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Multimodal representation learning
Multimodal representation learning is a subfield of representation learning focused on integrating and interpreting information from different modalities, such as text, images, audio, or video, by projecting them into a shared latent space. This allows for semantically similar content across modalities to be mapped to nearby points within that space, facilitating a unified understanding of diverse data types. By automatically learning meaningful features from each modality and capturing their inter-modal relationships, multimodal representation learning enables a unified representation that enhances performance in cross-media analysis tasks such as video classification, event detection, and sentiment analysis. It also supports cross-modal retrieval and translation, including image captioning, video description, and text-to-image synthesis. == Motivation == The primary motivations for multimodal representation learning arise from the inherent nature of real-world data and the limitations of unimodal approaches. Since multimodal data offers complementary and supplementary information about an object or event from different perspectives, it is more informative than relying on a single modality. A key motivation is to narrow the heterogeneity gap that exists between different modalities by projecting their features into a shared semantic subspace. This allows semantically similar content across modalities to be represented by similar vectors, facilitating the understanding of relationships and correlations between them. Multimodal representation learning aims to leverage the unique information provided by each modality to achieve a more comprehensive and accurate understanding of concepts. These unified representations are crucial for improving performance in various cross-media analysis tasks such as video classification, event detection, and sentiment analysis. They also enable cross-modal retrieval, allowing users to search and retrieve content across different modalities. Additionally, it facilitates cross-modal translation, where information can be converted from one modality to another, as seen in applications like image captioning and text-to-image synthesis. The abundance of ubiquitous multimodal data in real-world applications, including understudied areas like healthcare, finance, and human-computer interaction (HCI), further motivates the development of effective multimodal representation learning techniques. == Approaches and methods == === Canonical-correlation analysis based methods === Canonical-correlation analysis (CCA) was first introduced in 1936 by Harold Hotelling and is a fundamental approach for multimodal learning. CCA aims to find linear relationships between two sets of variables. Given two data matrices X ∈ R n × p {\displaystyle X\in \mathbb {R} ^{n\times p}} and Y ∈ R n × q {\displaystyle Y\in \mathbb {R} ^{n\times q}} representing different modalities, CCA finds projection vectors w x ∈ R p {\displaystyle w_{x}\in \mathbb {R} ^{p}} and w y ∈ R q {\displaystyle w_{y}\in \mathbb {R} ^{q}} that maximizes the correlation between the projected variables: ρ = max w x , w y w x ⊤ Σ x y w y w x ⊤ Σ x x w x w y ⊤ Σ y y w y {\displaystyle \rho =\max _{w_{x},w_{y}}{\frac {w_{x}^{\top }\Sigma _{xy}w_{y}}{{\sqrt {w_{x}^{\top }\Sigma _{xx}w_{x}}}{\sqrt {w_{y}^{\top }\Sigma _{yy}w_{y}}}}}} such that Σ x x {\displaystyle \Sigma _{xx}} and Σ y y {\displaystyle \Sigma _{yy}} are the within-modality covariance matrices, and Σ x y {\displaystyle \Sigma _{xy}} is the between-modality covariance matrix. However, standard CCA is limited by its linearity, which led to the development of nonlinear extensions, such as kernel CCA and deep CCA. ==== Kernel CCA ==== Kernel canonical correlation analysis (KCCA) extends traditional CCA to capture nonlinear relationships between modalities by implicitly mapping the data into high dimensional feature spaces using kernel functions. Given kernel functions K x {\displaystyle K_{x}} and K y {\displaystyle K_{y}} with corresponding Gram matrices K x ∈ R n × n {\displaystyle K_{x}\in \mathbb {R} ^{n\times n}} and K y ∈ R n × n {\displaystyle K_{y}\in \mathbb {R} ^{n\times n}} , KCCA seeks coefficients α {\displaystyle \alpha } and β {\displaystyle \beta } that maximize: ρ = max α , β α ⊤ K x K y β α ⊤ K x 2 α β ⊤ K y 2 β {\displaystyle \rho =\max _{\alpha ,\beta }{\frac {\alpha ^{\top }K_{x}Ky\beta }{{\sqrt {\alpha ^{\top }K_{x}^{2}\alpha }}{\sqrt {\beta ^{\top }K_{y}^{2}\beta }}}}} To prevent overfitting, regularization terms are typically added, resulting in: ρ = max α , β α T K x K y β α T ( K x 2 + λ x K x ) α β T ( K y 2 + λ y K y ) β {\displaystyle \rho =\max _{\alpha ,\beta }{\frac {\alpha ^{T}K_{x}K_{y}\beta }{{\sqrt {\alpha ^{T}\left(K_{x}^{2}+\lambda _{x}K_{x}\right)\alpha }}{\sqrt {\;\beta ^{T}\left(K_{y}^{2}+\lambda _{y}K_{y}\right)\beta }}}}} where λ x {\displaystyle \lambda _{x}} and λ y {\displaystyle \lambda _{y}} are regularization parameters. KCCA has proven effective for tasks such as cross-modal retrieval and semantic analysis, though it faces computational challenges with large datasets due to its O ( n 2 ) {\displaystyle O(n^{2})} memory requirement for sorting kernel matrices. KCCA was proposed independently by several researchers. ==== Deep CCA ==== Deep canonical correlation analysis (DCCA), introduced in 2013, employs neural networks to learn nonlinear transformations for maximizing the correlation between modalities. DCCA uses separate neural networks f x {\displaystyle f_{x}} and f y {\displaystyle f_{y}} for each modality to transform the original data before applying CCA: max W x , W y , θ x , θ y corr ( f x ( X ; θ x ) , f y ( Y ; θ y ) ) {\displaystyle \max _{W_{x},W_{y},\theta _{x},\theta _{y}}\operatorname {corr} \left(f_{x}(X;\theta _{x}),f_{y}(Y;\theta _{y})\right)} where θ x {\displaystyle \theta _{x}} and θ y {\displaystyle \theta _{y}} represent the parameters of the neural networks, and W x {\displaystyle W_{x}} and W y {\displaystyle W_{y}} are the CCA projection matrices. The correlation objective is computed as: corr ( H x , H y ) = tr ( T − 1 / 2 H x T H y S − 1 / 2 ) {\displaystyle \operatorname {corr} (H_{x},H_{y})=\operatorname {tr} \left(T^{-1/2}H_{x}^{T}H_{y}S^{-1/2}\right)} where H x = f x ( X ) {\displaystyle H_{x}=f_{x}(X)} and H y = f y ( Y ) {\displaystyle H_{y}=f_{y}(Y)} are the network outputs, T = H x T H x + r x I {\displaystyle T=H_{x}^{T}H_{x}+r_{x}I} , S = H y T H y + r y I {\displaystyle S=H_{y}^{T}H_{y}+r_{y}I} and r x , r y {\displaystyle r_{x},r_{y}} are the regularization parameters. DCCA overcomes the limitations of linear CCA and kernel CCA by learning complex nonlinear relationships while maintaining computational efficiency for large datasets through mini-batch optimization. === Graph-based methods === Graph-based approaches for multimodal representation learning leverage graph structure to model relationships between entities across different modalities. These methods typically represent each modality as a graph and then learn embedding that preserve cross-modal similarities, enabling more effective joint representation of heterogeneous data. One such method is cross-modal graph neural networks (CMGNNs) that extend traditional graph neural networks (GNNs) to handle data from multiple modalities by constructing graphs that capture both intra-modal and inter-modal relationships. These networks model interactions across modalities by representing them as nodes and their relationships as edges. Other graph-based methods include Probabilistic Graphical Models (PGMs) such as deep belief networks (DBN) and deep Boltzmann machines (DBM). These models can learn a joint representation across modalities, for instance, a multimodal DBN achieves this by adding a shared restricted Boltzmann Machine (RBM) hidden layer on top of modality-specific DBNs. Additionally, the structure of data in some domains like Human-Computer Interaction (HCI), such as the view hierarchy of app screens, can potentially be modeled using graph-like structures. The field of graph representation learning is also relevant, with ongoing progress in developing evaluation benchmarks. === Diffusion maps === Another set of methods relevant to multimodal representation learning are based on diffusion maps and their extensions to handle multiple modalities. ==== Multi-view diffusion maps ==== Multi-view diffusion maps address the challenge of achieving multi-view dimensionality reduction by effectively utilizing the availability of multiple views to extract a coherent low-dimensional representation of the data. The core idea is to exploit both the intrinsic relations within each view and the mutual relations between the different views, defining a cross-view model where a random walk process implicitly hops between objects in different views. A multi-view kernel matrix is constructed by combining these relations, defining a cross-view diffusion process and associ
Time-lock puzzle
A time-lock puzzle, or time-released cryptography, encrypts a message that cannot be decrypted until a specified amount of time has passed. The concept was first described by Timothy C. May, and a solution first introduced by Ron Rivest, Adi Shamir, and David A. Wagner in 1996. Time-lock puzzle are useful in cases where confidentiality of information is determined by time, such as a diarist who does not want their views released until 50 years after their death, an auction where bids are sealed until the bidding period is closed, electronic voting, and contract signing. They can additionally be used in creating further cryptographic primitives, such as verifiable delay functions and zero knowledge proofs. Time-released cryptography can be achieved through several different mechanisms. Use mathematical problems requiring sequential calculations to solve, and cannot be solved with parallelization. Thus, adding more computers to a problem will not help solve the problem faster. Use of a trusted agent, or multiple agents who each hold a part of the message and cryptographic keys, who release the message after a specified time period has passed. Distribute public encryption keys to users, and place private cryptographic keys with a trusted agent in an offline location, to be released at a later date.
Data Reference Model
The Data Reference Model (DRM) is one of the five reference models of the Federal Enterprise Architecture. == Overview == The DRM is a framework whose primary purpose is to enable information sharing and reuse across the United States federal government via the standard description and discovery of common data and the promotion of uniform data management practices. The DRM describes artifacts which can be generated from the data architectures of federal government agencies. The DRM provides a flexible and standards-based approach to accomplish its purpose. The scope of the DRM is broad, as it may be applied within a single agency, within a community of interest, or cross-community of interest. == Data Reference Model topics == === DRM structure === The DRM provides a standard means by which data may be described, categorized, and shared. These are reflected within each of the DRM's three standardization areas: Data Description: Provides a means to uniformly describe data, thereby supporting its discovery and sharing. Data Context: Facilitates discovery of data through an approach to the categorization of data according to taxonomies. Additionally, enables the definition of authoritative data assets within a community of interest. Data Sharing: Supports the access and exchange of data where access consists of ad hoc requests (such as a query of a data asset), and exchange consists of fixed, re-occurring transactions between parties. Enabled by capabilities provided by both the Data Context and Data Description standardization areas. === DRM Version 2 === The Data Reference Model version 2 released in November 2005 is a 114-page document with detailed architectural diagrams and an extensive glossary of terms. The DRM also make many references to ISO standards specifically the ISO/IEC 11179 metadata registry standard. === DRM usage === The DRM is not technically a published technical interoperability standard such as web services, it is an excellent starting point for data architects within federal and state agencies. Any federal or state agencies that are involved with exchanging information with other agencies or that are involved in data warehousing efforts should use this document as a guide.
Public Services Network
The Public Services Network (PSN) is a UK government's high-performance network, which helps public sector organisations work together, reduce duplication and share resources. It unified the provision of network infrastructure across the United Kingdom public sector into an interconnected "network of networks" to increase efficiency and reduce overall public expenditure. It is now a legacy network and public sector organisations are being migrated to using services on the public internet. == Origins == The Public Services Network (PSN) was launched officially as part of the Transformational Government Strategy commencing in 2005, under the original name of the Public Sector Network. Prior to this, some parts of local government had already successfully implemented the concept. The Hampshire Public Services Network (HPSN) was the first PSN, launched in 1999, followed closely by Kent County Councils partnerships with the KPSN. The HPSN, encompassing all of the borough, district and unitary councils, with the County Council, as well as the Fire Services, the Isle of Wight Council and 540 schools. National PSN technical and architecture compliance criteria were established from 2007, by GDS working with local government leaders from Socitm (the Society of Information Technology Management) on the National CIO Council and the Local CIO Council. The PSN's aim was to bring public services organisations with a common interest onto a single, coherent and standards-based ‘network of networks’. This would create influence, economies of scale and a commonality of standards for secure and easy inter-connection between public service organisations. The original concept of a network of networks strategy was based upon the work already undertaken in local government and recognition of Communities of Interest (COI) within the Criminal Justice Sector during work by the Office for Criminal Justice Reform (OCJR) between 2005 and 2007 to enable data sharing across business units. In this context a COI was defined as groups of Government departments and external partners who in combination provided services within a specific area of operation and used the same data, with a similar risk profile, shared risk appetite and common governance framework. Historically each group member had implemented their own networks and standards of operation in isolation with little or no consideration as to how services and data may be shared and resulting in increased costs of operation. The Network of Networks strategy proposed within OCJR recommended the creation of specific networks based upon these Communities of Interest which were joined together through data interchange gateways supporting common standards. Under this approach networks would be arranged by data type and business functions such as Criminal Justice, Health and Social Care, Defence and Intelligence or Public Finance rather than solely on established departmental boundaries. Within a COI, trust relationships and data interchange are readily supported, enabling data sharing without a need to cross network boundaries and providing benefits of scale without the challenges and compromises intrinsic to homogeneous cross sector networks. Data is made available without a need to transport it between organisations and control is retained by the data originator. In early 2007 a group of UK Government department CTOs in conjunction with the Office for Government Commerce Buying Solutions (OGC BS) established the vision for a single commonly provided, procured and managed public sector voice and data network infrastructure to replace the multitude of separately procured and managed networks serving various segments of the UK public sector; Education, Health, Central Government, Local Government etc. In 2008 an Industry Working Group was established to document the objectives and requirements more clearly. Their report set out the architectural and commercial principles as well as anticipated security, service management, governance and transition arrangements. == Architecture == The PSN comprises a core network, the Government Conveyancing Network or GCN provided by GCN Service Providers or GCNSPs. The GCN interconnects multiple operator networks, termed Direct Network Service Providers or DNSPs. Subscriber organisations contract to a connection from a local participating DNSP, connect via that to GCN and hence onwards to other interconnected networks and services. The GCN network is entirely based on IPv4 and MPLS and the GCNSPs are not currently mandated to provide IPv6, though they should have a roadmap to implementing it if and when required. == Commercial framework == In 2010 Virgin Media Business, BT, Cable & Wireless and Global Crossing signed Deeds of Undertaking (DoU) and subsequently achieved accreditation for providing GCN and IP VPN services. In March 2012, BT, Cable & Wireless, Capita Business Services, Eircom, Fujitsu, Kcom, Level 3, Logicalis, MDNX, Thales, Updata and Virgin Media Business were successful bidders for the initial two-year PSN Connectivity framework. In June 2012, 29 companies were confirmed as suppliers of ICT services to the UK public sector under the Government's PSN Services framework contract. Apart from most of the previous suppliers, additional companies also included 2e2, Airwave Solutions, Azzurri Communications, Cassidian, CSC Computer Sciences, Computacenter, Daisy Communications, Easynet Global Services, EE, Freedom Communications, Icom Holdings, NextiraOne, PageOne Communications, Phoenix IT Group, Siemens Communications, Specialist Computer Centres, Telefónica, telent Technology Services, Uniworld Communications and Vodafone. == Governance == The PSN is managed within the Cabinet Office where it is part of the Government Digital Service. == Early implementations == There were already notable initiatives in progress in county council areas, demonstrating public sector network integration in both the Hampshire HPSN2 network and in Kent's community network. Project Pathway was established as a pilot linking these two county-wide networks, with Virgin Media Business and Global Crossing the subscriber and GCN network elements. Staffordshire County Council was the first council in England to establish a PSN that included the county's NHS Health partners. Other county councils have since followed the leads of these councils. == Transition == Centrally procured public sector networks are expected to migrate across to the PSN framework as they reach the end of their contract terms, either through an interim framework or directly. The Government Secure Intranet (GSi) contracts expired in September 2011, running on to 12 February 2012 and were replaced by the transitional Government Secure Intranet Convergence Framework (GCF). The Managed Telephony Service (MTS) contract expired on 31 December 2011 and was replaced by the Managed Telephony Convergence Framework (MTCF). == Future plan == In a blog post published on 20 January 2017, Government Digital Service announced that the Technology Leaders Network (TLN) had agreed that government was starting a journey away from the PSN. This was because using the Internet was considered suitable for the vast majority of the work that the public sector does. The blog post confirmed that the 'move was not going to happen immediately' and stated that 'there's quite a bit of work to do across the public sector to prepare for the changes'. It also stated that it was too early for a full timeline to be provided, although all PSN-connected organisations would be updated as the process evolved. The blog post confirmed that organisations that need to access services that are only available on the PSN would still need to connect to it for the time being and continue to meet its assurance requirements. In a blog post published on 16 March 2017, Government Digital Service (GDS) set out its plans for PSN assurance. The blog post confirmed that the PSN compliance process wasn't 'going anywhere, certainly for a while yet'. It explained that the TLN agreed that – as one of the only recognised, externally accredited, cross-government common assurance standards – it 'needs to live on far beyond the end of the physical PSN network'. Government Digital Service, along with the National Cyber Security Centre (NCSC) and the Cyber and Government Security Directorate, are now looking at ways to expand and reframe PSN compliance in a new context that, while retaining the assurance principles that are the basis of the existing process, will aim to improve the process. A GDS blog post titled 'The road to closing down the PSN' published on 8 September 2020 describes how the public sector will migrate away from the PSN. The Cabinet Office has set up a programme called Future Networks for Government (FN4G) to help organisations move away from the PSN.
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
Cognos ReportNet
Cognos ReportNet (CRN) was a web-based software product for creating and managing ad hoc and custom-made reports. ReportNet was developed by the Ottawa-based company Cognos (formerly Cognos Incorporated), an IBM company. The web-based reporting tool was launched in September 2003. Since IBM's acquisition of Cognos, ReportNet has been renamed IBM Cognos ReportNet like all other Cognos products. ReportNet uses web services standards such as XML and Simple Object Access Protocol and also supports dynamic HTML and Java. ReportNet is compatible with multiple databases including Oracle, SAP, Teradata, Microsoft SQL server, DB2 and Sybase. The product provides interface in over 10 languages, has Web Services architecture to meet the needs of multi-national, diversified enterprises and helps reduce total cost of ownership. Multiple versions of Cognos ReportNet have since been released by the company. Cognos ReportNet was awarded the Software and Information Industry Association (SIIA) 2005 Codie awards for the "Best Business Intelligence or Knowledge Management Solution" category. CRN's capabilities have been further used in IBM Cognos 8 BI (2005), the latest reporting tool. CRN comes with its own software development kit (SDK). == Launch == Early adopters of Cognos ReportNet for their corporate reporting needs included Bear Stearns, BMW and Alfred Publishing. Around this same time of launch, Cognos competitor Business Objects released version 6.1 of its enterprise reporting tool. Cognos ReportNet has been successful since its launch, raising revenues in 2004 from licensing fees. == Controversy == Cognos rival Business Objects announced in 2005 that BusinessObjects XI significantly outperformed Cognos ReportNet in benchmark tests conducted by VeriTest, an independent software testing firm. The tests performed showed Cognos ReportNet performed poorly when processing styled reports, complex business reports and combination of both. The tests reported a massive 21 times higher report throughput for BusinessObjects XI than Cognos ReportNet at capacity loads. Cognos soon dismissed the claims by stating Business Objects dictated the environment and testing criteria and Cognos did not provide the software to participate in benchmark test. Cognos later performed their own test to demonstrate Cognos ReportNet capabilities. == Components == Cognos Report Studio – A Web-based product for creating complex professional looking reports. Cognos Query Studio - A Web-based product for creating ad-hoc reports. Cognos Framework Manager – A metadata modeling tool to create BI metadata for reporting and dashboard applications. Cognos Connection – Main portal used to access reports, schedule reports and perform administrator activities. == Versions == Cognos ReportNet 1.1 – Java EE-style professional web-based authoring tool. (base version) Cognos ReportNet IBM Special Edition – comes with an embedded version of IBM WebSphere as its application server and IBM DB2 as its data store. Cognos Linux – for Intel-based Linux platforms.