Bayesian hierarchical modelling is a statistical model written in multiple levels (hierarchical form) that estimates the posterior distribution of model parameters using the Bayesian method. The sub-models combine to form the hierarchical model, and Bayes' theorem is used to integrate them with the observed data and account for all the uncertainty that is present. This integration enables calculation of updated posterior over the (hyper)parameters, effectively updating prior beliefs in light of the observed data. Frequentist statistics may yield conclusions seemingly incompatible with those offered by Bayesian statistics due to the Bayesian treatment of the parameters as random variables and its use of subjective information in establishing assumptions on these parameters. As the approaches answer different questions the formal results are not technically contradictory but the two approaches disagree over which answer is relevant to particular applications. Bayesians argue that relevant information regarding decision-making and updating beliefs cannot be ignored and that hierarchical modeling has the potential to overrule classical methods in applications where respondents give multiple observational data. Moreover, the model has proven to be robust, with the posterior distribution less sensitive to the more flexible hierarchical priors. Hierarchical modeling, as its name implies, retains nested data structure, and is used when information is available at several different levels of observational units. For example, in epidemiological modeling to describe infection trajectories for multiple countries, observational units are countries, and each country has its own time-based profile of daily infected cases. In decline curve analysis to describe oil or gas production decline curve for multiple wells, observational units are oil or gas wells in a reservoir region, and each well has each own time-based profile of oil or gas production rates (usually, barrels per month). Hierarchical modeling is used to devise computation based strategies for multiparameter problems. == Philosophy == Statistical methods and models commonly involve multiple parameters that can be regarded as related or connected in such a way that the problem implies a dependence of the joint probability model for these parameters. Individual degrees of belief, expressed in the form of probabilities, come with uncertainty. Amidst this is the change of the degrees of belief over time. As was stated by Professor José M. Bernardo and Professor Adrian F. Smith, "The actuality of the learning process consists in the evolution of individual and subjective beliefs about the reality." These subjective probabilities are more directly involved in the mind rather than the physical probabilities. Hence, it is with this need of updating beliefs that Bayesians have formulated an alternative statistical model which takes into account the prior occurrence of a particular event. == Bayes' theorem == The assumed occurrence of a real-world event will typically modify preferences between certain options. This is done by modifying the degrees of belief attached, by an individual, to the events defining the options. Suppose in a study of the effectiveness of cardiac treatments, with the patients in hospital j having survival probability θ j {\displaystyle \theta _{j}} , the survival probability will be updated with the occurrence of y, the event in which a controversial serum is created which, as believed by some, increases survival in cardiac patients. In order to make updated probability statements about θ j {\displaystyle \theta _{j}} , given the occurrence of event y, we must begin with a model providing a joint probability distribution for θ j {\displaystyle \theta _{j}} and y. This can be written as a product of the two distributions that are often referred to as the prior distribution P ( θ ) {\displaystyle P(\theta )} and the sampling distribution P ( y ∣ θ ) {\displaystyle P(y\mid \theta )} respectively: P ( θ , y ) = P ( θ ) P ( y ∣ θ ) {\displaystyle P(\theta ,y)=P(\theta )P(y\mid \theta )} Using the basic property of conditional probability, the posterior distribution will yield: P ( θ ∣ y ) = P ( θ , y ) P ( y ) = P ( y ∣ θ ) P ( θ ) P ( y ) {\displaystyle P(\theta \mid y)={\frac {P(\theta ,y)}{P(y)}}={\frac {P(y\mid \theta )P(\theta )}{P(y)}}} This equation, showing the relationship between the conditional probability and the individual events, is known as Bayes' theorem. This simple expression encapsulates the technical core of Bayesian inference which aims to deconstruct the probability, P ( θ ∣ y ) {\displaystyle P(\theta \mid y)} , relative to solvable subsets of its supportive evidence. == Exchangeability == The usual starting point of a statistical analysis is the assumption that the n values y 1 , y 2 , … , y n {\displaystyle y_{1},y_{2},\ldots ,y_{n}} are exchangeable. If no information – other than data y – is available to distinguish any of the θ j {\displaystyle \theta _{j}} 's from any others, and no ordering or grouping of the parameters can be made, one must assume symmetry of prior distribution parameters. This symmetry is represented probabilistically by exchangeability. Generally, it is useful and appropriate to model data from an exchangeable distribution as independently and identically distributed, given some unknown parameter vector θ {\displaystyle \theta } , with distribution P ( θ ) {\displaystyle P(\theta )} . === Finite exchangeability === For a fixed number n, the set y 1 , y 2 , … , y n {\displaystyle y_{1},y_{2},\ldots ,y_{n}} is exchangeable if the joint probability P ( y 1 , y 2 , … , y n ) {\displaystyle P(y_{1},y_{2},\ldots ,y_{n})} is invariant under permutations of the indices. That is, for every permutation π {\displaystyle \pi } or ( π 1 , π 2 , … , π n ) {\displaystyle (\pi _{1},\pi _{2},\ldots ,\pi _{n})} of (1, 2, …, n), P ( y 1 , y 2 , … , y n ) = P ( y π 1 , y π 2 , … , y π n ) . {\displaystyle P(y_{1},y_{2},\ldots ,y_{n})=P(y_{\pi _{1}},y_{\pi _{2}},\ldots ,y_{\pi _{n}}).} The following is an exchangeable, but not independent and identical (iid), example: Consider an urn with a red ball and a blue ball inside, with probability 1 2 {\displaystyle {\frac {1}{2}}} of drawing either. Balls are drawn without replacement, i.e. after one ball is drawn from the n {\displaystyle n} balls, there will be n − 1 {\displaystyle n-1} remaining balls left for the next draw. Let Y i = { 1 , if the i th ball is red , 0 , otherwise . {\displaystyle {\text{Let }}Y_{i}={\begin{cases}1,&{\text{if the }}i{\text{th ball is red}},\\0,&{\text{otherwise}}.\end{cases}}} The probability of selecting a red ball in the first draw and a blue ball in the second draw is equal to the probability of selecting a blue ball on the first draw and a red on the second, both of which are 1/2: P ( y 1 = 1 , y 2 = 0 ) = P ( y 1 = 0 , y 2 = 1 ) = 1 2 {\displaystyle P(y_{1}=1,y_{2}=0)=P(y_{1}=0,y_{2}=1)={\frac {1}{2}}} . This makes y 1 {\displaystyle y_{1}} and y 2 {\displaystyle y_{2}} exchangeable. But the probability of selecting a red ball on the second draw given that the red ball has already been selected in the first is 0. This is not equal to the probability that the red ball is selected in the second draw, which is 1/2: P ( y 2 = 1 ∣ y 1 = 1 ) = 0 ≠ P ( y 2 = 1 ) = 1 2 {\displaystyle P(y_{2}=1\mid y_{1}=1)=0\neq P(y_{2}=1)={\frac {1}{2}}} . Thus, y 1 {\displaystyle y_{1}} and y 2 {\displaystyle y_{2}} are not independent. If x 1 , … , x n {\displaystyle x_{1},\ldots ,x_{n}} are independent and identically distributed, then they are exchangeable, but the converse is not necessarily true. === Infinite exchangeability === Infinite exchangeability is the property that every finite subset of an infinite sequence y 1 {\displaystyle y_{1}} , y 2 , … {\displaystyle y_{2},\ldots } is exchangeable. For any n, the sequence y 1 , y 2 , … , y n {\displaystyle y_{1},y_{2},\ldots ,y_{n}} is exchangeable. == Hierarchical models == === Components === Bayesian hierarchical modeling makes use of two important concepts in deriving the posterior distribution, namely: Hyperparameters: parameters of the prior distribution Hyperpriors: distributions of Hyperparameters Suppose a random variable Y follows a normal distribution with parameter θ {\displaystyle \theta } as the mean and 1 as the variance, that is Y ∣ θ ∼ N ( θ , 1 ) {\displaystyle Y\mid \theta \sim N(\theta ,1)} . The tilde relation ∼ {\displaystyle \sim } can be read as "has the distribution of" or "is distributed as". Suppose also that the parameter θ {\displaystyle \theta } has a distribution given by a normal distribution with mean μ {\displaystyle \mu } and variance 1, i.e. θ ∣ μ ∼ N ( μ , 1 ) {\displaystyle \theta \mid \mu \sim N(\mu ,1)} . Furthermore, μ {\displaystyle \mu } follows another distribution given, for example, by the standard normal distribution, N ( 0 , 1 ) {\displaystyle {\text{N}}(0,1)} . The parameter μ {\dis
Apertus (LLM)
Apertus is a public large language model, developed by the Swiss AI Initiative (a collaboration between EPFL, ETH Zurich, and the Swiss National Supercomputing Centre). It was released on September 2, 2025, under the free and open-source Apache 2.0 license. Designed initially for business and research use cases around the world, Apertus was trained on over 1800 languages, and comes in 8 billion or 70 billion parameter versions and is available on Hugging Face for download. The model was developed aiming to adhere to European copyright law, and is one of the first examples of AI as a public good in the vein of AI Sovereignty. It is also the first large model to comply with the European Union's Artificial Intelligence Act. At its launch, the model creators emphasized multilinguality, transparency, and auditability as priorities in contrast to commercial frontier model. While international reception was largely positive, the first iteration was significantly behind the capabilities of frontier models and needs adaptation for many use cases with chatbots being a secondary but not a primary use case. As of late 2025, it was considered the largest and most capable fully open model. The capability of future models will depend in part on how much more funding can be secured.
Asynchronous module definition
Asynchronous module definition (AMD) is a specification for the programming language JavaScript. It defines an application programming interface (API) that defines code modules and their dependencies, and loads them asynchronously if desired. Implementations of AMD provide the following benefits: Website performance improvements. AMD implementations load smaller JavaScript files, and then only when they are needed. Fewer page errors. AMD implementations allow developers to define dependencies that must load before a module is executed, so the module does not try to use outside code that is not available yet.... In addition to loading multiple JavaScript files at runtime, AMD implementations allow developers to encapsulate code in smaller, more logically-organized files, in a way similar to other programming languages such as Java. For production and deployment, developers can concatenate and minify JavaScript modules based on an AMD API into one file, the same as traditional JavaScript. AMD provides some CommonJS interoperability. It allows for using a similar exports and require() interface in the code, although its own define() interface is more basal and preferred. The AMD specification is implemented by Dojo Toolkit, RequireJS, and other libraries.
FreePBX Distro
The FreePBX Distro was a freeware unified communications software system that consisted of FreePBX, a graphical user interface (GUI) for configuring, controlling and managing Asterisk PBX software. The FreePBX Distro included packages that offer VoIP, PBX, Fax, IVR, voice-mail and email functions. The FreePBX Distro Linux distribution was based on CentOS, which maintains binary compatibility with Red Hat Enterprise Linux. FreePBX has contributed to the popularity of Asterisk. As a result of CentOS Linux being discontinued and the last version of CentOS 7 going out of support on June 30, 2024, FreePBX 17 has moved over to and is supported on Debian Linux. FreePBX will no longer be providing a pre-configured FreePBX Distro, but will provide a script to install FreePBX on a fresh install of Debian Linux. In-place migration will not be possible, but will be possible by restoring a backup on the new version from the previous version. As FreePBX 16 will be supported until the release of FreePBX 18, FreePBX on this distribution will still work and be supported, however, there will be no further support for the underlying operating system. == Installation == The Official FreePBX Distro is installed from a ISO image available by web download, that includes the system CentOS, Asterisk, FreePBX GUI and assorted dependencies. This can then either be burned to DVD or written to a USB stick for installation == Support for telephony hardware == The FreePBX Distro has built-in support for cards from multiple vendors, including Digium, OpenVox, Alto, Rhino Equipment, Xorcom and Sangoma. The FreePBX Distro supports a large number of phone models via open-source modules. Supported VoIP phone manufacturers include Algo, AND, AudioCodes, Cisco, Cyberdata, Digium, Grandstream, Mitel/Aastra, Nortel/Avaya, Panasonic, Polycom, Sangoma, Snom, Xorcom and Yealink. == Development == FreePBX made its debut in 2004 as the AMP project (Asterisk Management Portal). The FreePBX Distro was released in 2011 as an turnkey solution for building a PBX using Asterisk, CentOS and FreePBX. FreePBX has over 1 million active production PBXs and over 20,000 new systems added each month. The core telephony engine is Asterisk, as configured by the Open Source FreePBX GUI. The last stable release is FreePBX Distro Stable SNG7-PBX16-64bit-2302-1 based on these main components: FreePBX 16 CentOS 7.8 Asterisk 16, 18, 19 (20 supported by upgrade once installed)
Dynamic web page
A dynamic web page is a web page constructed at runtime (during software execution), as opposed to a static web page, delivered as it is stored. A server-side dynamic web page is a web page whose construction is controlled by an application server processing server-side scripts. In server-side scripting, parameters determine how the assembly of every new web page proceeds, and including the setting up of more client-side processing. A client-side dynamic web page processes the web page using JavaScript running in the browser as it loads. JavaScript can interact with the page via Document Object Model (DOM), to query page state and modify it. Even though a web page can be dynamic on the client-side, it can still be hosted on a static hosting service such as GitHub Pages or Amazon S3 as long as there is not any server-side code included. A dynamic web page is then reloaded by the user or by a computer program to change some variable content. The updating information could come from the server, or from changes made to that page's DOM. This may or may not truncate the browsing history or create a saved version to go back to, but a dynamic web page update using AJAX technologies will neither create a page to go back to, nor truncate the web browsing history forward of the displayed page. Using AJAX, the end user gets one dynamic page managed as a single page in the web browser while the actual web content rendered on that page can vary. The AJAX engine sits only on the browser requesting parts of its DOM, the DOM, for its client, from an application server. A particular application server could offer a standardized REST style interface to offer services to the web application. DHTML is the umbrella term for technologies and methods used to create web pages that are not static web pages, though it has fallen out of common use since the popularization of AJAX, a term which is now itself rarely used. Client-side-scripting, server-side scripting, or a combination of these make for the dynamic web experience in a browser. == Basic concepts == Classical hypertext navigation, with HTML or XHTML alone, provides "static" content, meaning that the user requests a web page and simply views the page and the information on that page. However, a web page can also provide a "live", "dynamic", or "interactive" user experience. Content (text, images, form fields, etc.) on a web page can change, in response to different contexts or conditions. There are two ways to create this kind of effect: Using client-side scripting to change interface behaviors within a specific web page, in response to mouse or keyboard actions, data received from a web API, websocket or at specified timing events. In this case the dynamic behavior occurs within the presentation. Using server-side scripting to change the supplied page source code between pages, adjusting the sequence or reload of the web pages or web content supplied to the browser. Server responses may be determined by such conditions as data in a posted HTML form, parameters in the URL, the type of browser being used, the passage of time, or a database or server state. Web pages that use client-side scripting must use presentation technology broadly called rich interfaced pages. Client-side scripting languages like JavaScript or ActionScript, used for Dynamic HTML (DHTML) and Flash technologies respectively, are frequently used to orchestrate media types (sound, animations, changing text, etc.) of the presentation. The scripting also allows use of remote scripting, a technique by which the DHTML page requests additional information from a server, using a hidden Frame, XMLHttpRequests, or a web service. It is also possible to use a web framework to create a web API, which the client, via the use of JavaScript, uses to obtain data and alter its appearance or behavior dynamically depending on the data. Web pages that use server-side scripting are often created with the help of server-side languages such as PHP, Perl, ASP, JSP, ColdFusion and other languages. These server-side languages typically use the Common Gateway Interface (CGI) to produce dynamic web pages. These kinds of pages can also use, on the client-side, the first kind (DHTML, etc.). == History == It is difficult to be precise about "dynamic web page beginnings" or chronology because the precise concept makes sense only after the "widespread development of web pages". HTTP has existed since 1989, HTML, publicly standardized since 1996. The web browser's rise in popularity started with Mosaic in 1993. Between 1995 and 1996, multiple dynamic web products were introduced to the market, including Coldfusion, WebObjects, PHP, and Active Server Pages. The introduction of JavaScript (then known as LiveScript) enabled the production of client-side dynamic web pages, with JavaScript code executed in the client's browser. The letter "J" in the term AJAX originally indicated the use of JavaScript, as well as XML. With the rise of server side JavaScript processing, for example, Node.js, originally developed in 2009, JavaScript is also used to dynamically create pages on the server that are sent fully formed to clients. MediaWiki, the content management system that powers Wikipedia, is an example for an originally server-side dynamic web page, interacted with through form submissions and URL parameters. Throughout time, progressively enhancing extensions such as the visual editor have also added elements that are dynamic on the client side, while the original dynamic server-side elements such as the classic edit form remain available to be fallen back on (graceful degradation) in case of error or incompatibility. == Server-side scripting == A program running on a web server is used to generate the web content on various web pages, manage user sessions, and control workflow. Server responses may be determined by such conditions as data in a posted HTML form, parameters in the URL, the type of browser being used, the passage of time, or a database or server state. Such web pages are often created with the help of server-side languages such as ASP, ColdFusion, Java, JavaScript, Perl, PHP, Ruby, Python, and other languages, by a support server that can run on the same hardware as the web server. These server-side languages often use the Common Gateway Interface (CGI) to produce dynamic web pages. Two notable exceptions are ASP.NET, and JSP, which reuse CGI concepts in their APIs but actually dispatch all web requests into a shared virtual machine. The server-side languages are used to embed tags or markers within the source file of the web page on the web server. When a user on a client computer requests that web page, the web server interprets these tags or markers to perform actions on the server. For example, the server may be instructed to insert information from a database or information such as the current date. Dynamic web pages are often cached when there are few or no changes expected and the page is anticipated to receive considerable amount of web traffic that would wastefully strain the server and slow down page loading if it had to generate the pages on the fly for each request. == Client-side scripting == Client-side scripting is changing interface behaviors within a specific web page in response to input device actions, or at specified timing events. In this case, the dynamic behavior occurs within the presentation. The client-side content is generated on the user's local computer system. Such web pages use presentation technology called rich interfaced pages. Client-side scripting languages like JavaScript or ActionScript, used for Dynamic HTML (DHTML) and Flash technologies respectively, are frequently used to orchestrate media types (sound, animations, changing text, etc.) of the presentation. Client-side scripting also allows the use of remote scripting, a technique by which the DHTML page requests additional information from a server, using a hidden frame, XMLHttpRequests, or a Web service. The first public use of JavaScript was in 1995, when the language was implemented in Netscape Navigator 2, standardized as ECMAScript two years later. Example The client-side content is generated on the client's computer. The web browser retrieves a page from the server, then processes the code embedded in the page (typically written in JavaScript) and displays the retrieved page's content to the user. The innerHTML property (or write command) can illustrate the client-side dynamic page generation: two distinct pages, A and B, can be regenerated (by an "event response dynamic") as document.innerHTML = A and document.innerHTML = B; or "on load dynamic" by document.write(A) and document.write(B). == Combination technologies == All of the client and server components that collectively build a dynamic web page are called a web application. Web applications manage user interactions, state, security, and performance. Ajax uses a combination of both client-side script
Brain technology
Brain technology, or self-learning know-how systems, defines a technology that employs latest findings in neuroscience. [see also neuro implants] The term was first introduced by the Artificial Intelligence Laboratory in Zurich, Switzerland, in the context of the Roboy project. Brain Technology can be employed in robots, know-how management systems and any other application with self-learning capabilities. In particular, Brain Technology applications allow the visualization of the underlying learning architecture often coined as "know-how maps". == Research and applications == The first demonstrations of BC in humans and animals took place in the 1960s when Grey Walter demonstrated use of non-invasively recorded encephalogram (EEG) signals from a human subject to control a slide projector (Graimann et al., 2010). Soon after Jacques J. Vidal coined the term brain–computer interface (BCI) in 1971, the Defense Advanced Research Projects Agency (DARPA) first starting funding brain–computer interface research and has since funded several brain–computer interface projects. That market is expected to reach a value of $1.72 billion by 2022. Brain–computer interfaces record brain activity, transmit the information out of the body, signal-process the data via algorithms, and convert them into command control signals. In 2012, a landmark study in Nature, led by pioneer Leigh Hochberg, MD, PhD, demonstrated that two people with tetraplegia were able to control robotic arms through thought when connected to the BrainGate neural interface system. The two participants were able to reach for and grasp objects in three-dimensional space, and one participant used the system to serve herself coffee for the first time since becoming paralyzed nearly 15 years prior. And in October 2020, two patients were able to wirelessly control an operating system to text, email, shop and bank using direct thought through the Stentrode brain computer interface (Journal of NeuroInterventional Surgery) in a study led by Thomas Oxley. This was the first time a brain–computer interface was implanted via the patient's blood vessels, eliminating the need for open brain surgery. Currently a number of groups are exploring a range of experimental devices using brain–computer interfaces, which have the potential to fundamentally change the way of life for patients with paralysis and a wide range of neurological disorders. These include: as Elon Musk, Facebook, and the University of California in San Francisco. The systems. This technology is also being explored as a neuromodulation device and may ultimately help diagnose and treat a range of brain pathologies, such as epilepsy and Parkinson's disease.
Contact cleaner
Contact cleaner, also known as switch-cleaner, is any of various chemicals, or mixtures of chemicals, intended to remove or prevent the build-up of oxides or other unwanted substances on the conductive surfaces of connectors, switches, and other electronic components with moving surface-contacts, and thus reduce the contact resistance encountered. The use of contact cleaner can help to minimize the wetting current across a pair of contacts. An example of a simple contact cleaner is isopropyl alcohol Some contact cleaners are designed to evaporate completely and rapidly, leaving no residue. Others may contain lubricants. Lubricants themselves should not necessarily be used as contact cleaners, especially if they are designed to leave an unsuitable residue. However, appropriate lubricants may work well as contact cleaners.