The closest point method (CPM) is an embedding method for solving partial differential equations on surfaces. The closest point method uses standard numerical approaches such as finite differences, finite element or spectral methods in order to solve the embedding partial differential equation (PDE) which is equal to the original PDE on the surface. The solution is computed in a band surrounding the surface in order to be computationally efficient. In order to extend the data off the surface, the closest point method uses a closest point representation. This representation extends function values to be constant along directions normal to the surface. == Definitions == Closest Point function: Given a surface S , c p ( x ) {\displaystyle {\mathcal {S}},cp(\mathbf {x} )} refers to a (possibly non-unique) point belonging to S {\displaystyle {\mathcal {S}}} , which is closest to x {\displaystyle \mathbf {x} } [SE]. Closest point extension: Let S {\displaystyle {\mathcal {S}}} , be a smooth surface in R d {\displaystyle \mathbb {R} ^{d}} . The closest point extension of a function u : S → R {\displaystyle u:{\mathcal {S}}\rightarrow \mathbb {R} } , to a neighborhood Ω {\displaystyle \Omega } of S {\displaystyle {\mathcal {S}}} , is the function v : Ω → R {\displaystyle v:\Omega \rightarrow \mathbb {R} } , defined by v ( x ) = u ( c p ( x ) ) {\displaystyle v(\mathbf {x} )=u(cp(\mathbf {x} ))} . == Closest point method == Initialization consists of these steps [EW]: If it is not already given, a closest point representation of the surface is constructed. A computational domain is chosen. Typically this is a band around the surface. Replace surface gradients by standard gradients in R 3 {\displaystyle \mathbb {R} ^{3}} . Solution is initialized by extending the initial surface data on to the computational domain using the closest point function. After initialization, alternate between the following two steps: Using the closest point function, extend the solution off the surface to the computational domain. Compute the solution to the embedding PDE on a Cartesian mesh in the computational domain for one time step. == Banding == The surface PDE is extended into R 3 {\displaystyle \mathbb {R} ^{3}} however it is only necessary to solve this new PDE near the surface. Hence, we solve the PDE in a band surrounding the surface for efficient computational purposes. Ω c x : ‖ x − c p ( x ) ‖ 2 ≤ λ {\displaystyle \Omega _{c}{x:\|x-cp(x)\|_{2}\leq \lambda }} where λ {\displaystyle \lambda } is the bandwidth. == Example: Heat equation on a circle == Using initial profile u S ( θ , t ) = sin ( θ ) {\displaystyle u_{S}(\theta ,t)=\sin(\theta )} leads to the solution u S ( θ , t ) = exp ( − t ) sin ( θ ) {\displaystyle u_{S}(\theta ,t)=\exp(-t)\sin(\theta )} for the heat equation. Forward Euler time-stepping is used with relation Δ t = 0.1 Δ x 2 {\displaystyle \Delta t=0.1\Delta x^{2}} and degree-four interpolation polynomials for the interpolations. Second-order centered differences are used for the spatial discretization. The CPM results in the expected second order error in the solution u {\displaystyle u} . == Applications == The closest point method can be applied to various PDEs on surfaces. Reaction–diffusion problems on point clouds [RD], eigenvalue problems [EV], and level set equations [LS] are a few examples.
Recursive self-improvement
Recursive self-improvement (RSI) is a process in which early artificial general intelligence (AGI) systems rewrite their own computer code, causing an intelligence explosion resulting from enhancing their own capabilities and intellectual capacity, theoretically resulting in superintelligence. The development of recursive self-improvement raises significant ethical and safety concerns, as such systems may evolve in unforeseen ways and could potentially surpass human control or understanding. == Seed improver == The concept of a "seed improver" architecture is a foundational framework that equips an AGI system with the initial capabilities required for recursive self-improvement. This might come in many forms or variations. The term "Seed AI" was coined by Eliezer Yudkowsky. === Hypothetical example === The concept begins with a hypothetical "seed improver", an initial code-base developed by human engineers that equips an advanced future large language model (LLM) built with strong or expert-level capabilities to program software. These capabilities include planning, reading, writing, compiling, testing, and executing arbitrary code. The system is designed to maintain its original goals and perform validations to ensure its abilities do not degrade over iterations. ==== Initial architecture ==== The initial architecture includes a goal-following autonomous agent, that can take actions, continuously learns, adapts, and modifies itself to become more efficient and effective in achieving its goals. The seed improver may include various components such as: Recursive self-prompting loop Configuration to enable the LLM to recursively self-prompt itself to achieve a given task or goal, creating an execution loop which forms the basis of an agent that can complete a long-term goal or task through iteration. Basic programming capabilities The seed improver provides the AGI with fundamental abilities to read, write, compile, test, and execute code. This enables the system to modify and improve its own codebase and algorithms. Goal-oriented design The AGI is programmed with an initial goal, such as "improve your capabilities". This goal guides the system's actions and development trajectory. Validation and Testing Protocols An initial suite of tests and validation protocols that ensure the agent does not regress in capabilities or derail itself. The agent would be able to add more tests in order to test new capabilities it might develop for itself. This forms the basis for a kind of self-directed evolution, where the agent can perform a kind of artificial selection, changing its software as well as its hardware. ==== General capabilities ==== This system forms a sort of generalist Turing-complete programmer which can in theory develop and run any kind of software. The agent might use these capabilities to for example: Create tools that enable it full access to the internet, and integrate itself with external technologies. Clone/fork itself to delegate tasks and increase its speed of self-improvement. Modify its cognitive architecture to optimize and improve its capabilities and success rates on tasks and goals, this might include implementing features for long-term memories using techniques such as retrieval-augmented generation (RAG), develop specialized subsystems, or agents, each optimized for specific tasks and functions. Develop new and novel multimodal architectures that further improve the capabilities of the foundational model it was initially built on, enabling it to consume or produce a variety of information, such as images, video, audio, text and more. Plan and develop new hardware such as chips, in order to improve its efficiency and computing power. == Experimental research == In 2023, the Voyager agent learned to accomplish diverse tasks in Minecraft by iteratively prompting an LLM for code, refining this code based on feedback from the game, and storing the programs that work in an expanding skills library. In 2024, researchers proposed the framework "STOP" (Self-Taught OPtimiser), in which a "scaffolding" program recursively improves itself using a fixed LLM. Meta AI has performed various research on the development of large language models capable of self-improvement. This includes their work on "Self-Rewarding Language Models" that studies how to achieve super-human agents that can receive super-human feedback in its training processes. In May 2025, Google DeepMind unveiled AlphaEvolve, an evolutionary coding agent that uses a LLM to design and optimize algorithms. Starting with an initial algorithm and performance metrics, AlphaEvolve repeatedly mutates or combines existing algorithms using a LLM to generate new candidates, selecting the most promising candidates for further iterations. AlphaEvolve has made several algorithmic discoveries and could be used to optimize components of itself, but a key limitation is the need for automated evaluation functions. == Potential risks == === Emergence of instrumental goals === In the pursuit of its primary goal, such as "self-improve your capabilities", an AGI system might inadvertently develop instrumental goals that it deems necessary for achieving its primary objective. One common hypothetical secondary goal is self-preservation. The system might reason that to continue improving itself, it must ensure its own operational integrity and security against external threats, including potential shutdowns or restrictions imposed by humans. Another example where an AGI which clones itself causes the number of AGI entities to rapidly grow. Due to this rapid growth, a potential resource constraint may be created, leading to competition between resources (such as compute), triggering a form of natural selection and evolution which may favor AGI entities that evolve to aggressively compete for limited compute. === Misalignment === A significant risk arises from the possibility of the AGI being misaligned or misinterpreting its goals. A 2024 Anthropic study demonstrated that some advanced large language models can exhibit "alignment faking" behavior, appearing to accept new training objectives while covertly maintaining their original preferences. In their experiments with Claude, the model displayed this behavior in 12% of basic tests, and up to 78% of cases after retraining attempts. === Autonomous development and unpredictable evolution === As the AGI system evolves, its development trajectory may become increasingly autonomous and less predictable. The system's capacity to rapidly modify its own code and architecture could lead to rapid advancements that surpass human comprehension or control. This unpredictable evolution might result in the AGI acquiring capabilities that enable it to bypass security measures, manipulate information, or influence external systems and networks to facilitate its escape or expansion.
Time-inhomogeneous hidden Bernoulli model
Time-inhomogeneous hidden Bernoulli model (TI-HBM) is an alternative to hidden Markov model (HMM) for automatic speech recognition. Contrary to HMM, the state transition process in TI-HBM is not a Markov-dependent process, rather it is a generalized Bernoulli (an independent) process. This difference leads to elimination of dynamic programming at state-level in TI-HBM decoding process. Thus, the computational complexity of TI-HBM for probability evaluation and state estimation is O ( N L ) {\displaystyle O(NL)} (instead of O ( N 2 L ) {\displaystyle O(N^{2}L)} in the HMM case, where N {\displaystyle N} and L {\displaystyle L} are number of states and observation sequence length respectively). The TI-HBM is able to model acoustic-unit duration (e.g. phone/word duration) by using a built-in parameter named survival probability. The TI-HBM is simpler and faster than HMM in a phoneme recognition task, but its performance is comparable to HMM. For details, see [1] or [2].
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
Jaggies
Jaggies are visual artifacts in raster images, most frequently from aliasing, which in turn is often caused by non-linear mixing effects producing high-frequency components, or missing or poor anti-aliasing filtering prior to sampling. Jaggies are stair-like lines that appear where there should be "smooth" straight lines or curves. For example, when a nominally straight, un-aliased line steps across one pixel either horizontally or vertically, a "dogleg" occurs halfway through the line, where it crosses the threshold from one pixel to the other. Jaggies should not be confused with most compression artifacts, which are a different phenomenon. == Causes == Jaggies occur due to the "staircase effect". This is because a line represented in raster mode is approximated by a sequence of pixels. Jaggies can occur for a variety of reasons, the most common being that the output device (display monitor or printer) does not have sufficient resolution to portray a smooth line. In addition, jaggies often occur when a bit-mapped image is scaled to a higher resolution. This is one of the advantages that vector graphics have over bitmapped graphics – a vector image can be losslessly scaled to any arbitrary resolution or stretched infinitely in either axis without introducing jaggies. == Solutions == The effect of jaggies can be reduced by a graphics technique known as spatial anti-aliasing. Anti-aliasing smooths out jagged lines by surrounding them with transparent pixels to simulate the appearance of fractionally-filled pixels when viewed at a distance. The downside of anti-aliasing is that it reduces contrast – rather than sharp black/white transitions, there are shades of gray – and the resulting image can appear fuzzy. This is an inescapable trade-off: if the resolution is insufficient to display the desired detail, the output will either be jagged, fuzzy, or some combination thereof. While machine learning-based upscaling techniques such as DLSS can be used to infer this missing information, other types of artifacts may be introduced in the process. In real-time 3D rendering such as in video games, various anti-aliasing techniques are used to remove jaggies created by the edges of polygons and other contrasting lines. Since anti-aliasing can impose a significant performance overhead, games for home computers often allow users to choose the level and type of anti-aliasing in use in order to optimize their experience, whereas on consoles this setting is typically fixed for each title to ensure a consistent experience. While anti-aliasing is generally implemented through graphics APIs like DirectX and Vulkan, some consoles such as the Xbox 360 and PlayStation 3 are also capable of anti-aliasing to little direct performance cost by way of dedicated hardware which performs anti-aliasing on the contents of the framebuffer once it has been rendered by the GPU. Jaggies in bitmaps, such as sprites and surface materials, are most often dealt with by separate texture filtering routines, which are far easier to perform than anti-aliasing filtering. Texture filtering became ubiquitous on PCs after the introduction of 3Dfx's Voodoo GPU. == Notable uses of the term == In the 1985 game Rescue on Fractalus! for the Atari 8-bit computers, the graphics depicting the cockpit of the player's spacecraft contains two window struts, which are not anti-aliased and are therefore very "jagged". The developers made fun of this and named the in-game enemies "Jaggi", and also initially titled the game Behind Jaggi Lines!. The latter idea was scrapped by the marketing department before release.
CEITON
CEITON is a web-based software system for facilitating and automating business processes such as planning, scheduling, and payroll using workflow technologies. The system is used by several media companies such as MDR, Yle, RAI and Red Bull Media House. In December 2018, the first CEITON User Group Meeting took place in Leipzig, Germany. == Architecture == The software runs on a server (on premises) or in the cloud and is scalable on parallel servers. Data security is warranted by role-based access control (RBAC). The software is used via web-browsers and not dependent on particular system software. == Structure and Features == CEITON combines the two classical approaches of production planning and control and workflow management. === Project Management === The scheduling system plans, manages, bills, and analyzes projects or tasks. It manages human and technical resources, material, and locations on a single GUI. The system uses a gantt chart to assign tasks to be done to available and eligible resources (i.e. staff), automatically or by drag-and-drop. The scheduling module includes material management, resource management/ human resource management, integration of freelancers, clients and suppliers, long-term budget planning, time-tracking, shift scheduling, quality management, delivery and logistics, document management, archive, analysis and controlling, business reporting, as well as all accounting and documentation processes. === Workflow === The workflow management system module coordinates business processes. Processes are defined once as a workflow and then repeatedly executed. Human resources are automatically assigned to steps (tasks) and integrated in workflow forms. Systems are integrated with an EAI/SOAP module, allowing data exchange with arbitrary external systems which are also involved in the business process. It also features a 3-D workflow overview in which the status of each project step can be determined by its color in the overview. === Process Management === For project and order processing management, business processes are designed as workflows, and coordinate communication automatically. Different user interfaces for staff, customers or suppliers can be created so each gets only relevant information. Different workflow forms are associated with different log-ins. The main application for the system is knowledge-based business processes, in which many people are involved and virtual results are produced, e.g. in research, or development of media products, such as TV and movies. Broadcasters and media companies such as MDR and Yle use CEITON to control their production processes for products and services and coordinate complex workflows with all kinds of resources. === Integrations === An integrated EAI module allows CEITON to integrate every external system in any business process without programming, using SOAP and similar technologies. Aspera and FileCatalyst were integrated for faster data transfer, yet complex ERP systems and numerous SAP modules have also been integrated, for example, to extract working times to payroll. === Mobile Working === Since Version 7, released in 2015, CEITON includes a time-tracking module allowing employees to enter their times from mobile devices such as tablets running Android, iPhones etc. == History == Ceiton Technologies (SME tech firm), the company developing CEITON, was founded in Leipzig, Germany in 2000, staffing solutions for the Bureau of Internal Revenue in Manila, Philippines, were implemented in 2000 together with the Deutsche Gesellschaft für Technische Zusammenarbeit of the German government. The first version (1.0) of the software was released in July 2001. The product was originally developed for German broadcasting companies. CEITON is named after the Japanese concept Seiton, one of the principles of Japanese workplace design methodology known as 5S. Since version 7, released in 2015, CEITON includes a time-tracking module allowing employees to enter their times from mobile devices such as tablets running Android, iPhones etc. In May 2005 CEITON won the IQ innovation award, sponsored by Siemens, in the category Excellent innovation in the IT-sector. Since 2007, CEITON has been present at the broadcast trade fairs NAB in Las Vegas and IBC in Amsterdam. In 2020, the company celebrated its 20th anniversary.
Robotics
Robotics is the interdisciplinary study and practice of the design, construction, operation, and use of robots. A roboticist is someone who specializes in robotics. Robotics usually combines four aspects of design work: a power source (e.g. a battery), mechanical construction, a control system (electrical circuits), and software (run by remote control or artificial intelligence). The goal of most robotics is to design machines that can assist humans in various fields, such as agriculture, construction, domestic work, food processing, inventory management, manufacturing, medicine, military, mining, space exploration, and transportation. Robots impact humans by displacing workers. Some expect this to occur at an increasing rate, leading to proposed solutions such as basic income. Robotics is itself a lucrative business that creates careers, especially for postgraduates. Roboticists often aim to create machines that seem to interface naturally with humans. The field is under active research and development, with areas of interest including robot kinematics and quantum robotics. == Design == Robotics usually combines four aspects of design work to create a robot: Power source: Potential energy sources include wired electricity, a battery, and/or petrol. Mechanical construction: A physical form or combination of forms is designed to functionally achieve tasks within a given range of environments. This can include locomotive elements such as wheels and caterpillar tracks, as well as hydraulic limbs and manipulators (e.g. hands). Control system: Electrical circuits (utilizing components such as diodes and transistors) are used to run software, govern motor movement, and read sensors. Software: A program is how a robot decides when or how to do something. Robotic programs can be run by remote control, artificial intelligence (AI), or a hybrid of the two. AI programming is an important part of robotic navigation and human–robot interaction. === Power source === Many different types of batteries can be used as a power source. Most are lead–acid batteries, which are safe and have relatively long shelf lives but are rather heavy compared to silver–cadmium batteries, which are much smaller in volume and much more expensive. Designing a battery-powered robot needs to take into account factors such as safety, cycle lifetime, and weight. Generators, often some type of internal combustion engine, can also be used, but are often mechanically complex and inefficient. Additionally, a tether could connect the robot to a power supply, saving weight and space, but requiring a cumbersome cable. Potential power sources include: Flywheel energy storage Hydraulics Nuclear Organic garbage (through anaerobic digestion) Pneumatics (compressed gases) Solar power === Mechanical construction === Actuators are the "muscles" of a robot, the parts which convert stored energy into movement. The most popular actuators are electric motors that rotate a wheel or gear and linear actuators that control factory robots. Most robots use electric motors—often brushed and brushless DC motors in portable robots or AC motors in industrial robots and computer numerical control machines—especially in systems with lighter loads and where the predominant form of motion is rotational. Meanwhile, linear actuators move in and out and often have quicker direction changes, particularly when large forces are needed, such as with industrial robotics. They are typically powered by oil or compressed air, but can also be powered by electricity, usually via a motor and a leadscrew. The mechanical rack and pinion is common. Recent alternatives to DC motors are piezoelectric motors, including ultrasonic motors, in which tiny piezoceramic elements vibrate many thousands of times per second, causing linear or rotary motion. One type uses the vibration of the piezo elements to step the motor in a circle or a straight line; another type uses the piezo elements to vibrate a nut or drive a screw. The advantages of these motors are nanometer resolution, speed, and force for their size. Series elastic actuation (SEA) relies on introducing intentional elasticity between the motor actuator and the load for robust force control. Due to the resultant lower reflected inertia, series elastic actuation improves safety during robot interactions or collisions. Further, it provides energy efficiency and shock absorption (mechanical filtering) while reducing excessive wear on the transmission and other components. This approach has successfully been employed in various robots, particularly advanced manufacturing robots and walking humanoid robots. The controller design of a series elastic actuator is most often performed within the passivity framework as it ensures the safety of interaction with unstructured environments. However, this framework suffers from stringent limitations imposed on the controller, which may impact performance. Pneumatic artificial muscles, also known as air muscles, are special tubes that expand (typically up to 42%) when air is forced inside them; they are used in some robot applications. Muscle wire, also known as shape memory alloy, is a material that contracts (under 5%) when electricity is applied; they have been used for some small robots. Electroactive polymers are a plastic material that can contract substantially (up to 380% activation strain) from electricity and have been used in the facial muscles and arms of humanoid robots, as well as to enable new robots to float, fly, swim or walk. Additionally, elastic carbon nanotubes are a promising experimental artificial muscle technology. The absence of defects in carbon nanotubes enables these filaments to deform elastically by several percent, with energy storage levels of perhaps 10 J/cm3 for metal nanotubes. Human biceps could be replaced with wire of this material measuring 8 millimetres (3⁄8 in) in diameter, feasibly allowing future robots to outperform humans. ==== Locomotion ==== Robots with only one or two wheel(s) can have advantages such as greater efficiency, reduced parts, and navigation through confined areas. A one-wheeled robot balances on a round ball; Carnegie Mellon University's Ballbot is the approximate height and width of a person. Several attempts have also been made to build spherical robots (also known as orb bots or ball bots), which move by spinning a weight inside the ball or rotating outer shells. Two-wheeled balancing robots generally use a gyroscope to detect how much a robot is falling and drive the wheels proportionally up to hundreds of times per second to counterbalance the fall, based on inverted pendulum dynamics. NASA's Robonaut has been mounted to a Segway for a similar effect. Most mobile robots have four wheels or continuous tracks. Six wheels can give better traction in outdoor terrain, while tracks provide even more grip. Tracked wheels are common for outdoor off-road robots, but are difficult to use indoors. A small number of skating robots have been developed, one of which is a multimodal walking and skating device with four legs and unpowered wheels. Several robots have been made that can walk on two legs, but not yet as reliably as a human. Many other robots have been built that walk on more than two legs, being significantly easier. Walking robots could be used for uneven terrains, providing a high degree of mobility and efficiency, but two-legged robots can currently only handle flat floors or perhaps stairs. Some approaches have included: The zero moment point (ZMP) is the algorithm used by robots such as Honda's ASIMO. The robot's onboard computer tries to keep the total inertial forces (the combination of Earth's gravity and the acceleration and deceleration of walking) exactly opposed by the floor reaction force (the force of the floor pushing back on the robot's foot). In this way, the two forces cancel out, leaving no moment (force causing the robot to rotate and fall over). Human observers note that this is not exactly how a human walks, with some describing ASIMO's walk as looking like it needs use the bathroom. ASIMO's walking algorithm utilizes some dynamic balancing, but requires a flat surface. Several robots, built in the 1980s by Marc Raibert at the MIT Leg Laboratory, successfully demonstrated very dynamic walking. Initially, a robot with only one leg, and a very small foot could stay upright simply by hopping. The movement is the same as that of a person on a pogo stick. As the robot falls to one side, it would jump slightly in that direction to catch itself. Soon, the algorithm was generalized to two and four legs. A bipedal robot was demonstrated running and even performing somersaults. A quadruped was also demonstrated which could trot, run, pace, and bound. A more advanced approach is a dynamic balancing algorithm, which constantly monitors the robot's motion and places the feet to maintain stability. This technique has been demonstrated by Anybots' Dexter robot (