AI Coding Benchmark Ranking

AI Coding Benchmark Ranking — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Pixel-art scaling algorithms

  Pixel art scaling algorithms are graphical filters that attempt to enhance the appearance of hand-drawn 2D pixel art graphics. These algorithms are a form of automatic image enhancement. Pixel art scaling algorithms employ methods significantly different than the common methods of image rescaling, which have the goal of preserving the appearance of images. As pixel art graphics are commonly used at very low resolutions, they employ careful coloring of individual pixels. This results in graphics that rely on a high amount of stylized visual cues to define complex shapes. Several specialized algorithms have been developed to handle re-scaling of such graphics. These specialized algorithms can improve the appearance of pixel-art graphics, but in doing so they introduce changes. Such changes may be undesirable, especially if the goal is to faithfully reproduce the original appearance. Since a typical application of this technology is improving the appearance of fourth-generation and earlier video games on arcade and console emulators, many pixel art scaling algorithms are designed to run in real-time for sufficiently small input images at 60-frames per second. This places constraints on the type of programming techniques that can be used for this sort of real-time processing. Many work only on specific scale factors. 2× is the most common scale factor, while 3×, 4×, 5×, and 6× exist but are less used. == Algorithms == === SAA5050 'Diagonal Smoothing' === The Mullard SAA5050 Teletext character generator chip (1980) used a primitive pixel scaling algorithm to generate higher-resolution characters on the screen from a lower-resolution representation from its internal ROM. Internally, each character shape was defined on a 5 × 9 pixel grid, which was then interpolated by smoothing diagonals to give a 10 × 18 pixel character, with a characteristically angular shape, surrounded to the top and the left by two pixels of blank space. The algorithm only works on monochrome source data, and assumes the source pixels will be logically true or false depending on whether they are 'on' or 'off'. Pixels 'outside the grid pattern' are assumed to be off. The algorithm works as follows: A B C --\ 1 2 D E F --/ 3 4 1 = B | (A & E & !B & !D) 2 = B | (C & E & !B & !F) 3 = E | (!A & !E & B & D) 4 = E | (!C & !E & B & F) Note that this algorithm, like the Eagle algorithm below, has a flaw: If a pattern of 4 pixels in a hollow diamond shape appears, the hollow will be obliterated by the expansion. The SAA5050's internal character ROM carefully avoids ever using this pattern. The degenerate case: becomes: === EPX/Scale2×/AdvMAME2× === Eric's Pixel Expansion (EPX) is an algorithm developed by Eric Johnston at LucasArts around 1992, when porting the SCUMM engine games from the IBM PC (which ran at 320 × 200 × 256 colors) to the early color Macintosh computers, which ran at more or less double that resolution. The algorithm works as follows, expanding P into 4 new pixels based on P's surroundings: 1=P; 2=P; 3=P; 4=P; IF C==A => 1=A IF A==B => 2=B IF D==C => 3=C IF B==D => 4=D IF of A, B, C, D, three or more are identical: 1=2=3=4=P Later implementations of this same algorithm (as AdvMAME2× and Scale2×, developed around 2001) are slightly more efficient but functionally identical: 1=P; 2=P; 3=P; 4=P; IF C==A AND C!=D AND A!=B => 1=A IF A==B AND A!=C AND B!=D => 2=B IF D==C AND D!=B AND C!=A => 3=C IF B==D AND B!=A AND D!=C => 4=D AdvMAME2× is available in DOSBox via the scaler=advmame2x dosbox.conf option. The AdvMAME4×/Scale4× algorithm is just EPX applied twice to get 4× resolution. ==== Scale3×/AdvMAME3× and ScaleFX ==== The AdvMAME3×/Scale3× algorithm (available in DOSBox via the scaler=advmame3x dosbox.conf option) can be thought of as a generalization of EPX to the 3× case. The corner pixels are calculated identically to EPX. 1=E; 2=E; 3=E; 4=E; 5=E; 6=E; 7=E; 8=E; 9=E; IF D==B AND D!=H AND B!=F => 1=D IF (D==B AND D!=H AND B!=F AND E!=C) OR (B==F AND B!=D AND F!=H AND E!=A) => 2=B IF B==F AND B!=D AND F!=H => 3=F IF (H==D AND H!=F AND D!=B AND E!=A) OR (D==B AND D!=H AND B!=F AND E!=G) => 4=D 5=E IF (B==F AND B!=D AND F!=H AND E!=I) OR (F==H AND F!=B AND H!=D AND E!=C) => 6=F IF H==D AND H!=F AND D!=B => 7=D IF (F==H AND F!=B AND H!=D AND E!=G) OR (H==D AND H!=F AND D!=B AND E!=I) => 8=H IF F==H AND F!=B AND H!=D => 9=F There is also a variant improved over Scale3× called ScaleFX, developed by Sp00kyFox, and a version combined with Reverse-AA called ScaleFX-Hybrid. === Eagle === Eagle works as follows: for every in pixel, we will generate 4 out pixels. First, set all 4 to the color of the pixel we are currently scaling (as nearest-neighbor). Next look at the three pixels above, to the left, and diagonally above left: if all three are the same color as each other, set the top left pixel of our output square to that color in preference to the nearest-neighbor color. Work similarly for all four pixels, and then move to the next one. Assume an input matrix of 3 × 3 pixels where the centermost pixel is the pixel to be scaled, and an output matrix of 2 × 2 pixels (i.e., the scaled pixel) first: |Then . . . --\ CC |S T U --\ 1 2 . C . --/ CC |V C W --/ 3 4 . . . |X Y Z | IF V==S==T => 1=S | IF T==U==W => 2=U | IF V==X==Y => 3=X | IF W==Z==Y => 4=Z Thus if we have a single black pixel on a white background it will vanish. This is a bug in the Eagle algorithm but is solved by other algorithms such as EPX, 2xSaI, and HQ2x. === 2×SaI === 2×SaI, short for 2× Scale and Interpolation engine, was inspired by Eagle. It was designed by Derek Liauw Kie Fa, also known as Kreed, primarily for use in console and computer emulators, and it has remained fairly popular in this niche. Many of the most popular emulators, including ZSNES and VisualBoyAdvance, offer this scaling algorithm as a feature. Several slightly different versions of the scaling algorithm are available, and these are often referred to as Super 2×SaI and Super Eagle. The 2xSaI family works on a 4 × 4 matrix of pixels where the pixel marked A below is scaled: I E F J G A B K --\ W X H C D L --/ Y Z M N O P For 16-bit pixels, they use pixel masks which change based on whether the 16-bit pixel format is 565 or 555. The constants colorMask, lowPixelMask, qColorMask, qLowPixelMask, redBlueMask, and greenMask are 16-bit masks. The lower 8 bits are identical in either pixel format. Two interpolation functions are described: INTERPOLATE(uint32 A, UINT32 B). -- linear midpoint of A and B if (A == B) return A; return ( ((A & colorMask) >> 1) + ((B & colorMask) >> 1) + (A & B & lowPixelMask) ); Q_INTERPOLATE(uint32 A, uint32 B, uint32 C, uint32 D) -- bilinear interpolation; A, B, C, and D's average x = ((A & qColorMask) >> 2) + ((B & qColorMask) >> 2) + ((C & qColorMask) >> 2) + ((D & qColorMask) >> 2); y = (A & qLowPixelMask) + (B & qLowPixelMask) + (C & qLowPixelMask) + (D & qLowPixelMask); y = (y >> 2) & qLowPixelMask; return x + y; The algorithm checks A, B, C, and D for a diagonal match such that A==D and B!=C, or the other way around, or if they are both diagonals or if there is no diagonal match. Within these, it checks for three or four identical pixels. Based on these conditions, the algorithm decides whether to use one of A, B, C, or D, or an interpolation among only these four, for each output pixel. The 2xSaI arbitrary scaler can enlarge any image to any resolution and uses bilinear filtering to interpolate pixels. Since Kreed released the source code under the GNU General Public License, it is freely available to anyone wishing to utilize it in a project released under that license. Developers wishing to use it in a non-GPL project would be required to rewrite the algorithm without using any of Kreed's existing code. It is available in DOSBox via scaler=2xsai option. === hqnx family === Maxim Stepin's hq2x, hq3x, and hq4x are for scale factors of 2:1, 3:1, and 4:1 respectively. Each work by comparing the color value of each pixel to those of its eight immediate neighbors, marking the neighbors as close or distant, and using a pre-generated lookup table to find the proper proportion of input pixels' values for each of the 4, 9 or 16 corresponding output pixels. The hq3x family will perfectly smooth any diagonal line whose slope is ±0.5, ±1, or ±2 and which is not anti-aliased in the input; one with any other slope will alternate between two slopes in the output. It will also smooth very tight curves. Unlike 2xSaI, it anti-aliases the output. hqnx was initially created for the Super NES emulator ZSNES. The author of bsnes has released a space-efficient implementation of hq2x to the public domain. A port to shaders, which has comparable quality to the early versions of xBR, is available. Before the port, a shader called "scalehq" has often been confused for hqx. === xBR family === There are 6 filters in this family: xBR , xBRZ, xBR-Hybrid, Super xBR, xBR+3D and Super xBR+3D. xBR ("scale by rules"), cre

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  Subject (documents)

  In library and information science documents (such as books, articles and pictures) are classified and searched by subject – as well as by other attributes such as author, genre and document type. This makes "subject" a fundamental term in this field. Library and information specialists assign subject labels to documents to make them findable. There are many ways to do this and in general there is not always consensus about which subject should be assigned to a given document. To optimize subject indexing and searching, we need to have a deeper understanding of what a subject is. The question: "what is to be understood by the statement 'document A belongs to subject category X'?" has been debated in the field for more than 100 years (see below) == Theoretical view == === Charles Ammi Cutter (1837–1903) === For Cutter the stability of subjects depends on a social process in which their meaning is stabilized in a name or a designation. A subject "referred [...] to those intellections [...] that had received a name that itself represented a distinct consensus in usage" (Miksa, 1983a, p. 60) and: the "systematic structure of established subjects" is "resident in the public realm" (Miksa, 1983a, p. 69); "[s]ubjects are by their very nature locations in a classificatory structure of publicly accumulated knowledge (Miksa, 1983a, p. 61). Bernd Frohmann adds: "The stability of the public realm in turn relies upon natural and objective mental structures which, with proper education, govern a natural progression from particular to general concepts. Since for Cutter, mind, society, and SKO [Systems of Knowledge Organization] stand one behind the other, each supporting each, all manifesting the same structure, his discursive construction of subjects invites connections with discourses of mind, education, and society. The Dewey Decimal Classification (DDC), by contrast, severs those connections. Melvil Dewey emphasized more than once that his system maps no structure beyond its own; there is neither a "transcendental deduction" of its categories nor any reference to Cutter's objective structure of social consensus. It is content-free: Dewey disdained any philosophical excogitation of the meaning of his class symbols, leaving the job of finding verbal equivalents to others. His innovation and the essence of the system lay in the notation. The DDC is a poorly semiotic system of expanding nests of ten digits, lacking any referent beyond itself. In it, a subject is wholly constituted in terms of its position in the system. The essential characteristic of a subject is a class symbol which refers only to other symbols. Its verbal equivalent is accidental, a merely pragmatic characteristic... .... The conflict of interpretations over "subjects" became explicit in the battles between "bibliography" (an approach to subjects having much in common with Cutter's) and Dewey's "close classification". William Fletcher spoke for the scholarly bibliographer.... Fletcher's "subjects", like Cutter's, referred to the categories of a fantasized, stable social order, whereas Dewey's subjects were elements of a semiological system of standardized, techno-bureaucratic administrative software for the library in its corporate, rather than high culture, incarnation". (Frohmann, 1994, 112–113). Cutter's early view on what a subject is, is probably wiser than most understandings that dominated the 20th century – and also the understanding reflected in the ISO-standard quoted below. The early statements quoted by Frohmann indicate that subjects are somehow shaped in social processes. When that is said, it should be added that they are not particularly detailed or clear. We only get a vague idea of the social nature of subjects. === S. R. Ranganathan (1892–1972) === A classification system with an explicit theoretical foundation is Ranganathan's Colon Classification. Ranganathan provided an explicit definition of the concept of "subject": Subject – an organized body of ideas, whose extension and intension are likely to fall coherently within the field of interests and comfortably within the intellectual competence and the field of inevitable specialization of a normal person. A related definition is given by one of Ranganathan's students: A subject is an organized and systematized body of ideas. It may consist of one idea or a combination of several... Ranganathan's definition of "subject" is strongly influenced by his Colon Classification system. The colon system is based on the combination of single elements from facets to subject designation. This is the reason why the combined nature of subjects are emphasized so strongly. It leads, however, to absurdities such as the claim that gold cannot be a subject (but is alternatively termed "an isolate"). This aspect of the theory has been criticized by Metcalfe (1973, p. 318). Metcalfe's skepticism regarding Ranganathan's theory is formulated in hard words (op. cit., p. 317): "This pseudo-science imposed itself on British disciples from about 1950 on...". It seems unacceptable that Ranganathan defines the word subject in a way that favors his own system. A scientific concept like "subject" should make it possible to compare different ways of establishing access to information. Whether or not subjects are combined or not should be examined once their definition has been given, it should not determined a priori, in the definition. Besides the emphasis on the combined, organizing and systematizing nature of subjects contains Ranganathan's definition of subject the pragmatic demand, that a subject should be determined in a way that suits a normal person's competency or specialization. Again we see a strange kind of wishful thinking mixing a general understanding of a concept with demands put by his own specific system. One thing is what the word subject means, quite another issue is how to provide subject descriptions that fulfill demands such as the specificity of a given information retrieval language which fulfill demands put on the system, such as precision and recall. If researchers too often define terms in ways that favor specific kinds of systems, that are such definitions not useful to provide more general theories about subjects, subject analysis and IR. Among other things are comparative studies of different kinds of systems made difficult. Based on these arguments, as well as additional arguments which have been used in the literature, we may conclude that Ranganathan's definition of the concept "subject" is not suited for scientific use. Like the definition of "subject" given by the ISO-standard for topic maps, may Ranganathan's definition be useful within his own closed system. The purpose of a scientific and scholarly field is, however, to examine the relative fruitfulness of systems such as topic maps and Colon Classification. For such purpose is another understanding of "subject" necessary. === Patrick Wilson (1927–2003) === In his book Wilson (1968) examined – in particular by thought experiments – the suitability of different methods of examining the subject of a document. The methods were: identifying the author's purpose for writing the document, weighing the relative dominance and subordination of different elements in the picture, which the reading imposes on the reader, grouping or count the document's use of concepts and references, construing a set of rules for selecting elements deemed necessary (as opposed to unnecessary) for the work as a whole. Patrick Wilson shows convincingly that each of these methods are insufficient to determine the subject of a document and is led to conclude ( p. 89): "The notion of the subject of a writing is indeterminate..." or, on p. 92 (about what users may expect to find using a particular position in a library classification system): "For nothing definite can be expected of the things found at any given position". In connection to the last quote has Wilson an interesting footnote in which he writes that authors of documents often use terms in ambiguous ways ("hostility" is used as an example). Even if the librarian could personally develop a very precise understanding of a concept, he would be unable to use it in his classification, because none of the documents use the term in the same precise way. Based on this argumentation is Wilson led to conclude: "If people write on what are for them ill-defined phenomena, a correct description of their subjects must reflect the ill-definedness". Wilson's concept of subject was discussed by Hjørland (1992) who found that it is problematic to give up the precise understanding of such a basic term in LIS. Wilson's arguments led him to an agnostic position which Hjørland found unacceptable and unnecessary. Concerning the authors' use of ambiguous terms, the role of the subject analysis is to determine which documents would be fruitful for users to identify whether or not the documents use one or another term or whether a given term i

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  Distributed transaction

  A distributed transaction operates within a distributed environment, typically involving multiple nodes across a network depending on the location of the data. A key aspect of distributed transactions is atomicity, which ensures that the transaction is completed in its entirety or not executed at all. It's essential to note that distributed transactions are not limited to databases. The Open Group, a vendor consortium, proposed the X/Open Distributed Transaction Processing Model (X/Open XA), which became a de facto standard for the behavior of transaction model components. Databases are common transactional resources and, often, transactions span a couple of such databases. In this case, a distributed transaction can be seen as a database transaction that must be synchronized (or provide ACID properties) among multiple participating databases which are distributed among different physical locations. The isolation property (the I of ACID) poses a special challenge for multi database transactions, since the (global) serializability property could be violated, even if each database provides it (see also global serializability). In practice most commercial database systems use strong strict two-phase locking (SS2PL) for concurrency control, which ensures global serializability, if all the participating databases employ it. A common algorithm for ensuring correct completion of a distributed transaction is the two-phase commit (2PC). This algorithm is usually applied for updates able to commit in a short period of time, ranging from couple of milliseconds to couple of minutes. There are also long-lived distributed transactions, for example a transaction to book a trip, which consists of booking a flight, a rental car and a hotel. Since booking the flight might take up to a day to get a confirmation, two-phase commit is not applicable here, it will lock the resources for this long. In this case more sophisticated techniques that involve multiple undo levels are used. The way you can undo the hotel booking by calling a desk and cancelling the reservation, a system can be designed to undo certain operations (unless they are irreversibly finished). In practice, long-lived distributed transactions are implemented in systems based on web services. Usually these transactions utilize principles of compensating transactions, Optimism and Isolation Without Locking. The X/Open standard does not cover long-lived distributed transactions. Several technologies, including Jakarta Enterprise Beans and Microsoft Transaction Server fully support distributed transaction standards. == Synchronization == In event-driven architectures, distributed transactions can be synchronized through using request–response paradigm and it can be implemented in two ways: Creating two separate queues: one for requests and the other for replies. The event producer must wait until it receives the response. Creating one dedicated ephemeral queue for each request.

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  Leiden algorithm

  The Leiden algorithm is a community detection algorithm developed by Traag et al at Leiden University. It was developed as a modification of the Louvain method. Like the Louvain method, the Leiden algorithm attempts to optimize modularity in extracting communities from networks; however, it addresses key issues present in the Louvain method, namely poorly connected communities and the resolution limit of modularity. == Improvement over Louvain method == Broadly, the Leiden algorithm uses the same two primary phases as the Louvain algorithm: a local node moving step (though, the method by which nodes are considered in Leiden is more efficient) and a graph aggregation step. However, to address the issues with poorly-connected communities and the merging of smaller communities into larger communities (the resolution limit of modularity), the Leiden algorithm employs an intermediate refinement phase in which communities may be split to guarantee that all communities are well-connected. Consider, for example, the following graph: Three communities are present in this graph (each color represents a community). Additionally, the center "bridge" node (represented with an extra circle) is a member of the community represented by blue nodes. Now consider the result of a node-moving step which merges the communities denoted by red and green nodes into a single community (as the two communities are highly connected): Notably, the center "bridge" node is now a member of the larger red community after node moving occurs (due to the greedy nature of the local node moving algorithm). In the Louvain method, such a merging would be followed immediately by the graph aggregation phase. However, this causes a disconnection between two different sections of the community represented by blue nodes. In the Leiden algorithm, the graph is instead refined: The Leiden algorithm's refinement step ensures that the center "bridge" node is kept in the blue community to ensure that it remains intact and connected, despite the potential improvement in modularity from adding the center "bridge" node to the red community. == Graph components == Before defining the Leiden algorithm, it will be helpful to define some of the components of a graph. === Vertices and edges === A graph is composed of vertices (nodes) and edges. Each edge is connected to two vertices, and each vertex may be connected to zero or more edges. Edges are typically represented by straight lines, while nodes are represented by circles or points. In set notation, let V {\displaystyle V} be the set of vertices, and E {\displaystyle E} be the set of edges: V := { v 1 , v 2 , … , v n } E := { e i j , e i k , … , e k l } {\displaystyle {\begin{aligned}V&:=\{v_{1},v_{2},\dots ,v_{n}\}\\E&:=\{e_{ij},e_{ik},\dots ,e_{kl}\}\end{aligned}}} where e i j {\displaystyle e_{ij}} is the directed edge from vertex v i {\displaystyle v_{i}} to vertex v j {\displaystyle v_{j}} . We can also write this as an ordered pair: e i j := ( v i , v j ) {\displaystyle {\begin{aligned}e_{ij}&:=(v_{i},v_{j})\end{aligned}}} === Community === A community is a unique set of nodes: C i ⊆ V C i ⋂ C j = ∅ ∀ i ≠ j {\displaystyle {\begin{aligned}C_{i}&\subseteq V\\C_{i}&\bigcap C_{j}=\emptyset ~\forall ~i\neq j\end{aligned}}} and the union of all communities must be the total set of vertices: V = ⋃ i = 1 C i {\displaystyle {\begin{aligned}V&=\bigcup _{i=1}C_{i}\end{aligned}}} === Partition === A partition is the set of all communities: P = { C 1 , C 2 , … , C n } {\displaystyle {\begin{aligned}{\mathcal {P}}&=\{C_{1},C_{2},\dots ,C_{n}\}\end{aligned}}} == Partition quality == How communities are partitioned is an integral part on the Leiden algorithm. How partitions are decided can depend on how their quality is measured. Additionally, many of these metrics contain parameters of their own that can change the outcome of their communities. === Modularity === Modularity is a highly used quality metric for assessing how well a set of communities partition a graph. The equation for this metric is defined for an adjacency matrix, A, as: Q = 1 2 m ∑ i j ( A i j − k i k j 2 m ) δ ( c i , c j ) {\displaystyle Q={\frac {1}{2m}}\sum _{ij}(A_{ij}-{\frac {k_{i}k_{j}}{2m}})\delta (c_{i},c_{j})} where: A i j {\displaystyle A_{ij}} represents the edge weight between nodes i {\displaystyle i} and j {\displaystyle j} ; see Adjacency matrix; k i {\displaystyle k_{i}} and k j {\displaystyle k_{j}} are the sum of the weights of the edges attached to nodes i {\displaystyle i} and j {\displaystyle j} , respectively; m {\displaystyle m} is the sum of all of the edge weights in the graph; c i {\displaystyle c_{i}} and c j {\displaystyle c_{j}} are the communities to which the nodes i {\displaystyle i} and j {\displaystyle j} belong; and δ {\displaystyle \delta } is Kronecker delta function: δ ( c i , c j ) = { 1 if c i and c j are the same community 0 otherwise {\displaystyle {\begin{aligned}\delta (c_{i},c_{j})&={\begin{cases}1&{\text{if }}c_{i}{\text{ and }}c_{j}{\text{ are the same community}}\\0&{\text{otherwise}}\end{cases}}\end{aligned}}} === Reichardt Bornholdt Potts Model (RB) === One of the most well used metrics for the Leiden algorithm is the Reichardt Bornholdt Potts Model (RB). This model is used by default in most mainstream Leiden algorithm libraries under the name RBConfigurationVertexPartition. This model introduces a resolution parameter γ {\displaystyle \gamma } and is highly similar to the equation for modularity. This model is defined by the following quality function for an adjacency matrix, A, as: Q = ∑ i j ( A i j − γ k i k j 2 m ) δ ( c i , c j ) {\displaystyle Q=\sum _{ij}(A_{ij}-\gamma {\frac {k_{i}k_{j}}{2m}})\delta (c_{i},c_{j})} where: γ {\displaystyle \gamma } represents a linear resolution parameter === Constant Potts Model (CPM) === Another metric similar to RB is the Constant Potts Model (CPM). This metric also relies on a resolution parameter γ {\displaystyle \gamma } The quality function is defined as: H = − ∑ i j ( A i j w i j − γ ) δ ( c i , c j ) {\displaystyle H=-\sum _{ij}(A_{ij}w_{ij}-\gamma )\delta (c_{i},c_{j})} === Understanding Potts Model resolution parameters/Resolution limit === Typically Potts models such as RB or CPM include a resolution parameter in their calculation. Potts models are introduced as a response to the resolution limit problem that is present in modularity maximization based community detection. The resolution limit problem is that, for some graphs, maximizing modularity may cause substructures of a graph to merge and become a single community and thus smaller structures are lost. These resolution parameters allow modularity adjacent methods to be modified to suit the requirements of the user applying the Leiden algorithm to account for small substructures at a certain granularity. The figure on the right illustrates why resolution can be a helpful parameter when using modularity based quality metrics. In the first graph, modularity only captures the large scale structures of the graph; however, in the second example, a more granular quality metric could potentially detect all substructures in a graph. == Algorithm == The Leiden algorithm starts with a graph of disorganized nodes (a) and sorts it by partitioning them to maximize modularity (the difference in quality between the generated partition and a hypothetical randomized partition of communities). The method it uses is similar to the Louvain algorithm, except that after moving each node it also considers that node's neighbors that are not already in the community it was placed in. This process results in our first partition (b), also referred to as P {\displaystyle {\mathcal {P}}} . Then the algorithm refines this partition by first placing each node into its own individual community and then moving them from one community to another to maximize modularity. It does this iteratively until each node has been visited and moved, and each community has been refined - this creates partition (c), which is the initial partition of P refined {\displaystyle {\mathcal {P}}_{\text{refined}}} . Then an aggregate network (d) is created by turning each community into a node. P refined {\displaystyle {\mathcal {P}}_{\text{refined}}} is used as the basis for the aggregate network while P {\displaystyle {\mathcal {P}}} is used to create its initial partition. Because we use the original partition P {\displaystyle {\mathcal {P}}} in this step, we must retain it so that it can be used in future iterations. These steps together form the first iteration of the algorithm. In subsequent iterations, the nodes of the aggregate network (which each represent a community) are once again placed into their own individual communities and then sorted according to modularity to form a new P refined {\displaystyle {\mathcal {P}}_{\text{refined}}} , forming (e) in the above graphic. In the case depicted by the graph, the nodes were already sorted optimally, so no change too

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  Camfecting

  In computer security, camfecting is the process of attempting to hack into a person's webcam and activate it without the webcam owner's permission. The remotely activated webcam can be used to watch anything within the webcam's field of vision, sometimes including the webcam owner themselves. Camfecting is most often carried out by infecting the victim's computer with a virus that can provide the hacker access to their webcam. This attack is specifically targeted at the victim's webcam, and hence the name camfecting, a portmanteau of the words camera and infecting. Typically, a webcam hacker or a camfecter sends his victim an innocent-looking application which has a hidden Trojan software through which the camfecter can control the victim's webcam. The camfecter virus installs itself silently when the victim runs the original application. Once installed, the camfecter can turn on the webcam and capture pictures/videos. The camfecter software works just like the original webcam software present in the victim computer, the only difference being that the camfecter controls the software instead of the webcam's owner. == Notable cases == Marcus Thomas, former assistant director of the FBI's Operational Technology Division in Quantico, said in a 2013 story in The Washington Post that the FBI had been able to covertly activate a computer's camera—without triggering the light that lets users know it is recording—for several years. In November 2013, American teenager Jared James Abrahams pleaded guilty to hacking over 100-150 women and installing the highly invasive malware Blackshades on their computers in order to obtain nude images and videos of them. One of his victims was Miss Teen USA 2013 Cassidy Wolf. Researchers from Johns Hopkins University have shown how to covertly capture images from the iSight camera on MacBook and iMac models released before 2008, by reprogramming the microcontroller's firmware. == Prevention == A computer that does not have an up-to-date webcam software or any anti-virus (or firewall) software installed and operational may be at increased risk for camfecting from different types of malware. Softcams may nominally increase this risk, if not maintained or configured properly. Although a person cannot protect themselves from zero-day exploits that could potentially activate a camera unknowingly, such as Pegasus is able to do on smartphones. The only way to truly avoid being watched through your own camera is by blocking it physically, since software blocks can be overriden by advanced persistent threats. A simple piece of tape is more commonly used to offuscate the feed of the camera. With even Mark Zuckerberg doing so on his personal laptop that appeared during a presentation. And it being the way Snowden, an ex-contractor for the NSA, is portrayed to do so to prevent camfecting in the biopic Snowden. There is now a market for the manufacture and sale of sliding lens covers that allow users to physically block their computer's camera and, in some cases, microphone. A number of phone and laptop manufacturers tried to implement pop-up cameras that can only be opened manually by the user. But the trend did not become mainstream because of the engineering it took to keep the mechanisms up to date, aswell as the fragility and durability of the cameras.

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  Algorism

  Algorism is the technique of performing basic arithmetic by writing numbers in place value form and applying a set of memorized rules and facts to the digits. One who practices algorism is known as an algorist. This positional notation system has largely superseded earlier calculation systems that used a different set of symbols for each numerical magnitude, such as Roman numerals, and in some cases required a device such as an abacus. == Etymology == The word algorism comes from the name Al-Khwārizmī (c. 780–850), a Persian mathematician, astronomer, geographer and scholar in the House of Wisdom in Baghdad, whose name means "the native of Khwarezm", which is now in modern-day Uzbekistan. He wrote a treatise in Arabic language in the 9th century, which was translated into Latin in the 12th century under the title Algoritmi de numero Indorum. This title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name. Al-Khwarizmi was the most widely read mathematician in Europe in the late Middle Ages, primarily through his other book, the Algebra. In late medieval Latin, algorismus, the corruption of his name, simply meant the "decimal number system" that is still the meaning of modern English algorism. During the 17th century, the French form for the word – but not its meaning – was changed to algorithm, following the model of the word logarithm, this form alluding to the ancient Greek arithmos = number. English adopted the French very soon afterwards, but it wasn't until the late 19th century that "algorithm" took on the meaning that it has in modern English. In English, it was first used about 1230 and then by Chaucer in 1391. Another early use of the word is from 1240, in a manual titled Carmen de Algorismo composed by Alexandre de Villedieu. It begins thus: Haec algorismus ars praesens dicitur, in qua / Talibus Indorum fruimur bis quinque figuris. which translates as: This present art, in which we use those twice five Indian figures, is called algorismus. The word algorithm also derives from algorism, a generalization of the meaning to any set of rules specifying a computational procedure. Occasionally algorism is also used in this generalized meaning, especially in older texts. == History == Starting with the integer arithmetic developed in India using base 10 notation, Al-Khwārizmī along with other mathematicians in medieval Islam, documented new arithmetic methods and made many other contributions to decimal arithmetic (see the articles linked below). These included the concept of the decimal fractions as an extension of the notation, which in turn led to the notion of the decimal point. This system was popularized in Europe by Leonardo of Pisa, now known as Fibonacci.

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  Algorithms and Combinatorics

  Algorithms and Combinatorics (ISSN 0937-5511) is a book series in mathematics, and particularly in combinatorics and the design and analysis of algorithms. It is published by Springer Science+Business Media, and was founded in 1987. == Books == The books published in this series include: The Simplex Method: A Probabilistic Analysis (Karl Heinz Borgwardt, 1987, vol. 1) Geometric Algorithms and Combinatorial Optimization (Martin Grötschel, László Lovász, and Alexander Schrijver, 1988, vol. 2; 2nd ed., 1993) Systems Analysis by Graphs and Matroids (Kazuo Murota, 1987, vol. 3) Greedoids (Bernhard Korte, László Lovász, and Rainer Schrader, 1991, vol. 4) Mathematics of Ramsey Theory (Jaroslav Nešetřil and Vojtěch Rödl, eds., 1990, vol. 5) Matroid Theory and its Applications in Electric Network Theory and in Statics (Andras Recszki, 1989, vol. 6) Irregularities of Partitions: Papers from the meeting held in Fertőd, July 7–11, 1986 (Gábor Halász and Vera T. Sós, eds., 1989, vol. 8) Paths, Flows, and VLSI-Layout: Papers from the meeting held at the University of Bonn, Bonn, June 20–July 1, 1988 (Bernhard Korte, László Lovász, Hans Jürgen Prömel, and Alexander Schrijver, eds., 1990, vol. 9) New Trends in Discrete and Computational Geometry (János Pach, ed., 1993, vol. 10) Discrete Images, Objects, and Functions in Z n {\displaystyle \mathbb {Z} ^{n}} (Klaus Voss, 1993, vol. 11) Linear Optimization and Extensions (Manfred Padberg, 1999, vol. 12) The Mathematics of Paul Erdős I (Ronald Graham and Jaroslav Nešetřil, eds., 1997, vol. 13) The Mathematics of Paul Erdős II (Ronald Graham and Jaroslav Nešetřil, eds., 1997, vol. 14) Geometry of Cuts and Metrics (Michel Deza and Monique Laurent, 1997, vol. 15) Probabilistic Methods for Algorithmic Discrete Mathematics (M. Habib, C. McDiarmid, J. Ramirez-Alfonsin, and B. Reed, 1998, vol. 16) Modern Cryptography, Probabilistic Proofs and Pseudorandomness (Oded Goldreich, 1999, vol. 17) Geometric Discrepancy: An Illustrated Guide (Jiří Matoušek, 1999, vol. 18) Applied Finite Group Actions (Adalbert Kerber, 1999, vol. 19) Matrices and Matroids for Systems Analysis (Kazuo Murota, 2000, vol. 20; corrected ed., 2010) Combinatorial Optimization (Bernhard Korte and Jens Vygen, 2000, vol. 21; 5th ed., 2012) The Strange Logic of Random Graphs (Joel Spencer, 2001, vol. 22) Graph Colouring and the Probabilistic Method (Michael Molloy and Bruce Reed, 2002, Vol. 23) Combinatorial Optimization: Polyhedra and Efficiency (Alexander Schrijver, 2003, vol. 24. In three volumes: A. Paths, flows, matchings; B. Matroids, trees, stable sets; C. Disjoint paths, hypergraphs) Discrete and Computational Geometry: The Goodman-Pollack Festschrift (B. Aronov, S. Basu, J. Pach, and M. Sharir, eds., 2003, vol. 25) Topics in Discrete Mathematics: Dedicated to Jarik Nešetril on the Occasion of his 60th birthday (M. Klazar, J. Kratochvíl, M. Loebl, J. Matoušek, R. Thomas, and P. Valtr, eds., 2006, vol. 26) Boolean Function Complexity: Advances and Frontiers (Stasys Jukna, 2012, Vol. 27) Sparsity: Graphs, Structures, and Algorithms (Jaroslav Nešetřil and Patrice Ossona de Mendez, 2012, vol. 28) Optimal Interconnection Trees in the Plane (Marcus Brazil and Martin Zachariasen, 2015, vol. 29) Combinatorics and Complexity of Partition Functions (Alexander Barvinok, 2016, vol. 30)

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  Magic state distillation

  Magic state distillation is a method for creating more accurate quantum states from multiple noisy ones, which is important for building fault tolerant quantum computers. It has also been linked to quantum contextuality, a concept thought to contribute to quantum computers' power. The technique was first proposed by Emanuel Knill in 2004, and further analyzed by Sergey Bravyi and Alexei Kitaev the same year. Thanks to the Gottesman–Knill theorem, it is known that some quantum operations (operations in the Clifford group) can be perfectly simulated in polynomial time on a classical computer. In order to achieve universal quantum computation, a quantum computer must be able to perform operations outside this set. Magic state distillation achieves this, in principle, by concentrating the usefulness of imperfect resources, represented by mixed states, into states that are conducive for performing operations that are difficult to simulate classically. A variety of qubit magic state distillation routines and distillation routines for qubits with various advantages have been proposed. == Stabilizer formalism == The Clifford group consists of a set of n {\displaystyle n} -qubit operations generated by the gates {H, S, CNOT} (where H is Hadamard and S is [ 1 0 0 i ] {\displaystyle {\begin{bmatrix}1&0\\0&i\end{bmatrix}}} ) called Clifford gates. The Clifford group generates stabilizer states which can be efficiently simulated classically, as shown by the Gottesman–Knill theorem. This set of gates with a non-Clifford operation is universal for quantum computation. == Magic states == Magic states are purified from n {\displaystyle n} copies of a mixed state ρ {\displaystyle \rho } . These states are typically provided via an ancilla to the circuit. A magic state for the π / 6 {\displaystyle \pi /6} rotation operator is | M ⟩ = cos ⁡ ( β / 2 ) | 0 ⟩ + e i π 4 sin ⁡ ( β / 2 ) | 1 ⟩ {\displaystyle |M\rangle =\cos(\beta /2)|0\rangle +e^{i{\frac {\pi }{4}}}\sin(\beta /2)|1\rangle } where β = arccos ⁡ ( 1 3 ) {\displaystyle \beta =\arccos \left({\frac {1}{\sqrt {3}}}\right)} . A non-Clifford gate can be generated by combining (copies of) magic states with Clifford gates. Since a set of Clifford gates combined with a non-Clifford gate is universal for quantum computation, magic states combined with Clifford gates are also universal. == Purification algorithm for distilling |M〉 == The first magic state distillation algorithm, invented by Sergey Bravyi and Alexei Kitaev, is as follows. Input: Prepare 5 imperfect states. Output: An almost pure state having a small error probability. repeat Apply the decoding operation of the five-qubit error correcting code and measure the syndrome. If the measured syndrome is | 0000 ⟩ {\displaystyle |0000\rangle } , the distillation attempt is successful. else Get rid of the resulting state and restart the algorithm. until The states have been distilled to the desired purity.

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  SeaTable

  SeaTable is a no-code platform that allows users to develop and implement business processes. The cloud collaboration service SeaTable is marketed by the GmbH of the same name with headquarters in Mainz and additional offices in Berlin and Beijing, and developed by the same company as Seafile. == History == SeaTable is a collaborative database and low-code application platform developed as part of a joint venture between Seafile Ltd., a software company based in Guangzhou, China, and SeaTable GmbH, a German firm headquartered in Mainz. Founded in 2020, the project represents the international expansion of Seafile, a Chinese developer originally known for its file synchronization and sharing software. While SeaTable's cloud services and European client operations are managed by the German entity, the platform itself is developed in China by Seafile's engineering team. This cross-border structure, described by TechCrunch as an “unconventional path” for a Chinese startup expanding abroad, reflects Seafile's effort to maintain its product development in China while addressing growing scrutiny in Western markets over data governance and corporate control. In 2021, an innovation project led by the Cyber Innovation Hub at the IT School of the German Armed Forces started to evaluate the possibilities of a large-scale deployment at the German Armed Forces. The evaluation project is currently still ongoing. In 2022, SeaTable is optimizing its database backend to allow millions of records within one base in the future. The focus of development is increasingly on automation and visualization. In 2025, SeaTable introduced AI-powered automations with version 6. The update enabled the integration of large language models (LLMs) for text analysis and automated decision-making. SeaTable operates a self-hosted LLM on servers provided by Hetzner (Germany), while self-hosted deployments can connect to any compatible model. == Features == SeaTable combines the traditional capabilities of a spreadsheet such as Excel and supplements them with a wide range of functions for process automation and visualization as well as a fully comprehensive API. SeaTable is not a pure cloud solution, but can alternatively be installed on a private server and operated completely autonomously. In this way, the owner retains full control over their own data. The installation is done via Docker on a Linux server. == Security and privacy == While most no-code platforms exist only as SaaS solutions, SeaTable describes itself as a data-sparse European solution. While initially the SeaTable Cloud was hosted on Amazon AWS, the move to the German data centers of Swiss provider Exoscale then took place in May 2021. This was followed by the replacement of the Freshdesk cloud ticketing system with a self-hosted Zammad instance, and since April 2022 SeaTable has completely dispensed with all tracking cookies on its website.

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  Knowledge spillover

  Knowledge spillover is an exchange of ideas among individuals. Knowledge spillover is usually replaced by terminations of technology spillover, R&D spillover and/or spillover (economics) when the concept is specific to technology management and innovation economics. In knowledge management economics, knowledge spillovers are non-rival knowledge market costs incurred by a party not agreeing to assume the costs that has a spillover effect of stimulating technological improvements in a neighbor through one's own innovation. Such innovations often come from specialization within an industry. There are two kinds of knowledge spillovers: internal and external. Internal knowledge spillover occurs if there is a positive impact of knowledge between individuals within an organization that produces goods and/or services. An external knowledge spillover occurs when the positive impact of knowledge is between individuals outside of a production organization. Marshall–Arrow–Romer (MAR) spillovers, Porter spillovers and Jacobs spillovers are three types of spillovers. == Conceptualizations == === Marshall–Arrow–Romer === Marshall–Arrow–Romer (MAR) spillover has its origins in 1890, where the English economist Alfred Marshall developed a theory of knowledge spillovers. Knowledge spillovers later were extended by economists Kenneth Arrow (1962) and Paul Romer (1986). In 1992, Edward Glaeser, Hedi Kallal, José Scheinkman, and Andrei Shleifer pulled together the Marshall–Arrow–Romer views on knowledge spillovers and accordingly named the view MAR spillover in 1992. Under the Marshall–Arrow–Romer (MAR) spillover view, the proximity of firms within a common industry often affects how well knowledge travels among firms to facilitate innovation and growth. The closer the firms are to one another, the greater the MAR spillover. The exchange of ideas is largely from employee to employee, in that employees from different firms in an industry exchange ideas about new products and new ways to produce goods. The opportunity to exchange ideas that lead to innovations key to new products and improved production methods. Research on the Cambridge IT Cluster (UK) suggests that technological knowledge spillovers might only happen rarely and are less important than other cluster benefits such as labour market pooling. === Porter === Porter (1990), like MAR, argues that knowledge spillovers in specialized, geographically concentrated industries stimulate growth. He insists, however, that local competition, as opposed to local monopoly, fosters the pursuit and rapid adoption of innovation. He gives examples of Italian ceramics and gold jewellery industries, in which hundreds of firms are located together and fiercely compete to innovate since the alternative to innovation is demise. Porter's externalities are maximized in cities with geographically specialized, competitive industries. === Jacobs === Under the Jacobs spillover view, the proximity of firms from different industries affect how well knowledge travels among firms to facilitate innovation and growth. This is in contrast to MAR spillovers, which focus on firms in a common industry. The diverse proximity of a Jacobs spillover brings together ideas among individuals with different perspectives to encourage an exchange of ideas and foster innovation in an industrially diverse environment. Developed in 1969 by urbanist Jane Jacobs and John Jackson the concept that Detroit’s shipbuilding industry from the 1830s was the critical antecedent leading to the 1890s development of the auto industry in Detroit since the gasoline engine firms easily transitioned from building gasoline engines for ships to building them for automobiles. == Incoming and outgoing spillovers == Knowledge spillover has asymmetric directions. The focal entity and receives or outflows know-how to others, creating incoming and outgoing spillovers. Cassiman and Veugelers (2002) use survey data and estimate incoming and outgoing spillover and study the economic impacts. Incoming spillover increases growth opportunity and productivity improvements of receivers, while outgoing spillover leads to free rider problem in the technology competition. Chen et al. (2013) use econometric method to gauge incoming spillover, a way that applies for all companies without survey. They find that incoming spillover explains R&D profits of industrial firms. == Policy implications == As information is largely non-rival in nature, certain measures must be taken to ensure that, for the originator, the information remains a private asset. As the market cannot do this efficiently, public regulations have been implemented to facilitate a more appropriate equilibrium. As a result, the concept of intellectual property rights have developed and ensure the ability of entrepreneurs to temporarily hold on to the profitability of their ideas through patents, copyrights, trade secrets, and other governmental safeguards. Conversely, such barriers to entry prevent the exploitation of informational developments by rival firms within an industry. For example, Wang (2023) indicates that technology spillovers are reduced by 27% to 51% when trade secrets laws are implemented by the Uniform Trade Secrets Act in the US. On the other hand, when the research and development of a private firm results in a social benefit, unaccounted for within the market price, often greater than the private return of the firm's research, then a subsidy to offset the underproduction of that benefit might be offered to the firm in return for its continued output of that benefit. Government subsidies are often controversial, and while they might often result in a more appropriate social equilibrium, they could also lead to undesirable political repercussions as such a subsidy must come from taxpayers, some of whom may not directly benefit from the researching firm's subsidized knowledge spillover. The concept of knowledge spillover is also used to justify subsidies to foreign direct investment, as foreign investors help diffuse technology among local firms. == Examples == Business parks are a good specific example of concentrated businesses that may benefit from MAR spillover. Many semiconductor firms intentionally located their research and development facilities in Silicon Valley to take advantage of MAR spillover. In addition, the film industry in Los Angeles, California, and elsewhere relies on a geographic concentration of specialists (directors, producers, scriptwriters, and set designers) to bring together narrow aspects of movie-making into a final product. A general example of a knowledge spillover could be the collective growth associated with the research and development of online social networking tools like Facebook, YouTube, and Twitter. Such tools have not only created a positive feedback loop, and a host of originally unintended benefits for their users, but have also created an explosion of new software, programming platforms, and conceptual breakthroughs that have perpetuated the development of the industry as a whole. The advent of online marketplaces, the utilization of user profiles, the widespread democratization of information, and the interconnectivity between tools within the industry have all been products of each tool's individual developments. These developments have since spread outside the industry into the mainstream media as news and entertainment firms have developed their own market feedback applications within the tools themselves, and their own versions of online networking tools (e.g. CNN’s iReport).

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  Query rewriting

  Query rewriting is a typically automatic transformation that takes a set of database tables, views, and/or queries, usually indices, often gathered data and query statistics, and other metadata, and yields a set of different queries, which produce the same results but execute with better performance (for example, faster, or with lower memory use). Query rewriting can be based on relational algebra or an extension thereof (e.g. multiset relational algebra with sorting, aggregation and three-valued predicates i.e. NULLs as in the case of SQL). The equivalence rules of relational algebra are exploited, in other words, different query structures and orderings can be mathematically proven to yield the same result. For example, filtering on fields A and B, or cross joining R and S can be done in any order, but there can be a performance difference. Multiple operations may be combined, and operation orders may be altered. The result of query rewriting may not be at the same abstraction level or application programming interface (API) as the original set of queries (though often is). For example, the input queries may be in relational algebra or SQL, and the rewritten queries may be closer to the physical representation of the data, e.g. array operations. Query rewriting can also involve materialization of views and other subqueries; operations that may or may not be available to the API user. The query rewriting transformation can be aided by creating indices from which the optimizer can choose (some database systems create their own indexes if deemed useful), mandating the use of specific indices, creating materialized and/or denormalized views, or helping a database system gather statistics on the data and query use, as the optimality depends on patterns in data and typical query usage. Query rewriting may be rule based or optimizer based. Some sources discuss query rewriting as a distinct step prior to optimization, operating at the level of the user accessible algebra API (e.g. SQL). There are other, largely unrelated concepts also named similarly, for example, query rewriting by search engines.

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  Golden record (informatics)

  In informatics, a golden record is the valid version of a data element (record) in a single source of truth system. It may refer to a database, specific table or data field, or any unit of information used. A golden copy is a consolidated data set, and is supposed to provide a single source of truth and a "well-defined version of all the data entities in an organizational ecosystem". Other names sometimes used include master source or master version. The term has been used in conjunction with data quality, master data management, and similar topics. (Different technical solutions exist, see master data management). == Master data == In master data management (MDM), the golden copy refers to the master data (master version) of the reference data which works as an authoritative source for the "truth" for all applications in a given IT landscape.

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  Multimedia database

  A Multimedia database (MMDB) is a collection of related for multimedia data. The multimedia data include one or more primary media data types such as text, images, graphic objects (including drawings, sketches and illustrations) animation sequences, audio and video. A Multimedia Database Management System (MMDBMS) is a framework that manages different types of data potentially represented in a wide diversity of formats on a wide array of media sources. It provides support for multimedia data types, and facilitate for creation, storage, access, query and control of a multimedia database. == Contents of MMDB == A Multimedia Database (MMDB) hosts one or more multimedia data types (i.e. text, images, graphic objects, audio, video, animation sequences). These data types are broadly categorized into three classes: Static media (time-independent: image and graphic object). Dynamic media (time-dependent: audio, video and animation). Dimensional media(3D game and computer aided drafting programs). === Comparison of multimedia data types === Additionally, a Multimedia Database (MMDB) needs to manage additional information pertaining to the actual multimedia data. The information is about the following: Media data: the actual data representing an object. Media format data: information about the format of the media data after it goes through the acquisition, processing, and encoding phases. Media keyword data: the keyword descriptions, usually relating to the generation of the media data. Media feature data: content dependent data such as contain information about the distribution of colours, the kinds of textures and the different shapes present in an image. The last three types are called metadata as they describe several different aspects of the media data. The media keyword data and media feature data are used as indices for searching purpose. The media format data is used to present the retrieved information. == Requirements of Multimedia databases == Like the traditional databases, Multimedia databases should address the following requirements: Integration Data items do not need to be duplicated for different programs invocations Data independence Separate the database and the management from the application programs Concurrency control Allows concurrent transactions Persistence Data objects can be saved and re-used by different transactions and program invocations Privacy Access and authorization control Integrity control Ensures database consistency between transactions Recovery Failures of transactions should not affect the persistent data storage Query support Allows easy querying of multimedia data Multimedia databases should have the ability to uniformly query data (media data, textual data) represented in different formats and have the ability to simultaneously query different media sources and conduct classical database operations across them. (Query support) They should have the ability to retrieve media objects from a local storage device in a good manner. (Storage support) They should have the ability to take the response generated by a query and develop a presentation of that response in terms of audio-visual media and have the ability to deliver this presentation. (Presentation and delivery support) == Issues and challenges == Multimedia data consists of a variety of media formats or file representations including TIFF, BMP, PPT, IVUE, FPX, JPEG, MPEG, AVI, MID, WAV, DOC, GIF, EPS, PNG, etc. Because of restrictions on the conversion from one format to the other, the use of the data in a specific format has been limited as well. Usually, the data size of multimedia is large such as video; therefore, multimedia data often require a large storage. Multimedia database consume a lot of processing time, as well as bandwidth. Some multimedia data types such as video, audio, and animation sequences have temporal requirements that have implications on their storage, manipulation and presentation, but images, video and graphics data have special constraints in terms of their content. == Application areas == Examples of multimedia database application areas: Digital Libraries News-on-Demand Video-on-Demand Music database Geographic Information Systems (GIS) Telemedicine

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  Collective operation

  Collective operations are building blocks for interaction patterns, that are often used in SPMD algorithms in the parallel programming context. Hence, there is an interest in efficient realizations of these operations. A realization of the collective operations is provided by the Message Passing Interface (MPI). == Definitions == In all asymptotic runtime functions, we denote the latency α {\displaystyle \alpha } (or startup time per message, independent of message size), the communication cost per word β {\displaystyle \beta } , the number of processing units p {\displaystyle p} and the input size per node n {\displaystyle n} . In cases where we have initial messages on more than one node we assume that all local messages are of the same size. To address individual processing units we use p i ∈ { p 0 , p 1 , … , p p − 1 } {\displaystyle p_{i}\in \{p_{0},p_{1},\dots ,p_{p-1}\}} . If we do not have an equal distribution, i.e. node p i {\displaystyle p_{i}} has a message of size n i {\displaystyle n_{i}} , we get an upper bound for the runtime by setting n = max ( n 0 , n 1 , … , n p − 1 ) {\displaystyle n=\max(n_{0},n_{1},\dots ,n_{p-1})} . A distributed memory model is assumed. The concepts are similar for the shared memory model. However, shared memory systems can provide hardware support for some operations like broadcast (§ Broadcast) for example, which allows convenient concurrent read. Thus, new algorithmic possibilities can become available. == Broadcast == The broadcast pattern is used to distribute data from one processing unit to all processing units, which is often needed in SPMD parallel programs to dispense input or global values. Broadcast can be interpreted as an inverse version of the reduce pattern (§ Reduce). Initially only root r {\displaystyle r} with i d {\displaystyle id} 0 {\displaystyle 0} stores message m {\displaystyle m} . During broadcast m {\displaystyle m} is sent to the remaining processing units, so that eventually m {\displaystyle m} is available to all processing units. Since an implementation by means of a sequential for-loop with p − 1 {\displaystyle p-1} iterations becomes a bottleneck, divide-and-conquer approaches are common. One possibility is to utilize a binomial tree structure with the requirement that p {\displaystyle p} has to be a power of two. When a processing unit is responsible for sending m {\displaystyle m} to processing units i . . j {\displaystyle i..j} , it sends m {\displaystyle m} to processing unit ⌈ ( i + j ) / 2 ⌉ {\displaystyle \left\lceil (i+j)/2\right\rceil } and delegates responsibility for the processing units ⌈ ( i + j ) / 2 ⌉ . . j {\displaystyle \left\lceil (i+j)/2\right\rceil ..j} to it, while its own responsibility is cut down to i . . ⌈ ( i + j ) / 2 ⌉ − 1 {\displaystyle i..\left\lceil (i+j)/2\right\rceil -1} . Binomial trees have a problem with long messages m {\displaystyle m} . The receiving unit of m {\displaystyle m} can only propagate the message to other units, after it received the whole message. In the meantime, the communication network is not utilized. Therefore pipelining on binary trees is used, where m {\displaystyle m} is split into an array of k {\displaystyle k} packets of size ⌈ n / k ⌉ {\displaystyle \left\lceil n/k\right\rceil } . The packets are then broadcast one after another, so that data is distributed fast in the communication network. Pipelined broadcast on balanced binary tree is possible in O ( α log ⁡ p + β n ) {\displaystyle {\mathcal {O}}(\alpha \log p+\beta n)} , whereas for the non-pipelined case it takes O ( ( α + β n ) log ⁡ p ) {\displaystyle {\mathcal {O}}((\alpha +\beta n)\log p)} cost. == Reduce == The reduce pattern is used to collect data or partial results from different processing units and to combine them into a global result by a chosen operator. Given p {\displaystyle p} processing units, message m i {\displaystyle m_{i}} is on processing unit p i {\displaystyle p_{i}} initially. All m i {\displaystyle m_{i}} are aggregated by ⊗ {\displaystyle \otimes } and the result is eventually stored on p 0 {\displaystyle p_{0}} . The reduction operator ⊗ {\displaystyle \otimes } must be associative at least. Some algorithms require a commutative operator with a neutral element. Operators like s u m {\displaystyle sum} , m i n {\displaystyle min} , m a x {\displaystyle max} are common. Implementation considerations are similar to broadcast (§ Broadcast). For pipelining on binary trees the message must be representable as a vector of smaller object for component-wise reduction. Pipelined reduce on a balanced binary tree is possible in O ( α log ⁡ p + β n ) {\displaystyle {\mathcal {O}}(\alpha \log p+\beta n)} . == All-Reduce == The all-reduce pattern (also called allreduce) is used if the result of a reduce operation (§ Reduce) must be distributed to all processing units. Given p {\displaystyle p} processing units, message m i {\displaystyle m_{i}} is on processing unit p i {\displaystyle p_{i}} initially. All m i {\displaystyle m_{i}} are aggregated by an operator ⊗ {\displaystyle \otimes } and the result is eventually stored on all p i {\displaystyle p_{i}} . Analog to the reduce operation, the operator ⊗ {\displaystyle \otimes } must be at least associative. All-reduce can be interpreted as a reduce operation with a subsequent broadcast (§ Broadcast). For long messages a corresponding implementation is suitable, whereas for short messages, the latency can be reduced by using a hypercube (Hypercube (communication pattern) § All-Gather/ All-Reduce) topology, if p {\displaystyle p} is a power of two. All-reduce can also be implemented with a butterfly algorithm and achieve optimal latency and bandwidth. All-reduce is possible in O ( α log ⁡ p + β n ) {\displaystyle {\mathcal {O}}(\alpha \log p+\beta n)} , since reduce and broadcast are possible in O ( α log ⁡ p + β n ) {\displaystyle {\mathcal {O}}(\alpha \log p+\beta n)} with pipelining on balanced binary trees. All-reduce implemented with a butterfly algorithm achieves the same asymptotic runtime. == Prefix-Sum/Scan == The prefix-sum or scan operation is used to collect data or partial results from different processing units and to compute intermediate results by an operator, which are stored on those processing units. It can be seen as a generalization of the reduce operation (§ Reduce). Given p {\displaystyle p} processing units, message m i {\displaystyle m_{i}} is on processing unit p i {\displaystyle p_{i}} . The operator ⊗ {\displaystyle \otimes } must be at least associative, whereas some algorithms require also a commutative operator and a neutral element. Common operators are s u m {\displaystyle sum} , m i n {\displaystyle min} and m a x {\displaystyle max} . Eventually processing unit p i {\displaystyle p_{i}} stores the prefix sum ⊗ i ′ <= i {\displaystyle \otimes _{i'<=i}} m i ′ {\displaystyle m_{i'}} . In the case of the so-called exclusive prefix sum, processing unit p i {\displaystyle p_{i}} stores the prefix sum ⊗ i ′ < i {\displaystyle \otimes _{i' Read more →

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  Sikidy

  Sikidy is a form of algebraic geomancy practiced by Malagasy peoples in Madagascar. It involves algorithmic operations performed on random data generated from tree seeds, which are ritually arranged in a tableau called a toetry and divinely interpreted after being mathematically operated on. Columns of seeds, designated "slaves" or "princes" belonging to respective "lands" for each, interact symbolically to express vintana ('fate') in the interpretation of the diviner. The diviner also prescribes solutions to problems and ways to avoid fated misfortune, often involving a sacrifice. The centuries-old practice derives from Islamic influence brought to the island by medieval Arab traders. The sikidy is consulted for a range of divinatory questions pertaining to fate and the future, including identifying sources of and rectifying misfortune, reading the fate of newborns, and planning annual migrations. The mathematics of sikidy involves Boolean algebra, symbolic logic and parity. == History == The practice is several centuries old, and is influenced by Arab geomantic traditions of Arab Muslim traders on the island. Most writers link the origins of sikidy to the "sea-going trade involving the southwest coast of India, the Persian Gulf, and the east coast of Africa in the 9th or 10th century C.E." Stephen Ellis and Solofo Randrianja describe sikidy as "probably one of the oldest components of Malagasy culture", writing that it most likely the product of an indigenous divinatory art later influenced by Islamic practice. Umar H. D. Danfulani writes that the integration of Arabic divination into indigenous divination is "clearly demonstrated" in Madagascar, where the Arabic astrological system was adapted to the indigenous agricultural system and meshed with Malagasy lunar months by "adapting indigenous months, volana, to the astrological months, vintana". Danfulani also describes the concepts in sikidy of "houses" (lands) and "kings in their houses" as retained from medieval Arabic astrology. Chemillier et al. say the practice's spread across Madagascar likely originated with the southeastern Antemoro people, among whom Arab influence was the strongest. Though the etymology of sikidy is unknown, it has been posited that the word derives from the Arabic sichr ('incantation' or 'charm'). Sikidy was of central importance to pre-Christian Malagasy religion, with one practitioner quoted in 1892 as calling sikidy "the Bible of our ancestors". A missionary report from 1616 describes one form of sikidy using tamarind seeds, and another using fingered markings in the sand. The early colonial French governor of Madagascar Étienne de Flacourt documented sikidy in the mid-17th century: Matatane country in southeastern Madagascar [...] where the Antemoro [...] live was a center of astrological study as early as the fourteenth century [...]. This area was also the site of early Arab settlements, although strict Islamic observances were lost centuries ago [...]. Historical evidence shows that Antemoro diviners, bearers of the astrological system, infiltrated nearly all the ancient kingdoms of Madagascar beginning in the sixteenth century. [...] Today, although many persons claim to be ombiasy [diviners], only the Antemoro diviners are considered true professionals. The area is still a famous place of learning where specialists go for training and then return to their home communities with a certain body of knowledge. Now we can better understand the degree of similarity of divination forms found throughout Madagascar. For centuries Matitanana has remained a training center for diviners who have migrated widely, usually attaining important positions in their home communities and with various royal families. Comparison of contemporary rites with centuries-old texts show that sikidy has been remarkably unchanged throughout its history. The "infiltration" of Malagasy kingdoms by Antemoro diviners, and Matitanana's role as a place for astrological and divinatory learning, help to explain the relatively uniform practicing of sikidy across Madagascar. Chemallier et al. write that the mathematical construction of the arrangement of seeds is procedurally consistent across all of Madagascar, with variations in practice between groups and regions being limited to more minor aspects, such as the alignment of figures according to cardinal directions. One exception is the simplified Merina sikidy joria. === Origin myths === Mythic tradition relating to the origin of sikidy "links [the practice] both to the return by walking on water of Arab ancestors who had intermarried with Malagasy but then left, and to the names of the days of the week" and holds that the art was supernaturally communicated to the ancestors, with Zanahary (the supreme deity of Malagasy religion) giving it to Ranakandriana, who then gave it to a line of diviners (Ranakandriana to Ramanitralanana to Rabibi-andrano to Andriambavi-maitso (who was a woman) to Andriam-bavi-nosy), the last of whom terminated the monopoly by giving it to the people, declaring: "Behold, I give you the sikidy, of which you may inquire what offerings you should present in order to obtain blessings; and what expiation you should make so as to avert evils, when any are ill or under apprehension of some future calamity". A mythic anecdote of Ranakandriana says that two men observed him one day playing in the sand. In fact he was practicing a form of sikidy worked in sand called sikidy alanana. The two men seized him, and Ranakandriana promised that he would teach them something if they released him. They agreed, and Ranakandriana taught them in depth how to work the sikidy. The two men then went to their chief and told him that they could tell him "the past and the future—what was good and what was bad—what increased and what diminished." The chief asked them to tell him how he could obtain plenty of cattle. The two men worked their sikidy and told the chief to kill all of his bulls, and that "great numbers would come to him" on the following Friday. The chieftain, doubting, asked what would happen if their prediction didn't come true, and the two men promised they would pay with their lives. The chief agreed and killed his bulls. On Thursday, thinking he'd been duped, he prematurely killed the first man of the two who'd told him about the divinatory art. On Friday, however, "vast herds" came amidst heavy rain, actually filling an immense plain in their crowd. The chieftain lamented the mpisikidy's wrongful execution and ordered for him a pompous funeral. The chieftain took the second man as his close adviser and friend, and trusted the sikidy forever afterwards. The British missionary William Ellis recorded in 1839 two idiomatic expressions used in Madagascar that come from this story: "Tsy mahandry andro Zoma" (lit. 'He cannot wait 'til Friday') is said of someone extremely impatient, and heavy rainshowers falling in rapid succession are called "sese omby" (lit. 'a crowding together of cattle'). == Rites and arrangement of seeds == The divination is performed by a practitioner called an mpisikidy, ny màsina (lit. 'sacred one'), ombiasy, or ambiàsa (derived from the Arabic anbia, meaning 'prophet') who guides the client through the process and interprets the results in the context of the client's inquiries and desires. As part of an mpisikidy's formal initiation into the art, which includes a long period of apprenticeship, the initiate (called a mianatsy) must gather 124 and 200 fàno (Entada sp.) or kily (tamarind) tree seeds for his subsequent ritual use in sikidy. Raymond Decary writes that, at least among the Sakalava, a man must be 40 years old before learning and practicing sikidy, or he risks death. Before beginning to study, a student practitioner must make incisions at the tips of his index finger, his middle finger, and his tongue, and put within the incisions a paste containing red pepper and crushed wasp. This paste impregnates the fingers that will move the seeds of the sikidy and the tongue that will speak their revelations with the power to decipher the sikidy. Once this is done, he leaves at dawn to search for a fano (Entada chrysostachys) tree. Upon finding it, he throws his spear at its branches, shaking the tree and causing its large seed pods to fall. During this act, some initiates say: "When you were on the steep peak and in the dense forest, on you the crabs climbed, from you the crocodiles made their bed, with their paws the birds trod on you. Whether you are suspended in the trees or buried, you are never dried up nor rotten." In his study (written in 1941 and revised in 1948), Decary reported that the salary paid by a mianatsy to his master is "not very high": up to five francs, plus a red rooster's feather. The mpisikidy ritually arranges his seeds into a sixteen-column table consisting of four columns of randomly-generated data (representing fate) and eight columns of data derived from logical ope

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