In signal processing, the chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets. Similar to the wavelet transform, chirplets are usually generated from (or can be expressed as being from) a single mother chirplet (analogous to the so-called mother wavelet of wavelet theory). == Definitions == The term chirplet transform was coined by Steve Mann, as the title of the first published paper on chirplets. The term chirplet itself (apart from chirplet transform) was also used by Steve Mann, Domingo Mihovilovic, and Ronald Bracewell to describe a windowed portion of a chirp function. In Mann's words: A wavelet is a piece of a wave, and a chirplet, similarly, is a piece of a chirp. More precisely, a chirplet is a windowed portion of a chirp function, where the window provides some time localization property. In terms of time–frequency space, chirplets exist as rotated, sheared, or other structures that move from the traditional parallelism with the time and frequency axes that are typical for waves (Fourier and short-time Fourier transforms) or wavelets. The chirplet transform thus represents a rotated, sheared, or otherwise transformed tiling of the time–frequency plane. Although chirp signals have been known for many years in radar, pulse compression, and the like, the first published reference to the chirplet transform described specific signal representations based on families of functions related to one another by time–varying frequency modulation or frequency varying time modulation, in addition to time and frequency shifting, and scale changes. In that paper, the Gaussian chirplet transform was presented as one such example, together with a successful application to ice fragment detection in radar (improving target detection results over previous approaches). The term chirplet (but not the term chirplet transform) was also proposed for a similar transform, apparently independently, by Mihovilovic and Bracewell later that same year. == Applications == The first practical application of the chirplet transform was in water-human-computer interaction (WaterHCI) for marine safety, to assist vessels in navigating through ice-infested waters, using marine radar to detect growlers (small iceberg fragments too small to be visible on conventional radar, yet large enough to damage a vessel). Other applications of the chirplet transform in WaterHCI include the SWIM (Sequential Wave Imprinting Machine). More recently other practical applications have been developed, including image processing (e.g. where there is periodic structure imaged through projective geometry), as well as to excise chirp-like interference in spread spectrum communications, in EEG processing, and Chirplet Time Domain Reflectometry. == Extensions == The warblet transform is a particular example of the chirplet transform introduced by Mann and Haykin in 1992 and now widely used. It provides a signal representation based on cyclically varying frequency modulated signals (warbling signals).
Huawei Member Center
Huawei Member Center is a benefits app which runs using Huawei Mobile Services. Originally launched in China, Huawei Member Center is now being developed primarily around devices such as P40 Pro and the Nova 7. == Membership Levels == The Huawei Member Center provides rewards in two primary ways, 1) device-specific & promotions and 2) via frequent use of Huawei products and apps, using points to redeem additional benefits. In China, Huawei members are already classified into three levels, the highest being “elite”. Membership level determines the level of perks received, from priority access to the service hotline, new device events & proprietary early-access opportunities. Huawei ran a number of member events in 2019 called "Huawei Member Day" to promote the Member Center including providing tips for the Mate 30 Pro and offering a 50Gb cloud storage upgrade to users. == HMC in China == Huawei Member Center Has seen significant adoption in China and the east, the rewards for use on the app have ranged from free book coupons, discounted travel and exclusive gifts of new devices, such as the Huawei Enjoy Z.
Almeida–Pineda recurrent backpropagation
Almeida–Pineda recurrent backpropagation is an extension to the backpropagation algorithm that is applicable to recurrent neural networks. It is a type of supervised learning. It was described somewhat cryptically in Richard Feynman's senior thesis, and rediscovered independently in the context of artificial neural networks by both Fernando Pineda and Luis B. Almeida. A recurrent neural network for this algorithm consists of some input units, some output units and eventually some hidden units. For a given set of (input, target) states, the network is trained to settle into a stable activation state with the output units in the target state, based on a given input state clamped on the input units.
ARKA descriptors in QSAR
In computational chemistry and cheminformatics, ARKA descriptors in QSAR are a class of molecular descriptors used in quantitative structure–activity relationship (QSAR) modeling (or related approaches such as QSPR and QSTR), a computational method for predicting the biological activity or toxicity of chemical compounds based on their molecular structure. Molecular descriptors are numerical values that summarize information about a molecule's structure, topology, geometry, or physicochemical properties in a form suitable for machine learning or statistical modeling. ARKA (Arithmetic Residuals in K-Groups Analysis) descriptors differ from traditional descriptors by encoding atomic-level information through recursive autoregression techniques, which aim to capture subtle structural patterns and improve predictive accuracy. They are designed to be both interpretable and well-suited to modeling nonlinear relationships in QSAR studies. == Comparisons == While QSAR is essentially a similarity-based approach, the occurrence of activity/property cliffs may greatly reduce the predictive accuracy of the developed models. The novel Arithmetic Residuals in K-groups Analysis (ARKA) approach is a supervised dimensionality reduction technique developed by the DTC Laboratory, Jadavpur University that can easily identify activity cliffs in a data set. Activity cliffs are similar in their structures but differ considerably in their activity. The basic idea of the ARKA descriptors is to group the conventional QSAR descriptors based on a predefined criterion and then assign weightage to each descriptor in each group. ARKA descriptors have also been used to develop classification-based and regression-based QSAR models with acceptable quality statistics. The ARKA descriptors have been used for the identification of activity cliffs in QSAR studies and/or model development by multiple researchers. A tutorial presentation on the ARKA descriptors is available. Recently a multi-class ARKA framework has been proposed for improved q-RASAR model generation.
Neural cryptography
Neural cryptography is a branch of cryptography dedicated to analyzing the application of stochastic algorithms, especially artificial neural network algorithms, for use in encryption and cryptanalysis. == Definition == Artificial neural networks are well known for their ability to selectively explore the solution space of a given problem. This feature finds a natural niche of application in the field of cryptanalysis. At the same time, neural networks offer a new approach to attack ciphering algorithms based on the principle that any function could be reproduced by a neural network, which is a powerful proven computational tool that can be used to find the inverse-function of any cryptographic algorithm. The ideas of mutual learning, self learning, and stochastic behavior of neural networks and similar algorithms can be used for different aspects of cryptography, like public-key cryptography, solving the key distribution problem using neural network mutual synchronization, hashing or generation of pseudo-random numbers. Another idea is the ability of a neural network to separate space in non-linear pieces using "bias". It gives different probabilities of activating the neural network or not. This is very useful in the case of Cryptanalysis. Two names are used to design the same domain of research: Neuro-Cryptography and Neural Cryptography. The first work that it is known on this topic can be traced back to 1995 in an IT Master Thesis. == Applications == In 1995, Sebastien Dourlens applied neural networks to cryptanalyze DES by allowing the networks to learn how to invert the S-tables of the DES. The bias in DES studied through Differential Cryptanalysis by Adi Shamir is highlighted. The experiment shows about 50% of the key bits can be found, allowing the complete key to be found in a short time. Hardware application with multi micro-controllers have been proposed due to the easy implementation of multilayer neural networks in hardware. One example of a public-key protocol is given by Khalil Shihab . He describes the decryption scheme and the public key creation that are based on a backpropagation neural network. The encryption scheme and the private key creation process are based on Boolean algebra. This technique has the advantage of small time and memory complexities. A disadvantage is the property of backpropagation algorithms: because of huge training sets, the learning phase of a neural network is very long. Therefore, the use of this protocol is only theoretical so far. == Neural key exchange protocol == The most used protocol for key exchange between two parties A and B in the practice is Diffie–Hellman key exchange protocol. Neural key exchange, which is based on the synchronization of two tree parity machines, should be a secure replacement for this method. Synchronizing these two machines is similar to synchronizing two chaotic oscillators in chaos communications. === Tree parity machine === The tree parity machine is a special type of multi-layer feedforward neural network. It consists of one output neuron, K hidden neurons and K×N input neurons. Inputs to the network take three values: x i j ∈ { − 1 , 0 , + 1 } {\displaystyle x_{ij}\in \left\{-1,0,+1\right\}} The weights between input and hidden neurons take the values: w i j ∈ { − L , . . . , 0 , . . . , + L } {\displaystyle w_{ij}\in \left\{-L,...,0,...,+L\right\}} Output value of each hidden neuron is calculated as a sum of all multiplications of input neurons and these weights: σ i = sgn ( ∑ j = 1 N w i j x i j ) {\displaystyle \sigma _{i}=\operatorname {sgn}(\sum _{j=1}^{N}w_{ij}x_{ij})} Signum is a simple function, which returns −1,0 or 1: sgn ( x ) = { − 1 if x < 0 , 0 if x = 0 , 1 if x > 0. {\displaystyle \operatorname {sgn}(x)={\begin{cases}-1&{\text{if }}x<0,\\0&{\text{if }}x=0,\\1&{\text{if }}x>0.\end{cases}}} If the scalar product is 0, the output of the hidden neuron is mapped to −1 in order to ensure a binary output value. The output of neural network is then computed as the multiplication of all values produced by hidden elements: τ = ∏ i = 1 K σ i {\displaystyle \tau =\prod _{i=1}^{K}\sigma _{i}} Output of the tree parity machine is binary. === Protocol === Each party (A and B) uses its own tree parity machine. Synchronization of the tree parity machines is achieved in these steps Initialize random weight values Execute these steps until the full synchronization is achieved Generate random input vector X Compute the values of the hidden neurons Compute the value of the output neuron Compare the values of both tree parity machines Outputs are the same: one of the suitable learning rules is applied to the weights Outputs are different: go to 2.1 After the full synchronization is achieved (the weights wij of both tree parity machines are same), A and B can use their weights as keys. This method is known as a bidirectional learning. One of the following learning rules can be used for the synchronization: Hebbian learning rule: w i + = g ( w i + σ i x i Θ ( σ i τ ) Θ ( τ A τ B ) ) {\displaystyle w_{i}^{+}=g(w_{i}+\sigma _{i}x_{i}\Theta (\sigma _{i}\tau )\Theta (\tau ^{A}\tau ^{B}))} Anti-Hebbian learning rule: w i + = g ( w i − σ i x i Θ ( σ i τ ) Θ ( τ A τ B ) ) {\displaystyle w_{i}^{+}=g(w_{i}-\sigma _{i}x_{i}\Theta (\sigma _{i}\tau )\Theta (\tau ^{A}\tau ^{B}))} Random walk: w i + = g ( w i + x i Θ ( σ i τ ) Θ ( τ A τ B ) ) {\displaystyle w_{i}^{+}=g(w_{i}+x_{i}\Theta (\sigma _{i}\tau )\Theta (\tau ^{A}\tau ^{B}))} Where: Θ ( a , b ) = 0 {\displaystyle \Theta (a,b)=0} if a ≠ b {\displaystyle a\neq b} otherwise Θ ( a , b ) = 1 {\displaystyle \Theta (a,b)=1} And: g ( x ) {\displaystyle g(x)} is a function that keeps the w i {\displaystyle w_{i}} in the range { − L , − L + 1 , . . . , 0 , . . . , L − 1 , L } {\displaystyle \{-L,-L+1,...,0,...,L-1,L\}} === Attacks and security of this protocol === In every attack it is considered, that the attacker E can eavesdrop messages between the parties A and B, but does not have an opportunity to change them. ==== Brute force ==== To provide a brute force attack, an attacker has to test all possible keys (all possible values of weights wij). By K hidden neurons, K×N input neurons and boundary of weights L, this gives (2L+1)KN possibilities. For example, the configuration K = 3, L = 3 and N = 100 gives us 310253 key possibilities, making the attack impossible with today's computer power. ==== Learning with own tree parity machine ==== One of the basic attacks can be provided by an attacker, who owns the same tree parity machine as the parties A and B. He wants to synchronize his tree parity machine with these two parties. In each step there are three situations possible: Output(A) ≠ Output(B): None of the parties updates its weights. Output(A) = Output(B) = Output(E): All the three parties update weights in their tree parity machines. Output(A) = Output(B) ≠ Output(E): Parties A and B update their tree parity machines, but the attacker can not do that. Because of this situation his learning is slower than the synchronization of parties A and B. It has been proven, that the synchronization of two parties is faster than learning of an attacker. It can be improved by increasing of the synaptic depth L of the neural network. That gives this protocol enough security and an attacker can find out the key only with small probability. ==== Other attacks ==== For conventional cryptographic systems, we can improve the security of the protocol by increasing of the key length. In the case of neural cryptography, we improve it by increasing of the synaptic depth L of the neural networks. Changing this parameter increases the cost of a successful attack exponentially, while the effort for the users grows polynomially. Therefore, breaking the security of neural key exchange belongs to the complexity class NP. Alexander Klimov, Anton Mityaguine, and Adi Shamir say that the original neural synchronization scheme can be broken by at least three different attacks—geometric, probabilistic analysis, and using genetic algorithms. Even though this particular implementation is insecure, the ideas behind chaotic synchronization could potentially lead to a secure implementation. === Permutation parity machine === The permutation parity machine is a binary variant of the tree parity machine. It consists of one input layer, one hidden layer and one output layer. The number of neurons in the output layer depends on the number of hidden units K. Each hidden neuron has N binary input neurons: x i j ∈ { 0 , 1 } {\displaystyle x_{ij}\in \left\{0,1\right\}} The weights between input and hidden neurons are also binary: w i j ∈ { 0 , 1 } {\displaystyle w_{ij}\in \left\{0,1\right\}} Output value of each hidden neuron is calculated as a sum of all exclusive disjunctions (exclusive or) of input neurons and these weights: σ i = θ N ( ∑ j = 1 N w i j ⊕ x i j ) {\displaystyle \sigma _{i}=\theta _{N}(\sum _{j=1}^{N}w_{ij}\oplus x_{ij})} (⊕ means XOR). Th
Cloud-to-cloud integration
Cloud-to-Cloud Integration ( C2I ) allows users to connect disparate cloud computing platforms. While Paas (Platform as a service) and Saas (Software as a service) continue to gain momentum, different vendors have different implementations for cloud computing, e.g. Database, REST, SOAP API. Another name for Cloud-to-Cloud Integration is Cloud-Surfing. See also Cloud-based integration
Correspondence analysis
Correspondence analysis (CA) is a multivariate statistical technique proposed by Herman Otto Hartley (Hirschfeld) and later developed by Jean-Paul Benzécri. It is conceptually similar to principal component analysis, but applies to categorical rather than continuous data. In a manner similar to principal component analysis, it provides a means of displaying or summarising a set of data in two-dimensional graphical form. Its aim is to display in a biplot any structure hidden in the multivariate setting of the data table. As such it is a technique from the field of multivariate ordination. Since the variant of CA described here can be applied either with a focus on the rows or on the columns it should in fact be called simple (symmetric) correspondence analysis. It is traditionally applied to the contingency table of a pair of nominal variables where each cell contains either a count or a zero value. If more than two categorical variables are to be summarized, a variant called multiple correspondence analysis should be chosen instead. CA may also be applied to binary data given the presence/absence coding represents simplified count data i.e. a 1 describes a positive count and 0 stands for a count of zero. Depending on the scores used CA preserves the chi-square distance between either the rows or the columns of the table. Because CA is a descriptive technique, it can be applied to tables regardless of a significant chi-squared test. Although the χ 2 {\displaystyle \chi ^{2}} statistic used in inferential statistics and the chi-square distance are computationally related they should not be confused since the latter works as a multivariate statistical distance measure in CA while the χ 2 {\displaystyle \chi ^{2}} statistic is in fact a scalar not a metric. == Details == Like principal components analysis, correspondence analysis creates orthogonal components (or axes) and, for each item in a table i.e. for each row, a set of scores (sometimes called factor scores, see Factor analysis). Correspondence analysis is performed on the data table, conceived as matrix C of size m × n where m is the number of rows and n is the number of columns. In the following mathematical description of the method capital letters in italics refer to a matrix while letters in italics refer to vectors. Understanding the following computations requires knowledge of matrix algebra. === Preprocessing === Before proceeding to the central computational step of the algorithm, the values in matrix C have to be transformed. First compute a set of weights for the columns and the rows (sometimes called masses), where row and column weights are given by the row and column vectors, respectively: w m = 1 n C C 1 , w n = 1 n C 1 T C . {\displaystyle w_{m}={\frac {1}{n_{C}}}C\mathbf {1} ,\quad w_{n}={\frac {1}{n_{C}}}\mathbf {1} ^{T}C.} Here n C = ∑ i = 1 n ∑ j = 1 m C i j {\displaystyle n_{C}=\sum _{i=1}^{n}\sum _{j=1}^{m}C_{ij}} is the sum of all cell values in matrix C, or short the sum of C, and 1 {\displaystyle \mathbf {1} } is a column vector of ones with the appropriate dimension. Put in simple words, w m {\displaystyle w_{m}} is just a vector whose elements are the row sums of C divided by the sum of C, and w n {\displaystyle w_{n}} is a vector whose elements are the column sums of C divided by the sum of C. The weights are transformed into diagonal matrices W m = diag ( 1 / w m ) {\displaystyle W_{m}=\operatorname {diag} (1/{\sqrt {w_{m}}})} and W n = diag ( 1 / w n ) {\displaystyle W_{n}=\operatorname {diag} (1/{\sqrt {w_{n}}})} where the diagonal elements of W n {\displaystyle W_{n}} are 1 / w n {\displaystyle 1/{\sqrt {w_{n}}}} and those of W m {\displaystyle W_{m}} are 1 / w m {\displaystyle 1/{\sqrt {w_{m}}}} respectively i.e. the vector elements are the inverses of the square roots of the masses. The off-diagonal elements are all 0. Next, compute matrix P {\displaystyle P} by dividing C {\displaystyle C} by its sum P = 1 n C C . {\displaystyle P={\frac {1}{n_{C}}}C.} In simple words, Matrix P {\displaystyle P} is just the data matrix (contingency table or binary table) transformed into portions i.e. each cell value is just the cell portion of the sum of the whole table. Finally, compute matrix S {\displaystyle S} , sometimes called the matrix of standardized residuals, by matrix multiplication as S = W m ( P − w m w n ) W n {\displaystyle S=W_{m}(P-w_{m}w_{n})W_{n}} Note, the vectors w m {\displaystyle w_{m}} and w n {\displaystyle w_{n}} are combined in an outer product resulting in a matrix of the same dimensions as P {\displaystyle P} . In words the formula reads: matrix outer ( w m , w n ) {\displaystyle \operatorname {outer} (w_{m},w_{n})} is subtracted from matrix P {\displaystyle P} and the resulting matrix is scaled (weighted) by the diagonal matrices W m {\displaystyle W_{m}} and W n {\displaystyle W_{n}} . Multiplying the resulting matrix by the diagonal matrices is equivalent to multiply the i-th row (or column) of it by the i-th element of the diagonal of W m {\displaystyle W_{m}} or W n {\displaystyle W_{n}} , respectively. === Interpretation of preprocessing === The vectors w m {\displaystyle w_{m}} and w n {\displaystyle w_{n}} are the row and column masses or the marginal probabilities for the rows and columns, respectively. Subtracting matrix outer ( w m , w n ) {\displaystyle \operatorname {outer} (w_{m},w_{n})} from matrix P {\displaystyle P} is the matrix algebra version of double centering the data. Multiplying this difference by the diagonal weighting matrices results in a matrix containing weighted deviations from the origin of a vector space. This origin is defined by matrix outer ( w m , w n ) {\displaystyle \operatorname {outer} (w_{m},w_{n})} . In fact matrix outer ( w m , w n ) {\displaystyle \operatorname {outer} (w_{m},w_{n})} is identical with the matrix of expected frequencies in the chi-squared test. Therefore S {\displaystyle S} is computationally related to the independence model used in that test. But since CA is not an inferential method the term independence model is inappropriate here. === Orthogonal components === The table S {\displaystyle S} is then decomposed by a singular value decomposition as S = U Σ V ∗ {\displaystyle S=U\Sigma V^{}\,} where U {\displaystyle U} and V {\displaystyle V} are the left and right singular vectors of S {\displaystyle S} and Σ {\displaystyle \Sigma } is a square diagonal matrix with the singular values σ i {\displaystyle \sigma _{i}} of S {\displaystyle S} on the diagonal. Σ {\displaystyle \Sigma } is of dimension p ≤ ( min ( m , n ) − 1 ) {\displaystyle p\leq (\min(m,n)-1)} hence U {\displaystyle U} is of dimension m×p and V {\displaystyle V} is of n×p. As orthonormal vectors U {\displaystyle U} and V {\displaystyle V} fulfill U ∗ U = V ∗ V = I {\displaystyle U^{}U=V^{}V=I} . In other words, the multivariate information that is contained in C {\displaystyle C} as well as in S {\displaystyle S} is now distributed across two (coordinate) matrices U {\displaystyle U} and V {\displaystyle V} and a diagonal (scaling) matrix Σ {\displaystyle \Sigma } . The vector space defined by them has as number of dimensions p, that is the smaller of the two values, number of rows and number of columns, minus 1. === Inertia === While a principal component analysis may be said to decompose the (co)variance, and hence its measure of success is the amount of (co-)variance covered by the first few PCA axes - measured in eigenvalue -, a CA works with a weighted (co-)variance which is called inertia. The sum of the squared singular values is the total inertia I {\displaystyle \mathrm {I} } of the data table, computed as I = ∑ i = 1 p σ i 2 . {\displaystyle \mathrm {I} =\sum _{i=1}^{p}\sigma _{i}^{2}.} The total inertia I {\displaystyle \mathrm {I} } of the data table can also computed directly from S {\displaystyle S} as I = ∑ i = 1 n ∑ j = 1 m s i j 2 . {\displaystyle \mathrm {I} =\sum _{i=1}^{n}\sum _{j=1}^{m}s_{ij}^{2}.} The amount of inertia covered by the i-th set of singular vectors is ι i {\displaystyle \iota _{i}} , the principal inertia. The higher the portion of inertia covered by the first few singular vectors i.e. the larger the sum of the principal inertiae in comparison to the total inertia, the more successful a CA is. Therefore, all principal inertia values are expressed as portion ϵ i {\displaystyle \epsilon _{i}} of the total inertia ϵ i = σ i 2 / ∑ i = 1 p σ i 2 {\displaystyle \epsilon _{i}=\sigma _{i}^{2}/\sum _{i=1}^{p}\sigma _{i}^{2}} and are presented in the form of a scree plot. In fact a scree plot is just a bar plot of all principal inertia portions ϵ i {\displaystyle \epsilon _{i}} . === Coordinates === To transform the singular vectors to coordinates which preserve the chi-square distances between rows or columns an additional weighting step is necessary. The resulting coordinates are called principal coordinates in CA text books. If principal coordinates are used for