical. A systematic pattern of bias across the cortical surface was evident in response to the axis of motion of the textures when data were pooled across the orientation of the kinetic contours. Comparison with flat maps of the visual field representation obtained from phase-encoded retinotopic analysis revealed that representations of the vertical (horizontal) meridian tended to respond more strongly to vertical (horizontal) motion. Specifically, a bias for horizontal motion was evident within V1 and along the borders between V2 and V3; a bias for vertical motion was apparent along the borders between V1 and V2 and at the extremes of V3. Pooling data across the axis of motion of the textures revealed a different pattern of bias: the response to a given orientation was stronger in the quadrants of the visual field for which contour orientation was predominantly radial. Specifically, the response to leftward (rightward) tilted gratings tended to be stronger in the dorsal part of the left (right) visual cortex and the ventral part of the right (left) visual cortex. Quantitative analysis of the variation in the proportion of voxels preferring a particular axis of motion as a function of the meridian angle of the visual field representation (in 10° bins) revealed a radial direction bias significant across subjects at p < 0.05 or better in each of areas V1, V2 and V3. Similar analysis showed a radial bias for the orientation of kinetic contours at p < 0.01 in each of these areas. Radial orientation bias likely results from a disproportionate number of neurons being tuned to radial orientations. The existence of radial biases for the orientation of kinetic (‘non-Fourier’) as well as luminance-defined (‘Fourier’) contours could reflect processing by cue-invariant orientation mechanisms or by distinct neuronal populations subject to similar anisotropies in orientation tuning. The radial bias for motion might be related to the phenomenon of ‘motion streaks’ whereby temporal integration by the visual system introduces oriented blur along the axis of motion. We speculate that all the observed forms of radial bias reflect a single underlying anisotropy in the way (Fourier and non-Fourier) stimulus energy is processed across the visual field. Conference: Computational and systems neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009. Presentation Type: Poster Presentation Topic: Poster Presentations Citation: (2009). Radial orientation and direction biases in the response of human visual cortex to kinetic contours. Front. Syst. Neurosci. Conference Abstract: Computational and systems neuroscience 2009. doi: 10.3389/conf.neuro.06.2009.03.016 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 29 Jan 2009; Published Online: 29 Jan 2009. Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Google Google Scholar PubMed Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Discrete conformal methods for cortical brain flattening

Locations and patterns of functional brain activity in humans are difficult to compare across subjects because of differences in cortical folding and functional foci are often buried within cortical sulci. Unfolding a cortical surface via flat mapping has become a key method for facilitating the recognition of new structural and functional relationships. Mathematical and other issues involved in flat mapping are the subject of this paper. It is mathematically impossible to flatten curved surfaces without metric and area distortion. Nevertheless, “metric” flattening has flourished based on a variety of computational methods that minimize distortion. However, it is mathematically possible to flatten without any angular distortion — a fact known for 150 years. Computational methods for this “conformal” flattening have only recently emerged. Conformal maps are particularly versatile and are backed by a uniquely rich mathematical theory. This paper presents a tutorial level introduction to the mathematics of conformal mapping and provides both conceptual and practical arguments for its use. Discrete conformal mapping computed via circle packing is a method that has provided the first practical realization of the Riemann Mapping Theorem (RMT). Maps can be displayed in three geometries, manipulated with Möbius transformations to zoom and focus on particular regions of interest, they respect canonical coordinates useful for intersubject registration and are locally Euclidean. The versatility and practical advantages of the circle packing approach are shown by producing conformal flat maps using MRI data of a human cerebral cortex, cerebellum and a specific region of interest (ROI).

Morphismes géométriquement plats et faisceaux dualisants

Let n be an integer, S a reduced pure dimensional complex analytic space. Let E ( S , n ) (resp. G ( S , n ) ) be the set of morphisms π : X → S from an countable at infinity analytic complex space X to S which are n-equidimensional and open (resp. the set of geometrically flat map that is the element of E ( S , n ) endowed with cycle of X × S which induce a good multiplicity on the fibers such that ( π −1 ( s ) ) s ∈ S become an analytic family of cycles in the sense of Barlet). After showing that each π of E ( S , n ) is endowed with a canonical O X -coherent analytic sheaf ω π n with many functorial properties, we state the main result of this Note which says that π is in G ( S , n ) if and only if there exists a canonical morphism (called a relative fundamental class of π) Ω X / S n → ω π n , compatible with any base change between reduced finite pure dimensional complex spaces, which satisfies the relative trace property and gives, in the local setting, the relative fundamental class of Barlet constructed in 1980. From this, we deduce that π belong to G ( S , n ) if and only if ω π n is stable by base change and is characterized by the relative trace property; that means precisely that the relative Kunz–Waldi (1988) sheaf of regular differential forms constructed for flat analytic algebra by Kersken (1983) exists in this setting. To cite this article: M. Kaddar, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

Low-dimensional singularities with free divisors as discriminants

We present versal complex analytic families, over a smooth base and of fibre dimension zero, one, or two, where the discriminant constitutes a free divisor. These families include finite flat maps, versal deformations of reduced curve singularities, and versal deformations of Gorenstein surface singularities in C 5 \mathbb {C}^5 . It is shown that such free divisors often admit a “fast normalization”, obtained by a single application of the Grauert-Remmert normalization algorithm. For a particular Gorenstein surface singularity in C 5 \mathbb {C}^5 , namely the simple elliptic singularity of type A ~ 4 \widetilde A_{4} , we exhibit an explicit discriminant matrix and show that the slice of the discriminant for a fixed j j -invariant is the cone over the dual variety of an elliptic curve.

Landscape Metrics and Visual Topology in the Analysis of Landscape Preference

Recognition of the value of landscapes, environmentally, economically, and to quality of life—and, importantly, the embedding of these concepts in legislation such as the European Landscape Convention—has led to the need for an ‘objective’ assessment of these values and the potential impact of changes to them. But studies relating preference information to metric analysis of planimetric viewsheds have so far provided only limited explanation of preference. It has been suggested that this is due to the effect of perspective on the visual topology of the view generating different metrics in perspective from those on the flat map. The completion of the Pan European Study under the EU Framework 5 Visulands project provided a large sample of preference responses to a limited number of computer-generated simple landscape scenarios. As such this is an ideal opportunity to test the significance of perspective on metric correlation with preference. This paper considers the degree to which metrics are altered by a panoramic or viewshed analysis, and the significance of this for any correlation with the preference scores. The implications for the role of the respective media in planning are considered, including that of 3D visualisation as a means for eliciting opinion on landscape preference.

Hyperphosphorylated tau in parahippocampal cortex impairs place learning in aged mice expressing wild-type human tau

To investigate how tau affects neuronal function during neurofibrillary tangle (NFT) formation, we examined the behavior, neural activity, and neuropathology of mice expressing wild-type human tau. Here, we demonstrate that aged (>20 months old) mice display impaired place learning and memory, even though they do not form NFTs or display neuronal loss. However, soluble hyperphosphorylated tau and synapse loss were found in the same regions. Mn-enhanced MRI showed that the activity of the parahippocampal area is strongly correlated with the decline of memory as assessed by the Morris water maze. Taken together, the accumulation of hyperphosphorylated tau and synapse loss in aged mice, leading to inhibition of neural activity in parahippocampal areas, including the entorhinal cortex, may underlie place learning impairment. Thus, the accumulation of hyperphosphorylated tau that occurs before NFT formation in entorhinal cortex may contribute to the memory problems seen in Alzheimer's disease (AD).

Simultaneous Cancellation of Fiber Loss, Dispersion, and Kerr Effect in Ultralong-Haul Optical Fiber Transmission by Midway Optical Phase Conjugation Incorporated With Distributed Raman Amplification

An alternative application of distributed Raman amplification (DRA) for ultralong-haul optical fiber transmission is proposed. In our study, the DRA is employed in a transmission system using midway optical phase conjugation (OPC) for amplifying an optical signal and, at the same time, for constructing signal power evolution, which is symmetrical with respect to the midpoint of the system where the OPC is performed. Then, the nonlinear signal waveform distortions that are caused by the Kerr effect, as well as fiber dispersion, are almost completely compensated by the OPC, whereas the fiber loss is compensated by the DRA. Three possible symmetrical signal power maps - a power map that has a reverse sign of the power map that is caused by lump amplification, a flat signal power map, and an arbitrary symmetrical signal power map - are numerically designed by using appropriate Raman pump powers. We show that the flat power map exhibits smaller difference from the target and a higher optical signal-to-noise ratio and requires lower pump power than the other two power maps. Numerical simulation results demonstrate that, by employing the flat power maps with a span of 40 km, a single-wavelength signal whose data rate is 160 Gb/s can be successfully transmitted over 5000 km, and the Kerr effect is sufficiently suppressed near limitation due to the nonlinear accumulation of noise. Finally, we study the feasibility of expanding our method to wavelength-division-multiplexed signal transmission by designing a DRA gain with multiple-wavelength pumping to simultaneously obtain a flat power map and a wide-and-flat gain bandwidth. By using four-wavelength Raman pumps while carefully choosing pump wavelengths and their powers, we achieve the DRA gain that simultaneously gives a fluctuation of the signal power of only 3.5%, a gain ripple of only 5.3%, and, at the same time, a gain bandwidth of as wide as 46 nm.

Introducing Plan Oblique Relief

Plan oblique relief is a new digital technique for rendering three dimensional terrain on otherwise planimetric (conventional flat) maps. Landforms shown realistically in side view have an illustrative quality that appeals to readers. Inspired by the work of manual mapmakers of the past, the paper begins with a historical review that includes maps by Xaver Imfeld of Switzerland, Erwin Raisz of the United States, and Heinrich Berann of Austria. In the next, digital techniques section, the projections and rendering parameters needed to create plan oblique relief receive attention, as does Natural Scene Designer 5.0, the first commercial software to offer this functionality. The section on design takes a candid look at the advantages and disadvantages of plan oblique relief. The paper ends on a practical note by discussing two maps made by the authors that feature plan oblique relief, one a panorama and the other a physical map.

With Nondiagnostic ECG, Use Body Surface Mapping

With Nondiagnostic ECG, Use Body Surface Mapping

Techniques for Mapping Theoretical Shadow Zones for Direct P and S Waves Propagated as Rays from an Earthquake Epicenter

This paper presents results about the effectiveness of different student-centered instructional methods on undergraduate student perceptions of a spatial phenomenon, earthquake P and S wave shadow zones, in introductory geology classes. Textbooks commonly illustrate earthquake P and S wave shadow zones using ray tracing techniques with an epicenter at the North Pole and the shadow zone south of the equator. Shadow zones differ for earthquake locations else where. Shadow zones for earthquakes at locations around the world can be hand plotted using a globe and a map of the Earth. The plotter gains experience in using latitude and longitude for plotting, understanding global geography, translating spherical geographic data to a two-dimensional map, and gains a better understanding of seismic waves and the Earth's interior. The concept also explains how satellite orbits appear on flat maps and the concept of great circle paths. The shadow zone can also be mapped digitally using a Geographic Information System (GIS), such as ArcView™ GIS with the similar results. Overall, 81.5% of the student participants considered both instructional methods an enhancement to their understanding of the earth's interior, globes, maps and shadow zones. The results suggest that student alternate conceptions of the representation of geospatial data in 2D and 3D can be influenced by both traditional paper exercises and activities that teach with GIS technology.

“All flat maps, and I am one”: Cartographic References in the Poems of John Donne

Drawing both on the medieval Mappae mundi and the Ptolemaic tradition revived in the Renaissance, the recurrent cartographic motif in John Donne’s poetry well reflects the preoccupations of a revolutionary period in the history of Western cartography. Yet, for all its cosmic magnitude, Donne’s poems, both holy and secular, are turned, not so much towards an exploration of the world as towards an exploration of the Self as the ultimate object of reflection.

A GIS-based borehole data management and 3D visualization system

The use of subsurface data for problem solving is limited in part by the freedom the user has in their choice of data structures. If a user is allowed to work with the data in a familiar way, they can spend more time performing analysis tasks and less time restructuring data, thus increasing productivity and reducing the risks associated with a series of data modification cycles. Borehole information system (BoreIS) is based upon this principle. Design was guided by interviews with geologists who were targeted as potential users of the software, and BoreIS was developed as an extension to ESRI's ArcScene three-dimensional (3D) GIS environment. BoreIS uses borehole or well data supplied by the user to develop a 3D GIS representation which can be queried, visualized, and analysed. By asking relevant questions about data stored in Excel spreadsheets, BoreIS can automate many high-level GIS functions so that an inexperienced GIS user can still use the system. By matching table elements to spatially and geologically significant terms through the interactive setup, users can work with the data more closely matched to the geological problem domain. This allows the novice user to use powerful GIS functions to discover spatial patterns in their data. BoreIS’ interactive manipulation of terms in complex queries, simple addition of contoured surfaces, and masking by lithology or formation helps geologists find spatial patterns in their data, beyond the limits of data tables and flat maps.

Multiple Objective Genetic Algorithms for Path-planning Optimization in Autonomous Mobile Robots

This paper describes the use of a genetic algorithm (GA) for the problem of offline point-to-point autonomous mobile robot path planning. The problem consists of generating “valid” paths or trajectories, for an Holonomic Robot to use to move from a starting position to a destination across a flat map of a terrain, represented by a two-dimensional grid, with obstacles and dangerous ground that the Robot must evade. This means that the GA optimizes possible paths based on two criteria: length and difficulty. First, we decided to use a conventional GA to evaluate its ability to solve this problem (using only one criteria for optimization). Due to the fact that we also wanted to optimize paths under two criteria or objectives, then we extended the conventional GA to implement the ideas of Pareto optimality, making it a multi-objective genetic algorithm (MOGA). We describe useful performance measures and simulation results of the conventional GA and of the MOGA that show that both types of GAs are effective tools for solving the point-to-point path-planning problem.

Map Projections and the Visual Detective: How to Tell if a Map is Equal-Area, Conformal, or Neither

The ability to see whether a map is equal-area, conformal, or neither is useful for looking intelligently at large-area maps. For example, only if a map is equal-area can reliable judgments of relative size be made. If a map is equal-area, latitude-longitude cells are equal in size between a given pair of parallels, the cells between a given pair of meridians get smaller toward the poles, cells the same number of degrees on either side of the equator are equal in size, and linear scale change in one direction is balanced by an opposite change in the perpendicular direction. If a map is conformal, parallels and meridians meet at right angles, linear scale change in one direction is the same as in the perpendicular direction, and the map is obviously not equal-area. If at least one observation is violated for both equal-area and conformal, the projection is neither. No flat map can be both.

A "Slice-and-Dice" Approach to Area Equivalence in Polyhedral Map Projections

For centuries, people have been intrigued by map projections upon polyhedra—the surface of the Earth laid out on the faces of polyhedral bodies (beautiful in themselves)—which are then unfolded to make flat maps of the world. This paper describes a simple "slice-and-dice" method to obtain area equivalence, which is applied to polyhedral globes. The implementations of this method include a projection that is equivalent to Snyder's equal-area projection for Platonic bodies, an equal-area projection with far smaller cusps, and an equal-area projection that obtains constant scale along the polyhedron's edges. The latter two are presented in terms of exact equations and are compared with Snyder's projection.

A COM-based expert system for selecting the suitable map projection in ArcGIS

Abstract A map projection is a systematic rendering of locations from the curved earth surface onto a flat map surface. It is impossible to make spherical maps into perfectly flat papers without some distortion. There are many projections, each with its own advantages and disadvantages. No single projection can maintain all of the important spatial variables such as shape, area, direction, and distance. A successful Geographic Information System (GIS) depends in large part on using map projections correctly, and a person's skills in managing and converting projections can dictate the value of a database. GIS software packages such as ArcGIS provides GIS analyst with many projections from which the analyst must choose the one suitable for his project. Map projection selection is a complex process involving an evaluation of map projection alternatives based on a set of characteristics that describe these projections and the types of analysis to be performed. This paper presents a prototype expert system for selecting the suitable map projection. The component object model (COM) technology is used in designing and integrating the prototype expert system with ArcGIS to achieve software interoperability.