In robotics and motion planning, kinodynamic planning is a class of problems for which velocity, acceleration, and force/torque bounds must be satisfied, together with kinematic constraints such as avoiding obstacles. The term was coined by Bruce Donald, Pat Xavier, John Canny, and John Reif. Donald et al. developed the first polynomial-time approximation schemes (PTAS) for the problem. By providing a provably polynomial-time ε-approximation algorithm, they resolved a long-standing open problem in optimal control. Their first paper considered time-optimal control ("fastest path") of a point mass under Newtonian dynamics, amidst polygonal (2D) or polyhedral (3D) obstacles, subject to state bounds on position, velocity, and acceleration. Later they extended the technique to many other cases, for example, to 3D open-chain kinematic robots under full Lagrangian dynamics. == Modern approaches == Since the foundational theoretical work of the 1990s, the field has evolved significantly with new algorithmic approaches that address the computational and practical limitations of early methods. === Sampling-based methods === Many practical heuristic algorithms based on stochastic optimization and iterative sampling have been developed by a wide range of authors to address the kinodynamic planning problem. Popular approaches include extensions of RRT algorithms such as RRT for kinodynamic systems, and sampling-based methods like Model Predictive Path Integral (MPPI) control. These stochastic techniques have been shown to work well in practice and can handle complex, high-dimensional state spaces more efficiently than deterministic methods. However, all motion planning methods are subject to the PSPACE-hardnesss of classical motion planning even without dynamics, which means (assuming the usual structural complexity conjectures) they all can be worst-case exponential-time in the state-space dimension (the number of degrees of freedom). On the other hand, the deterministic methods have provable guarantees of completeness, accuracy, and complexity (for fixed dimension, they are polynomial-time not only in the geometric complexity, but also in ( 1 / ε ) {\displaystyle (1/\varepsilon )} , the closeness of the desired approximation), whereas most of the recent heuristic/stochastic methods sacrifice at least one of these criteria. === Mixed-integer optimization approaches === Recent advances in mixed-integer programming have enabled new deterministic approaches to kinodynamic planning. These methods formulate the planning problem as an optimization task that simultaneously determines the spatial path and control sequence while respecting all kinodynamic constraints. By using techniques such as McCormick envelopes to handle bilinear constraints, these approaches can provide globally optimal solutions with mathematical guarantees while achieving significant computational speedups over traditional methods. === Genetic algorithm approaches === Genetic algorithms have also been adapted for kinodynamic planning, particularly for gradient-free optimization in challenging terrain. These methods use evolutionary computation to optimize trajectories over receding horizons, with specialized mutation operators that ensure vehicle controls remain within operational limits. This approach is particularly useful when dealing with non-differentiable cost functions or when gradient information is unavailable or unreliable. === Three-dimensional terrain planning === The foundational theoretical work of the 1990s was extended to higher degrees of freedom, and even to n {\displaystyle n} -link, 3D open-chain kinematic robots under full Lagrangian dynamics. However, many of the subsequent heuristic techniques (typically employing stochastic optimization) were confined to planar environments. More recent kinodynamic planning has extended beyond these planar environments to handle complex 3D terrains represented as simplicial complexes or triangular meshes. This advancement is particularly important for applications such as autonomous vehicle navigation in off-road environments, where elevation changes and terrain geometry significantly impact vehicle dynamics. These methods must account for pitch angles, surface curvature, and the coupling between terrain geometry and vehicle kinodynamic constraints. == Performance and guarantees == The landscape of performance guarantees in kinodynamic planning has evolved considerably. While early heuristic methods could not guarantee optimality, recent mixed-integer approaches have demonstrated the ability to find globally optimal solutions with proven constraint satisfaction. Experimental comparisons have shown that modern optimization-based planners can achieve execution times several orders of magnitude faster than sampling-based methods while maintaining strict adherence to kinodynamic constraints. However, the choice of method often depends on the specific application requirements. Sampling-based methods remain valuable for their ability to quickly find feasible solutions in high-dimensional spaces and their robustness to modeling uncertainties. Optimization-based methods excel when optimality guarantees and constraint compliance are critical, particularly in safety-critical applications. == Applications == Kinodynamic planning finds applications across numerous domains including: Autonomous vehicles: Path planning for cars, trucks, and other ground vehicles that must respect acceleration, steering, and velocity limits Aerial robotics: Trajectory planning for quadrotors and other unmanned aerial vehicles with dynamic constraints Manipulation: Planning for robotic arms where joint velocities, accelerations, and torques are limited Legged locomotion: Footstep and trajectory planning for walking and running robots Space robotics: Planning under thrust and fuel constraints for spacecraft and rovers
Nice (app)
Nice is a photo-sharing mobile app developed by Nice App Mobile Technology Co., Ltd. (Chinese: 北京极赞科技有限公司) in China. The app allows users to tag specific locations on images, enabling detailed labeling of items such as clothing and accessories. The company received a $36 million investment in C-round funding in 2014. Nice had 30 million registered users and 12 million active users as of late 2015. As of January 2024, it remained a popular app, the 6th most-downloaded in the iOS App Store for China. == Official website == Official website
Gaussian process emulator
In statistics, Gaussian process emulator is one name for a general type of statistical model that has been used in contexts where the problem is to make maximum use of the outputs of a complicated (often non-random) computer-based simulation model. Each run of the simulation model is computationally expensive and each run is based on many different controlling inputs. The variation of the outputs of the simulation model is expected to vary reasonably smoothly with the inputs, but in an unknown way. The overall analysis involves two models: the simulation model, or "simulator", and the statistical model, or "emulator", which notionally emulates the unknown outputs from the simulator. The Gaussian process emulator model treats the problem from the viewpoint of Bayesian statistics. In this approach, even though the output of the simulation model is fixed for any given set of inputs, the actual outputs are unknown unless the computer model is run and hence can be made the subject of a Bayesian analysis. The main element of the Gaussian process emulator model is that it models the outputs as a Gaussian process on a space that is defined by the model inputs. The model includes a description of the correlation or covariance of the outputs, which enables the model to encompass the idea that differences in the output will be small if there are only small differences in the inputs.
Representer theorem
For computer science, in statistical learning theory, a representer theorem is any of several related results stating that a minimizer f ∗ {\displaystyle f^{}} of a regularized empirical risk functional defined over a reproducing kernel Hilbert space can be represented as a finite linear combination of kernel products evaluated on the input points in the training set data. == Formal statement == The following Representer Theorem and its proof are due to Schölkopf, Herbrich, and Smola: Theorem: Consider a positive-definite real-valued kernel k : X × X → R {\displaystyle k:{\mathcal {X}}\times {\mathcal {X}}\to \mathbb {R} } on a non-empty set X {\displaystyle {\mathcal {X}}} with a corresponding reproducing kernel Hilbert space H k {\displaystyle H_{k}} . Let there be given a training sample ( x 1 , y 1 ) , … , ( x n , y n ) ∈ X × R {\displaystyle (x_{1},y_{1}),\dotsc ,(x_{n},y_{n})\in {\mathcal {X}}\times \mathbb {R} } , a strictly increasing real-valued function g : [ 0 , ∞ ) → R {\displaystyle g\colon [0,\infty )\to \mathbb {R} } , and an arbitrary error function E : ( X × R 2 ) n → R ∪ { ∞ } {\displaystyle E\colon ({\mathcal {X}}\times \mathbb {R} ^{2})^{n}\to \mathbb {R} \cup \lbrace \infty \rbrace } , which together define the following regularized empirical risk functional on H k {\displaystyle H_{k}} : f ↦ E ( ( x 1 , y 1 , f ( x 1 ) ) , … , ( x n , y n , f ( x n ) ) ) + g ( ‖ f ‖ ) . {\displaystyle f\mapsto E\left((x_{1},y_{1},f(x_{1})),\ldots ,(x_{n},y_{n},f(x_{n}))\right)+g\left(\lVert f\rVert \right).} Then, any minimizer of the empirical risk f ∗ = argmin f ∈ H k { E ( ( x 1 , y 1 , f ( x 1 ) ) , … , ( x n , y n , f ( x n ) ) ) + g ( ‖ f ‖ ) } , ( ∗ ) {\displaystyle f^{}={\underset {f\in H_{k}}{\operatorname {argmin} }}\left\lbrace E\left((x_{1},y_{1},f(x_{1})),\ldots ,(x_{n},y_{n},f(x_{n}))\right)+g\left(\lVert f\rVert \right)\right\rbrace ,\quad ()} admits a representation of the form: f ∗ ( ⋅ ) = ∑ i = 1 n α i k ( ⋅ , x i ) , {\displaystyle f^{}(\cdot )=\sum _{i=1}^{n}\alpha _{i}k(\cdot ,x_{i}),} where α i ∈ R {\displaystyle \alpha _{i}\in \mathbb {R} } for all 1 ≤ i ≤ n {\displaystyle 1\leq i\leq n} . Proof: Define a mapping φ : X → H k φ ( x ) = k ( ⋅ , x ) {\displaystyle {\begin{aligned}\varphi \colon {\mathcal {X}}&\to H_{k}\\\varphi (x)&=k(\cdot ,x)\end{aligned}}} (so that φ ( x ) = k ( ⋅ , x ) {\displaystyle \varphi (x)=k(\cdot ,x)} is itself a map X → R {\displaystyle {\mathcal {X}}\to \mathbb {R} } ). Since k {\displaystyle k} is a reproducing kernel, then φ ( x ) ( x ′ ) = k ( x ′ , x ) = ⟨ φ ( x ′ ) , φ ( x ) ⟩ , {\displaystyle \varphi (x)(x')=k(x',x)=\langle \varphi (x'),\varphi (x)\rangle ,} where ⟨ ⋅ , ⋅ ⟩ {\displaystyle \langle \cdot ,\cdot \rangle } is the inner product on H k {\displaystyle H_{k}} . Given any x 1 , … , x n {\displaystyle x_{1},\ldots ,x_{n}} , one can use orthogonal projection to decompose any f ∈ H k {\displaystyle f\in H_{k}} into a sum of two functions, one lying in span { φ ( x 1 ) , … , φ ( x n ) } {\displaystyle \operatorname {span} \left\lbrace \varphi (x_{1}),\ldots ,\varphi (x_{n})\right\rbrace } , and the other lying in the orthogonal complement: f = ∑ i = 1 n α i φ ( x i ) + v , {\displaystyle f=\sum _{i=1}^{n}\alpha _{i}\varphi (x_{i})+v,} where ⟨ v , φ ( x i ) ⟩ = 0 {\displaystyle \langle v,\varphi (x_{i})\rangle =0} for all i {\displaystyle i} . The above orthogonal decomposition and the reproducing property together show that applying f {\displaystyle f} to any training point x j {\displaystyle x_{j}} produces f ( x j ) = ⟨ ∑ i = 1 n α i φ ( x i ) + v , φ ( x j ) ⟩ = ∑ i = 1 n α i ⟨ φ ( x i ) , φ ( x j ) ⟩ , {\displaystyle f(x_{j})=\left\langle \sum _{i=1}^{n}\alpha _{i}\varphi (x_{i})+v,\varphi (x_{j})\right\rangle =\sum _{i=1}^{n}\alpha _{i}\langle \varphi (x_{i}),\varphi (x_{j})\rangle ,} which we observe is independent of v {\displaystyle v} . Consequently, the value of the error function E {\displaystyle E} in () is likewise independent of v {\displaystyle v} . For the second term (the regularization term), since v {\displaystyle v} is orthogonal to ∑ i = 1 n α i φ ( x i ) {\displaystyle \sum _{i=1}^{n}\alpha _{i}\varphi (x_{i})} and g {\displaystyle g} is strictly monotonic, we have g ( ‖ f ‖ ) = g ( ‖ ∑ i = 1 n α i φ ( x i ) + v ‖ ) = g ( ‖ ∑ i = 1 n α i φ ( x i ) ‖ 2 + ‖ v ‖ 2 ) ≥ g ( ‖ ∑ i = 1 n α i φ ( x i ) ‖ ) . {\displaystyle {\begin{aligned}g\left(\lVert f\rVert \right)&=g\left(\lVert \sum _{i=1}^{n}\alpha _{i}\varphi (x_{i})+v\rVert \right)\\&=g\left({\sqrt {\lVert \sum _{i=1}^{n}\alpha _{i}\varphi (x_{i})\rVert ^{2}+\lVert v\rVert ^{2}}}\right)\\&\geq g\left(\lVert \sum _{i=1}^{n}\alpha _{i}\varphi (x_{i})\rVert \right).\end{aligned}}} Therefore, setting v = 0 {\displaystyle v=0} does not affect the first term of (), while it strictly decreases the second term. Consequently, any minimizer f ∗ {\displaystyle f^{}} in () must have v = 0 {\displaystyle v=0} , i.e., it must be of the form f ∗ ( ⋅ ) = ∑ i = 1 n α i φ ( x i ) = ∑ i = 1 n α i k ( ⋅ , x i ) , {\displaystyle f^{}(\cdot )=\sum _{i=1}^{n}\alpha _{i}\varphi (x_{i})=\sum _{i=1}^{n}\alpha _{i}k(\cdot ,x_{i}),} which is the desired result. == Generalizations == The Theorem stated above is a particular example of a family of results that are collectively referred to as "representer theorems"; here we describe several such. The first statement of a representer theorem was due to Kimeldorf and Wahba for the special case in which E ( ( x 1 , y 1 , f ( x 1 ) ) , … , ( x n , y n , f ( x n ) ) ) = 1 n ∑ i = 1 n ( f ( x i ) − y i ) 2 , g ( ‖ f ‖ ) = λ ‖ f ‖ 2 {\displaystyle {\begin{aligned}E\left((x_{1},y_{1},f(x_{1})),\ldots ,(x_{n},y_{n},f(x_{n}))\right)&={\frac {1}{n}}\sum _{i=1}^{n}(f(x_{i})-y_{i})^{2},\\g(\lVert f\rVert )&=\lambda \lVert f\rVert ^{2}\end{aligned}}} for λ > 0 {\displaystyle \lambda >0} . Schölkopf, Herbrich, and Smola generalized this result by relaxing the assumption of the squared-loss cost and allowing the regularizer to be any strictly monotonically increasing function g ( ⋅ ) {\displaystyle g(\cdot )} of the Hilbert space norm. It is possible to generalize further by augmenting the regularized empirical risk functional through the addition of unpenalized offset terms. For example, Schölkopf, Herbrich, and Smola also consider the minimization f ~ ∗ = argmin { E ( ( x 1 , y 1 , f ~ ( x 1 ) ) , … , ( x n , y n , f ~ ( x n ) ) ) + g ( ‖ f ‖ ) ∣ f ~ = f + h ∈ H k ⊕ span { ψ p ∣ 1 ≤ p ≤ M } } , ( † ) {\displaystyle {\tilde {f}}^{}=\operatorname {argmin} \left\lbrace E\left((x_{1},y_{1},{\tilde {f}}(x_{1})),\ldots ,(x_{n},y_{n},{\tilde {f}}(x_{n}))\right)+g\left(\lVert f\rVert \right)\mid {\tilde {f}}=f+h\in H_{k}\oplus \operatorname {span} \lbrace \psi _{p}\mid 1\leq p\leq M\rbrace \right\rbrace ,\quad (\dagger )} i.e., we consider functions of the form f ~ = f + h {\displaystyle {\tilde {f}}=f+h} , where f ∈ H k {\displaystyle f\in H_{k}} and h {\displaystyle h} is an unpenalized function lying in the span of a finite set of real-valued functions { ψ p : X → R ∣ 1 ≤ p ≤ M } {\displaystyle \lbrace \psi _{p}\colon {\mathcal {X}}\to \mathbb {R} \mid 1\leq p\leq M\rbrace } . Under the assumption that the n × M {\displaystyle n\times M} matrix ( ψ p ( x i ) ) i p {\displaystyle \left(\psi _{p}(x_{i})\right)_{ip}} has rank M {\displaystyle M} , they show that the minimizer f ~ ∗ {\displaystyle {\tilde {f}}^{}} in ( † ) {\displaystyle (\dagger )} admits a representation of the form f ~ ∗ ( ⋅ ) = ∑ i = 1 n α i k ( ⋅ , x i ) + ∑ p = 1 M β p ψ p ( ⋅ ) {\displaystyle {\tilde {f}}^{}(\cdot )=\sum _{i=1}^{n}\alpha _{i}k(\cdot ,x_{i})+\sum _{p=1}^{M}\beta _{p}\psi _{p}(\cdot )} where α i , β p ∈ R {\displaystyle \alpha _{i},\beta _{p}\in \mathbb {R} } and the β p {\displaystyle \beta _{p}} are all uniquely determined. The conditions under which a representer theorem exists were investigated by Argyriou, Micchelli, and Pontil, who proved the following: Theorem: Let X {\displaystyle {\mathcal {X}}} be a nonempty set, k {\displaystyle k} a positive-definite real-valued kernel on X × X {\displaystyle {\mathcal {X}}\times {\mathcal {X}}} with corresponding reproducing kernel Hilbert space H k {\displaystyle H_{k}} , and let R : H k → R {\displaystyle R\colon H_{k}\to \mathbb {R} } be a differentiable regularization function. Then given a training sample ( x 1 , y 1 ) , … , ( x n , y n ) ∈ X × R {\displaystyle (x_{1},y_{1}),\ldots ,(x_{n},y_{n})\in {\mathcal {X}}\times \mathbb {R} } and an arbitrary error function E : ( X × R 2 ) m → R ∪ { ∞ } {\displaystyle E\colon ({\mathcal {X}}\times \mathbb {R} ^{2})^{m}\to \mathbb {R} \cup \lbrace \infty \rbrace } , a minimizer f ∗ = argmin f ∈ H k { E ( ( x 1 , y 1 , f ( x 1 ) ) , … , ( x n , y n , f ( x n ) ) ) + R ( f ) } ( ‡ ) {\displaystyle f^{}={\underset {f\in H_{k}}{\operatorname {argmin} }}\left\lbrace E\left((x_{1},y_{1},f(x_{1})),\ldots ,(x_{n},y_{n},f(x_{n}))\right)+R(f)\right\rbrace \quad (\ddagger )} of the regularized empirical risk admits a repr
Minimum Population Search
In evolutionary computation, Minimum Population Search (MPS) is a computational method that optimizes a problem by iteratively trying to improve a set of candidate solutions with regard to a given measure of quality. It solves a problem by evolving a small population of candidate solutions by means of relatively simple arithmetical operations. MPS is a metaheuristic as it makes few or no assumptions about the problem being optimized and can search very large spaces of candidate solutions. For problems where finding the precise global optimum is less important than finding an acceptable local optimum in a fixed amount of time, using a metaheuristic such as MPS may be preferable to alternatives such as brute-force search or gradient descent. MPS is used for multidimensional real-valued functions but does not use the gradient of the problem being optimized, which means MPS does not require for the optimization problem to be differentiable as is required by classic optimization methods such as gradient descent and quasi-newton methods. MPS can therefore also be used on optimization problems that are not even continuous, are noisy, change over time, etc. == Background == In a similar way to Differential evolution, MPS uses difference vectors between the members of the population in order to generate new solutions. It attempts to provide an efficient use of function evaluations by maintaining a small population size. If the population size is smaller than the dimensionality of the search space, then the solutions generated through difference vectors will be constrained to the n − 1 {\displaystyle n-1} dimensional hyperplane. A smaller population size will lead to a more restricted subspace. With a population size equal to the dimensionality of the problem ( n = d ) {\displaystyle (n=d)} , the “line/hyperplane points” in MPS will be generated within a d − 1 {\displaystyle d-1} dimensional hyperplane. Taking a step orthogonal to this hyperplane will allow the search process to cover all the dimensions of the search space. Population size is a fundamental parameter in the performance of population-based heuristics. Larger populations promote exploration, but they also allow fewer generations, and this can reduce the chance of convergence. Searching with a small population can increase the chances of convergence and the efficient use of function evaluations, but it can also induce the risk of premature convergence. If the risk of premature convergence can be avoided, then a population-based heuristic could benefit from the efficiency and faster convergence rate of a smaller population. To avoid premature convergence, it is important to have a diversified population. By including techniques for explicitly increasing diversity and exploration, it is possible to have smaller populations with less risk of premature convergence. === Thresheld Convergence === Thresheld Convergence (TC) is a diversification technique which attempts to separate the processes of exploration and exploitation. TC uses a “threshold” function to establish a minimum search step, and managing this step makes it possible to influence the transition from exploration to exploitation, convergence is thus “held” back until the last stages of the search process. The goal of a controlled transition is to avoid an early concentration of the population around a few search regions and avoid the loss of diversity which can cause premature convergence. Thresheld Convergence has been successfully applied to several population-based metaheuristics such as Particle Swarm Optimization, Differential evolution, Evolution strategies, Simulated annealing and Estimation of Distribution Algorithms. The ideal case for Thresheld Convergence is to have one sample solution from each attraction basin, and for each sample solution to have the same relative fitness with respect to its local optimum. Enforcing a minimum step aims to achieve this ideal case. In MPS Thresheld Convergence is specifically used to preserve diversity and avoid premature convergence by establishing a minimum search step. By disallowing new solutions which are too close to members of the current population, TC forces a strong exploration during the early stages of the search while preserving the diversity of the (small) population. == Algorithm == A basic variant of the MPS algorithm works by having a population of size equal to the dimension of the problem. New solutions are generated by exploring the hyperplane defined by the current solutions (by means of difference vectors) and performing an additional orthogonal step in order to avoid getting caught in this hyperplane. The step sizes are controlled by the Thresheld Convergence technique, which gradually reduces step sizes as the search process advances. An outline for the algorithm is given below: Generate the first initial population. Allowing these solutions to lie near the bounds of the search space generally gives good results: s k = ( r s 1 ∗ b o u n d 1 / 2 , r s 2 ∗ b o u n d 2 / 2 , . . . , r s n ∗ b o u n d n / 2 ) {\displaystyle s_{k}=(rs_{1}bound_{1}/2,rs_{2}bound_{2}/2,...,rs_{n}bound_{n}/2)} where s k {\displaystyle s_{k}} is the k {\displaystyle k} -th population member, r s i {\displaystyle rs_{i}} are random numbers which can be −1 or 1, and the b o u n d i {\displaystyle bound_{i}} are the lower and upper bounds on each dimension. While a stop condition is not reached: Update threshold convergence values ( m i n _ s t e p {\displaystyle min\_step} and m a x _ s t e p {\displaystyle max\_step} ) Calculate the centroid of the current population ( x c {\displaystyle x_{c}} ) For each member of the population ( x i {\displaystyle x_{i}} ), generate a new offspring as follows: Uniformly generate a scaling factor ( F i {\displaystyle F_{i}} ) between − m a x _ s t e p {\displaystyle -max\_step} and m a x _ s t e p {\displaystyle max\_step} Generate a vector ( x o {\displaystyle x_{o}} ) orthogonal to the difference vector between x i {\displaystyle x_{i}} and x c {\displaystyle x_{c}} Calculate a scaling factor for the orthogonal vector: m i n _ o r t h = s q r t ( m a x ( m i n _ s t e p 2 − F i 2 , 0 ) ) {\displaystyle min\_orth=sqrt(max(min\_step^{2}-F_{i}^{2},0))} m a x _ o r t h = s q r t ( m a x ( m a x _ s t e p 2 − F i 2 , 0 ) ) {\displaystyle max\_orth=sqrt(max(max\_step^{2}-F_{i}^{2},0))} o r t h _ s t e p = u n i f o r m ( m i n _ o r t h , m a x _ o r t h ) {\displaystyle orth\_step=uniform(min\_orth,max\_orth)} Generate the new solution by adding the difference and the orthogonal vectors to the original solution n e w _ s o l u t i o n = x i + F i ∗ ( x i − x c ) ∗ o r t h _ s t e p ∗ x o {\displaystyle new\_solution=x_{i}+F_{i}(x_{i}-x_{c})orth\_stepx_{o}} Pick the best members between the old population and the new one by discarding the least fit members. Return the single best solution or the best population found as the final result.
Split screen (computing)
Split screen is a display technique in computer graphics that consists of dividing graphics and/or text into non-overlapping adjacent parts, typically as two or four rectangular areas. This allows for the simultaneous presentation of (usually) related graphical and textual information on a computer display. TV sports adopted this presentation methodology in the 1960s for instant replay. Non-dynamic split screens differ from windowing systems in that the latter allowed overlapping and freely movable parts of the screen (the "windows") to present both related and unrelated application data to the user. In contrast, split-screen views are strictly limited to fixed positions. The split screen technique can also be used to run two instances of an application, potentially allowing another user to interact with the second instance. == In operating systems == Split screen modes are used by mobile operating systems to enable computer multitasking similar to the window interface present in desktop operating systems. Android supports split screen view of two apps natively on all devices, while certain devices, such as Samsung Galaxy Z TriFold, support three sumultaneous views. Split screen functionality is not supported on iOS, but a similar feature called Split View is present in iPadOS, first introduced in 2015 with the first generation of iPad Pro. == In video games == The split screen feature is commonly used in non-networked, also known as couch co-op, video games with multiplayer options. In its most easily understood form, a split screen for a multiplayer video game is an audiovisual output device (usually a standard television for video game consoles) where the display has been divided into 2-4 equally sized areas (depending on number of players) so that the players can explore different areas simultaneously without being close to each other. This has historically been remarkably popular on consoles, which until the 2000s did not have access to the Internet or any other network and is less common today with modern support for networked console-to-console multiplayer. In competitive split-screen games, it is customarily considered cheating to look at another player's screen section to gain an advantage. === History === Split screen gaming dates back to at least the 1970s, with games such Drag Race (1977) from Kee Games in the arcades being presented in this format. It has always been a common feature of two or more player home console and computer games too, with notable titles being Kikstart II for 8-bit systems, a number of 16-bit racing games (such as Lotus Esprit Turbo Challenge and Road Rash II), and action/strategy games (such as Toejam & Earl and Lemmings), all employing a vertical or horizontal screen split for two player games. Xenophobe is notable as a three-way split screen arcade title, although on home platforms it was reduced to one or two screens. The addition of four controller ports on home consoles also ushered in more four-way split screen games, with Mario Kart 64 and Goldeneye 007 on the Nintendo 64 being two well known examples. In arcades, machines tended to move towards having a whole screen for each player, or multiple connected machines, for multiplayer. On home machines, especially in the first and third person shooter genres, multiplayer is now more common over a network or the internet rather than locally with split screen. Starting from the late 2000s, the presence of split screen multiplayer has largely been declining due to the increasing prevalence of online multiplayer, though TechRadar reported a resurgence of split screen due to support from independent studios and increased interest from the players.
KNIME
KNIME ( ), the Konstanz Information Miner, is a data analytics, reporting and integrating platform. KNIME integrates various components for machine learning and data mining through its modular data pipelining "Building Blocks of Analytics" concept. A graphical user interface and use of Java Database Connectivity (JDBC) allows assembly of nodes blending different data sources, including preprocessing (extract, transform, load, or ETL), for modeling, data analysis and visualization with minimal, or no, programming. It is free and open-source software released under a GNU General Public License. Since 2006, KNIME has been used in pharmaceutical research, and in other areas including customer relationship management (CRM) and data analysis, business intelligence, text mining and financial data analysis. Recently, attempts were made to use KNIME as robotic process automation (RPA) tool. KNIME's headquarters are based in Zurich, with other offices in Konstanz, Berlin, and Austin (USA). == History == Development of KNIME began in January 2004, with a team of software engineers at the University of Konstanz, as an open-source platform. The original team, headed by Michael Berthold, came from a Silicon Valley pharmaceutical industry software company. The initial goal was to create a modular, highly scalable and open data processing platform that allows easy integration of different data loading, processing, transforming, analyzing, and visual exploring modules, without focus on any one application area. The platform was intended for collaborating, research, and for integrating various other data analysis projects. In 2006, the first version of KNIME was released. Several pharmaceutical companies began using KNIME, and several life science software vendors began integrating their tools into the platform. Later that year, after an article in the German magazine c't, users from a number of other areas joined ship. As of 2012, KNIME is in use by over 15,000 actual users (i.e. not counting downloads, but users regularly retrieving updates) in the life sciences and at banks, publishers, car manufacturer, telcos, consulting firms, and various other industries, and a large number of research groups, worldwide. Latest updates to KNIME Server and KNIME Big Data Extensions, provide support for Apache Spark 2.3, Parquet and HDFS-type storage. For the sixth year in a row, KNIME has been placed as a leader for data science and machine learning platforms in Gartner's Magic Quadrant. == Design philosophy, features == These are the design principles and features that KNIME software follows: Visual, Interactive Framework: KNIME Software prioritizes a user-friendly and intuitive approach to data analysis. This is achieved through a visual and interactive framework where data flows can be combined using a drag-and-drop interface. Users can develop customized and interactive applications by creating simple to advanced and highly-automated data pipelines. These may include, for example, access to databases, machine learning libraries, logic for workflow control (e.g., loops, switches, etc.), abstraction (e.g., interactive widgets), invocation, dynamic data apps, integrated deployment, or error handling. Modularity: processing units and data containers should remain independent of each other. This design choice enables easy distribution of computation and allows for the independent development of different algorithms. Data types within KNIME are encapsulated, meaning no types are predefined. This design choice facilitates adding new data types, and integrating them with extant types, while including type-specific renderers and comparators. This principle also enables inspecting results at the end of each single data operation. Extensibility: KNIME Software is designed to be extensible. Adding new processing nodes or views is made simple through a plug-in mechanism. This mechanism ensures that users can distribute their custom functionalities without the need for complicated install or uninstall procedures. Interleaving No-Code with Code: the platform supports integrating both visual programming (no-code) and script-based programming (e.g., Python, R, JavaScript) approaches to data analysis. This design principle is termed low-code. Automation and Scalability: for example, the use of parameterization via flow variables, or the encapsulation of workflow segments in components contribute to reduce manual work and errors in analyses. Further, the scheduling of workflow execution (available in KNIME Business Hub and KNIME Community Hub for Teams) reduces dependency on human resources. In terms of scalability, a few examples include the ability to handle large datasets (millions of rows), execute multiple processes simultaneously out of the box and reuse workflow segments. Full Usability: due to the open source nature, KNIME Analytics Platform provides free full usability with no limited trial periods. == Internals == KNIME allows users to visually create data flows (or pipelines), selectively execute some or all analysis steps, and later inspect the results, models, using interactive widgets and views. KNIME is written in Java and based on Eclipse. It makes use of an extension mechanism to add plug-ins providing added functions. The core version includes hundreds of modules for data integration (file input/output (I/O), database nodes supporting all common database management systems through JDBC or native connectors: SQLite, MS-Access, SQL Server, MySQL, Oracle, PostgreSQL, Vertica and H2), data transformation (filter, converter, splitter, combiner, joiner), and the commonly used methods of statistics, data mining, analysis and text analytics. Visualization is supported with the Report Designer extension. KNIME workflows can be used as data sets to create report templates that can be exported to document formats such as doc, ppt, xls, pdf and others. Other KNIME abilities are: KNIMEs core-architecture allows processing of large data volumes that are only limited by the available hard disk space (not limited to the available RAM). E.g., KNIME allows analyzing 300 million customer addresses, 20 million cell images, and 10 million molecular structures. Added plug-ins allow integrating methods for text mining, image mining, time series analysis, and networking. KNIME integrates various other open-source projects, e.g., machine learning algorithms from Weka, H2O, Keras, Spark, the R project and LIBSVM; plotly, JFreeChart, ImageJ, and the Chemistry Development Kit. KNIME is implemented in Java, allows for wrappers calling other code, in addition to providing nodes that allow it to run Java, Python, R, Ruby and other code fragments. Since 2021, KNIME's Python Integration utilizes Anaconda for Python distribution and environment management. == License == In 2024, KNIME version 5.3 is released under the same GPLv3 license as previous versions. As of version 2.1, KNIME is released under the GPLv3 license, with an exception that allow commercial software vendors to use the well-defined node application programming interface (API) to add proprietary extensions, or wrappers calling their tools from KNIME. == Courses == KNIME allows the performance of data analysis without programming skills. Several free, online courses are provided.