The skyline operator is the subject of an optimization problem and computes the Pareto optimum on tuples with multiple dimensions. This operator is an extension to SQL proposed by Börzsönyi et al. to filter results from a database to keep only those objects that are not dominated by any other point on all dimensions. The name skyline comes from the view on Manhattan from the Hudson River, where those buildings can be seen that are not hidden by any other. A building is visible if it is not dominated by a building that is taller or closer to the river (two dimensions, distance to the river minimized, height maximized). Another application of the skyline operator involves selecting a hotel for a holiday. The user wants the hotel to be both cheap and close to the beach. However, hotels that are close to the beach may also be expensive. In this case, the skyline operator would only present those hotels that are not worse than any other hotel in both price and distance to the beach. == Formal specification == The skyline operator returns tuples that are not dominated by any other tuple. A tuple dominates another if it is at least as good in all dimensions and better in at least one dimension. Formally, we can think of each tuple as a vector p , q ∈ R n {\displaystyle p,q\in \mathbb {R} ^{n}} . p {\displaystyle p} dominates q {\displaystyle q} (written: p ≻ q {\displaystyle p\succ q} ) if p {\displaystyle p} is at least as good as q {\displaystyle q} in every dimension, and superior in at least one: p ≻ q ⇔ ∀ i ∈ [ n ] . p [ i ] ⪰ q [ i ] ∧ ∃ j ∈ [ n ] . p [ j ] ≻ q [ j ] . {\displaystyle p\succ q\Leftrightarrow \forall i\in [n].p[i]\succeq q[i]\wedge \exists j\in [n].p[j]\succ q[j].} Dominance ( p ≻ q {\displaystyle p\succ q} ) can be defined as any strict partial ordering, for example greater (with ≻:=> {\displaystyle \succ :=>} and ⪰:=≥ {\displaystyle \succeq :=\geq } ) or less (with ≻:=< {\displaystyle \succ :=<} and ⪰:=≤ {\displaystyle \succeq :=\leq } ). Assuming two dimensions and defining dominance in both dimensions as greater, we can compute the skyline in SQL-92 as follows: == Proposed syntax == As an extension to SQL, Börzsönyi et al. proposed the following syntax for the skyline operator: where d1, ... dm denote the dimensions of the skyline and MIN, MAX and DIFF specify whether the value in that dimension should be minimised, maximised or simply be different. Without an SQL extension, the SQL query requires an antijoin with not exists: == Implementation == The skyline operator can be implemented directly in SQL using current SQL constructs, but this has been shown to be very slow in disk-based database systems. Other algorithms have been proposed that make use of divide and conquer, indices, MapReduce and general-purpose computing on graphics cards. Skyline queries on data streams (i.e. continuous skyline queries) have been studied in the context of parallel query processing on multicores, owing to their wide diffusion in real-time decision making problems and data streaming analytics. Exasol features a native implementation.
NER model
NER is one of several formulas for accessing live subtitles in television broadcasts and events that are produced using speech recognition. The three letters stand for number, edit error and recognition error. It has been promoted as an alternative to Word error rate (Word Error Rate) which is a more objective measure. The overall score is calculated as follows: Firstly, the number of edit and recognition errors is deducted from the total number of words in the live subtitles. This number is then divided by the total number of words in the live subtitles and finally multiplied by one hundred. N E R v a l u e = N − E − R N ∗ 100 {\displaystyle NERvalue={\frac {N-E-R}{N}}100} . The acronyms stand for the following: N (number) = total number of words in the live subtitles E (Edit error) = edit error R (Recognition error) = recognition error This measurement process has been used for public television broadcasts in European countries like Italy and Switzerland. One major drawback with NER is that it requires a human assessor to rate errors as either: 1 Minor edition or recognition errors 2 Normal edition or recognition errors 3 Serious errors which are then weighted in the assessment process. This is both subjective, time consuming and costly. Also, NER fails to account for words left out subtitles which is something that does not take account of the D/deaf audience who want verbatim subtitles. As a result, NER cannot accurately reflect the audience's experience of subtitles. Another problem is the inconsistency of human evaluation of subtitles, particularly with live subtitles, where there are differing opinions of the importance of subtitle errors. By way of contrast, Word error rate is an objective measure of subtitle errors, since it measures the textual discrepancy between the subtitles and the speech.
Probabilistic database
Most real databases contain data whose correctness is uncertain. In order to work with such data, there is a need to quantify the integrity of the data. This is achieved by using probabilistic databases. A probabilistic database is an uncertain database in which the possible worlds have associated probabilities. Probabilistic database management systems are currently an active area of research. "While there are currently no commercial probabilistic database systems, several research prototypes exist..." Probabilistic databases distinguish between the logical data model and the physical representation of the data much like relational databases do in the ANSI-SPARC Architecture. In probabilistic databases this is even more crucial since such databases have to represent very large numbers of possible worlds, often exponential in the size of one world (a classical database), succinctly. == Terminology == In a probabilistic database, each tuple is associated with a probability between 0 and 1, with 0 representing that the data is certainly incorrect, and 1 representing that it is certainly correct. === Possible worlds === A probabilistic database could exist in multiple states. For example, if there is uncertainty about the existence of a tuple in the database, then the database could be in two different states with respect to that tuple—the first state contains the tuple, while the second one does not. Similarly, if an attribute can take one of the values x, y or z, then the database can be in three different states with respect to that attribute. Each of these states is called a possible world. Consider the following database: (Here {b3, b3′, b3′′} denotes that the attribute can take any of the values b3, b3′ or b3′′) Assuming that there is uncertainty about the first tuple, certainty about the second tuple, and uncertainty about the value of attribute B in the third tuple. Then the actual state of the database may or may not contain the first tuple (depending on whether it is correct or not). Similarly, the value of the attribute B may be b3, b3′ or b3′′. Consequently, the possible worlds corresponding to the database are as follows: === Types of Uncertainties === There are essentially two kinds of uncertainties that could exist in a probabilistic database, as described in the table below: By assigning values to random variables associated with the data items, different possible worlds can be represented. == History == The first published use of the term "probabilistic database" was probably in the 1987 VLDB conference paper "The theory of probabilistic databases", by Cavallo and Pittarelli. The title (of the 11 page paper) was intended as a bit of a joke, since David Maier's 600 page monograph, The Theory of Relational Databases, would have been familiar at that time to many of the conference participants and readers of the conference proceedings.
Hindsight optimization
Hindsight optimisation (HOP) is a computer science technique used in artificial intelligence for analysis of actions which have stochastic results. HOP is used in combination with a deterministic planner. By creating sample results for each of the possible actions from the given state (i.e. determinising the actions), and using the deterministic planner to analyse those sample results, HOP allows an estimate of the actual action.
Stanhope Demonstrator
The Stanhope Demonstrator was the first machine to solve problems in logic. It was designed by Charles Stanhope, 3rd Earl Stanhope to demonstrate consequences in logic symbolically. The first model was constructed in 1775. It consisted of two slides coloured red and gray mounted in a square brass frame. This could be used to demonstrate the solution to a syllogistic type of problem in which objects might have two different properties and the question was how many would have both properties. Scales marked zero to ten were used to set the numbers or proportions of objects with the two properties. This form of inference anticipated the numerically definite syllogism which Augustus De Morgan laid out in his book, Formal Logic, in 1847. == Construction == The device was a brass plate about four inches square which was mounted on a piece of mahogany which was three-quarters of an inch thick. There was an opening with a depression in the wood about one and a half inches square and half an inch deep. This opening was called the holon, meaning "whole", and represented the full set of objects under consideration. A slide of red translucent glass could be inserted from the right across the holon. A slide of gray wood could be slid under the red slide. When the device was used for the "Rule for the Logic of Certainty", the gray slider was inserted from the left. When it was used for the "Rule for the Logic of Probability", the gray slider was inserted from above. The red and the gray sliders represented the two affirmative propositions which were being combined. Stanhope called these ho and los. At least four of the devices with this square style were built. In 1879, Robert Harley wrote that he had one which he had been given by Stanhope's great-grandson, Arthur, who had kept one. The other two were owned by Henry Prevost Babbage – the son of Charles Babbage, who continued his work on the Analytical Engine. One of the devices was donated to the Science Museum, London by the last Earl in 1953. Other styles, such as circular models, were constructed, but these were less convenient.
MeituPic
Meitu Xiu Xiu ("Meitu") (Chinese: 美图秀秀) is an image editing software that is mostly used in Mainland China but is also popular in Hong Kong and Taiwan. It is only available on Google Play and App Store in certain countries. It provides tools for editing photos: filters, retouching, collage, scenes, frames, and photo decorations, as well as generative AI features such as text-to-images, AI removal and AI repainting etc. Meitu is one of the apps developed by Meitu, Inc.; it also produced BeautyCam, Wink and X-Design. == History == Meitu's PC version was created in 2008 by Wu Xinhong, the CEO of Meitu. In 2013, its mobile version became one of the first must-have mobile apps in China. Meitu, Inc. is a photo and video-centered app developer, which was founded in 2008 in Xiamen. Currently, the major revenue source of Meitu is premium subscription. Meitu, Inc. was initially funded by Cai Wensheng, a well-known angel investor. The company has an approximately 250 million monthly active users globally. == Function == === Edit === MeituPic provides a number of photo-editing tools. The major functions are auto enhance, edit, enhance, filters, frames, magic brush, mosaic, text, and blur. Auto enhance focuses on the nature of photos taken, while Edit includes functions of cropping, rotation, sharpening, and adjustment of ratio. For Enhance, users can apply slight adjustment on the photo by controlling the levels of brightness, contrast, colour temperature, saturation, highlight, shadow and smart light. Major types of filters are LOMO, beauty, style as well as art. Different frames can be chosen from poster, simple, and fantasy. Magic brush provides a great variety of brushes with different colours and patterns for users to decorate the photos. Mosaic brush enables users to cover certain parts of the photo. Texts can be added to the photo. Choices of different bubbles, font as well as style of words are available. Blurring effect is also available to make the photo less distinct and clear. === Beauty Retouch === There are seven major functions for retouching a photo: automatic retouch, smooth and whiten skin, remove blemish, make slimmer, remove dark circles and bags under the eyes, make taller, and enhance the eyes. Automatic retouch enhances portraits by lightening the skin tone, brightening the eyes, and simulating a face-lift by tapping on just one button. This helps to remove wrinkles and optimizes the skin tone. Acne, blemishes, and other skin imperfections can also be removed. The face-lift and weight-loss functions in the slimming option can be used to reshape the body. The option to make the subject taller can be used to change the perceived height of the subject and give the impression of slimmer, longer legs. The option to enhance the eyes can enlarge and brighten the eyes. === Collage === Collage has four types: template, freestyle, poster, PicStrip, which all maximize to insert nine photos. Template integrates photos in a vertical rectangle tightly. MeituPic has 15 frames or free download function for users. MeituPic also provides different templates according to number of photos inserted. Freestyle separates photos on a background freely. There are two parts of background: custom and more. For custom, users choose from album. For more, there are plain and picture with 18 choices. Poster makes a poster with photos. Users choose a poster among 8 choices or tap ‘more’ to download a new one. PicStrip combines photos vertically making an elongated file. Users choose a frame from 15 choices. Pinching thumb and forefinger together or apart zooms photos in/out. Putting two fingers and turning hand rotates photos. Pressing moves photos to ideal location. After designing, users tap ‘save/share’ on the upper right corner and the photo made is saved into album automatically. == Awards ==
Stable Diffusion
Stable Diffusion is a deep learning, text-to-image model released in 2022 based on diffusion techniques. The generative artificial intelligence technology is the premier product of Stability AI and is considered to be a part of the ongoing AI boom. It is primarily used to generate detailed images conditioned on text descriptions, though it can also be applied to other tasks such as inpainting, outpainting, and generating image-to-image translations guided by a text prompt. Its development involved researchers from the CompVis Group at LMU Munich and Runway with a computational donation from Stability and training data from non-profit organizations. Stable Diffusion is a latent diffusion model, a kind of deep generative artificial neural network. Its code and model weights have been released publicly, and an optimized version can run on most consumer hardware equipped with a modest GPU with as little as 2.4 GB VRAM. This marked a departure from previous proprietary text-to-image models such as DALL-E and Midjourney which were accessible only via cloud services. == Development == Stable Diffusion originated from a project called Latent Diffusion, developed in Germany by researchers at LMU Munich in Munich and Heidelberg University. Four of the original 5 authors (Robin Rombach, Andreas Blattmann, Patrick Esser and Dominik Lorenz) later joined Stability AI and released subsequent versions of Stable Diffusion. The technical license for the model was released by the CompVis group at LMU Munich. Development was led by Patrick Esser of Runway and Robin Rombach of CompVis, who were among the researchers who had earlier invented the latent diffusion model architecture used by Stable Diffusion. Stability AI also credited EleutherAI and LAION (a German nonprofit which assembled the dataset on which Stable Diffusion was trained) as supporters of the project. == Technology == === Architecture === Diffusion models, introduced in 2015, are trained with the objective of removing successive applications of Gaussian noise on training images, which can be thought of as a sequence of denoising autoencoders. The name diffusion is from the thermodynamic diffusion, since they were first developed with inspiration from thermodynamics. Models in Stable Diffusion series before SD 3 all used a variant of diffusion models, called latent diffusion model (LDM), developed in 2021 by the CompVis (Computer Vision & Learning) group at LMU Munich. Stable Diffusion consists of 3 parts: the variational autoencoder (VAE), U-Net, and an optional text encoder. The VAE encoder compresses the image from pixel space to a smaller dimensional latent space, capturing a more fundamental semantic meaning of the image. Gaussian noise is iteratively applied to the compressed latent representation during forward diffusion. The U-Net block, composed of a ResNet backbone, denoises the output from forward diffusion backwards to obtain a latent representation. Finally, the VAE decoder generates the final image by converting the representation back into pixel space. The denoising step can be flexibly conditioned on a string of text, an image, or another modality. The encoded conditioning data is exposed to denoising U-Nets via a cross-attention mechanism. For conditioning on text, the fixed, pretrained CLIP ViT-L/14 text encoder is used to transform text prompts to an embedding space. Researchers point to increased computational efficiency for training and generation as an advantage of LDMs. With 860 million parameters in the U-Net and 123 million in the text encoder, Stable Diffusion is considered relatively lightweight by 2022 standards, and unlike other diffusion models, it can run on consumer GPUs, and even CPU-only if using the OpenVINO version of Stable Diffusion. ==== SD XL ==== The XL version uses the same LDM architecture as previous versions, except larger: larger UNet backbone, larger cross-attention context, two text encoders instead of one, and trained on multiple aspect ratios (not just the square aspect ratio like previous versions). The SD XL Refiner, released at the same time, has the same architecture as SD XL, but it was trained for adding fine details to preexisting images via text-conditional img2img. ==== SD 3.0 ==== The 3.0 version completely changes the backbone. Not a UNet, but a Rectified Flow Transformer, which implements the rectified flow method with a Transformer. The Transformer architecture used for SD 3.0 has three "tracks", for original text encoding, transformed text encoding, and image encoding (in latent space). The transformed text encoding and image encoding are mixed during each transformer block. The architecture is named "multimodal diffusion transformer (MMDiT), where the "multimodal" means that it mixes text and image encodings inside its operations. This differs from previous versions of DiT, where the text encoding affects the image encoding, but not vice versa. === Training data === Stable Diffusion was trained on pairs of images and captions taken from LAION-5B, a publicly available dataset derived from Common Crawl data scraped from the web, where 5 billion image-text pairs were classified based on language and filtered into separate datasets by resolution, a predicted likelihood of containing a watermark, and predicted "aesthetic" score (e.g. subjective visual quality). The dataset was created by LAION, a German non-profit which receives funding from Stability AI. The Stable Diffusion model was trained on three subsets of LAION-5B: laion2B-en, laion-high-resolution, and laion-aesthetics v2 5+. A third-party analysis of the model's training data identified that out of a smaller subset of 12 million images taken from the original wider dataset used, approximately 47% of the sample size of images came from 100 different domains, with Pinterest taking up 8.5% of the subset, followed by websites such as WordPress, Blogspot, Flickr, DeviantArt and Wikimedia Commons. An investigation by Bayerischer Rundfunk showed that LAION's datasets, hosted on Hugging Face, contain large amounts of private and sensitive data. === Training procedures === The model was initially trained on the laion2B-en and laion-high-resolution subsets, with the last few rounds of training done on LAION-Aesthetics v2 5+, a subset of 600 million captioned images which the LAION-Aesthetics Predictor V2 predicted that humans would, on average, give a score of at least 5 out of 10 when asked to rate how much they liked them. The LAION-Aesthetics v2 5+ subset also excluded low-resolution images and images which LAION-5B-WatermarkDetection identified as carrying a watermark with greater than 80% probability. Final rounds of training additionally dropped 10% of text conditioning to improve Classifier-Free Diffusion Guidance. The model was trained using 256 Nvidia A100 GPUs on Amazon Web Services for a total of 150,000 GPU-hours, at a cost of $600,000. === Limitations === Stable Diffusion has issues with degradation and inaccuracies in certain scenarios. Initial releases of the model were trained on a dataset that consists of 512×512 resolution images, meaning that the quality of generated images noticeably degrades when user specifications deviate from its "expected" 512×512 resolution; the version 2.0 update of the Stable Diffusion model later introduced the ability to natively generate images at 768×768 resolution. Another challenge is in generating human limbs due to poor data quality of limbs in the LAION database. The model is insufficiently trained to replicate human limbs and faces due to the lack of representative features in the database, and prompting the model to generate images of such type can confound the model. In addition to human limbs, Stable Diffusion is unable to generate legible ambigrams and some other forms of text and typography. Stable Diffusion XL (SDXL) version 1.0, released in July 2023, introduced native 1024x1024 resolution and improved generation for limbs and text. Accessibility for individual developers can also be a problem. In order to customize the model for new use cases that are not included in the dataset, such as generating anime characters ("waifu diffusion"), new data and further training are required. Fine-tuned adaptations of Stable Diffusion created through additional retraining have been used for a variety of different use-cases, from medical imaging to algorithmically generated music. However, this fine-tuning process is sensitive to the quality of new data; low resolution images or different resolutions from the original data can not only fail to learn the new task but degrade the overall performance of the model. Even when the model is additionally trained on high quality images, it is difficult for individuals to run models in consumer electronics. For example, the training process for waifu-diffusion requires a minimum 30 GB of VRAM, which exceeds the usual resource provided in such consumer GPUs as Nvidia's GeForce 30 series, w