Aspects of atomic decompositions and Bergman projections

The concept of an atomic decomposition was introduced by Coifman and Rochberg (1980) for weighted Bergman spaces on the unit disk. By the Riemann mapping theorem, functions in every simply connected domain in the complex plane have an atomic decomposition. However, a decomposition resulting from a conformal mapping of the unit disk tends to be very implicit and often lacks a clear connection to the geometry of the domain that it has been mapped into. The lattice of points, where the atoms of the decomposition are evaluated, usually follows the geometry of the original domain, but after mapping the domain into another this connection is easily lost and the layout of points becomes seemingly random. In the first article we construct an atomic decomposition directly on a weighted Bergman space on a class of regulated, simply connected domains. The construction uses the geometric properties of the regulated domain, but does not explicitly involve any conformal Riemann map from the unit disk. It is known that the Bergman projection is not bounded on the space L-infinity of bounded measurable functions. Taskinen (2004) introduced the locally convex spaces LV-infinity consisting of measurable and HV-infinity of analytic functions on the unit disk with the latter being a closed subspace of the former. They have the property that the Bergman projection is continuous from LV-infinity onto HV-infinity and, in some sense, the space HV-infinity is the smallest possible substitute to the space H-infinity of analytic functions. In the second article we extend the above result to a smoothly bounded strictly pseudoconvex domain. Here the related reproducing kernels are usually not known explicitly, and thus the proof of continuity of the Bergman projection is based on generalised Forelli-Rudin estimates instead of integral representations. The minimality of the space LV-infinity is shown by using peaking functions first constructed by Bell (1981). Taskinen (2003) showed that on the unit disk the space HV-infinity admits an atomic decomposition. This result is generalised in the third article by constructing an atomic decomposition for the space HV-infinity on a smoothly bounded strictly pseudoconvex domain. In this case every function can be presented as a linear combination of atoms such that the coefficient sequence belongs to a suitable Köthe co-echelon space.

Characteristics of Corticospinal Projections to the Intrinsic Hand Muscles in Skilled Harpists.

The process of learning to play a musical instrument necessarily alters the functional organisation of the cortical motor areas that are involved in generating the required movements. In the case of the harp, the demands placed on the motor system are quite specific. During performance, all digits with the sole exception of the little finger are used to pluck the strings. With a view to elucidating the impact of having acquired this highly specialized musical skill on the characteristics of corticospinal projections to the intrinsic hand muscles, focal transcranial magnetic stimulation (TMS) was used to elicit motor evoked potentials (MEPs) in three muscles (of the left hand): abductor pollicis brevis (APB); first dorsal interosseous (FDI); and abductor digiti minimi (ADM) in seven harpists. Seven non-musicians served as controls. With respect to the FDI muscle–which moves the index finger, the harpists exhibited reliably larger MEP amplitudes than those in the control group. In contrast, MEPs evoked in the ADM muscle–which activates the little finger, were smaller in the harpists than in the non-musicians. The locations on the scalp over which magnetic stimulation elicited discriminable responses in ADM also differed between the harpists and the non-musicians. This specific pattern of variation in the excitability of corticospinal projections to these intrinsic hand muscles exhibited by harpists is in accordance with the idiosyncratic functional demands that are imposed in playing this instrument.

Gene expression mapping in neuropathic pain : molecular plasticity in nociceptors and superficial dorsal horn

RESUME : La douleur neuropathique est le résultat d'une lésion ou d'un dysfonctionnement du système nerveux. Les symptômes qui suivent la douleur neuropathique sont sévères et leur traitement inefficace. Une meilleure approche thérapeutique peut être proposée en se basant sur les mécanismes pathologiques de la douleur neuropathique. Lors d'une lésion périphérique une douleur neuropathique peut se développer et affecter le territoire des nerfs lésés mais aussi les territoires adjacents des nerfs non-lésés. Une hyperexcitabilité des neurones apparaît au niveau des ganglions spinaux (DRG) et de la corne dorsale (DH) de la moelle épinière. Le but de ce travail consiste à mettre en évidence les modifications moléculaires associées aux nocicepteurs lésés et non-lésés au niveau des DRG et des laminae I et II de la corne dorsale, là où l'information nociceptive est intégrée. Pour étudier les changements moléculaires liés à la douleur neuropathique nous utilisons le modèle animal d'épargne du nerf sural (spared nerve injury model, SNI) une semaine après la lésion. Pour la sélection du tissu d'intérêt nous avons employé la technique de la microdissection au laser, afin de sélectionner une sous-population spécifique de cellules (notamment les nocicepteurs lésés ou non-lésés) mais également de prélever le tissu correspondant dans les laminae superficielles. Ce travail est couplé à l'analyse à large spectre du transcriptome par puce ADN (microarray). Par ailleurs, nous avons étudié les courants électriques et les propriétés biophysiques des canaux sodiques (Na,,ls) dans les neurones lésés et non-lésés des DRG. Aussi bien dans le système nerveux périphérique, entre les neurones lésés et non-lésés, qu'au niveau central avec les aires recevant les projections des nocicepteurs lésés ou non-lésés, l'analyse du transcriptome montre des différences de profil d'expression. En effet, nous avons constaté des changements transcriptionnels importants dans les nocicepteurs lésés (1561 gènes, > 1.5x et pairwise comparaison > 77%) ainsi que dans les laminae correspondantes (618 gènes), alors que ces modifications transcriptionelles sont mineures au niveau des nocicepteurs non-lésés (60 gènes), mais important dans leurs laminae de projection (459 gènes). Au niveau des nocicepteurs, en utilisant la classification par groupes fonctionnels (Gene Ontology), nous avons observé que plusieurs processus biologiques sont modifiés. Ainsi des fonctions telles que la traduction des signaux cellulaires, l'organisation du cytosquelette ainsi que les mécanismes de réponse au stress sont affectés. Par contre dans les neurones non-lésés seuls les processus biologiques liés au métabolisme et au développement sont modifiés. Au niveau de la corne dorsale de la moelle, nous avons observé des modifications importantes des processus immuno-inflammatoires dans l'aire affectée par les nerfs lésés et des changements associés à l'organisation et la transmission synaptique au niveau de l'aire des nerfs non-lésés. L'analyse approfondie des canaux sodiques a démontré plusieurs changements d'expression, principalement dans les neurones lésés. Les analyses fonctionnelles n'indiquent aucune différence entre les densités de courant tétrodotoxine-sensible (TTX-S) dans les neurones lésés et non-lésés même si les niveaux d'expression des ARNm des sous-unités TTX-S sont modifiés dans les neurones lésés. L'inactivation basale dépendante du voltage des canaux tétrodotoxine-insensible (TTX-R) est déplacée vers des potentiels positifs dans les cellules lésées et non-lésées. En revanche la vitesse de récupération des courants TTX-S et TTX-R après inactivation est accélérée dans les neurones lésés. Ces changements pourraient être à l'origine de l'altération de l'activité électrique des neurones sensoriels dans le contexte des douleurs neuropathiques. En résumé, ces résultats suggèrent l'existence de mécanismes différenciés affectant les neurones lésés et les neurones adjacents non-lésés lors de la mise en place la douleur neuropathique. De plus, les changements centraux au niveau de la moelle épinière qui surviennent après lésion sont probablement intégrés différemment selon la perception de signaux des neurones périphériques lésés ou non-lésés. En conclusion, ces modulations complexes et distinctes sont probablement des acteurs essentiels impliqués dans la genèse et la persistance des douleurs neuropathiques. ABSTRACT : Neuropathic pain (NP) results from damage or dysfunction of the peripheral or central nervous system. Symptoms associated with NP are severe and difficult to treat. Targeting NP mechanisms and their translation into symptoms may offer a better therapeutic approach.Hyperexcitability of the peripheral and central nervous system occurs in the dorsal root ganglia (DRG) and the dorsal horn (DH) of the spinal cord. We aimed to identify transcriptional variations in injured and in adjacent non-injured nociceptors as well as in corresponding laminae I and II of DH receiving their inputs.We investigated changes one week after the injury induced by the spared nerve injury model of NP. We employed the laser capture microdissection (LCM) for the procurement of specific cell-types (enrichment in nociceptors of injured/non-injured neurons) and laminae in combination with transcriptional analysis by microarray. In addition, we studied functionál properties and currents of sodium channels (Nav1s) in injured and neighboring non-injured DRG neurons.Microarray analysis at the periphery between injured and non-injured DRG neurons and centrally between the area of central projections from injured and non-injured neurons show significant and differential expression patterns. We reported changes in injured nociceptors (1561 genes, > 1.5 fold, >77% pairwise comparison) and in corresponding DH laminae (618 genes), while less modifications occurred in non-injured nociceptors (60 genes) and in corresponding DH laminae (459 genes). At the periphery, we observed by Gene Ontology the involvement of multiple biological processes in injured neurons such as signal transduction, cytoskeleton organization or stress responses. On contrast, functional overrepresentations in non-injured neurons were noted only in metabolic or developmentally related mechanisms. At the level of superficial laminae of the dorsal horn, we reported changes of immune and inflammatory processes in injured-related DH and changes associated with synaptic organization and transmission in DH corresponding to non-injured neurons. Further transcriptional analysis of Nav1s indicated several changes in injured neurons. Functional analyses of Nav1s have established no difference in tetrodotoxin-sensitive (TTX-S) current densities in both injured and non-injured neurons, despite changes in TTX-S Nav1s subunit mRNA levels. The tetrodotoxin-resistant (TTX-R) voltage dependence of steady state inactivation was shifted to more positive potentials in both injured and non-injured neurons, and the rate of recovery from inactivation of TTX-S and TTX-R currents was accelerated in injured neurons. These changes may lead to alterations in neuronal electrogenesis. Taken together, these findings suggest different mechanisms occurring in the injured neurons and the adjacent non-injured ones. Moreover, central changes after injury are probably driven in a different manner if they receive inputs from injured or non-injured neurons. Together, these distinct and complex modulations may contribute to NP.

A Framework for Exploring Multidimensional Data with 3D Projections

Visualization of high-dimensional data requires a mapping to a visual space. Whenever the goal is to preserve similarity relations a frequent strategy is to use 2D projections, which afford intuitive interactive exploration, e. g., by users locating and selecting groups and gradually drilling down to individual objects. In this paper, we propose a framework for projecting high-dimensional data to 3D visual spaces, based on a generalization of the Least-Square Projection (LSP). We compare projections to 2D and 3D visual spaces both quantitatively and through a user study considering certain exploration tasks. The quantitative analysis confirms that 3D projections outperform 2D projections in terms of precision. The user study indicates that certain tasks can be more reliably and confidently answered with 3D projections. Nonetheless, as 3D projections are displayed on 2D screens, interaction is more difficult. Therefore, we incorporate suitable interaction functionalities into a framework that supports 3D transformations, predefined optimal 2D views, coordinated 2D and 3D views, and hierarchical 3D cluster definition and exploration. For visually encoding data clusters in a 3D setup, we employ color coding of projected data points as well as four types of surface renderings. A second user study evaluates the suitability of these visual encodings. Several examples illustrate the framework`s applicability for both visual exploration of multidimensional abstract (non-spatial) data as well as the feature space of multi-variate spatial data.

Least square projection: A fast high-precision multidimensional projection technique and its application to document mapping

The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analyses of various kinds. This paper presents a novel multidimensional projection technique based on least square approximations. The approximations compute the coordinates of a set of projected points based on the coordinates of a reduced number of control points with defined geometry. We name the technique Least Square Projections ( LSP). From an initial projection of the control points, LSP defines the positioning of their neighboring points through a numerical solution that aims at preserving a similarity relationship between the points given by a metric in mD. In order to perform the projection, a small number of distance calculations are necessary, and no repositioning of the points is required to obtain a final solution with satisfactory precision. The results show the capability of the technique to form groups of points by degree of similarity in 2D. We illustrate that capability through its application to mapping collections of textual documents from varied sources, a strategic yet difficult application. LSP is faster and more accurate than other existing high-quality methods, particularly where it was mostly tested, that is, for mapping text sets.

Multidimensional Projections for Visual Analysis of Social Networks

Visual analysis of social networks is usually based on graph drawing algorithms and tools. However, social networks are a special kind of graph in the sense that interpretation of displayed relationships is heavily dependent on context. Context, in its turn, is given by attributes associated with graph elements, such as individual nodes, edges, and groups of edges, as well as by the nature of the connections between individuals. In most systems, attributes of individuals and communities are not taken into consideration during graph layout, except to derive weights for force-based placement strategies. This paper proposes a set of novel tools for displaying and exploring social networks based on attribute and connectivity mappings. These properties are employed to layout nodes on the plane via multidimensional projection techniques. For the attribute mapping, we show that node proximity in the layout corresponds to similarity in attribute, leading to easiness in locating similar groups of nodes. The projection based on connectivity yields an initial placement that forgoes force-based or graph analysis algorithm, reaching a meaningful layout in one pass. When a force algorithm is then applied to this initial mapping, the final layout presents better properties than conventional force-based approaches. Numerical evaluations show a number of advantages of pre-mapping points via projections. User evaluation demonstrates that these tools promote ease of manipulation as well as fast identification of concepts and associations which cannot be easily expressed by conventional graph visualization alone. In order to allow better space usage for complex networks, a graph mapping on the surface of a sphere is also implemented.

Gakara region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4673-I (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Gakara. Printed in: 1994. Covers portions of Gakara region, Burundi. Sheet: 4673-I. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Bubanza region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4674-I (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Bubanza. Printed in: 1994. Covers portions of Bubanza region, Burundi. Sheet: 4674-I. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Bujumbura region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4674-II (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Bujumbura. Printed in: 1994. Covers portions of Bujumbura region, Burundi. Sheet: 4674-II. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Butahana region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4675-I (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Butahana. Printed in: 1994. Covers portions of Butahana region, Burundi. Sheet: 4675-I. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Ndora region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4675-II (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Ndora. Printed in: 1994. Covers portions of Ndora region, Burundi. Sheet: 4675-II. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Cibitoke region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4675-III (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Cibitoke. Printed in: 1994. Covers portions of Cibitoke region, Burundi. Sheet: 4675-III. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Mabayi region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4675-IV (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Mabayi. Printed in: 1994. Covers portions of Mabayi region, Burundi. Sheet: 4675-IV. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Mabanda region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4772-II (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Mabanda. Printed in: 1994. Covers portions of Mabanda region, Burundi. Sheet: 4772-II. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Nyanza-Lac region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4772-III (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Nyanza-Lac. Printed in: 1994. Covers portions of Nyanza-Lac region, Burundi. Sheet: 4772-III. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.