Error tolerance (PAC learning)

In PAC learning, error tolerance refers to the ability of an algorithm to learn when the examples received have been corrupted in some way. In fact, this is a very common and important issue since in many applications it is not possible to access noise-free data. Noise can interfere with the learning process at different levels: the algorithm may receive data that have been occasionally mislabeled, or the inputs may have some false information, or the classification of the examples may have been maliciously adulterated. == Notation and the Valiant learning model == In the following, let X {\displaystyle X} be our n {\displaystyle n} -dimensional input space. Let H {\displaystyle {\mathcal {H}}} be a class of functions that we wish to use in order to learn a { 0 , 1 } {\displaystyle \{0,1\}} -valued target function f {\displaystyle f} defined over X {\displaystyle X} . Let D {\displaystyle {\mathcal {D}}} be the distribution of the inputs over X {\displaystyle X} . The goal of a learning algorithm A {\displaystyle {\mathcal {A}}} is to choose the best function h ∈ H {\displaystyle h\in {\mathcal {H}}} such that it minimizes e r r o r ( h ) = P x ∼ D ( h ( x ) ≠ f ( x ) ) {\displaystyle error(h)=P_{x\sim {\mathcal {D}}}(h(x)\neq f(x))} . Let us suppose we have a function s i z e ( f ) {\displaystyle size(f)} that can measure the complexity of f {\displaystyle f} . Let Oracle ( x ) {\displaystyle {\text{Oracle}}(x)} be an oracle that, whenever called, returns an example x {\displaystyle x} and its correct label f ( x ) {\displaystyle f(x)} . When no noise corrupts the data, we can define learning in the Valiant setting: Definition: We say that f {\displaystyle f} is efficiently learnable using H {\displaystyle {\mathcal {H}}} in the Valiant setting if there exists a learning algorithm A {\displaystyle {\mathcal {A}}} that has access to Oracle ( x ) {\displaystyle {\text{Oracle}}(x)} and a polynomial p ( ⋅ , ⋅ , ⋅ , ⋅ ) {\displaystyle p(\cdot ,\cdot ,\cdot ,\cdot )} such that for any 0 < ε ≤ 1 {\displaystyle 0<\varepsilon \leq 1} and 0 < δ ≤ 1 {\displaystyle 0<\delta \leq 1} it outputs, in a number of calls to the oracle bounded by p ( 1 ε , 1 δ , n , size ( f ) ) {\displaystyle p\left({\frac {1}{\varepsilon }},{\frac {1}{\delta }},n,{\text{size}}(f)\right)} , a function h ∈ H {\displaystyle h\in {\mathcal {H}}} that satisfies with probability at least 1 − δ {\displaystyle 1-\delta } the condition error ( h ) ≤ ε {\displaystyle {\text{error}}(h)\leq \varepsilon } . In the following we will define learnability of f {\displaystyle f} when data have suffered some modification. == Classification noise == In the classification noise model a noise rate 0 ≤ η < 1 2 {\displaystyle 0\leq \eta <{\frac {1}{2}}} is introduced. Then, instead of Oracle ( x ) {\displaystyle {\text{Oracle}}(x)} that returns always the correct label of example x {\displaystyle x} , algorithm A {\displaystyle {\mathcal {A}}} can only call a faulty oracle Oracle ( x , η ) {\displaystyle {\text{Oracle}}(x,\eta )} that will flip the label of x {\displaystyle x} with probability η {\displaystyle \eta } . As in the Valiant case, the goal of a learning algorithm A {\displaystyle {\mathcal {A}}} is to choose the best function h ∈ H {\displaystyle h\in {\mathcal {H}}} such that it minimizes e r r o r ( h ) = P x ∼ D ( h ( x ) ≠ f ( x ) ) {\displaystyle error(h)=P_{x\sim {\mathcal {D}}}(h(x)\neq f(x))} . In applications it is difficult to have access to the real value of η {\displaystyle \eta } , but we assume we have access to its upperbound η B {\displaystyle \eta _{B}} . Note that if we allow the noise rate to be 1 / 2 {\displaystyle 1/2} , then learning becomes impossible in any amount of computation time, because every label conveys no information about the target function. Definition: We say that f {\displaystyle f} is efficiently learnable using H {\displaystyle {\mathcal {H}}} in the classification noise model if there exists a learning algorithm A {\displaystyle {\mathcal {A}}} that has access to Oracle ( x , η ) {\displaystyle {\text{Oracle}}(x,\eta )} and a polynomial p ( ⋅ , ⋅ , ⋅ , ⋅ ) {\displaystyle p(\cdot ,\cdot ,\cdot ,\cdot )} such that for any 0 ≤ η ≤ 1 2 {\displaystyle 0\leq \eta \leq {\frac {1}{2}}} , 0 ≤ ε ≤ 1 {\displaystyle 0\leq \varepsilon \leq 1} and 0 ≤ δ ≤ 1 {\displaystyle 0\leq \delta \leq 1} it outputs, in a number of calls to the oracle bounded by p ( 1 1 − 2 η B , 1 ε , 1 δ , n , s i z e ( f ) ) {\displaystyle p\left({\frac {1}{1-2\eta _{B}}},{\frac {1}{\varepsilon }},{\frac {1}{\delta }},n,size(f)\right)} , a function h ∈ H {\displaystyle h\in {\mathcal {H}}} that satisfies with probability at least 1 − δ {\displaystyle 1-\delta } the condition e r r o r ( h ) ≤ ε {\displaystyle error(h)\leq \varepsilon } . == Statistical query learning == Statistical Query Learning is a kind of active learning problem in which the learning algorithm A {\displaystyle {\mathcal {A}}} can decide if to request information about the likelihood P f ( x ) {\displaystyle P_{f(x)}} that a function f {\displaystyle f} correctly labels example x {\displaystyle x} , and receives an answer accurate within a tolerance α {\displaystyle \alpha } . Formally, whenever the learning algorithm A {\displaystyle {\mathcal {A}}} calls the oracle Oracle ( x , α ) {\displaystyle {\text{Oracle}}(x,\alpha )} , it receives as feedback probability Q f ( x ) {\displaystyle Q_{f(x)}} , such that Q f ( x ) − α ≤ P f ( x ) ≤ Q f ( x ) + α {\displaystyle Q_{f(x)}-\alpha \leq P_{f(x)}\leq Q_{f(x)}+\alpha } . Definition: We say that f {\displaystyle f} is efficiently learnable using H {\displaystyle {\mathcal {H}}} in the statistical query learning model if there exists a learning algorithm A {\displaystyle {\mathcal {A}}} that has access to Oracle ( x , α ) {\displaystyle {\text{Oracle}}(x,\alpha )} and polynomials p ( ⋅ , ⋅ , ⋅ ) {\displaystyle p(\cdot ,\cdot ,\cdot )} , q ( ⋅ , ⋅ , ⋅ ) {\displaystyle q(\cdot ,\cdot ,\cdot )} , and r ( ⋅ , ⋅ , ⋅ ) {\displaystyle r(\cdot ,\cdot ,\cdot )} such that for any 0 < ε ≤ 1 {\displaystyle 0<\varepsilon \leq 1} the following hold: Oracle ( x , α ) {\displaystyle {\text{Oracle}}(x,\alpha )} can evaluate P f ( x ) {\displaystyle P_{f(x)}} in time q ( 1 ε , n , s i z e ( f ) ) {\displaystyle q\left({\frac {1}{\varepsilon }},n,size(f)\right)} ; 1 α {\displaystyle {\frac {1}{\alpha }}} is bounded by r ( 1 ε , n , s i z e ( f ) ) {\displaystyle r\left({\frac {1}{\varepsilon }},n,size(f)\right)} A {\displaystyle {\mathcal {A}}} outputs a model h {\displaystyle h} such that e r r ( h ) < ε {\displaystyle err(h)<\varepsilon } , in a number of calls to the oracle bounded by p ( 1 ε , n , s i z e ( f ) ) {\displaystyle p\left({\frac {1}{\varepsilon }},n,size(f)\right)} . Note that the confidence parameter δ {\displaystyle \delta } does not appear in the definition of learning. This is because the main purpose of δ {\displaystyle \delta } is to allow the learning algorithm a small probability of failure due to an unrepresentative sample. Since now Oracle ( x , α ) {\displaystyle {\text{Oracle}}(x,\alpha )} always guarantees to meet the approximation criterion Q f ( x ) − α ≤ P f ( x ) ≤ Q f ( x ) + α {\displaystyle Q_{f(x)}-\alpha \leq P_{f(x)}\leq Q_{f(x)}+\alpha } , the failure probability is no longer needed. The statistical query model is strictly weaker than the PAC model: any efficiently SQ-learnable class is efficiently PAC learnable in the presence of classification noise, but there exist efficient PAC-learnable problems such as parity that are not efficiently SQ-learnable. == Malicious classification == In the malicious classification model an adversary generates errors to foil the learning algorithm. This setting describes situations of error burst, which may occur when for a limited time transmission equipment malfunctions repeatedly. Formally, algorithm A {\displaystyle {\mathcal {A}}} calls an oracle Oracle ( x , β ) {\displaystyle {\text{Oracle}}(x,\beta )} that returns a correctly labeled example x {\displaystyle x} drawn, as usual, from distribution D {\displaystyle {\mathcal {D}}} over the input space with probability 1 − β {\displaystyle 1-\beta } , but it returns with probability β {\displaystyle \beta } an example drawn from a distribution that is not related to D {\displaystyle {\mathcal {D}}} . Moreover, this maliciously chosen example may strategically selected by an adversary who has knowledge of f {\displaystyle f} , β {\displaystyle \beta } , D {\displaystyle {\mathcal {D}}} , or the current progress of the learning algorithm. Definition: Given a bound β B < 1 2 {\displaystyle \beta _{B}<{\frac {1}{2}}} for 0 ≤ β < 1 2 {\displaystyle 0\leq \beta <{\frac {1}{2}}} , we say that f {\displaystyle f} is efficiently learnable using H {\displaystyle {\mathcal {H}}} in the malicious classification model, if there exist a learning algorithm A {\displaystyle {\mathcal {A}}} that has access to Oracle ( x , β ) {\displaystyle {\text{Oracle}}(x,\beta )}

Supermind AI

Supermind is a state-funded Chinese artificial intelligence platform that tracks scientists and researchers internationally. The platform is the flagship project of Shenzhen's International Science and Technology Information Center. It mines data from science and technology databases such as Springer, Wiley, Clarivate and Elsevier. It is intended to detect technological breakthroughs and to identify possible sources of talent as part of China's efforts to advance technologically. The platform also uses government data security and security intelligence organizations such as Peng Cheng Laboratory, the China National GeneBank, BGI Group and the Key Laboratory of New Technologies of Security Intelligence. According to Hong Kong-based Asia Times, the platform, "While not an overt espionage tool...may be used to identify key personnel who could be bribed, deceived or manipulated into divulging classified information". The Organisation for Economic Co-operation and Development (OECD) flagged the project as an incident, meaning it may be of interest to policymakers and other stakeholders. US technology group American Edge Project criticized the project as a global risk of China's security services using the platform to place agents in jobs with access to important information, recruit technical personnel, and identify targets for hacking operations.

Color layout descriptor

In digital image and video processing, a color layout descriptor (CLD) is designed to capture the spatial distribution of color in an image. The feature extraction process consists of two parts: grid based representative color selection and discrete cosine transform with quantization. Color is the most basic quality of the visual contents, therefore it is possible to use colors to describe and represent an image. The MPEG-7 standard has tested the most efficient procedure to describe the color and has selected those that have provided more satisfactory results. This standard proposes different methods to obtain these descriptors, and one tool defined to describe the color is the CLD, that permits describing the color relation between sequences or group of images. The CLD captures the spatial layout of the representative colors on a grid superimposed on a region or image. Representation is based on coefficients of the discrete cosine transform (DCT). This is a very compact descriptor being highly efficient in fast browsing and search applications. It can be applied to still images as well as to video segments. == Definition == The CLD is a very compact and resolution-invariant representation of color for high-speed image retrieval and it has been designed to efficiently represent the spatial distribution of colors. This feature can be used for a wide variety of similarity-based retrieval, content filtering and visualization. It is especially useful for spatial structure-based retrieval applications. This descriptor is obtained by applying the DCT transformation on a 2-D array of local representative colors in Y or Cb or Cr color space. The functionalities of the CLD are basically the matching: – Image-to-image matching – Video clip-to-video clip matching Remark that the CLD is one of the most precise and fast color descriptor. == Extraction == The extraction process of this color descriptor consists of four stages: Image partitioning Representative color selection DCT transformation Zigzag scanning The standard MPEG-7 recommends using the YCbCr color space for the CLD. === Image partitioning === In the image partitioning stage, the input picture (on RGB color space) is divided into 64 blocks to guarantee the invariance to resolution or scale. The inputs and outputs of this step are summarized in the following table: === Representative color selection === After the image partitioning stage, a single representative color is selected from each block. Any method to select the representative color can be applied, but the standard recommends the use of the average of the pixel colors in a block as the corresponding representative color, since it is simpler and the description accuracy is sufficient in general. The selection results in a tiny image icon of size 8x8. The next figure shows this process. Note that in the image of the figure, the resolution of the original image has been maintained only in order to facilitate its representation. The inputs and outputs of this stage are summarized in the next table: Once the tiny image icon is obtained, the color space conversion between RGB and YCbCr is applied. === DCT transformation === In the fourth stage, the luminance (Y) and the blue and red chrominance (Cb and Cr) are transformed by 8x8 DCT, so three sets of 64 DCT coefficients are obtained. To calculate the DCT in a 2D array, the formulas below are used. B p q = α p α q ∑ m = 0 M − 1 ∑ n = 0 N − 1 A m n cos ⁡ π ( 2 m + 1 ) p 2 M cos ⁡ π ( 2 n + 1 ) q 2 N , 0 ≤ p ≤ M − 1 , 0 ≤ q ≤ N − 1 {\displaystyle B_{pq}=\alpha _{p}\alpha _{q}\sum _{m=0}^{M-1}\sum _{n=0}^{N-1}A_{mn}\cos {\frac {\pi (2m+1)p}{2M}}\cos {\frac {\pi (2n+1)q}{2N}},\qquad 0\leq p\leq M-1,\;0\leq q\leq N-1} α p = { 1 M , p = 0 2 M , 1 ≤ p ≤ M − 1 α q = { 1 N , q = 0 2 N , 1 ≤ q ≤ N − 1 {\displaystyle \alpha _{p}={\begin{cases}{\frac {1}{\sqrt {M}}},&p=0\\{\sqrt {\frac {2}{M}}},&1\leq p\leq M-1\end{cases}}\qquad \alpha _{q}={\begin{cases}{\frac {1}{\sqrt {N}}},&q=0\\{\sqrt {\frac {2}{N}}},&1\leq q\leq N-1\end{cases}}} The inputs and outputs of this stage are summarized in the next table: === Zigzag scanning === A zigzag scanning is performed with these three sets of 64 DCT coefficients, following the schema presented in the figure. The purpose of the zigzag scan is to group the low frequency coefficients of the 8x8 matrix into a vector. The inputs and outputs of this stage are summarized in the next table: Finally, these three set of matrices correspond to the CLD of the input image. == Matching == The matching process helps to evaluate if two elements are equal comparing both elements and calculating the distance between them. In the case of color descriptors the matching process helps to evaluate if two images are similar. Its procedure is the following: – Given an image as an input, the application attempts to find an image with a similar descriptor in a data base of images. If we consider two CLDs: {DY, DCb, DCr} { DY‟, DCb‟, DCr‟ }, The distance between the two descriptors can be computed as: D = ∑ i w y i ( D Y i − D Y i ′ ) 2 + ∑ i w b i ( D C b i − D C b i ′ ) 2 + ∑ i w r i ( D C r i − D C r i ′ ) 2 {\displaystyle D={\sqrt {\sum _{i}w_{yi}(DY_{i}-DY_{i}')^{2}}}+{\sqrt {\sum _{i}w_{bi}(DCb_{i}-DCb_{i}')^{2}}}+{\sqrt {\sum _{i}w_{ri}(DCr_{i}-DCr_{i}')^{2}}}} The subscript i represents the zigzag-scanning order of the coefficients. Furthermore, notice that is possible to weight the coefficients (w) in order to adjust the performance of the matching process. These weights let us give to some components of the descriptor more importance than others. Observing the formula, it can be extracted that: – 2 images are the same if the distance is 0 – 2 images are similar if the distance is near to 0 Therefore, this matching process will let to identify images with similar color descriptors. Since the complexity of the similarity matching process shown above is low, high-speed image matching can be achieved.

Apache Parquet

Apache Parquet is a free and open-source column-oriented data storage format in the Apache Hadoop ecosystem inspired by Google Dremel interactive ad-hoc query system for analysis of read-only nested data. It is similar to RCFile and ORC, the other columnar-storage file formats in Hadoop, and is compatible with most of the data processing frameworks around Hadoop. It provides data compression and encoding schemes with enhanced performance to handle complex data in bulk. == History == The open-source project to build Apache Parquet began as a joint effort between Twitter and Cloudera using the record shredding and assembly algorithm as described in Google's Dremel. Parquet was designed as an improvement on the Trevni columnar storage format created by Doug Cutting, the creator of Hadoop. The name 'parquet' (lit. 'small compartment') refers to a style of decorative flooring and was chosen to "evoke the bottom layer of a database with an interesting layout". The first version, Apache Parquet 1.0, was released in July 2013. Since April 27, 2015, Apache Parquet has been a top-level Apache Software Foundation (ASF)-sponsored project. == Features == Apache Parquet is implemented using the record-shredding and assembly algorithm, which accommodates the complex data structures that can be used to store data. The values in each column are stored in contiguous memory locations, providing the following benefits: Column-wise compression is efficient in storage space Encoding and compression techniques specific to the type of data in each column can be used Queries that fetch specific column values need not read the entire row, thus improving performance Apache Parquet is implemented using the Apache Thrift framework, which increases its flexibility; it can work with a number of programming languages like C++, Java, Python, PHP, etc. As of August 2015, Parquet supports the big-data-processing frameworks including Apache Hive, Apache Drill, Apache Impala, Apache Crunch, Apache Pig, Cascading, Presto and Apache Spark. It is one of the external data formats used by the pandas Python data manipulation and analysis library. == Compression and encoding == In Parquet, compression is performed column by column, which enables different encoding schemes to be used for text and integer data. This strategy also keeps the door open for newer and better encoding schemes to be implemented as they are invented. Parquet supports various compression formats: snappy, gzip, LZO, brotli, zstd, and LZ4. === Dictionary encoding === Parquet has an automatic dictionary encoding enabled dynamically for data with a small number of unique values (i.e. below 105) that enables significant compression and boosts processing speed. === Bit packing === Storage of integers is usually done with dedicated 32 or 64 bits per integer. For small integers, packing multiple integers into the same space makes storage more efficient. === Run-length encoding (RLE) === To optimize storage of multiple occurrences of the same value, run-length encoding is used, which is where a single value is stored once along with the number of occurrences. Parquet implements a hybrid of bit packing and RLE, in which the encoding switches based on which produces the best compression results. This strategy works well for certain types of integer data and combines well with dictionary encoding. == Cloud Storage and Data Lakes == Parquet is widely used as the underlying file format in modern cloud-based data lake architectures. Cloud storage systems such as Amazon S3, Azure Data Lake Storage, and Google Cloud Storage commonly store data in Parquet format due to its efficient columnar representation and retrieval capabilities. Data lakehouse frameworks—including Apache Iceberg, Delta Lake, and Apache Hudi —build an additional metadata layer on top of Parquet files to support features such as schema evolution, time-travel queries, and ACID-compliant transactions. In these architectures, Parquet files serve as the immutable storage layer while the table formats manage data versioning and transactional integrity. == Comparison == Apache Parquet is comparable to RCFile and Optimized Row Columnar (ORC) file formats — all three fall under the category of columnar data storage within the Hadoop ecosystem. They all have better compression and encoding with improved read performance at the cost of slower writes. In addition to these features, Apache Parquet supports limited schema evolution, i.e., the schema can be modified according to the changes in the data. It also provides the ability to add new columns and merge schemas that do not conflict. Apache Arrow is designed as an in-memory complement to on-disk columnar formats like Parquet and ORC. The Arrow and Parquet projects include libraries that allow for reading and writing between the two formats. == Implementations == Known implementations of Parquet include:

Tiki Wiki CMS Groupware

Tiki Wiki CMS Groupware or simply Tiki, originally known as TikiWiki, is a free and open source Wiki-based content management system and online office suite written primarily in PHP and distributed under the GNU Lesser General Public License (LGPL-2.1-only) license. In addition to enabling websites and portals on the internet and on intranets and extranets, Tiki contains a number of collaboration features allowing it to operate as a Geospatial Content Management System (GeoCMS) and Groupware web application. Tiki includes all the basic features common to most CMSs such as the ability to register and maintain individual user accounts within a flexible and rich permission / privilege system, create and manage menus, RSS-feeds, customize page layout, perform logging, and administer the system. All administration tasks are accomplished through a browser-based user interface. Tiki features an all-in-one design, as opposed to a core+extensions model followed by other CMSs. This allows for future-proof upgrades (since all features are released together), but has the drawback of an extremely large codebase (more than 1,000,000 lines). Tiki can run on any computing platform that supports both a web server capable of running PHP 5 (including Apache HTTP Server, IIS, Lighttpd, Hiawatha, Cherokee, and nginx) and a MySQL/MariaDB database to store content and settings. == Major components == Tiki has four major categories of components: content creation and management tools, content organization tools and navigation aids, communication tools, and configuration and administration tools. These components enable administrators and users to create and manage content, as well as letting them communicate to others and configure sites. In addition, Tiki allows each user to choose from various visual themes. These themes are implemented using CSS and the open source Smarty template engine. Additional themes can be created by a Tiki administrator for branding or customization as well. == Internationalization == Tiki is an international project, supporting many languages. The default interface language in Tiki is English, but any language that can be encoded and displayed using the UTF-8 encoding can be supported. Translated strings can be included via an external language file, or by translating interface strings directly, through the database. As of 29 September 2005, Tiki had been fully translated into eight languages and reportedly 90% or more translated into another five languages, as well as partial translations for nine additional languages. Tiki also supports interactive translation of actual wiki pages and was the initial wiki engine used in the Cross Lingual Wiki Engine Project. This allows Tiki-based web sites to have translated content — not just the user interface. == Implementation == Tiki is developed primarily in PHP with some JavaScript code. It uses MySQL/MariaDB as a database. It will run on any server that provides PHP 5, including Apache and Microsoft's IIS. Tiki components make extensive use of other open source projects, including Zend Framework, Smarty, jQuery, HTML Purifier, FCKeditor, Raphaël, phpCAS, and Morcego. When used with Mapserver Tiki can become a Geospatial Content Management System. == Project team == Tiki is under active development by a large international community of over 300 developers and translators, and is one of the largest open-source teams in the world. Project members have donated the resources and bandwidth required to host the tiki.org website and various subdomains. The project members refer to this dependence on their own product as "eating their own dogfood", which they have been doing since the early days of the project. Tiki community members also participate in various related events such as WikiSym and the Libre Software Meeting. == History == Tiki has been hosted on SourceForge.net since its initial release (Release 0.9, named Spica) in October 2002. It was primarily the development of Luis Argerich (Buenos Aires, Argentina), Eduardo Polidor (São Paulo, Brazil), and Garland Foster (Green Bay, WI, United States). In July 2003, Tiki was named the SourceForge.net July 2003 Project of the Month. In late 2003, a fork of Tiki was used to create Bitweaver. In 2006, Tiki was named to CMS Report's Top 30 Web Applications. In 2008, Tiki was named to EContent magazine's Top 100 In 2009, Tiki adopted a six-month release cycle and announced the selection of a Long Term Support (LTS) version and the Tiki Software Community Association was formed as the legal steward for Tiki. The Tiki Software Association is a not-for-profit entity established in Canada. Previously, the entire project was run entirely by volunteers. In 2010, Tiki received Best of Open Source Software Applications Award (BOSSIE) from InfoWorld, in the Applications category. In 2011, Tiki was named to CMS Report's Top 30 Web Applications. In 2012, Tiki was named "Best Web Tool" by WebHostingSearch.com, and "People's Choice: Best Free CMS" by CMS Critic. In 2016, Tiki was named as one of the "10 Best Open Source Collaboration Software Tools" by Small Business Computing. == Name == The name TikiWiki is written in CamelCase, a common Wiki syntax indicating a hyperlink within the Wiki. It is most likely a compound word combining two Polynesian terms, Tiki and Wiki, to create a self-rhyming name similar to wikiwiki, a common variant of wiki. A backronym has also been formed for Tiki: Tightly Integrated Knowledge Infrastructure. == Release Information and History == In general, the Tiki Software Community Association releases a new major version of Tiki Wiki every 8 months where prior, non-LTS, major versions are supported until the first minor version release of the next major version (i.e., 16.0 ⇒ 17.1). Starting with version 12.x, Tiki Wiki LTS is supported for 5 years where it enters a security/maintenance release cycle upon the release of the next LTS version. Tiki Wiki's release history is outlined below.

Dynamic epistemic logic

Dynamic epistemic logic (DEL) is a logical framework dealing with knowledge and information change. Typically, DEL focuses on situations involving multiple agents and studies how their knowledge changes when events occur. These events can change factual properties of the actual world (they are called ontic events): for example a red card is painted in blue. They can also bring about changes of knowledge without changing factual properties of the world (they are called epistemic events): for example, a card is revealed publicly (or privately) to be red. Originally, DEL focused on epistemic events. Only some of the basic ideas are present in this entry of the original DEL framework; more details about DEL in general can be found in the references. Due to the nature of its object of study and its abstract approach, DEL is related and has applications to numerous research areas, such as computer science (artificial intelligence), philosophy (formal epistemology), economics (game theory) and cognitive science. In computer science, DEL is for example very much related to multi-agent systems, which are systems where multiple intelligent agents interact and exchange information. As a combination of dynamic logic and epistemic logic, dynamic epistemic logic is a young field of research. It really started in 1989 with Plaza's logic of public announcement. Independently, Gerbrandy and Groeneveld proposed a system dealing moreover with private announcement and that was inspired by the work of Veltman. Another system was proposed by van Ditmarsch whose main inspiration was the Cluedo game. But the most influential and original system was the system proposed by Baltag, Moss and Solecki. This system can deal with all the types of situations studied in the works above and its underlying methodology is conceptually grounded. This entry will present some of its basic ideas. Formally, DEL extends ordinary epistemic logic by the inclusion of event models to describe actions, and a product update operator that defines how epistemic models are updated as the consequence of executing actions described through event models. Epistemic logic will first be recalled. Then, actions and events will enter into the picture and we will introduce the DEL framework. == Epistemic logic == Epistemic logic is a modal logic dealing with the notions of knowledge and belief. As a logic, it is concerned with understanding the process of reasoning about knowledge and belief: which principles relating the notions of knowledge and belief are intuitively plausible? Like epistemology, it stems from the Greek word ϵ π ι σ τ η μ η {\displaystyle \epsilon \pi \iota \sigma \tau \eta \mu \eta } or ‘episteme’ meaning knowledge. Epistemology is nevertheless more concerned with analyzing the very nature and scope of knowledge, addressing questions such as “What is the definition of knowledge?” or “How is knowledge acquired?”. In fact, epistemic logic grew out of epistemology in the Middle Ages thanks to the efforts of Burley and Ockham. The formal work, based on modal logic, that inaugurated contemporary research into epistemic logic dates back only to 1962 and is due to Hintikka. It then sparked in the 1960s discussions about the principles of knowledge and belief and many axioms for these notions were proposed and discussed. For example, the interaction axioms K p → B p {\displaystyle Kp\rightarrow Bp} and B p → K B p {\displaystyle Bp\rightarrow KBp} are often considered to be intuitive principles: if an agent Knows p {\displaystyle p} then (s)he also Believes p {\displaystyle p} , or if an agent Believes p {\displaystyle p} , then (s)he Knows that (s)he Believes p {\displaystyle p} . More recently, these kinds of philosophical theories were taken up by researchers in economics, artificial intelligence and theoretical computer science where reasoning about knowledge is a central topic. Due to the new setting in which epistemic logic was used, new perspectives and new features such as computability issues were then added to the research agenda of epistemic logic. === Syntax === In the sequel, A G T S = { 1 , … , n } {\displaystyle AGTS=\{1,\ldots ,n\}} is a finite set whose elements are called agents and P R O P {\displaystyle PROP} is a set of propositional letters. The epistemic language is an extension of the basic multi-modal language of modal logic with a common knowledge operator C A {\displaystyle C_{A}} and a distributed knowledge operator D A {\displaystyle D_{A}} . Formally, the epistemic language L EL C {\displaystyle {\mathcal {L}}_{\textsf {EL}}^{C}} is defined inductively by the following grammar in BNF: L EL C : ϕ ::= p ∣ ¬ ϕ ∣ ( ϕ ∧ ϕ ) ∣ K j ϕ ∣ C A ϕ ∣ D A ϕ {\displaystyle {\mathcal {L}}_{\textsf {EL}}^{C}:\phi ~~::=~~p~\mid ~\neg \phi ~\mid ~(\phi \land \phi )~\mid ~K_{j}\phi ~\mid ~C_{A}\phi ~\mid ~D_{A}\phi } where p ∈ P R O P {\displaystyle p\in PROP} , j ∈ A G T S {\displaystyle j\in {AGTS}} and A ⊆ A G T S {\displaystyle A\subseteq {AGTS}} . The basic epistemic language L E L {\displaystyle {\mathcal {L}}_{EL}} is the language L E L C {\displaystyle {\mathcal {L}}_{EL}^{C}} without the common knowledge and distributed knowledge operators. The formula ⊥ {\displaystyle \bot } is an abbreviation for ¬ p ∧ p {\displaystyle \neg p\land p} (for a given p ∈ P R O P {\displaystyle p\in PROP} ), ⟨ K j ⟩ ϕ {\displaystyle \langle K_{j}\rangle \phi } is an abbreviation for ¬ K j ¬ ϕ {\displaystyle \neg K_{j}\neg \phi } , E A ϕ {\displaystyle E_{A}\phi } is an abbreviation for ⋀ j ∈ A K j ϕ {\displaystyle \bigwedge \limits _{j\in A}K_{j}\phi } and C ϕ {\displaystyle C\phi } an abbreviation for C A G T S ϕ {\displaystyle C_{AGTS}\phi } . Group notions: general, common and distributed knowledge. In a multi-agent setting there are three important epistemic concepts: general knowledge, distributed knowledge and common knowledge. The notion of common knowledge was first studied by Lewis in the context of conventions. It was then applied to distributed systems and to game theory, where it allows to express that the rationality of the players, the rules of the game and the set of players are commonly known. General knowledge. General knowledge of ϕ {\displaystyle \phi } means that everybody in the group of agents A G T S {\displaystyle {AGTS}} knows that ϕ {\displaystyle \phi } . Formally, this corresponds to the following formula: E ϕ := ⋀ j ∈ A G T S K j ϕ . {\displaystyle E\phi :={\underset {j\in {AGTS}}{\bigwedge }}K_{j}\phi .} Common knowledge. Common knowledge of ϕ {\displaystyle \phi } means that everybody knows ϕ {\displaystyle \phi } but also that everybody knows that everybody knows ϕ {\displaystyle \phi } , that everybody knows that everybody knows that everybody knows ϕ {\displaystyle \phi } , and so on ad infinitum. Formally, this corresponds to the following formula C ϕ := E ϕ ∧ E E ϕ ∧ E E E ϕ ∧ … {\displaystyle C\phi :=E\phi \land EE\phi \land EEE\phi \land \ldots } As we do not allow infinite conjunction the notion of common knowledge will have to be introduced as a primitive in our language. Before defining the language with this new operator, we are going to give an example introduced by Lewis that illustrates the difference between the notions of general knowledge and common knowledge. Lewis wanted to know what kind of knowledge is needed so that the statement p {\displaystyle p} : “every driver must drive on the right” be a convention among a group of agents. In other words, he wanted to know what kind of knowledge is needed so that everybody feels safe to drive on the right. Suppose there are only two agents i {\displaystyle i} and j {\displaystyle j} . Then everybody knowing p {\displaystyle p} (formally E p {\displaystyle Ep} ) is not enough. Indeed, it might still be possible that the agent i {\displaystyle i} considers possible that the agent j {\displaystyle j} does not know p {\displaystyle p} (formally ¬ K i K j p {\displaystyle \neg K_{i}K_{j}p} ). In that case the agent i {\displaystyle i} will not feel safe to drive on the right because he might consider that the agent j {\displaystyle j} , not knowing p {\displaystyle p} , could drive on the left. To avoid this problem, we could then assume that everybody knows that everybody knows that p {\displaystyle p} (formally E E p {\displaystyle EEp} ). This is again not enough to ensure that everybody feels safe to drive on the right. Indeed, it might still be possible that agent i {\displaystyle i} considers possible that agent j {\displaystyle j} considers possible that agent i {\displaystyle i} does not know p {\displaystyle p} (formally ¬ K i K j K i p {\displaystyle \neg K_{i}K_{j}K_{i}p} ). In that case and from i {\displaystyle i} ’s point of view, j {\displaystyle j} considers possible that i {\displaystyle i} , not knowing p {\displaystyle p} , will drive on the left. So from i {\displaystyle i} ’s point of view, j {\displaystyle j} might drive on the left as well (by the same argument as abov

Cloud management

Cloud management refers to the administration and oversight of cloud computing products and services. Public clouds are managed by cloud service providers, which operate the underlying infrastructure such as servers, storage, networking, and data center facilities. Users may also opt to manage their public cloud services with a third-party cloud management tool. Users of public cloud services can generally select from three basic cloud provisioning categories: User self-provisioning: Customers purchase cloud services directly from the provider, typically through a web form or console interface. The customer pays on a per-transaction basis. Advanced provisioning: Customers contract in advance a predetermined amount of resources, which are prepared in advance of service. The customer pays a flat fee or a monthly fee. Dynamic provisioning: The provider allocates resources when the customer needs them, then decommissions them when they are no longer needed. The customer is charged on a pay-per-use basis. Managing a private cloud requires software tools to help create a virtualized pool of compute resources, provide a self-service portal for end users and handle security, resource allocation, tracking and billing. Management tools for private clouds tend to be service driven, as opposed to resource driven, because cloud environments are typically highly virtualized and organized in terms of portable workloads. In hybrid cloud environments, compute, network and storage resources must be managed across multiple domains, so a good management strategy should start by defining what needs to be managed, and where and how to do it. Policies to help govern these domains should include configuration and installation of images, access control, and budgeting and reporting. Access control often includes the use of Single sign-on (SSO), in which a user logs in once and gains access to all systems without being prompted to log in again at each of them. == Characteristics of Cloud Management == Cloud management combines software and technologies in a design for managing cloud environments. Software developers have responded to the management challenges of cloud computing with a variety of cloud management platforms and tools. These tools include native tools offered by public cloud providers as well as third-party tools designed to provide consistent functionality across multiple cloud providers. Administrators must balance the competing requirements of efficient consistency across different cloud platforms with access to different native functionality within individual cloud platforms. The growing acceptance of public cloud and increased multicloud usage is driving the need for consistent cross-platform management. Rapid adoption of cloud services is introducing a new set of management challenges for those technical professionals responsible for managing IT systems and services. Cloud-management platforms and tools should have the ability to provide minimum functionality in the following categories. Functionality can be both natively provided or orchestrated via third-party integration. Provisioning and orchestration: create, modify, and delete resources as well as orchestrate workflows and management of workloads Automation: Enable cloud consumption and deployment of app services via infrastructure-as-code and other DevOps concepts Security and compliance: manage role-based access of cloud services and enforce security configurations Service request: collect and fulfill requests from users to access and deploy cloud resources. Monitoring and logging: collect performance and availability metrics as well as automate incident management and log aggregation Inventory and classification: discover and maintain pre-existing brownfield cloud resources plus monitor and manage changes Cost management and optimization: track and rightsize cloud spend and align capacity and performance to actual demand Migration, backup, and DR: enable data protection, disaster recovery, and data mobility via snapshots and/or data replication Organizations may group these criteria into key use cases including Cloud Brokerage, DevOps Automation, Governance, and Day-2 Life Cycle Operations. Enterprises with large-scale cloud implementations may require more robust cloud management tools which include specific characteristics, such as the ability to manage multiple platforms from a single point of reference, or intelligent analytics to automate processes like application lifecycle management. High-end cloud management tools should also have the ability to handle system failures automatically with capabilities such as self-monitoring, an explicit notification mechanism, and include failover and self-healing capabilities. == Multi-Cloud and Hybrid Cloud Management Challenges == Legacy management infrastructures, which are based on the concept of dedicated system relationships and architecture constructs, are not well suited to cloud environments where instances are continually launched and decommissioned. Instead, the dynamic nature of cloud computing requires monitoring and management tools that are adaptable, extensible and customizable. Cloud computing presents a number of management challenges. Companies using public clouds do not have ownership of the equipment hosting the cloud environment, and because the environment is not contained within their own networks, public cloud customers do not have full visibility or control. Users of public cloud services must also integrate with an architecture defined by the cloud provider, using its specific parameters for working with cloud components. Integration includes tying into the cloud APIs for configuring IP addresses, subnets, firewalls and data service functions for storage. Because control of these functions is based on the cloud provider’s infrastructure and services, public cloud users must integrate with the cloud infrastructure management. Capacity management is a challenge for both public and private cloud environments because end users have the ability to deploy applications using self-service portals. Applications of all sizes may appear in the environment, consume an unpredictable amount of resources, then disappear at any time. A possible solution is profiling the applications impact on computational resources. As result, the performance models allow the prediction of how resource utilization changes according to application patterns. Thus, resources can be dynamically scaled to meet the expected demand. This is critical to cloud providers that need to provision resources quickly to meet a growing demand by their applications. Charge-back—or, pricing resource use on a granular basis—is a challenge for both public and private cloud environments. Charge-back is a challenge for public cloud service providers because they must price their services competitively while still creating profit. Users of public cloud services may find charge-back challenging because it is difficult for IT groups to assess actual resource costs on a granular basis due to overlapping resources within an organization that may be paid for by an individual business unit, such as electrical power. For private cloud operators, charge-back is fairly straightforward, but the challenge lies in guessing how to allocate resources as closely as possible to actual resource usage to achieve the greatest operational efficiency. Exceeding budgets can be a risk. Hybrid cloud environments, which combine public and private cloud services, sometimes with traditional infrastructure elements, present their own set of management challenges. These include security concerns if sensitive data lands on public cloud servers, budget concerns around overuse of storage or bandwidth and proliferation of mismanaged images. Managing the information flow in a hybrid cloud environment is also a significant challenge. On-premises clouds must share information with applications hosted off-premises by public cloud providers, and this information may change constantly. Hybrid cloud environments also typically include a complex mix of policies, permissions and limits that must be managed consistently across both public and private clouds. == Cloud Management Platforms (CMP) == CMPs provide a means for a cloud service customer to manage the deployment and operation of applications and associated datasets across multiple cloud service infrastructures, including both on-premises cloud infrastructure and public cloud service provider infrastructure. In other words, CMPs provide management capabilities for hybrid cloud and multi-cloud environments. A cloud management platform (CMP) provides broad cloud management functionality atop both public cloud provider platforms and private cloud platforms. CMPs manage cloud services and resources that are distributed across multiple cloud platforms. The value of CMPs stands in delivering the maximum level of consistency between platforms without comp