Cobham's theorem is a theorem in combinatorics on words that has important connections with number theory, notably transcendental numbers, and automata theory. Informally, the theorem gives the condition for the members of a set S of natural numbers written in bases b1 and base b2 to be recognised by finite automata. Specifically, consider bases b1 and b2 such that they are not powers of the same integer. Cobham's theorem states that S written in bases b1 and b2 is recognised by finite automata if and only if S differs by a finite set from a finite union of arithmetic progressions. The theorem was proved by Alan Cobham in 1969 and has since given rise to many extensions and generalisations. == Definitions == Let n > 0 {\displaystyle n>0} be an integer. The representation of a natural number n {\textstyle n} in base b {\textstyle b} is the sequence of digits n 0 n 1 ⋯ n h {\displaystyle n_{0}n_{1}\cdots n_{h}} such that n = n 0 + n 1 b + ⋯ + n h b h {\displaystyle n=n_{0}+n_{1}b+\cdots +n_{h}b^{h}} where 0 ≤ n 0 , n 1 , … , n h < b {\displaystyle 0\leq n_{0},n_{1},\ldots ,n_{h} Glow is a fertility awareness and period-tracking app. It is part of a suite of mobile apps focused on women's reproductive health and childcare, which includes Eve by Glow (a dedicated period tracker), Glow Nurture (a pregnancy tracker), and Glow Baby (a baby development tracker). The Glow company also operates an online shop that sells several fertility-related products, including ovulation test strips, pregnancy tests, and wearable breast pumps. In 2024, Glow was reported to have approximately 25 million users across its various apps and community message boards. == History == Glow debuted in August 2013 as an iOS app. It was founded by Michael Huang and Max Levchin and launched with $6 million in Series A funding from venture capital firms Founders Fund and Andreesen Horowitz. In 2014, Glow raised an additional $17 million in Series B funding, with Formation 8 joining existing investors. In 2015, Glow launched Ruby, an app dedicated to sexual health. That year, Wired reported that the company had added features to their apps allowing men to monitor their fertility. Glow subsequently released an additional set of apps focused on pregnancy tracking and infant development. In 2016, Glow reported that it had a total of approximately 3 million users; by 2018, this had grown to 15 million. Vox described it as one of the “big two” period and fertility tracking apps and the one that had started the “boom” in the femtech space. == Application and features == Glow was initially described as a fertility application that applied data-driven methods to menstrual and ovulation tracking. Core features include cycle logging, ovulation prediction, and symptom tracking. The app also provides educational content related to reproductive health and childcare, as well as a set of online message boards that allow individuals to share experiences and seek peer support. == Privacy and legal issues == Glow has received significant media attention for its privacy and security practices. In 2016, Consumer Reports identified potential exploits in the Glow app that they claimed could have exposed private user data to hackers. Glow subsequently reported that it had fixed the vulnerabilities and told The Washington Post they had no evidence that user data had been compromised. In September 2020, the California Attorney General announced a settlement with Glow related to Consumer Reports’ findings, which included a $250,000 civil penalty. Following the US Supreme Court's 2022 Dobbs v. Jackson ruling, which legalized state-level bans on abortion, Glow (and other fertility trackers, such as Clue and Flo) came under additional scrutiny over concerns that user data on abortions could be reported to law enforcement. After this surge of media interest, a research team affiliated with the University of New South Wales conducted an investigation into the privacy practices of several popular fertility apps, including Glow. Their review of Glow was mixed, noting that they provided several privacy settings and de-identified sensitive data, but that user information could still be disclosed in the future if the app was sold. Glow rejected that claim, telling the Australian Associated Press that it "did not share" personal data. The company also cited several internal security measures it had implemented and its apps' offline data protection setting, which allows users to permanently delete their health-related data. == Reception == In 2014, Fast Company reported that 20,000 women had used Glow to conceive. Later that year, The Guardian included Glow Nurture on its list of the best iPhone apps of 2014. Media coverage often praised Glow's array of menstrual tracking options, although some reviews also noted that fertility apps are not birth control tools and cautioned against relying on them for that purpose. In 2019, Cosmopolitan singled Glow's community of users as one of its standout features. ViEWER, the Virtual Environment Workbench for Education and Research, is a proprietary, freeware computer program for Microsoft Windows written by researchers at the University of Idaho for the study of visual perception and complex immersive three-dimensional environments. It was created using C++ and OpenGL, and has been used by Dr. Brian Dyre, Dr. Steffen Werner, Dr. Ernesto Bustamante, Dr. Ben Barton, and their undergraduate and graduate researchers in visual perception, signal detection, and child-safety experiments. Seam carving (or liquid rescaling) is an algorithm for content-aware image resizing, developed by Shai Avidan, of Mitsubishi Electric Research Laboratories (MERL), and Ariel Shamir, of the Interdisciplinary Center and MERL. It functions by establishing a number of seams (paths of least importance) in an image and automatically removes seams to reduce image size or inserts seams to extend it. Seam carving also allows manually defining areas in which pixels may not be modified, and features the ability to remove whole objects from photographs. The purpose of the algorithm is image retargeting, which is the problem of displaying images without distortion on media of various sizes (cell phones, projection screens) using document standards, like HTML, that already support dynamic changes in page layout and text but not images. Image Retargeting was invented by Vidya Setlur, Saeko Takage, Ramesh Raskar, Michael Gleicher and Bruce Gooch in 2005. The work by Setlur et al. won the 10-year impact award in 2015. == Seams == Seams can be either vertical or horizontal. A vertical seam is a path of pixels connected from top to bottom in an image with one pixel in each row. A horizontal seam is similar with the exception of the connection being from left to right. The importance/energy function values a pixel by measuring its contrast with its neighbor pixels. == Process == The below example describes the process of seam carving: The seams to remove depends only on the dimension (height or width) one wants to shrink. It is also possible to invert step 4 so the algorithm enlarges in one dimension by copying a low energy seam and averaging its pixels with its neighbors. === Computing seams === Computing a seam consists of finding a path of minimum energy cost from one end of the image to another. This can be done via Dijkstra's algorithm, dynamic programming, greedy algorithm or graph cuts among others. ==== Dynamic programming ==== Dynamic programming is a programming method that stores the results of sub-calculations in order to simplify calculating a more complex result. Dynamic programming can be used to compute seams. If attempting to compute a vertical seam (path) of lowest energy, for each pixel in a row we compute the energy of the current pixel plus the energy of one of the three possible pixels above it. The images below depict a DP process to compute one optimal seam. Each square represents a pixel, with the top-left value in red representing the energy value of that pixel. The value in black represents the cumulative sum of energies leading up to and including that pixel. The energy calculation is trivially parallelized for simple functions. The calculation of the DP array can also be parallelized with some interprocess communication. However, the problem of making multiple seams at the same time is harder for two reasons: the energy needs to be regenerated for each removal for correctness and simply tracing back multiple seams can form overlaps. Avidan 2007 computes all seams by removing each seam iteratively and storing an "index map" to record all the seams generated. The map holds a "nth seam" number for each pixel on the image, and can be used later for size adjustment. If one ignores both issues however, a greedy approximation for parallel seam carving is possible. To do so, one starts with the minimum-energy pixel at one end, and keep choosing the minimum energy path to the other end. The used pixels are marked so that they are not picked again. Local seams can also be computed for smaller parts of the image in parallel for a good approximation. == Issues == The algorithm may need user-provided information to reduce errors. This can consist of painting the regions which are to be preserved. With human faces it is possible to use face detection. Sometimes the algorithm, by removing a low energy seam, may end up inadvertently creating a seam of higher energy. The solution to this is to simulate a removal of a seam, and then check the energy delta to see if the energy increases (forward energy). If it does, prefer other seams instead. == Implementations == Adobe Systems acquired a non-exclusive license to seam carving technology from MERL, and implemented it as a feature in Photoshop CS4, where it is called Content Aware Scaling. As the license is non-exclusive, other popular computer graphics applications (e. g. GIMP, digiKam, and ImageMagick) as well as some stand-alone programs (e. g. iResizer) also have implementations of this technique, some of which are released as free and open source software. There also exists an implementation for webpages. == Improvements and extensions == Better energy function and application to video by introducing 2D (time+1D) seams. Faster implementation on GPU. Application of this forward energy function to static images. Multi-operator: Combine with cropping and scaling. Much faster removal of multiple seams. Removing seams through neural deformation fields to extend to continuous domains like 3D scenes. A 2010 review of eight image retargeting methods found that seam carving produced output that was ranked among the worst of the tested algorithms. It was, however, a part of one of the highest-ranking algorithms: the multi-operator extension mentioned above (combined with cropping and scaling). The following outline is provided as an overview of and topical guide to automation: Automation – use of control systems and information technologies to reduce the need for human work in the production of goods and services. In the scope of industrialization, automation is a step beyond mechanization. == Essence of automation == Control system – a device, or set of devices to manage, command, direct or regulate the behavior of other devices or systems. Industrial control system (ICS) – encompasses several types of control systems used in industrial production, including supervisory control and data acquisition (SCADA) systems, distributed control systems (DCS), and other smaller control system configurations such as skid-mounted programmable logic controllers (PLC) often found in industrial sectors and critical infrastructures. Industrialization – period of social and economic change that transforms a human group from an agrarian society into an industrial one. Numerical control (NC) – refers to the automation of machine tools that are operated by abstractly programmed commands encoded on a storage medium, as opposed to controlled manually via handwheels or levers, or mechanically automated via cams alone. Robotics – the branch of technology that deals with the design, construction, operation, structural disposition, manufacture and application of robots and computer systems for their control, sensory feedback, and information processing. == Branches of automation == === General purpose === Autonomous automation – autonomous software agents to adapt the controllers of computer controlled industrial machinery and processes Banking automation Broadcast automation Building automation – advanced functionality provided by the control system of a building. A building automation system (BAS) is an example of a distributed control system. Home automation – control system of a home. Office automation – the varied computer machinery and software used to digitally create, collect, store, manipulate, and relay office information needed for accomplishing basic tasks such as business process automation and robotic process automation. Console automation Database automation Integrated library system Laboratory automation === Specific purpose === Automated attendant Automated guided vehicle Autonomous mobile robot Automated highway system Automated pool cleaner Automated teller machine Automatic painting (robotic) Pop music automation Remotely operated vehicle Robotic lawn mower Telephone switchboard Vending machine == Fields contributing to automation == Cybernetics – the interdisciplinary study of the structure of regulatory systems. Cognitive science – interdisciplinary scientific study of the mind and its processes. It examines what cognition is, what it does and how it works. Robotics – the branch of technology that deals with the design, construction, operation, structural disposition, manufacture and application of robots and computer systems for their control, sensory feedback, and information processing. == History of automation == History of mass production – Prerequisites of mass production were interchangeable parts, machine tools and power, especially in the form of electricity. Mass production was popularized in the 1910s and 1920s by Henry Ford's Ford Motor Company, which introduced electric motors to the then-well-known technique of chain or sequential production. History of home automation == Automated machines == Machine to Machine OLE for process control (OPC) Process control – a statistics and engineering discipline that deals with architectures, mechanisms and algorithms for maintaining the output of a specific process within a desired range. Run Book Automation (RBA) Robot – a mechanical or virtual intelligent agent that can perform tasks automatically or with guidance, typically by remote control. == Automated machine components == Artificial intelligence – the intelligence of machines and the branch of computer science that aims to create it. Friendly artificial intelligence – an artificial intelligence that has a positive rather than negative effect on humanity, and the field of knowledge required to build such an artificial intelligence. === Automation tools === Artificial neural network (ANN) – mathematical model or computational model that is inspired by the structure or functional aspects of biological neural networks. Human machine interface (HMI) – operator level local control panel that monitors field devices Laboratory information management system (LIMS) – software package that offers a set of key features that support a modern laboratory's operations. Industrial control system – encompasses several types of control systems used in industrial production, including supervisory control and data acquisition (SCADA) systems, distributed control systems (DCS), and other smaller control system configurations such as skid-mounted programmable logic controllers (PLC) often found in the industrial sectors and critical infrastructures. Distributed control system (DCS) – control system usually of a manufacturing system, process or any kind of dynamic system, in which the controller elements are not central in location (like the brain) but are distributed throughout the system with each component sub-system controlled by one or more controllers. Manufacturing execution system (MES) – system that manages manufacturing operations in a factory, including management of resources, scheduling production processes, dispatching production orders, execution of production orders, etc. Programmable automation controller (PAC) – digital computer used for automation of electromechanical processes, such as control of machinery on factory assembly lines, amusement rides, or light fixtures. Programmable logic controller (PLC)A Programmable Logic Controller, PLC or Programmable Controller is a digital computer used for automation of electromechanical processes, such as control of machinery on factory assembly lines, amusement rides, or light fixtures. The abbreviation "PLC" and the term "Programmable Logic Controller" are registered trademarks of the Allen-Bradley Company (Rockwell Automation). PLCs are used in many industries and machines. Unlike general-purpose computers, the PLC is designed for multiple inputs and output arrangements, extended temperature ranges, immunity to electrical noise, and resistance to vibration and impact. Programs to control machine operation are typically stored in battery-backed-up or non-volatile memory. A PLC is an example of a hard real time system since output results must be produced in response to input conditions within a limited time, otherwise unintended operation will result. Supervisory control and data acquisition (SCADA) – generally refers to industrial control systems (ICS): computer systems that monitor and control industrial, infrastructure, or facility-based processes, as described below: Industrial processes include those of manufacturing, production, power generation, fabrication, and refining, and may run in continuous, batch, repetitive, or discrete modes. Simulation § Engineering Technology simulation or Process simulation == Social movements == Automation-related social movement – a movement that advocates semi- or fully automatic systems to provide for human needs globally. For example, automation of farming and food distribution throughout the world so that no one will go hungry. One goal is to automate all mundane labor, to free humans to engage in more creative activities (or less work). The Technocracy movement – social movement active from the Great Depression (1930s) to date that proposes replacing politicians and business people with scientists and engineers who have the technical expertise to manage the economy. The Zeitgeist Movement – movement advocating the replacement of the market economy with an economy in which all resources are equitably, commonly and sustainably shared. == Automation in the future == Android – a robot or synthetic organism designed to look and act like a human, and with a body having a flesh-like resemblance Technological singularity – the hypothetical future emergence of greater-than-human intelligence through technological means Semi-automation – using a centralized computer controller to orchestrate the activities of man and machine. == Automation-related publications == IEEE Spectrum – the flagship publication of the Institute of Electrical and Electronics Engineers (IEEE), explores the development, applications and implications of new technologies, and provides a forum for understanding, discussion and leadership in these areas. IEEE Transactions on Information Theory – peer-reviewed scientific journal published by the Institute of Electrical and Electronics Engineers (IEEE), focused on the study of information theory, the mathematics of communications, including computer communications, robotics communications, etc. IEEE Transactions on Control S Ontology learning (ontology extraction, ontology augmentation generation, ontology generation, or ontology acquisition) is the automatic or semi-automatic creation of ontologies, including extracting the corresponding domain's terms and the relationships between the concepts that these terms represent from a corpus of natural language text, and encoding them with an ontology language for easy retrieval. As building ontologies manually is extremely labor-intensive and time-consuming, there is great motivation to automate the process. Typically, the process starts by extracting terms and concepts or noun phrases from plain text using linguistic processors such as part-of-speech tagging and phrase chunking. Then statistical or symbolic techniques are used to extract relation signatures, often based on pattern-based or definition-based hypernym extraction techniques. == Procedure == Ontology learning (OL) is used to (semi-)automatically extract whole ontologies from natural language text. The process is usually split into the following eight tasks, which are not all necessarily applied in every ontology learning system. === Domain terminology extraction === During the domain terminology extraction step, domain-specific terms are extracted, which are used in the following step (concept discovery) to derive concepts. Relevant terms can be determined, e.g., by calculation of the TF/IDF values or by application of the C-value / NC-value method. The resulting list of terms has to be filtered by a domain expert. In the subsequent step, similarly to coreference resolution in information extraction, the OL system determines synonyms, because they share the same meaning and therefore correspond to the same concept. The most common methods therefore are clustering and the application of statistical similarity measures. === Concept discovery === In the concept discovery step, terms are grouped to meaning bearing units, which correspond to an abstraction of the world and therefore to concepts. The grouped terms are these domain-specific terms and their synonyms, which were identified in the domain terminology extraction step. === Concept hierarchy derivation === In the concept hierarchy derivation step, the OL system tries to arrange the extracted concepts in a taxonomic structure. This is mostly achieved with unsupervised hierarchical clustering methods. Because the result of such methods is often noisy, a supervision step, e.g., user evaluation, is added. A further method for the derivation of a concept hierarchy exists in the usage of several patterns that should indicate a sub- or supersumption relationship. Patterns like “X, that is a Y” or “X is a Y” indicate that X is a subclass of Y. Such pattern can be analyzed efficiently, but they often occur too infrequently to extract enough sub- or supersumption relationships. Instead, bootstrapping methods are developed, which learn these patterns automatically and therefore ensure broader coverage. === Learning of non-taxonomic relations === In the learning of non-taxonomic relations step, relationships are extracted that do not express any sub- or supersumption. Such relationships are, e.g., works-for or located-in. There are two common approaches to solve this subtask. The first is based upon the extraction of anonymous associations, which are named appropriately in a second step. The second approach extracts verbs, which indicate a relationship between entities, represented by the surrounding words. The result of both approaches need to be evaluated by an ontologist to ensure accuracy. === Rule discovery === During rule discovery, axioms (formal description of concepts) are generated for the extracted concepts. This can be achieved, e.g., by analyzing the syntactic structure of a natural language definition and the application of transformation rules on the resulting dependency tree. The result of this process is a list of axioms, which, afterwards, is comprehended to a concept description. This output is then evaluated by an ontologist. === Ontology population === At this step, the ontology is augmented with instances of concepts and properties. For the augmentation with instances of concepts, methods based on the matching of lexico-syntactic patterns are used. Instances of properties are added through the application of bootstrapping methods, which collect relation tuples. === Concept hierarchy extension === In this step, the OL system tries to extend the taxonomic structure of an existing ontology with further concepts. This can be performed in a supervised manner with a trained classifier or in an unsupervised manner via the application of similarity measures. === Frame and Event detection === During frame/event detection, the OL system tries to extract complex relationships from text, e.g., who departed from where to what place and when. Approaches range from applying SVM with kernel methods to semantic role labeling (SRL) to deep semantic parsing techniques. == Tools == Dog4Dag (Dresden Ontology Generator for Directed Acyclic Graphs) is an ontology generation plugin for Protégé 4.1 and OBOEdit 2.1. It allows for term generation, sibling generation, definition generation, and relationship induction. Integrated into Protégé 4.1 and OBO-Edit 2.1, DOG4DAG allows ontology extension for all common ontology formats (e.g., OWL and OBO). Limited largely to EBI and Bio Portal lookup service extensions. Light Scanning Photomacrography (LSP), also known as Scanning Light Photomacrography (SLP) or Deep-Field Photomacrography, is a photographic film technique that allows for high magnification light imaging with exceptional depth of field (DOF). This method overcomes the limitations of conventional macro photography, which typically only keeps a portion of the subject in acceptable focus at high magnifications. == Historical background == The principles of LSP were first documented in the early 1960s by Dan McLachlan Jr., who highlighted its capability for extreme focal depth in microscopy and in 1968 patented the process. The technique was revived and further developed in the 1980s by photographers such as Darwin Dale and Nile Root, a faculty member at the Rochester Institute of Technology. In the early 1990s, William Sharp and Charles Kazilek, both researchers at Arizona State University, also published articles describing their technique and system setup for capturing SLP images. == Predecessor to stack image photography == Light Scanning Photomacrography offered a powerful analog tool for high-detail imaging in the age of film photography. It provided a comprehensive depth of field, making it invaluable in scientific and biomedical photography. As technology and techniques continue to evolve, LSP has been replaced by digital image focus stacking. This technique uses a collection of images captured in series at different focal depths, which are then processed using computer software to create a single image with a greater focus depth than any single image. == LSP technique and results == LSP involves the use of a thin plane of light that scans across the subject, which is mounted on a stage moving perpendicular to the film plane. The technique utilizes traditional optics and is governed by the physical laws of depth of field. By moving the subject through a narrow band of illumination, the entire subject can be recorded in sharp focus from the nearest details to the farthest ones. This analog process produces sharp and detailed images by slowly recording the image on film as the specimen passes through the sheet of light that is thinner than the effective DOF. Because the image is captured at the same relative distance from the camera lens, the resulting images are axonometric rather than perspective projection, which is what the human eye sees and is typically captured by a film camera. Because all parts of an LSP image are captured at the same distance from the lens, relative measurements can be taken from an LSP photograph and can be used for comparison. == Equipment and setup == A typical LSP setup includes: A stage that can move the subject perpendicular to the film plane. Light sources, in some cases modified projectors, are used to project a thin plane of light. A camera mounted on a stable stand such as a tabletop copy stand. In 1991, Sharp and Kazilek described their SLP system that used three Kodak Ektagraphic slide projectors with zoom lenses to create a thin plane of light. The projectors each had a slide mount with two razor blades placed edge-to-edge to create a thin slit for the light to pass through. The image was captured using a Nikon FE-2 SLR camera mounted above the specimen. Kodachrome 25 slide film was used to record the image and to minimize film grain size and maximize image sharpness == Commercial systems == A commercial SLP instrument was produced by the Irvine Optical Corp. Their DYNAPHOT system was based on a photomacroscope and could capture images on 4x5 film. The instrument came with two or three illumination sources and a motorized specimen stage. The system advertised a 2X – 40X magnification range and the ability to capture images in black and white and color. Other systems have been developed by Nile Root and Theodore Clarke and reported higher magnification (up to 100X). == LSP process == Alignment and Focusing: The light sources are aligned and focused to project a thin, consistent plane of light across the subject. Stage Movement: The subject stage moves at a controlled speed, scanning through the plane of light. Image Capture: The camera shutter is set to a long exposure or can be opened and closed manually. As the subject moves through the illuminated plane, it is recorded on the film. This process is very much like painting an image onto the film using photons instead of paint. == Applications == LSP was particularly useful in biomedical photography, where it was used to document magnified subjects with increased depth of field over traditional macro and micro photography. It has been employed to capture detailed images of biological specimens, such as imaging small insects and their parts. SLP has been used to document shell collections for scientific documentation and research. Other applications include forensic science, mineralogy, and the imaging of fractured surfaces and parts == Advantages and challenges of LSP imaging == === Advantages === Exceptional depth of field: Subjects are rendered in sharp focus throughout. High magnification: Detailed images at significant magnification without sacrificing DOF. Analog precision: Provides a non-digital solution with accurate image representation. Versatility: Can be used for a range of subject sizes, from macro to non-macro scales. === Challenges === Technical complexity: Requires precise setup and alignment. Exposure time: Typically requires long exposure times due to the scanning process. Contrast control: The highly directional lighting can create harsh shadows and high contrast, which may need to be managed. Digital competition: Focus stacking has largely replaced LSP in the digital era due to convenience and flexibility. == DIY contributions == Enthusiasts and researchers have contributed to the development and accessibility of LSP by creating and sharing DIY guides. These contributions have enabled others to build their own LSP systems using readily available materials and components. Nile Root's publications provide detailed instructions and recommendations for constructing an LSP setup. These DIY systems have allowed a wider audience to explore and utilize the benefits of LSP imaging in various fields.Glow (app)
ViEWER
Seam carving
Outline of automation
Ontology learning
Light scanning photomacrography