The representation of the Holocaust on social media has been a subject of scholarly inquiry and media attention. == Selfies at Holocaust memorial sites == Some visitors take selfies at Holocaust memorials, which has been the subject of controversy. In 2018, Rhian Sugden, a British model, received criticism after posting a selfie at the Memorial to the Murdered Jews of Europe in Berlin with the caption "ET phone home". She later removed the caption, but defended taking the photograph. Other celebrities have also been criticised for photographs at the Berlin memorial, including Indian actress Priyanka Chopra and US politician Pete Buttigieg, whose husband posted a photograph of him at the memorial on a personal social media account. The Israeli artist and satirist Shahak Shapira set up the website yolocaust.de in 2017 to expose people who take inappropriate selfies at the Holocaust memorial in Berlin. Shapira went through thousands of selfies posted to social media sites such as Facebook, Instagram, Tinder, and Grindr, choosing the twelve that he found most offensive. When the images were moused over, the website replaces the memorial backdrop with black and white images of Nazi victims. "Yolocaust" is a portmanteau of "Holocaust" and YOLO, an acronym for "you only live once". The website went viral, receiving 1.2 million views in the first 24 hours after its launch. Shapira honored requests to take down all of the photographs, which he had used without permission, and the website remains with only a textual documentation of the project. In an analysis of comments by Internet users on the project, Christoph Bareither estimated that 75% were positive. However, the memorial's architect, Peter Eisenman, criticized the website. In his 2018 book Postcards from Auschwitz, Grinnell professor Daniel P. Reynolds defends the practice of selfie-taking at Holocaust sites. In 2019, the Auschwitz-Birkenau State Museum requested that visitors not take inappropriate selfies, although the museum's staff acknowledged that other visitors take selfies in a thoughtful and respectful manner, which they did not criticize. In an academic paper, Gemma Commane and Rebekah Potton analyze the use of Instagram to share tourist photographs at Holocaust sites and conclude that "Instagram encourages conversation and empathy, keeping the Holocaust visible in youth discourses". According to their analysis, most images are tagged with respectful hashtags such as #tragic, #remembrance, and #sadness. The Auschwitz museum has an official Instagram account, auschwitzmemorial, which it uses to share selected appropriate Instagram posts. However, the image feed for the hashtag "Auschwitz" includes potentially offensive images such as an image of "Nazi Vs. Jews #beerpong". This image, according to the authors, expresses "mockery and contempt" for Holocaust victims. They also document offensive memes using images of Holocaust atrocities and shared on Instagram. Some social media users post in order to criticize what they see as inappropriate behavior at Holocaust sites, with one commenting, "Taking photos posing next to razor wire, selfies with victim's hair in the background, and even group shots in front of the crematoria had to be seen to be believed." == Assessment of tourism == Social media posts have been used by researchers to analyze the phenomenon of Holocaust-related tourism. == Social media groups == People have created groups on Facebook to discuss issues related to the Holocaust. One paper analyses two such groups, "The Holocaust and My Family" and "The Descendants of the Victims and Survivors of the Holocaust" in which people engage in collective trauma processing. == Eva.stories == In 2019, Israeli high-tech entrepreneur Mati Kochavi created a fictitious Instagram account for Eva Heyman, a Hungarian-Jewish girl who was murdered in Auschwitz concentration camp. The project met with mixed reception. Israeli prime minister Benjamin Netanyahu praised the project, saying that it "exposes the immense tragedy of our people through the story of one girl". == Holocaust denial == The issue of Holocaust denial on social media has also attracted attention. In October 2020, Facebook reversed its policy and banned Holocaust denial from the platform. Founder Mark Zuckerberg had previously argued that such content should not be banned on freedom of speech grounds.
Cloud load balancing
Cloud load balancing is a type of load balancing that is performed in cloud computing. Cloud load balancing is the process of distributing workloads across multiple computing resources. Cloud load balancing reduces costs associated with document management systems and maximizes availability of resources. It is a type of load balancing and not to be confused with Domain Name System (DNS) load balancing. While DNS load balancing uses software or hardware to perform the function, cloud load balancing uses services offered by various computer network companies. == Comparison With DNS load balancing == Cloud load balancing has an advantage over DNS load balancing as it can transfer loads to servers globally as opposed to distributing it across local servers. In the event of a local server outage, cloud load balancing delivers users to the closest regional server without interruption for the user. Cloud load balancing addresses issues relating to TTL reliance present during DNS load balancing. DNS directives can only be enforced once in every TTL cycle and can take several hours if switching between servers during a lag or server failure. Incoming server traffic will continue to route to the original server until the TTL expires and can create an uneven performance as different internet service providers may reach the new server before other internet service providers. Another advantage is that cloud load balancing improves response time by routing remote sessions to the best performing data centers. == Importance of Load Balancing == Cloud computing brings advantages in "cost, flexibility and availability of service users." Those advantages drive the demand for Cloud services. The demand raises technical issues in Service Oriented Architectures and Internet of Services (IoS)-style applications, such as high availability and scalability. As a major concern in these issues, load balancing allows cloud computing to "scale up to increasing demands" by efficiently allocating dynamic local workload evenly across all nodes. == Load Balancing Techniques == === Scheduling Algorithms === Opportunistic Load Balancing (OLB) is the algorithm that assigns workloads to nodes in free order. It is simple but does not consider the expected execution time of each node. Load balance Min-Min (LBMM) assigns sub-tasks to the node which requires minimum execution time. === Load Balancing Policies === Workload and Client Aware Policy (WCAP) specifies the unique and special property (USP) of requests and computing nodes. With the information of USP, the schedule can decide the most suitable node to complete a request. WCAP makes the most of computing nodes by reducing their idle time. Also, it reduces performance time through searches based on content information. === A Comparative Study of Algorithms === Biased Random Sampling bases its job allocation on the network represented by a directed graph. For each execution node in this graph, in-degree means available resources and out-degree means allocated jobs. In-degree will decrease during job execution while out-degree will increase after job allocation. Active Clustering is a self-aggregation algorithm to rewire the network. The experiment result is that"Active Clustering and Random Sampling Walk predictably perform better as the number of processing nodes is increased" while the Honeyhive algorithm does not show the increasing pattern. == Client-side Load Balancer Using Cloud Computing == Load balancer forwards packets to web servers according to different workloads on servers. However, it is hard to implement a scalable load balancer because of both the "cloud's commodity business model and the limited infrastructure control allowed by cloud providers." Client-side Load Balancer (CLB) solve this problem by using a scalable cloud storage service. CLB allows clients to choose back-end web servers for dynamic content although it delivers static content.
Rendering equation
In computer graphics, the rendering equation is an integral equation that expresses the amount of light leaving a point on a surface as the sum of emitted light and reflected light. It was independently introduced into computer graphics by David Immel et al. and James Kajiya in 1986. The equation is important in the theory of physically based rendering, describing the relationships between the bidirectional reflectance distribution function (BRDF) and the radiometric quantities used in rendering. The rendering equation is defined at every point on every surface in the scene being rendered, including points hidden from the camera. The incoming light quantities on the right side of the equation usually come from the left (outgoing) side at other points in the scene (ray casting can be used to find these other points). The radiosity rendering method solves a discrete approximation of this system of equations. In distributed ray tracing, the integral on the right side of the equation may be evaluated using Monte Carlo integration by randomly sampling possible incoming light directions. Path tracing improves and simplifies this method. The rendering equation can be extended to handle effects such as fluorescence (in which some absorbed energy is re-emitted at different wavelengths) and can support transparent and translucent materials by using a bidirectional scattering distribution function (BSDF) in place of a BRDF. The theory of path tracing sometimes uses a path integral (integral over possible paths from a light source to a point) instead of the integral over possible incoming directions. == Equation form == The rendering equation may be written in the form L o ( x , ω o , λ , t ) = L e ( x , ω o , λ , t ) + L r ( x , ω o , λ , t ) {\displaystyle L_{\text{o}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)=L_{\text{e}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)+L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} L r ( x , ω o , λ , t ) = ∫ Ω f r ( x , ω i , ω o , λ , t ) L i ( x , ω i , λ , t ) ( ω i ⋅ n ) d ω i {\displaystyle L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)=\int _{\Omega }f_{\text{r}}(\mathbf {x} ,\omega _{\text{i}},\omega _{\text{o}},\lambda ,t)L_{\text{i}}(\mathbf {x} ,\omega _{\text{i}},\lambda ,t)(\omega _{\text{i}}\cdot \mathbf {n} )\operatorname {d} \omega _{\text{i}}} where L o ( x , ω o , λ , t ) {\displaystyle L_{\text{o}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is the total spectral radiance of wavelength λ {\displaystyle \lambda } directed outward along direction ω o {\displaystyle \omega _{\text{o}}} at time t {\displaystyle t} , from a particular position x {\displaystyle \mathbf {x} } x {\displaystyle \mathbf {x} } is the location in space ω o {\displaystyle \omega _{\text{o}}} is the direction of the outgoing light λ {\displaystyle \lambda } is a particular wavelength of light t {\displaystyle t} is time L e ( x , ω o , λ , t ) {\displaystyle L_{\text{e}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is emitted spectral radiance L r ( x , ω o , λ , t ) {\displaystyle L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is reflected spectral radiance ∫ Ω … d ω i {\displaystyle \int _{\Omega }\dots \operatorname {d} \omega _{\text{i}}} is an integral over Ω {\displaystyle \Omega } Ω {\displaystyle \Omega } is the unit hemisphere centered around n {\displaystyle \mathbf {n} } containing all possible values for ω i {\displaystyle \omega _{\text{i}}} where ω i ⋅ n > 0 {\displaystyle \omega _{\text{i}}\cdot \mathbf {n} >0} f r ( x , ω i , ω o , λ , t ) {\displaystyle f_{\text{r}}(\mathbf {x} ,\omega _{\text{i}},\omega _{\text{o}},\lambda ,t)} is the bidirectional reflectance distribution function, the proportion of light reflected from ω i {\displaystyle \omega _{\text{i}}} to ω o {\displaystyle \omega _{\text{o}}} at position x {\displaystyle \mathbf {x} } , time t {\displaystyle t} , and at wavelength λ {\displaystyle \lambda } ω i {\displaystyle \omega _{\text{i}}} is the negative direction of the incoming light L i ( x , ω i , λ , t ) {\displaystyle L_{\text{i}}(\mathbf {x} ,\omega _{\text{i}},\lambda ,t)} is spectral radiance of wavelength λ {\displaystyle \lambda } coming inward toward x {\displaystyle \mathbf {x} } from direction ω i {\displaystyle \omega _{\text{i}}} at time t {\displaystyle t} n {\displaystyle \mathbf {n} } is the surface normal at x {\displaystyle \mathbf {x} } ω i ⋅ n {\displaystyle \omega _{\text{i}}\cdot \mathbf {n} } is the weakening factor of outward irradiance due to incident angle, as the light flux is smeared across a surface whose area is larger than the projected area perpendicular to the ray. This is often written as cos θ i {\displaystyle \cos \theta _{i}} . Two noteworthy features are: its linearity—it is composed only of multiplications and additions, and its spatial homogeneity—it is the same in all positions and orientations. These mean a wide range of factorings and rearrangements of the equation are possible. It is a Fredholm integral equation of the second kind, similar to those that arise in quantum field theory. Note this equation's spectral and time dependence — L o {\displaystyle L_{\text{o}}} may be sampled at or integrated over sections of the visible spectrum to obtain, for example, a trichromatic color sample. A pixel value for a single frame in an animation may be obtained by fixing t ; {\displaystyle t;} motion blur can be produced by averaging L o {\displaystyle L_{\text{o}}} over some given time interval (by integrating over the time interval and dividing by the length of the interval). Note that a solution to the rendering equation is the function L o {\displaystyle L_{\text{o}}} . The function L i {\displaystyle L_{\text{i}}} is related to L o {\displaystyle L_{\text{o}}} via a ray-tracing operation: The incoming radiance from some direction at one point is the outgoing radiance at some other point in the opposite direction. == Applications == Solving the rendering equation for any given scene is the primary challenge in realistic rendering. One approach to solving the equation is based on finite element methods, leading to the radiosity algorithm. Another approach using Monte Carlo methods has led to many different algorithms including path tracing, photon mapping, and Metropolis light transport, among others. == Limitations == Although the equation is very general, it does not capture every aspect of light reflection. Some missing aspects include the following: Transmission, which occurs when light is transmitted through the surface, such as when it hits a glass object or a water surface, Subsurface scattering, where the spatial locations for incoming and departing light are different. Surfaces rendered without accounting for subsurface scattering may appear unnaturally opaque — however, it is not necessary to account for this if transmission is included in the equation, since that will effectively include also light scattered under the surface, Polarization, where different light polarizations will sometimes have different reflection distributions, for example when light bounces at a water surface, Phosphorescence, which occurs when light or other electromagnetic radiation is absorbed at one moment and emitted at a later moment, usually with a longer wavelength (unless the absorbed electromagnetic radiation is very intense), Interference, where the wave properties of light are exhibited, Fluorescence, where the absorbed and emitted light have different wavelengths, Non-linear effects, where very intense light can increase the energy level of an electron with more energy than that of a single photon (this can occur if the electron is hit by two photons at the same time), and emission of light with higher frequency than the frequency of the light that hit the surface suddenly becomes possible, and Doppler effect, where light that bounces off an object moving at a very high speed will get its wavelength changed: if the light bounces off an object that is moving towards it, the light will be blueshifted and the photons will be packed more closely so the photon flux will be increased; if it bounces off an object moving away from it, it will be redshifted and the photon flux will be decreased. This effect becomes apparent only at speeds comparable to the speed of light, which is not the case for most rendering applications. For scenes that are either not composed of simple surfaces in a vacuum or for which the travel time for light is an important factor, researchers have generalized the rendering equation to produce a volume rendering equation suitable for volume rendering and a transient rendering equation for use with data from a time-of-flight camera.
Image tracing
In computer graphics, image tracing, raster-to-vector conversion or raster vectorization is the conversion of raster graphics into vector graphics. == Background == An image does not have any structure: it is just a collection of marks on paper, grains in film, or pixels in a bitmap. While such an image is useful, it has some limits. If the image is magnified enough, its artifacts appear. The halftone dots, film grains, and pixels become apparent. Images of sharp edges become fuzzy or jagged. See, for example, pixelation. Ideally, a vector image does not have the same problem. Edges and filled areas are represented as mathematical curves or gradients, and they can be magnified arbitrarily (though of course the final image must also be rasterized in to be rendered, and its quality depends on the quality of the rasterization algorithm for the given inputs). The task in vectorization is to convert a two-dimensional image into a two-dimensional vector representation of the image. It is not examining the image and attempting to recognize or extract a three-dimensional model that may be depicted; i.e. it is not a vision system. For most applications, vectorization also does not involve optical character recognition; characters are treated as lines, curves, or filled objects without attaching any significance to them. In vectorization, the shape of the character is preserved, so artistic embellishments remain. Vectorization is the inverse operation corresponding to rasterization, as integration is to differentiation. And, just as with these other operations, while rasterization is fairly straightforward and algorithmic, vectorization involves the reconstruction of lost information and therefore requires heuristic methods. Synthetic images such as maps, cartoons, logos, clip art, and technical drawings are suitable for vectorization. Those images could have been originally made as vector images because they are based on geometric shapes or drawn with simple curves. Continuous tone photographs (such as live portraits) are not good candidates for vectorization. The input to vectorization is an image, but an image may come in many forms such as a photograph, a drawing on paper, or one of several raster file formats. Programs that do raster-to-vector conversion may accept bitmap formats such as TIFF, BMP and PNG. The output is a vector file format. Common vector formats are SVG, DXF, EPS, EMF and AI. Vectorization can be used to update images or recover work. Personal computers often come with a simple paint program that produces a bitmap output file. These programs allow users to make simple illustrations by adding text, drawing outlines, and filling outlines with a specific color. Only the results of these operations (the pixels) are saved in the resulting bitmap; the drawing and filling operations are discarded. Vectorization can be used to recapture some of the information that was lost. Vectorization is also used to recover information that was originally in a vector format but has been lost or has become unavailable. A company may have commissioned a logo from a graphic arts firm. Although the graphics firm used a vector format, the client company may not have received a copy of that format. The company may then acquire a vector format by scanning and vectorizing a paper copy of the logo. == Process == Vectorization starts with an image. === Manual === The image can be vectorized manually. A person could look at the image, make some measurements, and then write the output file by hand. That was the case for the vectorization of a technical illustration about neutrinos. The illustration has a few geometric shapes and a lot of text; it was relatively easy to convert the shapes, and the SVG vector format allows the text (even subscripts and superscripts) to be entered easily. The original image did not have any curves (except for the text), so the conversion is straightforward. Curves make the conversion more complicated. Manual vectorization of complicated shapes can be facilitated by the tracing function built into some vector graphics editing programs. If the image is not yet in machine readable form, then it has to be scanned into a usable file format. Once there is a machine-readable bitmap, the image can be imported into a graphics editing program (such as Adobe Illustrator, CorelDRAW, or Inkscape). Then a person can manually trace the elements of the image using the program's editing features. Curves in the original image can be approximated with lines, arcs, and Bézier curves. An illustration program allows spline knots to be adjusted for a close fit. Manual vectorization is possible, but it can be tedious. Although graphics drawing programs have been around for a long time, artists may find the freehand drawing facilities awkward even when a drawing tablet is used. Instead of using a program, Pepper recommends making an initial sketch on paper. Instead of scanning the sketch and tracing it freehand in the computer, Pepper states: "Those proficient with a graphic tablet and stylus could make the following changes directly in CorelDRAW by using a scan of the sketch as an underlay and drawing over it. I prefer to use pen and ink, and a light table"; most of the final image was traced by hand in ink. Later the line-drawing image was scanned at 600 dpi, cleaned up in a paint program, and then automatically traced with a program. Once the black and white image was in the graphics program, some other elements were added and the figure was colored. Similarly, Ploch recreated a design from a digital photograph. The JPEG was imported and some "basic shapes" were traced by hand and colored in the graphics drawing program; more complex shapes were handled differently. Ploch used a bitmap editor to remove the background and crop the more complex image components. He then printed the image and traced it by hand onto tracing paper to get a clean black and white line drawing. That drawing was scanned and then vectorized with a program. === Automatic === Some programs automate the vectorization process. Example programs are Adobe Illustrator, Inkscape, Corel's PowerTRACE, and Potrace. Some of these programs have a command line interface while others are interactive that allow the user to adjust the conversion settings and view the result. Adobe Streamline is not only an interactive program, but it also allows a user to manually edit the input bitmap and the output curves. Corel's PowerTRACE is accessed through CorelDRAW; CorelDRAW can be used to modify the input bitmap and edit the output curves. Adobe Illustrator has a facility to trace individual curves. Automated programs can have mixed results. A program (PowerTRACE) was used to convert a PNG map to SVG. The program did a good job on the map boundaries (the most tedious task in the tracing) and the settings dropped out all the text (small objects). The text was manually re-inserted. Other conversions may not go as well. The results depend on having high-quality scans, reasonable settings, and good algorithms. Scanned images often have a lot of noise, which can require additional work to clean up. == Options == There are many different image styles and possibilities, and no single vectorization method works well on all images. Consequently, vectorization programs have many options that influence the result. One issue is what the predominant shapes are. If the image is of a fill-in form, then it will probably have just vertical and horizontal lines of a constant width. The program's vectorization should take that into account. On the other hand, a CAD drawing may have lines at any angle, there may be curved lines, and there may be several line weights (thick for objects and thin for dimension lines). Instead of (or in addition to) curves, the image may contain outlines filled with the same color. Adobe Streamline allows users to select a combination of line recognition (horizontal and vertical lines), centerline recognition, or outline recognition. Streamline also allows small outline shapes to be thrown out; the notion is such small shapes are noise. The user may set the noise level between 0 and 1000; an outline that has fewer pixels than that setting is discarded. Another issue is the number of colors in the image. Even images that were created as black on white drawings may end up with many shades of gray. Some line-drawing routines employ anti-aliasing; a pixel completely covered by the line will be black, but a pixel that is only partially covered will be gray. If the original image is on paper and is scanned, there is a similar result: edge pixels will be gray. Sometimes images are compressed (e.g., JPEG images), and the compression will introduce gray levels. Many of the vectorization programs will group same-color pixels into lines, curves, or outlined shapes. If each possible color is grouped into its object, there can be an enormous number of objects. Instead, the user is asked to s
Zero-knowledge service
In cloud computing, the term zero-knowledge (or occasionally no-knowledge or zero-access) is a commonly used term for online services that store, transfer or manipulate data with a high level of confidentiality, where the data is only accessible to the data's owner (the client), and not to the service provider. However, unlike "end-to-end encryption", the term "zero-knowledge" does not imply any specific threat model or security notion, and its use is commonly frowned-upon by the security community. The term "zero-knowledge" was popularized by backup service SpiderOak, which later switched to using the term "no knowledge", acknowledging that the previous terminology was not technically accurate. == Disadvantages == Most cloud storage services keep a copy of the client's password on their servers, allowing clients who have lost their passwords to retrieve and decrypt their data using alternative means of authentication; but since zero-knowledge services do not store copies of clients' passwords, if a client loses their password then their data cannot be decrypted, making it practically unrecoverable. Most of the most used cloud storage services, such as Google Drive, Dropbox, OneDrive or iCloud, are also able to furnish access requests from law enforcement agencies for similar reasons; zero-knowledge services, however, are unable to do so, since their systems are designed to make clients' data inaccessible without the client's explicit cooperation.
XLeratorDB
XLeratorDB is a suite of database function libraries that enable Microsoft SQL Server to perform a wide range of additional (non-native) business intelligence and ad hoc analytics. The libraries, which are embedded and run centrally on the database, include more than 450 individual functions similar to those found in Microsoft Excel spreadsheets. The individual functions are grouped and sold as six separate libraries based on usage: finance, statistics, math, engineering, unit conversions and strings. WestClinTech, the company that developed XLeratorDB, claims it is "the first commercial function package add-in for Microsoft SQL Server." == Company history == WestClinTech (LLC), founded by software industry veterans Charles Flock and Joe Stampf in 2008, is located in Irvington, New York, United States. Flock was a co-founder of The Frustum Group, developer of the OPICS enterprise banking and trading platform, which was acquired by London-based Misys, PLC in 1996. Stampf joined Frustum in 1994 and with Flock remained active with the company after acquisition, helping to develop successive generations of OPICS now employed by over 150 leading financial institutions worldwide. Following a full year of research, development and testing, WestClinTech introduced and recorded its first commercial sale of XLeratorDB in April 2009. In September 2009, XLeratorDB became available to all Federal agencies through NASA's Strategic Enterprise-Wide Procurement (SEWP-IV) program, a government-wide acquisition contract. == Technology == XLeratorDB uses Microsoft SQL CLR(Common Language Runtime) technology. SQL CLR allows managed code to be hosted by, and run in, the Microsoft SQL Server environment. SQL CLR relies on the creation, deployment and registration of .NET Framework assemblies that are physically stored in managed code dynamic-link libraries (DLL). The assemblies may contain .NET namespaces, classes, functions, and properties. Because managed code compiles to native code prior to execution, functions using SQL CLR can achieve significant performance increases versus the equivalent functions written in T-SQL in some scenarios. XLeratorDB requires Microsoft SQL Server 2005 or SQL Server 2005 Express editions, or later (compatibility mode 90 or higher). The product installs with PERMISSION_SET=SAFE. SAFE mode, the most restrictive permission set, is accessible by all users. Code executed by an assembly with SAFE permissions cannot access external system resources such as files, the network, the internet, environment variables, or the registry. == Functions == In computer science, a function is a portion of code within a larger program which performs a specific task and is relatively independent of the remaining code. As used in database and spreadsheet applications these functions generally represent mathematical formulas widely used across a variety of fields. While this code may be user-generated, it is also embedded as a pre-written sub-routine in applications. These functions are typically identified by common nomenclature which corresponds to their underlying operations: e.g. IRR identifies the function which calculates Internal Rate of Return on a series of periodic cash flows. === Function uses === As subroutines, functions can be integrated and used in a variety of ways, and as part of larger, more complicated applications. Within large enterprise applications they may, for example, play an important role in defining business rules or risk management parameters, while remaining virtually invisible to end users. Within database management systems and spreadsheets, however, these kinds of functions also represent discrete sets of tools; they can be accessed directly and utilized on a stand-alone basis, or in more complex, user-defined configurations. In this context, functions can be used for business intelligence and ad hoc analysis of data in fields such as finance, statistics, engineering, math, etc. === Function types === XLeratorDB uses three kinds of functions to perform analytic operations: scalar, aggregate, and a hybrid form which WestClinTech calls Range Queries. Scalar functions take a single value, perform an operation and return a single value. An example of this type of function is LOG, which returns the logarithm of a number to a specified base. Aggregate functions operate on a series of values but return a single, summarizing value. An example of this type of function is AVG, which returns the average of values in a specified group. In XLeratorDB there are some functions which have characteristics of aggregate functions (operating on multiple series of values) but cannot be processed in SQL CLR using single column inputs, such as AVG does. For example, irregular internal rate of return (XIRR), a financial function, operates on a collection of cash flow values from one column, but must also apply variable period lengths from another column and an initial iterative assumption from a third, in order to return a single, summarizing value. WestClinTech documentation notes that Range Queries specify the data to be included in the result set of the function independently of the WHERE clause associated with the T-SQL statement, by incorporating a SELECT statement into the function as a string argument; the function then traps that SELECT statement, executes it internally and processes the result. Some XLeratorDB functions that employ Range Queries are: NPV, XNPV, IRR, XIRR, MIRR, MULTINOMIAL, and SERIESSUM. Within the application these functions are identified by a "_q" naming convention: e.g. NPV_q, IRR_q, etc. == Analytic functions == === SQL Server functions === Microsoft SQL Server is the #3 selling database management system (DBMS), behind Oracle and IBM. (While versions of SQL Server have been on the market since 1987, XLeratorDB is compatible with only the 2005 edition and later.) Like all major DBMS, SQL Server performs a variety of data mining operations by returning or arraying data in different views (also known as drill-down). In addition, SQL Server uses Transact-SQL (T-SQL) to execute four major classes of pre-defined functions in native mode. Functions operating on the DBMS offer several advantages over client layer applications like Excel: they utilize the most up-to-date data available; they can process far larger quantities of data; and, the data is not subject to exporting and transcription errors. SQL Server 2008 includes a total of 58 functions that perform relatively basic aggregation (12), math (23) and string manipulation (23) operations useful for analytics; it includes no native functions that perform more complex operations directly related to finance, statistics or engineering. === Excel functions === Microsoft Excel, a component of Microsoft Office suite, is one of the most widely used spreadsheet applications on the market today. In addition to its inherent utility as a stand-alone desktop application, Excel overlaps and complements the functionality of DBMS in several ways: storing and arraying data in rows and columns; performing certain basic tasks such as pivot table and aggregating values; and facilitating sharing, importing and exporting of database data. Excel's chief limitation relative to a true database is capacity; Excel 2003 is limited to some 65k rows and 256 columns; Excel 2007 extends this capacity to roughly 1million rows and 16k columns. By comparison, SQL Server is able to manage over 500k terabytes of memory. Excel offers, however, an extensive library of specialized pre-written functions which are useful for performing ad hoc analysis on database data. Excel 2007 includes over 300 of these pre-defined functions, although customized functions can also be created by users, or imported from third party developers as add-ons. Excel functions are grouped by type: === Excel business intelligence functions === Operating on the client computing layer Excel plays an important role as a business intelligence tool because it: performs a wide array of complex analytic functions not native to most DBMS software offers far greater ad hoc reporting and analytic flexibility than most enterprise software provides a medium for sharing and collaborating because of its ubiquity throughout the enterprise Microsoft reinforces this positioning with Business Intelligence documentation that positions Excel in a clearly pivotal role. === XLeratorDB vs. Excel functions === While operating within the database environment, XLeratorDB functions utilize the same naming conventions and input formats, and in most cases, return the same calculation results as Excel functions. XLeratorDB, coupled with SQL Server's native capabilities, compares to Excel's function sets as follows:
Deductive language
A deductive language is a computer programming language in which the program is a collection of predicates ('facts') and rules that connect them. Such a language is used to create knowledge based systems or expert systems which can deduce answers to problem sets by applying the rules to the facts they have been given. An example of a deductive language is Prolog, or its database-query cousin, Datalog. == History == As the name implies, deductive languages are rooted in the principles of deductive reasoning; making inferences based upon current knowledge. The first recommendation to use a clausal form of logic for representing computer programs was made by Cordell Green (1969) at Stanford Research Institute (now SRI International). This idea can also be linked back to the battle between procedural and declarative information representation in early artificial intelligence systems. Deductive languages and their use in logic programming can also be dated to the same year when Foster and Elcock introduced Absys, the first deductive/logical programming language. Shortly after, the first Prolog system was introduced in 1972 by Colmerauer through collaboration with Robert Kowalski. == Components == The components of a deductive language are a system of formal logic and a knowledge base upon which the logic is applied. === Formal Logic === Formal logic is the study of inference in regards to formal content. The distinguishing feature between formal and informal logic is that in the former case, the logical rule applied to the content is not specific to a situation. The laws hold regardless of a change in context. Although first-order logic is described in the example below to demonstrate the uses of a deductive language, no formal system is mandated and the use of a specific system is defined within the language rules or grammar. As input, a predicate takes any object(s) in the domain of interest and outputs either one of two Boolean values: true or false. For example, consider the sentences "Barack Obama is the 44th president" and "If it rains today, I will bring an umbrella". The first is a statement with an associated truth value. The second is a conditional statement relying on the value of some other statement. Either of these sentences can be broken down into predicates which can be compared and form the knowledge base of a deductive language. Moreover, variables such as 'Barack Obama' or 'president' can be quantified over. For example, take 'Barack Obama' as variable 'x'. In the sentence "There exists an 'x' such that if 'x' is the president, then 'x' is the commander in chief." This is an example of the existential quantifier in first order logic. Take 'president' to be the variable 'y'. In the sentence "For every 'y', 'y' is the leader of their nation." This is an example of the universal quantifier. === Knowledge Base === A collection of 'facts' or predicates and variables form the knowledge base of a deductive language. Depending on the language, the order of declaration of these predicates within the knowledge base may or may not influence the result of applying logical rules. Upon application of certain 'rules' or inferences, new predicates may be added to a knowledge base. As new facts are established or added, they form the basis for new inferences. As the core of early expert systems, artificial intelligence systems which can make decisions like an expert human, knowledge bases provided more information than databases. They contained structured data, with classes, subclasses, and instances. == Prolog == Prolog is an example of a deductive, declarative language that applies first- order logic to a knowledge base. To run a program in Prolog, a query is posed and based upon the inference engine and the specific facts in the knowledge base, a result is returned. The result can be anything appropriate from a new relation or predicate, to a literal such as a Boolean (true/false), depending on the engine and type system.