Airfair

AirFair was a mobile travel application that checks flights, and shows whether a traveler is owed compensation. == History == AirFair was developed in 2016 by Allay Logic Ltd; a Newcastle-based tech-company. == Services == AirFair offered a free flight check to see if compensation is owed. The app could indicate how much the person is owed within minutes whether the flight was delayed, cancelled or the traveler is refused boarding.

Quantification (machine learning)

In machine learning, quantification (variously called learning to quantify, or supervised prevalence estimation, or class prior estimation) is the task of using supervised learning in order to train models (quantifiers) that estimate the relative frequencies (also known as prevalence values) of the classes of interest in a sample of unlabelled data items. For instance, in a sample of 100,000 unlabelled tweets known to express opinions about a certain political candidate, a quantifier may be used to estimate the percentage of these tweets which belong to class `Positive' (i.e., which manifest a positive stance towards this candidate), and to do the same for classes `Neutral' and `Negative'. Quantification may also be viewed as the task of training predictors that estimate a (discrete) probability distribution, i.e., that generate a predicted distribution that approximates the unknown true distribution of the items across the classes of interest. Quantification is different from classification, since the goal of classification is to predict the class labels of individual data items, while the goal of quantification it to predict the class prevalence values of sets of data items. Quantification is also different from regression, since in regression the training data items have real-valued labels, while in quantification the training data items have class labels. It has been shown in multiple research works that performing quantification by classifying all unlabelled instances and then counting the instances that have been attributed to each class (the 'classify and count' method) usually leads to suboptimal quantification accuracy. This suboptimality may be seen as a direct consequence of 'Vapnik's principle', which states: If you possess a restricted amount of information for solving some problem, try to solve the problem directly and never solve a more general problem as an intermediate step. It is possible that the available information is sufficient for a direct solution but is insufficient for solving a more general intermediate problem. In our case, the problem to be solved directly is quantification, while the more general intermediate problem is classification. As a result of the suboptimality of the 'classify and count' method, quantification has evolved as a task in its own right, different (in goals, methods, techniques, and evaluation measures) from classification. == Quantification tasks == === Quantification tasks according to the set of classes === The main variants of quantification, according to the characteristics of the set of classes used, are: Binary quantification, corresponding to the case in which there are only n = 2 {\displaystyle n=2} classes and each data item belongs to exactly one of them; Single-label multiclass quantification, corresponding to the case in which there are n > 2 {\displaystyle n>2} classes and each data item belongs to exactly one of them; Multi-label multiclass quantification, corresponding to the case in which there are n ≥ 2 {\displaystyle n\geq 2} classes and each data item can belong to zero, one, or several classes at the same time; Ordinal quantification, corresponding to the single-label multiclass case in which a total order is defined on the set of classes. Regression quantification, a task which stands to 'standard' quantification as regression stands to classification. Strictly speaking, this task is not a quantification task as defined above (since the individual items do not have class labels but are labelled by real values), but has enough commonalities with other quantification tasks to be considered one of them. Most known quantification methods address the binary case or the single-label multiclass case, and only few of them address the multi-label, ordinal, and regression cases. Binary-only methods include the Mixture Model (MM) method, the HDy method, SVM(KLD), and SVM(Q). Methods that can deal with both the binary case and the single-label multiclass case include probabilistic classify and count (PCC), adjusted classify and count (ACC), probabilistic adjusted classify and count (PACC), the Saerens-Latinne-Decaestecker EM-based method (SLD), and KDEy. Methods for multi-label quantification include regression-based quantification (RQ) and label powerset-based quantification (LPQ). Methods for the ordinal case include ordinal versions of the above-mentioned ACC, PACC, and SLD methods, and ordinal versions of the above-mentioned HDy method. Methods for the regression case include Regress and splice and Adjusted regress and sum. === Quantification tasks according to the type of data === Several subtasks of quantification may be identified according to the type of data involved. Example such tasks are: Quantification of networked data. This task consists of performing quantification when the datapoints are members of a relation, i.e., are interlinked. As such, this task is a strict relative of collective classification. Quantification over time. This task consists of performing quantification on sets that become available in a temporal sequence, i.e., as a data stream, and finds application in contexts in which class prevalence values must be monitored over time. == Evaluation measures for quantification == Several evaluation measures can be used for evaluating the error of a quantification method. Since quantification consists of generating a predicted probability distribution that estimates a true probability distribution, these evaluation measures are ones that compare two probability distributions. Most evaluation measures for quantification belong to the class of divergences. Evaluation measures for binary quantification, single-label multiclass quantification, and multi-label quantification, are Absolute Error Squared Error Relative Absolute Error Kullback–Leibler divergence Pearson Divergence Evaluation measures for ordinal quantification are Normalized Match Distance (a particular case of the Earth Mover's Distance) Root Normalized Order-Aware Distance == Applications == Quantification is of special interest in fields such as the social sciences, epidemiology, market research, allocating resources, and ecological modelling, since these fields are inherently concerned with aggregate data. However, quantification is also useful as a building block for solving other downstream tasks, such as improving the accuracy of classifiers on out-of-distribution data, measuring classifier bias and ranker bias, and estimating the accuracy of classifiers on out-of-distribution data. == Resources == LQ 2021: the 1st International Workshop on Learning to Quantify LQ 2022: the 2nd International Workshop on Learning to Quantify LQ 2023: the 3rd International Workshop on Learning to Quantify LQ 2024: the 4th International Workshop on Learning to Quantify LQ 2025: the 5th International Workshop on Learning to Quantify LeQua 2022: the 1st Data Challenge on Learning to Quantify LeQua 2024: the 2nd Data Challenge on Learning to Quantify QuaPy: An open-source Python-based software library for quantification QuantificationLib: A Python library for quantification and prevalence estimation

CrySyS Lab

CrySyS Lab (Hungarian pronunciation: [ˈkriːsis]) is part of the Department of Telecommunications at the Budapest University of Technology and Economics. The name is derived from "Laboratory of Cryptography and System Security", the full Hungarian name is CrySys Adat- és Rendszerbiztonság Laboratórium. == History == CrySyS Lab. was founded in 2003 by a group of security researchers at the Budapest University of Technology and Economics. Currently, it is located in the Infopark Budapest. The heads of the lab were Dr. István Vajda (2003–2010) and Dr. Levente Buttyán (2010-now). Since its establishment, the lab participated in several research and industry projects, including successful EU FP6 and FP7 projects (SeVeCom, a UbiSecSens and WSAN4CIP). == Research results == CrySyS Lab is recognized in research for its contribution to the area of security in wireless embedded systems. In this area, the members of the lab produced 5 books 4 book chapters 21 journal papers 47 conference papers 3 patents 2 Internet Draft The above publications had an impact factor of 30+ and obtained more than 7500 references. Several of these publications appeared in highly cited journals (e.g., IEEE Transactions on Dependable and Secure Systems, IEEE Transactions on Mobile Computing). == Forensics analysis of malware incidents == The laboratory was involved in the forensic analysis of several high-profile targeted attacks. In October 2011, CrySyS Lab discovered the Duqu malware; pursued the analysis of the Duqu malware and as a result of the investigation, identified a dropper file with an MS 0-day kernel exploit inside; and finally released a new open-source Duqu Detector Toolkit to detect Duqu traces and running Duqu instances. In May 2012, the malware analysis team at CrySyS Lab participated in an international collaboration aiming at the analysis of an as yet unknown malware, which they call sKyWIper. At the same time Kaspersky Lab analyzed the malware Flame and Iran National CERT (MAHER) the malware Flamer. Later, they turned out to be the same. Other analysis published by CrySyS Lab include the password analysis of the Hungarian ISP, Elender, and a thorough Hungarian security survey of servers after the publications of the Kaminsky DNS attack.

TRAME

TRAME (TRAnsmission of MEssages) was the name of the second computer network in the world similar to the internet to be used in an electric utility. Like the internet, the base technology was packet switching; it was developed by the electric utility ENHER in Barcelona. It was deployed by the same utility, first in Catalonia and Aragón, Spain, and later in other places. Its development started in 1974 and the first routers, called nodes at that time, were deployed by 1978. The network was in operation until 2016 (38 years) with successive technological software and hardware updates. == Beginnings == In 1974, packet switching was a technology known only in research circles. The concept began in 1968 in association with the United States' Advanced Research Projects Agency (ARPA) research project ARPANET. The idea of applying the packet switching concept to electric utilities control communication networks first appeared in 1974 when the Swedish power utility Vattenfall started to create its TIDAS packet-switching network and was followed by the Spanish electric utility ENHER, which aimed to telecontrol and automate its high-voltage power grid. For this purpose, ENHER created a specific team of people to develop both the packet-switching network and the supervisory control and data acquisition (SCADA) system, also called the telecontrol system. By 1978 the first four TRAME routers were available and by 1980, eight of them were deployed and operating. The printed circuit boards (PCBs) controlling the communication lines were connected to a shared memory PCB allowing them to exchange data and messages. The project was developed together with its main initial application, the Telecontrol or SCADA system SICL (Sistema Integral de Control Local) with which initially they shared a very similar hardware. The maximum link capacity was 9600 bit/s, which in 1980 was the maximum possible on a 4 kHz wide voice channel at the time. These channels were the basic unit of the then-analog communication systems in use. By that time power utilities used either telephone calls or low speed (below 1200bit/s) dedicated links for telecontrol, typically shared among ten high-voltage electrical substations. == Services == The basic service provided by the TRAME network was SCADA or Telecontrol to automate the high-voltage power grid, thus improving operational efficiency, which was until then operated manually with telephone communication between human operators. Each TRAME router was associated with one or more remote terminal units (RTUs) of the SICL telecontrol system. It also had connected screens, and later PCs, located in electrical substations to interchange messages between them and with the Control Center located in the well-known Casa Fuster in Barcelona. It was a kind of predecessor to today's e-mail. Later, in the 1990s, other protocols (X.25, IP) were developed to include corporate information technology (IT) terminals, company physical surveillance systems and other services. Additionally, applications and terminals were developed for the transmission of voice and video over the TRAME network. == Protocols == The TRAME routing system, like that of the original ARPANET, was based on the Bellman-Ford algorithm but with "split-horizon" as in the Swedish TIDAS network, but with an original improvement. This protocol allows optimal paths to be found in meshed networks for each packet to be transmitted, allowing the shared use of the same network by multiple services. In contrast, traditional circuit-switched technology used to establish dedicated circuits for each service or communication. The addressing of routers and terminals used a proprietary system with a 16-bit address; it would be the equivalent of the well-known IP (Internet Protocol) version 4 (IPv4), still in use on the internet today, which uses 32-bit addresses. It is necessary to take into account that in 1978, the IPv4 protocol did not yet exist since the IPv4 version used on the internet did not appear until 1981, and in fact, did not reach the general public until much later. The line protocols were also proprietary and were called UCL (Unidad de Control de Línea, 'line control unit'), which linked the routers together, and UTR (Unión TRAME-Remotas), the access protocol. They were designed to offer the highest quality of service required by the telecontrol/SCADA function in terms of data integrity and availability set by the International Electrotechnical Commission (IEC) IEC-870-5-1 and ANSI C37.1. standards, and because the protocol used at the time in corporate computer networks, HDLC (high-level data link control), did not offer enough quality for critical industrial applications. Later on, other protocols like X.25 and IP were also made compatible with the aforementioned TRAME protocols. In 2000, the UTR protocol was replaced by the international standard IEC 60870- 5-101/104. Initially network flow control was based on the management of eight data priorities in head-of-the-line (HOL) waiting queues. Later and after some experimentation, a flow control method based on a bit indicating route congestion and management of the gap between packets when accessing the network was adopted. This required measuring the capacity of the route bottleneck. An end-to-end protocol was also added for some flows requiring order preservation like X.25. == Evolution == To last for 38 years, the technology had to endure intense evolution. There were essentially four TRAME generations which are summarized in the table. A description of the four generations of TRAME is provided below. === TRAME 1 === The project began in 1974 and in 1978 a first network with four routers was already installed and in operation at the electric utility ENHER. In 1980, the network had eight nodes in operation (see Figure I). The hardware was based on the Zilog Z80 processor and had a multiprocessor structure with 16 processors sharing a common memory. The software was developed at ENHER's headquarters located in the well-known Casa Fuster, Passeig de Gràcia, 132, Barcelona, using the Z80 assembly language. Beyond 1980 the software began to be written in C programming language and an HP64000 Logic Development System emulator was used for the purpose. The hardware was produced by ISEL, an INI (Instituto Nacional de Indústria) company. The routing system was a variant of Bellman-Ford with split-horizon. It was an improvement of the original ARPA network routing system consisting of an original update procedure which allowed for a faster reaction to changes. The distance function was the number of packets in the output waiting queues plus one. The line protocols (UCL for internal lines linking routers and UTR for accessing the network) were designed to meet the stringent requirements set for telecontrol (SCADA) of high-voltage power networks (IEC-870-5-1 and ANSI C37.1 standards). At the OSI transport layer, windows with a width of 1 to 8, depending on the required service, residing in the terminals were used. Initially, addresses were only 14 bits long to address both the routers (called nodes by then) and the devices connected to them. They were made up of two fields, an 8-bit field to address the router and a 6-bit sub-address to address the terminals connected to it. The node address was assigned to the nodes and not to the ends of the links as in the internet. The basic advantages of TRAME over other technologies used in electric utilities at the time were in part due to the packet technology itself: ability to manage any network topology, automatic adaptability to topological and traffic changes, integration of different link technologies (digital or analog) and capacities in a single network, open and decentralized intercommunicability between users and devices, simultaneous communication with several users and locations from a single physical connection, and integrated network supervision. In fact, the network was provided from its inception with a supervision center consisting of a computer and a synoptic board located at the company's headquarters (see Figure II). But other advantages were due to the specific design of TRAME: high data integrity, priority support for packets, and ease of including special protocols such as the many SCADA protocols in use at that time. All of the above resulted in improved quality of service, especially with respect to data availability and data integrity, and in the integration of services in a single network. Part of the evolution of its deployment can be seen in Figures II to IV. === TRAME 2 === In 1990, TRAME 2 was fully deployed and TRAME 1 was replaced. The processor of the new hardware was Intel 80286 and the hardware structure and external appearance of the routers was very similar to that of TRAME 1. The software was written in C and the above-mentioned emulator continued to be used. Improvements over TRAME 1 were the introduction of the standardized X.25 access protocol

Social media reach

Social media reach is a media analytics metric that refers to the number of users who have come across a particular content on a particular social media platform. Social media platforms have their own individual ways of tracking, analyzing and reporting the traffic on each of the individual platforms. As these platforms are a main source of communication between companies and their target audiences, by conducting research, companies are able to utilize analytical information, such as the reach of their posts, to better understand the interactions between the users and their content. There are multiple underlying factors that will determine what shows up on a newsfeed or timeline. Algorithms, for example, are a type of factor that can alter the reach of a post due to the way the algorithm is coded, which can affect who sees a post and when. Other examples of factors that can impede the reach can include the time at which posts are made, as well as how frequent the posts are between one another. In comparison, an impression is the total number of circumstances where content has been shown on a social timeline, meanwhile, engagement looks at how people interact with the content that they see on a social platform such as like, share or retweet. == Reach on Facebook == Facebook has their own analytic platform which allows the user to see how other users are interacting with their posts, with the use of multiple metrics. This is not something the average user uses, but rather a tool that is used by pages or public figures. For example, Facebook pages that represent a business often look at the activity their posts have generated. There are three types of reach that can be looked at on the Facebook analytic platform. === Types of reach === ==== Organic Reach ==== This type of reach regards the number of distinct users that have seen a specific post on their feed. Organic reach, in other words is the number of people who have seen the post being analyzed on their Facebook newsfeed. Data gathered from this type of reach can give intel to those doing the analysis, such as the demographics of those who have seen the post. ==== Paid Reach ==== This type of reach regards the number of times that distinct users have come across sponsored posts, ads or content. In other words, paid reach is the number of times Facebook users have seen a post that has been paid for by a company. Data collected can give insight, to advertisers or marketers for example, on the activity based around the reach of their post. ==== Viral Reach ==== This type of reach regards the number of views by distinct users on posts that have been commented on or shared by their friends on Facebook. In other words, viral reach looks at the number of people who have seen a post after a friend of theirs commented or shared the original post, therefore it showed on their timeline. Viral reach can be looked at in terms of a collective number of times that the post has been on individual user's timelines. Data collected from viral reach can be used in multiple ways, for example, it can be used to analyze the type of content that gets shared or commented on and can be further used to compare to other posts. === Engaged users === This refers to the number of individual users who have clicked and interacted with a post on Facebook. == Reach on Twitter == Twitter gives access to any of their users to analytics of their tweets as well as their followers. Their dashboard is user friendly, which allows anyone to take a look at the analytics behind their Twitter account. This open access is useful for both the average user and companies as it can provide a quick glance or general outlook of who has seen their tweets. The way that Twitter works is slightly different than the way of Facebook in terms of the reach. On Twitter, especially for users with a higher profile, they are not only engaging with the people who follow them, but also with the followers of their own followers. The reach metric on Twitter looks at the quantity of Twitter users who have been engaged, but also the number of users that follow them as well. This metric is useful to see the if the tweets/content being shared on Twitter are contributing to the growth of audience on this platform. == Reach on Instagram == Instagram gives their users access to their reach, in the Instagram Insights section. Instagram insights can be used to learn more about an account's followers and performance. Reach indicates the total number of unique Instagram accounts that have seen your Instagram post or story. You can find this data by looking at each individual post insights. == Uses of reach == The reach can be a useful metric to analyze for marketers and advertisers. Social media is a platform that is used by marketers to directly target their intended audience with ease. These platforms not only allow marketers to get a better understanding of their audience, but also allow advertisers to insert their ads onto the timelines of specific users to later be able to conduct research to see the reach of their posts/content. The basic goal of marketers is to increase their reach as much as possible to impact bigger audiences of their dream customers and, in the end, make more sales. When doing organic social media marketing, using paid methods like ads or doing influencer marketing whether it is paid or free, it allows marketers to track the performance of their strategy and tweak it based on what works and what does not. == Analytics and reach == Social analytics looks at the data collected based on the interactions of users on social media platforms. A lot of information can be gathered which can provide intel based on user activities on social media. When looking into analytics in regard to social media, each company or group has a different goal in mind to engage their audience. At a glance, the three might seem as if they are very similar, however the differences between them are significant. There are many aspects that can be analyzed from the data gathered from social media platforms, depending on what is being observed, the correct metric would then be selected to further analyze. One example of the many metrics that can be used through social analytics is the reach. == Reach formula == To calculate social media reach one can use the following formula: R = I f ¯ {\displaystyle R={\frac {I}{\bar {f}}}} where R {\displaystyle R} — is social media reach, I {\displaystyle I} stands for the number of impressions, f ¯ {\displaystyle {\bar {f}}} is the average frequency of impressions per user. f ¯ {\displaystyle {\bar {f}}} represents the number of events when the ad is shown to a particular user. The average value should be calculated over the time period with stable settings of advertisement campaign. == Commenting For Better Reach == Commenting For Better Reach also known as "CFBR" is a widely used strategy for organically boosting post reach on social media platforms. Algorithms tend to favor posts with substantial likes and comments, granting them broader exposure compared to less engaging content. Primarily seen on LinkedIn, a platform geared toward professional networking and business connections, the use of CFBR signals active engagement aimed at enhancing post visibility. It is important to note that genuine and meaningful comments are key to effective engagement. Spammy or irrelevant comments not only detract from the conversation but may also limit a post's potential reach and impact.

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

Personal web page

Personal web pages are World Wide Web pages created by an individual to contain content of a personal nature rather than content pertaining to a company, organization or institution. Personal web pages are primarily used for informative or entertainment purposes but can also be used for personal career marketing (by containing a list of the individual's skills, experience and a CV), social networking with other people with shared interests, or as a space for personal expression. These terms do not usually refer to just a single "page" or HTML file, but to a website—a collection of webpages and related files under a common URL or Web address. In strictly technical terms, a site's actual home page (index page) often only contains sparse content with some catchy introductory material and serves mostly as a pointer or table of contents to the more content-rich pages inside, such as résumés, family, hobbies, family genealogy, a web log/diary ("blog"), opinions, online journals and diaries or other writing, examples of written work, digital audio sound clips, digital video clips, digital photos, or information about a user's other interests. Many personal pages only include information of interest to friends and family of the author. However, some webpages set up by hobbyists or enthusiasts of certain subject areas can be valuable topical web directories. == History == In the 1990s, most Internet service providers (ISPs) provided a free small personal, user-created webpage along with free Usenet News service. These were all considered part of full Internet service. Also several free web hosting services such as GeoCities provided free web space for personal web pages. These free web hosting services would typically include web-based site management and a few pre-configured scripts to easily integrate an input form or guestbook script into the user's site. Early personal web pages were often called "home pages" and were intended to be set as a default page in a web browser's preferences, usually by their owner. These pages would often contain links, to-do lists, and other information their author found useful. In the days when search engines were in their infancy, these pages (and the links they contained) could be an important resource in navigating the web. Since the early 2000s, the rise of blogging and the development of user friendly web page designing software made it easier for amateur users who did not have computer programming or website designer training to create personal web pages. Some website design websites provided free ready-made blogging scripts, where all the user had to do was input their content into a template. At the same time, a personal web presence became easier with the increased popularity of social networking services, some with blogging platforms such as LiveJournal and Blogger. These websites provided an attractive and easy-to-use content management system for regular users. Most of the early personal websites were Web 1.0 style, in which a static display of text and images or photos was displayed to individuals who came to the page. About the only interaction that was possible on these early websites was signing the virtual "guestbook". With the collapse of the dot-com bubble in the late 1990s, the ISP industry consolidated, and the focus of web hosting services shifted away from the surviving ISP companies to independent Internet hosting services and to ones with other affiliations. For example, many university departments provided personal pages for professors and television broadcasters provided them for their on-air personalities. These free webpages served as a perquisite ("perk") for staff, while at the same time boosting the Web visibility of the parent organization. Web hosting companies either charge a monthly fee, or provide service that is "free" (advertising based) for personal web pages. These are priced or limited according to the total size of all files in bytes on the host's hard drive, or by bandwidth, (traffic), or by some combination of both. For those customers who continue to use their ISP for these services, national ISPs commonly continue to provide both disk space and help including ready-made drop-in scripts. With the rise of Web 2.0-style websites, both professional websites and user-created, amateur websites tended to contain interactive features, such as "clickable" links to online newspaper articles or favourite websites, the option to comment on content displayed on the website, the option to "tag" images, videos or links on the site, the option of "clicking" on an image to enlarge it or find out more information, the option of user participation for website guests to evaluate or review the pages, or even the option to create new user-generated content for others to see. A key difference between Web 1.0 personal webpages and Web 2.0 personal pages was while the former tended to be created by hackers, computer programmers and computer hobbyists, the latter were created by a much wider variety of users, including individuals whose main interests lay in hobbies or topics outside of computers (e.g., indie music fans, political activists, and social entrepreneurs). == Motivations == In a study done by Zinkhan, participants had four main reasons to create personal web pages. First, people use personal web pages as a portrayal of self, in a sense marketing themselves, since creators have the freedom to portray their own identities. Second, personal web pages are a way to interact with people who have similar interests as the creator, possible employers, or colleagues. Third, personal web pages can gain social acceptance with groups that the creator is interested in depending on the information that the creator reveals about themselves. Fourth, personal web pages can give creators a sense of connection to the world since these web pages are public and a way to introduce oneself to other people around the globe. People may maintain personal web pages to serve as a showcase for their skills in professional life, creative skills or self promotion of their business, charity or band. The use of personal web pages to display an individual's professional life has become more common in the 21st century. Mary Madden, an expert researcher on privacy and technology, did a study that found a tenth of American jobs require Personal web pages that advertise an individual online. Personal web pages have become a source of initial impression of possible employees used by employers. It can also be used to express opinions on issues ranging from news and politics to movies. Others may use their personal web page as a communication method. For example, an aspiring artist might give out business cards with their personal web page, and invite people to visit their page and see their artwork, "like" their page or sign their guestbook. A personal web page gives the owner generally more control on presence in search results and how they wish to be viewed online. It also allows more freedom in types and quantity of content than a social network profile offers, and can link various social media profiles with each other. It can be used to correct the record on something, or clear up potential confusion between you and someone with the same name. In the 2010s, some amateur writers, bands and filmmakers release digital versions of their stories, songs and short films online, with the aim of gaining an audience and becoming more well-known. While the huge number of aspiring artists posting their work online makes it unlikely for individuals and groups to become popular via the Internet, there are a small number of YouTube stars who were unknown until their online performances garnered them a huge audience. == Sites of academics == Academic professionals (especially at the college and university level), including professors and researchers, are often given online space for creating and storing personal web documents, including personal web pages, CVs and a list of their books, academic papers and conference presentations, on the websites of their employers. This goes back to the early decade of the World Wide Web and its original purpose of providing a quick and easy way for academics to share research papers and data. Researchers may have a personal website to share more information about themselves, about their academic activities and for sharing (unpublished) results of their research. This has been noted as part of the success of open-access repositories such as arXiv.