Data Transformation Services (DTS) is a Microsoft database tool with a set of objects and utilities to allow the automation of extract, transform and load operations to or from a database. The objects are DTS packages and their components, and the utilities are called DTS tools. DTS was included with earlier versions of Microsoft SQL Server, and was almost always used with SQL Server databases, although it could be used independently with other databases. DTS allows data to be transformed and loaded from heterogeneous sources using OLE DB, ODBC, or text-only files, into any supported database. DTS can also allow automation of data import or transformation on a scheduled basis, and can perform additional functions such as FTPing files and executing external programs. In addition, DTS provides an alternative method of version control and backup for packages when used in conjunction with a version control system, such as Microsoft Visual SourceSafe. DTS has been superseded by SQL Server Integration Services in later releases of Microsoft SQL Server though there was some backwards compatibility and ability to run DTS packages in the new SSIS for a time. == History == In SQL Server versions 6.5 and earlier, database administrators (DBAs) used SQL Server Transfer Manager and Bulk Copy Program, included with SQL Server, to transfer data. These tools had significant shortcomings, and many DBAs used third-party tools such as Pervasive Data Integrator to transfer data more flexibly and easily. With the release of SQL Server 7 in 1998, "Data Transformation Services" was packaged with it to replace all these tools. The concept, design, and implementation of the Data Transformation Services was led by Stewart P. MacLeod (SQL Server Development Group Program Manager), Vij Rajarajan (SQL Server Lead Developer), and Ted Hart (SQL Server Lead Developer). The goal was to make it easier to import, export, and transform heterogeneous data and simplify the creation of data warehouses from operational data sources. SQL Server 2000 expanded DTS functionality in several ways. It introduced new types of tasks, including the ability to FTP files, move databases or database components, and add messages into Microsoft Message Queue. DTS packages can be saved as a Visual Basic file in SQL Server 2000, and this can be expanded to save into any COM-compliant language. Microsoft also integrated packages into Windows 2000 security and made DTS tools more user-friendly; tasks can accept input and output parameters. DTS comes with all editions of SQL Server 7 and 2000, but was superseded by SQL Server Integration Services in the Microsoft SQL Server 2005 release in 2005. == DTS packages == The DTS package is the fundamental logical component of DTS; every DTS object is a child component of the package. Packages are used whenever one modifies data using DTS. All the metadata about the data transformation is contained within the package. Packages can be saved directly in a SQL Server, or can be saved in the Microsoft Repository or in COM files. SQL Server 2000 also allows a programmer to save packages in a Visual Basic or other language file (when stored to a VB file, the package is actually scripted—that is, a VB script is executed to dynamically create the package objects and its component objects). A package can contain any number of connection objects, but does not have to contain any. These allow the package to read data from any OLE DB-compliant data source, and can be expanded to handle other sorts of data. The functionality of a package is organized into tasks and steps. A DTS Task is a discrete set of functionalities executed as a single step in a DTS package. Each task defines a work item to be performed as part of the data movement and data transformation process or as a job to be executed. Data Transformation Services supplies a number of tasks that are part of the DTS object model and that can be accessed graphically through the DTS Designer or accessed programmatically. These tasks, which can be configured individually, cover a wide variety of data copying, data transformation and notification situations. For example, the following types of tasks represent some actions that you can perform by using DTS: executing a single SQL statement, sending an email, and transferring a file with FTP. A step within a DTS package describes the order in which tasks are run and the precedence constraints that describe what to do in the case damage or of failure. These steps can be executed sequentially or in parallel. Packages can also contain global variables which can be used throughout the package. SQL Server 2000 allows input and output parameters for tasks, greatly expanding the usefulness of global variables. DTS packages can be edited, password protected, scheduled for execution, and retrieved by version. == DTS tools == DTS tools packaged with SQL Server include the DTS wizards, DTS Designer, and DTS Programming Interfaces. === DTS wizards === The DTS wizards can be used to perform simple or common DTS tasks. These include the Import/Export Wizard and the Copy of Database Wizard. They provide the simplest method of copying data between OLE DB data sources. There is a great deal of functionality that is not available by merely using a wizard. However, a package created with a wizard can be saved and later altered with one of the other DTS tools. A Create Publishing Wizard is also available to schedule packages to run at certain times. This only works if SQL Server Agent is running; otherwise the package will be scheduled, but will not be executed. === DTS Designer === The DTS Designer is a graphical tool used to build complex DTS Packages with workflows and event-driven logic. DTS Designer can also be used to edit and customize DTS Packages created with the DTS wizard. Each connection and task in DTS Designer is shown with a specific icon. These icons are joined with precedence constraints, which specify the order and requirements for tasks to be run. One task may run, for instance, only if another task succeeds (or fails). Other tasks may run concurrently. The DTS Designer has been criticized for having unusual quirks and limitations, such as the inability to visually copy and paste multiple tasks at one time. Many of these shortcomings have been overcome in SQL Server Integration Services, DTS's successor. === DTS Query Designer === A graphical tool used to build queries in DTS. === DTS Run Utility === DTS Packages can be run from the command line using the DTSRUN Utility. The utility is invoked using the following syntax: dtsrun /S server_name[\instance_name] { {/[~]U user_name [/[~]P password]} | /E } ] { {/[~]N package_name } | {/[~]G package_guid_string} | {/[~]V package_version_guid_string} } [/[~]M package_password] [/[~]F filename] [/[~]R repository_database_name] [/A global_variable_name:typeid=value] [/L log_file_name] [/W NT_event_log_completion_status] [/Z] [/!X] [/!D] [/!Y] [/!C] ] When passing in parameters which are mapped to Global Variables, you are required to include the typeid. This is rather difficult to find on the Microsoft site. Below are the TypeIds used in passing in these values.
Cloud computing
Cloud computing is defined by the International Organization for Standardization (ISO) as "a paradigm for enabling network access to a scalable and elastic pool of shareable physical or virtual resources with self-service provisioning and administration on demand". It is commonly referred to as "the cloud". == Characteristics == In 2011, the National Institute of Standards and Technology (NIST) identified five "essential characteristics" for cloud systems. Below are the exact definitions according to NIST: On-demand self-service: "A consumer can unilaterally provision computing capabilities, such as server time and network storage, as needed automatically without requiring human interaction with each service provider." Broad network access: "Capabilities are available over the network and accessed through standard mechanisms that promote use by heterogeneous thin or thick client platforms (e.g., mobile phones, tablets, laptops, and workstations)." Resource pooling: " The provider's computing resources are pooled to serve multiple consumers using a multi-tenant model, with different physical and virtual resources dynamically assigned and reassigned according to consumer demand." Rapid elasticity: "Capabilities can be elastically provisioned and released, in some cases automatically, to scale rapidly outward and inward commensurate with demand. To the consumer, the capabilities available for provisioning often appear unlimited and can be appropriated in any quantity at any time." Measured service: "Cloud systems automatically control and optimize resource use by leveraging a metering capability at some level of abstraction appropriate to the type of service (e.g., storage, processing, bandwidth, and active user accounts). Resource usage can be monitored, controlled, and reported, providing transparency for both the provider and consumer of the utilized service. By 2023, the International Organization for Standardization (ISO) had expanded and refined the list. == History == The history of cloud computing extends to the 1960s, with the initial concepts of time-sharing becoming popularized via remote job entry (RJE). The "data center" model, where users submitted jobs to operators to run on mainframes, was predominantly used during this era. This period saw broad experimentation with making large-scale computing power more accessible through time-sharing, while optimizing infrastructure, platforms, and applications to improve efficiency for end users. The "cloud" metaphor for virtualized services dates to 1994, when it was used by General Magic for the universe of "places" that mobile agents in the Telescript environment could "go". The metaphor is credited to David Hoffman, a General Magic communications specialist, based on its long-standing use in networking and telecom. The expression cloud computing became more widely known in 1996 when Compaq Computer Corporation drew up a business plan for future computing and the Internet. The company's ambition was to supercharge sales with "cloud computing-enabled applications". The business plan foresaw that online consumer file storage would likely be commercially successful. As a result, Compaq decided to sell server hardware to internet service providers. In the 2000s, the application of cloud computing began to take shape with the establishment of Amazon Web Services (AWS) in 2002, which allowed developers to build applications independently. In 2006 Amazon Simple Storage Service, known as Amazon S3, and the Amazon Elastic Compute Cloud (EC2) were released. In 2008 NASA's development of the first open-source software for deploying private and hybrid clouds. The following decade saw the launch of various cloud services. In 2010, Microsoft launched Microsoft Azure, and Rackspace Hosting and NASA initiated an open-source cloud-software project, OpenStack. IBM introduced the IBM SmartCloud framework in 2011, and Oracle announced the Oracle Cloud in 2012. In December 2019, Amazon launched AWS Outposts, a service that extends AWS infrastructure, services, APIs, and tools to customer data centers, co-location spaces, or on-premises facilities. == Value proposition == Cloud computing can shorten time to market by offering pre-configured tools, scalable resources, and managed services, allowing users to focus on core business value rather than maintaining infrastructure. Cloud platforms can enable organizations and individuals to reduce upfront capital expenditures on physical infrastructure by shifting to an operational expenditure model, where costs scale with usage. Cloud platforms also offer managed services and tools, such as artificial intelligence, data analytics, and machine learning, which might otherwise require significant in-house expertise and infrastructure investment. While cloud computing can offer cost advantages through effective resource optimization, organizations often face challenges such as unused resources, inefficient configurations, and hidden costs without proper oversight and governance. Many cloud platforms provide cost management tools, such as AWS Cost Explorer and Azure Cost Management, and frameworks like FinOps have emerged to standardize financial operations in the cloud. Cloud computing also facilitates collaboration, remote work, and global service delivery by enabling secure access to data and applications from any location with an internet connection. Cloud providers offer various redundancy options for core services, such as managed storage and managed databases, though redundancy configurations often vary by service tier. Advanced redundancy strategies, such as cross-region replication or failover systems, typically require explicit configuration and may incur additional costs or licensing fees. Cloud environments operate under a shared responsibility model, where providers are typically responsible for infrastructure security, physical hardware, and software updates, while customers are accountable for data encryption, identity and access management (IAM), and application-level security. These responsibilities vary depending on the cloud service model—Infrastructure as a Service (IaaS), Platform as a Service (PaaS), or Software as a Service (SaaS)—with customers typically having more control and responsibility in IaaS environments and progressively less in PaaS and SaaS models, often trading control for convenience and managed services. == Adoption and suitability == The decision to adopt cloud computing or maintain on-premises infrastructure depends on factors such as scalability, cost structure, latency requirements, regulatory constraints, and infrastructure customization. Organizations with variable or unpredictable workloads, limited capital for upfront investments, or a focus on rapid scalability benefit from cloud adoption. Startups, SaaS companies, and e-commerce platforms often prefer the pay-as-you-go operational expenditure (OpEx) model of cloud infrastructure. Additionally, companies prioritizing global accessibility, remote workforce enablement, disaster recovery, and leveraging advanced services such as AI/ML and analytics are well-suited for the cloud. In recent years, some cloud providers have started offering specialized services for high-performance computing and low-latency applications, addressing some use cases previously exclusive to on-premises setups. On the other hand, organizations with strict regulatory requirements, highly predictable workloads, or reliance on deeply integrated legacy systems may find cloud infrastructure less suitable. Businesses in industries like defense, government, or those handling highly sensitive data often favor on-premises setups for greater control and data sovereignty. Additionally, companies with ultra-low latency requirements, such as high-frequency trading (HFT) firms, rely on custom hardware (e.g., FPGAs) and physical proximity to exchanges, which most cloud providers cannot fully replicate despite recent advancements. Similarly, tech giants like Google, Meta, and Amazon build their own data centers due to economies of scale, predictable workloads, and the ability to customize hardware and network infrastructure for optimal efficiency. However, these companies also use cloud services selectively for certain workloads and applications where it aligns with their operational needs. In practice, many organizations are increasingly adopting hybrid cloud architectures, combining on-premises infrastructure with cloud services. This approach allows businesses to balance scalability, cost-effectiveness, and control, offering the benefits of both deployment models while mitigating their respective limitations. == Challenges and limitations == One of the primary challenges of cloud computing, compared with traditional on-premises systems, is maintaining data security and privacy. Cloud users entrust their sensitive data to third-party providers, who may not have adequate measures to protect it from unau
Hard sigmoid
In artificial intelligence, especially computer vision and artificial neural networks, a hard sigmoid is non-smooth function used in place of a sigmoid function. These retain the basic shape of a sigmoid, rising from 0 to 1, but using simpler functions, especially piecewise linear functions or piecewise constant functions. These are preferred where speed of computation is more important than precision. == Examples == The most extreme examples are the sign function or Heaviside step function, which go from −1 to 1 or 0 to 1 (which to use depends on normalization) at 0. Other examples include the Theano library, which provides two approximations: ultra_fast_sigmoid, which is a multi-part piecewise approximation and hard_sigmoid, which is a 3-part piecewise linear approximation (output 0, line with slope 0.2, output 1).
Pooling layer
In neural networks, a pooling layer is a kind of network layer that downsamples and aggregates information that is dispersed among many vectors into fewer vectors. It has several uses. It removes redundant information, thus reducing the amount of computation and memory required, which makes the model more robust to small variations in the input; and it increases the receptive field of neurons in later layers in the network. == Convolutional neural network pooling == Pooling is most commonly used in convolutional neural networks (CNN). Below is a description of pooling in 2-dimensional CNNs. The generalization to n-dimensions is immediate. As notation, we consider a tensor x ∈ R H × W × C {\displaystyle x\in \mathbb {R} ^{H\times W\times C}} , where H {\displaystyle H} is height, W {\displaystyle W} is width, and C {\displaystyle C} is the number of channels. A pooling layer outputs a tensor y ∈ R H ′ × W ′ × C ′ {\displaystyle y\in \mathbb {R} ^{H'\times W'\times C'}} . We define two variables f , s {\displaystyle f,s} called "filter size" (aka "kernel size") and "stride". Sometimes, it is necessary to use a different filter size and stride for horizontal and vertical directions. In such cases, we define 4 variables: f H , f W , s H , s W {\displaystyle f_{H},f_{W},s_{H},s_{W}} . The receptive field of an entry in the output tensor, y {\displaystyle y} , are all the entries in x {\displaystyle x} that can affect that entry. === Max pooling === Max Pooling (MaxPool) is commonly used in CNNs to reduce the spatial dimensions of feature maps. Define M a x P o o l ( x | f , s ) 0 , 0 , 0 = max ( x 0 : f − 1 , 0 : f − 1 , 0 ) {\displaystyle \mathrm {MaxPool} (x|f,s)_{0,0,0}=\max(x_{0:f-1,0:f-1,0})} where 0 : f − 1 {\displaystyle 0:f-1} means the range 0 , 1 , … , f − 1 {\displaystyle 0,1,\dots ,f-1} . Note that we need to avoid the off-by-one error. The next input is M a x P o o l ( x | f , s ) 1 , 0 , 0 = max ( x s : s + f − 1 , 0 : f − 1 , 0 ) {\displaystyle \mathrm {MaxPool} (x|f,s)_{1,0,0}=\max(x_{s:s+f-1,0:f-1,0})} and so on. The receptive field of y i , j , c {\displaystyle y_{i,j,c}} is x i s + f − 1 , j s + f − 1 , c {\displaystyle x_{is+f-1,js+f-1,c}} , so in general, M a x P o o l ( x | f , s ) i , j , c = m a x ( x i s : i s + f − 1 , j s : j s + f − 1 , c ) {\displaystyle \mathrm {MaxPool} (x|f,s)_{i,j,c}=\mathrm {max} (x_{is:is+f-1,js:js+f-1,c})} If the horizontal and vertical filter size and strides differ, then in general, M a x P o o l ( x | f , s ) i , j , c = m a x ( x i s H : i s H + f H − 1 , j s W : j s W + f W − 1 , c ) {\displaystyle \mathrm {MaxPool} (x|f,s)_{i,j,c}=\mathrm {max} (x_{is_{H}:is_{H}+f_{H}-1,js_{W}:js_{W}+f_{W}-1,c})} More succinctly, we can write y k = max ( { x k ′ | k ′ in the receptive field of k } ) {\displaystyle y_{k}=\max(\{x_{k'}|k'{\text{ in the receptive field of }}k\})} . If H {\displaystyle H} is not expressible as k s + f {\displaystyle ks+f} where k {\displaystyle k} is an integer, then for computing the entries of the output tensor on the boundaries, max pooling would attempt to take as inputs variables off the tensor. In this case, how those non-existent variables are handled depends on the padding conditions, illustrated on the right. Global Max Pooling (GMP) is a specific kind of max pooling where the output tensor has shape R C {\displaystyle \mathbb {R} ^{C}} and the receptive field of y c {\displaystyle y_{c}} is all of x 0 : H , 0 : W , c {\displaystyle x_{0:H,0:W,c}} . That is, it takes the maximum over each entire channel. It is often used just before the final fully connected layers in a CNN classification head. === Average pooling === Average pooling (AvgPool) is similarly defined A v g P o o l ( x | f , s ) i , j , c = a v e r a g e ( x i s : i s + f − 1 , j s : j s + f − 1 , c ) = 1 f 2 ∑ k ∈ i s : i s + f − 1 ∑ l ∈ j s : j s + f − 1 x k , l , c {\displaystyle \mathrm {AvgPool} (x|f,s)_{i,j,c}=\mathrm {average} (x_{is:is+f-1,js:js+f-1,c})={\frac {1}{f^{2}}}\sum _{k\in is:is+f-1}\sum _{l\in js:js+f-1}x_{k,l,c}} Global Average Pooling (GAP) is defined similarly to GMP. It was first proposed in Network-in-Network. Similarly to GMP, it is often used just before the final fully connected layers in a CNN classification head. === Interpolations === There are some interpolations of max pooling and average pooling. Mixed Pooling is a linear sum of max pooling and average pooling. That is, M i x e d P o o l ( x | f , s , w ) = w M a x P o o l ( x | f , s ) + ( 1 − w ) A v g P o o l ( x | f , s ) {\displaystyle \mathrm {MixedPool} (x|f,s,w)=w\mathrm {MaxPool} (x|f,s)+(1-w)\mathrm {AvgPool} (x|f,s)} where w ∈ [ 0 , 1 ] {\displaystyle w\in [0,1]} is either a hyperparameter, a learnable parameter, or randomly sampled anew every time. Lp Pooling is similar to average pooling, but uses Lp norm average instead of average: y k = ( 1 N ∑ k ′ in the receptive field of k | x k ′ | p ) 1 / p {\displaystyle y_{k}=\left({\frac {1}{N}}\sum _{k'{\text{ in the receptive field of }}k}|x_{k'}|^{p}\right)^{1/p}} where N {\displaystyle N} is the size of receptive field, and p ≥ 1 {\displaystyle p\geq 1} is a hyperparameter. If all activations are non-negative, then average pooling is the case of p = 1 {\displaystyle p=1} , and max pooling is the case of p → ∞ {\displaystyle p\to \infty } . Square-root pooling is the case of p = 2 {\displaystyle p=2} . Stochastic pooling samples a random activation x k ′ {\displaystyle x_{k'}} from the receptive field with probability x k ′ ∑ k ″ x k ″ {\displaystyle {\frac {x_{k'}}{\sum _{k''}x_{k''}}}} . It is the same as average pooling in expectation. Softmax pooling is like max pooling, but uses softmax, i.e. ∑ k ′ e β x k ′ x k ′ ∑ k ″ e β x k ″ {\displaystyle {\frac {\sum _{k'}e^{\beta x_{k'}}x_{k'}}{\sum _{k''}e^{\beta x_{k''}}}}} where β > 0 {\displaystyle \beta >0} . Average pooling is the case of β ↓ 0 {\displaystyle \beta \downarrow 0} , and max pooling is the case of β ↑ ∞ {\displaystyle \beta \uparrow \infty } Local Importance-based Pooling generalizes softmax pooling by ∑ k ′ e g ( x k ′ ) x k ′ ∑ k ″ e g ( x k ″ ) {\displaystyle {\frac {\sum _{k'}e^{g(x_{k'})}x_{k'}}{\sum _{k''}e^{g(x_{k''})}}}} where g {\displaystyle g} is a learnable function. === Other poolings === Spatial pyramidal pooling applies max pooling (or any other form of pooling) in a pyramid structure. That is, it applies global max pooling, then applies max pooling to the image divided into 4 equal parts, then 16, etc. The results are then concatenated. It is a hierarchical form of global pooling, and similar to global pooling, it is often used just before a classification head. Region of Interest Pooling (also known as RoI pooling) is a variant of max pooling used in R-CNNs for object detection. It is designed to take an arbitrarily-sized input matrix, and output a fixed-sized output matrix. Covariance pooling computes the covariance matrix of the vectors { x k , l , 0 : C − 1 } k ∈ i s : i s + f − 1 , l ∈ j s : j s + f − 1 {\displaystyle \{x_{k,l,0:C-1}\}_{k\in is:is+f-1,l\in js:js+f-1}} which is then flattened to a C 2 {\displaystyle C^{2}} -dimensional vector y i , j , 0 : C 2 − 1 {\displaystyle y_{i,j,0:C^{2}-1}} . Global covariance pooling is used similarly to global max pooling. As average pooling computes the average, which is a first-degree statistic, and covariance is a second-degree statistic, covariance pooling is also called "second-order pooling". It can be generalized to higher-order poolings. Blur Pooling means applying a blurring method before downsampling. For example, the Rect-2 blur pooling means taking an average pooling at f = 2 , s = 1 {\displaystyle f=2,s=1} , then taking every second pixel (identity with s = 2 {\displaystyle s=2} ). == Vision Transformer pooling == In Vision Transformers (ViT), there are the following common kinds of poolings. BERT-like pooling uses a dummy [CLS] token, "classification". For classification, the output at [CLS] is the classification token, which is then processed by a LayerNorm-feedforward-softmax module into a probability distribution, which is the network's prediction of class probability distribution. This is the one used by the original ViT and Masked Autoencoder. Global average pooling (GAP) does not use the dummy token, but simply takes the average of all output tokens as the classification token. It was mentioned in the original ViT as being equally good. Multihead attention pooling (MAP) applies a multi headed attention block to pooling. Specifically, it takes as input a list of vectors x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\dots ,x_{n}} , which might be thought of as the output vectors of a layer of a ViT. It then applies a feedforward layer F F N {\displaystyle \mathrm {FFN} } on each vector, resulting in a matrix V = [ F F N ( v 1 ) , … , F F N ( v n ) ] {\displaystyle V=[\mathrm {FFN} (v_{1}),\dots ,\mathrm {FFN} (v_{n})]} . This is then sent to a multi-headed attention, resulting in M u l t i h e a d e d A
Scale-space axioms
In image processing and computer vision, a scale space framework can be used to represent an image as a family of gradually smoothed images. This framework is very general and a variety of scale space representations exist. A typical approach for choosing a particular type of scale space representation is to establish a set of scale-space axioms, describing basic properties of the desired scale-space representation and often chosen so as to make the representation useful in practical applications. Once established, the axioms narrow the possible scale-space representations to a smaller class, typically with only a few free parameters. A set of standard scale space axioms, discussed below, leads to the linear Gaussian scale-space, which is the most common type of scale space used in image processing and computer vision. == Scale space axioms for the linear scale-space representation == The linear scale space representation L ( x , y , t ) = ( T t f ) ( x , y ) = g ( x , y , t ) ∗ f ( x , y ) {\displaystyle L(x,y,t)=(T_{t}f)(x,y)=g(x,y,t)f(x,y)} of signal f ( x , y ) {\displaystyle f(x,y)} obtained by smoothing with the Gaussian kernel g ( x , y , t ) {\displaystyle g(x,y,t)} satisfies a number of properties 'scale-space axioms' that make it a special form of multi-scale representation: linearity T t ( a f + b h ) = a T t f + b T t h {\displaystyle T_{t}(af+bh)=aT_{t}f+bT_{t}h} where f {\displaystyle f} and h {\displaystyle h} are signals while a {\displaystyle a} and b {\displaystyle b} are constants, shift invariance T t S ( Δ x , Δ y ) f = S ( Δ x , Δ y ) T t f {\displaystyle T_{t}S_{(\Delta x,\Delta _{y})}f=S_{(\Delta x,\Delta _{y})}T_{t}f} where S ( Δ x , Δ y ) {\displaystyle S_{(\Delta x,\Delta _{y})}} denotes the shift (translation) operator ( S ( Δ x , Δ y ) f ) ( x , y ) = f ( x − Δ x , y − Δ y ) {\displaystyle (S_{(\Delta x,\Delta _{y})}f)(x,y)=f(x-\Delta x,y-\Delta y)} semi-group structure g ( x , y , t 1 ) ∗ g ( x , y , t 2 ) = g ( x , y , t 1 + t 2 ) {\displaystyle g(x,y,t_{1})g(x,y,t_{2})=g(x,y,t_{1}+t_{2})} with the associated cascade smoothing property L ( x , y , t 2 ) = g ( x , y , t 2 − t 1 ) ∗ L ( x , y , t 1 ) {\displaystyle L(x,y,t_{2})=g(x,y,t_{2}-t_{1})L(x,y,t_{1})} existence of an infinitesimal generator A {\displaystyle A} ∂ t L ( x , y , t ) = ( A L ) ( x , y , t ) {\displaystyle \partial _{t}L(x,y,t)=(AL)(x,y,t)} non-creation of local extrema (zero-crossings) in one dimension, non-enhancement of local extrema in any number of dimensions ∂ t L ( x , y , t ) ≤ 0 {\displaystyle \partial _{t}L(x,y,t)\leq 0} at spatial maxima and ∂ t L ( x , y , t ) ≥ 0 {\displaystyle \partial _{t}L(x,y,t)\geq 0} at spatial minima, rotational symmetry g ( x , y , t ) = h ( x 2 + y 2 , t ) {\displaystyle g(x,y,t)=h(x^{2}+y^{2},t)} for some function h {\displaystyle h} , scale invariance g ^ ( ω x , ω y , t ) = h ^ ( ω x φ ( t ) , ω x φ ( t ) ) {\displaystyle {\hat {g}}(\omega _{x},\omega _{y},t)={\hat {h}}({\frac {\omega _{x}}{\varphi (t)}},{\frac {\omega _{x}}{\varphi (t)}})} for some functions φ {\displaystyle \varphi } and h ^ {\displaystyle {\hat {h}}} where g ^ {\displaystyle {\hat {g}}} denotes the Fourier transform of g {\displaystyle g} , positivity g ( x , y , t ) ≥ 0 {\displaystyle g(x,y,t)\geq 0} , normalization ∫ x = − ∞ ∞ ∫ y = − ∞ ∞ g ( x , y , t ) d x d y = 1 {\displaystyle \int _{x=-\infty }^{\infty }\int _{y=-\infty }^{\infty }g(x,y,t)\,dx\,dy=1} . In fact, it can be shown that the Gaussian kernel is a unique choice given several different combinations of subsets of these scale-space axioms: most of the axioms (linearity, shift-invariance, semigroup) correspond to scaling being a semigroup of shift-invariant linear operator, which is satisfied by a number of families integral transforms, while "non-creation of local extrema" for one-dimensional signals or "non-enhancement of local extrema" for higher-dimensional signals are the crucial axioms which relate scale-spaces to smoothing (formally, parabolic partial differential equations), and hence select for the Gaussian. The Gaussian kernel is also separable in Cartesian coordinates, i.e. g ( x , y , t ) = g ( x , t ) g ( y , t ) {\displaystyle g(x,y,t)=g(x,t)\,g(y,t)} . Separability is, however, not counted as a scale-space axiom, since it is a coordinate dependent property related to issues of implementation. In addition, the requirement of separability in combination with rotational symmetry per se fixates the smoothing kernel to be a Gaussian. There exists a generalization of the Gaussian scale-space theory to more general affine and spatio-temporal scale-spaces. In addition to variabilities over scale, which original scale-space theory was designed to handle, this generalized scale-space theory also comprises other types of variabilities, including image deformations caused by viewing variations, approximated by local affine transformations, and relative motions between objects in the world and the observer, approximated by local Galilean transformations. In this theory, rotational symmetry is not imposed as a necessary scale-space axiom and is instead replaced by requirements of affine and/or Galilean covariance. The generalized scale-space theory leads to predictions about receptive field profiles in good qualitative agreement with receptive field profiles measured by cell recordings in biological vision. In the computer vision, image processing and signal processing literature there are many other multi-scale approaches, using wavelets and a variety of other kernels, that do not exploit or require the same requirements as scale space descriptions do; please see the article on related multi-scale approaches. There has also been work on discrete scale-space concepts that carry the scale-space properties over to the discrete domain; see the article on scale space implementation for examples and references.
Lexxe
Lexxe is an internet search engine that applies Natural Language Processing in its semantic search technology. Founded in 2005 by Dr. Hong Liang Qiao, Lexxe is based in Sydney, Australia. Today, Lexxe's key focus is on sentiment search with the launch of a news sentiment search site at News & Moods (www.newsandmoods.com). Lexxe has experienced several stages of change of focus in search technology: Lexxe launched its Alpha version in 2005, featuring Natural Language question answering (i.e. users could ask questions in English to the search engine apart from keyword searches — this feature has been suspended for redevelopment since 2010). It used only algorithms to extract answers from web pages, with no question-answer pair databases prepared in advance. In 2011, Lexxe launched a beta version with a new search technology called Semantic Key. Semantic Keys enable users to query with a conceptual keyword (or a keyword with a special meaning, hence the term Semantic Key) in order to find instances under the concept, e.g. price → $5.95 or €200, color → red, yellow, white. For example, “price: a pound of apples”, “color: ferrari”. With initial 500 Semantic Keys at the Beta launch, Lexxe became the first search engine in the world to offer this unique and useful search technology to the users. The cost of building Semantic Keys was too heavy though. In 2017, Lexxe launched News & Moods (www.newsandmoods.com), an open platform for news sentiment search, a first step towards sentiment search feature for the entire Internet search in Lexxe search engine. News & Moods also comes with smartphone apps in Android and iOS.
Uncertain data
In computer science, uncertain data is data that contains noise that makes it deviate from the correct, intended or original values. In the age of big data, uncertainty or data veracity is one of the defining characteristics of data. Data is constantly growing in volume, variety, velocity and uncertainty (1/veracity). Uncertain data is found in abundance today on the web, in sensor networks, within enterprises both in their structured and unstructured sources. For example, there may be uncertainty regarding the address of a customer in an enterprise dataset, or the temperature readings captured by a sensor due to aging of the sensor. In 2012 IBM called out managing uncertain data at scale in its global technology outlook report that presents a comprehensive analysis looking three to ten years into the future seeking to identify significant, disruptive technologies that will change the world. In order to make confident business decisions based on real-world data, analyses must necessarily account for many different kinds of uncertainty present in very large amounts of data. Analyses based on uncertain data will have an effect on the quality of subsequent decisions, so the degree and types of inaccuracies in this uncertain data cannot be ignored. Uncertain data is found in the area of sensor networks; text where noisy text is found in abundance on social media, web and within enterprises where the structured and unstructured data may be old, outdated, or plain incorrect; in modeling where the mathematical model may only be an approximation of the actual process. When representing such data in a database, an appropriate uncertain database model needs to be selected. == Example data model for uncertain data == One way to represent uncertain data is through probability distributions. Let us take the example of a relational database. There are three main ways to do represent uncertainty as probability distributions in such a database model. In attribute uncertainty, each uncertain attribute in a tuple is subject to its own independent probability distribution. For example, if readings are taken of temperature and wind speed, each would be described by its own probability distribution, as knowing the reading for one measurement would not provide any information about the other. In correlated uncertainty, multiple attributes may be described by a joint probability distribution. For example, if readings are taken of the position of an object, and the x- and y-coordinates stored, the probability of different values may depend on the distance from the recorded coordinates. As distance depends on both coordinates, it may be appropriate to use a joint distribution for these coordinates, as they are not independent. In tuple uncertainty, all the attributes of a tuple are subject to a joint probability distribution. This covers the case of correlated uncertainty, but also includes the case where there is a probability of a tuple not belonging in the relevant relation, which is indicated by all the probabilities not summing to one. For example, assume we have the following tuple from a probabilistic database: Then, the tuple has 10% chance of not existing in the database.