In computer science, a single address space operating system (or SASOS) is an operating system that provides only one globally shared address space for all processes. In a single address space operating system, numerically identical (virtual memory) logical addresses in different processes all refer to exactly the same byte of data. In a traditional OS with private per-process address space, memory protection is based on address space boundaries ("address space isolation"). Single address-space operating systems make translation and protection orthogonal, which in no way weakens protection. The core advantage is that pointers (i.e. memory references) have global validity, meaning their meaning is independent of the process using it. This allows sharing pointer-connected data structures across processes, and making them persistent, i.e. storing them on backup store. Some processor architectures have direct support for protection independent of translation. On such architectures, a SASOS may be able to perform context switches faster than a traditional OS. Such architectures include Itanium, and Version 5 of the Arm architecture, as well as capability architectures such as CHERI. A SASOS should not be confused with a flat memory model, which provides no address translation and generally no memory protection. In contrast, a SASOS makes protection orthogonal to translation: it may be possible to name a data item (i.e. know its virtual address) while not being able to access it. SASOS projects using hardware-based protection include the following: Angel IBM i (formerly called OS/400) Iguana at NICTA, Australia Mungi at NICTA, Australia Nemesis Opal Scout Sombrero Related are OSes that provide protection through language-level type safety: Br1X Genera JX a research Java OS Phantom OS Singularity Theseus OS Torsion
Eager learning
In artificial intelligence, eager learning is a learning method in which the system tries to construct a general, input-independent target function during training of the system, as opposed to lazy learning, where generalization beyond the training data is delayed until a query is made to the system. The main advantage gained in employing an eager learning method, such as an artificial neural network, is that the target function will be approximated globally during training, thus requiring much less space than using a lazy learning system. Eager learning systems also deal much better with noise in the training data. Eager learning is an example of offline learning, in which post-training queries to the system have no effect on the system itself, and thus the same query to the system will always produce the same result. The main disadvantage with eager learning is that it is generally unable to provide good local approximations in the target function.
Swish function
The swish function is a family of mathematical function defined as follows: swish β ( x ) = x sigmoid ( β x ) = x 1 + e − β x . {\displaystyle \operatorname {swish} _{\beta }(x)=x\operatorname {sigmoid} (\beta x)={\frac {x}{1+e^{-\beta x}}}.} where β {\displaystyle \beta } can be constant (usually set to 1) or trainable and "sigmoid" refers to the logistic function. The swish family was designed to smoothly interpolate between a linear function and the Rectified linear unit (ReLU) function. When considering positive values, Swish is a particular case of doubly parameterized sigmoid shrinkage function defined in . Variants of the swish function include Mish. == Special values == For β = 0, the function is linear: f(x) = x/2. For β = 1, the function is the Sigmoid Linear Unit (SiLU). For β = 1.702, the function approximates GeLU. With β → ∞, the function converges to ReLU. Thus, the swish family smoothly interpolates between a linear function and the ReLU function. Since swish β ( x ) = swish 1 ( β x ) / β {\displaystyle \operatorname {swish} _{\beta }(x)=\operatorname {swish} _{1}(\beta x)/\beta } , all instances of swish have the same shape as the default swish 1 {\displaystyle \operatorname {swish} _{1}} , zoomed by β {\displaystyle \beta } . One usually sets β > 0 {\displaystyle \beta >0} . When β {\displaystyle \beta } is trainable, this constraint can be enforced by β = e b {\displaystyle \beta =e^{b}} , where b {\displaystyle b} is trainable. swish 1 ( x ) = x 2 + x 2 4 − x 4 48 + x 6 480 + O ( x 8 ) {\displaystyle \operatorname {swish} _{1}(x)={\frac {x}{2}}+{\frac {x^{2}}{4}}-{\frac {x^{4}}{48}}+{\frac {x^{6}}{480}}+O\left(x^{8}\right)} swish 1 ( x ) = x 2 tanh ( x 2 ) + x 2 swish 1 ( x ) + swish − 1 ( x ) = x tanh ( x 2 ) swish 1 ( x ) − swish − 1 ( x ) = x {\displaystyle {\begin{aligned}\operatorname {swish} _{1}(x)&={\frac {x}{2}}\tanh \left({\frac {x}{2}}\right)+{\frac {x}{2}}\\\operatorname {swish} _{1}(x)+\operatorname {swish} _{-1}(x)&=x\tanh \left({\frac {x}{2}}\right)\\\operatorname {swish} _{1}(x)-\operatorname {swish} _{-1}(x)&=x\end{aligned}}} == Derivatives == Because swish β ( x ) = swish 1 ( β x ) / β {\displaystyle \operatorname {swish} _{\beta }(x)=\operatorname {swish} _{1}(\beta x)/\beta } , it suffices to calculate its derivatives for the default case. swish 1 ′ ( x ) = x + sinh ( x ) 4 cosh 2 ( x 2 ) + 1 2 {\displaystyle \operatorname {swish} _{1}'(x)={\frac {x+\sinh(x)}{4\cosh ^{2}\left({\frac {x}{2}}\right)}}+{\frac {1}{2}}} so swish 1 ′ ( x ) − 1 2 {\displaystyle \operatorname {swish} _{1}'(x)-{\frac {1}{2}}} is odd. swish 1 ″ ( x ) = 1 − x 2 tanh ( x 2 ) 2 cosh 2 ( x 2 ) {\displaystyle \operatorname {swish} _{1}''(x)={\frac {1-{\frac {x}{2}}\tanh \left({\frac {x}{2}}\right)}{2\cosh ^{2}\left({\frac {x}{2}}\right)}}} so swish 1 ″ ( x ) {\displaystyle \operatorname {swish} _{1}''(x)} is even. == History == SiLU was first proposed alongside the GELU in 2016, then again proposed in 2017 as the Sigmoid-weighted Linear Unit (SiL) in reinforcement learning. The SiLU/SiL was then again proposed as the SWISH over a year after its initial discovery, originally proposed without the learnable parameter β, so that β implicitly equaled 1. The swish paper was then updated to propose the activation with the learnable parameter β. In 2017, after performing analysis on ImageNet data, researchers from Google indicated that using this function as an activation function in artificial neural networks improves the performance, compared to ReLU and sigmoid functions. It is believed that one reason for the improvement is that the swish function helps alleviate the vanishing gradient problem during backpropagation.
Physical neural network
A physical neural network is a type of artificial neural network in which an electrically adjustable material is used to emulate the function of a neural synapse or a higher-order (dendritic) neuron model. "Physical" neural network is used to emphasize the reliance on physical hardware used to emulate neurons as opposed to software-based approaches. More generally the term is applicable to other artificial neural networks in which a memristor or other electrically adjustable resistance material is used to emulate a neural synapse. == Types of physical neural networks == === ADALINE === In the 1960s Bernard Widrow and Ted Hoff developed ADALINE (Adaptive Linear Neuron) which used electrochemical cells called memistors (memory resistors) to emulate synapses of an artificial neuron. The memistors were implemented as 3-terminal devices operating based on the reversible electroplating of copper such that the resistance between two of the terminals is controlled by the integral of the current applied via the third terminal. The ADALINE circuitry was briefly commercialized by the Memistor Corporation in the 1960s enabling some applications in pattern recognition. However, since the memistors were not fabricated using integrated circuit fabrication techniques the technology was not scalable and was eventually abandoned as solid-state electronics became mature. === Analog VLSI === In 1989 Carver Mead published his book Analog VLSI and Neural Systems, which spun off perhaps the most common variant of analog neural networks. The physical realization is implemented in analog VLSI. This is often implemented as field effect transistors in low inversion. Such devices can be modelled as translinear circuits. This is a technique described by Barrie Gilbert in several papers around mid 1970th, and in particular his Translinear Circuits from 1981. With this method circuits can be analyzed as a set of well-defined functions in steady-state, and such circuits assembled into complex networks. === Physical Neural Network === Alex Nugent describes a physical neural network as one or more nonlinear neuron-like nodes used to sum signals and nanoconnections formed from nanoparticles, nanowires, or nanotubes which determine the signal strength input to the nodes. Alignment or self-assembly of the nanoconnections is determined by the history of the applied electric field performing a function analogous to neural synapses. Numerous applications for such physical neural networks are possible. For example, a temporal summation device can be composed of one or more nanoconnections having an input and an output thereof, wherein an input signal provided to the input causes one or more of the nanoconnection to experience an increase in connection strength thereof over time. Another example of a physical neural network is taught by U.S. Patent No. 7,039,619 entitled "Utilized nanotechnology apparatus using a neural network, a solution and a connection gap," which issued to Alex Nugent by the U.S. Patent & Trademark Office on May 2, 2006. A further application of physical neural network is shown in U.S. Patent No. 7,412,428 entitled "Application of hebbian and anti-hebbian learning to nanotechnology-based physical neural networks," which issued on August 12, 2008. Nugent and Molter have shown that universal computing and general-purpose machine learning are possible from operations available through simple memristive circuits operating the AHaH plasticity rule. More recently, it has been argued that also complex networks of purely memristive circuits can serve as neural networks. === Phase change neural network === In 2002, Stanford Ovshinsky described an analog neural computing medium in which phase-change material has the ability to cumulatively respond to multiple input signals. An electrical alteration of the resistance of the phase change material is used to control the weighting of the input signals. === Memristive neural network === Greg Snider of HP Labs describes a system of cortical computing with memristive nanodevices. The memristors (memory resistors) are implemented by thin film materials in which the resistance is electrically tuned via the transport of ions or oxygen vacancies within the film. DARPA's SyNAPSE project has funded IBM Research and HP Labs, in collaboration with the Boston University Department of Cognitive and Neural Systems (CNS), to develop neuromorphic architectures which may be based on memristive systems. === Protonic artificial synapses === In 2022, researchers reported the development of nanoscale brain-inspired artificial synapses, using the ion proton (H+), for 'analog deep learning'.
Canonical correspondence analysis
In multivariate analysis, canonical correspondence analysis (CCA) is an ordination technique that determines axes from the response data as a unimodal combination of measured predictors. CCA is commonly used in ecology in order to extract gradients that drive the composition of ecological communities. CCA extends correspondence analysis (CA) with regression, in order to incorporate predictor variables. == History == CCA was developed in 1986 by Cajo ter Braak and implemented in the program CANOCO, an extension of DECORANA. To date, CCA is one of the most popular multivariate methods in ecology, despite the availability of contemporary alternatives. CCA was originally derived and implemented using an algorithm of weighted averaging, though Legendre & Legendre (1998) derived an alternative algorithm. == Assumptions == The requirements of a CCA are that the samples are random and independent. Also, the data are categorical and that the independent variables are consistent within the sample site and error-free. The original publication states the need for equal species tolerances, equal species maxima, and equispaced or uniformly distributed species optima and site scores.
Lose It!
Lose It! is an American health and wellness mobile app developed by FitNow, Inc. The app generates calorie budgets for users by tracking weight, exercise, food and calorie intake, and personal goals, primarily to assist them in achieving weight loss. == History == Lose It! was developed in Boston and debuted in 2008. The app and its associated company were founded by J.J. Allaire, Charles Teague and Paul Dicristina. Prior to founding Lose It!, Teague and Allaire had founded the online research tool Onfolio, which was acquired by Microsoft in 2006. The Lose It! app was originally released as an iOS app before being released as a website in 2010 and an Android app in 2011. In 2015, Lose It! announced plans to release the app internationally. Lose It! was also available as an app for Apple Watch at its launch in 2015. The app’s “Snap It” feature, which allows users to approximate calorie counts by taking pictures of their daily meals and snacks, was released in beta in 2016. Snap It was named an Innovation Awards Honoree at the 2017 Consumer Electronics Show in Las Vegas. In 2020, Patrick Wetherille, one of the company’s earliest employees, was appointed chief executive officer. == App == Lose It! is weight loss app. The app allows users to set goals such as increasing strength, overall health/maintenance, and weight loss. It provides users recommended calorie budgets based on data such as their current weight and their desired weight. Lose It! also tracks data such as exercise/activity level and food consumption and allows users to track calories consumed by scanning barcodes for food products then retrieving calorie information for products. The app can also estimate the amount of calories in a food products. Lose It! has integration features connecting it to other apps such as Fitbit and Runkeeper. It also has social features such as joining groups and sharing progress with friends. The Premium version of the app allows users to track foods according to specific diets like keto, heart healthy or Mediterranean.
Sliced inverse regression
Sliced inverse regression (SIR) is a tool for dimensionality reduction in the field of multivariate statistics. In statistics, regression analysis is a method of studying the relationship between a response variable y and its input variable x _ {\displaystyle {\underline {x}}} , which is a p-dimensional vector. There are several approaches in the category of regression. For example, parametric methods include multiple linear regression, and non-parametric methods include local smoothing. As the number of observations needed to use local smoothing methods scales exponentially with high-dimensional data (as p grows), reducing the number of dimensions can make the operation computable. Dimensionality reduction aims to achieve this by showing only the most important dimension of the data. SIR uses the inverse regression curve, E ( x _ | y ) {\displaystyle E({\underline {x}}\,|\,y)} , to perform a weighted principal component analysis. == Model == Given a response variable Y {\displaystyle \,Y} and a (random) vector X ∈ R p {\displaystyle X\in \mathbb {R} ^{p}} of explanatory variables, SIR is based on the model Y = f ( β 1 ⊤ X , … , β k ⊤ X , ε ) ( 1 ) {\displaystyle Y=f(\beta _{1}^{\top }X,\ldots ,\beta _{k}^{\top }X,\varepsilon )\quad \quad \quad \quad \quad (1)} where β 1 , … , β k {\displaystyle \beta _{1},\ldots ,\beta _{k}} are unknown projection vectors, k {\displaystyle \,k} is an unknown number smaller than p {\displaystyle \,p} , f {\displaystyle \;f} is an unknown function on R k + 1 {\displaystyle \mathbb {R} ^{k+1}} as it only depends on k {\displaystyle \,k} arguments, and ε {\displaystyle \varepsilon } is a random variable representing error with E [ ε | X ] = 0 {\displaystyle E[\varepsilon |X]=0} and a finite variance of σ 2 {\displaystyle \sigma ^{2}} . The model describes an ideal solution, where Y {\displaystyle \,Y} depends on X ∈ R p {\displaystyle X\in \mathbb {R} ^{p}} only through a k {\displaystyle \,k} dimensional subspace; i.e., one can reduce the dimension of the explanatory variables from p {\displaystyle \,p} to a smaller number k {\displaystyle \,k} without losing any information. An equivalent version of ( 1 ) {\displaystyle \,(1)} is: the conditional distribution of Y {\displaystyle \,Y} given X {\displaystyle \,X} depends on X {\displaystyle \,X} only through the k {\displaystyle \,k} dimensional random vector ( β 1 ⊤ X , … , β k ⊤ X ) {\displaystyle (\beta _{1}^{\top }X,\ldots ,\beta _{k}^{\top }X)} . It is assumed that this reduced vector is as informative as the original X {\displaystyle \,X} in explaining Y {\displaystyle \,Y} . The unknown β i ′ s {\displaystyle \,\beta _{i}'s} are called the effective dimension reducing directions (EDR-directions). The space that is spanned by these vectors is denoted by the effective dimension reducing space (EDR-space). == Relevant linear algebra background == Given a _ 1 , … , a _ r ∈ R n {\displaystyle {\underline {a}}_{1},\ldots ,{\underline {a}}_{r}\in \mathbb {R} ^{n}} , then V := L ( a _ 1 , … , a _ r ) {\displaystyle V:=L({\underline {a}}_{1},\ldots ,{\underline {a}}_{r})} , the set of all linear combinations of these vectors is called a linear subspace and is therefore a vector space. The equation says that vectors a _ 1 , … , a _ r {\displaystyle {\underline {a}}_{1},\ldots ,{\underline {a}}_{r}} span V {\displaystyle \,V} , but the vectors that span space V {\displaystyle \,V} are not unique. The dimension of V ( ∈ R n ) {\displaystyle \,V(\in \mathbb {R} ^{n})} is equal to the maximum number of linearly independent vectors in V {\displaystyle \,V} . A set of n {\displaystyle \,n} linear independent vectors of R n {\displaystyle \mathbb {R} ^{n}} makes up a basis of R n {\displaystyle \mathbb {R} ^{n}} . The dimension of a vector space is unique, but the basis itself is not. Several bases can span the same space. Dependent vectors can still span a space, but the linear combinations of the latter are only suitable to a set of vectors lying on a straight line. == Inverse regression == Computing the inverse regression curve (IR) means instead of looking for E [ Y | X = x ] {\displaystyle \,E[Y|X=x]} , which is a curve in R p {\displaystyle \mathbb {R} ^{p}} it is actually E [ X | Y = y ] {\displaystyle \,E[X|Y=y]} , which is also a curve in R p {\displaystyle \mathbb {R} ^{p}} , but consisting of p {\displaystyle \,p} one-dimensional regressions. The center of the inverse regression curve is located at E [ E [ X | Y ] ] = E [ X ] {\displaystyle \,E[E[X|Y]]=E[X]} . Therefore, the centered inverse regression curve is E [ X | Y = y ] − E [ X ] {\displaystyle \,E[X|Y=y]-E[X]} which is a p {\displaystyle \,p} dimensional curve in R p {\displaystyle \mathbb {R} ^{p}} . == Inverse regression versus dimension reduction == The centered inverse regression curve lies on a k {\displaystyle \,k} -dimensional subspace spanned by Σ x x β i ′ s {\displaystyle \,\Sigma _{xx}\beta _{i}\,'s} . This is a connection between the model and inverse regression. Given this condition and ( 1 ) {\displaystyle \,(1)} , the centered inverse regression curve E [ X | Y = y ] − E [ X ] {\displaystyle \,E[X|Y=y]-E[X]} is contained in the linear subspace spanned by Σ x x β k ( k = 1 , … , K ) {\displaystyle \,\Sigma _{xx}\beta _{k}(k=1,\ldots ,K)} , where Σ x x = C o v ( X ) {\displaystyle \,\Sigma _{xx}=Cov(X)} . == Estimation of the EDR-directions == After having had a look at all the theoretical properties, the aim now is to estimate the EDR-directions. For that purpose, weighted principal component analyses are needed. If the sample means m ^ h ′ s {\displaystyle \,{\hat {m}}_{h}\,'s} , X {\displaystyle \,X} would have been standardized to Z = Σ x x − 1 / 2 { X − E ( X ) } {\displaystyle \,Z=\Sigma _{xx}^{-1/2}\{X-E(X)\}} . Corresponding to the theorem above, the IR-curve m 1 ( y ) = E [ Z | Y = y ] {\displaystyle \,m_{1}(y)=E[Z|Y=y]} lies in the space spanned by ( η 1 , … , η k ) {\displaystyle \,(\eta _{1},\ldots ,\eta _{k})} , where η i = Σ x x 1 / 2 β i {\displaystyle \,\eta _{i}=\Sigma _{xx}^{1/2}\beta _{i}} . As a consequence, the covariance matrix c o v [ E [ Z | Y ] ] {\displaystyle \,cov[E[Z|Y]]} is degenerate in any direction orthogonal to the η i ′ s {\displaystyle \,\eta _{i}\,'s} . Therefore, the eigenvectors η k ( k = 1 , … , K ) {\displaystyle \,\eta _{k}(k=1,\ldots ,K)} associated with the largest K {\displaystyle \,K} eigenvalues are the standardized EDR-directions. == Algorithm == === SIR algorithm === The algorithm from Li, K-C. (1991) to estimate the EDR-directions via SIR is as follows. 1. Let Σ x x {\displaystyle \,\Sigma _{xx}} be the covariance matrix of X {\displaystyle \,X} . Standardize X {\displaystyle \,X} to Z = Σ x x − 1 / 2 { X − E ( X ) } {\displaystyle \,Z=\Sigma _{xx}^{-1/2}\{X-E(X)\}} ( 1 ) {\displaystyle \,(1)} can also be rewritten as Y = f ( η 1 ⊤ Z , … , η k ⊤ Z , ε ) {\displaystyle Y=f(\eta _{1}^{\top }Z,\ldots ,\eta _{k}^{\top }Z,\varepsilon )} where η k = β k Σ x x 1 / 2 ∀ k {\displaystyle \,\eta _{k}=\beta _{k}\Sigma _{xx}^{1/2}\quad \forall \;k} .) 2. Divide the range of y i {\displaystyle \,y_{i}} into S {\displaystyle \,S} non-overlapping slices H s ( s = 1 , … , S ) . n s {\displaystyle \,H_{s}(s=1,\ldots ,S).\;n_{s}} is the number of observations within each slice and I H s {\displaystyle \,I_{H_{s}}} is the indicator function for the slice: n s = ∑ i = 1 n I H s ( y i ) {\displaystyle n_{s}=\sum _{i=1}^{n}I_{H_{s}}(y_{i})} 3. Compute the mean of z i {\displaystyle \,z_{i}} over all slices, which is a crude estimate m ^ 1 {\displaystyle \,{\hat {m}}_{1}} of the inverse regression curve m 1 {\displaystyle \,m_{1}} : z ¯ s = n s − 1 ∑ i = 1 n z i I H s ( y i ) {\displaystyle \,{\bar {z}}_{s}=n_{s}^{-1}\sum _{i=1}^{n}z_{i}I_{H_{s}}(y_{i})} 4. Calculate the estimate for C o v { m 1 ( y ) } {\displaystyle \,Cov\{m_{1}(y)\}} : V ^ = n − 1 ∑ i = 1 S n s z ¯ s z ¯ s ⊤ {\displaystyle \,{\hat {V}}=n^{-1}\sum _{i=1}^{S}n_{s}{\bar {z}}_{s}{\bar {z}}_{s}^{\top }} 5. Identify the eigenvalues λ ^ i {\displaystyle \,{\hat {\lambda }}_{i}} and the eigenvectors η ^ i {\displaystyle \,{\hat {\eta }}_{i}} of V ^ {\displaystyle \,{\hat {V}}} , which are the standardized EDR-directions. 6. Transform the standardized EDR-directions back to the original scale. The estimates for the EDR-directions are given by: β ^ i = Σ ^ x x − 1 / 2 η ^ i {\displaystyle \,{\hat {\beta }}_{i}={\hat {\Sigma }}_{xx}^{-1/2}{\hat {\eta }}_{i}} (which are not necessarily orthogonal.)