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
Signal-to-noise ratio (imaging)
Signal-to-noise ratio (SNR) is used in imaging to characterize image quality. The sensitivity of a (digital or film) imaging system is typically described in the terms of the signal level that yields a threshold level of SNR. Industry standards define sensitivity in terms of the ISO film speed equivalent, using SNR thresholds (at average scene luminance) of 40:1 for "excellent" image quality and 10:1 for "acceptable" image quality. SNR is sometimes quantified in decibels (dB) of signal power relative to noise power, though in the imaging field the concept of "power" is sometimes taken to be the power of a voltage signal proportional to optical power; so a 20 dB SNR may mean either 10:1 or 100:1 optical power, depending on which definition is in use. == Definition of SNR == Traditionally, SNR is defined to be the ratio of the average signal value μ s i g {\displaystyle \mu _{\mathrm {sig} }} to the standard deviation of the signal σ s i g {\displaystyle \sigma _{\mathrm {sig} }} : S N R = μ s i g σ s i g {\displaystyle \mathrm {SNR} ={\frac {\mu _{\mathrm {sig} }}{\sigma _{\mathrm {sig} }}}} when the signal is an optical intensity, or as the square of this value if the signal and noise are viewed as amplitudes (field quantities).
FactorDaily
FactorDaily is an Indian digital media publication founded in 2016 by Pankaj Mishra and Jayadevan PK. Mishra was formerly an Editor at TechCrunch and the Economic Times. The digital publication was launched with an intent to produce stories on the impact of technology on life in India. == History == FactorDaily began publishing in May 2016, with daily reported stories on technology, culture and life in India. Prior to its launch, the company had raised $1 million in seed funding from Accel India, Blume Ventures, Girish Mathrubootham of Freshdesk, Vijay Shekhar Sharma of PayTm, and Jay Vijayan of Tekion. Josey Puliyenthuruthel John, formerly Managing Editor at Business Today and National Corporate Editor at Mint, later joined the company as a Consulting Editor. In January 2017, FactorDaily launched its first Podcast called The Outliers. The inaugural episode featured a conversation with Manish Sharma of Printo on his journey starting up. == Awards == The FactorDaily team won the Bengaluru Editors Lab 2017, a journalism hackathon organised by the Global Editors Network (GEN). The story titled "India has 3,800 psychiatrists for 1.2bn people. Can tech step in to manage mental health?" won the first prize in the online category of the fifth Schizophrenia Research Foundation’s (SCARF) ‘Media for Mental Health’ awards. The story titled 'The dark hand of tech that stokes sex trafficking in India', won the Stop Slavery media Awards by the Thomson Reuters Foundation for the year 2020.
VibeOS
VibeOS is an operating system built from scratch entirely by generative artificial intelligence, using code produced through prompts to Claude (vibe coding). It is capable of running on QEMU and was successfully tested on a Raspberry Pi Zero. It has been released under the MIT license. == Features == === Core === Custom kernel with cooperative multitasking (preemptive backup) FAT32 filesystem with long filename support Memory allocator, process scheduler, interrupt handling GIC-400 (QEMU) and BCM2836/BCM2835 (Pi) interrupt controllers Configurable boot (splash screen, boot target) === GUI === Desktop environment with draggable windows Menu bar, dock, window minimize/maximize/close Mouse and keyboard input Modern macOS-inspired aesthetic === Networking === Full TCP/IP stack (Ethernet, ARP, IP, ICMP, UDP, TCP) DNS resolver HTTP client TLS 1.2 with HTTPS support === Apps === Web browser with HTML/CSS rendering Terminal emulator with readline-style shell Text editor (vim clone) with syntax highlighting File manager with drag-and-drop Music player (MP3/WAV) Calculator, system monitor VibeCode IDE Doom port === Development === TCC (Tiny C Compiler) - compile C programs directly on VibeOS MicroPython interpreter with full kernel API bindings 60+ userspace programs (coreutils, games, GUI apps) === Hardware === Runs on Raspberry Pi Zero 2W USB keyboard and mouse via DWC2 driver SD card via EMMC driver 1920×1080 framebuffer == Further projects == There are other independent projects under the VibeOS name, including an independent development by Ben, also developed using vibe coding, aimed at creating a Unix-like operating system for educational purposes. Another project is Vib-OS, an operating system also built using vibe coding, capable of booting on a Raspberry Pi. It offers a desktop environment with a customizable wallpaper, a file manager, and a web browser currently in an early stage of development, a functional Doom port, among other features that are not very polished given the state of development.
List of search appliance vendors
A search appliance is a type of computer which is attached to a corporate network for the purpose of indexing the content shared across that network in a way that is similar to a web search engine. It may be made accessible through a public web interface or restricted to users of that network. A search appliance is usually made up of: a gathering component, a standardizing component, a data storage area, a search component, a user interface component, and a management interface component. == Vendors of search appliances == Fabasoft Google InfoLibrarian Search Appliance™ Maxxcat Searchdaimon Thunderstone == Former/defunct vendors of search appliances == Black Tulip Systems Google Search Appliance Index Engines Munax Perfect Search Appliance
Model compression
Model compression is a machine learning technique for reducing the size of trained models. Large models can achieve high accuracy, but often at the cost of significant resource requirements. Compression techniques aim to compress models without significant performance reduction. Smaller models require less storage space, and consume less memory and compute during inference. Compressed models enable deployment on resource-constrained devices such as smartphones, embedded systems, edge computing devices, and consumer electronics computers. Efficient inference is also valuable for large corporations that serve large model inference over an API, allowing them to reduce computational costs and improve response times for users. Model compression is not to be confused with knowledge distillation, in which a smaller "student" model is trained to imitate the input-output behavior of a larger "teacher" model (as opposed to using the "teacher"'s trained parameters or the "teacher"'s training targets). == Techniques == Several techniques are employed for model compression. === Pruning === Pruning sparsifies a large model by setting some parameters to exactly zero. This effectively reduces the number of parameters. This allows the use of sparse matrix operations, which are faster than dense matrix operations. Pruning criteria can be based on magnitudes of parameters, the statistical pattern of neural activations, Hessian values, etc. === Quantization === Quantization reduces the numerical precision of weights and activations. For example, instead of storing weights as 32-bit floating-point numbers, they can be represented using 8-bit integers. Low-precision parameters take up less space, and takes less compute to perform arithmetic with. It is also possible to quantize some parameters more aggressively than others, so for example, a less important parameter can have 8-bit precision while another, more important parameter, can have 16-bit precision. Inference with such models requires mixed-precision arithmetic. Quantized models can also be used during training (rather than after training). PyTorch implements automatic mixed-precision (AMP), which performs autocasting, gradient scaling, and loss scaling. === Low-rank factorization === Weight matrices can be approximated by low-rank matrices. Let W {\displaystyle W} be a weight matrix of shape m × n {\displaystyle m\times n} . A low-rank approximation is W ≈ U V T {\displaystyle W\approx UV^{T}} , where U {\displaystyle U} and V {\displaystyle V} are matrices of shapes m × k , n × k {\displaystyle m\times k,n\times k} . When k {\displaystyle k} is small, this both reduces the number of parameters needed to represent W {\displaystyle W} approximately, and accelerates matrix multiplication by W {\displaystyle W} . Low-rank approximations can be found by singular value decomposition (SVD). The choice of rank for each weight matrix is a hyperparameter, and jointly optimized as a mixed discrete-continuous optimization problem. The rank of weight matrices may also be pruned after training, taking into account the effect of activation functions like ReLU on the implicit rank of the weight matrices. == Training == Model compression may be decoupled from training, that is, a model is first trained without regard for how it might be compressed, then it is compressed. However, it may also be combined with training. The "train big, then compress" method trains a large model for a small number of training steps (less than it would be if it were trained to convergence), then heavily compress the model. It is found that at the same compute budget, this method results in a better model than lightly compressed, small models. In Deep Compression, the compression has three steps. First loop (pruning): prune all weights lower than a threshold, then finetune the network, then prune again, etc. Second loop (quantization): cluster weights, then enforce weight sharing among all weights in each cluster, then finetune the network, then cluster again, etc. Third step: Use Huffman coding to losslessly compress the model. The SqueezeNet paper reported that Deep Compression achieved a compression ratio of 35 on AlexNet, and a ratio of ~10 on SqueezeNets.
Anti-social Media Bill (Nigeria)
Anti-social Media Bill was introduced by the Senate of the Federal Republic of Nigeria on 5 November 2019 to criminalise the use of the social media in peddling false or malicious information. The original title of the bill is Protection from Internet Falsehood and Manipulations Bill 2019. It was sponsored by Senator Mohammed Sani Musa from the largely conservative northern Nigeria. After the bill passed second reading on the floor of the Nigeria Senate and its details were made public, information emerged on the social media accusing the sponsor of the bill of plagiarising a similar law in Singapore which is at the bottom of global ranking in the freedom of speech and of the press. But the senator denied that he plagiarised Singaporean law. == Opposition to the bill == Angry reactions trailed the introduction of the bill, and a number of civil society organisations, human rights activists, and Nigerian citizens unanimously opposed the bill. International rights group, Amnesty International and Human Rights Watch condemned the proposed legislation saying it is aimed at gagging freedom of speech which is a universal right in a country of over two hundred million people. Opposition political parties are very critical of the bill and accused the government of attempting to strip bare, Nigerian citizens of their rights to free speech and destroying same social media on whose power and influence the ruling All Progressives Congress, APC came to power in 2015. Nigeria Information Minister, Lai Mohammed has been at the center of public criticism because he is suspected to be the brain behind the proposed act. Lai was a former spokesman of then opposition All Progressives Congress. A "Stop the Social Media Bill! You can no longer take our rights from us" online petition campaign to force the Nigeria parliament to drop the bill received over 90,000 signatures within 24 hours. In November 2019, after the bill passed second reading in the senate, Akon Eyakenyi, a senator from Akwa Ibom State publicly said he would resist the bill. === Support for the bill === Those who support the proposed act especially Senators have often argued that the law would help curtail hate speech. President Muhammad Buhari who is seen as a beneficiary of the influence and power of the social media and free speech has been mute about it. But the president's senior aides and family members have publicly spoken in support of the bill. In November 2019, the wife of the president, Aisha Buhari, told a gathering at the Nigeria's National Mosque in the capital, Abuja that if China with over one billion people could regulate the social media, Nigeria should do same. But Nigerians reacted saying Nigeria is not a one-party communist state like China. Days later, a daughter to the president, Zahra Indimi told a gathering of young people in Abuja that social media had become a potent weapon for bullying those they thought were doing better than them in terms of social class and called for a critical regulation. == Key provisions of the bill == === Title === Protection from Internet Falsehoods, Manipulations and Other Related Matters Bill 2019. === Explanatory memorandum === This Act is to prevent Falsehoods and Manipulations in Internet transmission and correspondences in Nigeria. To suppress falsehoods and manipulations and counter the effects of such communications and transmissions and to sanction offenders with a view to encouraging and enhancing transparency by Social Media Platforms using the internet correspondences. === Objectives === One objective of the bill is to prevent the transmission of false statements or declaration of facts in Nigeria. Another objective of the bill is to end the financing of online mediums that transmit false statements. Measures will be taken to detect and control inauthentic behaviour and misuse of online accounts (parody accounts). When paid content is posted towards a political end, there will be measures to ensure the poster discloses such information. There will be sanction for offenders. === Transmission of false statement === According to the bill, a person must not: Transmit a statement that is false or, Transmit a statement that might: i. Affect the security or any part of Nigeria. ii. Affect public health, public safety or public finance. iii. Affect Nigeria's relationship with other countries. iv. influence the outcome of an election to any office in a general election. v. Cause enmity or hatred towards a person or group of persons. Anyone guilty of the above is liable to a fine of N300,000 or three years' imprisonment or both (for individual); and a fine not exceeding ten million naira (for corporate organisations). Same punishment applies for fake online accounts that transmit statements listed above. === Parody accounts === The bill says a person shall not open an account to transmit false statement. Anyone found guilty will be fined N200,000 or three years' imprisonment or both (for an individual) or five million naira (for corporate organisations). If such accounts transmit a statement that will affect security or influence the outcome of an election, such a person will be fined N300,000 or three years' imprisonment or both. If a person receives payment or reward to help another to transmit false statements knowingly, he/she is liable to a fine of N150,000 or three years' imprisonment or both. If a person receives payment or reward to help another to transmit a statement affects security or influence the outcome of an election, the fine is N300,000 or three years' imprisonment or both (for individual) and ten million naira for organisations. === Declaration === According to the bill, a law enforcement department can issue a "declaration" to offenders. And this declaration will be issued even if the "false statement" has been corrected or pulled down. The offender will be required to publish a "correction notice" in a specified newspaper, online location or other printed publication of Nigeria. Failure to comply, a person is liable to N200,000 or 12 months' imprisonment or both (for individual) and five million naira for organisations. === Access blocking order === The bill says the law enforcement department will also issue an access blocking order to offenders. The law enforcement department may direct the NCC to order the internet access service provider to disable access by users in Nigeria to the online location and the NCC must give the internet access service provider an access blocking order. An internet access service provider that does not comply with any access blocking order is liable on conviction to a fine not exceeding ten million naira for each day during any part of which that order is not fully complied with, up to a total of five million naira.