The Wasserstein Generative Adversarial Network (WGAN) is a variant of generative adversarial network (GAN) proposed in 2017 that aims to "improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches". Compared with the original GAN discriminator, the Wasserstein GAN discriminator provides a better learning signal to the generator. This allows the training to be more stable when generator is learning distributions in very high dimensional spaces. == Motivation == === The GAN game === The original GAN method is based on the GAN game, a zero-sum game with 2 players: generator and discriminator. The game is defined over a probability space ( Ω , B , μ r e f ) {\displaystyle (\Omega ,{\mathcal {B}},\mu _{ref})} , The generator's strategy set is the set of all probability measures μ G {\displaystyle \mu _{G}} on ( Ω , B ) {\displaystyle (\Omega ,{\mathcal {B}})} , and the discriminator's strategy set is the set of measurable functions D : Ω → [ 0 , 1 ] {\displaystyle D:\Omega \to [0,1]} . The objective of the game is L ( μ G , D ) := E x ∼ μ r e f [ ln D ( x ) ] + E x ∼ μ G [ ln ( 1 − D ( x ) ) ] . {\displaystyle L(\mu _{G},D):=\mathbb {E} _{x\sim \mu _{ref}}[\ln D(x)]+\mathbb {E} _{x\sim \mu _{G}}[\ln(1-D(x))].} The generator aims to minimize it, and the discriminator aims to maximize it. A basic theorem of the GAN game states that Repeat the GAN game many times, each time with the generator moving first, and the discriminator moving second. Each time the generator μ G {\displaystyle \mu _{G}} changes, the discriminator must adapt by approaching the ideal D ∗ ( x ) = d μ r e f d ( μ r e f + μ G ) . {\displaystyle D^{}(x)={\frac {d\mu _{ref}}{d(\mu _{ref}+\mu _{G})}}.} Since we are really interested in μ r e f {\displaystyle \mu _{ref}} , the discriminator function D {\displaystyle D} is by itself rather uninteresting. It merely keeps track of the likelihood ratio between the generator distribution and the reference distribution. At equilibrium, the discriminator is just outputting 1 2 {\displaystyle {\frac {1}{2}}} constantly, having given up trying to perceive any difference. Concretely, in the GAN game, let us fix a generator μ G {\displaystyle \mu _{G}} , and improve the discriminator step-by-step, with μ D , t {\displaystyle \mu _{D,t}} being the discriminator at step t {\displaystyle t} . Then we (ideally) have L ( μ G , μ D , 1 ) ≤ L ( μ G , μ D , 2 ) ≤ ⋯ ≤ max μ D L ( μ G , μ D ) = 2 D J S ( μ r e f ‖ μ G ) − 2 ln 2 , {\displaystyle L(\mu _{G},\mu _{D,1})\leq L(\mu _{G},\mu _{D,2})\leq \cdots \leq \max _{\mu _{D}}L(\mu _{G},\mu _{D})=2D_{JS}(\mu _{ref}\|\mu _{G})-2\ln 2,} so we see that the discriminator is actually lower-bounding D J S ( μ r e f ‖ μ G ) {\displaystyle D_{JS}(\mu _{ref}\|\mu _{G})} . === Wasserstein distance === Thus, we see that the point of the discriminator is mainly as a critic to provide feedback for the generator, about "how far it is from perfection", where "far" is defined as Jensen–Shannon divergence. Naturally, this brings the possibility of using a different criteria of farness. There are many possible divergences to choose from, such as the f-divergence family, which would give the f-GAN. The Wasserstein GAN is obtained by using the Wasserstein metric, which satisfies a "dual representation theorem" that renders it highly efficient to compute: A proof can be found in the main page on Wasserstein metric. == Definition == By the Kantorovich-Rubenstein duality, the definition of Wasserstein GAN is clear:A Wasserstein GAN game is defined by a probability space ( Ω , B , μ r e f ) {\displaystyle (\Omega ,{\mathcal {B}},\mu _{ref})} , where Ω {\displaystyle \Omega } is a metric space, and a constant K > 0 {\displaystyle K>0} . There are 2 players: generator and discriminator (also called "critic"). The generator's strategy set is the set of all probability measures μ G {\displaystyle \mu _{G}} on ( Ω , B ) {\displaystyle (\Omega ,{\mathcal {B}})} . The discriminator's strategy set is the set of measurable functions of type D : Ω → R {\displaystyle D:\Omega \to \mathbb {R} } with bounded Lipschitz-norm: ‖ D ‖ L ≤ K {\displaystyle \|D\|_{L}\leq K} . The Wasserstein GAN game is a zero-sum game, with objective function L W G A N ( μ G , D ) := E x ∼ μ G [ D ( x ) ] − E x ∼ μ r e f [ D ( x ) ] . {\displaystyle L_{WGAN}(\mu _{G},D):=\mathbb {E} _{x\sim \mu _{G}}[D(x)]-\mathbb {E} _{x\sim \mu _{ref}}[D(x)].} The generator goes first, and the discriminator goes second. The generator aims to minimize the objective, and the discriminator aims to maximize the objective: min μ G max D L W G A N ( μ G , D ) . {\displaystyle \min _{\mu _{G}}\max _{D}L_{WGAN}(\mu _{G},D).} By the Kantorovich-Rubenstein duality, for any generator strategy μ G {\displaystyle \mu _{G}} , the optimal reply by the discriminator is D ∗ {\displaystyle D^{}} , such that L W G A N ( μ G , D ∗ ) = K ⋅ W 1 ( μ G , μ r e f ) . {\displaystyle L_{WGAN}(\mu _{G},D^{})=K\cdot W_{1}(\mu _{G},\mu _{ref}).} Consequently, if the discriminator is good, the generator would be constantly pushed to minimize W 1 ( μ G , μ r e f ) {\displaystyle W_{1}(\mu _{G},\mu _{ref})} , and the optimal strategy for the generator is just μ G = μ r e f {\displaystyle \mu _{G}=\mu _{ref}} , as it should. == Comparison with GAN == In the Wasserstein GAN game, the discriminator provides a better gradient than in the GAN game. Consider for example a game on the real line where both μ G {\displaystyle \mu _{G}} and μ r e f {\displaystyle \mu _{ref}} are Gaussian. Then the optimal Wasserstein critic D W G A N {\displaystyle D_{WGAN}} and the optimal GAN discriminator D {\displaystyle D} are plotted as below: For fixed discriminator, the generator needs to minimize the following objectives: For GAN, E x ∼ μ G [ ln ( 1 − D ( x ) ) ] {\displaystyle \mathbb {E} _{x\sim \mu _{G}}[\ln(1-D(x))]} . For Wasserstein GAN, E x ∼ μ G [ D W G A N ( x ) ] {\displaystyle \mathbb {E} _{x\sim \mu _{G}}[D_{WGAN}(x)]} . Let μ G {\displaystyle \mu _{G}} be parametrized by θ {\displaystyle \theta } , then we can perform stochastic gradient descent by using two unbiased estimators of the gradient: ∇ θ E x ∼ μ G [ ln ( 1 − D ( x ) ) ] = E x ∼ μ G [ ln ( 1 − D ( x ) ) ⋅ ∇ θ ln ρ μ G ( x ) ] {\displaystyle \nabla _{\theta }\mathbb {E} _{x\sim \mu _{G}}[\ln(1-D(x))]=\mathbb {E} _{x\sim \mu _{G}}[\ln(1-D(x))\cdot \nabla _{\theta }\ln \rho _{\mu _{G}}(x)]} ∇ θ E x ∼ μ G [ D W G A N ( x ) ] = E x ∼ μ G [ D W G A N ( x ) ⋅ ∇ θ ln ρ μ G ( x ) ] {\displaystyle \nabla _{\theta }\mathbb {E} _{x\sim \mu _{G}}[D_{WGAN}(x)]=\mathbb {E} _{x\sim \mu _{G}}[D_{WGAN}(x)\cdot \nabla _{\theta }\ln \rho _{\mu _{G}}(x)]} where we used the reparameterization trick. As shown, the generator in GAN is motivated to let its μ G {\displaystyle \mu _{G}} "slide down the peak" of ln ( 1 − D ( x ) ) {\displaystyle \ln(1-D(x))} . Similarly for the generator in Wasserstein GAN. For Wasserstein GAN, D W G A N {\displaystyle D_{WGAN}} has gradient 1 almost everywhere, while for GAN, ln ( 1 − D ) {\displaystyle \ln(1-D)} has flat gradient in the middle, and steep gradient elsewhere. As a result, the variance for the estimator in GAN is usually much larger than that in Wasserstein GAN. See also Figure 3 of. The problem with D J S {\displaystyle D_{JS}} is much more severe in actual machine learning situations. Consider training a GAN to generate ImageNet, a collection of photos of size 256-by-256. The space of all such photos is R 256 2 {\displaystyle \mathbb {R} ^{256^{2}}} , and the distribution of ImageNet pictures, μ r e f {\displaystyle \mu _{ref}} , concentrates on a manifold of much lower dimension in it. Consequently, any generator strategy μ G {\displaystyle \mu _{G}} would almost surely be entirely disjoint from μ r e f {\displaystyle \mu _{ref}} , making D J S ( μ G ‖ μ r e f ) = + ∞ {\displaystyle D_{JS}(\mu _{G}\|\mu _{ref})=+\infty } . Thus, a good discriminator can almost perfectly distinguish μ r e f {\displaystyle \mu _{ref}} from μ G {\displaystyle \mu _{G}} , as well as any μ G ′ {\displaystyle \mu _{G}'} close to μ G {\displaystyle \mu _{G}} . Thus, the gradient ∇ μ G L ( μ G , D ) ≈ 0 {\displaystyle \nabla _{\mu _{G}}L(\mu _{G},D)\approx 0} , creating no learning signal for the generator. Detailed theorems can be found in. == Training Wasserstein GANs == Training the generator in Wasserstein GAN is just gradient descent, the same as in GAN (or most deep learning methods), but training the discriminator is different, as the discriminator is now restricted to have bounded Lipschitz norm. There are several methods for this. === Upper-bounding the Lipschitz norm === Let the discriminator function D {\displaystyle D} to be implemented by a multilayer perceptron: D = D n ∘ D n − 1 ∘ ⋯ ∘ D 1 {\displaystyle D=D_{n}\circ D_{n-1}\circ \cdots \circ D_{1}} where D i ( x ) = h ( W i x ) {\displaystyle D_{i}(x)=h(W_
Dailyhunt
Dailyhunt (formerly Newshunt) is an Indian content and news aggregator application based in Bangalore, India that provides local language content in 14 Indian languages from multiple content providers. Viru serves as Founder of Dailyhunt with Co-founder Umang Bedi. == History == Dailyhunt, earlier called Newshunt, was created as a Symbian app in 2009 by two ex-Nokia employees Umesh Kulkarni and Chandrashekhar Sohoni. Later in 2011, Newshunt became available on the Android platform. It was by that time that Virendra Gupta, founder of Verse acquired the application. Virendra Gupta, better known as Viru, had started Verse in 2007 as a value-added service (VAS) company. In 2011, he acquired Newshunt from its owners Umesh and Chandrashekhar. Umesh became the CTO and stayed on to oversee its transition towards the smartphone era. In 2015, Viru renamed Newshunt as Dailyhunt. In early 2018, Viru roped in Umang Bedi, to be the President of Dailyhunt and lead the business with him while focusing on making the benefits of the platform available to a larger audience. Umang was elevated to co-founder in 2020. == Funding == In September 2014, Dailyhunt (then known as Newshunt) closed its Series B funding of INR 1 billion ( or approx $12 million in 2014) from Sequoia Capital India. The Series C funding round was led by Falcon Capital and was closed with $40 million in February 2015. In October 2016, the company received its Series D funding of $25 million from ByteDance and a Series E funding of $6.39 million from Falcon Edge Capital in September 2018. Additionally, Dailyhunt raised $3 Mn (INR 21.75 Cr) in a Series F funding round from Stonebridge Capital in August 2019. Other investors of Dailyhunt include Matrix Partners India, Omidyar Network, Goldman Sachs and Sofina. == Tie-ups and partnerships == In January 2021, Dailyhunt partnered with Twitter to bring ‘Twitter Moments’ to the Indian social app. Dailyhunt app now has a dedicated tab called “Twitter Moments India” to showcase curated tweets pertaining to news and other events. In January 2021, Dailyhunt announced the premiere of Season 2 of the popular show QuoteUnquote with KK (Kapil Khandelwal) on the app. It was the first podcast to have been launched on the Dailyhunt app. In September 2020, Dailyhunt signed up as an Associate Sponsor with Star Sports for Dream 11 IPL 2020. In May 2020, Snapdeal partnered with Dailyhunt to add new content on marketplace. In March 2019, Discovery Communications India, the factual entertainment network, entered into a multi-year partnership with Dailyhunt to showcase short-form content.
Online analytical processing
In computing, online analytical processing (OLAP) (), is an approach to quickly answer multi-dimensional analytical (MDA) queries. The term OLAP was created as a slight modification of the traditional database term online transaction processing (OLTP). OLAP is part of the broader category of business intelligence, which also encompasses relational databases, report writing and data mining. Typical applications of OLAP include business reporting for sales, marketing, management reporting, business process management (BPM), budgeting and forecasting, financial reporting and similar areas, with new applications emerging, such as agriculture. OLAP tools enable users to analyse multidimensional data interactively from multiple perspectives. OLAP consists of three basic analytical operations: consolidation (roll-up), drill-down, and slicing and dicing. Consolidation involves the aggregation of data that can be accumulated and computed in one or more dimensions. For example, all sales offices are rolled up to the sales department or sales division to anticipate sales trends. By contrast, the drill-down is a technique that allows users to navigate through the details. For instance, users can view the sales by individual products that make up a region's sales. Slicing and dicing is a feature whereby users can take out (slicing) a specific set of data of the OLAP cube and view (dicing) the slices from different viewpoints. These viewpoints are sometimes called dimensions (such as looking at the same sales by salesperson, or by date, or by customer, or by product, or by region, etc.). Databases configured for OLAP use a multidimensional data model, allowing for complex analytical and ad hoc queries with a rapid execution time. They borrow aspects of navigational databases, hierarchical databases and relational databases. OLAP is typically contrasted to OLTP (online transaction processing), which is generally characterized by much less complex queries, in a larger volume, to process transactions rather than for the purpose of business intelligence or reporting. Whereas OLAP systems are mostly optimized for read, OLTP has to process all kinds of queries (read, insert, update and delete). == Overview of OLAP systems == At the core of any OLAP system is an OLAP cube (also called a 'multidimensional cube' or a hypercube). It consists of numeric facts called measures that are categorized by dimensions. The measures are placed at the intersections of the hypercube, which is spanned by the dimensions as a vector space. The usual interface to manipulate an OLAP cube is a matrix interface, like Pivot tables in a spreadsheet program, which performs projection operations along the dimensions, such as aggregation or averaging. The cube metadata is typically created from a star schema or snowflake schema or fact constellation of tables in a relational database. Measures are derived from the records in the fact table and dimensions are derived from the dimension tables. Each measure can be thought of as having a set of labels, or meta-data associated with it. A dimension is what describes these labels; it provides information about the measure. A simple example would be a cube that contains a store's sales as a measure, and Date/Time as a dimension. Each Sale has a Date/Time label that describes more about that sale. For example: Sales Fact Table +-------------+----------+ | sale_amount | time_id | +-------------+----------+ Time Dimension | 930.10| 1234 |----+ +---------+-------------------+ +-------------+----------+ | | time_id | timestamp | | +---------+-------------------+ +---->| 1234 | 20080902 12:35:43 | +---------+-------------------+ === Multidimensional databases === Multidimensional structure is defined as "a variation of the relational model that uses multidimensional structures to organize data and express the relationships between data". The structure is broken into cubes and the cubes are able to store and access data within the confines of each cube. "Each cell within a multidimensional structure contains aggregated data related to elements along each of its dimensions". Even when data is manipulated it remains easy to access and continues to constitute a compact database format. The data still remains interrelated. Multidimensional structure is quite popular for analytical databases that use online analytical processing (OLAP) applications. Analytical databases use these databases because of their ability to deliver answers to complex business queries swiftly. Data can be viewed from different angles, which gives a broader perspective of a problem unlike other models. === Aggregations === It has been claimed that for complex queries OLAP cubes can produce an answer in around 0.1% of the time required for the same query on OLTP relational data. The most important mechanism in OLAP which allows it to achieve such performance is the use of aggregations. Aggregations are built from the fact table by changing the granularity on specific dimensions and aggregating up data along these dimensions, using an aggregate function (or aggregation function). The number of possible aggregations is determined by every possible combination of dimension granularities. The combination of all possible aggregations and the base data contains the answers to every query which can be answered from the data. Because usually there are many aggregations that can be calculated, often only a predetermined number are fully calculated; the remainder are solved on demand. The problem of deciding which aggregations (views) to calculate is known as the view selection problem. View selection can be constrained by the total size of the selected set of aggregations, the time to update them from changes in the base data, or both. The objective of view selection is typically to minimize the average time to answer OLAP queries, although some studies also minimize the update time. View selection is NP-complete. Many approaches to the problem have been explored, including greedy algorithms, randomized search, genetic algorithms and A search algorithm. Some aggregation functions can be computed for the entire OLAP cube by precomputing values for each cell, and then computing the aggregation for a roll-up of cells by aggregating these aggregates, applying a divide and conquer algorithm to the multidimensional problem to compute them efficiently. For example, the overall sum of a roll-up is just the sum of the sub-sums in each cell. Functions that can be decomposed in this way are called decomposable aggregation functions, and include COUNT, MAX, MIN, and SUM, which can be computed for each cell and then directly aggregated; these are known as self-decomposable aggregation functions. In other cases, the aggregate function can be computed by computing auxiliary numbers for cells, aggregating these auxiliary numbers, and finally computing the overall number at the end; examples include AVERAGE (tracking sum and count, dividing at the end) and RANGE (tracking max and min, subtracting at the end). In other cases, the aggregate function cannot be computed without analyzing the entire set at once, though in some cases approximations can be computed; examples include DISTINCT COUNT, MEDIAN, and MODE; for example, the median of a set is not the median of medians of subsets. These latter are difficult to implement efficiently in OLAP, as they require computing the aggregate function on the base data, either computing them online (slow) or precomputing them for possible rollouts (large space). == Types == OLAP systems have been traditionally categorized using the following taxonomy. === Multidimensional OLAP (MOLAP) === MOLAP (multi-dimensional online analytical processing) is the classic form of OLAP and is sometimes referred to as just OLAP. MOLAP stores this data in an optimized multi-dimensional array storage, rather than in a relational database. Some MOLAP tools require the pre-computation and storage of derived data, such as consolidations – the operation known as processing. Such MOLAP tools generally utilize a pre-calculated data set referred to as a data cube. The data cube contains all the possible answers to a given range of questions. As a result, they have a very fast response to queries. On the other hand, updating can take a long time depending on the degree of pre-computation. Pre-computation can also lead to what is known as data explosion. Other MOLAP tools, particularly those that implement the functional database model do not pre-compute derived data but make all calculations on demand other than those that were previously requested and stored in a cache. Advantages of MOLAP Fast query performance due to optimized storage, multidimensional indexing and caching. Smaller on-disk size of data compared to data stored in relational database due to compression techniques. Automated computation of higher-level aggregates of the data. It is very compact for low dimension data se
AVT Statistical filtering algorithm
AVT Statistical filtering algorithm is an approach to improving quality of raw data collected from various sources. It is most effective in cases when there is inband noise present. In those cases AVT is better at filtering data then, band-pass filter or any digital filtering based on variation of. Conventional filtering is useful when signal/data has different frequency than noise and signal/data is separated/filtered by frequency discrimination of noise. Frequency discrimination filtering is done using Low Pass, High Pass and Band Pass filtering which refers to relative frequency filtering criteria target for such configuration. Those filters are created using passive and active components and sometimes are implemented using software algorithms based on Fast Fourier transform (FFT). AVT filtering is implemented in software and its inner working is based on statistical analysis of raw data. When signal frequency/(useful data distribution frequency) coincides with noise frequency/(noisy data distribution frequency) we have inband noise. In this situations frequency discrimination filtering does not work since the noise and useful signal are indistinguishable and where AVT excels. To achieve filtering in such conditions there are several methods/algorithms available which are briefly described below. == Averaging algorithm == Collect n samples of data Calculate average value of collected data Present/record result as actual data == Median algorithm == Collect n samples of data Sort the data in ascending or descending order. Note that order does not matter Select the data that happen to be in n/2 position and present/record it as final result representing data sample == AVT algorithm == AVT algorithm stands for Antonyan Vardan Transform and its implementation explained below. Collect n samples of data Calculate the standard deviation and average value Drop any data that is greater or less than average ± one standard deviation Calculate average value of remaining data Present/record result as actual value representing data sample This algorithm is based on amplitude discrimination and can easily reject any noise that is not like actual signal, otherwise statistically different than 1 standard deviation of the signal. Note that this type of filtering can be used in situations where the actual environmental noise is not known in advance. Notice that it is preferable to use the median in above steps than average. Originally the AVT algorithm used average value to compare it with results of median on the data window. == Filtering algorithms comparison == Using a system that has signal value of 1 and has noise added at 0.1% and 1% levels will simplify quantification of algorithm performance. The R script is used to create pseudo random noise added to signal and analyze the results of filtering using several algorithms. Please refer to "Reduce Inband Noise with the AVT Algorithm" article for details. This graphs show that AVT algorithm provides best results compared with Median and Averaging algorithms while using data sample size of 32, 64 and 128 values. Note that this graph was created by analyzing random data array of 10000 values. Sample of this data is graphically represented below. From this graph it is apparent that AVT outperforms other filtering algorithms by providing 5% to 10% more accurate data when analyzing same datasets. Considering random nature of noise used in this numerical experiment that borderlines worst case situation where actual signal level is below ambient noise the precision improvements of processing data with AVT algorithm are significant. == AVT algorithm variations == === Cascaded AVT === In some situations better results can be obtained by cascading several stages of AVT filtering. This will produce singular constant value which can be used for equipment that has known stable characteristics like thermometers, thermistors and other slow acting sensors. === Reverse AVT === Collect n samples of data Calculate the standard deviation and average value Drop any data that is within one standard deviation ± average band Calculate average value of remaining data Present/record result as actual data This is useful for detecting minute signals that are close to background noise level. == Possible applications and uses == Use to filter data that is near or below noise level Used in planet detection to filter out raw data from the Kepler space telescope Filter out noise from sound sources where all other filtering methods (Low-pass filter, High-pass filter, Band-pass filter, Digital filter) fail. Pre-process scientific data for data analysis (Smoothness) before plotting see (Plot (graphics)) Used in SETI (Search for extraterrestrial intelligence) for detecting/distinguishing extraterrestrial signals from cosmic background Use AVT as image filtering algorithm to detect altered images. This image of Jupiter generated from this program, detecting alterations in original picture that was modified to be visually appealing by applying filters. Another version of this comparison is the Reverse AVT filter applied to the same original Jupiter Image, where we only see that altered portion as Noise that was eliminated by AVT algorithm. Use AVT as image filtering algorithm to estimate data density from images. Picture of Pillars of Creation Nebula shows data density in filtered images from Hubble and Webb. Note that image on the left has big patches of missing data marked with simpler color patterns.
Operational historian
In manufacturing, an operational historian is a time-series database application that is developed for operational process data. Historian software is often embedded or used in conjunction with standard DCS and PLC control systems to provide enhanced data capture, validation, compression, and aggregation capabilities. Historians have been deployed in almost every industry and contribute to functions such as supervisory control, performance monitoring, quality assurance, and, more recently, machine learning applications which can learn from vast quantities of historical data. These systems were originally developed to capture instrumentation and control data, which led many to use the term "tag" for a stream of process data, referring to the physical "tags" which had been placed on instrumentation for manually capturing data. Raw data may be accessed via OPC HDA, SQL, or REST API interfaces. == Operational Support == Operational historians are typically used within the manufacturing facility by engineers and operators for supervisory functions and analysis. An operational historian will typically capture all instrumentation and control data, whereas an enterprise historian that is deployed to support business functions will capture only a subset of the plant data. Typically, these applications offer data access through dedicated APIs (Application Programming Interfaces) and SDKs (Software Development Kits) which offer high-performance read and write operations. These operate through vendor-specific or custom applications. Front-end tools for trending process data over time are the most common interfaces to these databases. Because these applications are typically deployed next to or near the source of their process data, they are often marketed and sold as 'real-time database systems.' This distinction varies among vendors, who often have to make tradeoffs in performance between data capture and presentation, and application and analysis functionality. The following is a list of typical challenges for operational historians: data collection from instrumentation and controls storage and archiving of very large volumes of data organization of data in the form of "tags" or "points" limiting of monitoring (alarms) and validation aggregation and interpolation manual data entry (MDE) == Data access == As opposed to enterprise historians, the data access layer in the operational historian is designed to offer sophisticated data fetching modes without complex information analysis facilities. The following settings are typically available for data access operations: Data scope (single point or tag, history based on time range, history based on sample count) Request modes (raw data, last-known value, aggregation, interpolation) Sampling (single point, all points without sampling, all points with interval sampling) Data omission (based on the sample quality, based on the sample value, based on the count) Even though the operational historians are rarely relational database management systems, they often offer SQL-based interfaces to query the database. In most of such implementations, the dialect does not follow the SQL standard in order to provide syntax for specifying data access operations parameters.
Microsoft Whiteboard
Microsoft Whiteboard is a free multi-platform application, as well as an online service and a feature in Microsoft Teams, which simulates a virtual whiteboard and enables real-time collaboration between users. == Overview and features == Microsoft Whiteboard allows users to draw on a virtual whiteboard using input methods such as a stylus pen or a mouse and keyboard, and write down notes, draw connections between shareable ideas, and interact in real time. Microsoft Whiteboard is available to download on the following platforms and devices: Microsoft Windows (on Windows 10 or above) Android Apple iOS Surface Hub devices It is also available on the web and as a feature in Microsoft Teams. Microsoft Whiteboard allows users with Microsoft accounts to view, edit, and share whiteboards using the provided tools and options. The feature set includes tools for drawing, shapes, and media. Drawing in Microsoft Whiteboard is called inking. It works both on mobile devices and computers. The inking toolbar has customizable pencils, a ruler, a highlighter, an eraser, and an object selector. Whiteboard can recognize shapes drawn by hand and straighten them. Holding the Shift key on a computer while inking draws straight lines. Microsoft Whiteboard has keyboard shortcuts for some functions. Additional features include inserting sticky notes, text boxes, stickers, as well as images. Grid lines and colors are adjustable. Different templates can be inserted into the whiteboard. Users can also share their reactions. A feature limited to boards created in Microsoft Teams, is the ability to make them read-only; other participants from the meeting cannot edit them. == Reviews == PC Magazine gave Microsoft Whiteboard a score of 3.5 out of 5, praising the app's free availability and plentiful templates. It compared it to other, paid whiteboarding solutions, and concluded that Microsoft offers the best free one. Some of the cons, described by PCMag, include the inability to view boards without a Microsoft account and the inability to create custom templates.
Information
Information is an abstract concept that refers to something which has the power to inform. At the most fundamental level, it pertains to the interpretation (perhaps formally) of that which may be sensed, or their abstractions. Any natural process that is not completely random and any observable pattern in any medium can be said to convey some amount of information. Whereas digital signals and other data use discrete signs to convey information, other phenomena and artifacts such as analogue signals, poems, pictures, music or other sounds, and currents convey information in a more continuous form. Information is not knowledge itself, but the meaning that may be derived from a representation through interpretation. The concept of information is relevant to and connected with various concepts, including constraint, communication, control, data, form, education, knowledge, meaning, understanding, mental stimuli, pattern, perception, proposition, representation, and entropy. Information is often processed iteratively: Data available at one step are processed into information to be interpreted and processed at the next step. For example, in written text each symbol or letter conveys information relevant to the word it is part of, each word conveys information relevant to the phrase it is part of, each phrase conveys information relevant to the sentence it is part of, and so on until at the final step information is interpreted and becomes knowledge in a given domain. In a digital signal, bits may be interpreted into the symbols, letters, numbers, or structures that convey the information available at the next level up. The key characteristic of information is that it is subject to interpretation and processing. The derivation of information from a signal or message may be thought of as the resolution of ambiguity or uncertainty that arises during the interpretation of patterns within the signal or message. Information may be structured as data. Redundant data can be compressed up to an optimal size, which is the theoretical limit of compression. The information available through a collection of data may be derived by analysis. For example, a restaurant collects data from every customer order. That information may be analyzed to produce knowledge that is put to use when the business subsequently wants to identify the most popular or least popular dish. Information can be transmitted in time, via data storage, and space, via communication and telecommunication. Information is expressed either as the content of a message or through direct or indirect observation. That which is perceived can be construed as a message in its own right, and in that sense, all information is always conveyed as the content of a message. Information can be encoded into various forms for transmission and interpretation (for example, information may be encoded into a sequence of signs, or transmitted via a signal). It can also be encrypted for safe storage and communication. The uncertainty of an event is measured by its probability of occurrence. Uncertainty is proportional to the negative logarithm of the probability of occurrence. Information theory takes advantage of this by concluding that more uncertain events require more information to resolve their uncertainty. The bit is the standard unit of information. It is 'that which reduces uncertainty by half'. Other units such as the nat may be used. For example, the information encoded in one "fair" coin flip is log2(2/1) = 1 bit, and in two fair coin flips is log2(4/1) = 2 bits. A 2011 Science article estimates that 97% of technologically stored information was already in digital bits in 2007 and that the year 2002 was the beginning of the digital age for information storage (with digital storage capacity bypassing analogue for the first time). == Etymology and history of the concept == The English word "information" comes from Middle French enformacion/informacion/information 'a criminal investigation' and its etymon, Latin informatiō(n) 'conception, teaching, creation'. In English, "information" is an uncountable mass noun. References on "formation or molding of the mind or character, training, instruction, teaching" date from the 14th century in both English (according to Oxford English Dictionary) and other European languages. In the transition from Middle Ages to Modernity the use of the concept of information reflected a fundamental turn in epistemological basis – from "giving a (substantial) form to matter" to "communicating something to someone". Peters (1988, pp. 12–13) concludes: Information was readily deployed in empiricist psychology (though it played a less important role than other words such as impression or idea) because it seemed to describe the mechanics of sensation: objects in the world inform the senses. But sensation is entirely different from "form" – the one is sensual, the other intellectual; the one is subjective, the other objective. My sensation of things is fleeting, elusive, and idiosyncratic. For Hume, especially, sensory experience is a swirl of impressions cut off from any sure link to the real world... In any case, the empiricist problematic was how the mind is informed by sensations of the world. At first informed meant shaped by; later it came to mean received reports from. As its site of action drifted from cosmos to consciousness, the term's sense shifted from unities (Aristotle's forms) to units (of sensation). Information came less and less to refer to internal ordering or formation, since empiricism allowed for no preexisting intellectual forms outside of sensation itself. Instead, information came to refer to the fragmentary, fluctuating, haphazard stuff of sense. Information, like the early modern worldview in general, shifted from a divinely ordered cosmos to a system governed by the motion of corpuscles. Under the tutelage of empiricism, information gradually moved from structure to stuff, from form to substance, from intellectual order to sensory impulses. In the modern era, the most important influence on the concept of information is derived from the Information theory developed by Claude Shannon and others. This theory, however, reflects a fundamental contradiction. Northrup (1993) wrote: Thus, actually two conflicting metaphors are being used: The well-known metaphor of information as a quantity, like water in the water-pipe, is at work, but so is a second metaphor, that of information as a choice, a choice made by :an information provider, and a forced choice made by an :information receiver. Actually, the second metaphor implies that the information sent isn't necessarily equal to the information received, because any choice implies a comparison with a list of possibilities, i.e., a list of possible meanings. Here, meaning is involved, thus spoiling the idea of information as a pure "Ding an sich." Thus, much of the confusion regarding the concept of information seems to be related to the basic confusion of metaphors in Shannon's theory: is information an autonomous quantity, or is information always per SE information to an observer? Actually, I don't think that Shannon himself chose one of the two definitions. Logically speaking, his theory implied information as a subjective phenomenon. But this had so wide-ranging epistemological impacts that Shannon didn't seem to fully realize this logical fact. Consequently, he continued to use metaphors about information as if it were an objective substance. This is the basic, inherent contradiction in Shannon's information theory." (Northrup, 1993, p. 5). In their seminal book The Study of Information: Interdisciplinary Messages, Almach and Mansfield (1983) collected key views on the interdisciplinary controversy in computer science, artificial intelligence, library and information science, linguistics, psychology, and physics, as well as in the social sciences. Almach (1983, p. 660) himself disagrees with the use of the concept of information in the context of signal transmission, the basic senses of information in his view all referring "to telling something or to the something that is being told. Information is addressed to human minds and is received by human minds." All other senses, including its use with regard to nonhuman organisms as well to society as a whole, are, according to Machlup, metaphoric and, as in the case of cybernetics, anthropomorphic. Hjørland (2007) describes the fundamental difference between objective and subjective views of information and argues that the subjective view has been supported by, among others, Bateson, Yovits, Span-Hansen, Brier, Buckland, Goguen, and Hjørland. Hjørland provided the following example: A stone on a field could contain different information for different people (or from one situation to another). It is not possible for information systems to map all the stone's possible information for every individual. Nor is any one mapping the one "true" mapping. But peop