Within statistics, Dynamic topic models' are generative models that can be used to analyze the evolution of (unobserved) topics of a collection of documents over time. This family of models was proposed by David Blei and John Lafferty and is an extension to Latent Dirichlet Allocation (LDA) that can handle sequential documents. In LDA, both the order the words appear in a document and the order the documents appear in the corpus are oblivious to the model. Whereas words are still assumed to be exchangeable, in a dynamic topic model the order of the documents plays a fundamental role. More precisely, the documents are grouped by time slice (e.g.: years) and it is assumed that the documents of each group come from a set of topics that evolved from the set of the previous slice. == Topics == Similarly to LDA and pLSA, in a dynamic topic model, each document is viewed as a mixture of unobserved topics. Furthermore, each topic defines a multinomial distribution over a set of terms. Thus, for each word of each document, a topic is drawn from the mixture and a term is subsequently drawn from the multinomial distribution corresponding to that topic. The topics, however, evolve over time. For instance, the two most likely terms of a topic at time t could be "network" and "Zipf" (in descending order) while the most likely ones at time t+1 could be "Zipf" and "percolation" (in descending order). == Model == Define α t {\displaystyle \alpha _{t}} as the per-document topic distribution at time t. β t , k {\displaystyle \beta _{t,k}} as the word distribution of topic k at time t. η t , d {\displaystyle \eta _{t,d}} as the topic distribution for document d in time t, z t , d , n {\displaystyle z_{t,d,n}} as the topic for the nth word in document d in time t, and w t , d , n {\displaystyle w_{t,d,n}} as the specific word. In this model, the multinomial distributions α t + 1 {\displaystyle \alpha _{t+1}} and β t + 1 , k {\displaystyle \beta _{t+1,k}} are generated from α t {\displaystyle \alpha _{t}} and β t , k {\displaystyle \beta _{t,k}} , respectively. Even though multinomial distributions are usually written in terms of the mean parameters, representing them in terms of the natural parameters is better in the context of dynamic topic models. The former representation has some disadvantages due to the fact that the parameters are constrained to be non-negative and sum to one. When defining the evolution of these distributions, one would need to assure that such constraints were satisfied. Since both distributions are in the exponential family, one solution to this problem is to represent them in terms of the natural parameters, that can assume any real value and can be individually changed. Using the natural parameterization, the dynamics of the topic model are given by β t , k | β t − 1 , k ∼ N ( β t − 1 , k , σ 2 I ) {\displaystyle \beta _{t,k}|\beta _{t-1,k}\sim N(\beta _{t-1,k},\sigma ^{2}I)} and α t | α t − 1 ∼ N ( α t − 1 , δ 2 I ) {\displaystyle \alpha _{t}|\alpha _{t-1}\sim N(\alpha _{t-1},\delta ^{2}I)} . The generative process at time slice 't' is therefore: Draw topics β t , k | β t − 1 , k ∼ N ( β t − 1 , k , σ 2 I ) ∀ k {\displaystyle \beta _{t,k}|\beta _{t-1,k}\sim N(\beta _{t-1,k},\sigma ^{2}I)\forall k} Draw mixture model α t | α t − 1 ∼ N ( α t − 1 , δ 2 I ) {\displaystyle \alpha _{t}|\alpha _{t-1}\sim N(\alpha _{t-1},\delta ^{2}I)} For each document: Draw η t , d ∼ N ( α t , a 2 I ) {\displaystyle \eta _{t,d}\sim N(\alpha _{t},a^{2}I)} For each word: Draw topic Z t , d , n ∼ Mult ( π ( η t , d ) ) {\displaystyle Z_{t,d,n}\sim {\textrm {Mult}}(\pi (\eta _{t,d}))} Draw word W t , d , n ∼ Mult ( π ( β t , Z t , d , n ) ) {\displaystyle W_{t,d,n}\sim {\textrm {Mult}}(\pi (\beta _{t,Z_{t,d,n}}))} where π ( x ) {\displaystyle \pi (x)} is a mapping from the natural parameterization x to the mean parameterization, namely π ( x i ) = exp ( x i ) ∑ i exp ( x i ) {\displaystyle \pi (x_{i})={\frac {\exp(x_{i})}{\sum _{i}\exp(x_{i})}}} . == Inference == In the dynamic topic model, only W t , d , n {\displaystyle W_{t,d,n}} is observable. Learning the other parameters constitutes an inference problem. Blei and Lafferty argue that applying Gibbs sampling to do inference in this model is more difficult than in static models, due to the nonconjugacy of the Gaussian and multinomial distributions. They propose the use of variational methods, in particular, the Variational Kalman Filtering and the Variational Wavelet Regression. == Applications == In the original paper, a dynamic topic model is applied to the corpus of Science articles published between 1881 and 1999 aiming to show that this method can be used to analyze the trends of word usage inside topics. The authors also show that the model trained with past documents is able to fit documents of an incoming year better than LDA. A continuous dynamic topic model was developed by Wang et al. and applied to predict the timestamp of documents. Going beyond text documents, dynamic topic models were used to study musical influence, by learning musical topics and how they evolve in recent history.
Army Chief Information Officer/G-6
In September 2020, the Army realigned the previously consolidated CIO/G-6 function into two separate roles, Office of the Chief Information Officer and Deputy Chief of Staff, G-6, that report to the secretary of the Army and chief of staff of the Army, respectively. The realignment came after several months of planning and coordination. Lt. Gen. John Morrison was nominated to the Senate for promotion and assignment as the G-6 and confirmed, assuming that position in August 2020. Subsequently, the Secretary of the Army, Ryan McCarthy appointed Dr. Raj G. Iyer as the first civilian Chief Information Officer, a career Senior Executive Service position in November 2020. == G-6 == Advise chief of staff of the Army and the Chief Information Officer on planning, fielding, and execution of C4IT worldwide Army operations Develop and execute the plan for the Unified Network Implement Army information assurance Supervise C4IT, Signal support, Information security, Force structure and equipping activities in support of warfighting operations Oversee management of the Signal forces == Planned realignment == On June 11, 2020, the Army announced that the two roles of CIO and Deputy Chief of Staff, G-6 (DCS, G-6) would be realigned no later than August 31, 2020, with separate individuals responsible for each position. With the realignment: CIO core functions will be policy, governance, and oversight. Focus areas include: Information Environment, Cybersecurity, Enterprise Architecture, and Data Policy/Oversight/Governance, Enterprise Architecture, Enterprise Cloud Management and IT Spend/Category Management. DCS, G-6 core functions will be planning, strategy, and implementation. Focus areas include: Information Environment/Network, Planning and Integration, Theater Synchronization, Architecture Integration, Enterprise Information Environment (EIE) Mission Area Portfolio Management and Mission Decision Packet Management. In order to support multi-domain operations, the Army will have to connect Enterprise networks and tactical networks. —LTG Morrison, DCS, G-6 DCS G-6 released the Army Unified Network Plan under the Army Digital Transformation Strategy, to help the Army to establish a Multi-Domain Operations capable force by 2028. The Unified Network will enable Army formations, as part of the Joint Force, to operate in highly contested and congested operational environments with the speed and global range to achieve decision dominance and maintain overmatch. The plan shapes, synchronizes, integrates and governs Unified Network efforts and aligns the personnel, organizational structure and capabilities required to enable MDO at all echelons. == Chief signal officers and their successors == Chief signal officers (1860–1964) Maj. Albert J. Myer 1860–1863 Lt. Col. William J. L. Nicodemus 1863–1864 Col. Benjamin F. Fisher 1864–1866 Col. Albert J. Myer 1866–1880 (promoted to brigadier general 16 June 1880) Brig. Gen. William B. Hazen 1880–1887 Brig. Gen. Adolphus W. Greely 1887–1906 Brig. Gen. James Allen 1906–1913 Brig. Gen. George P. Scriven 1913–1917 Brig. Gen. George O. Squier 1917–1923 (promoted to major general 6 October 1917) Maj. Gen. Charles McK. Saltzman 1924–1928 Maj. Gen. George Sabin Gibbs 1928–1931 Maj. Gen. Irving J. Carr 1931–1934 Maj. Gen. James B. Allison 1935–1937 Maj. Gen. Joseph O. Mauborgne 1937–1941 Maj. Gen. Dawson Olmstead 1941–1943 Maj. Gen. Harry C. Ingles 1943–1947 Maj. Gen. Spencer B. Akin 1947–1951 Maj. Gen. George I. Back 1951–1955 Lt. Gen. James D. O’Connell 1955–1959 Maj. Gen. Ralph T. Nelson 1959–1962 Maj. Gen. Earle F. Cook 1962–1963 Maj. Gen. David Parker Gibbs 1963–1964 Chiefs of communications-electronics (1964–1967) Maj. Gen. David Parker Gibbs 1964–1966 Maj. Gen. Walter E. Lotz, Jr. 1966–1967 Assistant chiefs of staff for communications-electronics (1967–1974) Maj. Gen. Walter E. Lotz, Jr. 1967–1968 Maj. Gen. George E. Pickett 1968–1972 Lt. Gen. Thomas Rienzi 1972–1974 Directors of telecommunications and command and control (1974–1978) (a directorate of ODCSOPS) Lt. Gen. Thomas Rienzi 1974–1977 Lt. Gen. Charles R. Myer 1977–1978 Assistant chiefs of staff for automation and communications (1978–1981) Lt. Gen. Charles R. Myer 1978–1979 Maj. Gen. Clay T. Buckingham 1979–1981 Assistant deputy chiefs of staff for operations and plans (command, control, communications, and computers) (1981–1984) Maj. Gen. Clay T. Buckingham 1981–1982 Maj. Gen. James M. Rockwell 1982–1984 Assistant chiefs of staff for information management (1984–1987) Lt. Gen. David K. Doyle 1984–1986 Lt. Gen. Thurman D. Rodgers 1986–1987 Directors of information systems for command, control, communications, and computers Lt. Gen. Thurman D. Rodgers 1987–1988 Lt. Gen. Bruce R. Harris 1988–1990 Lt. Gen. Jerome B. Hilmes 1990–1992 Lt. Gen. Peter A. Kind 1992–1994 Lt. Gen. Otto J. Guenther 1995–1997 Lt. Gen. William H. Campbell Chief Information Officer, Military Deputy to the Army Acquisition Executive, and Director of Information Systems for Command, Control, Communications and Computers Lt. Gen. William H. Campbell 1997–2000
Masking (art)
In art, craft, and engineering, masking is the use of materials to protect areas from change, or to focus change on other areas. This can describe either the techniques and materials used to control the development of a work of art by protecting a desired area from change; or a phenomenon that (either intentionally or unintentionally) causes a sensation to be concealed from conscious attention. The term is derived from the word mask, in the sense that it hides the face from view. == In painting == Masking materials supplement a painter's dexterity and choice of applicator to control where paint is laid. Examples include the use of a stencil or masking tape to protect areas which are not to be painted. === Solid masks === Most solid masks require an adhesive to hold the mask in place while work is performed. Some, such as masking tape and frisket, come with adhesive pre-applied. Solid masks are readily available in bulk, and are used in large painting jobs. Paper products Kraft paper Butcher paper Masking tape Plastic film Frisket Polyester tape Stencils Silk screen === Liquid masks === Liquid masks are preferred where precision is needed; they prevent paint from seeping underneath, resulting in clean edges. Care must be taken to remove them without damaging the work underneath. Latex or other polymers Molten wax Gesso, typically a substrate for painting, but can also be applied to achieve masking effects == In photography == Masks used for photography are used to enhance the quality of an image. Representations of a scene—whether film, video display, or printed—do not have the dynamic contrast range available to the human eye looking directly at the same scene. Adjusting the contrast in an image helps restore some of the perceived qualities of the original scene. These adjustments are typically performed on "blown-out" highlights, and "crushed" or "muddy" shadow areas, where clipping has occurred; or on desaturated colors. Photographic masks are peculiar in that they are produced from the image they will alter, an exercise in recursion. Masks used to produce other effects are similar to those used in painting. === Controlling exposure === ==== Film ==== The basic methods of controlling exposure are dodging and burning, which respectively lighten (reduce exposure) and darken (increase exposure) areas of an image. The tools a film photographer uses range from shaped pieces of black material (such as studio foil, foam, and paper) to the photographer's hands. To create a photographic mask, a sheet of negative film is contact-exposed to the original film negative or slide positive in a particular way. Both films are then combined to produce a processed positive. The process is similar when applied using digital techniques: the inverse of the working image is reduced to an image mask; filters or other adjustments are then applied, using the mask to selectively block portions of the image. ==== Digital ==== Image editors offer at the very least a "Select All" command and a rectangular "marquee" selection tool. (The word "marquee" describes the "crawling ants" border used to highlight the active region.) Once a selection is created, further changes to the image will be confined to that area. To continue editing the rest of the image, the selection is either "deselected" or the entire image is selected. Advanced suites offer more ways to select portions of an image, as well as ways to combine these selections through. Selection masks can be switched between an editable greyscale image and a mask. They allow the user to create a mask using the suite's painting tools. === Contrast masking === When the contrast range of an image needs to be adjusted, a contrast mask is a simple solution. The processed image resembles what would be achieved when exposing through a neutral density filter, but the effects are focused highly upon the extreme regions of the image. The blocking areas of the mask coincide with the highlights of the image, and the permissive areas with the shadows, resulting in more detail appearing in each. ==== Film ==== The mask is often made from high-quality black-and-white film, such as Kodak Technical Pan, which allows for a degree of softening on the mask. Its processing time is reduced so as to not completely oppose the original negative. Both negatives are combined and registered, and collectively exposed with additional time to compensate for the presence of the mask. ==== Digital ==== Contrast masking is made simpler with digital editing. A grayscale version of the image is produced, either by desaturation or by calculating selected ratios of the image's color channels, inverted, and blurred. The mask and original image are blended together to produce the final processed image. Some image editors allow for refinement of the effect by changing the strength of the blend. Contrast masking can be considered to be the opposite of gamma correction, which adjusts the midtones of an image. Effects similar to contrast masking can be achieved by adjusting the response curves of an image. === Unsharp masking === A derivative of contrast masking is unsharp masking, an unusual term for a process intended to increase the apparent sharpness (acutance) of an image. Unsharp masking uses a blurred form of the image to increase contrast along regions of moderate contrast difference. Around edges, the blur region causes highlights to overexpose and shadows to underexpose. Taken to an extreme, the edges become overly visible and detract from the quality of the image—this is referred to as halation. Unsharp masking does not increase the actual sharpness, as it cannot recover details lost to blurring. ==== Film ==== Unsharp masking allows the photographer to sharpen areas that have become blurred in the original negative, due to long shutter speed/exposure time, or from using a wide aperture/"fast" lens. When creating the unsharp mask, extra space or diffusing material is added between the image and the mask to produce the necessary blur. ==== Digital ==== Unsharp masking has become automated in digital editing, with higher-end suites offering the process as a "tool" or "filter" in their standard sharpening kits—the actual creation of a mask is bypassed in favor of calculations that represent the mask's effect. The process depends on three factors: the radius of the blur, the strength of the effect, and the threshold degree of contrast above which the effect will be applied. (Adjusting the threshold allows the editor to apply the effect selectively upon moderately defined edges and ignore image noise.) Unsharp masking is computationally more complex than other sharpening algorithms, but results in a higher-quality remedy. Deconvolution allows for truer sharpening, but is much more complex than unsharp masking.
Enterprise mobile application
The term enterprise mobile application is used in the context of mobile apps created/brought by individual organizations for their workers to carry out the functions required to run the organization. It is the process of building a mobile application for the requirements of an enterprise. An enterprise mobile application belonging to an organization is expected to be used by only the workers of that organization. The definition of enterprise mobile application does not include the mobile apps that an organization create for its customers or consumers of the products or services generated by the organization. == Example == An organization, whether for-profit or non-profit, may create a mobile app for its members to track inventory levels of supplies they distribute to their target communities or materials used in product manufacturing. Such a mobile app comes under the definition of enterprise mobile application. However, the same organization may also create another mobile app to sell their products to end users or spread awareness of their services to various communities, and that mobile app would not come under definition of enterprise mobile application. == Enterprise mobile solution providers == Enterprise Mobile solution providers create and develop apps for individual organizations that can buy instead of creating the apps themselves. Reasons for Organizations buying the apps include time and cost savings, technical expertise. Today Enterprise Mobility is playing track role for enterprise transformation. Today, enterprises needs productivity is a fast way. Enterprise mobility helps business owners to build their work in a progressive way by assisting enterprise mobility solutions.
Tensor operator
In pure and applied mathematics, quantum mechanics and computer graphics, a tensor operator generalizes the notion of operators which are scalars and vectors. A special class of these are spherical tensor operators which apply the notion of the spherical basis and spherical harmonics. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. The coordinate-free generalization of a tensor operator is known as a representation operator. == The general notion of scalar, vector, and tensor operators == In quantum mechanics, physical observables that are scalars, vectors, and tensors, must be represented by scalar, vector, and tensor operators, respectively. Whether something is a scalar, vector, or tensor depends on how it is viewed by two observers whose coordinate frames are related to each other by a rotation. Alternatively, one may ask how, for a single observer, a physical quantity transforms if the state of the system is rotated. Consider, for example, a system consisting of a molecule of mass M {\displaystyle M} , traveling with a definite center of mass momentum, p z ^ {\displaystyle p{\mathbf {\hat {z}} }} , in the z {\displaystyle z} direction. If we rotate the system by 90 ∘ {\displaystyle 90^{\circ }} about the y {\displaystyle y} axis, the momentum will change to p x ^ {\displaystyle p{\mathbf {\hat {x}} }} , which is in the x {\displaystyle x} direction. The center-of-mass kinetic energy of the molecule will, however, be unchanged at p 2 / 2 M {\displaystyle p^{2}/2M} . The kinetic energy is a scalar and the momentum is a vector, and these two quantities must be represented by a scalar and a vector operator, respectively. By the latter in particular, we mean an operator whose expected values in the initial and the rotated states are p z ^ {\displaystyle p{\mathbf {\hat {z}} }} and p x ^ {\displaystyle p{\mathbf {\hat {x}} }} . The kinetic energy on the other hand must be represented by a scalar operator, whose expected value must be the same in the initial and the rotated states. In the same way, tensor quantities must be represented by tensor operators. An example of a tensor quantity (of rank two) is the electrical quadrupole moment of the above molecule. Likewise, the octupole and hexadecapole moments would be tensors of rank three and four, respectively. Other examples of scalar operators are the total energy operator (more commonly called the Hamiltonian), the potential energy, and the dipole-dipole interaction energy of two atoms. Examples of vector operators are the momentum, the position, the orbital angular momentum, L {\displaystyle {\mathbf {L} }} , and the spin angular momentum, S {\displaystyle {\mathbf {S} }} . (Fine print: Angular momentum is a vector as far as rotations are concerned, but unlike position or momentum it does not change sign under space inversion, and when one wishes to provide this information, it is said to be a pseudovector.) Scalar, vector and tensor operators can also be formed by products of operators. For example, the scalar product L ⋅ S {\displaystyle {\mathbf {L} }\cdot {\mathbf {S} }} of the two vector operators, L {\displaystyle {\mathbf {L} }} and S {\displaystyle {\mathbf {S} }} , is a scalar operator, which figures prominently in discussions of the spin–orbit interaction. Similarly, the quadrupole moment tensor of our example molecule has the nine components Q i j = ∑ α q α ( 3 r α , i r α , j − r α 2 δ i j ) . {\displaystyle Q_{ij}=\sum _{\alpha }q_{\alpha }\left(3r_{\alpha ,i}r_{\alpha ,j}-r_{\alpha }^{2}\delta _{ij}\right).} Here, the indices i {\displaystyle i} and j {\displaystyle j} can independently take on the values 1, 2, and 3 (or x {\displaystyle x} , y {\displaystyle y} , and z {\displaystyle z} ) corresponding to the three Cartesian axes, the index α {\displaystyle \alpha } runs over all particles (electrons and nuclei) in the molecule, q α {\displaystyle q_{\alpha }} is the charge on particle α {\displaystyle \alpha } , and r α , i {\displaystyle r_{\alpha ,i}} is the i {\displaystyle i} -th component of the position of this particle. Each term in the sum is a tensor operator. In particular, the nine products r α , i r α , j {\displaystyle r_{\alpha ,i}r_{\alpha ,j}} together form a second rank tensor, formed by taking the outer product of the vector operator r α {\displaystyle {\mathbf {r} }_{\alpha }} with itself. == Rotations of quantum states == === Quantum rotation operator === The rotation operator about the unit vector n (defining the axis of rotation) through angle θ is U [ R ( θ , n ^ ) ] = exp ( − i θ ℏ n ^ ⋅ J ) {\displaystyle U[R(\theta ,{\hat {\mathbf {n} }})]=\exp \left(-{\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right)} where J = (Jx, Jy, Jz) are the rotation generators (also the angular momentum matrices): J x = ℏ 2 ( 0 1 0 1 0 1 0 1 0 ) J y = ℏ 2 ( 0 i 0 − i 0 i 0 − i 0 ) J z = ℏ ( − 1 0 0 0 0 0 0 0 1 ) {\displaystyle J_{x}={\frac {\hbar }{\sqrt {2}}}{\begin{pmatrix}0&1&0\\1&0&1\\0&1&0\end{pmatrix}}\,\quad J_{y}={\frac {\hbar }{\sqrt {2}}}{\begin{pmatrix}0&i&0\\-i&0&i\\0&-i&0\end{pmatrix}}\,\quad J_{z}=\hbar {\begin{pmatrix}-1&0&0\\0&0&0\\0&0&1\end{pmatrix}}} and let R ^ = R ^ ( θ , n ^ ) {\displaystyle {\widehat {R}}={\widehat {R}}(\theta ,{\hat {\mathbf {n} }})} be a rotation matrix. According to the Rodrigues' rotation formula, the rotation operator then amounts to U [ R ( θ , n ^ ) ] = 1 1 − i sin θ ℏ n ^ ⋅ J − 1 − cos θ ℏ 2 ( n ^ ⋅ J ) 2 . {\displaystyle U[R(\theta ,{\hat {\mathbf {n} }})]=1\!\!1-{\frac {i\sin \theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} -{\frac {1-\cos \theta }{\hbar ^{2}}}({\hat {\mathbf {n} }}\cdot \mathbf {J} )^{2}.} An operator Ω ^ {\displaystyle {\widehat {\Omega }}} is invariant under a unitary transformation U if Ω ^ = U † Ω ^ U ; {\displaystyle {\widehat {\Omega }}={U}^{\dagger }{\widehat {\Omega }}U;} in this case for the rotation U ^ ( R ) {\displaystyle {\widehat {U}}(R)} , Ω ^ = U ( R ) † Ω ^ U ( R ) = exp ( i θ ℏ n ^ ⋅ J ) Ω ^ exp ( − i θ ℏ n ^ ⋅ J ) . {\displaystyle {\widehat {\Omega }}={U(R)}^{\dagger }{\widehat {\Omega }}U(R)=\exp \left({\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right){\widehat {\Omega }}\exp \left(-{\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right).} === Angular momentum eigenkets === The orthonormal basis set for total angular momentum is | j , m ⟩ {\displaystyle |j,m\rangle } , where j is the total angular momentum quantum number and m is the magnetic angular momentum quantum number, which takes values −j, −j + 1, ..., j − 1, j. A general state within the j subspace | ψ ⟩ = ∑ m c j m | j , m ⟩ {\displaystyle |\psi \rangle =\sum _{m}c_{jm}|j,m\rangle } rotates to a new state by: | ψ ¯ ⟩ = U ( R ) | ψ ⟩ = ∑ m c j m U ( R ) | j , m ⟩ {\displaystyle |{\bar {\psi }}\rangle =U(R)|\psi \rangle =\sum _{m}c_{jm}U(R)|j,m\rangle } Using the completeness condition: I = ∑ m ′ | j , m ′ ⟩ ⟨ j , m ′ | {\displaystyle I=\sum _{m'}|j,m'\rangle \langle j,m'|} we have | ψ ¯ ⟩ = I U ( R ) | ψ ⟩ = ∑ m m ′ c j m | j , m ′ ⟩ ⟨ j , m ′ | U ( R ) | j , m ⟩ {\displaystyle |{\bar {\psi }}\rangle =IU(R)|\psi \rangle =\sum _{mm'}c_{jm}|j,m'\rangle \langle j,m'|U(R)|j,m\rangle } Introducing the Wigner D matrix elements: D ( R ) m ′ m ( j ) = ⟨ j , m ′ | U ( R ) | j , m ⟩ {\displaystyle {D(R)}_{m'm}^{(j)}=\langle j,m'|U(R)|j,m\rangle } gives the matrix multiplication: | ψ ¯ ⟩ = ∑ m m ′ c j m D m ′ m ( j ) | j , m ′ ⟩ ⇒ | ψ ¯ ⟩ = D ( j ) | ψ ⟩ {\displaystyle |{\bar {\psi }}\rangle =\sum _{mm'}c_{jm}D_{m'm}^{(j)}|j,m'\rangle \quad \Rightarrow \quad |{\bar {\psi }}\rangle =D^{(j)}|\psi \rangle } For one basis ket: | j , m ¯ ⟩ = ∑ m ′ D ( R ) m ′ m ( j ) | j , m ′ ⟩ {\displaystyle |{\overline {j,m}}\rangle =\sum _{m'}{D(R)}_{m'm}^{(j)}|j,m'\rangle } For the case of orbital angular momentum, the eigenstates | ℓ , m ⟩ {\displaystyle |\ell ,m\rangle } of the orbital angular momentum operator L and solutions of Laplace's equation on a 3d sphere are spherical harmonics: Y ℓ m ( θ , ϕ ) = ⟨ θ , ϕ | ℓ , m ⟩ = ( 2 ℓ + 1 ) 4 π ( ℓ − m ) ! ( ℓ + m ) ! P ℓ m ( cos θ ) e i m ϕ {\displaystyle Y_{\ell }^{m}(\theta ,\phi )=\langle \theta ,\phi |\ell ,m\rangle ={\sqrt {{(2\ell +1) \over 4\pi }{(\ell -m)! \over (\ell +m)!}}}\,P_{\ell }^{m}(\cos {\theta })\,e^{im\phi }} where Pℓm is an associated Legendre polynomial, ℓ is the orbital angular momentum quantum number, and m is the orbital magnetic quantum number which takes the values −ℓ, −ℓ + 1, ... ℓ − 1, ℓ The formalism of spherical harmonics have wide applications in applied mathematics, and are closely related to the formalism of spherical tensors, as shown below. Spherical harmonics are functions of the polar and azimuthal angles, ϕ and θ respectively, which can be conveniently collected into a unit vector n(θ, ϕ) pointing in the direction of those angles, in the Cartesian basis it is: n ^ ( θ , ϕ ) = cos ϕ sin θ e x + s
Tandem (app)
Tandem is a mobile language exchange and language learning app. == History == Tandem was founded in Hannover, Germany in 2014 by Arnd Aschentrup, Tobias Dickmeis, and Matthias Kleimann. Prior to founding Tandem, the trio had launched Vive, a members-only mobile video chat platform. Tandem has been criticised for not accepting members into the community immediately, as opposed to competitors including HelloTalk, Speaky or Cafehub. In some countries, there is a waiting list and applicants can wait up to seven days for their application to be processed by human moderators. In 2015, Tandem completed its first funding round (seed funding) of €600,000. Participating investors included business angels such as Atlantic Labs (Christophe Maire), Hannover Beteiligungsfonds, Marcus Englert (Chairman of the Supervisory Board of Rocket Internet SE ), Catagonia, Ludwig zu Salm, Florian Langenscheidt, Heiko Hubertz, Martin Sinner, and Zehden Enterprises. In 2016, the company received a further €2 million from new investors Rubylight and Faber Ventures, as well as from existing investors Hannover Beteiligungsfonds, Atlantic Labs, and Zehden Enterprises. Since 2018, the premium membership Tandem Pro has been available, which offers members unlimited access to all language learning features of the app as well as the removal of advertising for a monthly fee.
Voice user interface
A voice user interface (VUI) enables spoken human interaction with computers, using speech recognition to understand spoken commands and answer questions, and typically text to speech to play a reply. A voice command device is a device controlled with a voice user interface. Voice user interfaces have been added to automobiles, home automation systems, computer operating systems, home appliances like washing machines and microwave ovens, and television remote controls. They are the primary way of interacting with virtual assistants on smartphones and smart speakers. Older automated attendants (which route phone calls to the correct extension) and interactive voice response systems (which conduct more complicated transactions over the phone) can respond to the pressing of keypad buttons via DTMF tones, but those with a full voice user interface allow callers to speak requests and responses without having to press any buttons. Newer voice command devices are speaker-independent, so they can respond to multiple voices, regardless of accent or dialectal influences. They are also capable of responding to several commands at once, separating vocal messages, and providing appropriate feedback, accurately imitating a natural conversation. == Overview == A VUI is the interface to any speech application. Only a short time ago, controlling a machine by simply talking to it was only possible in science fiction. Until recently, this area was considered to be artificial intelligence. However, advances in technologies like text-to-speech, speech-to-text, natural language processing, and cloud services contributed to the mass adoption of these types of interfaces. VUIs have become more commonplace, and people are taking advantage of the value that these hands-free, eyes-free interfaces provide in many situations. VUIs rely on the ability to process input reliably, inconsistent performance often leads to decreased user engagement and negative feedback. Designing a good VUI requires interdisciplinary talents of computer science, linguistics and human factors such as psychology. Even with advanced development tools, constructing an effective VUI requires understanding of both the tasks to be performed, as well as the target audience that will use the final system. The closer the VUI matches the user's mental model of the task, the easier it will be to use with little or no training, resulting in both higher efficiency and higher user satisfaction. A VUI designed for the general public should emphasize ease of use and provide a lot of help and guidance for first-time callers. In contrast, a VUI designed for a small group of power users (including field service workers), should focus more on productivity and less on help and guidance. Such applications should streamline the call flows, minimize prompts, eliminate unnecessary iterations and allow elaborate "mixed initiative dialogs", which enable callers to enter several pieces of information in a single utterance and in any order or combination. In short, speech applications have to be carefully crafted for the specific business process that is being automated. Not all business processes render themselves equally well for speech automation. In general, the more complex the inquiries and transactions are, the more challenging they will be to automate, and the more likely they will be to fail with the general public. In some scenarios, automation is simply not applicable, so live agent assistance is the only option. A legal advice hotline, for example, would be very difficult to automate. On the flip side, speech is perfect for handling quick and routine transactions, like changing the status of a work order, completing a time or expense entry, or transferring funds between accounts. == History == Early applications for VUI included voice-activated dialing of phones, either directly or through a (typically Bluetooth) headset or vehicle audio system. In 2007, a CNN business article reported that voice command was over a billion dollar industry and that companies like Google and Apple were trying to create speech recognition features. In the years since the article was published, the world has witnessed a variety of voice command devices. Additionally, Google has created a speech recognition engine called Pico TTS and Apple released Siri. Voice command devices are becoming more widely available, and innovative ways for using the human voice are always being created. For example, Business Week suggests that the future remote controller is going to be the human voice. Currently Xbox Live allows such features and Jobs hinted at such a feature on the new Apple TV. == Voice command software products on computing devices == Both Apple Mac and Windows PC provide built in speech recognition features for their latest operating systems. === Microsoft Windows === Two Microsoft operating systems, Windows 7 and Windows Vista, provide speech recognition capabilities. Microsoft integrated voice commands into their operating systems to provide a mechanism for people who want to limit their use of the mouse and keyboard, but still want to maintain or increase their overall productivity. ==== Windows Vista ==== With Windows Vista voice control, a user may dictate documents and emails in mainstream applications, start and switch between applications, control the operating system, format documents, save documents, edit files, efficiently correct errors, and fill out forms on the Web. The speech recognition software learns automatically every time a user uses it, and speech recognition is available in English (U.S.), English (U.K.), German (Germany), French (France), Spanish (Spain), Japanese, Chinese (Traditional), and Chinese (Simplified). In addition, the software comes with an interactive tutorial, which can be used to train both the user and the speech recognition engine. ==== Windows 7 ==== In addition to all the features provided in Windows Vista, Windows 7 provides a wizard for setting up the microphone and a tutorial on how to use the feature. ==== Mac OS X ==== All Mac OS X computers come pre-installed with the speech recognition software. The software is user-independent, and it allows for a user to, "navigate menus and enter keyboard shortcuts; speak checkbox names, radio button names, list items, and button names; and open, close, control, and switch among applications." However, the Apple website recommends a user buy a commercial product called Dictate. === Commercial products === If a user is not satisfied with the built in speech recognition software or a user does not have a built speech recognition software for their OS, then a user may experiment with a commercial product such as Braina Pro or DragonNaturallySpeaking for Windows PCs, and Dictate, the name of the same software for Mac OS. == Voice command mobile devices == Any mobile device running Android OS, Microsoft Windows Phone, iOS 9 or later, or Blackberry OS provides voice command capabilities. In addition to the built-in speech recognition software for each mobile phone's operating system, a user may download third party voice command applications from each operating system's application store: Apple App store, Google Play, Windows Phone Marketplace (initially Windows Marketplace for Mobile), or BlackBerry App World. === Android OS === Google has developed an open source operating system called Android, which allows a user to perform voice commands such as: send text messages, listen to music, get directions, call businesses, call contacts, send email, view a map, go to websites, write a note, and search Google. The speech recognition software is available for all devices since Android 2.2 "Froyo", but the settings must be set to English. Google allows for the user to change the language, and the user is prompted when he or she first uses the speech recognition feature if he or she would like their voice data to be attached to their Google account. If a user decides to opt into this service, it allows Google to train the software to the user's voice. Google introduced the Google Assistant with Android 7.0 "Nougat". It is much more advanced than the older version. Amazon.com has the Echo that uses Amazon's custom version of Android to provide a voice interface. === Microsoft Windows === Windows Phone is Microsoft's mobile device's operating system. On Windows Phone 7.5, the speech app is user independent and can be used to: call someone from your contact list, call any phone number, redial the last number, send a text message, call your voice mail, open an application, read appointments, query phone status, and search the web. In addition, speech can also be used during a phone call, and the following actions are possible during a phone call: press a number, turn the speaker phone on, or call someone, which puts the current call on hold. Windows 10 introduces Cortana, a voice control system that replaces the formerly used voice control on Windows