In the areas of computer vision, image analysis and signal processing, the notion of scale-space representation is used for processing measurement data at multiple scales, and specifically enhance or suppress image features over different ranges of scale (see the article on scale space). A special type of scale-space representation is provided by the Gaussian scale space, where the image data in N dimensions is subjected to smoothing by Gaussian convolution. Most of the theory for Gaussian scale space deals with continuous images, whereas one when implementing this theory will have to face the fact that most measurement data are discrete. Hence, the theoretical problem arises concerning how to discretize the continuous theory while either preserving or well approximating the desirable theoretical properties that lead to the choice of the Gaussian kernel (see the article on scale-space axioms). This article describes basic approaches for this that have been developed in the literature, see also for an in-depth treatment regarding the topic of approximating the Gaussian smoothing operation and the Gaussian derivative computations in scale-space theory, and for a complementary treatment regarding hybrid discretization methods. == Statement of the problem == The Gaussian scale-space representation of an N-dimensional continuous signal, f C ( x 1 , ⋯ , x N , t ) , {\displaystyle f_{C}\left(x_{1},\cdots ,x_{N},t\right),} is obtained by convolving fC with an N-dimensional Gaussian kernel: g N ( x 1 , ⋯ , x N , t ) . {\displaystyle g_{N}\left(x_{1},\cdots ,x_{N},t\right).} In other words: L ( x 1 , ⋯ , x N , t ) = ∫ u 1 = − ∞ ∞ ⋯ ∫ u N = − ∞ ∞ f C ( x 1 − u 1 , ⋯ , x N − u N , t ) ⋅ g N ( u 1 , ⋯ , u N , t ) d u 1 ⋯ d u N . {\displaystyle L\left(x_{1},\cdots ,x_{N},t\right)=\int _{u_{1}=-\infty }^{\infty }\cdots \int _{u_{N}=-\infty }^{\infty }f_{C}\left(x_{1}-u_{1},\cdots ,x_{N}-u_{N},t\right)\cdot g_{N}\left(u_{1},\cdots ,u_{N},t\right)\,du_{1}\cdots du_{N}.} However, for implementation, this definition is impractical, since it is continuous. When applying the scale space concept to a discrete signal fD, different approaches can be taken. This article is a brief summary of some of the most frequently used methods. == Separability == Using the separability property of the Gaussian kernel g N ( x 1 , … , x N , t ) = G ( x 1 , t ) ⋯ G ( x N , t ) {\displaystyle g_{N}\left(x_{1},\dots ,x_{N},t\right)=G\left(x_{1},t\right)\cdots G\left(x_{N},t\right)} the N-dimensional convolution operation can be decomposed into a set of separable smoothing steps with a one-dimensional Gaussian kernel G along each dimension L ( x 1 , ⋯ , x N , t ) = ∫ u 1 = − ∞ ∞ ⋯ ∫ u N = − ∞ ∞ f C ( x 1 − u 1 , ⋯ , x N − u N , t ) G ( u 1 , t ) d u 1 ⋯ G ( u N , t ) d u N , {\displaystyle L(x_{1},\cdots ,x_{N},t)=\int _{u_{1}=-\infty }^{\infty }\cdots \int _{u_{N}=-\infty }^{\infty }f_{C}(x_{1}-u_{1},\cdots ,x_{N}-u_{N},t)G(u_{1},t)\,du_{1}\cdots G(u_{N},t)\,du_{N},} where G ( x , t ) = 1 2 π t e − x 2 2 t {\displaystyle G(x,t)={\frac {1}{\sqrt {2\pi t}}}e^{-{\frac {x^{2}}{2t}}}} and the standard deviation of the Gaussian σ is related to the scale parameter t according to t = σ2. Separability will be assumed in all that follows, even when the kernel is not exactly Gaussian, since separation of the dimensions is the most practical way to implement multidimensional smoothing, especially at larger scales. Therefore, the rest of the article focuses on the one-dimensional case. == The sampled Gaussian kernel == When implementing the one-dimensional smoothing step in practice, the presumably simplest approach is to convolve the discrete signal fD with a sampled Gaussian kernel: L ( x , t ) = ∑ n = − ∞ ∞ f ( x − n ) G ( n , t ) {\displaystyle L(x,t)=\sum _{n=-\infty }^{\infty }f(x-n)\,G(n,t)} where G ( n , t ) = 1 2 π t e − n 2 2 t {\displaystyle G(n,t)={\frac {1}{\sqrt {2\pi t}}}e^{-{\frac {n^{2}}{2t}}}} (with t = σ2) which in turn is truncated at the ends to give a filter with finite impulse response L ( x , t ) = ∑ n = − M M f ( x − n ) G ( n , t ) {\displaystyle L(x,t)=\sum _{n=-M}^{M}f(x-n)\,G(n,t)} for M chosen sufficiently large (see error function) such that 2 ∫ M ∞ G ( u , t ) d u = 2 ∫ M t ∞ G ( v , 1 ) d v < ε . {\displaystyle 2\int _{M}^{\infty }G(u,t)\,du=2\int _{\frac {M}{\sqrt {t}}}^{\infty }G(v,1)\,dv<\varepsilon .} A common choice is to set M to a constant C times the standard deviation of the Gaussian kernel M = C σ + 1 = C t + 1 {\displaystyle M=C\sigma +1=C{\sqrt {t}}+1} where C is often chosen somewhere between 3 and 6. Using the sampled Gaussian kernel can, however, lead to implementation problems, in particular when computing higher-order derivatives at finer scales by applying sampled derivatives of Gaussian kernels. When accuracy and robustness are primary design criteria, alternative implementation approaches should therefore be considered. For small values of ε (10−6 to 10−8) the errors introduced by truncating the Gaussian are usually negligible. For larger values of ε, however, there are many better alternatives to a rectangular window function. For example, for a given number of points, a Hamming window, Blackman window, or Kaiser window will do less damage to the spectral and other properties of the Gaussian than a simple truncation will. Notwithstanding this, since the Gaussian kernel decreases rapidly at the tails, the main recommendation is still to use a sufficiently small value of ε such that the truncation effects are no longer important. == The discrete Gaussian kernel == A more refined approach is to convolve the original signal with the discrete Gaussian kernel T(n, t) L ( x , t ) = ∑ n = − ∞ ∞ f ( x − n ) T ( n , t ) {\displaystyle L(x,t)=\sum _{n=-\infty }^{\infty }f(x-n)\,T(n,t)} where T ( n , t ) = e − t I n ( t ) {\displaystyle T(n,t)=e^{-t}I_{n}(t)} and I n ( t ) {\displaystyle I_{n}(t)} denotes the modified Bessel functions of integer order, n. This is the discrete counterpart of the continuous Gaussian in that it is the solution to the discrete diffusion equation (discrete space, continuous time), just as the continuous Gaussian is the solution to the continuous diffusion equation. This filter can be truncated in the spatial domain as for the sampled Gaussian L ( x , t ) = ∑ n = − M M f ( x − n ) T ( n , t ) {\displaystyle L(x,t)=\sum _{n=-M}^{M}f(x-n)\,T(n,t)} or can be implemented in the Fourier domain using a closed-form expression for its discrete-time Fourier transform: T ^ ( θ , t ) = ∑ n = − ∞ ∞ T ( n , t ) e − i θ n = e t ( cos θ − 1 ) . {\displaystyle {\widehat {T}}(\theta ,t)=\sum _{n=-\infty }^{\infty }T(n,t)\,e^{-i\theta n}=e^{t(\cos \theta -1)}.} With this frequency-domain approach, the scale-space properties transfer exactly to the discrete domain, or with excellent approximation using periodic extension and a suitably long discrete Fourier transform to approximate the discrete-time Fourier transform of the signal being smoothed. Moreover, higher-order derivative approximations can be computed in a straightforward manner (and preserving scale-space properties) by applying small support central difference operators to the discrete scale space representation. As with the sampled Gaussian, a plain truncation of the infinite impulse response will in most cases be a sufficient approximation for small values of ε, while for larger values of ε it is better to use either a decomposition of the discrete Gaussian into a cascade of generalized binomial filters or alternatively to construct a finite approximate kernel by multiplying by a window function. If ε has been chosen too large such that effects of the truncation error begin to appear (for example as spurious extrema or spurious responses to higher-order derivative operators), then the options are to decrease the value of ε such that a larger finite kernel is used, with cutoff where the support is very small, or to use a tapered window. == Recursive filters == Since computational efficiency is often important, low-order recursive filters are often used for scale-space smoothing. For example, Young and van Vliet use a third-order recursive filter with one real pole and a pair of complex poles, applied forward and backward to make a sixth-order symmetric approximation to the Gaussian with low computational complexity for any smoothing scale. By relaxing a few of the axioms, Lindeberg concluded that good smoothing filters would be "normalized Pólya frequency sequences", a family of discrete kernels that includes all filters with real poles at 0 < Z < 1 and/or Z > 1, as well as with real zeros at Z < 0. For symmetry, which leads to approximate directional homogeneity, these filters must be further restricted to pairs of poles and zeros that lead to zero-phase filters. To match the transfer function curvature at zero frequency of the discrete Gaussian, which ensures an approximate semi-group property of additive t, two poles at Z = 1 + 2 t − ( 1 + 2 t ) 2 − 1 {\displaystyle
Confused deputy problem
In information security, a confused deputy is a computer program that is tricked by another program (with fewer privileges or less rights) into misusing its authority on the system. It is a specific type of privilege escalation. The confused deputy problem is often cited as an example of why capability-based security is important. Capability systems protect against the confused deputy problem, whereas access-control list–based systems do not. Such systems can mitigate the confused deputy problem by eliminating ambient authority, allowing programs to act only on resources for which they hold explicit capabilities, whereas access-control list–based systems are more susceptible to it. However, this protection depends on correct implementation; in formally verified capability systems such as seL4, it can be shown that the kernel enforces capability constraints correctly, preventing such behavior at the system level. == Example == In the original example of a confused deputy, there was a compiler program provided on a commercial timesharing service. Users could run the compiler and optionally specify a filename where it would write debugging output, and the compiler would be able to write to that file if the user had permission to write there. The compiler also collected statistics about language feature usage. Those statistics were stored in a file called "(SYSX)STAT", in the directory "SYSX". To make this possible, the compiler program was given permission to write to files in SYSX. But there were other files in SYSX: in particular, the system's billing information was stored in a file "(SYSX)BILL". A user ran the compiler and named "(SYSX)BILL" as the desired debugging output file. This produced a confused deputy problem. The compiler made a request to the operating system to open (SYSX)BILL. Even though the user did not have access to that file, the compiler did, so the open succeeded. The compiler wrote the compilation output to the file (here "(SYSX)BILL") as normal, overwriting it, and the billing information was destroyed. === The confused deputy === In this example, the compiler program is the deputy because it is acting at the request of the user. The program is seen as 'confused' because it was tricked into overwriting the system's billing file. Whenever a program tries to access a file, the operating system needs to know two things: which file the program is asking for, and whether the program has permission to access the file. In the example, the file is designated by its name, “(SYSX)BILL”. The program receives the file name from the user, but does not know whether the user had permission to write the file. When the program opens the file, the system uses the program's permission, not the user's. When the file name was passed from the user to the program, the permission did not go along with it; the permission was increased by the system silently and automatically. It is not essential to the attack that the billing file be designated by a name represented as a string. The essential points are that: the designator for the file does not carry the full authority needed to access the file; the program's own permission to access the file is used implicitly. == Other examples == A cross-site request forgery (CSRF) is an example of a confused deputy attack that uses the web browser to perform sensitive actions against a web application. A common form of this attack occurs when a web application uses a cookie to authenticate all requests transmitted by a browser. Using JavaScript, an attacker can force a browser into transmitting authenticated HTTP requests. The Samy computer worm used cross-site scripting (XSS) to turn the browser's authenticated MySpace session into a confused deputy. Using XSS the worm forced the browser into posting an executable copy of the worm as a MySpace message which was then viewed and executed by friends of the infected user. Clickjacking is an attack where the user acts as the confused deputy. In this attack a user thinks they are harmlessly browsing a website (an attacker-controlled website) but they are in fact tricked into performing sensitive actions on another website. An FTP bounce attack can allow an attacker to connect indirectly to TCP ports to which the attacker's machine has no access, using a remote FTP server as the confused deputy. Another example relates to personal firewall software. It can restrict Internet access for specific applications. Some applications circumvent this by starting a browser with instructions to access a specific URL. The browser has authority to open a network connection, even though the application does not. Firewall software can attempt to address this by prompting the user in cases where one program starts another which then accesses the network. However, the user frequently does not have sufficient information to determine whether such an access is legitimate—false positives are common, and there is a substantial risk that even sophisticated users will become habituated to clicking "OK" to these prompts. Not every program that misuses authority is a confused deputy. Sometimes misuse of authority is simply a result of a program error. The confused deputy problem occurs when the designation of an object is passed from one program to another, and the associated permission changes unintentionally, without any explicit action by either party. It is insidious because neither party did anything explicit to change the authority. Another example is when an administrator authorizes an AI agent to act on their behalf, and that AI subsequently delegates authority to another AI agent neither vetted nor authorized by the original administrator. The unvetted AI can then act without permissions or oversight from the original developer. == Solutions == In some systems it is possible to ask the operating system to open a file using the permissions of another client. This solution has some drawbacks: It requires explicit attention to security by the server. A naive or careless server might not take this extra step. It becomes more difficult to identify the correct permission if the server is in turn the client of another service and wants to pass along access to the file. It requires the client to trust the server to not abuse the borrowed permissions. Note that intersecting the server and client's permissions does not solve the problem either, because the server may then have to be given very wide permissions (all of the time, rather than those needed for a given request) in order to act for arbitrary clients. The simplest way to solve the confused deputy problem is to bundle together the designation of an object and the permission to access that object. This is exactly what a capability is. Using capability security in the compiler example, the client would pass to the server a capability to the output file, such as a file descriptor, rather than the name of the file. Since it lacks a capability to the billing file, it cannot designate that file for output. In the cross-site request forgery example, a URL supplied "cross"-site would include its own authority independent of that of the client of the web browser.
Distributed manufacturing
Distributed manufacturing, also known as distributed production, cloud producing, distributed digital manufacturing, and local manufacturing, is a form of decentralized manufacturing practiced by enterprises using a network of geographically dispersed manufacturing facilities that are coordinated using information technology. It can also refer to local manufacture via the historic cottage industry model, or manufacturing that takes place in the homes of consumers. == Enterprise == In enterprise environments, the primary attribute of distributed manufacturing is the ability to create value at geographically dispersed locations. For example, shipping costs could be minimized when products are built geographically close to their intended markets. Also, products manufactured in a number of small facilities distributed over a wide area can be customized with details adapted to individual or regional tastes. Manufacturing components in different physical locations and then managing the supply chain to bring them together for final assembly of a product is also considered a form of distributed manufacturing. Digital networks combined with additive manufacturing allow companies a decentralized and geographically independent distributed production (cloud manufacturing). == Consumer == Within the maker movement and DIY culture, small scale production by consumers often using peer-to-peer resources is being referred to as distributed manufacturing. Consumers download digital designs from an open design repository website like Youmagine or Thingiverse and produce a product for low costs through a distributed network of 3D printing services such as 3D Hubs, Geomiq. In the most distributed form of distributed manufacturing the consumer becomes a prosumer and manufacturers products at home with an open-source 3-D printer such as the RepRap. In 2013 a desktop 3-D printer could be economically justified as a personal product fabricator and the number of free and open hardware designs were growing exponentially. Today there are millions of open hardware product designs at hundreds of repositories and there is some evidence consumers are 3-D printing to save money. For example, 2017 case studies probed the quality of: (1) six common complex toys; (2) Lego blocks; and (3) the customizability of open source board games and found that all filaments analyzed saved the prosumer over 75% of the cost of commercially available true alternative toys and over 90% for recyclebot filament. Overall, these results indicate a single 3D printing repository, MyMiniFactory, is saving consumers well over $60 million/year in offset purchases of only toys. These 3-D printers can now be used to make sophisticated high-value products like scientific instruments. Similarly, a study in 2022 found that 81% of open source designs provided economic savings and the total savings for the 3D printing community is more than $35 million from downloading only the top 100 products at YouMagine. In general, the savings are largest when compared to conventional products when prosumers use recycled materials in 'distributed recycling and additive manufacturing' (DRAM). == Emergency Distributed Manufacturing During COVID-19 Pandemic == Distributed manufacturing became far more visible during the COVID-19 pandemic because it offered a practical response to the breakdown of centralized global supply chains. As lock downs, border restrictions, and factory shutdowns disrupted conventional production, decentralized networks using local facilities such as Open Source Medical Supplies stepped in and manufactured over 48 million products. Additive manufacturing /3D printing were used to produce urgently needed items such as face shields, ventilators and their components, nasopharyngeal swabs, and other personal protective equipment. This demonstrated that distributed manufacturing could reduce lead times, improve responsiveness, and lessen dependence on distant suppliers during crisis conditions for a wide range of products. Peer-reviewed studies on pandemic-era manufacturing note that additive manufacturing was especially valuable because digital design files could be shared rapidly and produced close to the point of need, enabling hospitals, universities, small firms, and maker communities to supplement strained medical supply chains. The pandemic also helped shift distributed manufacturing from being seen as a niche or experimental model to a credible strategy for resilience, flexibility, and emergency response. At the same time, scholars caution that its wider adoption depends on solving issues related to quality assurance, regulation, material consistency, and coordination across distributed production sites. Overall, COVID-19 popularized distributed manufacturing by showing that localized, digitally enabled production could complement traditional manufacturing systems when speed, adaptability, and supply-chain resilience were critical. == Social change == Some call attention to the conjunction of commons-based peer production with distributed manufacturing techniques. The self-reinforced fantasy of a system of eternal growth can be overcome with the development of economies of scope, and here, the civil society can play an important role contributing to the raising of the whole productive structure to a higher plateau of more sustainable and customised productivity. Further, it is true that many issues, problems and threats rise due to the large democratization of the means of production, and especially regarding the physical ones. For instance, the recyclability of advanced nanomaterials is still questioned; weapons manufacturing could become easier; not to mention the implications on counterfeiting and on "intellectual property". It might be maintained that in contrast to the industrial paradigm whose competitive dynamics were about economies of scale, commons-based peer production and distributed manufacturing could develop economies of scope. While the advantages of scale rest on cheap global transportation, the economies of scope share infrastructure costs (intangible and tangible productive resources), taking advantage of the capabilities of the fabrication tools. And following Neil Gershenfeld in that "some of the least developed parts of the world need some of the most advanced technologies", commons-based peer production and distributed manufacturing may offer the necessary tools for thinking globally but act locally in response to certain problems and needs. As well as supporting individual personal manufacturing social and economic benefits are expected to result from the development of local production economies. In particular, the humanitarian and development sector are becoming increasingly interested in how distributed manufacturing can overcome the supply chain challenges of last mile distribution. Further, distributed manufacturing has been proposed as a key element in the Cosmopolitan localism or cosmolocalism framework to reconfigure production by prioritizing socio-ecological well-being over corporate profits, over-production and excess consumption. == Technology == By localizing manufacturing, distributed manufacturing may enable a balance between two opposite extreme qualities in technology development: Low technology and High tech. This balance is understood as an inclusive middle, a "mid-tech", that may go beyond the two polarities, incorporating them into a higher synthesis. Thus, in such an approach, low-tech and high-tech stop being mutually exclusive. They instead become a dialectic totality. Mid-tech may be abbreviated to "both…and…" instead of "neither…nor…". Mid-tech combines the efficiency and versatility of digital/automated technology with low-tech's potential for autonomy and resilience. == Contracting in Distributed Manufacturing == Research into contracting and order processing models tailored for distributed manufacturing has highlighted the need for flexible, role-based frameworks and advanced digital tools. These tools and frameworks are essential for addressing issues related to quality assurance, payment structures, legal compliance, and coordination among multiple actors. By addressing these challenges, contracting models for distributed manufacturing can unlock its potential for more localized, efficient, and sustainable production systems. A system prototype has been developed to simplify contracting for distributed manufacturing. This tool allows buyers to manage orders across multiple manufacturers using a single interface, automating workflows to ensure clarity and accountability for everyone involved. This research was led by the Internet of Production, as part of the mAkE project (African European Maker Innovation Ecosystem), funded by the European Horizon 2020 research and innovation programme.
ISPConfig
ISPConfig is an open source hosting control panel for Linux, licensed under BSD license and developed by the company ISPConfig UG. The ISPConfig project was started in autumn 2005 by Till Brehm from the German company projektfarm GmbH. == Overview == Using the dashboard, administrators have the ability to manage websites, email addresses, MySQL and MariaDB as well as PostgreSQL (since version 3.3) databases, FTP accounts, Shell accounts and DNS records through a web-based interface. The software has 4 login levels: administrator, reseller, client, and email-user, each with a different set of permissions. == Operating Systems == ISPConfig is only available on Linux, with CentOS, Debian, and Ubuntu being among the supported distributions. == Features == The following services and features are supported: Management of a single or multiple servers from one control panel. Web server management for Apache HTTP Server and Nginx. Mail server management (with virtual mail users) with spam and antivirus filter using Postfix (software) and Dovecot (software). DNS server management (BIND, Powerdns). Configuration mirroring and clusters. Administrator, reseller, client and mail-user login. Virtual server management for OpenVZ Servers. Website statistics using Webalizer and AWStats
Write or Die
Write or Die is an online web application designed to combat writer's block by letting users of the application punish themselves if they slow down or stop typing in the application's window. How severe the punishments are depends on the mode the user chooses, which ranges from "Gentle" to "Kamikaze". It was reviewed by publications PCWorld, the Los Angeles Times and The Guardian, and it was most notably used by writers Helen Oyeyemi and David Nicholls. The creator, Jeff Printy, explained that he wrote the application because he wants "to be published and make a living as a writer."
Simulation noise
Simulation noise is a function that creates a divergence-free vector field. This signal can be used in artistic simulations for the purpose of increasing the perception of extra detail. The function can be calculated in three dimensions by dividing the space into a regular lattice grid. With each edge is associated a random value, indicating a rotational component of material revolving around the edge. By following rotating material into and out of faces, one can quickly sum the flux passing through each face of the lattice. Flux values at lattice faces are then interpolated to create a field value for all positions. Perlin noise is the earliest form of lattice noise, which has become very popular in computer graphics. Perlin Noise is not suited for simulation because it is not divergence-free. Noises based on lattices, such as simulation noise and Perlin noise, are often calculated at different frequencies and summed together to form band-limited fractal signals. Other approaches developed later that use vector calculus identities to produce divergence free fields, such as "Curl-Noise" as suggested by Rook Bridson, and "Divergence-Free Noise" due to Ivan DeWolf. These often require calculation of lattice noise gradients, which sometimes are not readily available. A naive implementation would call a lattice noise function several times to calculate its gradient, resulting in more computation than is strictly necessary. Unlike these noises, simulation noise has a geometric rationale in addition to its mathematical properties. It simulates vortices scattered in space, to produce its pleasing aesthetic. == Curl noise == The vector field is created as follows, for every point (x,y,z) in the space a vector field G is created, every component x, y and z of the vector field (Gx, Gy, Gz) is defined by a 3D perlin or simplex noise function with x, y and z as parameters. The partial derivative of Gx, Gy, and Gz respect to x, y and z is obtained with the gradient of the perlin or simplex noise by finite differences of implicit calculation inside the simplex noise. The partial derivatives are used to calculate F as the curl of G given by F = ( ∂ G z ∂ y − ∂ G y ∂ z , ∂ G x ∂ z − ∂ G z ∂ x , ∂ G y ∂ x − ∂ G x ∂ y ) {\displaystyle F=({\frac {\partial Gz}{\partial y}}-{\frac {\partial Gy}{\partial z}},{\frac {\partial Gx}{\partial z}}-{\frac {\partial Gz}{\partial x}},{\frac {\partial Gy}{\partial x}}-{\frac {\partial Gx}{\partial y}})} == Bitangent noise == This method is based in the fact that the curl of the gradient of scalar field is zero and the identity that expand the divergence of a cross product of two vectors A and B as the difference of the dot products of each vector with the curl of the other: ∇ × ( ∇ φ ) = 0 . {\displaystyle \nabla \times (\nabla \varphi )=\mathbf {0} .} ∇ ⋅ ( A × B ) = ( ∇ × A ) ⋅ B − A ⋅ ( ∇ × B ) {\displaystyle \nabla \cdot (\mathbf {A} \times \mathbf {B} )=\ (\nabla {\times }\mathbf {A} )\cdot \mathbf {B} \,-\,\mathbf {A} \cdot (\nabla {\times }\mathbf {B} )} which means that if the curl of both vector fields is zero then the divergence of the product of two vectors that are the gradients of scalar fields is zero too. This result in a divergence free vector field by construction only calling two noise functions to create the scalar fields. The vector field es created as follows, two scalar fields are calculated ϕ {\displaystyle \phi } and ψ {\displaystyle \psi } using 3D perlin or simplex noise functions, then the gradients A and B of each of this fields is calculated, the cross product of A and B gives a divergence free vector field. == Signed distance noise == The vector field is created based on a closed and differentiable implicit surface S = F(x,y,z) = 0. For every point in the space, frequently outside or near the surface, we get a vector g that is normal to the surface, this is the gradient of S or the partial derivatives respect to x, y and z, this vector is not unitary, but we can get a unitary normal n by dividing each component of the point by the magnitude of the gradient g. Outside of the surface all these normals point away from the surface. g = ∇ F ( x , y , z ) = ( ∂ F ∂ x , ∂ F ∂ y , ∂ F ∂ z ) {\displaystyle g=\nabla F(x,y,z)=\left({\frac {\partial F}{\partial x}},{\frac {\partial F}{\partial y}},{\frac {\partial F}{\partial z}}\right)} n = g ( x , y , z ) ‖ ∇ F ( x , y , z ) ‖ {\displaystyle \mathbf {n} ={\frac {g(x,y,z)}{\|\nabla F(x,y,z)\|}}} ‖ ∇ F ( x , y , z ) ‖ = ( ∂ F ∂ x ) 2 + ( ∂ F ∂ y ) 2 + ( ∂ F ∂ z ) 2 {\displaystyle \|\nabla F(x,y,z)\|={\sqrt {\left({\frac {\partial F}{\partial x}}\right)^{2}+\left({\frac {\partial F}{\partial y}}\right)^{2}+\left({\frac {\partial F}{\partial z}}\right)^{2}}}} Afterwards we calculate a scalar value p for that point in the space using a 3D perlin or simplex noise function. Now we create a vector field V = pn pointing outside of the surface. The curl of this vector field gives the direction in every point in the space where the particles should move. S D N = ( ∂ V z ∂ y − ∂ V y ∂ z , ∂ V x ∂ z − ∂ V z ∂ x , ∂ V y ∂ x − ∂ V x ∂ y ) {\displaystyle SDN=({\frac {\partial Vz}{\partial y}}-{\frac {\partial Vy}{\partial z}},{\frac {\partial Vx}{\partial z}}-{\frac {\partial Vz}{\partial x}},{\frac {\partial Vy}{\partial x}}-{\frac {\partial Vx}{\partial y}})} By construction this vector SDN will point in a tangent direction to an isosurface at the level of the signed distance to the original surface and can be used to confine the movements of the particles to stay in that surface.
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