Smartglasses or smart glasses are eye or head-worn wearable computers. Many smartglasses include displays that add information alongside or to what the wearer sees. Alternatively, smartglasses are sometimes defined as glasses that are able to change their optical properties, such as smart sunglasses that are programmed to change tint by electronic means. Alternatively, smartglasses are sometimes defined as glasses that include headphone functionality. A pair of smartglasses can be considered an augmented reality device if it performs pose tracking. Superimposing information onto a field of view is achieved through an optical head-mounted display (OHMD) or embedded wireless glasses with transparent heads-up display (HUD) or augmented reality (AR) overlay. These systems have the capability to reflect projected digital images as well as allowing the user to see through it or see better with it. While early models can perform basic tasks, such as serving as a front end display for a remote system, as in the case of smartglasses utilizing cellular technology or Wi-Fi, modern smart glasses are effectively wearable computers which can run self-contained mobile apps. Some are handsfree and can communicate with the Internet via natural language voice commands, while others use touch buttons. Like other computers, smartglasses may collect information from internal or external sensors. It may control or retrieve data from other instruments or computers. In most cases, it supports wireless technologies like Bluetooth, Wi-Fi, and GPS. A small number of models run a mobile operating system and function as portable media players to send audio and video files to the user via a Bluetooth or WiFi headset. Some smartglasses models also feature full lifelogging and activity tracker capability. Smartglasses devices may also have features found on a smartphone. Some have activity tracker functionality features (also known as "fitness tracker") as seen in some GPS watches. == Features and applications == As with other lifelogging and activity tracking devices, the GPS tracking unit and digital camera of some smartglasses can be used to record historical data. For example, after the completion of a workout, data can be uploaded into a computer or online to create a log of exercise activities for analysis. Some smart watches can serve as full GPS navigation devices, displaying maps and current coordinates. Users can "mark" their current location and then edit the entry's name and coordinates, which enables navigation to those new coordinates. Although some smartglasses models manufactured in the 21st century are completely functional as standalone products, most manufacturers recommend or even require that consumers purchase mobile phone handsets that run the same operating system so that the two devices can be synchronized for additional and enhanced functionality. The smartglasses can work as an extension, for head-up display (HUD) or remote control of the phone and alert the user to communication data such as calls, SMS messages, emails, and calendar invites. === Security applications === Smart glasses could be used as a body camera. In 2018, Chinese police in Zhengzhou and Beijing were using smart glasses to take photos which are compared against a government database using facial recognition to identify suspects, retrieve an address, and track people moving beyond their home areas. === Sport applications === Smart glasses are used in sports like cycling, running, skiing, golf, tennis, or sailing, giving athletes real-time, heads-up data without looking down at the screen of a watch or smartphone. In 2025, Meta has announced a new partnership with sports eyewear brand Oakley. === Healthcare applications === Several proofs of concept for Google Glasses have been proposed in healthcare. In July 2013, Lucien Engelen started research on the usability and impact of Google Glass in health care. Engelen, who is based at Singularity University and in Europe at Radboud University Medical Center, is participating in the Glass Explorer program. Key findings of Engelen's research included: The quality of pictures and video are usable for healthcare education, reference, and remote consultation. The camera needs to be tilted to different angle for most of the operative procedures Tele-consultation is possible—depending on the available bandwidth—during operative procedures. A stabilizer should be added to the video function to prevent choppy transmission when a surgeon looks to screens or colleagues. Battery life can be easily extended with the use of an external battery. Controlling the device and/or programs from another device is needed for some features because of a sterile environment. Text-to-speech ("Take a Note" to Evernote) exhibited a correction rate of 60 percent, without the addition of a medical thesaurus. A protocol or checklist displayed on the screen of Google Glass can be helpful during procedures. Dr. Phil Haslam and Dr. Sebastian Mafeld demonstrated the first concept for Google Glass in the field of interventional radiology. They demonstrated the manner in which the concept of Google Glass could assist a liver biopsy and fistulaplasty, and the pair stated that Google Glass has the potential to improve patient safety, operator comfort, and procedure efficiency in the field of interventional radiology. In June 2013, surgeon Dr. Rafael Grossmann was the first person to integrate Google Glass into the operating theater, when he wore the device during a PEG (percutaneous endoscopic gastrostomy) procedure. In August 2013, Google Glass was also used at Wexner Medical Center at Ohio State University. Surgeon Dr. Christopher Kaeding used Google Glass to consult with a colleague in a distant part of Columbus, Ohio. A group of students at The Ohio State University College of Medicine also observed the operation on their laptop computers. Following the procedure, Kaeding stated, "To be honest, once we got into the surgery, I often forgot the device was there. It just seemed very intuitive and fit seamlessly." 16 November 2013, in Santiago de Chile, the maxillofacial team led by Dr.gn Antonio Marino conducted the first orthognathic surgery assisted with Google Glass in Latin America, interacting with them and working with simultaneous three-dimensional navigation. The surgical team was interviewed by ADN radio. In January 2014, Indian Orthopedic Surgeon Selene G. Parekh conducted the foot and ankle surgery using Google Glass in Jaipur, which was broadcast live on Google website via the internet. The surgery was held during a three-day annual Indo-US conference attended by a team of experts from the US and co-organized by Ashish Sharma. Sharma said Google Glass allows looking at an X-Ray or MRI without taking the eye off of the patient and allows a doctor to communicate with a patient's family or friends during a procedure. In Australia, during January 2014, Melbourne tech startup Small World Social collaborated with the Australian Breastfeeding Association to create the first hands-free breastfeeding Google Glass application for new mothers. The application, named Google Glass Breastfeeding app trial, allows mothers to nurse their baby while viewing instructions about common breastfeeding issues (latching on, posture etc.) or call a lactation consultant via a secure Google Hangout, who can view the issue through the mother's Google Glass camera. The trial was successfully concluded in Melbourne in April 2014, and 100% of participants were breastfeeding confidently. == Display types == Various techniques have existed for see-through HMDs. Most of these techniques can be summarized into two main families: "Curved Mirror" (or Curved Combiner) based and "Waveguide" or "Light-guide" based. The mirror technique has been used in EyeTaps, by Meta in their Meta 1, by Vuzix in their Star 1200 product, by Olympus, and by Laster Technologies. Various waveguide techniques have existed for some time. These techniques include diffraction optics, holographic optics, polarized optics, reflective optics, and projection: Diffractive waveguide – slanted diffraction grating elements (nanometric 10E-9). Nokia technique now licensed to Vuzix. Holographic waveguide – 3 holographic optical elements (HOE) sandwiched together (RGB). Used by Sony and Konica Minolta. Reflective waveguide – A thick light guide with single semi-reflective mirror is used by Epson in their Moverio product. A curved light guide with partial-reflective segmented mirror array to out-couple the light is used by tooz technologies GmbH. Virtual retinal display (VRD) – Also known as a retinal scan display (RSD) or retinal projector (RP), is a display technology that draws a raster display (like a television) directly onto the retina of the eye - developed by MicroVision, Inc. OLED microdisplays for near-eye applications (outdoor optical equipment, night vision glasses, ocular equipment for medical devices, augme
Onshape
Onshape is a computer-aided design (CAD) software system, delivered over the Internet via a software as a service (SaaS) model. It makes extensive use of cloud computing, with compute-intensive processing and rendering performed on Internet-based servers, and users are able to interact with the system via a web browser or the iOS and Android apps. As a SaaS system, Onshape upgrades are released directly to the web interface, and the software does not require maintenance by the user. Onshape allows teams to collaborate on a single shared design, the same way multiple writers can work together editing a shared document via cloud services. It is primarily focused on mechanical CAD (MCAD) and is used for product and machinery design across many industries, including consumer electronics, mechanical machinery, medical devices, 3D printing, machine parts, and industrial equipment. As of 2025, Onshape is popularly used as a CAD suite for the FIRST Robotics Competition (FRC) alongside the MKCad application available in the Onshape App Store. == Company history == Onshape was developed by a company with the same name. Founded in 2012, Onshape was based in Cambridge, Massachusetts (USA), with offices in Singapore and Pune, India. Its leadership team includes several engineers and executives who originated from SolidWorks, a popular 3D CAD program that runs on Microsoft Windows. Onshape’s co-founders include two former SolidWorks CEOs, Jon Hirschtick and John McEleney. In November 2012, former SolidWorks CEOs Jon Hirschtick and John McEleney led six co-founders launching Belmont Technology, a placeholder name that was later changed to Onshape. The company’s first round of funding was $9 million from North Bridge Venture Partners and Commonwealth Capital. In March 2015, Onshape released the public beta version of its cloud CAD software, after pre-production testing with more than a thousand CAD professionals in 52 countries. Included in the beta launch was Onshape for iPhone. In August 2015, the company released its Onshape for Android app. In December 2015, Onshape launched its full commercial release. The company also launched the Onshape App Store, offering CAM, simulation, rendering and other cloud-based engineering tools. The Onshape App Store was launched with 24 developer partners. In April 2016, Onshape introduced its Education Plan, with a free version of Onshape Professional geared for college students and educators. In May 2016, Onshape released FeatureScript, a new open source (MIT licensed) programming language for creating and customizing CAD features. In October 2019, Onshape agreed to be acquired by PTC. The acquisition closed in November 2019 for $470 million. In February 2024, Onshape released iOS support for the Apple Vision Pro, allowing for real world applications of CAD models and prototypes. In January 2025, Onshape released the CAM studio, allowing users to generate G-code for up to 5-axis Simultaneous milling. == Funding == Onshape was a venture-backed company with investments from firms including Andreessen Horowitz, Commonwealth Capital Ventures, New Enterprise Associates (NEA) and North Bridge Venture Partners. Total venture funding amounted to $169 million. == Supported file formats == === Modelling === ==== Importing ==== As of May 2025, Onshape supported importing (opening) the following common CAD file formats: Parasolid X_T (Preferred) STEP (ISO 10303) ISO JT (ISO 14306) ACIS IGES CATIA v4, v5, v6 Autodesk Inventor Part (.IPT) Assembly (.IAM) Presentation (.IPN) Drawing (.IDW) Pro/ENGINEER, Creo Rhinoceros 3D: .3dm .STL .OBJ SolidWorks file formats Siemens NX file formats Drawings (.DXF/.DWG) ==== Exporting ==== Onshape supports exporting to the following formats: STEP (ISO 10303) Parasolid XT ACIS IGES SolidWorks file formats .STL Rhinoceros 3D: .3dm Collada XML-spec based textual file === Drawing === Ordinary engineering or technical drawing can be exported as .PDF file. === Other Formats === In addition to CAD file formats, Onshape supports importing some Non-CAD file formats for viewing and referencing. === Assembly === Assemblies can be imported and exported to: STEP (ISO 10303) Parasolid XT ACIS Pro/ENGINEER, Creo ISO JT Rhinoceros 3D: .3dm Siemens NX file formats SolidWorks Pack and Go zip file File formats that assemblies can be only-exported to, are: IGES .STL Collada XML-spec based textual file
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Nicholas Carlini
Nicholas Carlini is an American researcher affiliated with Anthropic and previously with Google DeepMind who has published research in the fields of computer security and machine learning. He is known for his work on adversarial machine learning, particularly his work on the Carlini & Wagner attack in 2016. This attack was particularly useful in defeating defensive distillation, a method used to increase model robustness, and has since been effective against other defenses against adversarial input. In 2018, Carlini demonstrated an attack on Mozilla's DeepSpeech model, showing that hidden commands could be embedded in speech inputs, which the model would execute even if they were inaudible to humans. He also led a team at UC Berkeley that successfully broke seven out of nine defenses against adversarial attacks presented at the 2018 International Conference on Learning Representations. In addition to his work on adversarial attacks, Carlini has made significant contributions to understanding the privacy risks of machine learning models. In 2020, he revealed that large language models, like GPT-2, could memorize and output personally identifiable information. His research demonstrated that this issue worsened with larger models, and he later showed similar vulnerabilities in generative image models, such as Stable Diffusion. == Life and career == Nicholas Carlini obtained his Bachelor of Arts in Computer Science and Mathematics from the University of California, Berkeley, in 2013. He then continued his studies at the same university, where he pursued a PhD under the supervision of David Wagner, completing it in 2018. Carlini became known for his work on adversarial machine learning. In 2016, he worked alongside Wagner to develop the Carlini & Wagner attack, a method of generating adversarial examples against machine learning models. The attack was proved to be useful against defensive distillation, a popular mechanism where a student model is trained based on the features of a parent model to increase the robustness and generalizability of student models. The attack gained popularity when it was shown that the methodology was also effective against most other defenses, rendering them ineffective. In 2018, Carlini demonstrated an attack against Mozilla Foundation's DeepSpeech model where he showed that by hiding malicious commands inside normal speech input the speech model would respond to the hidden commands even when the commands were not discernible by humans. In the same year, Carlini and his team at UC Berkeley showed that out of the 11 papers presenting defenses to adversarial attacks accepted in that year's ICLR conference, seven of the defenses could be broken. Since 2021, he and his team have been working on large language models, creating a questionnaire where humans typically scored 35% whereas AI models scored in the 40%, with GPT-3 getting 38% which could be improved to 40% through few shot prompting. The best performer in the test was UnifiedQA, a model developed by Google specifically for answer questions and answer sets. Carlini has also developed methods to cause large language models like ChatGPT to answer harmful questions like how to construct bombs. He is also known for his work studying the privacy of machine learning models. In 2020, he showed for the first time that large language models would memorize some of the text data that they were trained on. For example, he found that GPT-2 could output personally identifiable information. He then led an analysis of larger models and studied how memorization increased with model size. Then, in 2022 he showed the same vulnerability in generative image models, and specifically diffusion models, by showing that Stable Diffusion could output images of people's faces that it was trained on. Following on this, Carlini then showed that ChatGPT would also sometimes output exact copies of webpages it was trained on, including personally identifiable information. Some of these studies have since been referenced by the courts in debating the copyright status of AI models. == Other work == Carlini received the Best of Show award at the 2020 IOCCC for implementing a tic-tac-toe game entirely with calls to printf, expanding on work from a research paper of his from 2015. The judges commented on his submission "This year's Best of Show (carlini) is such a novel way of obfuscation that it would be worth of a special mention in the (future) Best of IOCCC list!". [sic] == Awards == Best Student Paper Award, IEEE S&P 2017 ("Towards Evaluating the Robustness of Neural Networks") Best Paper Award, ICML 2018 ("Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples") Distinguished Paper Award, USENIX 2021 ("Poisoning the Unlabeled Dataset of Semi-Supervised Learning") Distinguished Paper Award, USENIX 2023 ("Tight Auditing of Differentially Private Machine Learning") Best Paper Award, ICML 2024 ("Stealing Part of a Production Language Model") Best Paper Award, ICML 2024 ("Considerations for Differentially Private Learning with Large-Scale Public Pretraining")
Dilek Hakkani-Tür
Dilek Z. Hakkani-Tür is a Turkish-American computer scientist focusing on speech processing, speech recognition, and dialogue systems. She is a professor of computer science at the University of Illinois Urbana-Champaign. == Education and career == Hakkani-Tür is a 1994 graduate of Middle East Technical University in Ankara, Turkey. She continued her studies at Bilkent University, also in Ankara, where she earned a master's degree in 1996 and completed her Ph.D. in 2000. She worked as a researcher at AT&T Labs from 2001 to 2005, at the International Computer Science Institute from 2006 to 2010, at Microsoft Research from 2010 to 2016, at Google Research from 2016 to 2018, and at Amazon Alexa from 2018 to 2023. At Microsoft, she was in the team of scientists that built the first prototype of the Cortana virtual assistant. While working for Amazon Alexa, she also taught at the University of California, Santa Cruz as a distinguished visiting instructor. She joined the University of Illinois Urbana-Champaign faculty in 2023. She was editor-in-chief of IEEE/ACM Transactions on Audio, Speech and Language Processing from 2019 to 2021, and is president of the Special Interest Group on Discourse and Dialogue of the Association for Computational Linguistics for the 2023–2025 term. She has served as co-editor-in-chief of Transactions of the Association for Computational Linguistics since 2024. == Recognition == In 2014, Hakkani-Tür was elected as an IEEE Fellow "for contributions to spoken language processing", and as a Fellow of the International Speech Communication Association "for contributions to advancing the state-of-the-art in spoken language processing, especially for human/human and human/machine conversational understanding". In 2024, she was elected as a Fellow of the Association for Computational Linguistics for her contributions to spoken dialogue systems.
Bayesian programming
Bayesian programming is a formalism and a methodology for having a technique to specify probabilistic models and solve problems when less than the necessary information is available. Edwin T. Jaynes proposed that probability could be considered as an alternative and an extension of logic for rational reasoning with incomplete and uncertain information. In his founding book Probability Theory: The Logic of Science he developed this theory and proposed what he called "the robot," which was not a physical device, but an inference engine to automate probabilistic reasoning—a kind of Prolog for probability instead of logic. Bayesian programming is a formal and concrete implementation of this "robot". Bayesian programming may also be seen as an algebraic formalism to specify graphical models such as, for instance, Bayesian networks, dynamic Bayesian networks, Kalman filters or hidden Markov models. Indeed, Bayesian programming is more general than Bayesian networks and has a power of expression equivalent to probabilistic factor graphs. == Formalism == A Bayesian program is a means of specifying a family of probability distributions. The constituent elements of a Bayesian program are presented below: Program { Description { Specification ( π ) { Variables Decomposition Forms Identification (based on δ ) Question {\displaystyle {\text{Program}}{\begin{cases}{\text{Description}}{\begin{cases}{\text{Specification}}(\pi ){\begin{cases}{\text{Variables}}\\{\text{Decomposition}}\\{\text{Forms}}\\\end{cases}}\\{\text{Identification (based on }}\delta )\end{cases}}\\{\text{Question}}\end{cases}}} A program is constructed from a description and a question. A description is constructed using some specification ( π {\displaystyle \pi } ) as given by the programmer and an identification or learning process for the parameters not completely specified by the specification, using a data set ( δ {\displaystyle \delta } ). A specification is constructed from a set of pertinent variables, a decomposition and a set of forms. Forms are either parametric forms or questions to other Bayesian programs. A question specifies which probability distribution has to be computed. === Description === The purpose of a description is to specify an effective method of computing a joint probability distribution on a set of variables { X 1 , X 2 , ⋯ , X N } {\displaystyle \left\{X_{1},X_{2},\cdots ,X_{N}\right\}} given a set of experimental data δ {\displaystyle \delta } and some specification π {\displaystyle \pi } . This joint distribution is denoted as: P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) {\displaystyle P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)} . To specify preliminary knowledge π {\displaystyle \pi } , the programmer must undertake the following: Define the set of relevant variables { X 1 , X 2 , ⋯ , X N } {\displaystyle \left\{X_{1},X_{2},\cdots ,X_{N}\right\}} on which the joint distribution is defined. Decompose the joint distribution (break it into relevant independent or conditional probabilities). Define the forms of each of the distributions (e.g., for each variable, one of the list of probability distributions). ==== Decomposition ==== Given a partition of { X 1 , X 2 , … , X N } {\displaystyle \left\{X_{1},X_{2},\ldots ,X_{N}\right\}} containing K {\displaystyle K} subsets, K {\displaystyle K} variables are defined L 1 , ⋯ , L K {\displaystyle L_{1},\cdots ,L_{K}} , each corresponding to one of these subsets. Each variable L k {\displaystyle L_{k}} is obtained as the conjunction of the variables { X k 1 , X k 2 , ⋯ } {\displaystyle \left\{X_{k_{1}},X_{k_{2}},\cdots \right\}} belonging to the k t h {\displaystyle k^{th}} subset. Recursive application of Bayes' theorem leads to: P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) = P ( L 1 ∧ ⋯ ∧ L K ∣ δ ∧ π ) = P ( L 1 ∣ δ ∧ π ) × P ( L 2 ∣ L 1 ∧ δ ∧ π ) × ⋯ × P ( L K ∣ L K − 1 ∧ ⋯ ∧ L 1 ∧ δ ∧ π ) {\displaystyle {\begin{aligned}&P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)\\={}&P\left(L_{1}\wedge \cdots \wedge L_{K}\mid \delta \wedge \pi \right)\\={}&P\left(L_{1}\mid \delta \wedge \pi \right)\times P\left(L_{2}\mid L_{1}\wedge \delta \wedge \pi \right)\times \cdots \times P\left(L_{K}\mid L_{K-1}\wedge \cdots \wedge L_{1}\wedge \delta \wedge \pi \right)\end{aligned}}} Conditional independence hypotheses then allow further simplifications. A conditional independence hypothesis for variable L k {\displaystyle L_{k}} is defined by choosing some variable X n {\displaystyle X_{n}} among the variables appearing in the conjunction L k − 1 ∧ ⋯ ∧ L 2 ∧ L 1 {\displaystyle L_{k-1}\wedge \cdots \wedge L_{2}\wedge L_{1}} , labelling R k {\displaystyle R_{k}} as the conjunction of these chosen variables and setting: P ( L k ∣ L k − 1 ∧ ⋯ ∧ L 1 ∧ δ ∧ π ) = P ( L k ∣ R k ∧ δ ∧ π ) {\displaystyle P\left(L_{k}\mid L_{k-1}\wedge \cdots \wedge L_{1}\wedge \delta \wedge \pi \right)=P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)} We then obtain: P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) = P ( L 1 ∣ δ ∧ π ) × P ( L 2 ∣ R 2 ∧ δ ∧ π ) × ⋯ × P ( L K ∣ R K ∧ δ ∧ π ) {\displaystyle {\begin{aligned}&P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)\\={}&P\left(L_{1}\mid \delta \wedge \pi \right)\times P\left(L_{2}\mid R_{2}\wedge \delta \wedge \pi \right)\times \cdots \times P\left(L_{K}\mid R_{K}\wedge \delta \wedge \pi \right)\end{aligned}}} Such a simplification of the joint distribution as a product of simpler distributions is called a decomposition, derived using the chain rule. This ensures that each variable appears at the most once on the left of a conditioning bar, which is the necessary and sufficient condition to write mathematically valid decompositions. ==== Forms ==== Each distribution P ( L k ∣ R k ∧ δ ∧ π ) {\displaystyle P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)} appearing in the product is then associated with either a parametric form (i.e., a function f μ ( L k ) {\displaystyle f_{\mu }\left(L_{k}\right)} ) or a question to another Bayesian program P ( L k ∣ R k ∧ δ ∧ π ) = P ( L ∣ R ∧ δ ^ ∧ π ^ ) {\displaystyle P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)=P\left(L\mid R\wedge {\widehat {\delta }}\wedge {\widehat {\pi }}\right)} . When it is a form f μ ( L k ) {\displaystyle f_{\mu }\left(L_{k}\right)} , in general, μ {\displaystyle \mu } is a vector of parameters that may depend on R k {\displaystyle R_{k}} or δ {\displaystyle \delta } or both. Learning takes place when some of these parameters are computed using the data set δ {\displaystyle \delta } . An important feature of Bayesian programming is this capacity to use questions to other Bayesian programs as components of the definition of a new Bayesian program. P ( L k ∣ R k ∧ δ ∧ π ) {\displaystyle P\left(L_{k}\mid R_{k}\wedge \delta \wedge \pi \right)} is obtained by some inferences done by another Bayesian program defined by the specifications π ^ {\displaystyle {\widehat {\pi }}} and the data δ ^ {\displaystyle {\widehat {\delta }}} . This is similar to calling a subroutine in classical programming and provides an easy way to build hierarchical models. === Question === Given a description (i.e., P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) {\displaystyle P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)} ), a question is obtained by partitioning { X 1 , X 2 , ⋯ , X N } {\displaystyle \left\{X_{1},X_{2},\cdots ,X_{N}\right\}} into three sets: the searched variables, the known variables and the free variables. The 3 variables S e a r c h e d {\displaystyle Searched} , K n o w n {\displaystyle Known} and F r e e {\displaystyle Free} are defined as the conjunction of the variables belonging to these sets. A question is defined as the set of distributions: P ( S e a r c h e d ∣ Known ∧ δ ∧ π ) {\displaystyle P\left(Searched\mid {\text{Known}}\wedge \delta \wedge \pi \right)} made of many "instantiated questions" as the cardinal of K n o w n {\displaystyle Known} , each instantiated question being the distribution: P ( Searched ∣ Known ∧ δ ∧ π ) {\displaystyle P\left({\text{Searched}}\mid {\text{Known}}\wedge \delta \wedge \pi \right)} === Inference === Given the joint distribution P ( X 1 ∧ X 2 ∧ ⋯ ∧ X N ∣ δ ∧ π ) {\displaystyle P\left(X_{1}\wedge X_{2}\wedge \cdots \wedge X_{N}\mid \delta \wedge \pi \right)} , it is always possible to compute any possible question using the following general inference: P ( Searched ∣ Known ∧ δ ∧ π ) = ∑ Free [ P ( Searched ∧ Free ∣ Known ∧ δ ∧ π ) ] = ∑ Free [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] P ( Known ∣ δ ∧ π ) = ∑ Free [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] ∑ Free ∧ Searched [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] = 1 Z × ∑ Free [ P ( Searched ∧ Free ∧ Known ∣ δ ∧ π ) ] {\displaystyle {\begin{aligned}&P\left({\text{Searched}}\mid {\text{Known}}\wedge \delta \wedge \pi \right)\\={}&\sum _{\text{Free}}\left[P\left({\text{Searched}}\wedge {\text{Free}}\mid {\text{Known}}\wedge \delta \wedge \
AI Essay Writers: Free vs Paid (2026)
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