Stencil buffer

A stencil buffer is an extra data buffer, in addition to the color buffer and Z-buffer, found on modern graphics hardware. The buffer is per pixel and works on integer values, usually with a depth of one byte per pixel. The Z-buffer and stencil buffer often share the same area in the RAM of the graphics hardware. In the simplest case, the stencil buffer is used to limit the area of rendering (stenciling). More advanced usage of the stencil buffer makes use of the strong connection between the Z-buffer and the stencil buffer in the rendering pipeline. For example, stencil values can be automatically increased/decreased for every pixel that fails or passes the depth test. The simple combination of depth test and stencil modifiers make a vast number of effects possible (such as stencil shadow volumes, Two-Sided Stencil, compositing, decaling, dissolves, fades, swipes, silhouettes, outline drawing, or highlighting of intersections between complex primitives) though they often require several rendering passes and, therefore, can put a heavy load on the graphics hardware. The most typical application is still to add shadows to 3D applications. It is also used for planar reflections. Other rendering techniques, such as portal rendering, use the stencil buffer in other ways; for example, it can be used to find the area of the screen obscured by a portal and re-render those pixels correctly. The stencil buffer and its modifiers can be accessed in computer graphics by using APIs like OpenGL, Direct3D, Vulkan or Metal. == Architecture == The stencil buffer typically shares the same memory space as the Z-buffer, and typically the ratio is 24 bits for Z-buffer + 8 bits for stencil buffer or, in the past, 15 bits for Z-buffer + 1 bit for stencil buffer. Another variant is 4 + 24, where 28 of the 32 bits are used and 4 ignored. Stencil and Z-buffers are part of the frame buffer, coupled to the color buffer. The first chip available to a wider market was 3Dlabs' Permedia II, which supported a one-bit stencil buffer. The bits allocated to the stencil buffer can be used to represent numerical values in the range [0, 2n-1], and also as a Boolean matrix (n is the number of allocated bits), each of which may be used to control the particular part of the scene. Any combination of these two ways of using the available memory is also possible. == Stencil test == Stencil test or stenciling is among the operations on the pixels/fragments (Per-pixel operations), located after the alpha test, and before the depth test. The stencil test ensures undesired pixels do not reach the depth test. This saves processing time for the scene. Similarly, the alpha test can prevent corresponding pixels to reach the stencil test. The test itself is carried out over the stencil buffer to some value in it, or altered or used it, and carried out through the so-called stencil function and stencil operations. The stencil function is a function by which the stencil value of a certain pixel is compared to a given reference value. If this comparison is logically true, the stencil test passes. Otherwise not. In doing so, the possible reaction caused by the result of comparing three different state-depth and stencil buffer: Stencil test is not passed Stencil test is passed but not the depth test Both tests are passed (or stencil test is passed, and the depth is not enabled) For each of these cases, different operations can be set over the examined pixel. In the OpenGL stencil functions, the reference value and mask, respectively, define the function glStencilFunc. In Direct3D each of these components is adjusted individually using methods SetRenderState devices currently in control. This method expects two parameters, the first of which is a condition that is set and the other its value. In the order that was used above, these conditions are called D3DRS_STENCILFUNC, D3DRS_STENCILREF, and D3DRS_STENCILMASK. Stencil operations in OpenGL adjust glStencilOp function that expects three values. In Direct3D, again, each state sets a specific method SetRenderState. The three states that can be assigned to surgery are called D3DRS_STENCILFAIL, D3DRENDERSTATE_STENCILZFAIL, and D3DRENDERSTATE_STENCILPASS. == Z-fighting == Due to the lack of precision in the Z-buffer, coplanar polygons that are short-range, or overlapping, can be portrayed as a single plane with a multitude of irregular cross-sections. These sections can vary depending on the camera position and other parameters and are rapidly changing. This is called Z-fighting. There exist multiple solutions to this issue: - Bring the far plane closer to restrict the scene's depth, thus increasing the accuracy of the Z-buffer, or reducing the distance at which objects are visible in the scene. - Increase the number of bits allocated to the Z-buffer, which is possible at the expense of memory for the stencil buffer. - Move polygons farther apart from one another, which restricts the possibilities for the artist to create an elaborate scene. All of these approaches to the problem can only reduce the likelihood that the polygons will experience Z-fighting, and do not guarantee a definitive solution in the general case. A solution that includes the stencil buffer is based on the knowledge of which polygon should be in front of the others. The silhouette of the front polygon is drawn into the stencil buffer. After that, the rest of the scene can be rendered only where the silhouette is negative, and so will not clash with the front polygon. == Shadow volume == Shadow volume is a technique used in 3D computer graphics to add shadows to a rendered scene. They were first proposed by Frank Crow in 1977 as the geometry describing the 3D shape of the region occluded from a light source. A shadow volume divides the virtual world in two: areas that are in shadow and areas that are not. The stencil buffer implementation of shadow volumes is generally considered among the most practical general-purpose real-time shadowing techniques for use on modern 3D graphics hardware. It has been popularised by the video game Doom 3, and a particular variation of the technique used in this game has become known as Carmack's Reverse. == Reflections == Reflection of a scene is drawn as the scene itself transformed and reflected relative to the "mirror" plane, which requires multiple render passes and using of stencil buffer to restrict areas where the current render pass works: Draw the scene excluding mirror areas – for each mirror lock the Z-buffer and color buffer Render visible part of the mirror Depth test is set up so that each pixel is passed to enter the maximum value and always passes for each mirror: Depth test is set so that it passes only if the distance of a pixel is less than the current (default behavior) The matrix transformation is changed to reflect the scene relative to the mirror plane Unlock the Z-buffer and color buffer Draw the scene, but only the part of it that lies between the mirror plane and the camera. In other words, a mirror plane is also a clipping plane Again locks color buffer, depth test is set so that it always passes, reset stencil for the next mirror. == Planar Shadows == While drawing a plane of shadows, there are two dominant problems: The first concerns the problem of deep struggle in case the flat geometry is not awarded on the part covered with the shadow of shadows and outside. See the section that relates to this. Another problem relates to the extent of the shadows outside the area where the plane there. Another problem, which may or may not appear, depending on the technique, the design of more polygons in one part of the shadow, resulting in darker and lighter parts of the same shade. All three problems can be solved geometrically, but because of the possibility that hardware acceleration is directly used, it is a far more elegant implementation using the stencil buffer: 1. Enable lights and the lights 2. Draw a scene without any polygon that should be projected shadows 3. Draw all polygons which should be projected shadows, but without lights. In doing so, the stencil buffer, the pixel of each polygon to be assigned to a specific value for the ground to which they belong. The distance between these values should be at least two, because for each plane to be used two values for two states: in the shadows and bright. 4. Disable any global illumination (to ensure that the next steps will affect only individual selected light) For each plane: For each light: 1. Edit a stencil buffer and only the pixels that carry a specific value for the selected level. Increase the value of all the pixels that are projected objects between the date of a given level and bright. 2. Allow only selected light for him to draw level at which part of her specific value was not changed. == Spatial shadows == Stencil buffer implementation of spatial drawing shadows is any shadow of a geometric body that its volume includes part of the scene that is

PowerBuilder

PowerBuilder is an integrated development environment owned by SAP since the acquisition of Sybase in 2010. On July 5, 2016, SAP and Appeon entered into an agreement whereby Appeon, an independent company, would be responsible for developing, selling, and supporting PowerBuilder. Over the years, PowerBuilder has been updated with new standards. In 2010, a major upgrade of PowerBuilder was released to provide support for the Microsoft .NET Framework. In 2014, support was added for OData, dockable windows, and 64-bit native applications. In 2019 support was added for rapidly creating RESTful Web APIs and non-visual .NET assemblies using the C# language and the .NET Core framework. And PowerScript client app development was revamped with new UI technologies and cloud architecture. In 2025 the IDE was revamped with new code editor and ultra-fast compiler. Appeon has been releasing new features every 6-12 month cycles, which per the product roadmap focus on four key focus areas: sustaining core features, modernizing application UI, improving developer productivity, and incorporating more Cloud technology. == Features == PowerBuilder has a native data-handling component called a DataWindow, which can be used to create, edit, and display data from a database. This object gives the programmer a number of tools for specifying and controlling user interface appearance and behavior, and also provides simplified access to database content and JSON or XML from Web services. To some extent, the DataWindow frees the programmer from considering the differences between Database Management Systems from different vendors. DataWindow can display data using multiple presentation styles and can connect to various data sources. == Usage == PowerBuilder is used primarily for building business-oriented CRUD applications. Although new software products are rarely built with PowerBuilder, many client-server ERP products and line-of-business applications built in the late 1980s to early 2000s with PowerBuilder still provide core database functions for large enterprises in government, higher education, manufacturing, insurance, banking, energy, and telecommunications. == History == === Early history === PowerBuilder originated from Computer Solutions Inc. (CSI), a software consulting firm founded in 1974 by Mitchell Kertzman in Massachusetts. CSI developed GrowthPower, an MRP II software package with integrated financial modules released in 1981, which ran exclusively on the HP 3000 platform and achieved over 1,000 customer installations at its peak. In the late 1980s, as demand increased for graphical user interfaces amid the rise of Microsoft Windows, Kertzman partnered with Dave Litwack, former executive vice president of product development at Cullinet Software (acquired by Computer Associates in 1989). Litwack joined the company in 1988 as head of research and development to develop a client/server GUI tool, leading to its rebranding as Powersoft Corporation in 1990. PowerBuilder 1.0 was released in July 1991 as a rapid application development tool featuring the DataWindow and PowerScript language. Powersoft went public on February 3, 1993, with shares closing at $38 from an initial $20 price. Sybase announced its acquisition of Powersoft on November 15, 1994, in a stock swap valued at approximately $940 million; the merger closed on February 14, 1995, at a revised value of about $904 million due to Sybase's stock fluctuations. === Recent history === In December 2013 SAP announced the new version going directly to number 15 and released a beta version. Key features included support for the .NET Framework v4.5, SQL Server 2012, Oracle 12, Windows 8, OData and Dockable Windows. SAP later released this as version 12.6. On May 31, 2019, PowerBuilder 2019 was released by Appeon. This release supports C# development. It provides a new C# IDE, .NET data access objects, C# migration solution, Web API client, and UI themes. On April 3, 2020, PowerBuilder 2019 R2 was launched by Appeon. This release includes a first-ever PowerScript-to-C# code converter, which can automatically migrate 80-95% of PowerBuilder business logic and DataWindows to C#. Interoperability between PowerScript and .NET programming languages is also now supported. Many existing features have also been enhanced. On January 22, 2021, PowerBuilder 2019 R3 was launched by Appeon. This release provides a groundbreaking new app deployment technology called PowerClient, which securely automates the installation and update of client apps over HTTPS. C# Web API development has been greatly enhanced with asynchronous programming and support for Amazon Aurora and Azure cloud databases. Aside from many other new features, PowerBuilder 2019 R3 is a long-term support (LTS) version that replaces previous LTS versions On August 6, 2021, PowerBuilder 2021 was launched by Appeon. The Cloud deployment capability of the PowerBuilder 2021 IDE, in conjunction with the matching PowerServer 2021 runtime, was revamped, bringing PowerBuilder up-to-date with the latest .NET technologies. The presentation layer now executes PowerScript natively on Windows devices. The middle-tier has been rebuilt around REST API standard with a pure .NET Core implementation. A new CI/CD utility that integrates with Git/SVN and Jenkins, witch compiles all PowerBuilder projects using the command-line interface, was added alongside other features. On September 4, 2022, PowerBuilder 2022 was launched by Appeon. This release brings enhancements to the productivity of developing both client/server & installable cloud apps and more security measures to safeguard your apps. It includes many new features, including Windows 11 support, introducing time-saving functionalities to the IDE, such as Tabbed Code Editor, Jump to Objects, and Quick Code Search, and supports the latest HTTP/2 and TLS 1.3 protocols and two-way TLS authentication. On August 4, 2023, PowerBuilder 2022 R2 was launched by Appeon. This release introduces a range of new features aimed at helping developers build powerful, feature-rich, and secure client/server and installable cloud apps more efficiently, including tabbed windows, fillable PDFs, and SMTP client. On January 8, 2024, PowerBuilder 2022 R3 was launched by Appeon. This release is a long-term support version. Features previously released in earlier releases have been enhanced and/or corrected. On May 7, 2025, PowerBuilder 2025 was launched by Appeon. This release delivers a revamped IDE that boosts developer productivity throughout the SLDC—from writing and extending code to debugging, automating builds, and deploying applications. It features a new-generation code editor, ultra-fast compiler, automatic REST API creation, faster GIT operations, and codeless UI modernization features. == Features == PowerBuilder is an object-oriented programming language. Nearly all of the visual and non-visual objects support inheritance, polymorphism, and encapsulation. The programmer may utilize a common code framework such as PowerBuilder Foundation Classes, also known as PFC, to inherit objects from and leverage pre-existing code. The DataWindow is the key component (and selling point) of PowerBuilder. The DataWindow offers a visual SQL painter which supports outer joins, unions and subquery operations. It can convert SQL to visual representation and back, so the developer can use native SQL if desired. DataWindow updates are automatic — it produces the proper SQL at runtime based on the DBMS to which the user is currently connected. This feature makes it easier for developers who are not experienced with SQL. The DataWindow also has the built-in ability to both retrieve data and update data via stored procedures or REST Web APIs as well as import/export JSON data. The RESTClient object introduced in PowerBuilder 2017 facilitates bridging the DataWindow with REST Web APIs and requiring minimal coding. === RDBMS interfaces === PowerBuilder offers native interfaces to all major databases, as well as ODBC and OLE-DB, in the Enterprise version. There are many connectivity options that allow performance monitoring and tuning, such as: Integrated security Tracing of all SQL Isolation level Password expiration dialog Blocking factor Number of SQL statements to cache Use connection pool Thread safety Trace ODBC API calls Due to the information about the database schema (such as primary key information) that are stored in PowerBuilder's data dictionary, the code required to implement data display and browsing is greatly simplified, because the dictionary information allows generation of the appropriate SQL behind the scenes. PowerBuilder supports the following ways of interacting with a database: DataWindow this is the simplest approach, relying on automatically generated SQL. Embedded SQL Embedded SQL supports SELECT, INSERT, UPDATE, DELETE and cursors. This option is used when the developer desires more control than is available with the

Trust federation

A trust federation is part of the evolving Identity Metasystem that will bring a new layer of persistent identity and trusted data sharing to the Internet. Although the concept of trust federations is technology neutral, several protocols like SAML, OpenID, Information Card, XDI can handle the challenges of technical interoperability. The challenge of business and social interoperability requires a new type of cooperative association similar to a credit card association. Instead of banks, however, a trust federation is an alliance of i-brokers and their customers who agree to abide by a common set of agreements in the care and handling of customer data. A model for trust federations is offered by Open Identity Exchange and Kantara Initiative, which is applied in the U.S. Government ICAM Trust Framework. Some operational trust federations are: InCommon (academic, USA) REFEDs (Research and Education Federations, Europe) IGTF Interoperable Global Trust Federation Portalverbund Government Portal Federation, Austria Trust federations are not limited to the social web use case, but apply to all federations where trust in identity and compliance to other objectives of information security such as confidentiality, integrity and privacy is brokered.

Conditional disclosure of secrets

Conditional disclosure of secrets (CDS) is a primitive, studied in information-theoretic cryptography, that allows distributed, non-communicating parties to coordinate the release of information to a third party. CDS was initially introduced for use in the context of private information retrieval, and has been related to communication complexity and non-local quantum computation. == Definition of conditional disclosure of secrets == The conditional disclosure of secrets setting involves three players; Alice, Bob and the referee. Alice receives an input x ∈ { 0 , 1 } n {\displaystyle x\in \{0,1\}^{n}} and a secret z ∈ { 0 , 1 } {\displaystyle z\in \{0,1\}} , and Bob receives a string y ∈ { 0 , 1 } n {\displaystyle y\in \{0,1\}^{n}} . A choice of Boolean function f : { 0 , 1 } 2 n → { 0 , 1 } {\displaystyle f:\{0,1\}^{2n}\rightarrow \{0,1\}} is fixed in advance and known to all players. Alice and Bob cannot communicate with one another, but share a string of random bits which we label r {\displaystyle r} . Alice and Bob compute messages m A = m A ( x , z , r ) {\displaystyle m_{A}=m_{A}(x,z,r)} and m B = m B ( y , r ) {\displaystyle m_{B}=m_{B}(y,r)} , which they send to the referee. The referee knows ( x , y ) {\displaystyle (x,y)} . A CDS protocol consists of the encoding maps applied by Alice and Bob. A protocol is said to be ϵ {\displaystyle \epsilon } -correct if, for all ( x , y ) ∈ f − 1 ( 1 ) {\displaystyle (x,y)\in f^{-1}(1)} , the referee can determine z {\displaystyle z} with probability 1 − ϵ {\displaystyle 1-\epsilon } . A protocol is said to be δ {\displaystyle \delta } -secure if, for all ( x , y ) ∈ f − 1 ( 0 ) {\displaystyle (x,y)\in f^{-1}(0)} the distribution of the messages is δ {\displaystyle \delta } close to a simulator distribution (in total variation distance), where the simulator distribution is independent of z {\displaystyle z} . The communication complexity of a CDS protocol P is the total number of bits of message sent by Alice and Bob. The CDS communication cost of a function, C D S ϵ , δ ( f ) {\displaystyle CDS_{\epsilon ,\delta }(f)} is the minimal communication cost of an ϵ {\displaystyle \epsilon } -correct, δ {\displaystyle \delta } secure protocol that implements f {\displaystyle f} . The randomness complexity and randomness cost of implementing a function in the CDS model are defined similarly, but consider the number of bits of shared random bits held by Alice and Bob. == Basic properties of the primitive == === Amplification === Supposing we have an ϵ {\displaystyle \epsilon } -correct and δ {\displaystyle \delta } -secure CDS protocol, it is known that we can find a new protocol which reduces the correctness and privacy errors at the expense of an increased communication and randomness cost. More specifically, the following theorem has been proven Theorem (Amplification). A CDS protocol for f which supports a single-bit secret with privacy and correctness error of 1/3 can be transformed into a new CDS protocol with privacy and correctness error of 2 − Ω ( k ) {\displaystyle 2^{-\Omega (k)}} and communication/randomness complexity which are larger than those of the original protocol by a multiplicative factor of O(k). In fact, somewhat more than the above theorem is true in that the size of the secret can also be made to be of length k {\displaystyle k} , while simultaneously reducing the correctness and privacy errors as above. The proof involves first encoding the secret z {\displaystyle z} into a secret sharing scheme, and then running the original CDS protocol on each share of the resulting scheme. === Closure === If a CDS protocol for a function f {\displaystyle f} is known, then certain simple modifications of f {\displaystyle f} have CDS protocols with similar efficiency. The simplest case is to consider a CDS protocol for function f {\displaystyle f} and ask for a similarly efficient protocol for the negation of f {\displaystyle f} , labelled ¬ f {\displaystyle \neg f} . This is addressed by the following theorem Theorem (CDS is closed under complement). Suppose that f has a CDS protocol with randomness cost of ρ {\displaystyle \rho } bits, communication complexity of t {\displaystyle t} bits, and privacy and correctness errors δ = ϵ = 2 − k {\displaystyle \delta =\epsilon =2^{-k}} . Then ¬ f {\displaystyle \neg f} has a CDS scheme with similar privacy and correctness errors, and randomness and communication complexity of O ( k 3 ρ 2 t + k 3 ρ 3 ) {\displaystyle O(k^{3}\rho ^{2}t+k^{3}\rho ^{3})} . The cost of a CDS protocol is also closed under formula's, in the following sense. Consider two functions f 1 {\displaystyle f_{1}} and f 2 {\displaystyle f_{2}} . Then, the communication and randomness costs of f 1 ∧ f 2 {\displaystyle f_{1}\wedge f_{2}} as well as f 1 ∨ f 2 {\displaystyle f_{1}\vee f_{2}} are not much larger than the sum of the costs for f 1 {\displaystyle f_{1}} and f 2 {\displaystyle f_{2}} . See Applebaum et al. for a precise statement. == Upper and lower bounds on communication cost == Given a function f {\displaystyle f} we would like to understand the communication and randomness costs to implement f {\displaystyle f} in the CDS setting. Towards understanding this, protocols for implementing CDS have been developed (which give an upper bound on the cost) and lower bound strategies have been developed. For most functions, there is a large gap between the known upper and lower bound, so understanding the cost of CDS remains largely an open problem. This section presents some of what is known so far about the cost of CDS. === Secret sharing based upper bound === A subject with a close relationship to CDS is secret sharing. Secret sharing constructions provide an upper bound on the cost of CDS protocols. A secret sharing scheme encodes a secret, s {\displaystyle s} into a set of shares S 1 , . . . , S n {\displaystyle S_{1},...,S_{n}} . Associated to any secret sharing scheme is an access structure, which consists of a set of authorized sets A = A 1 , . . . , A k {\displaystyle {\mathcal {A}}={A_{1},...,A_{k}}} with A i ⊆ { S 1 , . . . , S n } {\displaystyle A_{i}\subseteq \{S_{1},...,S_{n}\}} . The authorized sets are those subsets of the A i {\displaystyle A_{i}} from which it is possible to recover the secret recorded into the scheme. A succinct way to describe an access structure is in terms of a function f A : { 0 , 1 } n → { 0 , 1 } {\displaystyle f_{\mathcal {A}}:\{0,1\}^{n}\rightarrow \{0,1\}} . Each subset of the shares K [ x ] ⊂ { S 1 , . . . , S n } {\displaystyle K[x]\subset \{S_{1},...,S_{n}\}} is labelled by a string x ∈ { 0 , 1 } n {\displaystyle x\in \{0,1\}^{n}} such that x i = 1 {\displaystyle x_{i}=1} if and only if S i ∈ K {\displaystyle S_{i}\in K} . Then we define f A {\displaystyle f_{\mathcal {A}}} to be such that f A ( x ) = 1 {\displaystyle f_{\mathcal {A}}(x)=1} if and only if K [ x ] ∈ A {\displaystyle K[x]\in {\mathcal {A}}} . In words, the function f A {\displaystyle f_{\mathcal {A}}} is 1 when given an authorized subset as input, and 0 otherwise. A basic result in the theory of secret sharing is that an access structure A {\displaystyle {\mathcal {A}}} can be realized in a secret sharing scheme if and only if f A {\displaystyle f_{\mathcal {A}}} is monotone. The size of a secret sharing scheme is defined as the total number of bits in the shares S i {\displaystyle S_{i}} . For monotone functions, there is an upper bound on the communication cost in CDS for any monotone function f {\displaystyle f} in terms of the size of any secret sharing scheme with access structure given by f {\displaystyle f} , C D S ϵ = 0 , δ = 0 ( f ) ≤ S h a r i n g S i z e ( f ) {\displaystyle CDS_{\epsilon =0,\delta =0}(f)\leq SharingSize(f)} For some concrete classes of secret sharing schemes, this relationship can be extended to general (non-monotone) Boolean functions. This leads to an upper bound on CDS cost in terms of the size of any span program that computes f {\displaystyle f} , C D S ϵ = 0 , δ = 0 ( f ) ≤ S P k ( f ) {\displaystyle CDS_{\epsilon =0,\delta =0}(f)\leq SP_{k}(f)} The class of problems with efficient (polynomial size) span program is the complexity class M o d k L {\displaystyle Mod_{k}L} , so problems in this class have efficient CDS protocols. === Sub-exponential upper bounds for all functions === Using a matching vector family based construction, it has been proven that ∀ f , C D S ϵ = 0 , δ = 0 ( f ) ≤ 2 O ( n log ⁡ n ) {\displaystyle \forall f,\,\,\,\,\,\,CDS_{\epsilon =0,\delta =0}(f)\leq 2^{O({\sqrt {n\log n}})}} . The technique for this proof is similar to one used to prove upper bounds on private information retrieval. This upper bound on CDS also leads to sub-exponential upper bounds on the size of a large class of secret sharing schemes. === Lower bounds from communication complexity === In a CDS protocol, the referee is given the inputs ( x , y ) {\displaystyle (x,y)} . This means it is not clear if the messages sent by Alice a

Social media and psychology

Social media began in the form of generalized online communities. These online communities formed on websites like Geocities.com in 1994, Theglobe.com in 1995, and Tripod.com in 1995. Many of these early communities focused on social interaction by bringing people together through the use of chat rooms. The chat rooms encouraged users to share personal information, ideas, or even personal web pages. Later the social networking community Classmates took a different approach by simply having people link to each other by using their personal email addresses. By the late 1990s, social networking websites began to develop more advanced features to help users find and manage friends. These newer generation of social networking websites began to flourish with the emergence of SixDegrees.com in 1997, Makeoutclub in 2000, Hub Culture in 2002, and Friendster in 2002. However, the first profitable mass social networking website was the South Korean service, Cyworld. Cyworld initially launched as a blog-based website in 1999 and social networking features were added to the website in 2001. Other social networking websites emerged like Myspace in 2002, LinkedIn in 2003, and Bebo in 2005. In 2009, the social networking website Facebook (launched in 2004) became the largest social networking website in the world. Both Instagram and Kik were launched in October 2010. Active users of Facebook increased from just a million in 2004 to over 750 million by the year 2011. Making internet-based social networking both a cultural and financial phenomenon. In September 2011, Snapchat was launched and reported over 300 million users in 2021. == Psychology of social networking == A social network is a social structure made up of individuals or organizations who communicate and interact with each other. Social networking sites – such as Facebook, Twitter, Instagram, Pinterest and LinkedIn – are defined as technology-enabled tools that assist users with creating and maintaining their relationships. A study found that middle schoolers reported using social media to see what their friends are doing, to post pictures, and to connect with friends. Human behavior related to social networking is influenced by major individual differences, meaning that people differ quite systematically in the quantity and quality of their social relationships. Two of the main personality traits that are responsible for this variability are the traits of extraversion and introversion. Extraversion refers to the tendency to be socially dominant, exert leadership, and influence on others. In contrast, introversion reflects a tendency towards shyness, social phobia, or even avoid social situations altogether, which could potentially reduce the number of social contacts a person may have. These individual differences may result in different social networking outcomes. Other psychology factors related to social media and Media psychology are depression, anxiety, attachment, self-identity, well-being, and the need to belong. === Neuroscience === The three domains that neural systems rely on to be strengthened to support social media use are social cognition, self-referential cognition, and social rewarding. When someone posts something on social media, they think of how their audience will react, while the audience thinks of the motivations behind posting the information. Both parties are analyzing the other's thoughts and feelings, which coherently rely on multiple network systems of the brain including the dorsomedial prefrontal cortex, bilateral temporoparietal junction, anterior temporal lobes, inferior frontal gyri, and posterior cingulate cortex. All of these systems work to help us process social behaviors and thoughts drawn out on social media. Social media requires a great deal of self-referential thought. People use social media as a platform to express their opinions and show off their past and present selves. In other words, as Bailey Parnell said in her Ted Talk, we're showing off our "highlight reel" (4). When one receives feedback from others, the individual obtains more reflected self-appraisal which leads to comparisons of their social behaviors or "highlights" to other users. Self-referential thought involves activity in the medial prefrontal cortex and the posterior cingulate cortex. The brain uses these systems when thinking of oneself. A 2021 umbrella review found that most associations between adolescent social media use and mental health were characterized as weak or inconsistent, though certain studies identified 'substantial' negative impacts, particularly linked to passive consumption and problematic use. Social media also provides a constant supply of rewards that keeps users coming back for more. Whenever users receive a like or a new follower, it activates the brain's social reward system which includes the ventromedial prefrontal cortex, ventral striatum, and ventral tegmental area. This system has been found to activate in response to positive feedback from peers, suggesting that users experience online acceptance in a similar manner to other material rewards or positive experiences, further acting as a potential reward. While these areas of the brain become strengthened, other parts of the brain start to weaken. Technology is encouraging multi-tasking, especially because of how easy it is to switch from one task to another by opening another tab or using two devices at once. The brain's hippocampus is mainly associated with long-term memory. In a study done by Russell Poldark, a professor at UCLA, they found that "for the task learned without distraction, the hippocampus was involved. However, for the task learned with the distraction of the beeps, the hippocampus was not involved; but the striatum was, which is the brain system that underlies our ability to learn new skills." The study concludes that multitasking can cause reliance on the striatum more than the hippocampus, which can change the way we learn. The striatum is known to be connected to mainly the brain's reward system. The brain will strengthen the neurons to the striatum while it weakens the neurons to the hippocampus to make the brain more efficient. Because our brain starts to rely on the striatum more than the hippocampus, it becomes harder for us to process new information. Nicholas Carr, author of The Shallows: How The Internet Is Changing Our Brains, agrees: "What psychologists and brain scientists tell us about interruptions is that they have a fairly profound effect on the way we think. It becomes much harder to sustain attention, to think about one thing for a long period of time, and to think deeply when new stimuli are pouring at you all day long. I argue that the price we pay for being constantly inundated with information is a loss of our ability to be contemplative and to engage in the kind of deep thinking that requires you to concentrate on one thing." === Well-Being === How does well-being relate to social media? In an article titled Social Impact of Psychological Research on Well-Being Shared in Social Media, Pulido et al. found a 15.7% social impact in their results. These new results were compared to a previous study conducted by Pulido et al., which had a high of 4.98% compared to 27.5% in the new study. These results show the ESISM, which is evidence of social impact present. In a two-year span, the difference between social impact rose 22.52% according to these studies. When taking into consideration that an increasingly large number of teens report either being active on, or having used, some form of social media, ranging from apps such as Facebook to TikTok, researching the effects of social media on the well-being of teens and young adults has become more of a topic of focus in recent years. === Depression === Especially in today's society, social media has gained a new perspective on younger generations. It is what younger generations are born into and are growing up to use, particularly what is running today's society. Social Media has its downfalls regarding depression and mental health. Many users often compare their lives regarding what they see on these platforms. In an article Does Social Media Cause Depression? by the Child Mind Institute, Miller states that "several studies, teenage and young adult users who spend the most time on Instagram, Facebook and other platforms for have shown to have substantially (from 13 to 66 percent) higher rates of reported depression than those who spent the least time", what the study shows how Facebook and Instagram, platforms showcasing daily lives and or lifestyles, or less fulfilling or less satisfied or more flaunting base or superficial. Instead of social community, there has become a perception of individuals striving for a life that is not real, whether that is editing photos or making life seem perfect when it is not. This causes a sense of depression by the weight of a comparing game. In "How Social Media Affects Y

Sample complexity

The sample complexity of a machine learning algorithm represents the number of training-samples that it needs in order to successfully learn a target function. More precisely, the sample complexity is the number of training-samples that we need to supply to the algorithm, so that the function returned by the algorithm is within an arbitrarily small error of the best possible function, with probability arbitrarily close to 1. There are two variants of sample complexity: The weak variant fixes a particular input-output distribution; The strong variant takes the worst-case sample complexity over all input-output distributions. The No free lunch theorem, discussed below, proves that, in general, the strong sample complexity is infinite, i.e. that there is no algorithm that can learn the globally-optimal target function using a finite number of training samples. However, if we are only interested in a particular class of target functions (e.g., only linear functions) then the sample complexity is finite, and it depends linearly on the VC dimension on the class of target functions. == Definition == Let X {\displaystyle X} be a space which we call the input space, and Y {\displaystyle Y} be a space which we call the output space, and let Z {\displaystyle Z} denote the product X × Y {\displaystyle X\times Y} . For example, in the setting of binary classification, X {\displaystyle X} is typically a finite-dimensional vector space and Y {\displaystyle Y} is the set { − 1 , 1 } {\displaystyle \{-1,1\}} . Fix a hypothesis space H {\displaystyle {\mathcal {H}}} of functions h : X → Y {\displaystyle h\colon X\to Y} . A learning algorithm over H {\displaystyle {\mathcal {H}}} is a computable map from Z {\displaystyle Z} to H {\displaystyle {\mathcal {H}}} . In other words, it is an algorithm that takes as input a finite sequence of training samples and outputs a function from X {\displaystyle X} to Y {\displaystyle Y} . Typical learning algorithms include empirical risk minimization, without or with Tikhonov regularization. Fix a loss function L : Y × Y → R ≥ 0 {\displaystyle {\mathcal {L}}\colon Y\times Y\to \mathbb {R} _{\geq 0}} , for example, the square loss L ( y , y ′ ) = ( y − y ′ ) 2 {\displaystyle {\mathcal {L}}(y,y')=(y-y')^{2}} , where h ( x ) = y ′ {\displaystyle h(x)=y'} . For a given distribution ρ {\displaystyle \rho } on X × Y {\displaystyle X\times Y} , the expected risk of a hypothesis (a function) h ∈ H {\displaystyle h\in {\mathcal {H}}} is E ( h ) := E ρ [ L ( h ( x ) , y ) ] = ∫ X × Y L ( h ( x ) , y ) d ρ ( x , y ) {\displaystyle {\mathcal {E}}(h):=\mathbb {E} _{\rho }[{\mathcal {L}}(h(x),y)]=\int _{X\times Y}{\mathcal {L}}(h(x),y)\,d\rho (x,y)} In our setting, we have h = A ( S n ) {\displaystyle h={\mathcal {A}}(S_{n})} , where A {\displaystyle {\mathcal {A}}} is a learning algorithm and S n = ( ( x 1 , y 1 ) , … , ( x n , y n ) ) ∼ ρ n {\displaystyle S_{n}=((x_{1},y_{1}),\ldots ,(x_{n},y_{n}))\sim \rho ^{n}} is a sequence of vectors which are all drawn independently from ρ {\displaystyle \rho } . Define the optimal risk E H ∗ = inf h ∈ H E ( h ) . {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}={\underset {h\in {\mathcal {H}}}{\inf }}{\mathcal {E}}(h).} Set h n = A ( S n ) {\displaystyle h_{n}={\mathcal {A}}(S_{n})} , for each sample size n {\displaystyle n} . h n {\displaystyle h_{n}} is a random variable and depends on the random variable S n {\displaystyle S_{n}} , which is drawn from the distribution ρ n {\displaystyle \rho ^{n}} . The algorithm A {\displaystyle {\mathcal {A}}} is called consistent if E ( h n ) {\displaystyle {\mathcal {E}}(h_{n})} probabilistically converges to E H ∗ {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}} . In other words, for all ϵ , δ > 0 {\displaystyle \epsilon ,\delta >0} , there exists a positive integer N {\displaystyle N} , such that, for all sample sizes n ≥ N {\displaystyle n\geq N} , we have Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] < δ . {\displaystyle \Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]<\delta .} The sample complexity of A {\displaystyle {\mathcal {A}}} is then the minimum N {\displaystyle N} for which this holds, as a function of ρ , ϵ {\displaystyle \rho ,\epsilon } , and δ {\displaystyle \delta } . We write the sample complexity as N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} to emphasize that this value of N {\displaystyle N} depends on ρ , ϵ {\displaystyle \rho ,\epsilon } , and δ {\displaystyle \delta } . If A {\displaystyle {\mathcal {A}}} is not consistent, then we set N ( ρ , ϵ , δ ) = ∞ {\displaystyle N(\rho ,\epsilon ,\delta )=\infty } . If there exists an algorithm for which N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is finite, then we say that the hypothesis space H {\displaystyle {\mathcal {H}}} is learnable. In others words, the sample complexity N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} defines the rate of consistency of the algorithm: given a desired accuracy ϵ {\displaystyle \epsilon } and confidence δ {\displaystyle \delta } , one needs to sample N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} data points to guarantee that the risk of the output function is within ϵ {\displaystyle \epsilon } of the best possible, with probability at least 1 − δ {\displaystyle 1-\delta } . In probably approximately correct (PAC) learning, one is concerned with whether the sample complexity is polynomial, that is, whether N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is bounded by a polynomial in 1 / ϵ {\displaystyle 1/\epsilon } and 1 / δ {\displaystyle 1/\delta } . If N ( ρ , ϵ , δ ) {\displaystyle N(\rho ,\epsilon ,\delta )} is polynomial for some learning algorithm, then one says that the hypothesis space H {\displaystyle {\mathcal {H}}} is PAC-learnable. This is a stronger notion than being learnable. == Unrestricted hypothesis space: infinite sample complexity == One can ask whether there exists a learning algorithm so that the sample complexity is finite in the strong sense, that is, there is a bound on the number of samples needed so that the algorithm can learn any distribution over the input-output space with a specified target error. More formally, one asks whether there exists a learning algorithm A {\displaystyle {\mathcal {A}}} , such that, for all ϵ , δ > 0 {\displaystyle \epsilon ,\delta >0} , there exists a positive integer N {\displaystyle N} such that for all n ≥ N {\displaystyle n\geq N} , we have sup ρ ( Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] ) < δ , {\displaystyle \sup _{\rho }\left(\Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]\right)<\delta ,} where h n = A ( S n ) {\displaystyle h_{n}={\mathcal {A}}(S_{n})} , with S n = ( ( x 1 , y 1 ) , … , ( x n , y n ) ) ∼ ρ n {\displaystyle S_{n}=((x_{1},y_{1}),\ldots ,(x_{n},y_{n}))\sim \rho ^{n}} as above. The No Free Lunch Theorem says that without restrictions on the hypothesis space H {\displaystyle {\mathcal {H}}} , this is not the case, i.e., there always exist "bad" distributions for which the sample complexity is arbitrarily large. Thus, in order to make statements about the rate of convergence of the quantity sup ρ ( Pr ρ n [ E ( h n ) − E H ∗ ≥ ε ] ) , {\displaystyle \sup _{\rho }\left(\Pr _{\rho ^{n}}[{\mathcal {E}}(h_{n})-{\mathcal {E}}_{\mathcal {H}}^{}\geq \varepsilon ]\right),} one must either constrain the space of probability distributions ρ {\displaystyle \rho } , e.g. via a parametric approach, or constrain the space of hypotheses H {\displaystyle {\mathcal {H}}} , as in distribution-free approaches. == Restricted hypothesis space: finite sample-complexity == The latter approach leads to concepts such as VC dimension and Rademacher complexity which control the complexity of the space H {\displaystyle {\mathcal {H}}} . A smaller hypothesis space introduces more bias into the inference process, meaning that E H ∗ {\displaystyle {\mathcal {E}}_{\mathcal {H}}^{}} may be greater than the best possible risk in a larger space. However, by restricting the complexity of the hypothesis space it becomes possible for an algorithm to produce more uniformly consistent functions. This trade-off leads to the concept of regularization. It is a theorem from VC theory that the following three statements are equivalent for a hypothesis space H {\displaystyle {\mathcal {H}}} : H {\displaystyle {\mathcal {H}}} is PAC-learnable. The VC dimension of H {\displaystyle {\mathcal {H}}} is finite. H {\displaystyle {\mathcal {H}}} is a uniform Glivenko-Cantelli class. This gives a way to prove that certain hypothesis spaces are PAC learnable, and by extension, learnable. === An example of a PAC-learnable hypothesis space === X = R d , Y = { − 1 , 1 } {\displaystyle X=\mathbb {R} ^{d},Y=\{-1,1\}} , and let H {\displaystyle {\mathcal {H}}} be the space of affine functions on X {\displaystyle X} , that is, functions of the form x ↦ ⟨ w , x ⟩ + b {\displaystyle x\mapsto \langl

Atomicity (database systems)

In database systems, atomicity (; from Ancient Greek: ἄτομος, romanized: átomos, lit. 'undividable') is the property of a database transaction consisting of an indivisible and irreducible series of database operations such that either all occur, or none occur. It is one of the ACID transaction properties: Atomicity, Consistency, Isolation, Durability. A guarantee of atomicity prevents partial database updates from occurring, because they can cause greater problems than rejecting the whole series outright. As a consequence, an atomic transaction cannot be observed to be in progress by another database client: at one moment in time, it has not yet happened, and at the next it has already occurred in whole (or nothing happened if the transaction was cancelled in progress). An example of transaction atomicity could be a digital monetary transfer from bank account A to account B. It consists of two operations, debiting the money from account A and crediting it to account B. Performing both of these operations inside of an atomic transaction ensures that the database remains in a consistent state, if either operation fails there will not be any unaccountable credits or debits affecting either account. The same term is also used in the definition of First normal form in database systems, where it instead refers to the concept that the values for fields may not consist of multiple smaller values to be decomposed, such as a string into which multiple names, numbers, dates, or other types may be packed. == Orthogonality == Atomicity does not behave completely orthogonally with regard to the other ACID properties of transactions. For example, isolation relies on atomicity to roll back the enclosing transaction in the event of an isolation violation such as a deadlock; consistency also relies on atomicity to roll back the enclosing transaction in the event of a consistency violation by an illegal transaction. As a result of this, a failure to detect a violation and roll back the enclosing transaction may cause an isolation or consistency failure. == Implementation == Typically, systems implement Atomicity by providing some mechanism to indicate which transactions have started and which finished; or by keeping a copy of the data before any changes occurred (Read-copy-update). Several filesystems have developed methods for avoiding the need to keep multiple copies of data, using journaling (see journaling file system). Databases usually implement this using some form of logging/journaling to track changes. The system synchronizes the logs (often the metadata) as necessary after changes have successfully taken place. Afterwards, crash recovery ignores incomplete entries. Although implementations vary depending on factors such as concurrency issues, the principle of atomicity – i.e. complete success or complete failure – remain. Ultimately, any application-level implementation relies on operating-system functionality. At the file-system level, POSIX-compliant systems provide system calls such as open(2) and flock(2) that allow applications to atomically open or lock a file. At the process level, POSIX Threads provide adequate synchronization primitives. The hardware level requires atomic operations such as Test-and-set, Fetch-and-add, Compare-and-swap, or Load-Link/Store-Conditional, together with memory barriers. Portable operating systems cannot simply block interrupts to implement synchronization, since hardware that lacks concurrent execution such as hyper-threading or multi-processing is now extremely rare. In distributed and sharded databases, atomicity is complicated by network latency and the potential for partial failures. While traditional distributed systems often employ locking protocols (like 2PC) to ensure cross-shard atomicity, these can introduce performance bottlenecks. Recent research into distributed ledger consensus suggests alternative models, such as "braided synchronization". This technique, utilized in protocols like Cerberus, intertwines the consensus phases of multiple shards to enforce atomic guarantees without a global ordering of all transactions.