# field Published articles for field. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## Lifesaving Lincoln Laboratory device wins 2026 Excellence in Technology Transfer Award DevFeed: [Lifesaving Lincoln Laboratory device wins 2026 Excellence in Technology Transfer Award]() Original publisher: [Read original article]() Author: Erin Lee | Lincoln Laboratory Published: 2026-09-11T13:45:00Z Content type: news Language: en Sources: [MIT AI News]() Topics: [Artificial Intelligence](), [Development](), [Software]() Tags: [2026](), [ai](), [ai-assisted-catheterization-device](), [ai-guide](), [artificial-intelligence](), [asha-rajagopal](), [autonomus-medical-technologies](), [awards-honors-and-fellowships](), [devices](), [emergency-medicine](), [engineering](), [excellence-in-technology-transfer-awards](), [federal-laboratory-consortium-for-technology-transfer](), [field](), [funding](), [health-sciences-and-technology](), [industry](), [invention](), [lincoln-laboratory](), [mass-general-hospital](), [medical-device-invention](), [medical-devices](), [medicine](), [mgh](), [military-medics](), [mit-intellectual-property](), [mit-lincoln-laboratory](), [mit-startups](), [mit-technology-licensing-office-tlo](), [national-institutes-of-health-nih](), [nih-funding](), [portable](), [prototype](), [real-world](), [research](), [samuel-kesner](), [startup](), [startups](), [technology](), [u-s-armed-forces](), [u-s-army]() ### AI overview AI-GUIDE, a portable catheterization device developed by MIT Lincoln Laboratory and Massachusetts General Hospital, received the Federal Laboratory Consortium's 2026 Excellence in Technology Transfer Award. The project is transferring its prototype to AutonomUS Medical Technologies for commercialization. ### Source excerpt The handheld catheterization device AI-GUIDE, created by Lincoln Laboratory and Massachusetts General Hospital, promises improved health outcomes for injured service members and civilians. ## AI Prototyping in 2026: The PM Field Guide DevFeed: [AI Prototyping in 2026: The PM Field Guide]() Original publisher: [Read original article]() Author: Paweł Huryn Published: 2026-08-19T12:19:16Z Content type: tutorial Language: en Sources: [The Product Compass]() Topics: [Artificial Intelligence](), [prompt](), [Tool](), [Security](), [pixel]() Tags: [2026](), [ai](), [context](), [field](), [guide](), [pixel](), [prompt](), [security](), [tool]() ### AI overview A field guide to AI prototyping that compares tools for different jobs, presents a context prompt, recommends a security check before sharing a link, and addresses pixel-perfect handoff. ### Source excerpt I built the same CRM four times in just over an hour, live. The field guide: which tool for which job, the context prompt that beats a spec, the security check before you share a link, and the pixel-perfect handoff ## Creating a custom field in Craft CMS DevFeed: [Creating a custom field in Craft CMS]() Original publisher: [Read original article]() Author: andrew@nystudio107.com (Andrew Welch) Published: 2020-08-27T04:00:00Z Content type: tutorial Language: en Sources: [nystudio107 | Articles on modern web development.]() Topics: [Content Management System](), [Code]() Tags: [cms](), [code](), [craft](), [create](), [custom](), [field](), [how-to](), [insights](), [learn](), [leveraging](), [little](), [platform](), [possible](), [writing]() ### AI overview A tutorial on creating a custom field in Craft CMS whose dropdown options come from Craft Commerce country data. It recommends subclassing the built-in Craft Dropdown field and changing only the required behavior to reduce code and maintenance. ### Source excerpt Learn how to create a custom field in Craft CMS, writing as little code as possible by leveraging the platform. ## Testing Polynomial Equality DevFeed: [Testing Polynomial Equality]() Original publisher: [Read original article]() Published: 2017-04-24T09:00:14Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Testing](), [function]() Tags: [field](), [function](), [polynomials](), [random](), [roots](), [testing](), [variables]() ### AI overview The article explains how to test whether two multivariable polynomial expressions represent the same function. It presents randomized evaluation over a finite subset of a field and uses the Schwartz-Zippel lemma to bound the probability of an incorrect equality judgment. ### Source excerpt Problem: Determine if two polynomial expressions represent the same function. Specifically, if $ p(x_1, x_2, \dots, x_n)$ and $ q(x_1, x_2, \dots, x_n)$ are a polynomial with inputs, outputs and coefficients in a field $ F$, where $ |F|$ is sufficiently large, then the problem is to determine if $ p(\mathbf{x}) = q(\mathbf{x})$ for every $ x \in F$, in time polynomial in the number of bits required to write down $ p$ and $ q$. ## Creating a Content Builder in Craft CMS DevFeed: [Creating a Content Builder in Craft CMS]() Original publisher: [Read original article]() Author: andrew@nystudio107.com (Andrew Welch) Published: 2017-01-16T18:59:00Z Content type: tutorial Language: en Sources: [nystudio107 | Articles on modern web development.]() Topics: [Content Management System](), [Matrix](), [Front end](), [User experience (UX)](), [Website]() Tags: [article](), [authoring](), [better](), [block](), [blocks](), [builder](), [client](), [cms](), [content](), [create](), [field](), [frontend](), [giving](), [insights](), [just](), [matrix](), [rich](), [text](), [using]() ### AI overview This tutorial explains how to use Craft CMS's Matrix Block to build a structured content builder for clients. It argues that constrained block-based authoring can provide a better experience than an unrestricted Rich Text field. ### Source excerpt Using the Matrix block to create a "content builder" for your client is much better than just giving them a Rich Text field ## (Finite) Fields -- A Primer DevFeed: [(Finite) Fields -- A Primer]() Original publisher: [Read original article]() Published: 2014-02-26T10:00:01Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Mathematics](), [Math and Logic]() Tags: [complex-numbers](), [cryptography](), [euclidean-domains](), [field](), [field-characteristic](), [finite-fields](), [groups](), [ideals](), [mathematics](), [monoids](), [operations](), [polynomial-ring](), [vector-spaces]() ### AI overview This primer introduces fields as commutative rings with 0 and 1 in which every nonzero element has a multiplicative inverse. It defines the field axioms, places fields within related algebraic structures, and raises the question of finite fields. ### Source excerpt So far on this blog we've given some introductory notes on a few kinds of algebraic structures in mathematics (most notably groups and rings, but also monoids). Fields are the next natural step in the progression. If the reader is comfortable with rings, then a field is extremely simple to describe: they're just commutative rings with 0 and 1, where every nonzero element has a multiplicative inverse. We'll give a list of all of the properties that go into this "simple" definition in a moment, but an even more simple way to describe a field is as a place where "arithmetic makes sense. ## The Fundamental Theorem of Algebra (with Galois Theory) DevFeed: [The Fundamental Theorem of Algebra (with Galois Theory)]() Original publisher: [Read original article]() Published: 2012-02-02T22:42:11Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [Mathematics](), [Math and Logic]() Tags: [field](), [fundamental-theorem-of-algebra](), [galois-theory](), [group-theory](), [mathematics](), [polynomials](), [roots]() ### AI overview This mathematics post presents a Galois-theoretic proof strategy for the fundamental theorem of algebra. It assumes familiarity with field extensions, Galois theory, and group theory, and develops the argument using splitting fields, an intermediate extension of degree 2, Sylow subgroups, and the Galois correspondence. ### Source excerpt This post assumes familiarity with some basic concepts in abstract algebra, specifically the terminology of field extensions, and the classical results in Galois theory and group theory. The fundamental theorem of algebra has quite a few number of proofs (enough to fill a book!). In fact, it seems a new tool in mathematics can prove its worth by being able to prove the fundamental theorem in a different way. This series of proofs of the fundamental theorem also highlights how in mathematics there are many many ways to prove a single theorem, and in re-proving an established theorem we introduce new concepts and strategies. ## Row Reduction Over A Field DevFeed: [Row Reduction Over A Field]() Original publisher: [Read original article]() Published: 2011-12-30T15:36:28Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Computing](), [Optimization]() Tags: [eigenvalues](), [eigenvectors](), [field](), [linear-algebra](), [linear-maps](), [mathematics](), [matrices](), [optimization](), [programming](), [python](), [row-reduction]() ### AI overview This tutorial introduces row reduction over a field through matrices representing linear maps between finite-dimensional vector spaces. It explains row equivalence and describes how suitable matrix forms help determine kernels, images, dimensions, eigenvalues, and eigenvectors, with applications to persistent homology and optimization problems. ### Source excerpt We're quite eager to get to applications of algebraic topology to things like machine learning (in particular, persistent homology). Even though there's a massive amount of theory behind it (and we do plan to cover some of the theory), a lot of the actual computations boil down to working with matrices. Of course, this means we're in the land of linear algebra; for a refresher on the terminology, see our primers on linear algebra.