ARD Sounds (until March 2026: ARD Audiothek) is the joint audio portal of the state broadcasting stations of the ARD and Deutschlandradio on the Internet. The service was officially launched as a mobile app on November 8, 2017, on the occasion of the ARD Radio Play Days in Karlsruhe. A beta web version has also been available since November 2018; it replaces the radio features in the ARD Mediathek, which has since offered only video content. Editorial support for the ARD Audiothek is provided by the ARD, the online editorial team in Mainz. In April 2018, the ARD Audiothek won the German Digital Award in silver in the category "Mobile Apps - User Experience / Usability". Within a year, the mobile app version had been installed more than 510,000 times and had around 21 million audio views. The Android app recorded more than 100,000 downloads in October 2019, according to the Google Play Store.
Opponent process
The opponent process is a hypothesis of color vision that states that the human visual system interprets information about color by processing signals from the three types of photoreceptor cells in an antagonistic manner. The three types of cones are called L, M, and S. The names stand for "Long wavelength sensitive,” "middle wavelength sensitive," and "short wavelength sensitive." The opponent-process theory implicates three opponent channels: L versus M, S versus (L+M), and a luminance channel (+ versus -). These cone-opponent mechanisms were at one time thought to be the neural substrate for a psychological theory called Hering's Opponent Colors Theory, which calls for three psychologically important opponent color processes: red versus green, blue versus yellow, and black versus white (luminance). The Opponent Colors Theory is named for the German physiologist Ewald Hering who proposed the idea in the late 19th century. However, it has been argued that Hering’s Opponent Colors Theory lacks adequate phenomenological and empirical support, and may not be a necessary feature of normal human color experience. Correspondingly, considerable physiological and behavioral evidence proves that the physiological cone opponent mechanisms do not constitute the neurobiological basis for Hering's Opponent Colors Theory. == Color theory == === Complementary colors === When staring at a bright color for a while (e.g. red), then looking away at a white field, an afterimage is perceived, such that the original color will evoke its complementary color (cyan, in the case of red input). When complementary colors are combined or mixed, they "cancel each other out" and become neutral (white or gray). That is, complementary colors are never perceived as a mixture; there is no "greenish red" or "yellowish blue", despite claims to the contrary. The strongest color contrast that a color can have is its complementary color. Complementary colors may also be called "opposite colors" and they were originally considered the primary evidence in support of Hering's Opponent Colors Theory. There are two fatal problems with this evidence. First, the complement of red is not green, as called for by Hering's theory; it is bluish-green. And second, there exists a complementary color for every color, so there is nothing special about the set of complementary pairs picked out by Hering's theory. === Unique hues === The colors that define the extremes for each opponent channel are called unique hues, as opposed to composite (mixed) hues. Ewald Hering first defined the unique hues as red, green, blue, and yellow, and based them on the concept that these colors could not be simultaneously perceived. For example, a color cannot appear both red and green. These definitions have been experimentally refined and are represented today by average hue angles of 353° (carmine red), 128° (cobalt green), 228° (cobalt blue), 58° (yellow). The unique hues are a defining feature of many psychological color spaces, but there is substantial evidence showing that the unique hues are not hard wired in the nervous system, contrary to the stipulations of Hering's Opponent Colors Theory. Unique hues can differ between individuals and are often used in psychophysical research to measure variations in color perception due to color-vision deficiencies or color adaptation. While there is considerable inter-subject variability when defining unique hues experimentally, an individual's unique hues are very consistent, to within a few nanometers of wavelength. == Physiological basis == === Relation to LMS color space === The trichromatic theory is in conflict with Hering's Opponent Colors Theory, although it is compatible with a physiological opponent process that compares the outputs of the different classes of cone types. The poles of these cone opponent mechanisms do not correspond to the unique hues of Hering's Opponent Colors Theory and unlike the unique hues, have no privilege in color perception. Most humans have three different cone cells in their retinas that facilitate trichromatic color vision. Colors are determined by the proportional excitation of these three cone types, i.e. their quantum catch. The levels of excitation of each cone type are the parameters that define LMS color space. To calculate the opponent process tristimulus values from the LMS color space, the cone excitations must be compared: The luminous (achromatic) opponent channel is a weighted sum of all three cone cells (plus the rod cells in some conditions). The red–green opponent channel is equal to the difference of the L- and M-cones. The blue–yellow opponent channel is equal to the difference of the S-cone and the average/weighted sum of the L- and M-cones. Most mammals have no L cone (the primate L cone arose from a gene duplication of the M cone opsin gene). These mammals still show two kinds of opponent channels in their retinal ganglion cells: the achromatic channel and the blue-yellow opponency channel. === Cone opponent mechanisms are encoded in the retina === The output of different types of cones are compared by cells in the retina including retina bipolar cells (which compare signals from L and M cones) and bistratified retinal ganglion cells (which compare S cone signals with L and M cone signals). The output of bipolar cells is relayed to the visual cortex by the retinal ganglion cells (RGCs) by way of a thalamic relay station called the lateral geniculate nucleus (LGN) of the thalamus. Much of the scientific knowledge of retinal ganglion cell physiology was obtained by neural recordings of cells in the LGN. The cone-opponent mechanisms in the retina and LGN represent a fundamental physiological opponent process but do not represent the unique hues (or Hering's Opponent Colors Theory). For example, the colors that best elicit responses of the bistratified S-(L+M)-opponent neurons are best described as purplish (or lavender) and lime-green, not "blue" and "yellow". The neurons are sometimes referred to as "blue–yellow" neurons, but this is a historical artifact dating to the time when it was thought that Hering's Opponent Colors Theory was hardwired by the retina and the mismatch between the colors to which they are optimally tuned and Hering's Opponent Colors was overlooked. Cone opponent mechanisms exist in the retinas of many mammals, including monkeys, mice, and cats. In primates, the LGN contains three major classes of layers: Magnocellular layers (M, large-cell) – responsible largely for the luminance channel Parvocellular layers (P, small-cell) – responsible largely for red–green opponency Koniocellular layers (K) – responsible largely for blue–yellow opponency, poor spatial resolution, long latency Other mammals such as cats also have three cell types denoted as X (magno), Y (parvo), and W (konio). The W type is beyond most doubt homologous to the primate K type. There are some subtle differences between the M and X types as well as the Y and P types to make the correspondence unclear. === Advantage === Transmitting information in opponent-channel color space could be advantageous over transmitting it in LMS color space ("raw" signals from each cone type). There is some overlap in the wavelengths of light to which the three types of cones (L for long-wave, M for medium-wave, and S for short-wave light) respond, so it is more efficient for the visual system (from a perspective of dynamic range) to record differences between the responses of cones, rather than each type of cone's individual response. Hurvich and Jameson argued that the use of opponent-channel color space would increase color contrast, making the information easier to process by later stages of vision. === Color blindness === Color blindness can be classified by the cone cell that is affected (protan, deutan, tritan) or by the opponent channel that is affected (red–green or blue–yellow). In either case, the channel can either be inactive (in the case of dichromacy) or have a lower dynamic range (in the case of anomalous trichromacy). For example, individuals with deuteranopia see little difference between the red and green unique hues. == History == Johann Wolfgang von Goethe first studied the physiological effect of opposed colors in his Theory of Colours in 1810. Goethe arranged his color wheel symmetrically "for the colours diametrically opposed to each other in this diagram are those which reciprocally evoke each other in the eye. Thus, yellow demands purple; orange, blue; red, green; and vice versa: Thus again all intermediate gradations reciprocally evoke each other." Ewald Hering proposed opponent color theory in 1892. He thought that the colors red, yellow, green, and blue are special in that any other color can be described as a mix of them, and that they exist in opposite pairs. That is, either red or green is perceived and never greenish-red: Even though yellow is a mixture of red and green in the RGB color theory, humans
The Citation Project
The Citation Project is a series of studies that measure and analyze first-year college writing students' source use and their ability to understand and implement sources within their own writing. The Citation Project reveals students' source-use habits and the issues that can be seen based on their lack of proper citation skills, such as the prevalence of plagiarism, institution policies, and the results of current writing pedagogy. The Citation Project's central findings were first presented at the Conference on College Composition and Communication in 2012. Although The Citation Project originally referred to this single 2012 study, the feedback received led to the conception of the Project as a broader initiative and as a place to gather and publish studies and data relating to student writing habits for the usage of other researches. == Method == The Citation Project's data comes from the work of 20 researchers analyzing 174 first-year composition students' research papers. The student papers studied originated from 16 institutions across the United States of America, including community colleges, public and private universities, denominational colleges, and Ivy Leagues. Researchers used bibliographic coding to aggregate data regarding the type, length, reading level, and usage of students' sources. == Findings == === Student source assessment and use === This study found that students were capable of identifying, locating, and accessing librarian-approved academic sources, most commonly accessing them with the internet. Despite students demonstrating their ability to find appropriate sources, they tend to exclusively cite the first few pages of their sources. Students' use and analysis of their citations are often limited, frequently resorting to patchwriting, directly restating their source's points, and omitting their own interpretations of their reference's ideas. The Citation Project also highlights students' struggle to accurately determine, address, and value their sources' bias, authority, and credibility. According to the Project's researchers' analysis, these habits demonstrate that first-year college writing students minimally engage with their sources and the academic conversations between them. One researcher from the Citation Project, Rebecca Moore Howard, believes these findings do not point towards students being lazy, but is rather a result of a writing pedagogy that prioritizes efficient, product-focused writing. Another interpretation offered by Sandra Jamieson, another researcher from the Citation Project explains their findings as a result of a lack of adherence to Information Learning (IL) Standards. === Pedagogy === A significant focus of The Citation Project is the development of pedagogical practices intended to equip students with writing and research techniques that will set them up for future success. Writers associated with The Citation Project, such as Tricia Serviss, believe that the practices of teachers surrounding academic integrity and writing practices are what form the foundation of how students think about writing and how to engage with assignments throughout their academic career. They also stress the importance of teaching students to effectively engage with sources rather than simply how to correctly cite them. The Citation Project asserts that endowing students with the ability to read, understand, and synthesize a variety of sources in their writing is a skill that will benefit them throughout their academic careers, and that the surface level typographical focus that many writing programs utilize is inadequate. == Plagiarism == One of the areas that The Citation Project also looks at is how students commit plagiarism throughout their writing. Plagiarism tends to be a checkpoint that gives instructors a sense where students' citation skills stand. Findings from The Citation Project reveal that the most common type of plagiarism is patchwriting which is the act of using the same sentence with only changing a couple of words. These types of issues can be seen as a learning curve due to lack of proper training. Student's that commit plagiarism are often unaware. === Policies === Another issue found is that academic plagiarism policies may not benefit a student's growth but may instead obstruct it. Policies against plagiarism tend to be harsh on the student that committed of offense. Even though student plagiarism is often unintentional academic institutions see this behavior as intentional. Student may then face harsh consequences as a result from their lack of citation knowledge. Additionally, higher level institutions assume that new students already have the skill set to avoid plagiarism which may be an unrealistic expectation. == Legacy == === Inspired studies === ==== Parrott and Napier ==== In one study, "Critical Reading and Student Self-Selected Texts: Results of a Collaborative, Explicit Curricular Approach," Jill Parrot and Trenia Napier quoted the Citation Project's findings as evidence that current collegiate writing curriculums are an ineffective means of teaching students how to properly write academic research papers. The researchers accredited current writing pedagogy's lack of emphasis on teaching critical reading skills. Parrott and Napier tested their thesis by seeing if students would produce more academic writing if they partook in a writing course that taught critical reading. Their results mostly went against this hypothesis, finding students who received additional critical reading training only significantly improved in how they integrated their sources. ==== Kocatepe ==== In May Mehtap Kocatep's study, "Reconceptualising the notion of finding information: How undergraduate students construct information as they read-to-write in an academic writing class," Kocatep expresses that she believes current conversations around writing pedagogy, including the Citation Project, operate with the underlying misconception that information is an easily discoverable static entity and its retrieval is an objective, unbiased decision. Kocatepe instead offers the analysis of what students view as valuable information and if it is worth using is influenced by the socially constructed meanings available to writers at the moment. To further examine students' source engagement, Kocatepe did a study on how female university students from the United Arab Emirates find, retrieve, use, and value sources. Kocatepe's results mainly noted students' almost exclusive reliance on using Google to find sources, as well as how students' navigated mainly English-speaking academic conversations as non-native English speakers. ==== Dahlen, Nordstrom-Sanchez, and Graff ==== Dahlen, Nordstrom-Sanchez, and Graff built their study off The Citation Project research in order to explore the attitudes and practices of students in an undergraduate writing course. As the researchers acknowledge, data collected by the Citation Project was the subject of the bulk of their analysis. This study sought to examine undergraduate writing practices tied to source-usage and elucidate any relevant trends. Dahlen, Nordstrom-Sanchez and Graff found that undergraduate writing students were not engaging with outside sources properly. Key issues discussed include lack of engagement with broad source ideas (in favor of picking out quotes), lack of paraphrasing, and inability to link information between multiple sources. ==== Davis ==== Phillip M. Davis based much of the analysis in his study on data gathered by the Citation Project. This study aimed to examine the particular effects web-based research and study had on undergraduate's papers and the replicability of their bibliographies. Davis sought to see how the shift from physical in-person library based research to online, often at-home research changed the function and usability of the bibliography as a form of documenting source usage in a given work. The primary method of analysis involved examining students' bibliographies to see where they were finding information online and how these sources were accessed. A main issue Davis found was "persistency" of URLs used for online citations. He found that only 18% of URL-based citations continued to function (the others either no longer pointing to the correct document or ceasing to exist altogether) within 3 years of their usage by students, and more than half of claimed online citations could not be found in any form. He suggests that this result brings up questions about how web-based citations should be dealt with in a university context.
Online public access catalog
The online public access catalog (OPAC), now frequently synonymous with library catalog, is an online database of materials held by a library or group of libraries. Online catalogs have largely replaced the analog card catalogs previously used in libraries. == History == === Early online === Although a handful of experimental systems existed as early as the 1960s, the first large-scale online catalogs were developed at Ohio State University in 1975 and the Dallas Public Library in 1978. These and other early online catalog systems tended to closely reflect the card catalogs that they were intended to replace. Using a dedicated terminal or telnet client, users could search a handful of pre-coordinate indexes and browse the resulting display in much the same way they had previously navigated the card catalog. Throughout the 1980s, the number and sophistication of online catalogs grew. The first commercial systems appeared, and would by the end of the decade largely replace systems built by libraries themselves. Library catalogs began providing improved search mechanisms, including Boolean and keyword searching, as well as ancillary functions, such as the ability to place holds on items that had been checked-out. At the same time, libraries began to develop applications to automate the purchase, cataloging, and circulation of books and other library materials. These applications, collectively known as an integrated library system (ILS) or library management system, included an online catalog as the public interface to the system's inventory. Most library catalogs are closely tied to their underlying ILS system. === Stagnation and dissatisfaction === The 1990s saw a relative stagnation in the development of online catalogs. Although the earlier character-based interfaces were replaced with ones for the Web, both the design and the underlying search technology of most systems did not advance much beyond that developed in the late 1980s. At the same time, organizations outside of libraries began developing more sophisticated information retrieval systems. Web search engines like Google and popular e-commerce websites such as Amazon.com provided simpler to use (yet more powerful) systems that could provide relevancy ranked search results using probabilistic and vector-based queries. Prior to the widespread use of the Internet, the online catalog was often the first information retrieval system library users ever encountered. Now accustomed to web search engines, newer generations of library users have grown increasingly dissatisfied with the complex (and often arcane) search mechanisms of older online catalog systems. This has, in turn, led to vocal criticisms of these systems within the library community itself, and in recent years to the development of newer (often termed 'next-generation') catalogs. === Next-generation catalogs === Newer generations of library catalog systems, typically called discovery systems (or a discovery layer), are distinguished from earlier OPACs by their use of more sophisticated search technologies, including relevancy ranking and faceted search, as well as features aimed at greater user interaction and participation with the system, including tagging and reviews. These new features rely heavily on existing metadata which may be poor or inconsistent, particularly for older records. Newer catalog platforms may be independent of the organization's integrated library system (ILS), instead providing drivers that allow for the synchronization of data between the two systems. While the original online catalog interfaces were almost exclusively built by ILS vendors, libraries have increasingly sought next-generation catalogs built by enterprise search companies and open-source software projects, often led by libraries themselves. == Union catalogs == Although library catalogs typically reflect the holdings of a single library, they can also contain the holdings of a group or consortium of libraries. These systems, known as union catalogs, are usually designed to aid the borrowing of books and other materials among the member institutions via interlibrary loan. Examples of this type of catalogs include COPAC, SUNCAT, NLA Trove, and WorldCat—the last catalogs the collections of libraries worldwide. == Related systems == There are a number of systems that share much in common with library catalogs, but have traditionally been distinguished from them. Libraries utilize these systems to search for items not traditionally covered by a library catalog, although these systems are sometimes integrated into a more comprehensive discovery system. Bibliographic databases—such as Medline, ERIC, PsycINFO, Scopus, Web of Science, and many others—index journal articles and other research data. There are also a number of applications aimed at managing documents, photographs, and other digitized or born-digital items such as Digital Commons and DSpace. Particularly in academic libraries, these systems (often known as digital library systems or institutional repository systems) assist with efforts to preserve documents created by faculty and students. Electronic resource management helps librarians to track selection, acquisition, and licensing of a library's electronic information resources.
QuickPar
QuickPar is a computer program that creates parchives used as verification and recovery information for a file or group of files, and uses the recovery information, if available, to attempt to reconstruct the originals from the damaged files and the PAR volumes. Designed for the Microsoft Windows operating system, in the past it was often used to recover damaged or missing files that have been downloaded through Usenet. QuickPar may also be used under Linux via Wine. There are two main versions of PAR files: PAR and PAR2. The PAR2 file format lifts many of its previous restrictions. QuickPar is freeware but not open-source. It uses the Reed-Solomon error correction algorithm internally to create the error correcting information. == Replacement == Since QuickPar hasn't been updated in 21 years, it is considered abandonware. Currently, MultiPar is accepted as the software that replaces QuickPar. MultiPar is actively being developed by Yutaka Sawada. == 64-bit versions == At present the command line version of QuickPar for Linux command line is available as a 64-bit version. None of the GUI versions available presently offer a 64-bit version.
Collision detection
Collision detection is the computational problem of detecting an intersection of two or more objects in virtual space. More precisely, it deals with the questions of if, when, and where two or more objects intersect. Collision detection is a classic problem of computational geometry with applications in computer graphics, physical simulation, video games, robotics (including autonomous driving), and computational physics. Collision detection algorithms can be divided into operating on 2D or 3D spatial objects. == Overview == Collision detection is closely linked to calculating the distance between objects, as objects collide when the distance between them is less than or equal to zero. Negative distances indicate that one object has penetrated another. Performing collision detection requires more context than just the distance between the objects. Accurately identifying the points of contact on both objects' surfaces is also essential for computing a physically accurate collision response. The complexity of this task increases with the level of detail in the objects' representations: the more intricate the model, the greater the computational cost. Collision detection frequently involves dynamic objects, adding a temporal dimension to distance calculations. Instead of simply measuring distance between static objects, collision detection algorithms often aim to determine whether the objects' motion will bring them to a point in time when their distance is zero—an operation that adds significant computational overhead. In collision detection involving multiple objects, a naive approach would require detecting collisions for all pairwise combinations of objects. As the number of objects increases, the number of required comparisons grows rapidly: for n {\displaystyle n} objects, n ( n − 1 ) / 2 {n(n-1)}/{2} intersection tests are needed with a naive approach. This quadratic growth makes such an approach computationally expensive as n {\displaystyle n} increases. Due to the complexity mentioned above, collision detection is a computationally intensive process. Nevertheless, it is essential for interactive applications like video games, robotics, and real-time physics engines. To manage these computational demands, extensive efforts have gone into optimizing collision detection algorithms. A commonly used approach towards accelerating the required computations is to divide the process into two phases: the broad phase and the narrow phase. The broad phase aims to answer the question of whether objects might collide, using a conservative but efficient approach to rule out pairs that clearly do not intersect, thus avoiding unnecessary calculations. Objects that cannot be definitively separated in the broad phase are passed to the narrow phase. Here, more precise algorithms determine whether these objects actually intersect. If they do, the narrow phase often calculates the exact time and location of the intersection. == Broad phase == This phase aims at quickly finding objects or parts of objects for which it can be quickly determined that no further collision test is needed. A useful property of such approach is that it is output sensitive. In the context of collision detection this means that the time complexity of the collision detection is proportional to the number of objects that are close to each other. An early example of that is the I-COLLIDE where the number of required narrow phase collision tests was O ( n + m ) {\displaystyle O(n+m)} where n {\displaystyle n} is the number of objects and m {\displaystyle m} is the number of objects at close proximity. This is a significant improvement over the quadratic complexity of the naive approach. === Spatial partitioning === Several approaches can be grouped under the spatial partitioning umbrella, which includes octrees (for 3D), quadtrees (for 2D), binary space partitioning (or BSP trees) and other, similar approaches. If one splits space into a number of simple cells, and if two objects can be shown not to be in the same cell, then they need not be checked for intersection. Dynamic scenes and deformable objects require updating the partitioning which can add overhead. === Bounding volume hierarchy === Bounding Volume Hierarchy (BVH) is a tree structure over a set of bounding volumes. Collision is determined by doing a tree traversal starting from the root. If the bounding volume of the root doesn't intersect with the object of interest, the traversal can be stopped. If, however there is an intersection, the traversal proceeds and checks the branches for each there is an intersection. Branches for which there is no intersection with the bounding volume can be culled from further intersection test. Therefore, multiple objects can be determined to not intersect at once. BVH can be used with deformable objects such as cloth or soft-bodies but the volume hierarchy has to be adjusted as the shape deforms. For deformable objects we need to be concerned about self-collisions or self intersections. BVH can be used for that end as well. Collision between two objects is computed by computing intersection between the bounding volumes of the root of the tree as there are collision we dive into the sub-trees that intersect. Exact collisions between the actual objects, or its parts (often triangles of a triangle mesh) need to be computed only between intersecting leaves. The same approach works for pair wise collision and self-collisions. === Exploiting temporal coherence === During the broad-phase, when the objects in the world move or deform, the data-structures used to cull collisions have to be updated. In cases where the changes between two frames or time-steps are small and the objects can be approximated well with axis-aligned bounding boxes, the sweep and prune algorithm can be a suitable approach. Several key observation make the implementation efficient: Two bounding-boxes intersect if, and only if, there is overlap along all three axes; overlap can be determined, for each axis separately, by sorting the intervals for all the boxes; and lastly, between two frames updates are typically small (making sorting algorithms optimized for almost-sorted lists suitable for this application). The algorithm keeps track of currently intersecting boxes, and as objects move, re-sorting the intervals helps keep track of the status. === Pairwise pruning === Once a pair of physical bodies has been selected for further investigation, collisions need to be checked more carefully. However, in many applications, individual objects (if they are not too deformable) are described by a set of smaller primitives, mainly triangles. So there are two sets of triangles, S = S 1 , S 2 , … , S n {\displaystyle S={S_{1},S_{2},\dots ,S_{n}}} and T = T 1 , T 2 , … , T n {\displaystyle T={T_{1},T_{2},\dots ,T_{n}}} (for simplicity, each set has the same number of triangles.) The obvious thing to do is to check all triangles S j {\displaystyle S_{j}} against all triangles T k {\displaystyle T_{k}} for collisions, but this involves n 2 {\displaystyle n^{2}} comparisons, which is highly inefficient. If possible, it is desirable to use a pruning algorithm to reduce the number of pairs of triangles that need to be checked. The most widely used family of algorithms is known as the hierarchical bounding volumes method. As a preprocessing step, for each object (e.g., S {\displaystyle S} and T {\displaystyle T} ) calculates a hierarchy of bounding volumes. Then, at each time step, when collisions need to be checked between S {\displaystyle S} and T {\displaystyle T} , the hierarchical bounding volumes are used to reduce the number of pairs of triangles under consideration. For simplicity, provide an example using bounding spheres, although it has been noted that spheres are undesirable in many cases. If E {\displaystyle E} is a set of triangles, a bounding sphere is pre-calculated. B ( E ) {\displaystyle B(E)} . There are many ways of choosing B ( E ) {\displaystyle B(E)} , B ( E ) {\displaystyle B(E)} is a sphere that completely contains E {\displaystyle E} and is as small as possible. Ahead of time, B ( S ) {\displaystyle B(S)} and B ( T ) {\displaystyle B(T)} can be computed. Clearly, if these two spheres do not intersect (and that is very easy to test), then neither do S {\displaystyle S} and T {\displaystyle T} . This is not much better than an n-body pruning algorithm, however. If E = E 1 , E 2 , … , E m {\displaystyle E={E_{1},E_{2},\dots ,E_{m}}} is a set of triangles, then split it into two halves L ( E ) := E 1 , E 2 , … , E m / 2 {\displaystyle L(E):={E_{1},E_{2},\dots ,E_{m/2}}} and R ( E ) := E m / 2 + 1 , … , E m − 1 , E m {\displaystyle R(E):={E_{m/2+1},\dots ,E_{m-1},E_{m}}} . Apply this to S {\displaystyle S} and T {\displaystyle T} , and calculate (ahead of time) the bounding spheres B ( L ( S ) ) , B ( R ( S ) ) {\displaystyle B(L(S)),B(R(S))} and B ( L ( T ) ) , B ( R ( T ) ) {\displaystyle B(L(T)),B(R(T))} . T
Semantic heterogeneity
Semantic heterogeneity is when database schema or datasets for the same domain are developed by independent parties, resulting in differences in meaning and interpretation of data values. Beyond structured data, the problem of semantic heterogeneity is compounded due to the flexibility of semi-structured data and various tagging methods applied to documents or unstructured data. Semantic heterogeneity is one of the more important sources of differences in heterogeneous datasets. Yet, for multiple data sources to interoperate with one another, it is essential to reconcile these semantic differences. Decomposing the various sources of semantic heterogeneities provides a basis for understanding how to map and transform data to overcome these differences. == Classification == One of the first known classification schemes applied to data semantics is from William Kent in the late 80s. Kent's approach dealt more with structural mapping issues than differences in meaning, which he pointed to data dictionaries as potentially solving. One of the most comprehensive classifications is from Pluempitiwiriyawej and Hammer, "Classification Scheme for Semantic and Schematic Heterogeneities in XML Data Sources". They classify heterogeneities into three broad classes: Structural conflicts arise when the schema of the sources representing related or overlapping data exhibit discrepancies. Structural conflicts can be detected when comparing the underlying schema. The class of structural conflicts includes generalization conflicts, aggregation conflicts, internal path discrepancy, missing items, element ordering, constraint and type mismatch, and naming conflicts between the element types and attribute names. Domain conflicts arise when the semantics of the data sources that will be integrated exhibit discrepancies. Domain conflicts can be detected by looking at the information contained in the schema and using knowledge about the underlying data domains. The class of domain conflicts includes schematic discrepancy, scale or unit, precision, and data representation conflicts. Data conflicts refer to discrepancies among similar or related data values across multiple sources. Data conflicts can only be detected by comparing the underlying sources. The class of data conflicts includes ID-value, missing data, incorrect spelling, and naming conflicts between the element contents and the attribute values. Moreover, mismatches or conflicts can occur between set elements (a "population" mismatch) or attributes (a "description" mismatch). Michael Bergman expanded upon this schema by adding a fourth major explicit category of language, and also added some examples of each kind of semantic heterogeneity, resulting in about 40 distinct potential categories . This table shows the combined 40 possible sources of semantic heterogeneities across sources: A different approach toward classifying semantics and integration approaches is taken by Sheth et al. Under their concept, they split semantics into three forms: implicit, formal and powerful. Implicit semantics are what is either largely present or can easily be extracted; formal languages, though relatively scarce, occur in the form of ontologies or other description logics; and powerful (soft) semantics are fuzzy and not limited to rigid set-based assignments. Sheth et al.'s main point is that first-order logic (FOL) or description logic is inadequate alone to properly capture the needed semantics. == Relevant applications == Besides data interoperability, relevant areas in information technology that depend on reconciling semantic heterogeneities include data mapping, semantic integration, and enterprise information integration, among many others. From the conceptual to actual data, there are differences in perspective, vocabularies, measures and conventions once any two data sources are brought together. Explicit attention to these semantic heterogeneities is one means to get the information to integrate or interoperate. A mere twenty years ago, information technology systems expressed and stored data in a multitude of formats and systems. The Internet and Web protocols have done much to overcome these sources of differences. While there is a large number of categories of semantic heterogeneity, these categories are also patterned and can be anticipated and corrected. These patterned sources inform what kind of work must be done to overcome semantic differences where they still reside.