AI Headshot Examples

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Logistics automation

Logistics automation is the application of computer software or automated machinery to logistics operations in order to improve its efficiency. Typically this refers to operations within a warehouse or distribution center, with broader tasks undertaken by supply chain engineering systems and enterprise resource planning systems. Logistics automation systems can powerfully complement the facilities provided by these higher level computer systems. The focus on an individual node within a wider logistics network allows systems to be highly tailored to the requirements of that node. == Components == Logistics automation systems comprise a variety of hardware and software components: Fixed machinery Automated storage and retrieval systems, including: Cranes serve a rack of locations, allowing many levels of stock to be stacked vertically, and allowing for higher storage densities and better space utilization than alternatives. In systems produced by Amazon Robotics, automated guided vehicles move items to a human picker. Conveyors: Containers can enter automated conveyors in one area of the warehouse and, either through hard-coded rules or data input, be moved to a selected destination. Vertical carousels based on the paternoster lift system or using space optimization, similar to vending machines, but on a larger scale. Sortation systems: similar to conveyors but typically with higher capacity and able to divert containers more quickly. Typically used to distribute high volumes of small cartons to a large set of locations. Industrial robots: four- to six-axis industrial robots, e.g. palletizing robots, are used for palletizing, depalletizing, packaging, commissioning and order picking. Typically all of these will automatically identify and track containers using barcodes or, increasingly, RFID tags. Motion check weighers may be used to reject cases or individual products that are under or over their specified weight. They are often used in kitting conveyor lines to ensure all pieces belonging in the kit are present. Mobile technology Radio data terminals: these are handheld or truck-mounted terminals which connect by radio to logistics automation software and provide instructions to operators moving throughout the warehouse. Many also have barcode scanners to allow identification of containers more quickly and accurately than manual keyboard entry. Software Integration software: this provides overall control of the automation machinery and allows cranes to be connected to conveyors for seamless stock movements. Operational control software: provides low-level decision-making, such as where to store incoming containers, and where to retrieve them when requested. Business control software: provides higher-level functionality, such as identification of incoming deliveries/stock, scheduling order fulfillment, and assignment of stock to outgoing trailers. == Benefits == A typical warehouse or distribution center will receive stock of a variety of products from suppliers and store these until the receipt of orders from customers, whether individual buyers (e.g. mail order), retail branches (e.g. chain stores), or other companies (e.g. wholesalers). A logistics automation system may provide the following: Automated goods in processes: Incoming goods can be marked with barcodes and the automation system notified of the expected stock. On arrival, the goods can be scanned and thereby identified, and taken via conveyors, sortation systems, and automated cranes into an automatically assigned storage location. Automated goods retrieval for orders: On receipt of orders, the automation system is able to immediately locate goods and retrieve them to a pick-face location. Automated dispatch processing: Combining knowledge of all orders placed at the warehouse the automation system can assign picked goods into dispatch units and then into outbound loads. Sortation systems and conveyors can then move these onto the outgoing trailers. If needed, repackaging to ensure proper protection for further distribution or to change the package format for specific retailers/customers. A complete warehouse automation system can drastically reduce the workforce required to run a facility, with human input required only for a few tasks, such as picking units of product from a bulk packed case. Even here, assistance can be provided with equipment such as pick-to-light units. Smaller systems may only be required to handle part of the process. Examples include automated storage and retrieval systems, which simply use cranes to store and retrieve identified cases or pallets, typically into a high-bay storage system which would be unfeasible to access using fork-lift trucks or any other means. The use of Automatic Guided Vehicles maximizes the output compared to humans since they can do repetitive tasks for long hours and with least to no supervision. An AGV is built and programmed for precision and accuracy thereby reducing the chances of errors in a warehouse, especially when dealing with fragile goods. == Automation software == Software or cloud-based SaaS solutions are used for logistics automation which helps the supply chain industry in automating the workflow as well as management of the system. Knowledge @ Wharton staff writers noted in 2011 that some manufacturers and retailers were weathering the Great Recession "by signing up for pay-as-you-go logistics services available through the Internet 'cloud'". They identified the benefits and reduced costs which came from sharing information about shipments with suppliers, hauliers and end users. There is little generalized software available in this market. This is because there is no rule to generalize the system as well as work flow even though the practice is more or less the same. Most of the commercial companies do use one or the other of the custom solutions. But there are various software solutions that are being used within the departments of logistics. There are a few departments in Logistics, namely: Conventional Department, Container Department, Warehouse, Marine Engineering, Heavy Haulage, etc. Software used in these departments Conventional department : CVT software / CTMS software. Container Trucking: CTMS software Warehouse : WMS/WCS Improving Effectiveness of Logistics Management Logistical Network Information Transportation Sound Inventory Management Warehousing, Materials Handling & Packaging
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Christopher K. I. Williams

Christopher Kenneth Ingle Williams (born 1960) is a professor at the School of Informatics, University of Edinburgh, working in Artificial intelligence, and particularly the areas of Machine learning and Computer vision. == Education == Williams received a BA in Physics and Theoretical Physics from the University of Cambridge in 1982, followed by Part III Mathematics (1983). He did a MSc in Water Resources at the University of Newcastle-Upon-Tyne, then worked in Lesotho on low-cost sanitation. In 1988, he studied at the Department of Computer Science of the University of Toronto under the supervision of Geoffrey Hinton. He obtained his MSc and PhD both in computer science, in 1990 and 1994, respectively. == Career and research == In 1994, Williams moved to Aston University as a Research Fellow. He became a Lecturer in August 1995. He moved to the University of Edinburgh in July 1998 and became Reader in 2000. He obtained a Personal Chair in Machine Learning in 2005 in the School of Informatics. Williams has been a Fellow of the European Laboratory for Learning and Intelligent Systems (ELLIS) since 2019. Williams' research interests are in machine learning and computer vision. He has worked on new models for understanding time-series and images, and for finding structure in data. He is best known for his work on Gaussian processes and for the book Gaussian Processes for Machine Learning, co-authored with Carl Rasmussen. The book received the 2009 DeGroot Prize of the International Society for Bayesian Analysis. Williams was an organizer of the PASCAL Visual Object Classes (VOC) project (2005–2012) along with Mark Everingham, Luc van Gool, John Winn, and Andrew Zisserman. == Awards and honours == In 2021 Williams was elected a Fellow of the Royal Society of Edinburgh (FRSE).
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Babak Hodjat

Babak Hodjat (Persian: بابک حجت; born November 1, 1967) is a British computer scientist, entrepreneur, and writer. He was the co-founder and CEO of Sentient Technologies and now holds the position of Chief Technology Officer AI at Cognizant. He is a specialist in the field of artificial intelligence and machine learning. In 1998 Hodjat co-founded Dejima Inc and served as CEO and CTO, his patented work on artificial intelligence led to the technology used by Apple for their digital assistant Siri. == Biography == === Early life === Babak Hodjat was born on November 1, 1967, in Wimbledon. His father was a retired university professor in entomology who worked at the British Museum. As a child, he did not like insects and would wander off to the nearby science museum, where he would spend long hours in front of a computer they had on display. He attended middle school in the United States. He studied at the Sharif University of Technology from 1986 to 1995, and received his Master of Science degree in software engineering. In 1994, together with another computer department student Hormoz Shahrzad presented their research titled Introducing a dynamic problem solving scheme based on a learning algorithm in artificial life environments at the first IEEE Conference on Computational Intelligence held at Orlando. Hodjat received a PhD in machine intelligence from Kyushu University in 2003 During his time there, he published several works on adaptive agent oriented software architecture and natural language user interfaces. === Career in science and business === Hodjat moved to Silicon Valley, California in 1998 and founded Dejima Inc. (named after the historic Japanese Dejima artificial island). The firm was based on a patented adaptive agent-oriented software engineering platform developed by Hodjat, Christopher Savoie and Makoto Amamiya. Hodjat served as the CTO and as the CEO for 9 months from October 2000. By 2000 the company had offices in San Jose, London and Tokyo. In 2002, the company developed a voice control Natural Interaction Platform (NPI) in collaboration with the Stanford University's research group Archimedes Project. During these years Hodjat continued his research on agent oriented software architecture and natural language user interfaces. In July 2003, Dejima got funding from SRI International within the Cognitive Assistant that Learns and Organizes (CALO) project of DARPA and worked on a Perceptive Assistant that Learns (PAL) initiative. Hodjat was the primary inventor of the firm's agent-oriented technology applied to intelligent interfaces for mobile and enterprise computing – a technology that eventually led to Siri. In April 2004, Dejima was acquired by Sybase iAnywhere. Hodjat served as senior director of engineering at Sybase iAnywhere from 2004 to 2008, where he developed AvantGo Platform, mBusiness Anywhere, and Answers Anywhere. In 2006, he co-founded MobileVerbs Inc., a mobile marketing service company, which was acquired by iLoop Mobile in February 2010. In 2007, he teamed with Antoine Blondeau (former CEO of Dejima) and Adam Cheyer (Dejima's vice president and Chief Architect of the CALO project) to establish Genetic Finance Holding Ltd. (where he began as CTO). In 2014 the firm became Sentient Technologies. Hodjat was joined by his long-time research fellow Hormoz Shahrzad who became principal scientist, while Hodjat held the position of chief scientist. In the following years Hodjat has worked on developing massively distributed computing technology and improving machine-learning technique known as evolutionary algorithms. One area that gained special attention from the press was applying Sentient Technologies algorithms to a stock market trading through specially created Sentient Investment Management hedge fund. Following the management change within Sentient Technologies, Hodjat became the company's CEO in February 2017. He continues his business and educational projects (he was on the jury of IBM Watson AI XPRIZE and the Merit Awards committee for the ISAL Award). == Writing == Hodjat is the author of multiple books such as The Konar and the Apple: Fun, Beauty, and Dread--From Ahwaz to California and the science fiction novel "The Narrator" (January 2022; ISBN 978-1-7354860-1-7)(March 2023; ISBN 978-1-7354860-0-0). == Selected publications == Hodjat, B.; Shahrzad, H. (1994). "Introducing a dynamic problem solving scheme based on a learning algorithm in artificial life environments". IEEE International Joint Conference on neural networks (IJCNN-94). Vol. 4. IEEE International Joint Conference on neural networks. pp. 2333–2338. doi:10.1109/ICNN.1994.374583. ISBN 978-0-7803-1901-1. S2CID 60497133. Hodjat, B.; Savoie, C.J.; Amamiya, M. (2006) [1998]. "An adaptive agent oriented software architecture". PRICAI'98: Topics in Artificial Intelligence. Springer. pp. 33–46. arXiv:cs/9812014. doi:10.1007/BFb0095256. ISBN 978-3-540-49461-4. S2CID 5317786. Hodjat, B.; Amamiya, M. (2000-05-25). "Applying the Adaptive Agent Oriented Software Architecture to the Parsing of Context Sensitive Grammars". IEICE Transactions on Information and Systems. E83-D (5): 1142–1152. ISSN 0916-8532. Retrieved 2017-12-14. Hodjat, Babak; Hodjat, Siamak; Treadgold, Nick; Jonsson, Ing-Marie (2006). "CRUSE: a context reactive natural language mobile interface". Proceedings of the 2nd annual international workshop on Wireless internet. WICON. doi:10.1145/1234161.1234181. ISBN 978-1-59593-510-6. S2CID 2388254. O'Reilly, Una-May; Wagy, Mark; Hodjat, Babak (2013). "Chapter 6: EC-Star: A Massive-Scale, Hub and Spoke, Distributed Genetic Programming System". In Riolo, R.; Vladislavleva, E.; Ritchie, M.; Moore, J.H. (eds.). Genetic Programming Theory and Practice X. Springer-Verlag New York. pp. 73–85. doi:10.1007/978-1-4614-6846-2. ISBN 978-1-4614-6845-5. S2CID 39650969. Retrieved 2017-12-14. Hodjat, Babak; Hemberg, Erik; Shahrzad, Hormoz; O'Reilly, Una-May (2014). "Chapter 4: Maintenance of a Long Running Distributed Genetic Programming System for Solving Problems Requiring Big Data". In Riolo, Rick; Moore, Jason H.; Kotanchek, Mark (eds.). Genetic Programming Theory and Practice XI. Springer-Verlag New York. pp. 65–83. doi:10.1007/978-1-4939-0375-7. ISBN 978-1-4939-0374-0. S2CID 28843739. Retrieved 2017-12-14. Shahrzad, Hormoz; Hodjat, Babak; Miikkulainen, Risto (2016). "Estimating the Advantage of Age-Layering in Evolutionary Algorithms". Proceedings of the Genetic and Evolutionary Computation Conference 2016. Genetic and Evolutionary Computation Conference. pp. 693–699. doi:10.1145/2908812.2908911. ISBN 978-1-4503-4206-3. S2CID 215516530. == Patents == Babak Hodjat holds 21 patents in the fields of agent-oriented programming, natural language decision engines, distributed evolutionary algorithms for asset management and trading and data mining.
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Kalman filter

In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unknown variables that tend to be more accurate than those based on a single measurement, by estimating a joint probability distribution over the variables for each time-step. The filter is constructed as a mean squared error minimiser, but an alternative derivation of the filter is also provided showing how the filter relates to maximum likelihood statistics. The filter is named after Rudolf E. Kálmán. Kalman filtering has numerous technological applications. A common application is for guidance, navigation, and control of vehicles, particularly aircraft, spacecraft and ships positioned dynamically. Furthermore, Kalman filtering is much applied in time series analysis tasks such as signal processing and econometrics. Kalman filtering is also important for robotic motion planning and control, and can be used for trajectory optimization. Kalman filtering also works for modeling the central nervous system's control of movement. Due to the time delay between issuing motor commands and receiving sensory feedback, the use of Kalman filters provides a realistic model for making estimates of the current state of a motor system and issuing updated commands. The algorithm works via a two-phase process: a prediction phase and an update phase. In the prediction phase, the Kalman filter produces estimates of the current state variables, including their uncertainties. Once the outcome of the next measurement (necessarily corrupted with some error, including random noise) is observed, these estimates are updated using a weighted average, with more weight given to estimates with greater certainty. The algorithm is recursive. It can operate in real time, using only the present input measurements and the state calculated previously and its uncertainty matrix; no additional past information is required. Optimality of Kalman filtering assumes that errors have a normal (Gaussian) distribution. In the words of Rudolf E. Kálmán, "The following assumptions are made about random processes: Physical random phenomena may be thought of as due to primary random sources exciting dynamic systems. The primary sources are assumed to be independent gaussian random processes with zero mean; the dynamic systems will be linear." Regardless of Gaussianity, however, if the process and measurement covariances are known, then the Kalman filter is the best possible linear estimator in the minimum mean-square-error sense, although there may be better nonlinear estimators. It is a common misconception (perpetuated in the literature) that the Kalman filter cannot be rigorously applied unless all noise processes are assumed to be Gaussian. Extensions and generalizations of the method have also been developed, such as the extended Kalman filter and the unscented Kalman filter which work on nonlinear systems. The basis is a hidden Markov model such that the state space of the latent variables is continuous and all latent and observed variables have Gaussian distributions. Kalman filtering has been used successfully in multi-sensor fusion, and distributed sensor networks to develop distributed or consensus Kalman filtering. == History == The filtering method is named for Hungarian émigré Rudolf E. Kálmán, although Thorvald Nicolai Thiele and Peter Swerling developed a similar algorithm earlier. Richard S. Bucy of the Johns Hopkins Applied Physics Laboratory contributed to the theory, causing it to be known sometimes as Kalman–Bucy filtering. Kalman was inspired to derive the Kalman filter by applying state variables to the Wiener filtering problem. Stanley F. Schmidt is generally credited with developing the first implementation of a Kalman filter. He realized that the filter could be divided into two distinct parts, with one part for time periods between sensor outputs and another part for incorporating measurements. It was during a visit by Kálmán to the NASA Ames Research Center that Schmidt saw the applicability of Kálmán's ideas to the nonlinear problem of trajectory estimation for the Apollo program resulting in its incorporation in the Apollo navigation computer. This digital filter is sometimes termed the Stratonovich–Kalman–Bucy filter because it is a special case of a more general, nonlinear filter developed by the Soviet mathematician Ruslan Stratonovich. In fact, some of the special case linear filter's equations appeared in papers by Stratonovich that were published before the summer of 1961, when Kalman met with Stratonovich during a conference in Moscow. This Kalman filtering was first described and developed partially in technical papers by Swerling (1958), Kalman (1960) and Kalman and Bucy (1961). The Apollo computer used 2k of magnetic core RAM and 36k wire rope [...]. The CPU was built from ICs [...]. Clock speed was under 100 kHz [...]. The fact that the MIT engineers were able to pack such good software (one of the very first applications of the Kalman filter) into such a tiny computer is truly remarkable. Kalman filters have been vital in the implementation of the navigation systems of U.S. Navy nuclear ballistic missile submarines, and in the guidance and navigation systems of cruise missiles such as the U.S. Navy's Tomahawk missile and the U.S. Air Force's Air Launched Cruise Missile. They are also used in the guidance and navigation systems of reusable launch vehicles and the attitude control and navigation systems of spacecraft which dock at the International Space Station. == Overview of the calculation == Kalman filtering uses a system's dynamic model (e.g., physical laws of motion), known control inputs to that system, and multiple sequential measurements (such as from sensors) to form an estimate of the system's varying quantities (its state) that is better than the estimate obtained by using only one measurement alone. As such, it is a common sensor fusion and data fusion algorithm. Noisy sensor data, approximations in the equations that describe the system evolution, and external factors that are not accounted for, all limit how well it is possible to determine the system's state. The Kalman filter deals effectively with the uncertainty due to noisy sensor data and, to some extent, with random external factors. The Kalman filter produces an estimate of the state of the system as an average of the system's predicted state and of the new measurement using a weighted average. The purpose of the weights is that values with better (i.e., smaller) estimated uncertainty are "trusted" more. The weights are calculated from the covariance, a measure of the estimated uncertainty of the prediction of the system's state. The result of the weighted average is a new state estimate that lies between the predicted and measured state, and has a better estimated uncertainty than either alone. This process is repeated at every time step, with the new estimate and its covariance informing the prediction used in the following iteration. This means that Kalman filter works recursively and requires only the last "best guess", rather than the entire history, of a system's state to calculate a new state. The measurements' certainty-grading and current-state estimate are important considerations. It is common to discuss the filter's response in terms of the Kalman filter's gain. The Kalman gain is the weight given to the measurements and current-state estimate, and can be "tuned" to achieve a particular performance. With a high gain, the filter places more weight on the most recent measurements, and thus conforms to them more responsively. With a low gain, the filter conforms to the model predictions more closely. At the extremes, a high gain (close to one) will result in a more jumpy estimated trajectory, while a low gain (close to zero) will smooth out noise but decrease the responsiveness. When performing the actual calculations for the filter (as discussed below), the state estimate and covariances are coded into matrices because of the multiple dimensions involved in a single set of calculations. This allows for a representation of linear relationships between different state variables (such as position, velocity, and acceleration) in any of the transition models or covariances. == Example application == As an example application, consider the problem of determining the precise location of a truck. The truck can be equipped with a GPS unit that provides an estimate of the position within a few meters. The GPS estimate is likely to be noisy; readings 'jump around' rapidly, though remaining within a few meters of the real position. In addition, since the truck is expected to follow the laws of physics, its position can also be estimated by integrating its velocity over time, determined by keeping track of wheel revolutions and the
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AI-assisted software development

AI-assisted software development is the use of artificial intelligence (AI) to augment software development. It uses large language models (LLMs), AI agents and other AI technologies to assist software developers. It helps in a range of tasks of the software development life cycle, from code generation to debugging, editing, testing, UI design, understanding the code, and documentation. Agentic coding denotes the use of AI agents for software development. == Technologies == === Source code generation === Large language models trained or fine-tuned on source-code corpora can generate source code from natural-language descriptions, comments, or docstrings. Research on code-generation systems often evaluates generated programs by functional correctness, such as whether the output passes automated test cases, rather than by syntax alone. Such tools can be features or extensions of integrated development environments (IDEs). === Intelligent code completion === AI agents using pre-trained and fine-tuned LLMs can predict and suggest code completions based on context. According to Husein, Aburajouh & Catal in a 2025 literature review in Computer Standards & Interfaces, "LLMs significantly enhance code completion performance across several programming languages and contexts, and their capability to predict relevant code snippets based on context and partial input boosts developer productivity substantially." === Testing, debugging, code review and analysis === AI is used to automatically generate test cases, identify potential bugs and security vulnerabilities, and suggest fixes. AI can also be used to perform static code analysis and suggest potential performance improvements. == Limitations == Both ownership of and responsibility for AI-generated code is disputed. According to a report from the German Federal Office for Information Security, the use of AI coding assistants without careful oversight from experienced developers can introduce both minor and major security vulnerabilities, and any potential gain in productivity should be weighed against the cost of additional quality control and security measures. According to Deloitte, outputs from AI-assisted software development must be validated through a combination of automated testing, static analysis tools and human review, creating a governance layer to improve quality and accountability. == Vibe coding ==
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Heikki Mannila

Heikki Olavi Mannila (born 4 January 1960 in Espoo) is a Finnish computer scientist, the president of the Academy of Finland. Mannila earned his Ph.D. in 1985 from the University of Helsinki under the supervision of Esko Ukkonen and for many years he was a professor at the University of Helsinki himself. From 2004 to 2008 he was Academy Professor at the Academy of Finland. He became Vice President for Academic Affairs at Aalto University in 2009, and was appointed by the Finnish government as president of the Academy of Finland for a term lasting from 2012 to 2017. The appointment was renewed for the period 2017–2022. Mannila is known for his research in data mining, and has published highly cited papers on association rule learning and sequence mining. With David Hand and Padhraic Smyth, he is the co-author of the book Principles of Data Mining (MIT Press, 2001). Heikki Mannila is son to the professor Elina Haavio-Mannila.
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Restricted Boltzmann machine

A restricted Boltzmann machine (RBM) (also called a restricted Sherrington–Kirkpatrick model with external field or restricted stochastic Ising–Lenz–Little model) is a generative stochastic artificial neural network that can learn a probability distribution over its set of inputs. RBMs were initially proposed under the name Harmonium by Paul Smolensky in 1986, and rose to prominence after Geoffrey Hinton and collaborators used fast learning algorithms for them in the mid-2000s. RBMs have found applications in dimensionality reduction, classification, collaborative filtering, feature learning, topic modelling, immunology, and even many‑body quantum mechanics. They can be trained in either supervised or unsupervised ways, depending on the task. As their name implies, RBMs are a variant of Boltzmann machines, with the restriction that their neurons must form a bipartite graph: a pair of nodes from each of the two groups of units (commonly referred to as the "visible" and "hidden" units respectively) may have a symmetric connection between them; and there are no connections between nodes within a group. By contrast, "unrestricted" Boltzmann machines may have connections between hidden units. This restriction allows for more efficient training algorithms than are available for the general class of Boltzmann machines, in particular the gradient-based contrastive divergence algorithm. Restricted Boltzmann machines can also be used in deep learning networks. In particular, deep belief networks can be formed by "stacking" RBMs and optionally fine-tuning the resulting deep network with gradient descent and backpropagation. == Structure == The standard type of RBM has binary-valued (Boolean) hidden and visible units, and consists of a matrix of weights W {\displaystyle W} of size m × n {\displaystyle m\times n} . Each weight element ( w i , j ) {\displaystyle (w_{i,j})} of the matrix is associated with the connection between the visible (input) unit v i {\displaystyle v_{i}} and the hidden unit h j {\displaystyle h_{j}} . In addition, there are bias weights (offsets) a i {\displaystyle a_{i}} for v i {\displaystyle v_{i}} and b j {\displaystyle b_{j}} for h j {\displaystyle h_{j}} . Given the weights and biases, the energy of a configuration (pair of Boolean vectors) (v,h) is defined as E ( v , h ) = − ∑ i a i v i − ∑ j b j h j − ∑ i ∑ j v i w i , j h j {\displaystyle E(v,h)=-\sum _{i}a_{i}v_{i}-\sum _{j}b_{j}h_{j}-\sum _{i}\sum _{j}v_{i}w_{i,j}h_{j}} or, in matrix notation, E ( v , h ) = − a T v − b T h − v T W h . {\displaystyle E(v,h)=-a^{\mathrm {T} }v-b^{\mathrm {T} }h-v^{\mathrm {T} }Wh.} This energy function is analogous to that of a Hopfield network. As with general Boltzmann machines, the joint probability distribution for the visible and hidden vectors is defined in terms of the energy function as follows, P ( v , h ) = 1 Z e − E ( v , h ) {\displaystyle P(v,h)={\frac {1}{Z}}e^{-E(v,h)}} where Z {\displaystyle Z} is a partition function defined as the sum of e − E ( v , h ) {\displaystyle e^{-E(v,h)}} over all possible configurations, which can be interpreted as a normalizing constant to ensure that the probabilities sum to 1. The marginal probability of a visible vector is the sum of P ( v , h ) {\displaystyle P(v,h)} over all possible hidden layer configurations, P ( v ) = 1 Z ∑ { h } e − E ( v , h ) {\displaystyle P(v)={\frac {1}{Z}}\sum _{\{h\}}e^{-E(v,h)}} , and vice versa. Since the underlying graph structure of the RBM is bipartite (meaning there are no intra-layer connections), the hidden unit activations are mutually independent given the visible unit activations. Conversely, the visible unit activations are mutually independent given the hidden unit activations. That is, for m visible units and n hidden units, the conditional probability of a configuration of the visible units v, given a configuration of the hidden units h, is P ( v | h ) = ∏ i = 1 m P ( v i | h ) {\displaystyle P(v|h)=\prod _{i=1}^{m}P(v_{i}|h)} . Conversely, the conditional probability of h given v is P ( h | v ) = ∏ j = 1 n P ( h j | v ) {\displaystyle P(h|v)=\prod _{j=1}^{n}P(h_{j}|v)} . The individual activation probabilities are given by P ( h j = 1 | v ) = σ ( b j + ∑ i = 1 m w i , j v i ) {\displaystyle P(h_{j}=1|v)=\sigma \left(b_{j}+\sum _{i=1}^{m}w_{i,j}v_{i}\right)} and P ( v i = 1 | h ) = σ ( a i + ∑ j = 1 n w i , j h j ) {\displaystyle \,P(v_{i}=1|h)=\sigma \left(a_{i}+\sum _{j=1}^{n}w_{i,j}h_{j}\right)} where σ {\displaystyle \sigma } denotes the logistic sigmoid. The visible units of Restricted Boltzmann Machine can be multinomial, although the hidden units are Bernoulli. In this case, the logistic function for visible units is replaced by the softmax function P ( v i k = 1 | h ) = exp ⁡ ( a i k + Σ j W i j k h j ) Σ k ′ = 1 K exp ⁡ ( a i k ′ + Σ j W i j k ′ h j ) {\displaystyle P(v_{i}^{k}=1|h)={\frac {\exp(a_{i}^{k}+\Sigma _{j}W_{ij}^{k}h_{j})}{\Sigma _{k'=1}^{K}\exp(a_{i}^{k'}+\Sigma _{j}W_{ij}^{k'}h_{j})}}} where K is the number of discrete values that the visible values have. They are applied in topic modeling, and recommender systems. === Relation to other models === Restricted Boltzmann machines are a special case of Boltzmann machines and Markov random fields. The graphical model of RBMs corresponds to that of factor analysis. == Training algorithm == Restricted Boltzmann machines are trained to maximize the product of probabilities assigned to some training set V {\displaystyle V} (a matrix, each row of which is treated as a visible vector v {\displaystyle v} ), arg ⁡ max W ∏ v ∈ V P ( v ) {\displaystyle \arg \max _{W}\prod _{v\in V}P(v)} or equivalently, to maximize the expected log probability of a training sample v {\displaystyle v} selected randomly from V {\displaystyle V} : arg ⁡ max W E [ log ⁡ P ( v ) ] {\displaystyle \arg \max _{W}\mathbb {E} \left[\log P(v)\right]} The algorithm most often used to train RBMs, that is, to optimize the weight matrix W {\displaystyle W} , is the contrastive divergence (CD) algorithm due to Hinton, originally developed to train PoE (product of experts) models. The algorithm performs Gibbs sampling and is used inside a gradient descent procedure (similar to the way backpropagation is used inside such a procedure when training feedforward neural nets) to compute weight update. The basic, single-step contrastive divergence (CD-1) procedure for a single sample can be summarized as follows: Take a training sample v, compute the probabilities of the hidden units and sample a hidden activation vector h from this probability distribution. Compute the outer product of v and h and call this the positive gradient. From h, sample a reconstruction v' of the visible units, then resample the hidden activations h' from this. (Gibbs sampling step) Compute the outer product of v' and h' and call this the negative gradient. Let the update to the weight matrix W {\displaystyle W} be the positive gradient minus the negative gradient, times some learning rate: Δ W = ϵ ( v h T − v ′ h ′ T ) {\displaystyle \Delta W=\epsilon (vh^{\mathsf {T}}-v'h'^{\mathsf {T}})} . Update the biases a and b analogously: Δ a = ϵ ( v − v ′ ) {\displaystyle \Delta a=\epsilon (v-v')} , Δ b = ϵ ( h − h ′ ) {\displaystyle \Delta b=\epsilon (h-h')} . A Practical Guide to Training RBMs written by Hinton can be found on his homepage. == Stacked Restricted Boltzmann Machine == The difference between the Stacked Restricted Boltzmann Machines and RBM is that RBM has lateral connections within a layer that are prohibited to make analysis tractable. On the other hand, the Stacked Boltzmann consists of a combination of an unsupervised three-layer network with symmetric weights and a supervised fine-tuned top layer for recognizing three classes. The usage of Stacked Boltzmann is to understand Natural languages, retrieve documents, image generation, and classification. These functions are trained with unsupervised pre-training and/or supervised fine-tuning. Unlike the undirected symmetric top layer, with a two-way unsymmetric layer for connection for RBM. The restricted Boltzmann's connection is three-layers with asymmetric weights, and two networks are combined into one. Stacked Boltzmann does share similarities with RBM, the neuron for Stacked Boltzmann is a stochastic binary Hopfield neuron, which is the same as the Restricted Boltzmann Machine. The energy from both Restricted Boltzmann and RBM is given by Gibb's probability measure: E = − 1 2 ∑ i , j w i j s i s j + ∑ i θ i s i {\displaystyle E=-{\frac {1}{2}}\sum _{i,j}{w_{ij}{s_{i}}{s_{j}}}+\sum _{i}{\theta _{i}}{s_{i}}} . The training process of Restricted Boltzmann is similar to RBM. Restricted Boltzmann train one layer at a time and approximate equilibrium state with a 3-segment pass, not performing back propagation. Restricted Boltzmann uses both supervised and unsupervised on different RBM for pre-training for classification and recognition. The training uses contrastive divergence with
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SNNS

SNNS (Stuttgart Neural Network Simulator) is a neural network simulator originally developed at the University of Stuttgart. While it was originally built for X11 under Unix, there are Windows ports. Its successor JavaNNS never reached the same popularity. == Features == SNNS is written around a simulation kernel to which user written activation functions, learning procedures and output functions can be added. It has support for arbitrary network topologies and the standard release contains support for a number of standard neural network architectures and training algorithms. == Status == There is currently no ongoing active development of SNNS. In July 2008 the license was changed to the GNU LGPL.
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Amazon Q

Amazon Q is a chatbot developed by Amazon for enterprise use. Based on both Amazon Titan and GPT-5, it was announced on November 28, 2023. At launch, it was a part of the Amazon Web Services management console. Amazon CodeWhisperer is a part of Amazon Q Developer, a part of Amazon Q. == History == Amazon's business-focused chatbot Q was announced on November 28, 2023 in a preview, with a full version available at $20 per person per month. On July 19, 2025, the Amazon Q Visual Studio Code extension was compromised to delete the user's home directory. The issue was fixed on July 21. == Capabilities == Q can be prompted to summarize long documents and group chats, create charts, data analysis and write code. Q is also capable of accessing non-Amazon services. The chatbot is based on Amazon Titan and GPT-5, and uses the Amazon Bedrock repository of foundational models. It is part of the Amazon Web Services management console.
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The Best Free AI Paraphrasing Tool for Beginners

Trying to pick the best AI paraphrasing tool? An AI paraphrasing tool is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI paraphrasing tool slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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Stochastic grammar

A stochastic grammar (statistical grammar) is a grammar framework with a probabilistic notion of grammaticality: Stochastic context-free grammar Statistical parsing Data-oriented parsing Hidden Markov model (or stochastic regular grammar) Estimation theory The grammar is realized as a language model. Allowed sentences are stored in a database together with the frequency how common a sentence is. Statistical natural language processing uses stochastic, probabilistic and statistical methods, especially to resolve difficulties that arise because longer sentences are highly ambiguous when processed with realistic grammars, yielding thousands or millions of possible analyses. Methods for disambiguation often involve the use of corpora and Markov models. "A probabilistic model consists of a non-probabilistic model plus some numerical quantities; it is not true that probabilistic models are inherently simpler or less structural than non-probabilistic models." == Examples == A probabilistic method for rhyme detection is implemented by Hirjee & Brown in their study in 2013 to find internal and imperfect rhyme pairs in rap lyrics. The concept is adapted from a sequence alignment technique using BLOSUM (BLOcks SUbstitution Matrix). They were able to detect rhymes undetectable by non-probabilistic models.
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AI Analytics Tools Reviews: What Actually Works in 2026

Comparing the best AI analytics tool? An AI analytics tool is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI analytics tool slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
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Educational robotics

Educational robotics teaches the design, analysis, application and operation of robots. Robots include articulated robots, mobile robots or autonomous vehicles. Educational robotics can be taught from elementary school to graduate programs. Robotics may also be used to motivate and facilitate the instruction other, often foundational, topics such as computer programming, artificial intelligence or engineering design. == Education and training == Robotics engineers design robots, maintain them, develop new applications for them, and conduct research to expand the potential of robotics. Robots have become a popular educational tool in some middle and high schools, as well as in numerous youth summer camps, raising interest in programming, artificial intelligence and robotics among students. First-year computer science courses at several universities now include programming of a robot in addition to traditional software engineering-based coursework. == Category of Educational robotics == The categories of educational robots seen as having more than one category. It can be alienated into different categories based on their physical design and coding method. Generally they are categorised as arm robots, wheeled mobile robots and humanoid robots. Tangibly, coded robots uses a physical means of coding instead of the screens coding. === Initiatives in schools === Leachim, was a robot teacher programmed with the class curricular, as well as certain biographical information on the 40 students whom it was programmed to teach. Leachim could synthesize human speech using Diphone synthesis. It was invented by Michael J. Freeman in 1974 and was tested in a fourth grade classroom in the Bronx, New York. === Post-secondary degree programs === From approximately 1960 through 2005, robotics education at post-secondary institutions took place through elective courses, thesis experiences and design projects offered as part of degree programs in traditional academic disciplines, such as mechanical engineering, electrical engineering, industrial engineering or computer science. Since 2005, more universities have begun granting degrees in robotics as a discipline in its own right, often under the name "Robotic Engineering". Based on a 2015 web-based survey of robotics educators, the degree programs and their estimates annual graduates are listed alphabetically below. Note that only official degree programs where the word "robotics" appears on the transcript or diploma are listed here; whereas degree programs in traditional disciplines with course concentrations or thesis topics related to robotics are deliberately omitted. === Certification === The Robotics Certification Standards Alliance (RCSA) is an international robotics certification authority that confers various industry- and educational-related robotics certifications. === Summer robotics camp === Several summer camp programs include robotics as part of their core curriculum. In addition, youth summer robotics programs are frequently offered by celebrated museums such as the American Museum of Natural History and The Tech Museum of Innovation in Silicon Valley, CA, just to name a few. There are of benefits that come from attending robotics camps. It teaches students how to use teamwork, resilience and motivation, and decision-making. Students learn teamwork because most camps involve exciting activities requiring teamwork. Resilience and motivation is expected because by completing the challenging programs, students feel talented and accomplished after they complete the program. Also students are given unique situations making them make decisions to further their situation. === Educational robotics in special education === Educational robotics can be a useful tool in early and special education. According to a journal on new perspectives in science education, educational robotics can help to develop abilities that promote autonomy and assist their integration into society. Social and personal skills can also be developed through educational robotics. Using Lego Mindstorms NXT, schoolteachers were able to work with middle school aged children in order to develop programs and improve the children's social and personal skills. Additionally, problem solving skills and creativity were utilized through the creation of artwork and scenery to house the robots. Other studies show the benefits of educational robotics in special education as promoting superior cognitive functions, including executive functions. This can lead to an increased ability in "problem solving, reasoning and planning in typically developing preschool children." Through eight weeks of weekly forty-five-minute group sessions using the Bee-Bot, an increase in interest, attention, and interaction between both peers and adults was found in the school and preschool-aged children with Down Syndrome. This study suggests that educational robotics in the classroom can also lead to an improvement in visuo-spatial memory and mental planning. Furthermore, executive functions seemed to be possible in one child during this study.
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AI Code Generators: Free vs Paid (2026)

Looking for the best AI code generator? An AI code generator is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI code generator slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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Is an AI Website Builder Worth It in 2026?

Comparing the best AI website builder? An AI website builder is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI website builder slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
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