In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the root node, which has no parent (i.e., the root node as the top-most node in the tree hierarchy). These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes (parent and children nodes of a node under consideration, if they exist) in a single straight line (called edge or link between two adjacent nodes). Binary trees are a commonly used type, which constrain the number of children for each parent to at most two. When the order of the children is specified, this data structure corresponds to an ordered tree in graph theory. A value or pointer to other data may be associated with every node in the tree, or sometimes only with the leaf nodes, which have no children nodes. The abstract data type (ADT) can be represented in a number of ways, including a list of parents with pointers to children, a list of children with pointers to parents, or a list of nodes and a separate list of parent-child relations (a specific type of adjacency list). Representations might also be more complicated, for example using indexes or ancestor lists for performance. Trees as used in computing are similar to but can be different from mathematical constructs of trees in graph theory, trees in set theory, and trees in descriptive set theory. == Terminology == A node is a structure which may contain data and connections to other nodes, sometimes called edges or links. Each node in a tree has zero or more child nodes, which are below it in the tree (by convention, trees are drawn with descendants going downwards). A node that has a child is called the child's parent node (or superior). All nodes have exactly one parent, except the topmost root node, which has none. A node might have many ancestor nodes, such as the parent's parent. Child nodes with the same parent are sibling nodes. Typically siblings have an order, with the first one conventionally drawn on the left. Some definitions allow a tree to have no nodes at all, in which case it is called empty. An internal node (also known as an inner node, inode for short, or branch node) is any node of a tree that has child nodes. Similarly, an external node (also known as an outer node, leaf node, or terminal node) is any node that does not have child nodes. The height of a node is the length of the longest downward path to a leaf from that node. The height of the root is the height of the tree. The depth of a node is the length of the path to its root (i.e., its root path). Thus the root node has depth zero, leaf nodes have height zero, and a tree with only a single node (hence both a root and leaf) has depth and height zero. Conventionally, an empty tree (tree with no nodes, if such are allowed) has height −1. Each non-root node can be treated as the root node of its own subtree, which includes that node and all its descendants. Other terms used with trees: Neighbor Parent or child. Ancestor A node reachable by repeated proceeding from child to parent. Descendant A node reachable by repeated proceeding from parent to child. Also known as subchild. Degree For a given node, its number of children. A leaf, by definition, has degree zero. Degree of tree The degree of a tree is the maximum degree of a node in the tree. Distance The number of edges along the shortest path between two nodes. Level The level of a node is the number of edges along the unique path between it and the root node. This is the same as depth. Width The number of nodes in a level. Breadth The number of leaves. Complete tree A tree with every level filled, except the last. Forest A set of one or more disjoint trees. Ordered tree A rooted tree in which an ordering is specified for the children of each vertex. Size of a tree Number of nodes in the tree. == Common operations == Enumerating all the items Enumerating a section of a tree Searching for an item Adding a new item at a certain position on the tree Deleting an item Pruning: Removing a whole section of a tree Grafting: Adding a whole section to a tree Finding the root for any node Finding the lowest common ancestor of two nodes === Traversal and search methods === Stepping through the items of a tree, by means of the connections between parents and children, is called walking the tree, and the action is a walk of the tree. Often, an operation might be performed when a pointer arrives at a particular node. A walk in which each parent node is traversed before its children is called a pre-order walk; a walk in which the children are traversed before their respective parents are traversed is called a post-order walk; a walk in which a node's left subtree, then the node itself, and finally its right subtree are traversed is called an in-order traversal. (This last scenario, referring to exactly two subtrees, a left subtree and a right subtree, assumes specifically a binary tree.) A level-order walk effectively performs a breadth-first search over the entirety of a tree; nodes are traversed level by level, where the root node is visited first, followed by its direct child nodes and their siblings, followed by its grandchild nodes and their siblings, etc., until all nodes in the tree have been traversed. == Representations == There are many different ways to represent trees. In working memory, nodes are typically dynamically allocated records with pointers to their children, their parents, or both, as well as any associated data. If of a fixed size, the nodes might be stored in a list. Nodes and relationships between nodes might be stored in a separate special type of adjacency list. In relational databases, nodes are typically represented as table rows, with indexed row IDs facilitating pointers between parents and children. Nodes can also be stored as items in an array, with relationships between them determined by their positions in the array (as in a binary heap). A binary tree can be implemented as a list of lists: the head of a list (the value of the first term) is the left child (subtree), while the tail (the list of second and subsequent terms) is the right child (subtree). This can be modified to allow values as well, as in Lisp S-expressions, where the head (value of first term) is the value of the node, the head of the tail (value of second term) is the left child, and the tail of the tail (list of third and subsequent terms) is the right child. Ordered trees can be naturally encoded by finite sequences, for example with natural numbers. == Examples of trees and non-trees == == Type theory == As an abstract data type, the abstract tree type T with values of some type E is defined, using the abstract forest type F (list of trees), by the functions: value: T → E children: T → F nil: () → F node: E × F → T with the axioms: value(node(e, f)) = e children(node(e, f)) = f In terms of type theory, a tree is an inductive type defined by the constructors nil (empty forest) and node (tree with root node with given value and children). == Mathematical terminology == Viewed as a whole, a tree data structure is an ordered tree, generally with values attached to each node. Concretely, it is (if required to be non-empty): A rooted tree with the "away from root" direction (a more narrow term is an "arborescence"), meaning: A directed graph, whose underlying undirected graph is a tree (any two vertices are connected by exactly one simple path), with a distinguished root (one vertex is designated as the root), which determines the direction on the edges (arrows point away from the root; given an edge, the node that the edge points from is called the parent and the node that the edge points to is called the child), together with: an ordering on the child nodes of a given node, and a value (of some data type) at each node. Often trees have a fixed (more properly, bounded) branching factor (outdegree), particularly always having two child nodes (possibly empty, hence at most two non-empty child nodes), hence a "binary tree". Allowing empty trees makes some definitions simpler, some more complicated: a rooted tree must be non-empty, hence if empty trees are allowed the above definition instead becomes "an empty tree or a rooted tree such that ...". On the other hand, empty trees simplify defining fixed branching factor: with empty trees allowed, a binary tree is a tree such that every node has exactly two children, each of which is a tree (possibly empty). == Applications == Trees are commonly used to represent or manipulate hierarchical data in ap
Catie Cuan
Catie Cuan is an artist, entrepeuneur, and innovator in the field of robotic art and human-robot interaction, where she specializes in choreorobotics, an emerging field at the intersection of choreographic dance and robotics. Catie Cuan is currently one of the academic researchers pioneering the field of choreorobotics and currently holds a post-doctoral fellowship at Stanford University. == Career == Catie Cuan earned a bachelor's degree from the University of California, Berkeley. She graduated with a Ph.D. from the Department of Mechanical Engineering at Stanford University, focusing in robotics. Her most cited publication is about how to improve robotic expressive systems using tools from dance theory, such as the Laban/Bartenieff Movement Analysis. In her most recent research projects, she explores a predictive model of imitation learning for robots moving around humans, a project that advances the field of social robotics. Cuan credits her work in robotics to the experience with her father when he had a stroke and was surrounded by many medical machines, which made her think about how people might feel empowered and hopeful rather than afraid. As a ballet dancer and choreographer, she has performed with the Metropolitan Opera Ballet and the Lyric Opera of Chicago. In 2020, she was the dancer and choreographer of the show Output, which was part of a collaboration with ThoughtWorks Arts and the Pratt Institute. In the production, she danced with an ABB IRB 6700 industrial robot. In 2022, she was named as an IF/THEN ambassador for the American Association for the Advancement of Science. The same year, she was appointed Futurist-in-Residence at the Smithsonian Arts and Industries Building, where she performed at the closing ceremonies of the FUTURES exhibit on July 6, 2022. Cuan has also contributed to product designs, working with IDEO and Dutch interior design firm moooi on their Piro project, which launched a dancing scent diffuser robot during Milan Design Week in June 2022. She is a TED speaker with talks about how to teach robots to dance, and what is coming up for dancing robots in the AI era.
OpenAI Operator
OpenAI Operator was an AI agent developed by OpenAI, capable of autonomously performing tasks through web browser interactions, including filling forms, placing online orders, scheduling appointments, and other repetitive browser-based tasks. It uses OpenAI's advanced models to expand practical automation capabilities for users in daily activities. Operator was launched on January 23, 2025. It was released as a limited-access research preview to ChatGPT Pro-tier subscribers in the United States on February 1, 2025, with future plans to broaden availability. Operator was deprecated after the release of ChatGPT agent, and shut down on August 31, 2025. == Performance and limitations == In benchmark assessments, Operator achieved notable success, scoring 38.1% on OSWorld benchmarks (OS-level tasks) and 58.1% on WebArena benchmarks (web interactions). However, it did not reach human-level accuracy and faced limitations with intricate user interfaces and extended workflows. == Safety and privacy == OpenAI emphasized privacy and safety measures within Operator, including stringent data protection protocols and built-in safety checks designed to prevent unauthorized sensitive actions or information misuse. == Availability == Initially, Operator was only available to ChatGPT Pro subscribers in the U.S., with plans for broader availability to Plus, Team, and Enterprise users in the future.
Yann LeCun
Yann André Le Cun ( lə-KUN; French: [ləkœ̃]; usually spelled LeCun; born 8 July 1960) is a French-American computer scientist working in the fields of artificial intelligence, machine learning, computer vision, robotics and image compression. He is the Jacob T. Schwartz Professor of Computer Science at the Courant Institute of Mathematical Sciences at New York University. He served as Chief AI Scientist at Meta Platforms before co-founding Advanced Machine Intelligence Labs in December 2025. He is well known for his work on optical character recognition and computer vision using convolutional neural networks (CNNs). He is also one of the main creators of the DjVu image compression technology, alongside Léon Bottou and Patrick Haffner. He co-developed the Lush programming language with Léon Bottou. In 2018, LeCun, Yoshua Bengio, and Geoffrey Hinton received the Turing Award from the Association for Computing Machinery (ACM) for their work on deep learning. LeCun, Bengio, and Hinton, and occasionally Jürgen Schmidhuber, are sometimes referred to as the "Godfathers of AI" and "Godfathers of Deep Learning". == Early life and education == Yann André Le Cun was born on 8 July 1960 at Soisy-sous-Montmorency, in the suburbs of Paris. His surname, Le Cun, derives from the old Breton form Le Cunff and originates from the region of Guingamp in northern Brittany. Yann is the Breton form of Jean, the French form of John. He received a Diplôme d'Ingénieur from the ESIEE Paris in 1983 and a PhD in computer science from Université Pierre et Marie Curie (now Sorbonne University) in 1987, during which he proposed an early form of backpropagation, an algorithm crucial for enabling neural networks to learn. Before joining AT&T, LeCun was a postdoctoral researcher for a year, starting in 1987, supervised by Geoffrey Hinton at the University of Toronto. LeCun has three sons, and his brother is employed by Google. He has American citizenship. == Career and research == LeCun's career has been spent primarily at Bell Labs, New York University and Meta Platforms, Inc. === Bell Labs === In 1988, LeCun joined the Adaptive Systems Research Department at AT&T Bell Laboratories in Holmdel, New Jersey, United States, headed by Lawrence D. Jackel, where he developed a number of new machine learning methods, such as a biologically inspired model of image recognition called convolutional neural networks (LeNet), the "Optimal Brain Damage" regularization methods, and the Graph Transformer Networks method (similar to conditional random field), which he applied to handwriting recognition and Optical character recognition (OCR). The bank check recognition system that he helped develop was widely deployed by NCR and other companies. In 1996, he joined AT&T Labs-Research as head of the Image Processing Research Department, which was part of Lawrence Rabiner's Speech and Image Processing Research Lab, and worked primarily on the DjVu image compression technology, a format designed for efficient distribution of scanned documents, and used by the Internet Archive to provide access to digitized texts. His collaborators at AT&T include Léon Bottou and Vladimir Vapnik. === New York University === After a brief tenure as a fellow of NEC Research Institute, LeCun joined New York University in 2003, where he is Jacob T. Schwartz Chaired Professor of Computer Science and Neural Science at the Courant Institute of Mathematical Sciences and the Center for Neural Science. At NYU, he has worked primarily on energy-based models for supervised and unsupervised learning, feature learning for object recognition in computer vision, and mobile robotics. In 2012, he became the founding director of the NYU Center for Data Science. On 9 December 2013, LeCun became the first director of Meta AI Research in New York City and in early 2014 stepped down from the NYU–CDS directorship. In 2013, he and Yoshua Bengio co-founded the International Conference on Learning Representations, which adopted a post-publication open review process he previously advocated on his website. He was the chair and organiser of the "Learning Workshop" held every year between 1986 and 2012 in Snowbird, Utah. He is a member of the Science Advisory Board of the Institute for Pure and Applied Mathematics at UCLA. He is the co-director of the Learning in Machines and Brain research program (formerly Neural Computation & Adaptive Perception) of CIFAR. In 2016, he was the visiting professor of computer science on the Chaire Annuelle Informatique et Sciences Numériques at Collège de France in Paris, where he presented the leçon inaugurale (inaugural lecture). In 2023, he was named as the inaugural Jacob T. Schwartz Chaired Professor in Computer Science at NYU's Courant Institute. LeCun is also a scientific advisor to French research group Kyutai which is being funded by Xavier Niel, Rodolphe Saadé, Eric Schmidt, and others. === Meta Platforms === LeCun joined Facebook (now Meta Platforms) in 2013 as chief AI scientist and led the company's AI research laboratory, FAIR. === AMI Labs === On 19 November 2025, LeCun confirmed that he would be leaving Meta after ten years to found his own company focused on world-model architectures and human-like artificial intelligence he calls superintelligence. The company he founded, Advanced Machine Intelligence Labs (or AMI Labs), is run by CEO Alex LeBrun, with LeCun serving as Executive Chair. This venture is focused on building AI "world models": systems that learn to understand the physical world's structure and dynamics rather than just predict text like large language models. In March 2026, AMI announced it had raised $1.03 billion in funding at a $3.5 billion pre-money valuation. The funding round was co-led by investors including Cathay Innovation, Greycroft, Hiro Capital, HV Capital and Bezos Expeditions. In January 2026, LeCun became founding chair of the Technical Research Board of Logical Intelligence, an AI company developing energy-based (EBM) reasoning systems. == Honours and awards == LeCun is a member of the US National Academy of Sciences, National Academy of Engineering and the French Académie des Sciences. He has received honorary doctorates from Instituto Politécnico Nacional (IPN) in Mexico City in 2016, from EPFL in 2018, from Université Côte d'Azur in 2021, from Università di Siena in 2023, and from Hong Kong University of Science and Technology in 2023. In 2014, he received the IEEE Neural Network Pioneer Award and in 2015, the PAMI Distinguished Researcher Award. In 2018, LeCun was awarded the IRI Medal, established by the Industrial Research Institute (IRI), and the Harold Pender Award, given by the University of Pennsylvania. In 2019, he received the Golden Plate Award of the American Academy of Achievement. In March 2019, LeCun won the 2018 Turing Award, sharing it with Yoshua Bengio and Geoffrey Hinton. In 2022, he received the Princess of Asturias Award in the category "Scientific Research", along with Yoshua Bengio, Geoffrey Hinton and Demis Hassabis. In 2023, the President of France made him a Chevalier (Knight) of the French Legion of Honour. During the World Economic Forum (WEF) 2024 in Davos, he received the Global Swiss AI Award 2023. The same year, he received the grand prize of the VinFuture Prize alongside Yoshua Bengio, Jensen Huang, Geoffrey Hinton, and Fei-Fei Li for their groundbreaking contributions to neural networks and deep learning algorithms. In 2025 he was awarded the Queen Elizabeth Prize for Engineering jointly with Yoshua Bengio, Bill Dally, Geoffrey E. Hinton, John Hopfield, Jensen Huang and Fei-Fei Li.
NLWeb
Natural Language Web or NLWeb was introduced by Microsoft in 2025. It is an open Python project designed to simplify the creation of natural language interfaces for websites. It enables users to query website contents using natural language, similar to interacting with an AI assistant. Every instance functions as a Model Context Protocol (MCP) server allowing websites to make their content discoverable and accessible to AI agents and other participants. NLWeb leverages existing web standards like Schema.org and RSS to build conversational capabilities of processing user queries through language models, performing semantic searches against website content and generating natural responses. It is platform-agnostic, running on all major systems and connecting to any vector database. Content to be indexed by NLWeb works best when it is organized in an AI friendly way. This means short, interlinked and semantically annotated articles work best. Initial adopters of NLWeb include TripAdvisor, Shopify, Eventbrite, and Hearst.
Zamzar
Zamzar is an online file converter and compressor, created by brothers Mike and Chris Whyley in England in 2006. It allows users to convert files online, without downloading a software tool, and supports over 1,200 different conversion types. Since its formation, the service has converted over 510 million files for users from 245 different countries. The service supports the conversion of documents, images, audio, video, e-Books, CAD files and compressed file formats. Users can type in a URL or upload one or more files (if they are all of the same format) from their computer; Zamzar will then convert the file(s) to another user-specified format, such as an Adobe PDF file to a Microsoft Word document. Once conversion is complete, users can immediately download the file from their web browser. Users can also choose to receive an email with a link to download the converted file. In February 2021 Zamzar expanded their tool and announced a new file compression service. The compressor is visually similar to the conversion tool with a drag and drop download feature. As with the converter, users have the option to subscribe for a paid plan if they wish to compress multiple or larger files than the free service permits == File conversion API == in 2015 Zamzar launched a file conversion API, allowing users to integrate file conversion capabilities into their own websites and applications. Sample code is provided to allow users to integrate file conversion capabilities in C#, Java, Node.js, PHP, Python and cURL. Zamzar also maintains a project on GitHub which allows users to perform file conversion from the command line on Linux, MacOS or Windows systems. == Email file conversion == It is also possible to send files for conversion by emailing them to Zamzar. Zamzar launched this capability in 2012, allowing users to email files to dedicated email addresses for the file to be automatically converted to a different format. A link is then emailed back to the end user to allow them to download their converted file. == User privilege levels == Zamzar is currently free to use, but there is a limit of two conversions per hour for files up to 100MB. Users can pay a monthly subscription in order to access preferential features, such as unlimited file conversions, online file management, shorter response and queuing times and other benefits. == Name == Its name comes from Franz Kafka's The Metamorphosis. Its main character is called Gregor Samsa and it is from his surname that Zamzar is derived. The founders of the service considered three other names – Konvertieren, Khamailen and Obrogo – before settling on Zamzar.
Chainer
Chainer is an open source deep learning framework written purely in Python on top of NumPy and CuPy Python libraries. The development is led by Japanese venture company Preferred Networks in partnership with IBM, Intel, Microsoft, and Nvidia. Chainer is notable for its early adoption of "define-by-run" scheme, as well as its performance on large scale systems. The first version was released in June 2015 and has gained large popularity in Japan since then. Furthermore, in 2017, it was listed by KDnuggets in top 10 open source machine learning Python projects. In December 2019, Preferred Networks announced the transition of its development effort from Chainer to PyTorch and it will only provide maintenance patches after releasing v7. == Define-by-run == Chainer was the first deep learning framework to introduce the define-by-run approach. The traditional procedure to train a network was in two phases: define the fixed connections between mathematical operations (such as matrix multiplication and nonlinear activations) in the network, and then run the actual training calculation. This is called the define-and-run or static-graph approach. Theano and TensorFlow are among the notable frameworks that took this approach. In contrast, in the define-by-run or dynamic-graph approach, the connection in a network is not determined when the training is started. The network is determined during the training as the actual calculation is performed. One of the advantages of this approach is that it is intuitive and flexible. If the network has complicated control flows such as conditionals and loops, in the define-and-run approach, specially designed operations for such constructs are needed. On the other hand, in the define-by-run approach, programming language's native constructs such as if statements and for loops can be used to describe such flow. This flexibility is especially useful to implement recurrent neural networks. Another advantage is ease of debugging. In the define-and-run approach, if an error (such as numeric error) has occurred in the training calculation, it is often difficult to inspect the fault, because the code written to define the network and the actual place of the error are separated. In the define-by-run approach, you can just suspend the calculation with the language's built-in debugger and inspect the data that flows on your code of the network. Define-by-run has gained popularity since the introduction by Chainer and is now implemented in many other frameworks, including PyTorch and TensorFlow. == Extension libraries == Chainer has four extension libraries, ChainerMN, ChainerRL, ChainerCV and ChainerUI. ChainerMN enables Chainer to be used on multiple GPUs with performance significantly faster than other deep learning frameworks. A supercomputer running Chainer on 1024 GPUs processed 90 epochs of ImageNet dataset on ResNet-50 network in 15 minutes, which is four times faster than the previous record held by Facebook. ChainerRL adds state of art deep reinforcement learning algorithms, and ChainerUI is a management and visualization tool. == Applications == Chainer is used as the framework for PaintsChainer, a service which does automatic colorization of black and white, line only, draft drawings with minimal user input.