Gcore is an edge AI, cloud, network, and security company headquartered in Luxembourg. Founded in 2014, the company provides low-latency services to industries including finance, healthcare, manufacturing, gaming, media and telecommunications internationally. As of March 2024, its global network includes over 180 Points of Presence (PoPs) across six continents. == History == Gcore was founded in 2014 in Luxembourg. The company built its own content delivery network, originally designed for the needs of the gaming industry. In 2016, Gcore's infrastructure expanded to multiple regions that were underserved by hyperscale cloud providers. In 2020, the company formed partnerships with Intel and Equinix. In 2022, Gcore launched the European AI Cloud, providing access to infrastructure for machine learning tasks. In March 2024, Gcore announced the acquisition of a web application and API protection (WAAP) solution from StackPath. In April 2024, Gcore received a commendation in the Industry Innovation category at the NVIDIA Partner Network Awards EMEA for developing the first speech-to-text technology for Luxembourgish, using the LuxemBERT AI model. In May 2024, Philipp Rösler, former vice-chancellor of Germany and federal minister of health joined the Gcore board. In July 2024, Gcore raised $60 million in a Series A funding round, marking the company's first external investment since its founding. In August 2024, Gcore was recognized as a Major Player in the IDC MarketScape report for European public cloud Infrastructure (IaaS) 2024 by IDC, the global market intelligence firm. In May 2025, Feiyu Xu became a member of the Gcore advisory board. == Network infrastructure == According to the company's website, Gcore has network locations in six continents: Europe, North America, Asia, South America, Africa, and Australia with over 14,000 peering partners and a network capacity exceeding 200 Tbps. According to a 2025 review by Geekflare, Gcore's CDN achieved an average global response time of around 30 milliseconds. Gcore offers AI cloud clusters, including a generative AI cluster with Nvidia GPUs in Luxembourg and additional sites in the Netherlands and Wales, as part of its European AI infrastructure. == Products and services == Gcore offers a range of services, including content delivery network (CDN), cloud computing,virtual machines, bare-metal servers, object storage AI infrastructure and inference, Kubernetes, video streaming, DDoS mitigation, web application and API protection (WAAP), Domain Name System (DNS). Gcore provides AI services and GPU cloud infrastructure to support model development, training, fine-tuning, and inference. In January 2025, the company introduced Everywhere Inference, a serverless inference solution that enables AI model deployment. == Controversies == Correctiv and Tageszeitung reported that Gcore supported the distribution of the TV network RT until April 2023, which has been under sanctions by the EU since March 2022. However, Gcore denies these allegations. == Collaborations == In 2024, Gcore and Qareeb Data Centres, a data center provider in the Middle East, launched a collaboration to integrate Gcore's AI, cloud and edge services across data centers in multiple Middle Eastern countries. In June 2025, Gcore joined the SmartSpires initiative, a €3.1 million smart city project co-funded by the Connecting Europe Facility. The three-year programme is coordinated by a public–private consortium including 5SKYE, the Luxembourg Institute of Science and Technology (LIST), Orange Luxembourg, and Gcore. The project aims to transform the Belval campus into a smart city by deploying 5G-enabled smart towers that integrate edge computing, artificial intelligence and IoT services. Within the consortium, Gcore acts as project coordinator and is responsible for the deployment of the edge infrastructure.
Isotropic position
In the fields of machine learning, the theory of computation, and random matrix theory, a probability distribution over vectors is said to be in isotropic position if its covariance matrix is proportional to the identity matrix. == Formal definitions == Let D {\textstyle D} be a distribution over vectors in the vector space R n {\textstyle \mathbb {R} ^{n}} . Then D {\textstyle D} is in isotropic position if, for vector v {\textstyle v} sampled from the distribution, E v v T = I d . {\displaystyle \mathbb {E} \,vv^{\mathsf {T}}=\mathrm {Id} .} A set of vectors is said to be in isotropic position if the uniform distribution over that set is in isotropic position. In particular, every orthonormal set of vectors is isotropic. As a related definition, a convex body K {\textstyle K} in R n {\textstyle \mathbb {R} ^{n}} is called isotropic if it has volume | K | = 1 {\textstyle |K|=1} , center of mass at the origin, and there is a constant α > 0 {\textstyle \alpha >0} such that ∫ K ⟨ x , y ⟩ 2 d x = α 2 | y | 2 , {\displaystyle \int _{K}\langle x,y\rangle ^{2}dx=\alpha ^{2}|y|^{2},} for all vectors y {\textstyle y} in R n {\textstyle \mathbb {R} ^{n}} ; here | ⋅ | {\textstyle |\cdot |} stands for the standard Euclidean norm.
Trie
In computer science, a trie (, ), also known as a digital tree or prefix tree, is a specialized search tree data structure used to store and retrieve strings from a dictionary or set. Unlike a binary search tree, nodes in a trie do not store their associated key. Instead, each node's position within the trie determines its associated key, with the connections between nodes defined by individual characters rather than the entire key. Tries are particularly effective for tasks such as autocomplete, spell checking, and IP routing, offering advantages over hash tables due to their prefix-based organization and lack of hash collisions. Every child node shares a common prefix with its parent node, and the root node represents the empty string. While basic trie implementations can be memory-intensive, various optimization techniques such as compression and bitwise representations have been developed to improve their efficiency. A notable optimization is the radix tree, which provides more efficient prefix-based storage. While tries store character strings, they can be adapted to work with any ordered sequence of elements, such as permutations of digits or shapes. A notable variant is the bitwise trie, which uses individual bits from fixed-length binary data (such as integers or memory addresses) as keys. == History, etymology, and pronunciation == The idea of a trie for representing a set of strings was first abstractly described by Axel Thue in 1912. Tries were first described in a computer context by René de la Briandais in 1959. The idea was independently described in 1960 by Edward Fredkin, who coined the term trie, pronouncing it (as "tree"), after the middle syllable of retrieval. However, other authors pronounce it (as "try"), in an attempt to distinguish it verbally from "tree". == Overview == Tries are a form of string-indexed look-up data structure, which is used to store a dictionary list of words that can be searched on in a manner that allows for efficient generation of completion lists. A prefix trie is an ordered tree data structure used in the representation of a set of strings over a finite alphabet set, which allows efficient storage of words with common prefixes. Tries can be efficacious on string-searching algorithms such as predictive text, approximate string matching, and spell checking in comparison to binary search trees. A trie can be seen as a tree-shaped deterministic finite automaton. == Operations == Tries support various operations: insertion, deletion, and lookup of a string key. Tries are composed of nodes that contain links, which either point to other suffix child nodes or null. As for every tree, each node except the root is pointed to by only one other node, called its parent. Each node contains as many links as the number of characters in the applicable alphabet (although tries tend to have a substantial number of null links). In some cases, the alphabet used is simply that of the character encoding—resulting in, for example, a size of 128 in the case of ASCII. The null links within the children of a node emphasize the following characteristics: Characters and string keys are implicitly stored in the trie, and include a character sentinel value indicating string termination. Each node contains one possible link to a prefix of strong keys of the set. A basic structure type of nodes in the trie is as follows: Node {\displaystyle {\text{Node}}} may contain an optional Value {\displaystyle {\text{Value}}} , which is associated with the key that corresponds to the node. === Searching === Searching for a value in a trie is guided by the characters in the search string key, as each node in the trie contains a corresponding link to each possible character in the given string. Thus, following the string within the trie yields the associated value for the given string key. A null link during the search indicates the inexistence of the key. The following pseudocode implements the search procedure for a given string key in a rooted trie x. In the above pseudocode, x and key correspond to the pointer of the trie's root node and the string key, respectively. The search operation takes O ( m ) {\displaystyle O(m)} time, where m {\displaystyle m} is the size of the string parameter key. In a balanced binary search tree, on the other hand, it takes O ( m log n ) {\displaystyle O(m\log n)} time, in the worst case, since key needs to be compared with O ( log n ) {\displaystyle O(\log n)} other keys and each comparison takes O ( m ) {\displaystyle O(m)} time, in the worst case. The trie occupies less space, in comparison with a binary search tree, in the case of a large number of short strings, since nodes share common initial string subsequences and store the keys implicitly. === Insertion === Insertion into a trie is guided by using the character sets as indexes to the children array until the last character of the string key is reached. Each node in the trie corresponds to one call of the radix sorting routine, as the trie structure reflects the execution pattern of the top-down radix sort. If null links are encountered before reaching the last character of the string key, new nodes are created. The input value is assigned to the value of the last node traversed, which is the node that corresponds to the key. === Deletion === Deletion of a key–value pair from a trie involves finding the node corresponding to the key, setting its value to null, and recursively removing nodes that have no children. The procedure begins by examining key; an empty string indicates arrival at the node corresponding to the (original) key, in which case its value is set to null. If the node, then, has null value and no children, it is removed from the trie by returning null; otherwise, the node is kept by returning the node itself. == Replacing other data structures == === Replacement for hash tables === A trie can be used to replace a hash table, over which it has the following advantages: Searching for a node with an associated key of size m {\displaystyle m} has the complexity of O ( m ) {\displaystyle O(m)} , whereas an imperfect hash function may have numerous colliding keys, and the worst-case lookup speed of such a table would be O ( N ) {\displaystyle O(N)} , where N {\displaystyle N} denotes the total number of nodes within the table. Tries do not need a hash function for the operation, unlike a hash table; there are also no collisions of different keys in a trie. Within a trie, keys can be efficiently sorted lexicographically. However, tries are less efficient than a hash table when the data is directly accessed on a secondary storage device such as a hard disk drive that has higher random access time than the main memory. == Implementation strategies == Tries can be represented in several ways, corresponding to different trade-offs between memory use and speed of the operations. Using a vector of pointers for representing a trie consumes enormous space; however, memory space can be reduced at the expense of running time if a singly linked list is used for each node vector, as most entries of the vector contains nil {\displaystyle {\text{nil}}} . Techniques such as alphabet reduction may reduce the large space requirements by reinterpreting the original string as a longer string over a smaller alphabet. For example, a string of n bytes can alternatively be regarded as a string of 2n four-bit units. This can reduce memory usage by a factor of eight; but lookups need to visit twice as many nodes in the worst case. Another technique includes storing a vector of 256 ASCII pointers as a bitmap of 256 bits representing ASCII alphabet, which reduces the size of individual nodes dramatically. === Bitwise tries === Bitwise tries are used to address the enormous space requirement for the trie nodes in a naive simple pointer vector implementations. Each character in the string key set is represented via individual bits, which are used to traverse the trie over a string key. The implementations for these types of trie use vectorized CPU instructions to find the first set bit in a fixed-length key input (e.g. GCC's __builtin_clz() intrinsic function). Accordingly, the set bit is used to index the first item, or child node, in the 32- or 64-entry based bitwise tree. Search then proceeds by testing each subsequent bit in the key. This procedure is also cache-local and highly parallelizable due to register independency, and thus performant on out-of-order execution CPUs. === Compressed tries === Radix tree, also known as a compressed trie, is a space-optimized variant of a trie in which any node with only one child gets merged with its parent; elimination of branches of the nodes with a single child results in better metrics in both space and time. This works best when the trie remains static and set of keys stored are very sparse within their representation space. One more approach for static tries is to "pack" the trie by storing disjoint
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Stefano Soatto
Stefano Soatto is professor of computer science at the University of California, Los Angeles (UCLA), in Los Angeles, CA, where he is also professor of electrical engineering and founding director of the UCLA Vision Lab. He is also Vice President of applied science for Amazon Web Services' (AWS) AI division. == Academic biography == Soatto obtained his D. Eng. in electrical engineering, cum laude, from the University of Padua in 1992, was an EAP Fellow at the University of California, Berkeley in 1990–1991, and received his Ph.D. in control and dynamical systems from the California Institute of Technology in 1996 with dissertation "A Geometric Approach to Dynamic Vision". In 1996–97 he was a postdoctoral scholar at Harvard University, and subsequently held positions as assistant and associate professor of electrical engineering and biomedical engineering at Washington University in St. Louis, and of mathematics and computer science at the University of Udine, Italy. He has been at UCLA since 2000. He is also Vice President of applied science for Amazon Web Services' (AWS) AI division. == Research == Soatto's research focuses on computer vision, machine learning and robotics. He co-developed optimal algorithms for structure from motion (SFM, or visual SLAM, simultaneous localization and mapping, in robotics; Best Paper Award at CVPR 1998), characterized its ambiguities (David Marr Prize at ICCV 1999), also characterized the identifiability and observability of visual-inertial sensor fusion (Best Paper Award at ICRA 2015). His research focus is the development of representations, that are functions of the data that capture their informative content and discard irrelevant variability in the data (a generalized form of 'noise' or 'clutter'). Soatto's lab first to demonstrate real-time SFM and augmented reality (AR) on commodity hardware in live demos at CVPR 2000, ICCV 2001, and ECCV 2002. He also co-led the UCLA-Golem Team in the second DARPA Grand Challenge for autonomous vehicles, with Emilio Frazzoli (co-founder of NuTonomy), and Amnon Shashua (co-founder of Mobileye). == Recognition == Soatto was named Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in 2013 for contributions to dynamic visual processes. He received the David Marr Prize in Computer Vision in 1999. He was named to the 2022 class of ACM Fellows, "for contributions to the foundations and applications of visual geometry and visual representations learning".
Webmail
Webmail (or web-based email) is an email service that can be accessed using a standard web browser. It contrasts with email service accessible through a specialised email client software. Additionally, many internet service providers (ISP) provide webmail as part of their internet service package. Similarly, some web hosting providers also provide webmail as a part of their hosting package. As with any web application, webmail's main advantage over the use of a desktop email client is the ability to send and receive email anywhere from a web browser. == History == === Early implementations === The first Web Mail implementation was developed at CERN in 1993 by Phillip Hallam-Baker as a test of the HTTP protocol stack, but was not developed further. In the next two years, however, several people produced working webmail applications. In Europe, there were three implementations, Søren Vejrum's "WWW Mail", Luca Manunza's "WebMail", and Remy Wetzels' "WebMail". Søren Vejrum's "WWW Mail" was written when he was studying and working at the Copenhagen Business School in Denmark, and was released on February 28, 1995. Luca Manunza's "WebMail" was written while he was working at CRS4 in Sardinia, from an idea of Gianluigi Zanetti, with the first source release on March 30, 1995. Remy Wetzels' "WebMail" was written while he was studying at the Eindhoven University of Technology in the Netherlands for the DSE and was released early January 1995. In the United States, Matt Mankins wrote "Webex", and Bill Fitler, while at Lotus cc:Mail, began working on an implementation which he demonstrated publicly at Lotusphere on January 24, 1995. Customers who saw the cc:Mail demonstration were very enthusiastic, one recalling that they were "like an angry mob. People were yelling, 'We want this now!'". Matt Mankins, under the supervision of Dr. Burt Rosenberg at the University of Miami, released his "Webex" application source code in a post to comp.mail.misc on August 8, 1995, although it had been in use as the primary email application at the School of Architecture where Mankins worked for some months prior. Bill Fitler's webmail implementation was further developed as a commercial product, which Lotus announced and released in the fall of 1995 as cc:Mail for the World Wide Web 1.0; thereby providing an alternative means of accessing a cc:Mail message store (the usual means being a cc:Mail desktop application that operated either via dialup or within the confines of a local area network). Early commercialization of webmail was also achieved when "Webex" began to be sold by Mankins' company, DotShop, Inc., at the end of 1995. Within DotShop, "Webex" changed its name to "EMUmail"; which would be sold to companies like UPS and Rackspace until its sale to Accurev in 2001. EMUmail was one of the first applications to feature a free version that included embedded advertising, as well as a licensed version that did not. Hotmail and Four11's RocketMail both launched in 1996 as free services and immediately became very popular. === Widespread deployment === As the 1990s progressed, and into the 2000s, it became more common for the general public to have access to webmail because: many Internet service providers (such as EarthLink) and web hosting providers (such as Verio) began bundling webmail into their service offerings (often in parallel with POP/SMTP services); many other enterprises (such as universities and large corporations) also started offering webmail as a way for their user communities to access their email (either locally managed or outsourced); webmail service providers (such as Hotmail and RocketMail) emerged in 1996 as a free service to the general public, and rapidly gained in popularity. In some cases, webmail application software is developed in-house by the organizations running and managing the application, and in some cases it is obtained from software companies that develop and sell such applications, usually as part of an integrated mail server package (an early example being Netscape Messaging Server). The market for webmail application software has continued into the 2010s. == Rendering and compatibility == Email users may find the use of both a webmail client and a desktop client using the POP3 protocol presents some difficulties. For example, email messages that are downloaded by the desktop client and are removed from the server will no longer be available on the webmail client. The user is limited to previewing messages using the web client before they are downloaded by the desktop email client. However, one may choose to leave the emails on the server, in which case this problem does not occur. The use of both a webmail client and a desktop client using the IMAP4 protocol allows the contents of the mailbox to be consistently displayed in both the webmail and desktop clients and any action the user performs on messages in one interface will be reflected when the email is accessed via the other interface. There are significant differences in rendering capabilities for many popular webmail services such as Gmail, Outlook.com and Yahoo! Mail. Due to the varying treatment of HTML tags, such as