Outline of computer security

The following outline is provided as an overview of and topical guide to computer security: Computer security (also cybersecurity, digital security, or information technology (IT) security) is a subdiscipline within the field of information security. It focuses on protecting computer software, systems, and networks from threats that can lead to unauthorized information disclosure, theft, or damage to hardware, software, or data, as well as to the disruption or misdirection of the services they provide. The growing significance of computer security reflects the increasing dependence on computer systems, the Internet, and evolving wireless network standards. This reliance has expanded with the proliferation of smart devices, including smartphones, televisions, and other components of the Internet of things (IoT). (yes) == Essence of computer security == Computer security can be described as all of the following: a branch of security Network security application security == Areas of computer security == Access control – selective restriction of access to a place or other resource. The act of accessing may mean consuming, entering, or using. Permission to access a resource is called authorization. Computer access control – includes authorization, authentication, access approval, and audit. Authentication Knowledge-based authentication Integrated Windows Authentication Password Password length parameter Secure Password Authentication Secure Shell Kerberos (protocol) SPNEGO NTLMSSP AEGIS SecureConnect TACACS Cyber security and countermeasure Device fingerprint Physical security – protecting property and people from damage or harm (such as from theft, espionage, or terrorist attacks). It includes security measures designed to deny unauthorized access to facilities, (such as a computer room), equipment (such as your computer), and resources (like the data storage devices, and data, in your computer). If a computer gets stolen, then the data goes with it. In addition to theft, physical access to a computer allows for ongoing espionage, like the installment of a hardware keylogger device, and so on. Data security – protecting data, such as a database, from destructive forces and the unwanted actions of unauthorized users. Information privacy – relationship between collection and dissemination of data, technology, the public expectation of privacy, and the legal and political issues surrounding them. Privacy concerns exist wherever personally identifiable information or other sensitive information is collected and stored – in digital form or otherwise. Improper or non-existent disclosure control can be the root cause for privacy issues. Internet privacy – involves the right or mandate of personal privacy concerning the storing, repurposing, provision to third parties, and displaying of information pertaining to oneself via the Internet. Privacy can entail either Personally Identifying Information (PII) or non-PII information such as a site visitor's behavior on a website. PII refers to any information that can be used to identify an individual. For example, age and physical address alone could identify who an individual is without explicitly disclosing their name, as these two factors relate to a specific person. Mobile security – security pertaining to smartphones, especially with respect to the personal and business information stored on them. Network security – provisions and policies adopted by a network administrator to prevent and monitor unauthorized access, misuse, modification, or denial of a computer network and network-accessible resources. Network security involves the authorization of access to data in a network, which is controlled by the network administrator. Network Security Toolkit Internet security – computer security specifically related to the Internet, often involving browser security but also network security on a more general level as it applies to other applications or operating systems on a whole. Its objective is to establish rules and measures to use against attacks over the Internet. The Internet represents an insecure channel for exchanging information leading to a high risk of intrusion or fraud, such as phishing. Different methods have been used to protect the transfer of data, including encryption. World Wide Web Security – dealing with the vulnerabilities of users who visit websites. Cybercrime on the Web can include identity theft, fraud, espionage and intelligence gathering. For criminals, the Web has become the preferred way to spread malware. == Computer security threats == Methods of Computer Network Attack and Computer Network Exploitation Social engineering is a frequent method of attack, and can take the form of phishing, or spear phishing in the corporate or government world, as well as counterfeit websites. Password sharing and insecure password practices Poor patch management Computer crime – Computer criminals – Hackers – in the context of computer security, a hacker is someone who seeks and exploits weaknesses in a computer system or computer network. Password cracking – Software cracking – Script kiddies – List of computer criminals – Identity theft – Computer malfunction – Operating system failure and vulnerabilities Hard disk drive failure – occurs when a hard disk drive malfunctions and the stored information cannot be accessed with a properly configured computer. A disk failure may occur in the course of normal operation, or due to an external factor such as exposure to fire or water or high magnetic fields, or suffering a sharp impact or environmental contamination, which can lead to a head crash. Data recovery from a failed hard disk is problematic and expensive. Backups are essential Computer and network surveillance – Man in the Middle Loss of anonymity – when one's identity becomes known. Identification of people or their computers allows their activity to be tracked. For example, when a person's name is matched with the IP address they are using, their activity can be tracked thereafter by monitoring the IP address. HTTP Cookie Local Shared Object Web bug Spyware Adware Cyber spying – obtaining secrets without the permission of the holder of the information (personal, sensitive, proprietary or of classified nature), from individuals, competitors, rivals, groups, governments and enemies for personal, economic, political or military advantage using methods on the Internet, networks or individual computers through the use of cracking techniques and malicious software including Trojan horses and spyware. It may be done online from by professionals sitting at their computer desks on bases in far away countries, or it may involve infiltration at home by computer trained conventional spies and moles, or it may be the criminal handiwork of amateur malicious hackers, software programmers, or thieves. Computer and network eavesdropping Lawful Interception War Driving Packet analyzer (aka packet sniffer) – mainly used as a security tool (in many ways, including for the detection of network intrusion attempts), packet analyzers can also be used for spying, to collect sensitive information (e.g., login details, cookies, personal communications) sent through a network, or to reverse engineer proprietary protocols used over a network. One way to protect data sent over a network such as the Internet is by using encryption software. Cyberwarfare – Exploit – piece of software, a chunk of data, or a sequence of commands that takes advantage of a bug, glitch or vulnerability in order to cause unintended or unanticipated behavior to occur on computer software, hardware, or something electronic (usually computerized). Such behavior frequently includes things like gaining control of a computer system, allowing privilege escalation, or a denial-of-service attack. Trojan Computer virus Computer worm Denial-of-service attack – an attempt to make a machine or network resource unavailable to its intended users, usually consisting of efforts to temporarily or indefinitely interrupt or suspend services of a host connected to the Internet. One common method of attack involves saturating the target machine with external communications requests, so much so that it cannot respond to legitimate traffic, or responds so slowly as to be rendered essentially unavailable. Distributed denial-of-service attack (DDoS) – DoS attack sent by two or more persons. Hacking tool Malware Computer virus Computer worm Keylogger – program that does keystroke logging, which is the action of recording (or logging) the keys struck on a keyboard, typically in a covert manner so that the person using the keyboard is unaware that their actions are being monitored. There are also HID spoofing hardware keyloggers, like a USB device inserting stored keystores when connected. Rootkit – stealthy type of software, typically malicious, designed to hide the existence of certain processes or programs from normal methods of detection and enable contin

Flask (web framework)

Flask is a micro web framework written in Python. It is classified as a microframework because it does not require particular tools or libraries. It has no database abstraction layer, form validation, or any other components where pre-existing third-party libraries provide common functions. However, Flask supports extensions that can add application features as if they were implemented in Flask itself. Extensions exist for object-relational mappers, form validation, upload handling, various open authentication technologies and several common framework related tools. Applications that use the Flask framework include Pinterest and LinkedIn. == History == Flask was created by Armin Ronacher of Pocoo, an international group of Python enthusiasts formed in 2004. According to Ronacher, the idea was originally an April Fool's joke that was popular enough to make into a serious application. The name is a play on the earlier Bottle framework. When Ronacher and Georg Brandl created a bulletin board system written in Python in 2004, the Pocoo projects Werkzeug and Jinja were developed. In April 2016, the Pocoo team was disbanded and development of Flask and related libraries passed to the newly formed Pallets project. Flask has become popular among Python enthusiasts. As of October 2020, it has the second-most number of stars on GitHub among Python web-development frameworks, only slightly behind Django, and was voted the most popular web framework in the Python Developers Survey for years between and including 2018 and 2022. == Components == The microframework Flask is part of the Pallets Projects (formerly Pocoo), and based on several others of them, all under a BSD license. === Werkzeug === Werkzeug (German for "tool") is a utility library for the Python programming language for Web Server Gateway Interface (WSGI) applications. Werkzeug can instantiate objects for request, response, and utility functions. It can be used as the basis for a custom software framework and supports Python 2.7 and 3.5 and later. === Jinja === Jinja, also by Ronacher, is a template engine for the Python programming language. Similar to the Django web framework, it handles templates in a sandbox. === MarkupSafe === MarkupSafe is a string handling library for the Python programming language. The eponymous MarkupSafe type extends the Python string type and marks its contents as "safe"; combining MarkupSafe with regular strings automatically escapes the unmarked strings, while avoiding double escaping of already marked strings. === ItsDangerous === ItsDangerous is a safe data serialization library for the Python programming language. It is used to store the session of a Flask application in a cookie without allowing users to tamper with the session contents. === Click === Click is a Python package used by Flask to create command-line interfaces (CLI) by providing a simple and composable way to define commands, arguments, and options. == Features == Development server and debugger Integrated support for unit testing RESTful request dispatching Uses Jinja templating Support for secure cookies (client side sessions) 100% WSGI 1.0 compliant Unicode-based Complete documentation Google App Engine compatibility Extensions available to extend functionality == Example == The following code shows a simple web application that displays "Hello World!" when visited: === Render Template with Flask === ==== Jinja in HTML for the Render Template ====

Genotypic and phenotypic repair

Genotypic and phenotypic repair are optional components of an evolutionary algorithm (EA). An EA reproduces essential elements of biological evolution as a computer algorithm in order to solve demanding optimization or planning tasks, at least approximately. A candidate solution is represented by a - usually linear - data structure that plays the role of an individual's chromosome. New solution candidates are generated by mutation and crossover operators following the example of biology. These offspring may be defective, which is corrected or compensated for by genotypic or phenotypic repair. == Description == Genotypic repair, also known as genetic repair, is the removal or correction of impermissible entries in the chromosome that violate restrictions. In phenotypic repair, the corrections are only made in the genotype-phenotype mapping and the chromosome remains unchanged. Michalewicz wrote about the importance of restrictions in real-world applications: "In general, constraints are an integral part of the formulation of any problem". Restriction violations are application-specific and therefore it depends on the current problem whether and which type of repair is useful. They can usually also be treated by a correspondingly extended evaluation and it depends on the problem which measures are possible and which is the most suitable. If a phenotypic repair is feasible, then it is usually the most efficient compared to the other measures. A survey on repair methods used as constraint handling techniques can be found in. Violations of the range limits of genes should be avoided as far as possible by the formulation of the genome. If this is not possible or if restrictions within the search space defined by the genome are involved, their violations are usually handled by the evaluation. This can be done, for example, by penalty functions that lower the fitness. Repair is often also required for combinatorial tasks. The application of a 1- or n-point crossover operator can, for example, lead to genes being missing in one of the child genomes that are present in duplicate in the other. In this case, a suitable genotypic repair measure is to move the surplus genes to the other genome in a positional manner. The use of the aforementioned operators in combinatorial tasks has also proven to be useful in combination with crossover types specially developed for permutations, at least for certain problems. Particularly in combinatorial problems, it has been observed that genotypic repair can promote premature convergence to a suboptimum, but can also significantly accelerate a successful search. Studies on various tasks have shown that this is application-dependent. An effective measure to avoid premature convergence is generally the use of structured populations instead of the usual panmictic ones. Sequence restrictions play a role in many scheduling tasks, for example when it comes to planning workflows. If, for example, it is specified that step A must be carried out before step B and the gene of step B is located before the gene of A in the chromosome, then there is an impermissible gene sequence. This is because the scheduling operation of step B requires the planned end of step A for correct scheduling, but this is not yet scheduled at the time gene B is processed. The problem can be solved in two ways: The scheduling operation of step B is postponed until the gene from step A has been processed. The genome remains unchanged and the repair only influences the genotype-phenotype mapping. Since only the phenotype is changed, this is referred to as phenotypic repair. If, on the other hand, the gene of step B is moved behind the gene of step A, this is a genotypic repair. The same applies to the alternative shift of gene A in front of gene B. In this case, genotypic repair has the disadvantage that it prevents a meaningful restructuring of the gene sequence in the chromosome if this requires several intermediate steps (mutations) that at least partially violate restrictions.

FERET (facial recognition technology)

The Facial Recognition Technology (FERET) program was a government-sponsored project that aimed to create a large, automatic face-recognition system for intelligence, security, and law enforcement purposes. The program began in 1993 under the combined leadership of Dr. Harry Wechsler at George Mason University (GMU) and Dr. Jonathon Phillips at the Army Research Laboratory (ARL) in Adelphi, Maryland and resulted in the development of the Facial Recognition Technology (FERET) database. The goal of the FERET program was to advance the field of face recognition technology by establishing a common database of facial imagery for researchers to use and setting a performance baseline for face-recognition algorithms. Potential areas where this face-recognition technology could be used include: Automated searching of mug books using surveillance photos Controlling access to restricted facilities or equipment Checking the credentials of personnel for background and security clearances Monitoring airports, border crossings, and secure manufacturing facilities for particular individuals Finding and logging multiple appearances of individuals over time in surveillance videos Verifying identities at ATM machines Searching photo ID records for fraud detection The FERET database has been used by more than 460 research groups and is currently managed by the National Institute of Standards and Technology (NIST). By 2017, the FERET database has been used to train artificial intelligence programs and computer vision algorithms to identify and sort faces. == History == The origin of facial recognition technology is largely attributed to Woodrow Wilson Bledsoe and his work in the 1960s, when he developed a system to identify faces from a database of thousands of photographs. The FERET program first began as a way to unify a large body of face-recognition technology research under a standard database. Before the program's inception, most researchers created their own facial imagery database that was attuned to their own specific area of study. These personal databases were small and usually consisted of images from less than 50 individuals. The only notable exceptions were the following: Alex Pentland’s database of around 7500 facial images at the Massachusetts Institute of Technology (MIT) Joseph Wilder's database of around 250 individuals at Rutgers University Christoph von der Malsburg’s database of around 100 facial images at the University of Southern California (USC) The lack of a common database made it difficult to compare the results of face recognition studies in the scientific literature because each report involved different assumptions, scoring methods, and images. Most of the papers that were published did not use images from a common database nor follow a standard testing protocol. As a result, researchers were unable to make informed comparisons between the performances of different face-recognition algorithms. In September 1993, the FERET program was spearheaded by Dr. Harry Wechsler and Dr. Jonathon Phillips under the sponsorship of the U.S. Department of Defense Counterdrug Technology Development Program through DARPA with ARL serving as technical agent. === Phase I === The first facial images for the FERET database were collected from August 1993 to December 1994, a time period known as Phase I. The pictures were initially taken with a 35-mm camera at both GMU and ARL facilities, and the same physical setup was used in each photography session to keep the images consistent. For each individual, the pictures were taken in sets, including two frontal views, a right and left profile, a right and left quarter profile, a right and left half profile, and sometimes at five extra locations. Therefore, a set of images consisted of 5 to 11 images per person. At the end of Phase I, the FERET database had collected 673 sets of images, resulting in over 5000 total images. At the end of Phase I, five organizations were given the opportunity to test their face-recognition algorithm on the newly created FERET database in order to compare how they performed against each other. There five principal investigators were: MIT, led by Alex Pentland Rutgers University, led by Joseph Wilder The Analytic Science Company (TASC), led by Gale Gordon The University of Illinois at Chicago (UIC) and the University of Illinois at Urbana-Champaign, led by Lewis Sadler and Thomas Huang USC, led by Christoph von der Malsburg During this evaluation, three different automatic tests were given to the principal investigators without human intervention: The large gallery test, which served to baseline how algorithms performed against a database when it has not been properly tuned. The false-alarm test, which tested how well the algorithm monitored an airport for suspected terrorists. The rotation test, which measured how well the algorithm performed when the images of an individual in the gallery had different poses compared to those in the probe set. For most of the test trials, the algorithms developed by USC and MIT managed to outperform the other three algorithms for the Phase I evaluation. === Phase II === Phase II began after Phase I, and during this time, the FERET database acquired more sets of facial images. By the start of the Phase II evaluation in March 1995, the database contained 1109 sets of images for a total of 8525 images of 884 individuals. During the second evaluation, the same algorithms from the Phase I evaluation were given a single test. However, the database now contained significantly more duplicate images (463, compared to the previous 60), making the test more challenging. === Phase III === Afterwards, the FERET program entered Phase III where another 456 sets of facial images were added to the database. The Phase III evaluation, which took place in September 1996, aimed to not only gauge the progress of the algorithms since the Phase I assessment but also identify the strengths and weaknesses of each algorithm and determine future objectives for research. By the end of 1996, the FERET database had accumulated a total of 14,126 facial images pertaining to 1199 different individuals as well as 365 duplicate sets of images. As a result of the FERET program, researchers were able to establish a common baseline for comparing different face-recognition algorithms and create a large standard database of facial images that is open for research. In 2003, DARPA released a high-resolution, 24-bit color version of the images in the FERET database (existing reference).

Diffusion model

In machine learning, diffusion models, also known as diffusion-based generative models or score-based generative models, are a class of latent variable generative models. A diffusion model consists of two major components: the forward diffusion process, and the reverse sampling process. The goal of diffusion models is to learn a diffusion process for a given dataset, such that the process can generate new elements that are distributed similarly as the original dataset. A diffusion model models data as generated by a diffusion process, whereby a new datum performs a random walk with drift through the space of all possible data. A trained diffusion model can be sampled in many ways, with different efficiency and quality. There are various equivalent formalisms, including Markov chains, denoising diffusion probabilistic models, noise conditioned score networks, and stochastic differential equations. They are typically trained using variational inference. The model responsible for denoising is typically called its "backbone". The backbone may be of any kind, but they are typically U-nets or transformers. As of 2024, diffusion models are mainly used for computer vision tasks, including image denoising, inpainting, super-resolution, image generation, and video generation. These typically involve training a neural network to sequentially denoise images blurred with Gaussian noise. The model is trained to reverse the process of adding noise to an image. After training to convergence, it can be used for image generation by starting with an image composed of random noise, and applying the network iteratively to denoise the image. Diffusion-based image generators have seen widespread commercial interest, such as Stable Diffusion and DALL-E. These models typically combine diffusion models with other models, such as text-encoders and cross-attention modules to allow text-conditioned generation. Other than computer vision, diffusion models have also found applications in natural language processing such as text generation and summarization, sound generation, and reinforcement learning. == Denoising diffusion model == === Non-equilibrium thermodynamics === Diffusion models were introduced in 2015 as a method to train a model that can sample from a highly complex probability distribution. They used techniques from non-equilibrium thermodynamics, especially diffusion. Consider, for example, how one might model the distribution of all naturally occurring photos. Each image is a point in the space of all images, and the distribution of naturally occurring photos is a "cloud" in space, which, by repeatedly adding noise to the images, diffuses out to the rest of the image space, until the cloud becomes all but indistinguishable from a Gaussian distribution N ( 0 , I ) {\displaystyle {\mathcal {N}}(0,I)} . A model that can approximately undo the diffusion can then be used to sample from the original distribution. This is studied in "non-equilibrium" thermodynamics, as the starting distribution is not in equilibrium, unlike the final distribution. The equilibrium distribution is the Gaussian distribution N ( 0 , I ) {\displaystyle {\mathcal {N}}(0,I)} , with pdf ρ ( x ) ∝ e − 1 2 ‖ x ‖ 2 {\displaystyle \rho (x)\propto e^{-{\frac {1}{2}}\|x\|^{2}}} . This is just the Maxwell–Boltzmann distribution of particles in a potential well V ( x ) = 1 2 ‖ x ‖ 2 {\displaystyle V(x)={\frac {1}{2}}\|x\|^{2}} at temperature 1. The initial distribution, being very much out of equilibrium, would diffuse towards the equilibrium distribution, making biased random steps that are a sum of pure randomness (like a Brownian walker) and gradient descent down the potential well. The randomness is necessary: if the particles were to undergo only gradient descent, then they will all fall to the origin, collapsing the distribution. === Denoising Diffusion Probabilistic Model (DDPM) === The 2020 paper proposed the Denoising Diffusion Probabilistic Model (DDPM), which improves upon the previous method by variational inference. ==== Forward diffusion ==== To present the model, some notation is required. β 1 , . . . , β T ∈ ( 0 , 1 ) {\displaystyle \beta _{1},...,\beta _{T}\in (0,1)} are fixed constants. α t := 1 − β t {\displaystyle \alpha _{t}:=1-\beta _{t}} α ¯ t := α 1 ⋯ α t {\displaystyle {\bar {\alpha }}_{t}:=\alpha _{1}\cdots \alpha _{t}} σ t := 1 − α ¯ t {\displaystyle \sigma _{t}:={\sqrt {1-{\bar {\alpha }}_{t}}}} σ ~ t := σ t − 1 σ t β t {\displaystyle {\tilde {\sigma }}_{t}:={\frac {\sigma _{t-1}}{\sigma _{t}}}{\sqrt {\beta _{t}}}} μ ~ t ( x t , x 0 ) := α t ( 1 − α ¯ t − 1 ) x t + α ¯ t − 1 ( 1 − α t ) x 0 σ t 2 {\displaystyle {\tilde {\mu }}_{t}(x_{t},x_{0}):={\frac {{\sqrt {\alpha _{t}}}(1-{\bar {\alpha }}_{t-1})x_{t}+{\sqrt {{\bar {\alpha }}_{t-1}}}(1-\alpha _{t})x_{0}}{\sigma _{t}^{2}}}} N ( μ , Σ ) {\displaystyle {\mathcal {N}}(\mu ,\Sigma )} is the normal distribution with mean μ {\displaystyle \mu } and variance Σ {\displaystyle \Sigma } , and N ( x | μ , Σ ) {\displaystyle {\mathcal {N}}(x|\mu ,\Sigma )} is the probability density at x {\displaystyle x} . A vertical bar denotes conditioning. A forward diffusion process starts at some starting point x 0 ∼ q {\displaystyle x_{0}\sim q} , where q {\displaystyle q} is the probability distribution to be learned, then repeatedly adds noise to it by x t = 1 − β t x t − 1 + β t z t {\displaystyle x_{t}={\sqrt {1-\beta _{t}}}x_{t-1}+{\sqrt {\beta _{t}}}z_{t}} where z 1 , . . . , z T {\displaystyle z_{1},...,z_{T}} are IID (Independent and identically distributed random variables) samples from N ( 0 , I ) {\displaystyle {\mathcal {N}}(0,I)} . The coefficients 1 − β t {\displaystyle {\sqrt {1-\beta _{t}}}} and β t {\displaystyle {\sqrt {\beta _{t}}}} ensure that Var ( X t ) = I {\displaystyle {\mbox{Var}}(X_{t})=I} assuming that Var ( X 0 ) = I {\displaystyle {\mbox{Var}}(X_{0})=I} . The values of β t {\displaystyle \beta _{t}} are chosen such that for any starting distribution of x 0 {\displaystyle x_{0}} , if it has finite second moment, then lim t → ∞ x t | x 0 {\displaystyle \lim _{t\to \infty }x_{t}|x_{0}} converges to N ( 0 , I ) {\displaystyle {\mathcal {N}}(0,I)} . The entire diffusion process then satisfies q ( x 0 : T ) = q ( x 0 ) q ( x 1 | x 0 ) ⋯ q ( x T | x T − 1 ) = q ( x 0 ) N ( x 1 | α 1 x 0 , β 1 I ) ⋯ N ( x T | α T x T − 1 , β T I ) {\displaystyle q(x_{0:T})=q(x_{0})q(x_{1}|x_{0})\cdots q(x_{T}|x_{T-1})=q(x_{0}){\mathcal {N}}(x_{1}|{\sqrt {\alpha _{1}}}x_{0},\beta _{1}I)\cdots {\mathcal {N}}(x_{T}|{\sqrt {\alpha _{T}}}x_{T-1},\beta _{T}I)} or ln ⁡ q ( x 0 : T ) = ln ⁡ q ( x 0 ) − ∑ t = 1 T 1 2 β t ‖ x t − 1 − β t x t − 1 ‖ 2 + C {\displaystyle \ln q(x_{0:T})=\ln q(x_{0})-\sum _{t=1}^{T}{\frac {1}{2\beta _{t}}}\|x_{t}-{\sqrt {1-\beta _{t}}}x_{t-1}\|^{2}+C} where C {\displaystyle C} is a normalization constant and often omitted. In particular, we note that x 1 : T | x 0 {\displaystyle x_{1:T}|x_{0}} is a Gaussian process, which affords us considerable freedom in reparameterization. For example, by standard manipulation with Gaussian process, x t | x 0 ∼ N ( α ¯ t x 0 , σ t 2 I ) {\displaystyle x_{t}|x_{0}\sim N\left({\sqrt {{\bar {\alpha }}_{t}}}x_{0},\sigma _{t}^{2}I\right)} x t − 1 | x t , x 0 ∼ N ( μ ~ t ( x t , x 0 ) , σ ~ t 2 I ) {\displaystyle x_{t-1}|x_{t},x_{0}\sim {\mathcal {N}}({\tilde {\mu }}_{t}(x_{t},x_{0}),{\tilde {\sigma }}_{t}^{2}I)} In particular, notice that for large t {\displaystyle t} , the variable x t | x 0 ∼ N ( α ¯ t x 0 , σ t 2 I ) {\displaystyle x_{t}|x_{0}\sim N\left({\sqrt {{\bar {\alpha }}_{t}}}x_{0},\sigma _{t}^{2}I\right)} converges to N ( 0 , I ) {\displaystyle {\mathcal {N}}(0,I)} . That is, after a long enough diffusion process, we end up with some x T {\displaystyle x_{T}} that is very close to N ( 0 , I ) {\displaystyle {\mathcal {N}}(0,I)} , with all traces of the original x 0 ∼ q {\displaystyle x_{0}\sim q} gone. For example, since x t | x 0 ∼ N ( α ¯ t x 0 , σ t 2 I ) {\displaystyle x_{t}|x_{0}\sim N\left({\sqrt {{\bar {\alpha }}_{t}}}x_{0},\sigma _{t}^{2}I\right)} we can sample x t | x 0 {\displaystyle x_{t}|x_{0}} directly "in one step", instead of going through all the intermediate steps x 1 , x 2 , . . . , x t − 1 {\displaystyle x_{1},x_{2},...,x_{t-1}} . ==== Backward diffusion ==== The key idea of DDPM is to use a neural network parametrized by θ {\displaystyle \theta } . The network takes in two arguments x t , t {\displaystyle x_{t},t} , and outputs a vector μ θ ( x t , t ) {\displaystyle \mu _{\theta }(x_{t},t)} and a matrix Σ θ ( x t , t ) {\displaystyle \Sigma _{\theta }(x_{t},t)} , such that each step in the forward diffusion process can be approximately undone by x t − 1 ∼ N ( μ θ ( x t , t ) , Σ θ ( x t , t ) ) {\displaystyle x_{t-1}\sim {\mathcal {N}}(\mu _{\theta }(x_{t},t),\Sigma _{\theta }(x_{t},t))} . This then gives us a backward diffusion process p θ {\displaystyle p_{\theta }} defined by p θ ( x T ) = N ( x T | 0 , I ) {\displaystyle p_{\theta }(x

Linguatec

The Linguatec Sprachtechnologien GmbH is a language technology provider, specialized in the field of machine translation, speech synthesis and speech recognition. Linguatec was founded in Munich in 1996 and its headquarters are in Pasing. Linguatec has won the European Information Society Technologies Prize three times. On their website, they are now using the online service Voice Reader Web, so that the information can be read out in every language by means of a text-to-speech function. == Core areas == Machine translation The different versions of Personal Translator (seven language pairs) can be used "for home use" or for professional business use in the company network. In addition to this, specialist dictionaries are offered to broaden standard vocabulary. Speech synthesis The Voice Reader text-to-speech program reads in twelve languages: German, British English, American English, French, Quebec French, Spanish, Mexican Spanish, Italian, Dutch, Portuguese, Czech, Chinese. Speech recognition Voice Pro is based on ViaVoice technology from IBM. There are special software programs for doctors and lawyers. == Patents == 2005 pending patent application for a newly developed hybrid technology that uses the intelligence of neural networks for machine translation. == Awards == 2004 European IT Prize for Beyond Babel 2004 test winner Stiftung Warentest – best voice recognition 1998 European IT Prize – applied voice recognition 1996 European IT Prize – automated translation == Studies == 2005 University of Regensburg: Voice Reader user test 2002 Fraunhofer Institute for Industrial Engineering and Organization IAO: user study on the efficiency of machine translation

Dynamic time warping

In time series analysis, dynamic time warping (DTW) is an algorithm for measuring similarity between two temporal sequences, which may vary in speed. For instance, similarities in walking could be detected using DTW, even if one person was walking faster than the other, or if there were accelerations and decelerations during the course of an observation. DTW has been applied to temporal sequences of video, audio, and graphics data — indeed, any data that can be turned into a one-dimensional sequence can be analyzed with DTW. A well-known application has been automatic speech recognition, to cope with different speaking speeds. Other applications include speaker recognition and online signature recognition. It can also be used in partial shape matching applications. In general, DTW is a method that calculates an optimal match between two given sequences (e.g. time series) with certain restriction and rules: Every index from the first sequence must be matched with one or more indices from the other sequence, and vice versa The first index from the first sequence must be matched with the first index from the other sequence (but it does not have to be its only match) The last index from the first sequence must be matched with the last index from the other sequence (but it does not have to be its only match) The mapping of the indices from the first sequence to indices from the other sequence must be monotonically increasing, and vice versa, i.e. if j > i {\displaystyle j>i} are indices from the first sequence, then there must not be two indices l > k {\displaystyle l>k} in the other sequence, such that index i {\displaystyle i} is matched with index l {\displaystyle l} and index j {\displaystyle j} is matched with index k {\displaystyle k} , and vice versa We can plot each match between the sequences 1 : M {\displaystyle 1:M} and 1 : N {\displaystyle 1:N} as a path in a M × N {\displaystyle M\times N} matrix from ( 1 , 1 ) {\displaystyle (1,1)} to ( M , N ) {\displaystyle (M,N)} , such that each step is one of ( 0 , 1 ) , ( 1 , 0 ) , ( 1 , 1 ) {\displaystyle (0,1),(1,0),(1,1)} . In this formulation, we see that the number of possible matches is the Delannoy number. The optimal match is denoted by the match that satisfies all the restrictions and the rules and that has the minimal cost, where the cost is computed as the sum of absolute differences, for each matched pair of indices, between their values. The sequences are "warped" non-linearly in the time dimension to determine a measure of their similarity independent of certain non-linear variations in the time dimension. This sequence alignment method is often used in time series classification. Although DTW measures a distance-like quantity between two given sequences, it doesn't guarantee the triangle inequality to hold. In addition to a similarity measure between the two sequences (a so called "warping path" is produced), by warping according to this path the two signals may be aligned in time. The signal with an original set of points X(original), Y(original) is transformed to X(warped), Y(warped). This finds applications in genetic sequence and audio synchronisation. In a related technique sequences of varying speed may be averaged using this technique see the average sequence section. This is conceptually very similar to the Needleman–Wunsch algorithm. == Implementation == This example illustrates the implementation of the dynamic time warping algorithm when the two sequences s and t are strings of discrete symbols. For two symbols x and y, d ( x , y ) {\displaystyle d(x,y)} is a distance between the symbols, e.g., d ( x , y ) = | x − y | {\displaystyle d(x,y)=|x-y|} . int DTWDistance(s: array [1..n], t: array [1..m]) { DTW := array [0..n, 0..m] for i := 0 to n for j := 0 to m DTW[i, j] := infinity DTW[0, 0] := 0 for i := 1 to n for j := 1 to m cost := d(s[i], t[j]) DTW[i, j] := cost + minimum(DTW[i-1, j ], // insertion DTW[i , j-1], // deletion DTW[i-1, j-1]) // match return DTW[n, m] } where DTW[i, j] is the distance between s[1:i] and t[1:j] with the best alignment. We sometimes want to add a locality constraint. That is, we require that if s[i] is matched with t[j], then | i − j | {\displaystyle |i-j|} is no larger than w, a window parameter. We can easily modify the above algorithm to add a locality constraint (differences marked). However, the above given modification works only if | n − m | {\displaystyle |n-m|} is no larger than w, i.e. the end point is within the window length from diagonal. In order to make the algorithm work, the window parameter w must be adapted so that | n − m | ≤ w {\displaystyle |n-m|\leq w} (see the line marked with () in the code). int DTWDistance(s: array [1..n], t: array [1..m], w: int) { DTW := array [0..n, 0..m] w := max(w, abs(n-m)) // adapt window size () for i := 0 to n for j:= 0 to m DTW[i, j] := infinity DTW[0, 0] := 0 for i := 1 to n for j := max(1, i-w) to min(m, i+w) DTW[i, j] := 0 for i := 1 to n for j := max(1, i-w) to min(m, i+w) cost := d(s[i], t[j]) DTW[i, j] := cost + minimum(DTW[i-1, j ], // insertion DTW[i , j-1], // deletion DTW[i-1, j-1]) // match return DTW[n, m] } == Warping properties == The DTW algorithm produces a discrete matching between existing elements of one series to another. In other words, it does not allow time-scaling of segments within the sequence. Other methods allow continuous warping. For example, Correlation Optimized Warping (COW) divides the sequence into uniform segments that are scaled in time using linear interpolation, to produce the best matching warping. The segment scaling causes potential creation of new elements, by time-scaling segments either down or up, and thus produces a more sensitive warping than DTW's discrete matching of raw elements. == Complexity == The time complexity of the DTW algorithm is O ( N M ) {\displaystyle O(NM)} , where N {\displaystyle N} and M {\displaystyle M} are the lengths of the two input sequences. The 50 years old quadratic time bound was broken in 2016: an algorithm due to Gold and Sharir enables computing DTW in O ( N 2 / log ⁡ log ⁡ N ) {\displaystyle O({N^{2}}/\log \log N)} time and space for two input sequences of length N {\displaystyle N} . This algorithm can also be adapted to sequences of different lengths. Despite this improvement, it was shown that a strongly subquadratic running time of the form O ( N 2 − ϵ ) {\displaystyle O(N^{2-\epsilon })} for some ϵ > 0 {\displaystyle \epsilon >0} cannot exist unless the Strong exponential time hypothesis fails. While the dynamic programming algorithm for DTW requires O ( N M ) {\displaystyle O(NM)} space in a naive implementation, the space consumption can be reduced to O ( min ( N , M ) ) {\displaystyle O(\min(N,M))} using Hirschberg's algorithm. == Fast computation == Fast techniques for computing DTW include PrunedDTW, SparseDTW, FastDTW, and the MultiscaleDTW. A common task, retrieval of similar time series, can be accelerated by using lower bounds such as LB_Keogh, LB_Improved, or LB_Petitjean. However, the Early Abandon and Pruned DTW algorithm reduces the degree of acceleration that lower bounding provides and sometimes renders it ineffective. In a survey, Wang et al. reported slightly better results with the LB_Improved lower bound than the LB_Keogh bound, and found that other techniques were inefficient. Subsequent to this survey, the LB_Enhanced bound was developed that is always tighter than LB_Keogh while also being more efficient to compute. LB_Petitjean is the tightest known lower bound that can be computed in linear time. == Average sequence == Averaging for dynamic time warping is the problem of finding an average sequence for a set of sequences. NLAAF is an exact method to average two sequences using DTW. For more than two sequences, the problem is related to that of multiple alignment and requires heuristics. DBA is currently a reference method to average a set of sequences consistently with DTW. COMASA efficiently randomizes the search for the average sequence, using DBA as a local optimization process. == Supervised learning == A nearest-neighbour classifier can achieve state-of-the-art performance when using dynamic time warping as a distance measure. == Amerced Dynamic Time Warping == Amerced Dynamic Time Warping (ADTW) is a variant of DTW designed to better control DTW's permissiveness in the alignments that it allows. The windows that classical DTW uses to constrain alignments introduce a step function. Any warping of the path is allowed within the window and none beyond it. In contrast, ADTW employs an additive penalty that is incurred each time that the path is warped. Any amount of warping is allowed, but each warping action incurs a direct penalty. ADTW significantly outperforms DTW with windowing when applied as a nearest neighbor classifier on a set of benchmark time series classification tasks. == Alternative approaches == In functional data analysis, time series are regarde