Peter Gerstoft is a Danish-American scientist and engineer specializing in ocean acoustics, seismology, and signal processing. He is currently a professor in the Department of Electrical and Photonics Engineering at the Technical University of Denmark. He was previously a Distinguished Data Scientist at the Scripps Institution of Oceanography at the University of California, San Diego and an adjunct professor in the Department of Electrical and Computer Engineering at UC San Diego. == Education == Gerstoft received his MSc in engineering from the Technical University of Denmark in 1983 and another MSc from the University of Western Ontario in 1984. He completed his PhD in engineering at the Technical University of Denmark in 1986. == Career == Gerstoft began his career in acoustics and vibrations at Odegaard & Danneskiold-Samsøe (1987–1992). He then served as a Senior Scientist at the NATO SACLANT Undersea Research Centre in La Spezia, Italy, from 1992 to 1997. Between 1999 and 2000, Gerstoft worked as a Senior Seismic Acoustic Officer with the Comprehensive Nuclear-Test-Ban Treaty Organization. He has been a Data Scientist at the Scripps Institution of Oceanography since 1997. From 2013, he held an adjunct faculty position in Electrical and Computer Engineering at UC San Diego, where he taught courses on seismology, data assimilation, and machine learning for physical systems. Gerstoft retired from UC San Diego in 2025 and accepted an appointment as Professor of Electrical and Photonics Engineering at the Technical University of Denmark in 2026 . == Research and contributions == Gerstoft's research focuses on environmental signal processing, with a particular emphasis on inversion methods, including their theoretical development, algorithmic implementation, and practical applications. In the 1990s, he investigated the use of nonlinear optimization and Bayesian approaches in acoustic inverse problems related to source localization and environmental parameter estimation. His work integrated physical propagation models with Bayesian sampling methods and a range of likelihood functions. These techniques have been applied to various data types, including vertical sensor arrays, single-sensor broadband data, and transmission loss measurements, and contributed to a general framework for inversion based on Gaussian assumptions. He has also conducted research in machine learning and sparse signal processing, particularly in the context of sensor array data. This includes applications such as direction of arrival estimation and source localization, including for seismic events such as the 2011 Tōhoku earthquake and for ship tracking in ocean environments. His work on sparse Bayesian sequential methods and techniques for estimating Lagrange multipliers in constrained optimization problems has contributed to the development of adaptive and high-resolution signal processing techniques. Gerstoft has applied supervised learning and deep neural networks to problems in physical acoustics, including source localization in ocean waveguides. He has also co-authored several review articles on the use of machine learning in acoustics and seismology. == Honors == Fulbright Scholar, Massachusetts Institute of Technology (1989–1990) Fellow, Acoustical Society of America (2003) Member, American Geophysical Union (since 2004) Senior Member, Institute of Electrical and Electronics Engineers (2018) Fellow, Institute of Electrical and Electronics Engineers (2023) == Selected publications == === Book === Diachok, O., Caiti, A., Gerstoft, P., & Schmidt, H. (Eds.). Full Field Inversion Methods in Ocean and Seismo-Acoustics. Kluwer Academic Publishers, 1995. === Selected articles === Gerstoft, P. (1994). "Inversion of seismo-acoustic data using genetic algorithms and a posteriori probability distributions". Journal of the Acoustical Society of America. 95 (2): 770–782. doi:10.1121/1.408467. Gerstoft, P., & Mecklenbrauker, C. F. (1998). "Ocean acoustic inversion with estimation of a posteriori probability distributions". Journal of the Acoustical Society of America. 104 (2): 808–819. doi:10.1121/1.423287. Sabra, K. G., Gerstoft, P., Roux, P., Kuperman, W. A., & Fehler, M. (2005). "Extracting time-domain Green's function estimates from ambient seismic noise". Geophysical Research Letters. 32, L03310. Xenaki, A., Gerstoft, P., & Mosegaard, K. (2014). "Compressive beamforming". Journal of the Acoustical Society of America. 136, 260–271. Niu, H., Reeves, D., & Gerstoft, P. (2017). "Source localization in an ocean waveguide using supervised machine learning". Journal of the Acoustical Society of America. 142, 1176–1188.
Tribute (website)
Tribute is an American video-sharing website headquartered in Brooklyn. Created in 2014 by Andrew Horn and Rory Petty, the platform lets customers create video montages (called "tributes") for occasions including weddings, birthdays, anniversaries, get well soon, and memorials. Tribute.co allows users to record video messages, request submissions from friends and family, insert photos, add music, and send the resulting video tribute montage to a recipient. == Overview == Tribute's collaborative technology starts with inviting people to contribute via email, SMS or social media. Participants receive a prompt to record a short video via their phone, computer or tablet. The site's video editing software allows users to drag and drop the clips in their desired order without prior video editing experience. == History == When Andrew Horn turned twenty-seven, his girlfriend, Miki Agrawal surprised him with a video montage containing clips of his family and closest friends explaining why they loved him. This resulted in Andrew's idea to create Tribute–a "living eulogy" video-compilation service that he co-founded with software engineer Rory Petty. Founded in 2014, Tribute's activity accelerated in 2020 due to the COVID-19 pandemic, and it had sent over 5 million videos as of December 2021. While social distance restrictions were in effect, the site provided a way for people to connect while in-person celebrations were put on hold. For each video sold, Tribute makes one available to hospitals for free and has partnered with Cleveland Clinic Cancer Center in Ohio, Lurie Children's Hospital in Illinois and CarePoint Health in New Jersey.
Fuzzy logic
Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by mathematician Lotfi Zadeh. Basic fuzzy logic had, however, been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski. The works of Zadeh and Joseph Goguen in the 1960s and 1970s went further by considering issues such as linguistic variables and lattices. Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy models or fuzzy sets are mathematical means of representing vagueness and imprecise information (hence the term fuzzy). These models have the capability of recognising, representing, manipulating, interpreting, and using data and information that are vague and lack certainty. Fuzzy logic has been applied to many fields, from control theory to artificial intelligence. == Overview == Classical logic only permits conclusions that are either true or false. However, there are also propositions with variable answers, which one might find when asking a group of people to identify a color. In such instances, the truth appears as the result of reasoning from inexact or partial knowledge in which the sampled answers are mapped on a spectrum. Both degrees of truth and probabilities range between 0 and 1 and hence may seem identical at first, but fuzzy logic uses degrees of truth as a mathematical model of vagueness, while probability is a mathematical model of ignorance. === Applying truth values === A basic application might characterize various sub-ranges of a continuous variable. For instance, a temperature measurement for anti-lock brakes might have several separate membership functions defining particular temperature ranges needed to control the brakes properly. Each function maps the same temperature value to a truth value in the 0 to 1 range. These truth values can then be used to determine how the brakes should be controlled. Fuzzy set theory provides a means for representing uncertainty. === Linguistic variables === In fuzzy logic applications, non-numeric values are often used to facilitate the expression of rules and facts. A linguistic variable such as age may accept values such as young and its antonym old. Because natural languages do not always contain enough value terms to express a fuzzy value scale, it is common practice to modify linguistic values with adjectives or adverbs. For example, we can use the hedges rather and somewhat to construct the additional values rather old or somewhat young. == Fuzzy systems == === Mamdani === The most well-known system is the Mamdani rule-based one. It uses the following rules: Fuzzify all input values into fuzzy membership functions. Execute all applicable rules in the rulebase to compute the fuzzy output functions. De-fuzzify the fuzzy output functions to get "crisp" output values. ==== Fuzzification ==== Fuzzification is the process of assigning the numerical input of a system to fuzzy sets with some degree of membership. This degree of membership may be anywhere within the interval [0,1]. If it is 0 then the value does not belong to the given fuzzy set, and if it is 1 then the value completely belongs within the fuzzy set. Any value between 0 and 1 represents the degree of uncertainty that the value belongs in the set. These fuzzy sets are typically described by words, and so by assigning the system input to fuzzy sets, we can reason with it in a linguistically natural manner. For example, in the image below, the meanings of the expressions cold, warm, and hot are represented by functions mapping a temperature scale. A point on that scale has three "truth values"—one for each of the three functions. The vertical line in the image represents a particular temperature that the three arrows (truth values) gauge. Since the red arrow points to zero, this temperature may be interpreted as "not hot"; i.e. this temperature has zero membership in the fuzzy set "hot". The orange arrow (pointing at 0.2) may describe it as "slightly warm" and the blue arrow (pointing at 0.8) "fairly cold". Therefore, this temperature has 0.2 membership in the fuzzy set "warm" and 0.8 membership in the fuzzy set "cold". The degree of membership assigned for each fuzzy set is the result of fuzzification. Fuzzy sets are often defined as triangle or trapezoid-shaped curves, as each value will have a slope where the value is increasing, a peak where the value is equal to 1 (which can have a length of 0 or greater) and a slope where the value is decreasing. They can also be defined using a sigmoid function. One common case is the standard logistic function defined as S ( x ) = 1 1 + e − x {\displaystyle S(x)={\frac {1}{1+e^{-x}}}} which has the following symmetry property S ( x ) + S ( − x ) = 1. {\displaystyle S(x)+S(-x)=1.} From this it follows that ( S ( x ) + S ( − x ) ) ⋅ ( S ( y ) + S ( − y ) ) ⋅ ( S ( z ) + S ( − z ) ) = 1 {\displaystyle (S(x)+S(-x))\cdot (S(y)+S(-y))\cdot (S(z)+S(-z))=1} ==== Fuzzy logic operators ==== Fuzzy logic works with membership values in a way that mimics Boolean logic. To this end, replacements for basic operators ("gates") AND, OR, NOT must be available. There are several ways to accomplish this. A common replacement is called the Zadeh operators: For TRUE/1 and FALSE/0, the fuzzy expressions produce the same result as the Boolean expressions. There are also other operators, more linguistic in nature, called hedges that can be applied. These are generally adverbs such as very, or somewhat, which modify the meaning of a set using a mathematical formula. However, an arbitrary choice table does not always define a fuzzy logic function. In the paper (Zaitsev, et al), a criterion has been formulated to recognize whether a given choice table defines a fuzzy logic function and a simple algorithm of fuzzy logic function synthesis has been proposed based on introduced concepts of constituents of minimum and maximum. A fuzzy logic function represents a disjunction of constituents of minimum, where a constituent of minimum is a conjunction of variables of the current area greater than or equal to the function value in this area (to the right of the function value in the inequality, including the function value). Another set of AND/OR operators is based on multiplication, where Given any two of AND/OR/NOT, it is possible to derive the third. The generalization of AND is an instance of a t-norm. ==== IF-THEN rules ==== IF-THEN rules map input or computed truth values to desired output truth values. Example: Given a certain temperature, the fuzzy variable hot has a certain truth value, which is copied to the high variable. Should an output variable occur in several THEN parts, the values from the respective IF parts are combined using the OR operator. ==== Defuzzification ==== The goal is to get a continuous variable from fuzzy truth values. This would be easy if the output truth values were exactly those obtained from fuzzification of a given number. Since, however, all output truth values are computed independently, in most cases they do not represent such a set of numbers. One has then to decide for a number that matches best the "intention" encoded in the truth value. For example, for several truth values of fan_speed, an actual speed must be found that best fits the computed truth values of the variables 'slow', 'moderate' and so on. There is no single algorithm for this purpose. A common algorithm is For each truth value, cut the membership function at this value Combine the resulting curves using the OR operator Find the center-of-weight of the area under the curve The x position of this center is then the final output. === Takagi–Sugeno–Kang (TSK) === The Takagi–Sugeno or Takagi–Sugeno–Kang (TSK) system was introduced by Tomohiro Takagi and Michio Sugeno for fuzzy identification of systems and applications to modeling and control. Sugeno and Kang later developed methods for structure identification of such fuzzy models from input-output data. The TSK system is similar to Mamdani, but the defuzzification process is included in the execution of the fuzzy rules. These are also adapted, so that instead the consequent of the rule is represented through a polynomial function, usually constant in a zero-order model or linear in a first-order model. An example of a rule with a constant output would be: In this case, the output will be equal to the constant of the consequent (e.g. 2). In most scenarios we would have an entire rule base, with 2 or more rules. If this is the case, the output of the entire rule base will be the average of the consequent of each rule i (Y
Course of Action Display and Evaluation Tool
Course of Action Display and Evaluation Tool (CADET) was a research program, and the eponymous prototype software system, that applied knowledge-based techniques of Artificial Intelligence to the problem of battle planning. CADET was also known as Course of Action Display and Elaboration Tool. It was considered an early example of such systems and was funded by the United States Army and by the Defense Advanced Research Projects Agency (DARPA). CADET influenced a later DARPA program called RAID which in turn produced a technology adopted by the United States Army and the United States Marine Corps. == History == The development of Course of Action Display and Evaluation Tool (CADET) began in 1996, at the Carnegie Group, Inc., Pittsburgh PA, funded under the Small Business Innovation Research (SBIR) program. The goal of the first phase SBIR project was to produce “...a live storyboard of [Course of Action] COA development, wargaming, animation, and assessment.” In 1997, the United States Army awarded the Carnegie Group Inc. $750K for SBIR Phase II. The intent was to develop “...a war-gaming modeling and analysis Decision Support System (DSS), … CADET will consist of a combination of Knowledge-Based and decision analytic tools and technologies to provide fast nimble COA war-gaming modeling, simulation, and animation under direct control of the commander and staff. ...Phase II will result in an operations prototype (OP) suitable for use and evaluation in field exercises.” In 2000, CADET was integrated and experimentally evaluated within the framework of the Integrated Course of Action Critiquing and Elaboration System (ICCES) experiment, conducted by the Battle Command Battle Laboratory – Leavenworth (BCBL-L) within the program Concept Experimentation Program (CEP) sponsored by TRADOC. In 2000-2002, DARPA applied CADET in the program titled Command Post of the Future (CPoF) as a tool to generate a course of action. Under the umbrella of the CPoF program, CADET was integrated with the FOX GA system to provide a detailed planner, coupled with COA generation capability. In the same period, Battle Command Battle Lab-Huachuca (BCBL-H) performed an integration CADET with the system called All Source Analysis System-Light (ASAS-L); here CADET was intended to generate plans for intelligence assets, and conduct wargames of different COAs, enemy versus friendly. From 1996 through 2002, work on CADET was performed by the Carnegie Group, Inc., and supported by funding from the US Army CECOM (CADET SBIR Phase I, CADET SBIR Phase II and CADET Enhancements); DARPA (Command Post of the Future); and TRADOC BCBL-H. == Operation == CADET was intended to be used by the staff of the United States Army Brigade, within the Military Decision Making Process (MDMP). In particular, CADET helped produce, automatically or semi-automatically, the products generated within the step of MDMP called Course of Action (COA) Development and the following step of MDMP called COA Analysis and Wargaming. CADET software resided on a laptop computer. Using the computer, the staff officers entered the input to CADET, or alternatively this input arrived at CADET from upstream computer systems. The input consisted of: Order of Battle, i.e., the units constituting the friendly brigade and the enemy units participating in the battle, and their various characteristics; primary activities of the Course of Action, where each activity is typically linked to one or more geographic areas or a route, and sometimes to a major unit executing the activity; digital map of the region where the battle was to take place, including the digital description of significant features such as locations of friendly and enemy units, roads, assembly areas, objectives, and axes of attacks. Taking this input, CADET automatically performed the following tasks (not sequentially): Planning and scheduling the low-level tasks necessary for a given COA Allocating tasks to various units and assets constituting the brigade Assigning suitable locations and routes Estimating the battle losses (attrition) of friendly and enemy forces, and consumption of resources (e.g., fuel and ammunition) Predicting enemy actions or reactions. CADET produced the following outputs: Synchronization matrix, directly editable and printable; synchronization matrix is a kind of Gantt chart that shows assignments of activities to units, to locations/routes and to time periods Map overlays in PPT or JPG formats Animation output XML formally-encoded plan Textual Operation Plan (OPLAN) draft E-mail messages with attachments: XML and text versions of OPLAN == Design == The core algorithm is a planning algorithm where CADET uses a knowledge-based approach of the hierarchical-task-network type. Each task class is associated with a model of more detailed subtasks that should be performed in order to accomplish the higher-level task. Algorithms selected (heuristically) a task and then decomposes it into subtasks. Although similar to hierarchical-task-network planning algorithm, CADET’s algorithm includes elements of adversarial reasoning. After adding a subtask, the algorithm uses rules to determine the enemy’s probable actions and reactions as well as friendly counteractions This approximated the action-reaction-counteraction technique of manual wargaming used by the United States Army. When a task involves movements of a unit, the algorithm performs routing, i.e., finds a route for the movement that minimizes the time required for the movement as well as exposure to the enemy attacks. Each added tasks (subtask) normally requires a unit which would execute the task, and a time period when the task would be executed. Therefore, when a certain number of subtasks is added by the planning process, the algorithm also performs the allocation of the newly added subtasks to units and to time periods (i.e., scheduling). allocation and scheduling of tasks relies on both domain-specific and constraint-guided heuristics. A tasks may also require expenditures of fuel and ammunition. If the tasks involves engagement with the enemy, the performing units will experience lossesof personnel and weapon systems (attrition). CADET’s algorithm includes estimates of consumption of different types of consumables, and also attrition. Depending on the degree of attrition and consumption, CADET adds tasks that are needed to refuel or reconstitute the units. The algorithm continually interleaves incremental steps of planning, routing, scheduling, and attrition and consumption estimates. == Evaluation == Two evaluation experiments are described in literature. The first experiment called ICCES took three days. The subjects were Army officers from combat arms branches, with 11 to 23 years of active service, in the ranks of majors and lieutenant colonels, a total of 8. Each officer was given 4 hours of training learning to operate CADET and related computer tools. Officers were divided into two groups and given a tactical scenario. One group (the control group) used the traditional, manual process; the other used the system called ICCES, the automated core of which was CADET. Each group produced three COA sketches and statements and one COA synchronization matrix. Then, the experiment was repeated with another scenario but the control group became the automated group and vice versa. The users were generally satisfied with the quality of the ICCES-generated products. The group using ICCES made only a few changes to the product that was automatically generated, indicating that they agreed with the majority of the plan that ICCES produced. The second experiment was reminiscent of Turing test. The experiment involved one user, nine judges (active-duty officers, mainly colonels and lieutenant colonels), and five scenarios obtained from several US Army exercises. For each scenario, experimenters obtained synchronization matrices that were produced in earlier exercises, typically by a team of four to five officers in three to four hours, spending approximately 16 person-hours in total. Using these scenarios and COAs, the user had CADET generate automatically detailed plans and express them as synchronization matrices. The user, a retired US Army officer, reviewed and slightly edited the matrices. The entire process took less than two minutes of computations by and approximately 20 minutes of review and post-editing, approximately 0.4 person-hour in total per product. The experimenters gave the resulting matrices the same visual style as those produced by humans. The judges, who did not know whether a planning product was a traditional product of humans, or with computerized aids, were asked to grade the products. The result was that the average grades for manual products and CADET-generated products were statistically indistinguishable, even though CADET-generated products required far less time to produce. == Legacy == CADET served as “...an example of how even relatively basic A
They're Made Out of Meat
"They're Made Out of Meat" is a short story by American writer Terry Bisson. It was originally published in OMNI. It consists entirely of dialogue between two characters. Bisson's website hosts a theatrical adaptation. A film adaptation won the Grand Prize at the Seattle Science Fiction Museum's 2006 film festival. The story was collected in the 1993 anthology Bears Discover Fire and Other Stories, and has circulated widely on the Internet, which Bisson found "flattering". It has been quoted in cognitive, cosmological, and philosophical scholarship. == Plot == The two characters are intelligent beings capable of traveling faster than light, on a mission to "contact, welcome and log in any and all sentient races or multibeings in this quadrant of the Universe." Bisson's stage directions represent them as "two lights moving like fireflies among the stars" on a projection screen. One of them tells the incredulous other about the recent discovery of carbon-based lifeforms "made up entirely of meat". After conversing briefly about it, they both deem such beings and communication with them too bizarre and agree to "erase the records and forget the whole thing", marking the Solar System "unoccupied". == Film adaptations == === They're Made out of Meat (2005) === In 2005, Stephen O'Regan wrote and directed a live film adaptation starring Tom Noonan and Ben Bailey. The film was made as a final project for the New York Film Academy. The main action takes place inside a diner full of teenagers in Staten Island, New York. The music for the film was scored by Bob Reynolds. === They're Made out of Meat (2010) === Jeff Frumess and Trevor Scott produced a version in 2010. They added the character of a homeless conspiracy theorist with an original score by musician Sam Belkin. The film was shot at Hartsdale station in Westchester County, New York. === Meat (2021) === Masha Maksimova developed a version in Cinemiracle format, a triple split-screen process, as a student project at the Berlin University of Applied Sciences in the communication design course. The dialogue is conducted by two telepathic humanoid aliens and the thoughts are visualised by found-footage collages.
Landweber iteration
The Landweber iteration or Landweber algorithm is an algorithm to solve ill-posed linear inverse problems, and it has been extended to solve non-linear problems that involve constraints. The method was first proposed in the 1950s by Louis Landweber, and it can be now viewed as a special case of many other more general methods. == Basic algorithm == The original Landweber algorithm attempts to recover a signal x from (noisy) measurements y. The linear version assumes that y = A x {\displaystyle y=Ax} for a linear operator A. When the problem is in finite dimensions, A is just a matrix. When A is nonsingular, then an explicit solution is x = A − 1 y {\displaystyle x=A^{-1}y} . However, if A is ill-conditioned, the explicit solution is a poor choice since it is sensitive to any noise in the data y. If A is singular, this explicit solution doesn't even exist. The Landweber algorithm is an attempt to regularize the problem, and is one of the alternatives to Tikhonov regularization. We may view the Landweber algorithm as solving: min x ‖ A x − y ‖ 2 2 / 2 {\displaystyle \min _{x}\|Ax-y\|_{2}^{2}/2} using an iterative method. The algorithm is given by the update x k + 1 = x k − ω A ∗ ( A x k − y ) . {\displaystyle x_{k+1}=x_{k}-\omega A^{}(Ax_{k}-y).} where the relaxation factor ω {\displaystyle \omega } satisfies 0 < ω < 2 / σ 1 2 {\displaystyle 0<\omega <2/\sigma _{1}^{2}} . Here σ 1 {\displaystyle \sigma _{1}} is the largest singular value of A {\displaystyle A} . If we write f ( x ) = ‖ A x − y ‖ 2 2 / 2 {\displaystyle f(x)=\|Ax-y\|_{2}^{2}/2} , then the update can be written in terms of the gradient x k + 1 = x k − ω ∇ f ( x k ) {\displaystyle x_{k+1}=x_{k}-\omega \nabla f(x_{k})} and hence the algorithm is a special case of gradient descent. For ill-posed problems, the iterative method needs to be stopped at a suitable iteration index, because it semi-converges. This means that the iterates approach a regularized solution during the first iterations, but become unstable in further iterations. The reciprocal of the iteration index 1 / k {\displaystyle 1/k} acts as a regularization parameter. A suitable parameter is found, when the mismatch ‖ A x k − y ‖ 2 2 {\displaystyle \|Ax_{k}-y\|_{2}^{2}} approaches the noise level. Using the Landweber iteration as a regularization algorithm has been discussed in the literature. == Nonlinear extension == In general, the updates generated by x k + 1 = x k − τ ∇ f ( x k ) {\displaystyle x_{k+1}=x_{k}-\tau \nabla f(x_{k})} will generate a sequence f ( x k ) {\displaystyle f(x_{k})} that converges to a minimizer of f whenever f is convex and the stepsize τ {\displaystyle \tau } is chosen such that 0 < τ < 2 / ( ‖ ∇ f ‖ 2 ) {\displaystyle 0<\tau <2/(\|\nabla f\|^{2})} where ‖ ⋅ ‖ {\displaystyle \|\cdot \|} is the spectral norm. Since this is special type of gradient descent, there currently is not much benefit to analyzing it on its own as the nonlinear Landweber, but such analysis was performed historically by many communities not aware of unifying frameworks. The nonlinear Landweber problem has been studied in many papers in many communities; see, for example. == Extension to constrained problems == If f is a convex function and C is a convex set, then the problem min x ∈ C f ( x ) {\displaystyle \min _{x\in C}f(x)} can be solved by the constrained, nonlinear Landweber iteration, given by: x k + 1 = P C ( x k − τ ∇ f ( x k ) ) {\displaystyle x_{k+1}={\mathcal {P}}_{C}(x_{k}-\tau \nabla f(x_{k}))} where P {\displaystyle {\mathcal {P}}} is the projection onto the set C. Convergence is guaranteed when 0 < τ < 2 / ( ‖ A ‖ 2 ) {\displaystyle 0<\tau <2/(\|A\|^{2})} . This is again a special case of projected gradient descent (which is a special case of the forward–backward algorithm) as discussed in. == Applications == Since the method has been around since the 1950s, it has been adopted and rediscovered by many scientific communities, especially those studying ill-posed problems. In X-ray computed tomography it is called simultaneous iterative reconstruction technique (SIRT). It has also been used in the computer vision community and the signal restoration community. It is also used in image processing, since many image problems, such as deconvolution, are ill-posed. Variants of this method have been used also in sparse approximation problems and compressed sensing settings.
Oxa
Oxa (formerly Oxbotica) is an autonomous vehicle software company, headquartered in Oxfordshire, England, and founded by Paul Newman and Ingmar Posner. == History == In 2013, Newman and Posner led the RobotCar UK project as part of Oxford University's Department of Engineering Science Mobile Robotics Group. RobotCar became the first autonomous vehicle on UK roads. In 2014, the pair used the newly developed technology to found Oxbotica. Oxbotica has raised over $18 million to date and is backed by the IP Group, Parkwalk Advisors and AXA XL. In 2018, Uber's former EMEA business head, Fraser Robinson, was appointed to the board of directors. In May 2019, Ozgur Tohumcu replaced Dr Graeme Smith as Oxbotica's CEO. Also in 2019, the company opened an office in Toronto, Canada. In January 2021, Oxbotica announced it had raised $47 million in a Series B round. In August 2021, the company achieved a safety landmark as the first company to have its autonomy safety case assessed by BSI (British Standards Institution) against the requirements of the UK Code of Practice 2019, PAS 1881:2020 and PAS 1883:2020, certifying the safety conformity of its autonomous vehicle trials and testing. The assessment was completed as part of Project Endeavour, the UK's first multi-city demonstration of autonomous vehicle services and capability. In December 2021, Gavin Jackson was named CEO. In January 2023, the company raised $140 million in a Series C round. In May 2023, the company changed its name to Oxa. Oxa raised $103 million (£77 million) in March 2026, including $50 million from the UK National Wealth Fund. Nvidia's venture capital division, NVentures, also invested in the Series D funding round, along with existing Oxa shareholders IP Group, Australian pension fund Hostplus, and BP Ventures, a division of the UK oil company. == Technology == Oxa designs software and hardware for the conversion of industrial vehicles into autonomous ones. Its full stack, end-to-end Universal Autonomy software is both vehicle and platform-agnostic, with no dependence on external infrastructure such as GPS. It can be deployed in any environment and on any terrain. In addition to underground uses, the technology is also useful in natural canyons and forests, where GPS signals are weak or non-existent, but also in "urban canyons" — cities with tall buildings that obstruct GPS signals for proper navigation. == Public deployments == The LUTZ Pathfinder pod had its first public demonstration in February 2015 in Milton Keynes. The Government-funded project was designed to ensure that autonomous vehicles would comply with the Highway Code. The pod featured autonomous control software from Oxbotica, including 19 sensors, cameras, radar and Lidar. As part of the GATEway Project in 2017, Oxbotica trialled seven autonomous shuttle buses in Greenwich, navigating a two-mile riverside path near London's O2 Arena on a route that is also used by pedestrians and cyclists. Oxbotica ran the UK's first trial of autonomous grocery deliveries that year, with British online supermarket Ocado in London, as the next step in the GATEway Project. In 2018, Oxbotica deployed its autonomous vehicle software at London's Gatwick Airport, which subsequently became the first airport in the world to trial an autonomous shuttle service. The electric-powered vehicles transported staff via airside roads between the airport's North and South terminals. An airside trial of Oxbotica's autonomous driving technology was then successfully completed at Heathrow Airport in partnership with IAG Cargo, the first airside trial of an autonomous vehicle at a UK airport. The Oxbotica-designed CargoPod ran autonomously along a cargo route around the airside perimeter for three weeks. As part of the UK Centre for Connected and Autonomous Vehicles-funded DRIVEN project, Oxbotica is developing and deploying a fleet of Ford Fusion autonomous vehicles running in both London and Oxford on public roads, and in conjunction with its consortium partners, running real-time insurance. AXA XL is partnering with Oxbotica on the development of smart insurance products using Oxbotica's autonomy technology to improve road safety. In 2018, Oxbotica announced a partnership with London private taxi firm Addison Lee to develop and deploy autonomous taxis in the city of London by 2021. A 3D street mapping exercise was conducted in London's Canary Wharf. In 2019, Oxbotica deployed a fleet of their autonomous technology within Ford Mondeo cars on public roads in Stratford, London to test their use in city environments. The £13.2 million project is in collaboration with The DRIVEN Project to develop self-driving cars. == Awards == 2019 Royal Academy of Engineering Silver Medal - Paul Newman 2017 Financial Times ArcelorMittal Boldness in Business Award Barclays Award for Innovation 2016 Frost & Sullivan Award, Technology Leadership for Autonomous Driving Software