The Enterprise Objects Framework, or simply EOF, was introduced by NeXT in 1994 as a pioneering object-relational mapping product for its NeXTSTEP and OpenStep development platforms. EOF abstracts the process of interacting with a relational database by mapping database rows to Java or Objective-C objects. This largely relieves developers from writing low-level SQL code. EOF enjoyed some niche success in the mid-1990s among financial institutions who were attracted to the rapid application development advantages of NeXT's object-oriented platform. Since Apple Inc's merger with NeXT in 1996, EOF has evolved into a fully integrated part of WebObjects, an application server also originally from NeXT. Many of the core concepts of EOF re-emerged as part of Core Data, which further abstracts the underlying data formats to allow it to be based on non-SQL stores. == History == In the early 1990s NeXT Computer recognized that connecting to databases was essential to most businesses and yet also potentially complex. Every data source has a different data-access language (or API), driving up the costs to learn and use each vendor's product. The NeXT engineers wanted to apply the advantages of object-oriented programming, by getting objects to "talk" to relational databases. As the two technologies are very different, the solution was to create an abstraction layer, insulating developers from writing the low-level procedural code (SQL) specific to each data source. The first attempt came in 1992 with the release of Database Kit (DBKit), which wrapped an object-oriented framework around any database. Unfortunately, NEXTSTEP at the time was not powerful enough and DBKit had serious design flaws. NeXT's second attempt came in 1994 with the Enterprise Objects Framework (EOF) version 1, a complete rewrite that was far more modular and OpenStep compatible. EOF 1.0 was the first product released by NeXT using the Foundation Kit and introduced autoreleased objects to the developer community. The development team at the time was only four people: Jack Greenfield, Rich Williamson, Linus Upson and Dan Willhite. EOF 2.0, released in late 1995, further refined the architecture, introducing the editing context. At that point, the development team consisted of Dan Willhite, Craig Federighi, Eric Noyau and Charly Kleissner. EOF achieved a modest level of popularity in the financial programming community in the mid-1990s, but it would come into its own with the emergence of the World Wide Web and the concept of web applications. It was clear that EOF could help companies plug their legacy databases into the Web without any rewriting of that data. With the addition of frameworks to do state management, load balancing and dynamic HTML generation, NeXT was able to launch the first object-oriented Web application server, WebObjects, in 1996, with EOF at its core. In 2000, Apple Inc. (which had merged with NeXT) officially dropped EOF as a standalone product, meaning that developers would be unable to use it to create desktop applications for the forthcoming Mac OS X. It would, however, continue to be an integral part of a major new release of WebObjects. WebObjects 5, released in 2001, was significant for the fact that its frameworks had been ported from their native Objective-C programming language to the Java language. Critics of this change argue that most of the power of EOF was a side effect of its Objective-C roots, and that EOF lost the beauty or simplicity it once had. Third-party tools, such as EOGenerator, help fill the deficiencies introduced by Java (mainly due to the loss of categories). The Objective-C code base was re-introduced with some modifications to desktop application developers as Core Data, part of Apple's Cocoa API, with the release of Mac OS X Tiger in April 2005. == How EOF works == Enterprise Objects provides tools and frameworks for object-relational mapping. The technology specializes in providing mechanisms to retrieve data from various data sources, such as relational databases via JDBC and JNDI directories, and mechanisms to commit data back to those data sources. These mechanisms are designed in a layered, abstract approach that allows developers to think about data retrieval and commitment at a higher level than a specific data source or data source vendor. Central to this mapping is a model file (an "EOModel") that you build with a visual tool — either EOModeler, or the EOModeler plug-in to Xcode. The mapping works as follows: Database tables are mapped to classes. Database columns are mapped to class attributes. Database rows are mapped to objects (or class instances). You can build data models based on existing data sources or you can build data models from scratch, which you then use to create data structures (tables, columns, joins) in a data source. The result is that database records can be transposed into Java objects. The advantage of using data models is that applications are isolated from the idiosyncrasies of the data sources they access. This separation of an application's business logic from database logic allows developers to change the database an application accesses without needing to change the application. EOF provides a level of database transparency not seen in other tools and allows the same model to be used to access different vendor databases and even allows relationships across different vendor databases without changing source code. Its power comes from exposing the underlying data sources as managed graphs of persistent objects. In simple terms, this means that it organizes the application's model layer into a set of defined in-memory data objects. It then tracks changes to these objects and can reverse those changes on demand, such as when a user performs an undo command. Then, when it is time to save changes to the application's data, it archives the objects to the underlying data sources. === Using Inheritance === In designing Enterprise Objects developers can leverage the object-oriented feature known as inheritance. A Customer object and an Employee object, for example, might both inherit certain characteristics from a more generic Person object, such as name, address, and phone number. While this kind of thinking is inherent in object-oriented design, relational databases have no explicit support for inheritance. However, using Enterprise Objects, you can build data models that reflect object hierarchies. That is, you can design database tables to support inheritance by also designing enterprise objects that map to multiple tables or particular views of a database table. == Enterprise Objects (EOs) == An Enterprise Object is analogous to what is often known in object-oriented programming as a business object — a class which models a physical or conceptual object in the business domain (e.g. a customer, an order, an item, etc.). What makes an EO different from other objects is that its instance data maps to a data store. Typically, an enterprise object contains key-value pairs that represent a row in a relational database. The key is basically the column name, and the value is what was in that row in the database. So it can be said that an EO's properties persist beyond the life of any particular running application. More precisely, an Enterprise Object is an instance of a class that implements the com.webobjects.eocontrol.EOEnterpriseObject interface. An Enterprise Object has a corresponding model (called an EOModel) that defines the mapping between the class's object model and the database schema. However, an enterprise object doesn't explicitly know about its model. This level of abstraction means that database vendors can be switched without it affecting the developer's code. This gives Enterprise Objects a high degree of reusability. == EOF and Core Data == Despite their common origins, the two technologies diverged, with each technology retaining a subset of the features of the original Objective-C code base, while adding some new features. === Features Supported Only by EOF === EOF supports custom SQL; shared editing contexts; nested editing contexts; and pre-fetching and batch faulting of relationships, all features of the original Objective-C implementation not supported by Core Data. Core Data also does not provide the equivalent of an EOModelGroup—the NSManagedObjectModel class provides methods for merging models from existing models, and for retrieving merged models from bundles. === Features Supported Only by Core Data === Core Data supports fetched properties; multiple configurations within a managed object model; local stores; and store aggregation (the data for a given entity may be spread across multiple stores); customization and localization of property names and validation warnings; and the use of predicates for property validation. These features of the original Objective-C implementation are not supported by the Java implementation.
Spatial anti-aliasing
In digital signal processing, spatial anti-aliasing is a technique for minimizing the distortion artifacts (aliasing) when representing a high-resolution image at a lower resolution. Anti-aliasing is used in digital photography, computer graphics, digital audio, and many other applications. Anti-aliasing means removing signal components that have a higher frequency than is able to be properly resolved by the recording (or sampling) device. This removal is done before (re)sampling at a lower resolution. When sampling is performed without removing this part of the signal, it causes undesirable artifacts such as black-and-white noise. In signal acquisition and audio, anti-aliasing is often done using an analog anti-aliasing filter to remove the out-of-band component of the input signal prior to sampling with an analog-to-digital converter. In digital photography, optical anti-aliasing filters made of birefringent materials smooth the signal in the spatial optical domain. The anti-aliasing filter essentially blurs the image slightly in order to reduce the resolution to or below that achievable by the digital sensor (the larger the pixel pitch, the lower the achievable resolution at the sensor level). == Examples == In computer graphics, anti-aliasing improves the appearance of "jagged" polygon edges, or "jaggies", so they are smoothed out on the screen. However, it incurs a performance cost for the graphics card and uses more video memory. The level of anti-aliasing determines how smooth polygon edges are (and how much video memory it consumes). Near the top of an image with a receding checker-board pattern, the image is difficult to recognise and often not considered aesthetically pleasing. In contrast, when anti-aliased the checker-board near the top blends into grey, which is usually the desired effect when the resolution is insufficient to show the detail. Even near the bottom of the image, the edges appear much smoother in the anti-aliased image. Multiple methods exist, including the sinc filter, which is considered a better anti-aliasing algorithm. When magnified, it can be seen how anti-aliasing interpolates the brightness of the pixels at the boundaries to produce grey pixels since the space is occupied by both black and white tiles. These help make the sinc filter antialiased image appear much smoother than the original. In a simple diamond image, anti-aliasing blends the boundary pixels; this reduces the aesthetically jarring effect of the sharp, step-like boundaries that appear in the aliased graphic. Anti-aliasing is often applied in rendering text on a computer screen, to suggest smooth contours that better emulate the appearance of text produced by conventional ink-and-paper printing. Particularly with fonts displayed on typical LCD screens, it is common to use subpixel rendering techniques like ClearType. Sub-pixel rendering requires special colour-balanced anti-aliasing filters to turn what would be severe colour distortion into barely-noticeable colour fringes. Equivalent results can be had by making individual sub-pixels addressable as if they were full pixels, and supplying a hardware-based anti-aliasing filter as is done in the OLPC XO-1 laptop's display controller. Pixel geometry affects all of this, whether the anti-aliasing and sub-pixel addressing are done in software or hardware. == Simplest approach to anti-aliasing == The most basic approach to anti-aliasing a pixel is determining what percentage of the pixel is occupied by a given region in the vector graphic - in this case a pixel-sized square, possibly transposed over several pixels - and using that percentage as the colour. A Python program producing a basic plot of a single, white-on-black anti-aliased point using the method is as follows: This method is generally best suited for simple graphics, such as basic lines or curves, and applications that would otherwise have to convert absolute coordinates to pixel-constrained coordinates, such as 3D graphics. It is a fairly fast function, but it is relatively low-quality, and gets slower as the complexity of the shape increases. For purposes requiring very high-quality graphics or very complex vector shapes, this will probably not be the best approach. Note: The plot_antialiased_point routine above cannot blindly set the colour value to the percent calculated. It must add the new value to the existing value at that location up to a maximum of 1. Otherwise, the brightness of each pixel will be equal to the darkest value calculated in time for that location which produces a very bad result. For example, if one point sets a brightness level of 0.90 for a given pixel and another point calculated later barely touches that pixel and has a brightness of 0.05, the final value set for that pixel should be 0.95, not 0.05. For more sophisticated shapes, the algorithm may be generalized as rendering the shape to a pixel grid with higher resolution than the target display surface (usually a multiple that is a power of 2 to reduce distortion), then using bicubic interpolation to determine the average intensity of each real pixel on the display surface. == Signal processing approach to anti-aliasing == In this approach, the ideal image is regarded as a signal. The image displayed on the screen is taken as samples, at each (x,y) pixel position, of a filtered version of the signal. Ideally, one would understand how the human brain would process the original signal, and provide an on-screen image that will yield the most similar response by the brain. The most widely accepted analytic tool for such problems is the Fourier transform; this decomposes a signal into basis functions of different frequencies, known as frequency components, and gives us the amplitude of each frequency component in the signal. The waves are of the form: cos ( 2 j π x ) cos ( 2 k π y ) {\displaystyle \ \cos(2j\pi x)\cos(2k\pi y)} where j and k are arbitrary non-negative integers. There are also frequency components involving the sine functions in one or both dimensions, but for the purpose of this discussion, the cosine will suffice. The numbers j and k together are the frequency of the component: j is the frequency in the x direction, and k is the frequency in the y direction. The goal of an anti-aliasing filter is to greatly reduce frequencies above a certain limit, known as the Nyquist frequency, so that the signal will be accurately represented by its samples, or nearly so, in accordance with the sampling theorem; there are many different choices of detailed algorithm, with different filter transfer functions. Current knowledge of human visual perception is not sufficient, in general, to say what approach will look best. == Two dimensional considerations == The previous discussion assumes that the rectangular mesh sampling is the dominant part of the problem. The filter usually considered optimal is not rotationally symmetrical, as shown in this first figure; this is because the data is sampled on a square lattice, not using a continuous image. This sampling pattern is the justification for doing signal processing along each axis, as it is traditionally done on one dimensional data. Lanczos resampling is based on convolution of the data with a discrete representation of the sinc function. If the resolution is not limited by the rectangular sampling rate of either the source or target image, then one should ideally use rotationally symmetrical filter or interpolation functions, as though the data were a two dimensional function of continuous x and y. The sinc function of the radius has too long a tail to make a good filter (it is not even square-integrable). A more appropriate analog to the one-dimensional sinc is the two-dimensional Airy disc amplitude, the 2D Fourier transform of a circular region in 2D frequency space, as opposed to a square region. One might consider a Gaussian plus enough of its second derivative to flatten the top (in the frequency domain) or sharpen it up (in the spatial domain), as shown. Functions based on the Gaussian function are natural choices, because convolution with a Gaussian gives another Gaussian whether applied to x and y or to the radius. Similarly to wavelets, another of its properties is that it is halfway between being localized in the configuration (x and y) and in the spectral (j and k) representation. As an interpolation function, a Gaussian alone seems too spread out to preserve the maximum possible detail, and thus the second derivative is added. As an example, when printing a photographic negative with plentiful processing capability and on a printer with a hexagonal pattern, there is no reason to use sinc function interpolation. Such interpolation would treat diagonal lines differently from horizontal and vertical lines, which is like a weak form of aliasing. == Practical real-time anti-aliasing approximations == There are only a handful of primitives used at the lowest level in a real-time rend
External memory algorithm
In computing, external memory algorithms or out-of-core algorithms are algorithms that are designed to process data that are too large to fit into a computer's main memory at once. Such algorithms must be optimized to efficiently fetch and access data stored in slow bulk memory (auxiliary memory) such as hard drives or tape drives, or when memory is on a computer network. External memory algorithms are analyzed in the external memory model. == Model == External memory algorithms are analyzed in an idealized model of computation called the external memory model (or I/O model, or disk access model). The external memory model is an abstract machine similar to the RAM machine model, but with a cache in addition to main memory. The model captures the fact that read and write operations are much faster in a cache than in main memory, and that reading long contiguous blocks is faster than reading randomly using a disk read-and-write head. The running time of an algorithm in the external memory model is defined by the number of reads and writes to memory required. The model was introduced by Alok Aggarwal and Jeffrey Vitter in 1988. The external memory model is related to the cache-oblivious model, but algorithms in the external memory model may know both the block size and the cache size. For this reason, the model is sometimes referred to as the cache-aware model. The model consists of a processor with an internal memory or cache of size M, connected to an unbounded external memory. Both the internal and external memory are divided into blocks of size B. One input/output or memory transfer operation consists of moving a block of B contiguous elements from external to internal memory, and the running time of an algorithm is determined by the number of these input/output operations. == Algorithms == Algorithms in the external memory model take advantage of the fact that retrieving one object from external memory retrieves an entire block of size B. This property is sometimes referred to as locality. Searching for an element among N objects is possible in the external memory model using a B-tree with branching factor B. Using a B-tree, searching, insertion, and deletion can be achieved in O ( log B N ) {\displaystyle O(\log _{B}N)} time (in Big O notation). Information theoretically, this is the minimum running time possible for these operations, so using a B-tree is asymptotically optimal. External sorting is sorting in an external memory setting. External sorting can be done via distribution sort, which is similar to quicksort, or via a M B {\displaystyle {\tfrac {M}{B}}} -way merge sort. Both variants achieve the asymptotically optimal runtime of O ( N B log M B N B ) {\displaystyle O\left({\frac {N}{B}}\log _{\frac {M}{B}}{\frac {N}{B}}\right)} to sort N objects. This bound also applies to the fast Fourier transform in the external memory model. The permutation problem is to rearrange N elements into a specific permutation. This can either be done either by sorting, which requires the above sorting runtime, or inserting each element in order and ignoring the benefit of locality. Thus, permutation can be done in O ( min ( N , N B log M B N B ) ) {\displaystyle O\left(\min \left(N,{\frac {N}{B}}\log _{\frac {M}{B}}{\frac {N}{B}}\right)\right)} time. == Applications == The external memory model captures the memory hierarchy, which is not modeled in other common models used in analyzing data structures, such as the random-access machine, and is useful for proving lower bounds for data structures. The model is also useful for analyzing algorithms that work on datasets too big to fit in internal memory. A typical example is geographic information systems, especially digital elevation models, where the full data set easily exceeds several gigabytes or even terabytes of data. This methodology extends beyond general purpose CPUs and also includes GPU computing as well as classical digital signal processing. In general-purpose computing on graphics processing units (GPGPU), powerful graphics cards (GPUs) with little memory (compared with the more familiar system memory, which is most often referred to simply as RAM) are utilized with relatively slow CPU-to-GPU memory transfer (when compared with computation bandwidth). == History == An early use of the term "out-of-core" as an adjective is in 1962 in reference to devices that are other than the core memory of an IBM 360. An early use of the term "out-of-core" with respect to algorithms appears in 1971.
Generalized distributive law
The generalized distributive law (GDL) is a generalization of the distributive property which gives rise to a general message passing algorithm. It is a synthesis of the work of many authors in the information theory, digital communications, signal processing, statistics, and artificial intelligence communities. The law and algorithm were introduced in a semi-tutorial by Srinivas M. Aji and Robert J. McEliece with the same title. == Introduction == "The distributive law in mathematics is the law relating the operations of multiplication and addition, stated symbolically, a ∗ ( b + c ) = a ∗ b + a ∗ c {\displaystyle a(b+c)=ab+ac} ; that is, the monomial factor a {\displaystyle a} is distributed, or separately applied, to each term of the binomial factor b + c {\displaystyle b+c} , resulting in the product a ∗ b + a ∗ c {\displaystyle ab+ac} " – Britannica. As it can be observed from the definition, application of distributive law to an arithmetic expression reduces the number of operations in it. In the previous example the total number of operations reduced from three (two multiplications and an addition in a ∗ b + a ∗ c {\displaystyle ab+ac} ) to two (one multiplication and one addition in a ∗ ( b + c ) {\displaystyle a(b+c)} ). Generalization of distributive law leads to a large family of fast algorithms. This includes the FFT and Viterbi algorithm. This is explained in a more formal way in the example below: α ( a , b ) = d e f ∑ c , d , e ∈ A f ( a , c , b ) g ( a , d , e ) {\displaystyle \alpha (a,\,b){\stackrel {\mathrm {def} }{=}}\displaystyle \sum \limits _{c,d,e\in A}f(a,\,c,\,b)\,g(a,\,d,\,e)} where f ( ⋅ ) {\displaystyle f(\cdot )} and g ( ⋅ ) {\displaystyle g(\cdot )} are real-valued functions, a , b , c , d , e ∈ A {\displaystyle a,b,c,d,e\in A} and | A | = q {\displaystyle |A|=q} (say) Here we are "marginalizing out" the independent variables ( c {\displaystyle c} , d {\displaystyle d} , and e {\displaystyle e} ) to obtain the result. When we are calculating the computational complexity, we can see that for each q 2 {\displaystyle q^{2}} pairs of ( a , b ) {\displaystyle (a,b)} , there are q 3 {\displaystyle q^{3}} terms due to the triplet ( c , d , e ) {\displaystyle (c,d,e)} which needs to take part in the evaluation of α ( a , b ) {\displaystyle \alpha (a,\,b)} with each step having one addition and one multiplication. Therefore, the total number of computations needed is 2 ⋅ q 2 ⋅ q 3 = 2 q 5 {\displaystyle 2\cdot q^{2}\cdot q^{3}=2q^{5}} . Hence the asymptotic complexity of the above function is O ( n 5 ) {\displaystyle O(n^{5})} . If we apply the distributive law to the RHS of the equation, we get the following: α ( a , b ) = d e f ∑ c ∈ A f ( a , c , b ) ⋅ ∑ d , e ∈ A g ( a , d , e ) {\displaystyle \alpha (a,\,b){\stackrel {\mathrm {def} }{=}}\displaystyle \sum \limits _{c\in A}f(a,\,c,\,b)\cdot \sum _{d,\,e\in A}g(a,\,d,\,e)} This implies that α ( a , b ) {\displaystyle \alpha (a,\,b)} can be described as a product α 1 ( a , b ) ⋅ α 2 ( a ) {\displaystyle \alpha _{1}(a,\,b)\cdot \alpha _{2}(a)} where α 1 ( a , b ) = d e f ∑ c ∈ A f ( a , c , b ) {\displaystyle \alpha _{1}(a,b){\stackrel {\mathrm {def} }{=}}\displaystyle \sum \limits _{c\in A}f(a,\,c,\,b)} and α 2 ( a ) = d e f ∑ d , e ∈ A g ( a , d , e ) {\displaystyle \alpha _{2}(a){\stackrel {\mathrm {def} }{=}}\displaystyle \sum \limits _{d,\,e\in A}g(a,\,d,\,e)} Now, when we are calculating the computational complexity, we can see that there are q 3 {\displaystyle q^{3}} additions in α 1 ( a , b ) {\displaystyle \alpha _{1}(a,\,b)} and α 2 ( a ) {\displaystyle \alpha _{2}(a)} each and there are q 2 {\displaystyle q^{2}} multiplications when we are using the product α 1 ( a , b ) ⋅ α 2 ( a ) {\displaystyle \alpha _{1}(a,\,b)\cdot \alpha _{2}(a)} to evaluate α ( a , b ) {\displaystyle \alpha (a,\,b)} . Therefore, the total number of computations needed is q 3 + q 3 + q 2 = 2 q 3 + q 2 {\displaystyle q^{3}+q^{3}+q^{2}=2q^{3}+q^{2}} . Hence the asymptotic complexity of calculating α ( a , b ) {\displaystyle \alpha (a,b)} reduces to O ( n 3 ) {\displaystyle O(n^{3})} from O ( n 5 ) {\displaystyle O(n^{5})} . This shows by an example that applying distributive law reduces the computational complexity which is one of the good features of a "fast algorithm". == History == Some of the problems that used distributive law to solve can be grouped as follows: Decoding algorithms: A GDL like algorithm was used by Gallager's for decoding low density parity-check codes. Based on Gallager's work Tanner introduced the Tanner graph and expressed Gallagers work in message passing form. The tanners graph also helped explain the Viterbi algorithm. It is observed by Forney that Viterbi's maximum likelihood decoding of convolutional codes also used algorithms of GDL-like generality. Forward–backward algorithm: The forward backward algorithm helped as an algorithm for tracking the states in the Markov chain. And this also was used the algorithm of GDL like generality Artificial intelligence: The notion of junction trees has been used to solve many problems in AI. Also the concept of bucket elimination used many of the concepts. == The MPF problem == MPF or marginalize a product function is a general computational problem which as special case includes many classical problems such as computation of discrete Hadamard transform, maximum likelihood decoding of a linear code over a memory-less channel, and matrix chain multiplication. The power of the GDL lies in the fact that it applies to situations in which additions and multiplications are generalized. A commutative semiring is a good framework for explaining this behavior. It is defined over a set K {\displaystyle K} with operators " + {\displaystyle +} " and " . {\displaystyle .} " where ( K , + ) {\displaystyle (K,\,+)} and ( K , . ) {\displaystyle (K,\,.)} are a commutative monoids and the distributive law holds. Let p 1 , … , p n {\displaystyle p_{1},\ldots ,p_{n}} be variables such that p 1 ∈ A 1 , … , p n ∈ A n {\displaystyle p_{1}\in A_{1},\ldots ,p_{n}\in A_{n}} where A {\displaystyle A} is a finite set and | A i | = q i {\displaystyle |A_{i}|=q_{i}} . Here i = 1 , … , n {\displaystyle i=1,\ldots ,n} . If S = { i 1 , … , i r } {\displaystyle S=\{i_{1},\ldots ,i_{r}\}} and S ⊂ { 1 , … , n } {\displaystyle S\,\subset \{1,\ldots ,n\}} , let A S = A i 1 × ⋯ × A i r {\displaystyle A_{S}=A_{i_{1}}\times \cdots \times A_{i_{r}}} , p S = ( p i 1 , … , p i r ) {\displaystyle p_{S}=(p_{i_{1}},\ldots ,p_{i_{r}})} , q S = | A S | {\displaystyle q_{S}=|A_{S}|} , A = A 1 × ⋯ × A n {\displaystyle \mathbf {A} =A_{1}\times \cdots \times A_{n}} , and p = { p 1 , … , p n } {\displaystyle \mathbf {p} =\{p_{1},\ldots ,p_{n}\}} Let S = { S j } j = 1 M {\displaystyle S=\{S_{j}\}_{j=1}^{M}} where S j ⊂ { 1 , . . . , n } {\displaystyle S_{j}\subset \{1,...\,,n\}} . Suppose a function is defined as α i : A S i → R {\displaystyle \alpha _{i}:A_{S_{i}}\rightarrow R} , where R {\displaystyle R} is a commutative semiring. Also, p S i {\displaystyle p_{S_{i}}} are named the local domains and α i {\displaystyle \alpha _{i}} as the local kernels. Now the global kernel β : A → R {\displaystyle \beta :\mathbf {A} \rightarrow R} is defined as: β ( p 1 , . . . , p n ) = ∏ i = 1 M α ( p S i ) {\displaystyle \beta (p_{1},...\,,p_{n})=\prod _{i=1}^{M}\alpha (p_{S_{i}})} Definition of MPF problem: For one or more indices i = 1 , . . . , M {\displaystyle i=1,...\,,M} , compute a table of the values of S i {\displaystyle S_{i}} -marginalization of the global kernel β {\displaystyle \beta } , which is the function β i : A S i → R {\displaystyle \beta _{i}:A_{S_{i}}\rightarrow R} defined as β i ( p S i ) = ∑ p S i c ∈ A S i c β ( p ) {\displaystyle \beta _{i}(p_{S_{i}})\,=\displaystyle \sum \limits _{p_{S_{i}^{c}}\in A_{S_{i}^{c}}}\beta (p)} Here S i c {\displaystyle S_{i}^{c}} is the complement of S i {\displaystyle S_{i}} with respect to { 1 , . . . , n } {\displaystyle \mathbf {\{} 1,...\,,n\}} and the β i ( p S i ) {\displaystyle \beta _{i}(p_{S_{i}})} is called the i t h {\displaystyle i^{th}} objective function, or the objective function at S i {\displaystyle S_{i}} . It can observed that the computation of the i t h {\displaystyle i^{th}} objective function in the obvious way needs M q 1 q 2 q 3 ⋯ q n {\displaystyle Mq_{1}q_{2}q_{3}\cdots q_{n}} operations. This is because there are q 1 q 2 ⋯ q n {\displaystyle q_{1}q_{2}\cdots q_{n}} additions and ( M − 1 ) q 1 q 2 . . . q n {\displaystyle (M-1)q_{1}q_{2}...q_{n}} multiplications needed in the computation of the i th {\displaystyle i^{\text{th}}} objective function. The GDL algorithm which is explained in the next section can reduce this computational complexity. The following is an example of the MPF problem. Let p 1 , p 2 , p 3 , p 4 , {\displaystyle p_{1},\,p_{2},\,p_{3},\,p_{4},} and p 5 {\displaystyle p_{5}} be variables such that p 1 ∈ A 1 , p 2 ∈ A 2 , p 3 ∈ A 3 , p 4 ∈ A 4 , {\displaystyle p_{1}\in
Software intelligence
Software intelligence is insight into the inner workings and structural condition of software assets produced by software designed to analyze database structure, software framework and source code to better understand and control complex software systems in information technology environments. Similarly to business intelligence (BI), software intelligence is produced by a set of software tools and techniques for the mining of data and the software's inner-structure. Results are automatically produced and feed a knowledge base containing technical documentation and blueprints of the innerworking of applications, and make it available to all to be used by business and software stakeholders to make informed decisions, measure the efficiency of software development organizations, communicate about the software health, prevent software catastrophes. == History == Software intelligence has been used by Kirk Paul Lafler, an American engineer, entrepreneur, and consultant, and founder of Software Intelligence Corporation in 1979. At that time, it was mainly related to SAS activities, in which he has been an expert since 1979. In the early 1980s, Victor R. Basili participated in different papers detailing a methodology for collecting valid software engineering data relating to software engineering, evaluation of software development, and variations. In 2004, different software vendors in software analysis started using the terms as part of their product naming and marketing strategy. Then in 2010, Ahmed E. Hassan and Tao Xie defined software intelligence as a "practice offering software practitioners up-to-date and pertinent information to support their daily decision-making processes and Software Intelligence should support decision-making processes throughout the lifetime of a software system". They go on by defining software intelligence as a "strong impact on modern software practice" for the upcoming decades. == Capabilities == Because of the complexity and wide range of components and subjects implied in software, software intelligence is derived from different aspects of software: Software composition is the construction of software application components. Components result from software coding, as well as the integration of the source code from external components: Open source, 3rd party components, or frameworks. Other components can be integrated using application programming interface call to libraries or services. Software architecture refers to the structure and organization of elements of a system, relations, and properties among them. Software flaws designate problems that can cause security, stability, resiliency, and unexpected results. There is no standard definition of software flaws but the most accepted is from The MITRE Corporation where common flaws are cataloged as Common Weakness Enumeration. Software grades assess attributes of the software. Historically, the classification and terminology of attributes have been derived from the ISO 9126-3 and the subsequent ISO 25000:2005 quality model. Software economics refers to the resource evaluation of software in the past, present, or future to make decisions and to govern. == Components == The capabilities of software intelligence platforms include an increasing number of components: Code analyzer to serve as an information basis for other software intelligence components identifying objects created by the programming language, external objects from Open source, third parties objects, frameworks, API, or services Graphical visualization and blueprinting of the inner structure of the software product or application considered including dependencies, from data acquisition (automated and real-time data capture, end-user entries) up to data storage, the different layers within the software, and the coupling between all elements. Navigation capabilities within components and impact analysis features List of flaws, architectural and coding violations, against standardized best practices, cloud blocker preventing migration to a Cloud environment, and rogue data-call entailing the security and integrity of software Grades or scores of the structural and software quality aligned with industry-standard like OMG, CISQ or SEI assessing the reliability, security, efficiency, maintainability, and scalability to cloud or other systems. Metrics quantifying and estimating software economics including work effort, sizing, and technical debt Industry references and benchmarking allowing comparisons between outputs of analysis and industry standards == User aspect == Some considerations must be made in order to successfully integrate the usage of software Intelligence systems in a company. Ultimately the software intelligence system must be accepted and utilized by the users in order for it to add value to the organization. If the system does not add value to the users' mission, they simply don't use it as stated by M. Storey in 2003. At the code level and system representation, software intelligence systems must provide a different level of abstractions: an abstract view for designing, explaining and documenting and a detailed view for understanding and analyzing the software system. At the governance level, the user acceptance for software intelligence covers different areas related to the inner functioning of the system as well as the output of the system. It encompasses these requirements: Comprehensive: missing information may lead to a wrong or inappropriate decision, as well as it is a factor influencing the user acceptance of a system. Accurate: accuracy depends on how the data is collected to ensure fair and indisputable opinion and judgment. Precise: precision is usually judged by comparing several measurements from the same or different sources. Scalable: lack of scalability in the software industry is a critical factor leading to failure. Credible: outputs must be trusted and believed. Deploy-able and usable. == Applications == Software intelligence has many applications in all businesses relating to the software environment, whether it is software for professionals, individuals, or embedded software. Depending on the association and the usage of the components, applications will relate to: Change and modernization: uniform documentation and blueprinting on all inner components, external code integrated, or call to internal or external components of the software Resiliency and security: measuring against industry standards to diagnose structural flaws in an IT environment. Compliance validation regarding security, specific regulations or technical matters. Decisions making and governance: Providing analytics about the software itself or stakeholders involved in the development of the software, e.g. productivity measurement to inform business and IT leaders about progress towards business goals. Assessment and Benchmarking to help business and IT leaders to make informed, fact-based decision about software. == Marketplace == Software intelligence is a high-level discipline and has been gradually growing covering the applications listed above. There are several markets driving the need for it: Application Portfolio Analysis (APA) aiming at improving the enterprise performance. Software Assessment for producing the software KPI and improving quality and productivity. Software security and resiliency measures and validation. Software evolution or legacy modernization, for which blueprinting the software systems are needed nor tools improving and facilitating modifications.
Something Big Is Happening
"Something Big Is Happening" is an essay by Matt Shumer, an AI entrepreneur, about the impact of artificial intelligence, published in February 2026, that has since been reportedly viewed more than 80 million times and widely discussed. Shumer noted that the technology has crossed an important threshold, where AI has become capable of creating self-improving systems. Referring to one the most recent AI models, he wrote: "It was making intelligent decisions. It had something that felt, for the first time, like judgment. Like taste." Speaking to CNBC's Power Lunch, Shumer said that his "core message" is "people in the workforce should start to use and experiment with AI tools so they can understand what’s coming". Even as the essay was widely shared and discussed, the essay also elicited criticism. Paulo Carvao, in an essay published by the Forbes Magazine stated that some of his advice is sound, but added: "It reads at times like a sales pitch. He urges readers to subscribe to the most advanced AI tools. He implies that those with access to premium models will outpace those without. He frames paid AI subscriptions as a form of insurance against obsolescence." Writing in The Guardian, Dan Milmo and Aisha Down mentioned Shumer as having a history of AI hype and stated, "He previously excited the internet by announcing the release of the world's "top open-source model", which it was not". Many workers in the technology sector criticized the article in blog posts shared on Hacker News; Edward Zitron commented that "while coding LLMs can test products, or scan/fix some bugs, this suggests they A) do this autonomously without human input, B) they do this correctly every time (or ever!)." In an article alluding to Shumer's original post, Ari Colaprete wrote "the LLM is fundamentally a writing machine, it does everything via text, and if you make it produce writing that exists purely to serve some sort of mechanical function, and you train it to succeed in that task, then it will tend to do so, even with vast intricacy."
Browsing
Browsing is a kind of orienting strategy. It is supposed to identify something of relevance for the browsing organism. In context of humans, it is a metaphor taken from the animal kingdom. It is used, for example, about people browsing open shelves in libraries, window shopping, or browsing databases or the Internet. In library and information science, it is an important subject, both purely theoretically and as applied science aiming at designing interfaces which support browsing activities for the user. == Definition == In 2011, Birger Hjørland provided the following definition: "Browsing is a quick examination of the relevance of a number of objects which may or may not lead to a closer examination or acquisition/selection of (some of) these objects. It is a kind of orienting strategy that is formed by our "theories", "expectations" and "subjectivity". == Controversies == As with any kind of human psychology, browsing can be understood in biological, behavioral, or cognitive terms on the one hand or in social, historical, and cultural terms on the other hand. In 2007, Marcia Bates researched browsing from "behavioural" approaches, while Hjørland (2011a+b) defended a social view. Bates found that browsing is rooted in our history as exploratory, motile animals hunting for food and nesting opportunities. According to Hjørland (2011a), on the other hand, Marcia Bates' browsing for information about browsing is governed by her behavioral assumptions, while Hjørland's browsing for information about browsing is governed by his socio-cultural understanding of human psychology. In short: Human browsing is based on our conceptions and interests. === Is browsing a random activity? === Browsing is often understood as a random activity. Dictionary.com, for example, has this definition: "to glance at random through a book, magazine, etc.". Hjørland suggests, however, that browsing is an activity that is governed by our metatheories. We may dynamically change our theories and conceptions but when we browse, the activity is governed by the interests, conceptions, priorities and metatheories that we have at that time. Therefore, browsing is not totally random. == Browsing versus analytical search strategies == In 1997, Gary Marchionini wrote: "A fundamental distinction is made between analytical and browsing strategies [...]. Analytical strategies depend on careful planning, the recall of query terms, and iterative query reformulations and examinations of results. Browsing strategies are heuristic and opportunistic and depend on recognizing relevant information. Analytic strategies are batch oriented and half duplex (turn talking) like human conversation, whereas browsing strategies are more interactive, real-time exchanges and collaborations between the information seeker and the information system. Browsing strategies demand a lower cognitive load in advance and a steadier attentional load throughout the information-seeking process. When it comes to Browsing, giblets are amazing." == Orienting strategies == Some sociologists, such as Berger and Zelditch in 1993, Wagner in 1984, and Wagner & Berger in 1985, have used the term "orienting strategies". They find that orienting strategies should be understood as metatheories: "Consider the very large proportion of sociological theory that is in the form of metatheory. It is discussion about theory: about what concepts it should include, about how those concepts should be linked, and about how theory should be studied. Similar to Kuhn’s paradigms, theories of this sort provide guidelines or strategies for understanding social phenomena and suggest the proper orientation of the theorist to these phenomena; they are orienting strategies. Textbooks in theory frequently focus on orienting strategies such as functionalism, exchange, or ethnomethodology." Sociologists thus use metatheories as orienting strategies. We may generalize and say that all people use metatheories as orienting strategies and that this is what direct our attention and also our browsing – also when we are not conscious about it.