Thinking Machines Lab Inc. is an American artificial intelligence (AI) startup founded by Mira Murati, the former chief technology officer of OpenAI. The company was founded in February 2025, and by July had completed an early-stage funding round led by Andreessen Horowitz, raising $2 billion at a valuation of $12 billion overall from investors such as Nvidia, AMD, Cisco, and Jane Street. The company is based in San Francisco and structured as a public benefit corporation. == History == By its launch in February 2025, Thinking Machines Lab was reported to have hired about 30 researchers and engineers from competitors including OpenAI, Meta AI, and Mistral AI. Its founding team members include Barret Zoph, former OpenAI VP of Research (Post-Training), Lilian Weng, former OpenAI VP, and OpenAI cofounder John Schulman, who joined after a brief stint at the lab's competitor Anthropic. In January 2026, it was reported that Barret Zoph and Luke Metz, departed the startup to return to OpenAI. Other former OpenAI employees who have been hired include Jonathan Lachman and Andrew Tulloch (although Tulloch departed after getting recruited for Meta Superintelligence Labs). Thinking Machines Lab's advisers include Bob McGrew, previously OpenAI's chief research officer, and Alec Radford, who was a lead researcher for OpenAI. On October 1, 2025, it announced Tinker, an API for fine-tuning language models. Users would submit jobs through the API for fine-tuning one of the various open-weight models supported. The Lab would run the jobs on its internal clusters and training infrastructure. == Business structure == Thinking Machines Lab grants Mira Murati a deciding vote on board matters, weighted to provide her with a majority decision-making capability. Additionally, founding shareholders possess votes weighted 100 times greater than those of regular shareholders. In July 2025, Andreessen Horowitz was reported to have led the company's initial funding round, raising "about $2 billion at a valuation of $12 billion". The government of Albania (Murati's country of origin) was also included in this round, making a $10 million investment which required an amendment to the country's 2025 budget. == Partnership == In March 2026, Thinking Machines Lab announced a strategic partnership with NVIDIA involving an undisclosed investment and a multi-year agreement to deploy one gigawatt of Vera Rubin computing capacity.
And–or tree
An and–or tree is a graphical representation of the reduction of problems (or goals) to conjunctions and disjunctions of subproblems (or subgoals). == Example == The and–or tree: represents the search space for solving the problem P, using the goal-reduction methods: P if Q and R P if S Q if T Q if U == Definitions == Given an initial problem P0 and set of problem solving methods of the form: P if P1 and … and Pn the associated and–or tree is a set of labelled nodes such that: The root of the tree is a node labelled by P0. For every node N labelled by a problem or sub-problem P and for every method of the form P if P1 and ... and Pn, there exists a set of children nodes N1, ..., Nn of the node N, such that each node Ni is labelled by Pi. The nodes are conjoined by an arc, to distinguish them from children of N that might be associated with other methods. A node N, labelled by a problem P, is a success node if there is a method of the form P if nothing (i.e., P is a "fact"). The node is a failure node if there is no method for solving P. If all of the children of a node N, conjoined by the same arc, are success nodes, then the node N is also a success node. Otherwise the node is a failure node. == Search strategies == An and–or tree specifies only the search space for solving a problem. Different search strategies for searching the space are possible. These include searching the tree depth-first, breadth-first, or best-first using some measure of desirability of solutions. The search strategy can be sequential, searching or generating one node at a time, or parallel, searching or generating several nodes in parallel. == Relationship with logic programming == The methods used for generating and–or trees are propositional logic programs (without variables). In the case of logic programs containing variables, the solutions of conjoint sub-problems must be compatible. Subject to this complication, sequential and parallel search strategies for and–or trees provide a computational model for executing logic programs. == Relationship with two-player games == And–or trees can also be used to represent the search spaces for two-person games. The root node of such a tree represents the problem of one of the players winning the game, starting from the initial state of the game. Given a node N, labelled by the problem P of the player winning the game from a particular state of play, there exists a single set of conjoint children nodes, corresponding to all of the opponents responding moves. For each of these children nodes, there exists a set of non-conjoint children nodes, corresponding to all of the player's defending moves. For solving game trees with proof-number search family of algorithms, game trees are to be mapped to and–or trees. MAX-nodes (i.e. maximizing player to move) are represented as OR nodes, MIN-nodes map to AND nodes. The mapping is possible, when the search is done with only a binary goal, which usually is "player to move wins the game".
Omni-Path
Omni-Path Architecture (OPA) is a high-performance communication architecture developed by Intel. It aims for low communication latency, low power consumption and a high throughput. It directly competes with InfiniBand. Intel planned to develop technology based on this architecture for exascale computing. The current owner of Omni-Path is Cornelis Networks. == History == Production of Omni-Path products started in 2015 and delivery of these products started in the first quarter of 2016. In November 2015, adapters based on the 2-port "Wolf River" ASIC were announced, using QSFP28 connectors with channel speeds up to 100 Gbit/s. Simultaneously, switches based on the 48-port "Prairie River" ASIC were announced. First models of that series were available starting in 2015. In April 2016, implementation of the InfiniBand "verbs" interface for the Omni-Path fabric was discussed. In October 2016, IBM, Hewlett Packard Enterprise, Dell, Lenovo, Samsung, Seagate Technology, Micron Technology, Western Digital and SK Hynix announced a joint consortium called Gen-Z to develop an open specification and architecture for non-volatile storage and memory products—including Intel's 3D Xpoint technology—which might in part compete against Omni-Path. Intel offered their Omni-Path products and components via other (hardware) vendors. For example, Dell EMC offered Intel Omni-Path as Dell Networking H-series, following the naming-standard of Dell Networking in 2017. In July 2019, Intel announced it would not continue development of Omni-Path networks and canceled OPA 200 series (200-Gbps variant of Omni-Path). In September 2020, Intel announced that the Omni-Path network products and technology would be spun out into a new venture with Cornelis Networks. Intel would continue to maintain support for legacy Omni-Path products, while Cornelis Networks continues the product line, leveraging existing Intel intellectual property related to Omni-Path architecture. In 2021, Cornelis announced Omni-Path Express, which replaces PSM2-based drivers and middleware, which trace back to PathScale's PSM created in 2003, for the existing Omni-Path hardware, with a native libfabric provider.
Factorization of polynomials over finite fields
In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them. All factorization algorithms, including the case of multivariate polynomials over the rational numbers, reduce the problem to this case; see polynomial factorization. It is also used for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory. As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article. == Background == === Finite field === The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches of mathematics. Due to the applicability of the concept in other topics of mathematics and sciences like computer science there has been a resurgence of interest in finite fields and this is partly due to important applications in coding theory and cryptography. Applications of finite fields introduce some of these developments in cryptography, computer algebra and coding theory. A finite field or Galois field is a field with a finite order (number of elements). The order of a finite field is always a prime or a power of prime. For each prime power q = pr, there exists exactly one finite field with q elements, up to isomorphism. This field is denoted GF(q) or Fq. If p is prime, GF(p) is the prime field of order p; it is the field of residue classes modulo p, and its p elements are denoted 0, 1, ..., p−1. Thus a = b in GF(p) means the same as a ≡ b (mod p). === Irreducible polynomials === Let F be a finite field. As for general fields, a non-constant polynomial f in F[x] is said to be irreducible over F if it is not the product of two polynomials of positive degree. A polynomial of positive degree that is not irreducible over F is called reducible over F. Irreducible polynomials allow us to construct the finite fields of non-prime order. In fact, for a prime power q, let Fq be the finite field with q elements, unique up to isomorphism. A polynomial f of degree n greater than one, which is irreducible over Fq, defines a field extension of degree n which is isomorphic to the field with qn elements: the elements of this extension are the polynomials of degree lower than n; addition, subtraction and multiplication by an element of Fq are those of the polynomials; the product of two elements is the remainder of the division by f of their product as polynomials; the inverse of an element may be computed by the extended GCD algorithm (see Arithmetic of algebraic extensions). It follows that, to compute in a finite field of non prime order, one needs to generate an irreducible polynomial. For this, the common method is to take a polynomial at random and test it for irreducibility. For sake of efficiency of the multiplication in the field, it is usual to search for polynomials of the shape xn + ax + b. Irreducible polynomials over finite fields are also useful for pseudorandom number generators using feedback shift registers and discrete logarithm over F2n. The number of irreducible monic polynomials of degree n over Fq is the number of aperiodic necklaces, given by Moreau's necklace-counting function Mq(n). The closely related necklace function Nq(n) counts monic polynomials of degree n which are primary (a power of an irreducible); or alternatively irreducible polynomials of all degrees d which divide n. === Example === The polynomial P = x4 + 1 is irreducible over Q but not over any finite field. On any field extension of F2, P = (x + 1)4. On every other finite field, at least one of −1, 2 and −2 is a square, because the product of two non-squares is a square and so we have If − 1 = a 2 , {\displaystyle -1=a^{2},} then P = ( x 2 + a ) ( x 2 − a ) . {\displaystyle P=(x^{2}+a)(x^{2}-a).} If 2 = b 2 , {\displaystyle 2=b^{2},} then P = ( x 2 + b x + 1 ) ( x 2 − b x + 1 ) . {\displaystyle P=(x^{2}+bx+1)(x^{2}-bx+1).} If − 2 = c 2 , {\displaystyle -2=c^{2},} then P = ( x 2 + c x − 1 ) ( x 2 − c x − 1 ) . {\displaystyle P=(x^{2}+cx-1)(x^{2}-cx-1).} === Complexity === Polynomial factoring algorithms use basic polynomial operations such as products, divisions, gcd, powers of one polynomial modulo another, etc. A multiplication of two polynomials of degree at most n can be done in O(n2) operations in Fq using "classical" arithmetic, or in O(nlog(n) log(log(n)) ) operations in Fq using "fast" arithmetic. A Euclidean division (division with remainder) can be performed within the same time bounds. The cost of a polynomial greatest common divisor between two polynomials of degree at most n can be taken as O(n2) operations in Fq using classical methods, or as O(nlog2(n) log(log(n)) ) operations in Fq using fast methods. For polynomials h, g of degree at most n, the exponentiation hq mod g can be done with O(log(q)) polynomial products, using exponentiation by squaring method, that is O(n2log(q)) operations in Fq using classical methods, or O(nlog(q)log(n) log(log(n))) operations in Fq using fast methods. In the algorithms that follow, the complexities are expressed in terms of number of arithmetic operations in Fq, using classical algorithms for the arithmetic of polynomials. == Factoring algorithms == Many algorithms for factoring polynomials over finite fields include the following three stages: Square-free factorization Distinct-degree factorization Equal-degree factorization An important exception is Berlekamp's algorithm, which combines stages 2 and 3. === Berlekamp's algorithm === Berlekamp's algorithm is historically important as being the first factorization algorithm which works well in practice. However, it contains a loop on the elements of the ground field, which implies that it is practicable only over small finite fields. For a fixed ground field, its time complexity is polynomial, but, for general ground fields, the complexity is exponential in the size of the ground field. === Square-free factorization === The algorithm determines a square-free factorization for polynomials whose coefficients come from the finite field Fq of order q = pm with p a prime. This algorithm firstly determines the derivative and then computes the gcd of the polynomial and its derivative. If it is not one then the gcd is again divided into the original polynomial, provided that the derivative is not zero (a case that exists for non-constant polynomials defined over finite fields). This algorithm uses the fact that, if the derivative of a polynomial is zero, then it is a polynomial in xp, which is, if the coefficients belong to Fp, the pth power of the polynomial obtained by substituting x by x1/p. If the coefficients do not belong to Fp, the pth root of a polynomial with zero derivative is obtained by the same substitution on x, completed by applying the inverse of the Frobenius automorphism to the coefficients. This algorithm works also over a field of characteristic zero, with the only difference that it never enters in the blocks of instructions where pth roots are computed. However, in this case, Yun's algorithm is much more efficient because it computes the greatest common divisors of polynomials of lower degrees. A consequence is that, when factoring a polynomial over the integers, the algorithm which follows is not used: one first computes the square-free factorization over the integers, and to factor the resulting polynomials, one chooses a p such that they remain square-free modulo p. Algorithm: SFF (Square-Free Factorization) Input: A monic polynomial f in Fq[x] where q = pm Output: Square-free factorization of f R ← 1 # Make w be the product (without multiplicity) of all factors of f that have # multiplicity not divisible by p c ← gcd(f, f′) w ← f/c # Step 1: Identify all factors in w i ← 1 while w ≠ 1 do y ← gcd(w, c) fac ← w / y R ← R · faci w ← y; c ← c / y; i ← i + 1 end while # c is now the product (with multiplicity) of the remaining factors of f # Step 2: Identify all remaining factors using recursion # Note that these are the factors of f that have multiplicity divisible by p if c ≠ 1 then c ← c1/p R ← R·SFF(c)p end if Output(R) The idea is to identify the product of all irreducible factors of f with the same multiplicity. This is done in two steps. The first step uses the formal d
Big memory
Big-memory computers are machines with a large amount of random-access memory (RAM). The computers are required for databases, graph analytics, or more generally, high-performance computing, data science, and big data. Some database systems called in-memory databases are designed to run mostly in memory, rarely if ever retrieving data from disk or flash memory. See list of in-memory databases. == Details == The performance of big-memory systems depends on how the central processing units (CPUs) access the memory, via a conventional memory controller or via non-uniform memory access (NUMA). Performance also depends on the size and design of the CPU cache. Performance also depends on operating system (OS) design. The huge pages feature in Linux and other OSes can improve the efficiency of virtual memory. The transparent huge pages feature in Linux can offer better performance for some big-memory workloads. The "Large-Page Support" in Microsoft Windows enables server applications to establish large-page memory regions which are typically three orders of magnitude larger than the native page size.
Princh
Princh is a Danish software company, which is headquartered in Aarhus, Denmark. Founded in 2015, Princh develops cloud printing and electronic payment products. The company is headquartered in the city of Aarhus. While utilizing a smartphone or web app, users can locate a nearby printer to their current location, get directions to access said printer, and/or authorize a print and pay for the print job in question. The product is available as a native mobile apps for Android and iOS, as well as on web and desktop products for businesses and libraries. The app connects a network of printer owners and users around the world. Princh supports an array of printable files. == History == The company was founded in 2015. The company is currently based in the southern part of Aarhus. The Princh printing service was officially launched on June 23, 2015. Currently, Princh is available as a service in a multitude of locations such as print shops, libraries, hotels, or universities. Princh is a popular printing and payment product among libraries and can among other places be found in Denmark, Sweden, Norway, Germany, United Kingdom, United States, and Canada. == How it works == With the Princh app, users will be able to locate their nearest printer. Once the user is at the printer, the user chooses the document to be printed out and shares it with the Princh app. The user then selects the desired nearby printer entering the printer ID number or scanning the QR-code located on top of the printer, pays electronically and the print job is processed by the printer. Printer owners get access to a personal control panel where they can set printing prices and monitor all Princh activity for their business. == Notes and references ==
Social media coverage of the Olympics
Over the years, television broadcast rights have distinguished what Olympic-related content can be accessed by fans online. By doing so, mobile-friendly social platforms began to integrate into the Olympics. Athletes and fans use these platforms to share live updates, special moments, and behind-the-scenes specials. Various social media platforms have been used for Olympic content, including Twitter and Facebook. Some marketers credit social media for prompting the official U.S. broadcasters, NBC, to live stream events, including early rounds. == Background == The Olympics is able to advertise to its viewers and its host country with the use of data it collects through Social media marketing. Prominent social media platforms include: Twitter, Facebook, Instagram, Tumblr, YouTube, Google, MSN, Yahoo and many more. Campaign Initiatives and Artificial Intelligence technologies have been used to analyze the social media content of users. Information from consumers such as their preferences, demographics, age and locality are all analyzed to gain consumer insight. Campaign initiatives and AI technologies were used for such purposes in the 2010 Vancouver Winter Olympics and are in use currently. Social media marketing of the Olympics is a new phenomena, beginning prior to the 2008 Beijing Olympics == Variations == There are two classifications of social media marketing recognized by the IOC: Officially sanctioned content from rights holders and sponsors that maximizes the use of Olympic content (imagery, hashtag) Unofficial content that is generated by brands that leverage the excitement of the Olympics == 2008 Beijing Summer Olympics == Social media marketing emerged as a phenomenon during the 2008 Beijing Olympics, which progressed as a marketing and an advertising tactic ever since. The Beijing Olympics became the test subject for social media marketing initiatives started by advertising agencies. In 2008, social media marketing began the transition from one-sided communication to mass communication of the Olympic Games. Although social media marketing of the Olympic Games began in 2008, the audience to the Olympics was still primarily reached through television–reaching an audience of 4.3 billion viewers. At the time, the viewers of the Olympic Games through Internet website platforms made up an audience of approximately 390 million individuals. What was the beginning of Olympic social media marketing, was also the beginning of a more globalized experience of the Olympic Games via social media. Twitter, now a prominent social media platform, began in 2006 and grew to three million active users by the beginning of the 2008 Beijing Olympics. Members of Facebook, another prominent social media platform, tracking the Olympic Games grew from approximately one million during the Olympic Games of Athens 2004 to 90 million during the 2008 Beijing Olympics. Social media use, in general, increased by 24 percent between 2007 and 2008–from 63 percent of U.S. adults to 87 percent of U.S. adults. == 2010 Vancouver Winter Olympics == The International Olympic Committee (IOC) deemed The Vancouver Winter Olympics as "the first social media games” based on its fan base through social media platforms. The IOC launched their Facebook page a month before the games began, attracting 1.5 million fans. Shifting to online viewing attracted a younger audience than past Olympic games with over 60 percent of Facebook fans being under 24 years of age. Athletes like Lindsey Vonn and Shaun White reached fans on social media as the platform posted behind-the-scenes coverage on their experiences. The IOC used social media to create competitions between athletes and fans streamed online. Its YouTube channel hosted a “Best of Us” challenge in which the public could compete in games with their favorite athletes, acquiring three million viewers. Photos spread across social media platforms, such as Flickr, which had 11,000 photos posted by 600 photographers, bringing a new perspective to the games. Twitter contributed constant live updates of the competitions. The IOC's Twitter following doubled to 12,000 followers during the Vancouver Olympics, creating a larger viewer population for the games. The IOC created social media guidelines as more athletes and fans got online to interact with the Olympics. Social media was still relatively new as a marketing platform, so these guidelines confused many individuals. == 2012 London Summer Olympics == The London 2012 Olympic Games succeeded in broadcasting, participation and marketing. For the first time, the IOC broadcast the Olympic Games live and on-demand through YouTube, allowing fans to access the Games anytime, anywhere through live streaming. The combination of conventional broadcasting and mobile platforms reached a global audience of 4.8 billion people. Social media soared with Facebook, Twitter and Google+, attracting 4.7 million followers. Athletes shared photographs, interacted online with fans and updated daily, either in person or via an agent. Instagram was established by 2012, making itself a premier photo-sharing platform perfect for athletes to capture their emotions. Lewis Wiltshire, head of sport for Twitter UK said, "Never before have fans had such direct access to their sporting heroes." Social media created conversation on fan opinions regarding athletes, including 962,756 total mentions of Usain Bolt, “Fastest Man in History,” who defended the 100 meter and 200 meter gold medals. Michael Phelps followed with 828,081 total mentions. Olympic sponsors were active on social media; created several campaigns to promote their brands; and inspired viewers with mass participation and personalized events. The Adidas “Take the Stage” Campaign recognized talent around the world, installing a photo booth and inviting the 550 Olympics athletes to take the stage. (IOC Marketing Report 2012). David Beckham surprised fans at the photo booth in Westfield shopping centre, gaining popularity in UK media. Coca-Cola, Acer Inc., McDonald's, Visa Inc. and several others used similar tactics of participation to attract viewers. == 2014 Sochi Winter Olympics == === Channels === The 2014 Winter Olympic Games were held in Sochi, a city in Krasnodar Krai, Russia, establishing the first “social media Olympics” for Russia. The most popular Russian social media and networking service, VK, created an Olympic page, similar to Facebook's. The Olympic VK page has 2.8 million fans and—the most popular official community on the platform. Throughout the games, VK had 54 million Olympic mentions, an average of 1.5 million per day. Numbers grew on other social media pages: more than 2 million fans joined the Olympic Facebook page, 168,101 followed the Olympic Twitter, 150,000 followed the Olympic Instagram and three million visited the Olympic website in February 2014. There were 90,000 total updates on social media by Sochi 2014 Olympians and teams. The United States was the most active country during the games logging 22,598 posts across Facebook, Twitter, and Instagram. === Engagement === With social media there is also hashtags. The most popular hashtag was #sochi2014 with almost 11,000 uses. The next top five hashtags were #wearewinter, #teamusa, #olympics, #goaus and #wirfuerD. Another popular hashtag was #Sochiproblems, depicting local struggles. Photos of the poor state of Sochi on all platforms made the games the number one trending topic one week before the opening ceremony. #SochiFail and #SochiProblems gave multiple reports of the poor living arrangements, incomplete construction, broken elevators, and polluted waters. This was one way that social media provided awareness to its users. === Media Perceptions === Media perceptions varied during the games; the Olympics was viewed as a confrontation between Eastern and Western Civilizations. The LGBT community took a stand against the games. Sponsors for the games including Coca-Cola, Mcdonald's, and P&G protested against Russian authorities and Russian anti-LGBT laws. Many protests took a stand against Russian laws, which created a discussion between human rights advocates. Advocates believed organizations should not promote certain values in western markets while supporting an anti-human rights government in another market. == 2016 Rio Summer Olympics == Social media marketing was an influential tool in the promotion and analysis of the 2016 Rio Olympics. Thomas Bach, President of the International Olympic Committee said that the power of sport demonstrates that diversity and interconnectedness can enlighten us all. With over 25,000+ sources of accredited media covering the games, the 2016 games were the most consumed Olympic games to date. Marketing for the Rio Olympics began in 2013 and ultimately lasted 3 years. There were 26 million visits to Olympic.org, the official website of the Olympic games, and over 7 billion views of official Olympic content on social media. There were o