Cleo Communications LLC, simply referred to as Cleo, is a privately held software company founded in 1976. The company is best known for its ecosystem integration platform, Cleo Integration Cloud with RADAR. == History == Cleo originally began as a division of Phone 1 Inc., a voice data gathering systems manufacturer, and built data concentrators and terminal emulators — multi-bus computers, modems, and terminals to interface with IBM mainframes via bisynchronous communications. The company then began developing mainframe middleware in the 1980s, and with the rise of the PC, moved into B2B data communications and secure file transfer software. Cleo Communications was acquired in 2012 by Global Equity Partners along with other investment companies. Since being acquired in 2012, the company’s offerings have evolved into Cleo Integration Cloud, a platform for enterprise business integration. == Business == Based in Rockford, Illinois (USA), with offices in Chicago, Pennsylvania, London, and Bangalore, Cleo has about 400 employees and more than 4,100 direct customers. The company's flagship offering, Cleo Integration Cloud, provides both on-premise and cloud-based integration technologies and comprises solutions for B2B/EDI, application integration, data movement and data transformation. Previous products now incorporated into the Cleo Integration Cloud platform include Cleo Harmony, Cleo Clarify, and Cleo Jetsonic. Cleo solutions span a variety of industries, including manufacturing, logistics and supply chain, retail, third-party logistics, warehouse management and transportation management, healthcare, financial services and government. The U.S. Department of Veterans Affairs adopted Cleo's fax technology, Cleo Streem, in 2013 when in need of FIPS 140-2-compliant technology to protect information, and the City of Atlanta has used Cleo Streem for network and desktop faxing since 2006. Cleo also serves U.S. transportation logistics company MercuryGate International and SaaS-based food logistics organization ArrowStream. It powers the architecture for several major supply chain companies, such as Blue Yonder and SAP. Cleo integrates the pharmaceutical supply chain for such companies as Octapharma. Key partners include FourKites and ClientsFirst, among many others. In May 2023, Cleo announced it entered a global partnership with consulting and multinational information technology services company, Cognizant (NASDAQ: CTSH). Together, the companies announced CCIB, powered by Cleo, which is a B2B iPaaS solution that provides B2B managed services with built-in, scalable infrastructure on the cloud. The solution comprises elements from Cleo’s flagship offering, Cleo Integration Cloud. == Expansion == In June 2014, Cleo opened an office in Chicago for members of its support and Ashok and teams. In 2014, the company hired Jorge Rodriguez as Senior Vice President of Product Development and John Thielens as Vice President of Technology. Cleo hired Dave Brunswick as Vice President of Solutions for North America in 2015, and Cleo hired Ken Lyons to lead global sales in 2016. Lyons now serves as the company's Chief Revenue Officer. More recent additions to the company's leadership team include Vipin Mittal, Vice President, Customer Experience, and Tushar Patel, CMO. Cleo opened its product development facility in Bengaluru, India, in 2015 and expanded its hybrid cloud integration teams into a new office there in 2017. The company also opened a London office in 2016 and expanded its network of channel partners in EMEA. In 2016, Cleo acquired EXTOL International, a Pottsville, Pa.-based business and EDI integration and data transformation company for an undisclosed amount. In 2017, the company moved its headquarters from Loves Park, Illinois, to Rockford. In 2021 the company received a significant growth investment from H.I.G. Capital. In July 2022, Cleo opened a new, 5,000-square-foot office located in Chicago's Loop. In November 2022, Cleo launched an accelerator for Microsoft Dynamics 365 SCM-to-X12 and a connector for Microsoft Dynamics 365 Business Central. These pre-built solutions allow businesses and users to quickly build integration flows that integrate their digital ecosystems. In March 2023, Cleo released CIC PAVE (Procurement Automation and Vendor Enablement). PAVE provides customers with enhanced supply chain visibility via a supplier portal that allows the customer to keep vendor interaction in a single location, even if they cannot use EDI or have API-ready applications. In December 2023, Cleo acquired ECS International, an integration technology company based in the Netherlands. == Certification == Cleo regularly submits its products to Drummond Group's interoperability software testing for AS2, AS3 and ebMS 2.0. In January 2020, Cleo announced that its new application connector for Acumatica ERP has been recognized as an Acumatica-Certified Application (ACA). The company also holds SOC 2, Type 2 certification. == Awards == Cleo was a Xerox partner of the year award for five years, from 2009 to 2014. The Cleo Streem solution integrates with Xerox multi-function products, providing customers with solutions for network fax and interactive messaging needs. Cleo was named to Food Logistics’ FL100+ Top Software and Technology Providers Lists in 2016, 2017, 2019 and 2020. Cleo CEO, Mahesh Rajasekharan was named an Ernst & Young Entrepreneur Of The Year 2022 Midwest Award winner. Rajasekharan is serving as a judge for the 2023 Ernst & Young Entrepreneur Of the Year Awards. As of April 2022, Cleo has been named a Leader in EDI on the G2 Grid, a peer-to-peer review site, for 20 straight quarters. In Spring 2023, Cleo won 23 G2 awards—including EDI Leader Enterprise, MFT Leader Enterprise, On-Premise Data Integration Best Support Enterprise, and iPaaS High Performer Asia.
Alerts.in.ua
alerts.in.ua is an online service that visualizes information about air alerts and other threats on the map of Ukraine. == History == The idea of the site appeared in the first weeks of the 2022 Russian invasion of Ukraine, during the development of other projects related to alerting the population about alarms. So, on March 2, 2022, the "Lviv Siren" bot was created, which reported on air alarms in Lviv on Twitter. Later, the idea arose to monitor alarms all over Ukraine and display them on a map. However, the lack of a single official source reporting alarms made this task much more difficult. On March 15, 2022, the Ajax Systems company announced the creation of the official Telegram channel "Air Alarm". This channel receives signals from the "Air Alarm" application and instantly publishes messages about the start and end of alarms in different regions of Ukraine. This immediately solved the problem with the source of information and gave impetus to the further implementation of the project. On March 22, 2022, the first version of the "Air Alarm Map" website was published, located on the war.ukrzen.in.ua domain. The map quickly gained popularity in social networks. It, like several other similar projects, began to be widely distributed by the mass media: Suspilne, Novyi Kanal, UNIAN, DW, Fakty ICTV, Vikna TV, Ukrainian Radio, STB, Espresso, dev.ua, itc.ua and state bodies: Center for Countering Disinformation at the National Security and Defense Council of Ukraine, Verkhovna Rada of Ukraine, Khmelnytska OVA, etc. On April 8, 2022, the site moved to the alerts.in.ua domain, where it is still available today. On August 25, 2022, the service began monitoring local official channels in addition to the main "Air Alarm". On September 11, 2022, the English version of the site was published. On March 22, 2023, its own Android application was published. The project is actively developing and has its own community. == Description == The main part of the site is a map of Ukraine, on which the regions where an air alert or other threats have been declared are highlighted in real time. As of October 16, 2022, 5 types of threats are supported: Air alarm. The threat of artillery fire. The threat of street fighting. Chemical threat. Nuclear threat. Additionally, based on media reports, information is published about other dangerous events, such as explosions, demining, etc. On the site, you can view the history of announced alarms with links to sources. Alarm statistics for different time periods are also available. For developers, there is an API that allows you to develop your own services based on information about declared alarms. The site is available in Ukrainian, English, Polish and Japanese. == Use == The map is used by: To monitor the situation in the country and the region. To illustrate the alarms announced in the mass media: TSN, Ukrainian truth, Channel 24, Suspilne, RBC Ukraine, Gromadske, Glavkom. As a map of alarms in mobile applications, there is Alarm and AirAlert. As an API for its services, including alternative alarm maps, Telegram, Viber channels, Discord bots, IoT projects, etc. == Statistics == 89.5% of users use the map from a mobile phone, 10% from a PC and 1% from a tablet. Top 6 countries by visit: Ukraine, United States, Poland, Germany, Great Britain and Japan . == Alternative projects == eMap was created by the developer Vadym Klymenko. AlarmMap is an online from the Ukrainian office of Agroprep. The official map of air alarms was developed by Ajax Systems together with the developer Artem Lemeshev, Stfalcon with the support of the Ministry of Statistics.
SHRDLU
SHRDLU is an early natural-language understanding computer program that was developed by Terry Winograd at MIT in 1968–1970. In the program, the user carries on a conversation with the computer, moving objects, naming collections and querying the state of a simplified "blocks world", essentially a virtual box filled with different blocks. SHRDLU was written in the Micro Planner and Lisp programming language on the DEC PDP-6 computer and a DEC graphics terminal. Later additions were made at the computer graphics labs at the University of Utah, adding a full 3D rendering of SHRDLU's "world". The name SHRDLU was derived from ETAOIN SHRDLU, the arrangement of the letter keys on a Linotype machine, arranged in descending order of usage frequency in English. == Functionality == SHRDLU is primarily a language parser that allows user interaction using English terms. The user instructs SHRDLU to move various objects around in the "blocks world" containing various basic objects such as blocks, cones and balls. SHRDLU combined four simple ideas to make the simulation of "understanding" more convincing. One was that SHRDLU's world is so simple that the entire set of objects and locations could be described by including as few as 50 words: nouns like "block" and "cone", verbs like "place on" and "move to", and adjectives like "big" and "blue". The possible combinations of these basic language building blocks are quite simple. SHRDLU also includes a basic memory to supply context. One could ask SHRDLU to "put the green cone on the red block" and then "take the cone off"; "the cone" would be taken to mean the green cone one had just talked about. SHRDLU can search back further through the interactions to find the proper context in most cases when additional adjectives were supplied. One could also ask questions about the history; for instance, one could ask "did you pick up anything before the cone?" A side effect of this memory, and the original rules SHRDLU was supplied with, is that the program can answer questions about what was possible in the world and what was not. For instance, SHRDLU can deduce that blocks could be stacked by looking for examples, but also realize that triangles could not be stacked, after having tried it. The "world" contains basic physics to make blocks fall over, independent of the language parser. Finally, SHRDLU can also remember names given to objects, or arrangements of them. For instance one could say "a steeple is a small triangle on top of a tall rectangle"; SHRDLU can then answer questions about steeples in the blocks world, and build new ones. This is an example of a SHRDLU session: Person: Pick up a big red block. Computer: OK. Person: Grasp the pyramid. Computer: I DON'T UNDERSTAND WHICH PYRAMID YOU MEAN. Person (changing their mind): Find a block which is taller than the one you are holding and put it into the box. Computer: BY "IT", I ASSUME YOU MEAN THE BLOCK WHICH IS TALLER THAN THE ONE I AM HOLDING. Computer: OK. Person: What does the box contain? Computer: THE BLUE PYRAMID AND THE BLUE BLOCK. Person: What is the pyramid supported by? Computer: THE BOX. Person: How many blocks are not in the box? Computer: FOUR OF THEM. Person: Is at least one of them narrower than the one which i told you to pick up? Computer: YES, THE RED CUBE. Person: Is it supported? Computer: YES, BY THE TABLE. Person: Can the table pick up blocks? Computer: NO. Person: Can a pyramid be supported by a block? Computer: YES. Person: Can a pyramid support a pyramid? Computer: I DON'T KNOW. Person: Stack up two pyramids. Computer: I CAN'T. Person: Will you please stack up both of the red blocks and either a green cube or a pyramid? Computer: OK. Person: Which cube is sitting on the table? Computer: THE LARGE GREEN ONE WHICH SUPPORTS THE RED PYRAMID. Person: Is there a large block behind a pyramid? Computer: YES, THREE OF THEM: A LARGE RED ONE, A LARGE GREEN CUBE, AND THE BLUE ONE. Person: Put a small one onto the green cube which supports a pyramid. Computer: OK. Person: Put the littlest pyramid on top of it. Computer: OK. Person: Does the shortest thing the tallest pyramid's support supports support anything green? Computer: YES, THE GREEN PYRAMID. Person: What color is it? Computer: BY "IT", I ASSUME YOU MEAN THE SHORTEST THING THE TALLEST PYRAMID'S SUPPORT SUPPORTS. Computer: RED Person: How many things are on top of green cubes? Computer: I'M NOT SURE WHAT YOU MEAN BY "ON TOP OF" IN THE PHRASE "ON TOP OF GREEN CUBES" . DO YOU MEAN: 1 - DIRECTLY ON THE SURFACE 2 - ANWHERE ON TOP OF ? Person: 2 Computer: THREE OF THEM. Person: Had you touched any pyramid before you put the green one on the little cube? Computer: YES, THE GREEN ONE. Person: When did you pick it up? Computer: WHILE I WAS STACKING UP THE RED CUBE, A LARGE RED BLOCK AND A LARGE GREEN CUBE. Person: Why? Computer: TO GET RID OF IT. Person: Why did you do that? Computer: TO CLEAN OFF THE RED CUBE. Person: Why did you clear off that cube? Computer: TO PUT IT ON A LARGE GREEN CUBE. Person: Why did you do that? Computer: TO STACK UP THE RED CUBE , A LARGE RED BLOCK AND A LARGE GREEN CUBE. Person: Why did you do that? Computer: BECAUSE YOU ASKED ME TO. Person: How did you do it? Computer: BY PUTTING A LARGE RED BLOCK ON THE TABLE ; THEN LETTING GO OF IT ; THEN PUTTING A LARGE GREEN CUBE ON IT ; THEN LETTING GO OF THAT CUBE ; THEN PUTTING THE RED CUBE ON THAT CUBE; THEN LETTING GO OF THAT CUBE. Person: How many objects did you touch while you were doing it? Computer: FOUR OF THEM. Person: What did the red cube support before you started to clean it off? Computer: THE GREEN PYRAMID. Person: There were five blocks to the left of the box then. Computer: NO, ONLY FOUR OF THEM: THE RED CUBE, TWO LARGE GREEN CUBES AND A LARGE RED BLOCK. Person: Put the blue pyramid on the block in the box. Computer: OK. Person: Is there anything which is bigger than every pyramid but is not as wide as the thing that supports it? Computer: YES, THE BLUE BLOCK. Person: Does a steeple Computer (interrupting): SORRY, I DON'T KNOW THE WORD "STEEPLE". Person: A "steeple" is a stack which contains two green cubes and a pyramid. Computer: I UNDERSTAND. Person: Are there any steeples now? Computer: NO. Person: Build one. Computer: OK. Person: Call the biggest block "superblock". Computer: OK. Person: Have you picked superblock up since we began? Computer: YES. Person: Why did you drop it? Computer: BY "IT", I ASSUME YOU MEAN THE SUPERBLOCK. I CAN'T EXPLAIN A NON-EXISTENT EVENT. Person: Is there anything to the right of the red pyramid? Computer: YES, FOUR THINGS: THE BOX, THE RED CUBE, THE BLUE PYRAMID AND THE BLOCK NAMED SUPERBLOCK Person: Thank you. Computer: YOU'RE WELCOME! == Consequences == SHRDLU was considered a tremendously successful demonstration of artificial intelligence (AI). This led other AI researchers to excessive optimism which was soon lost when later systems attempted to deal with situations with a more realistic level of ambiguity and complexity. Subsequent efforts of the SHRDLU type, such as Cyc, have tended to focus on providing the program with considerably more information from which it can draw conclusions. In a 1991 interview, Winograd said about SHRDLU: [...] the famous dialogue with SHRDLU where you could pick up a block, and so on, I very carefully worked through, line by line. If you sat down in front of it, and asked it a question that wasn't in the dialogue, there was some probability it would answer it. I mean, if it was reasonably close to one of the questions that was there in form and in content, it would probably get it. But there was no attempt to get it to the point where you could actually hand it to somebody and they could use it to move blocks around. And there was no pressure for that whatsoever. Pressure was for something you could demo. Take a recent example, Negroponte's Media Lab, where instead of "perish or publish" it's "demo or die." I think that's a problem. I think AI suffered from that a lot, because it led to "Potemkin villages", things which - for the things they actually did in the demo looked good, but when you looked behind that there wasn't enough structure to make it really work more generally. Though not intentionally developed as such, SHRDLU is considered the first known formal example of interactive fiction, as the user interacts with simple commands to move objects around a virtual environment, though lacking the distinct story-telling normally present in the interactive fiction genre. The 1976-1977 game Colossal Cave Adventure is broadly considered to be the first true work of interactive fiction.
VP-Expert
VP-Expert is an artificial intelligence development tool that gained popularity in the late 1980s and early 1990s. Published by Paperback Software, VP-Expert was designed to facilitate the creation of rule-based expert systems, primarily for applications in business and industry. It was the best-selling expert-system software for microcomputers in the late 1980s. == History == VP-Expert was created by Brian Sawyer and published by Paperback Software in 1987. VP-Expert was widely adopted during the late 1980s. By April 1989, InfoWorld described it as "the best-selling expert-system software for personal computers." In June 1991, ownership of VP-Expert transferred from Paperback Software to WordTech Systems, Inc. following Paperback Software’s liquidation after a legal dispute with Lotus Development Corporation regarding its VP-Planner spreadsheet. VP-Expert continued to receive positive reviews with InfoWorld stating in 1992 "for automatically creating simple expert systems and being able to edit them into more sophisticated applications, hardly a better product exists than VP-Expert". == Features == VP-Expert used an inference engine based on backward chaining to reach conclusions through English-like if/then rules. It operated through a text interface and included an explanation facility that showed the reasoning steps used to justify its conclusions. == Applications == VP-Expert found applications across various domains. In environmental analysis, researchers used VP-Expert to develop a knowledge-based system for analyzing the impact of particulate matter air pollution on human health. In engineering design, VP-Expert was utilized in the creation of a prototype expert system to assist in fishway design. In aviation management, the tool was employed to develop an expert system aimed at maximizing airport capacity while adhering to noise-mitigation plans. == Limitations == While VP-Expert offered certain advantages, it also had limitations. Its rule-based approach could become challenging to manage for large and complex knowledge bases, and the process of eliciting and encoding knowledge from experts could be time-consuming and difficult.
Ari Holtzman
Ari Holtzman is a professor of Computer Science at the University of Chicago and an expert in the area of natural language processing and computational linguistics. Previously, Holtzman was a PhD student at the University of Washington where he was advised by Luke Zettlemoyer. In 2017, he was a member of the winning team for the inaugural Alexa Prize for developing a conversational AI system for the Amazon Alexa device. Holtzman has made multiple contributions in the area of text generation and language models such as the introduction of nucleus sampling in 2019, his work on AI safety and neural fake news detection, and the fine-tuning of quantized large language models.
Hexagonal sampling
A multidimensional signal is a function of M independent variables where M ≥ 2 {\displaystyle M\geq 2} . Real world signals, which are generally continuous time signals, have to be discretized (sampled) in order to ensure that digital systems can be used to process the signals. It is during this process of discretization where sampling comes into picture. Although there are many ways of obtaining a discrete representation of a continuous time signal, periodic sampling is by far the simplest scheme. Theoretically, sampling can be performed with respect to any set of points. But practically, sampling is carried out with respect to a set of points that have a certain algebraic structure. Such structures are called lattices. Mathematically, the process of sampling an N {\displaystyle N} -dimensional signal can be written as: w ( t ^ ) = w ( V . n ^ ) {\displaystyle w({\hat {t}})=w(V.{\hat {n}})} where t ^ {\displaystyle {\hat {t}}} is continuous domain M-dimensional vector (M-D) that is being sampled, n ^ {\displaystyle {\hat {n}}} is an M-dimensional integer vector corresponding to indices of a sample, and V is an N × N {\displaystyle N\times N} sampling matrix. == Motivation == Multidimensional sampling provides the opportunity to look at digital methods to process signals. Some of the advantages of processing signals in the digital domain include flexibility via programmable DSP operations, signal storage without the loss of fidelity, opportunity for encryption in communication, lower sensitivity to hardware tolerances. Thus, digital methods are simultaneously both powerful and flexible. In many applications, they act as less expensive alternatives to their analog counterparts. Sometimes, the algorithms implemented using digital hardware are so complex that they have no analog counterparts. Multidimensional digital signal processing deals with processing signals represented as multidimensional arrays such as 2-D sequences or sampled images.[1] Processing these signals in the digital domain permits the use of digital hardware where in signal processing operations are specified by algorithms. As real world signals are continuous time signals, multidimensional sampling plays a crucial role in discretizing the real world signals. The discrete time signals are in turn processed using digital hardware to extract information from the signal. == Preliminaries == === Region of Support === The region outside of which the samples of the signal take zero values is known as the Region of support (ROS). From the definition, it is clear that the region of support of a signal is not unique. === Fourier transform === The Fourier transform is a tool that allows us to simplify mathematical operations performed on the signal. The transform basically represents any signal as a weighted combination of sinusoids. The Fourier and the inverse Fourier transform of an M-dimensional signal can be defined as follows: X a ( Ω ^ ) = ∫ − ∞ + ∞ x a ( t ^ ) e − j Ω ^ T t ^ d t ^ {\displaystyle X_{a}({\hat {\Omega }})=\int _{-\infty }^{+\infty }\!x_{a}({\hat {t}})e^{-j{\hat {\Omega }}^{T}{\hat {t}}}d{\hat {t}}} x a ( t ^ ) = 1 2 π M ∫ − ∞ + ∞ X ( Ω ^ ) e ( j Ω ^ T t ^ ) d Ω ^ {\displaystyle x_{a}({\hat {t}})={\frac {1}{2\pi ^{M}}}\int _{-\infty }^{+\infty }\!X({\hat {\Omega }})e^{(j{\hat {\Omega }}^{T}{\hat {t}})}\,\mathrm {d} {\hat {\Omega }}} The cap symbol ^ indicates that the operation is performed on vectors. The Fourier transform of the sampled signal is observed to be a periodic extension of the continuous time Fourier transform of the signal. This is mathematically represented as: X ( ω ) = 1 | d e t ( V ) | ∑ k X a ( Ω ^ − U k ) {\displaystyle X(\omega )={\frac {1}{|det(V)|}}\sum _{k}\!X_{a}({\hat {\Omega }}-Uk)} where ω = V ~ Ω {\displaystyle \omega ={\tilde {V}}\Omega } and U = 2 π V ~ {\displaystyle U=2\pi {\tilde {V}}} is the periodicity matrix where ~ denotes matrix transposition. Thus sampling in the spatial domain results in periodicity in the Fourier domain. === Aliasing === A band limited signal may be periodically replicated in many ways. If the replication results in an overlap between replicated regions, the signal suffers from aliasing. Under such conditions, a continuous time signal cannot be perfectly recovered from its samples. Thus in order to ensure perfect recovery of the continuous signal, there must be zero overlap multidimensional sampling of the replicated regions in the transformed domain. As in the case of 1-dimensional signals, aliasing can be prevented if the continuous time signal is sampled at an adequate sufficiently high rate. === Sampling density === It is a measure of the number of samples per unit area. It is defined as: S . D = 1 | d e t ( V ) | = | d e t ( U ) | 4 π 2 {\displaystyle S.D={\frac {1}{|det(V)|}}={\frac {|det(U)|}{4\pi ^{2}}}} . The minimum number of samples per unit area required to completely recover the continuous time signal is termed as optimal sampling density. In applications where memory or processing time are limited, emphasis must be given to minimizing the number of samples required to represent the signal completely. == Existing approaches == For a bandlimited waveform, there are infinitely many ways the signal can be sampled without producing aliases in the Fourier domain. But only two strategies are commonly used: rectangular sampling and hexagonal sampling. === Rectangular and Hexagonal sampling === In rectangular sampling, a 2-dimensional signal, for example, is sampled according to the following V matrix: V r e c t = [ T 1 0 0 T 2 ] {\displaystyle V_{rect}={\begin{bmatrix}T1&0\\0&T2\end{bmatrix}}} where T1 and T2 are the sampling periods along the horizontal and vertical direction respectively. In hexagonal sampling, the V matrix assumes the following general form: V h e x = [ T 1 T 1 − T 2 T 2 ] {\displaystyle V_{hex}={\begin{bmatrix}T1&T1\\-T2&T2\end{bmatrix}}} The difference in the efficiency of the two schemes is highlighted using a bandlimited signal with a circular region of support of radius R. The circle can be inscribed in a square of length 2R or a regular hexagon of length 2 R 3 {\displaystyle {\frac {2R}{\sqrt {3}}}} . Consequently, the region of support is now transformed into a square and a hexagon respectively. If these regions are periodically replicated in the frequency domain such that there is zero overlap between any two regions, then by periodically replicating the square region of support, we effectively sample the continuous signal on a rectangular lattice. Similarly periodic replication of the hexagonal region of support maps to sampling the continuous signal on a hexagonal lattice. From U, the periodicity matrix, we can calculate the optimal sampling density for both the rectangular and hexagonal schemes. It is found that in order to completely recover the circularly band-limited signal, the hexagonal sampling scheme requires 13.4% fewer samples than the rectangular sampling scheme. The reduction may appear to be of little significance for a 2-dimensional signal. But as the dimensionality of the signal increases, the efficiency of the hexagonal sampling scheme will become far more evident. For instance, the reduction achieved for an 8-dimensional signal is 93.8%. To highlight the importance of the obtained result [2], try and visualize an image as a collection of infinite number of samples. The primary entity responsible for vision, i.e. the photoreceptors (rods and cones) are present on the retina of all mammals. These cells are not arranged in rows and columns. By adapting a hexagonal sampling scheme, our eyes are able to process images much more efficiently. The importance of hexagonal sampling lies in the fact that the photoreceptors of the human vision system lie on a hexagonal sampling lattice and, thus, perform hexagonal sampling.[3] In fact, it can be shown that the hexagonal sampling scheme is the optimal sampling scheme for a circularly band-limited signal. == Applications == === Aliasing effects minimized by the use of optimal sampling grids === Recent advances in the CCD technology has made hexagonal sampling feasible for real life applications. Historically, because of technology constraints, detector arrays were implemented only on 2-dimensional rectangular sampling lattices with rectangular shape detectors. But the super [CCD] detector introduced by Fuji has an octagonal shaped pixel in a hexagonal grid. Theoretically, the performance of the detector was greatly increased by introducing an octagonal pixel. The number of pixels required to represent the sample was reduced and there was significant improvement in the Signal-to-Noise Ratio (SNR) when compared with that of a rectangular pixel. But the drawback of using hexagonal pixels is that the associated fill factor will be less than 82%. An alternative method would be to interpolate hexagonal pixels in such a manner that we ultimately end up with a rectangular grid. The Spot 5 satellite incorporates a
Type–token distinction
The type–token distinction is the difference between a type of objects (analogous to a class) and the individual tokens of that type (analogous to instances). Since each type may be instantiated by multiple tokens, there are generally more tokens than types of an object. For example, the sentence "A rose is a rose is a rose" contains three word types: three word tokens of the type a, two word tokens of the type is, and three word tokens of the type rose. The distinction is important in disciplines such as logic, linguistics, metalogic, typography, and computer programming. == Overview == The type–token distinction separates types (abstract descriptive concepts) from tokens (objects that instantiate concepts). For example, in the sentence "the bicycle is becoming more popular" the word bicycle represents the abstract concept of bicycles and this abstract concept is a type, whereas in the sentence "the bicycle is in the garage", it represents a particular object and this particular object is a token. Similarly, the word type 'letter' uses only four letter types: L, E, T and R. Nevertheless, it uses both E and T twice. One can say that the word type 'letter' has six letter tokens, with two tokens each of the letter types E and T. Whenever a word type is inscribed, the number of letter tokens created equals the number of letter occurrences in the word type. Some logicians consider a word type to be the class of its tokens. Other logicians counter that the word type has a permanence and constancy not found in the class of its tokens. The type remains the same while the class of its tokens is continually gaining new members and losing old members. == Typography == In typography, the type–token distinction is used to determine the presence of a text printed by movable type: The defining criteria which a typographic print has to fulfill is that of the type identity of the various letter forms which make up the printed text. In other words: each letter form which appears in the text has to be shown as a particular instance ("token") of one and the same type which contains a reverse image of the printed letter. == Charles Sanders Peirce == The distinctions between using words as types or tokens were first made by American logician and philosopher Charles Sanders Peirce in 1906 using terminology that he established. Peirce's type–token distinction applies to words, sentences, paragraphs and so on: to anything in a universe of discourse of character-string theory, or concatenation theory. Peirce's original words are the following: A common mode of estimating the amount of matter in a ... printed book is to count the number of words. There will ordinarily be about twenty 'thes' on a page, and, of course, they count as twenty words. In another sense of the word 'word,' however, there is but one word 'the' in the English language; and it is impossible that this word should lie visibly on a page, or be heard in any voice .... Such a ... Form, I propose to term a Type. A Single ... Object ... such as this or that word on a single line of a single page of a single copy of a book, I will venture to call a Token. .... In order that a Type may be used, it has to be embodied in a Token which shall be a sign of the Type, and thereby of the object the Type signifies.