AI Chatbot No Filter No Limit

AI Chatbot No Filter No Limit — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  AVS Video Editor

  AVS Video Editor is a video editing software published by Online Media Technologies Ltd. It is a part of AVS4YOU software suite which includes video, audio, image editing and conversion, disc editing and burning, document conversion and registry cleaner programs. It offers the opportunity to create and edit videos with a vast variety of video and audio effects, text and transitions; capture video from screen, web or DV cameras and VHS tape; record voice; create menus for discs, as well as to save them to plenty of video file formats, burn to discs or publish on Facebook, YouTube, Flickr, etc. == Description == === Interface === The layout consists of the timeline or storyboard view, preview pane and media library (transitions, video effects, text or disc menus) collections. The storyboard view shows the sequence of video clips with the transitions between them and used to change the order of clips or add transitions. Timeline view consists of main video, audio, effects, video overlay and text lines for editing. Once on the timeline video can be duplicated, split, muted, frozen, cropped, stabilized, its speed can be slowed down or increased, audio and color corrected. === Importing footage === Video, audio and image files necessary for video project can be imported into the program from computer hard disk drive. User can also capture video from computer screen, web or mini DV camera, as well as from VHS tape, record voice. === Output (web, device, disc, format) === AVS Video Editor gives the opportunity to save video to a computer hard drive to one of the video formats: AVI, DVD, Blu-ray, MOV, MP4, M4V, MPEG, WMV, MKV, WebM, M2TS, TS, FLV, SWF, RM, 3GP, GIF, DPG, AMV, MTV; burn to DVD or Blu-ray disc with menus; create a video for mobile players, mobile phones or gaming consoles and upload it right to the device. The most popular devices such as Apple iPod, Apple iPhone, Apple iPad, Sony PSP, Samsung Galaxy, Android and BlackBerry smartphones and tablets are supported. There is also an option to create a video that can be streamed via web and save it into Flash or WebM format or for the popular web services: YouTube, Facebook, Telly (Twitvid), Dailymotion, Flickr and Dropbox. === Features === Single and multithread modes: if a computer supports multi-threading, video creation process is performed faster in multithread mode, especially on a multi-core system. Customization of the output file settings, such as bitrate, frame rate, frame size, video and audio codecs, etc. Transitions - help video clips smoothly go into one another, dissolve or overlap two video or image files. Fade in and fade out video and audio files - dissolve a video to and from a blank image, reduce the audio volume at the end of the video and increase at the beginning. Slideshow creation - create a presentation of a series of still images. Voice recording Projects - once a project is created and saved, the next time saving video to some other format will be fast, projects are also used if a user do not have a possibility to create, edit and save video all at once. Video overlay option - superpose video image over the video clip that is being edited. Disk menu and chapters creation - an option for DVD and Blu-ray video. Freeze frame - make a still shot from a video clip. Stabilization feature - reduce jittering or blurring caused by shaky motions of a camera. Enhanced deinterlacing method - increase video quality for interlaced input file - spots and blurred areas are compensated. Scene detection - search and separate one scene of the video from the other. Loop DVD and SWF - output SWF and DVD video are played back continuously. Caching for processing high definition files - create a duplicate video file smaller in size to use it on the preview window and accelerate processing of HD files. Chroma key option - add video overlay half transparent so that only part of it is visible and all the rest disappears to reveal the video underneath. Capture video material from DV tapes, VHS tapes, web cameras, etc. Movie closing credits - add information on movie editing, e.g. crew, cast, data, etc. Creeping line, subtitles, text - add different captions (static and animated), shapes and images to video. Speech balloons and other graphic objects - geometrical shapes to highlight an object in the video. Zoom effect - magnify or reduce the view of the image. Rotate effect - rotate video image at different degrees, e.g. 90, 180, etc. Grayscale and old movie effects - create a black and white video image. Old movie adds also scratches, noise, shake and dust to video, as if it's being played on an old projector. Blur and sharpen effects - visually smooth and soften an image, or make video image better focused. Snow and particles effects - adds snow or various objects (bubbles, flowers, leaves, butterflies etc.) that are moving, flying or falling on the video. Pan and zoom Timer, countdown effects - add a timepiece that measures or counts down a time interval to the video being edited. Snapshots - capture a particular moment of a video clip. Sound track replacement - mute audio track from video and add another one. Audio amplify, noise removal, equalizer, etc. - make video sound louder, attenuate the noise, change frequency pattern of the audio, make some other audio adjustments. Trim and multi-trim options - change video clip duration cutting out unnecessary parts or detect scenes and cut out parts in any place of the video clip. Color correction (brightness, temperature, contrast, saturation, gamma, etc.) effects - allow adjustment of tonal range, color, and sharpness of video files. Crop scale effect - get rid of mattes that appear after changing aspect ratio of a video file. Adjusting the Playback Speed Volume and balance - change sound volume in the output video. Change volume value proportion for main video and added soundtrack, completely mute main video audio and leave added soundtrack only, etc. === Utilities embedded into AVS Video Editor === AVS Mobile Uploader is used to transfer edited and converted media files to portable devices via Bluetooth, Infrared or USB connection. AVS Video Burner is used to burn converted video files to different disc types: CD, DVD, Blu-ray. AVS Video Recorder is used to capture video from analog video sources and supports different types of devices: capture card, web camera (webcam), DV camera, HDV camera. AVS Video Uploader is used to transfer video files to popular video-sharing websites, like Facebook, Dailymotion, YouTube, Photobucket, TwitVid, MySpace, Flickr. AVS Screen Capture is used to capture any actions on the desktop to make presentations or video tutorials more vivid and easily comprehensible. == Important upgrades == The initial release of AVS Video Editor was in 2003 when the program was offered inside AVS software bundles together with AVS Video Tools, AVS Audio Tools and DVD Copy software. In 2005 the program is offered as a part of multifunctional AVS4YOU software suite. AVS Video Editor is frequently updated. The main updates include adding several important features for video editing

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  Evolutionary programming

  Evolutionary programming is an evolutionary algorithm, where a share of new population is created by mutation of previous population without crossover. Evolutionary programming differs from evolution strategy ES( μ + λ {\displaystyle \mu +\lambda } ) in one detail. All individuals are selected for the new population, while in ES( μ + λ {\displaystyle \mu +\lambda } ), every individual has the same probability to be selected. It is one of the four major evolutionary algorithm paradigms. == History == It was first used by Lawrence J. Fogel in the US in 1960 in order to use simulated evolution as a learning process aiming to generate artificial intelligence. It was used to evolve finite-state machines as predictors.

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  Multiclass classification

  In machine learning and statistical classification, multiclass classification or multinomial classification is the problem of classifying instances into one of three or more classes (classifying instances into one of two classes is called binary classification). For example, deciding on whether an image is showing a banana, peach, orange, or an apple is a multiclass classification problem, with four possible classes (banana, peach, orange, apple), while deciding on whether an image contains an apple or not is a binary classification problem (with the two possible classes being: apple, no apple). While many classification algorithms (e.g., decision trees, k-NN, neural networks and multinomial logistic regression) naturally permit the use of more than two classes, some are by nature binary algorithms (e.g., classical binary support vector machine) and require decomposition strategies such as one-vs-all, one-vs-one, or ECOC to solve multiclass problems. Multiclass classification should not be confused with multi-label classification, where multiple labels are to be predicted for each instance (e.g., predicting that an image contains both an apple and an orange, in the previous example). == Better-than-random multiclass models == From the confusion matrix of a multiclass model, we can determine whether a model does better than chance. Let K ≥ 3 {\displaystyle K\geq 3} be the number of classes, O {\displaystyle {\mathcal {O}}} a set of observations, y ^ : O → { 1 , . . . , K } {\displaystyle {\hat {y}}:{\mathcal {O}}\to \{1,...,K\}} a model of the target variable y : O → { 1 , . . . , K } {\displaystyle y:{\mathcal {O}}\to \{1,...,K\}} and n i , j {\displaystyle n_{i,j}} be the number of observations in the set { y = i } ∩ { y ^ = j } {\displaystyle \{y=i\}\cap \{{\hat {y}}=j\}} . We note n i . = ∑ j n i , j {\displaystyle n_{i.}=\sum _{j}n_{i,j}} , n . j = ∑ i n i , j {\displaystyle n_{.j}=\sum _{i}n_{i,j}} , n = ∑ j n . j = ∑ i n i . {\displaystyle n=\sum _{j}n_{.j}=\sum _{i}n_{i.}} , λ i = n i . n {\displaystyle \lambda _{i}={\frac {n_{i.}}{n}}} and μ j = n . j n {\displaystyle \mu _{j}={\frac {n_{.j}}{n}}} . It is assumed that the confusion matrix ( n i , j ) i , j {\displaystyle (n_{i,j})_{i,j}} contains at least one non-zero entry in each row, that is λ i > 0 {\displaystyle \lambda _{i}>0} for any i {\displaystyle i} . Finally we call "normalized confusion matrix" the matrix of conditional probabilities ( P ( y ^ = j ∣ y = i ) ) i , j = ( n i , j n i . ) i , j {\displaystyle (\mathbb {P} ({\hat {y}}=j\mid y=i))_{i,j}=\left({\frac {n_{i,j}}{n_{i.}}}\right)_{i,j}} . === Intuitive explanation === The lift is a way of measuring the deviation from independence of two events A {\displaystyle A} and B {\displaystyle B} : L i f t ( A , B ) = P ( A ∩ B ) P ( A ) P ( B ) = P ( A ∣ B ) P ( A ) = P ( B ∣ A ) P ( B ) {\displaystyle \mathrm {Lift} (A,B)={\frac {\mathbb {P} (A\cap B)}{\mathbb {P} (A)\mathbb {P} (B)}}={\frac {\mathbb {P} (A\mid B)}{\mathbb {P} (A)}}={\frac {\mathbb {P} (B\mid A)}{\mathbb {P} (B)}}} We have L i f t ( A , B ) > 1 {\displaystyle \mathrm {Lift} (A,B)>1} if and only if events A {\displaystyle A} and B {\displaystyle B} occur simultaneously with a greater probability than if they were independent. In other words, if one of the two events occurs, the probability of observing the other event increases. A first condition to satisfy is to have L i f t ( y = i , y ^ = i ) ≥ 1 {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)\geq 1} for any i {\displaystyle i} . And the quality of a model (better or worse than chance) does not change if we over- or undersample the dataset, that is if we multiply each row R i {\displaystyle R_{i}} of the confusion matrix by a constant c i {\displaystyle c_{i}} . Thus the second condition is that the necessary and sufficient conditions for doing better than chance need only depend on the normalized confusion matrix. The condition on lifts can be reformulated with One versus Rest binary models : for any i {\displaystyle i} , we define the binary target variable y i {\displaystyle y_{i}} which is the indicator of event { y = i } {\displaystyle \{y=i\}} , and the binary model y ^ i {\displaystyle {\hat {y}}_{i}} of y i {\displaystyle y_{i}} which is the indicator of event { y ^ = i } {\displaystyle \{{\hat {y}}=i\}} . Each of the y ^ i {\displaystyle {\hat {y}}_{i}} models is a "One versus Rest" model. L i f t ( y = i , y ^ = i ) {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)} only depends on the events { y = i } {\displaystyle \{y=i\}} and { y ^ = i } {\displaystyle \{{\hat {y}}=i\}} , so merging or not merging the other classes doesn't change its value. We therefore have L i f t ( y = i , y ^ = i ) = L i f t ( y i = 1 , y ^ i = 1 ) {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)=\mathrm {Lift} (y_{i}=1,{\hat {y}}_{i}=1)} and the first condition is that all binary One versus Rest models are better than chance. ==== Example ==== If K = 2 {\displaystyle K=2} and 2 is the class of interest , the normalized confusion matrix is ( s p e c i f i c i t y 1 − s p e c i f i c i t y 1 − s e n s i t i v i t y s e n s i t i v i t y ) {\displaystyle {\begin{pmatrix}\mathrm {specificity} &1-\mathrm {specificity} \\1-\mathrm {sensitivity} &\mathrm {sensitivity} \end{pmatrix}}} and we have L i f t ( y = 1 , y ^ = 1 ) − 1 = P ( y = y ^ = 1 ) λ 1 μ 1 − 1 = n 1 , 1 n n 1. n .1 − 1 {\displaystyle \mathrm {Lift} (y=1,{\hat {y}}=1)-1={\frac {\mathbb {P} (y={\hat {y}}=1)}{\lambda _{1}\mu _{1}}}-1={\frac {n_{1,1}n}{n_{1.}n_{.1}}}-1} = n 1 , 1 ( n 1 , 1 + n 1 , 2 + n 2 , 1 + n 2 , 2 ) − ( n 1 , 1 + n 1 , 2 ) ( n 1 , 1 + n 2 , 1 ) n 1. n .1 = n 1 , 1 n 2 , 2 − n 1 , 2 n 2 , 1 n 1. n .1 {\displaystyle ={\frac {n_{1,1}(n_{1,1}+n_{1,2}+n_{2,1}+n_{2,2})-(n_{1,1}+n_{1,2})(n_{1,1}+n_{2,1})}{n_{1.}n_{.1}}}={\frac {n_{1,1}n_{2,2}-n_{1,2}n_{2,1}}{n_{1.}n_{.1}}}} . Thus L i f t ( y = 1 , y ^ = 1 ) ≥ 1 ⟺ n 1 , 1 n 2 , 2 − n 1 , 2 n 2 , 1 ≥ 0 {\displaystyle \mathrm {Lift} (y=1,{\hat {y}}=1)\geq 1\iff n_{1,1}n_{2,2}-n_{1,2}n_{2,1}\geq 0} . Similarly, by swapping the roles of 1 and 2, we find that L i f t ( y = 2 , y ^ = 2 ) ≥ 1 ⟺ n 1 , 1 n 2 , 2 − n 1 , 2 n 2 , 1 ≥ 0 {\displaystyle \mathrm {Lift} (y=2,{\hat {y}}=2)\geq 1\iff n_{1,1}n_{2,2}-n_{1,2}n_{2,1}\geq 0} . Dividing by n 1. n 2. {\displaystyle n_{1.}n_{2.}} we find that the necessary and sufficient condition on the normalized confusion matrix is s e n s i t i v i t y s p e c i f i c i t y − ( 1 − s e n s i t i v i t y ) ( 1 − s p e c i f i c i t y ) ≥ 0 ⟺ s e n s i t i v i t y + s p e c i f i c i t y − 1 ≥ 0 ⟺ J ≥ 0 {\displaystyle \mathrm {sensitivity} \ \mathrm {specificity} -(1-\mathrm {sensitivity} )(1-\mathrm {specificity} )\geq 0\iff \mathrm {sensitivity} +\mathrm {specificity} -1\geq 0\iff J\geq 0} . This brings us back to the classical binary condition: Youden's J must be positive (or zero for random models). === Random models === A random model is a model that is independent of the target variable. This property is easily reformulated with the confusion matrix. This proposition shows that the model y ^ {\displaystyle {\hat {y}}} of y {\displaystyle y} is uninformative if and only if there are two families of numbers ( α i ) i {\displaystyle (\alpha _{i})_{i}} and ( β j ) j {\displaystyle (\beta _{j})_{j}} such that P ( { y = i } ∩ { y ^ = j } ) = α i β j {\displaystyle \mathbb {P} (\{y=i\}\cap \{{\hat {y}}=j\})=\alpha _{i}\beta _{j}} for any i {\displaystyle i} and j {\displaystyle j} . === Multiclass likelihood ratios and diagnostic odds ratios === We define generalized likelihood ratios calculated from the normalized confusion matrix: for any i {\displaystyle i} and j ≠ i {\displaystyle j\not =i} , let L R i , j = P ( y ^ = j ∣ y = j ) P ( y ^ = j ∣ y = i ) {\displaystyle \mathrm {LR} _{i,j}={\frac {\mathbb {P} ({\hat {y}}=j\mid y=j)}{\mathbb {P} ({\hat {y}}=j\mid y=i)}}} . When K = 2 {\displaystyle K=2} , if 2 is the class of interest,, we find the classical likelihood ratios L R 1 , 2 = L R + {\displaystyle \mathrm {LR} _{1,2}=\mathrm {LR} _{+}} and L R 2 , 1 = 1 L R − {\displaystyle \mathrm {LR} _{2,1}={\frac {1}{\mathrm {LR} _{-}}}} . Multiclass diagnostic odds ratios can also be defined using the formula D O R i , j = D O R j , i = L R i , j L R j , i = n i , i n j , j n i , j n j , i = P ( y ^ = j ∣ y = j ) / P ( y ^ = i ∣ y = j ) P ( y ^ = j ∣ y = i ) / P ( y ^ = i ∣ y = i ) {\displaystyle \mathrm {DOR} _{i,j}=\mathrm {DOR} _{j,i}=\mathrm {LR} _{i,j}\mathrm {LR} _{j,i}={\frac {n_{i,i}n_{j,j}}{n_{i,j}n_{j,i}}}={\frac {\mathbb {P} ({\hat {y}}=j\mid y=j)/\mathbb {P} ({\hat {y}}=i\mid y=j)}{\mathbb {P} ({\hat {y}}=j\mid y=i)/\mathbb {P} ({\hat {y}}=i\mid y=i)}}} We saw above that a better-than-chance model (or a random model) must verify L i f t ( y = i , y ^ = i ) ≥ 1 {\displaystyle \mathrm {Lift} (y=i,{\hat {y}}=i)\geq 1} for any i {\displaystyle i} and λ i {\displaystyle \lambda _{i}} . According to the previous corollary, likelihood ratios are thus greater

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  Inverted pendulum

  An inverted pendulum is a pendulum that has its center of mass above its pivot point. It is unstable and falls over without additional help. It can be suspended stably in this inverted position by using a control system to monitor the angle of the pole and move the pivot point horizontally back under the center of mass when it starts to fall over, keeping it balanced. The inverted pendulum is a classic problem in dynamics and control theory and is used as a benchmark for testing control strategies. It is often implemented with the pivot point mounted on a cart that can move horizontally under control of an electronic servo system as shown in the photo; this is called a cart and pole apparatus. Most applications limit the pendulum to 1 degree of freedom by affixing the pole to an axis of rotation. Whereas a normal pendulum is stable when hanging downward, an inverted pendulum is inherently unstable, and must be actively balanced in order to remain upright; this can be done either by applying a torque at the pivot point, by moving the pivot point horizontally as part of a feedback system, changing the rate of rotation of a mass mounted on the pendulum on an axis parallel to the pivot axis and thereby generating a net torque on the pendulum, or by oscillating the pivot point vertically. A simple demonstration of moving the pivot point in a feedback system is achieved by balancing an upturned broomstick on the end of one's finger. A second type of inverted pendulum is a tiltmeter for tall structures, which consists of a wire anchored to the bottom of the foundation and attached to a float in a pool of oil at the top of the structure that has devices for measuring movement of the neutral position of the float away from its original position. == Overview == A pendulum with its bob hanging directly below the support pivot is at a stable equilibrium point, where it remains motionless because there is no torque on the pendulum. If displaced from this position, it experiences a restoring torque that returns it toward the equilibrium position. A pendulum with its bob in an inverted position, supported on a rigid rod directly above the pivot, 180° from its stable equilibrium position, is at an unstable equilibrium point. At this point again there is no torque on the pendulum, but the slightest displacement away from this position causes a gravitation torque on the pendulum that accelerates it away from equilibrium, causing it to fall over. In order to stabilize a pendulum in this inverted position, a feedback control system can be used, which monitors the pendulum's angle and moves the position of the pivot point sideways when the pendulum starts to fall over, to keep it balanced. The inverted pendulum is a classic problem in dynamics and control theory and is widely used as a benchmark for testing control algorithms (PID controllers, state-space representation, neural networks, fuzzy control, genetic algorithms, etc.). Variations on this problem include multiple links, allowing the motion of the cart to be commanded while maintaining the pendulum, and balancing the cart-pendulum system on a see-saw. The inverted pendulum is related to rocket or missile guidance, where the center of gravity is located behind the center of drag causing aerodynamic instability. The understanding of a similar problem can be shown by simple robotics in the form of a balancing cart. Balancing an upturned broomstick on the end of one's finger is a simple demonstration, and the problem is solved by self-balancing personal transporters such as the Segway PT, the self-balancing hoverboard and the self-balancing unicycle. Another way that an inverted pendulum may be stabilized, without any feedback or control mechanism, is by oscillating the pivot rapidly up and down. This is called Kapitza's pendulum. If the oscillation is sufficiently strong (in terms of its acceleration and amplitude) then the inverted pendulum can recover from perturbations in a strikingly counterintuitive manner. If the driving point moves in simple harmonic motion, the pendulum's motion is described by the Mathieu equation. == Equations of motion == The equations of motion of inverted pendulums are dependent on what constraints are placed on the motion of the pendulum. Inverted pendulums can be created in various configurations resulting in a number of Equations of Motion describing the behavior of the pendulum. === Stationary pivot point === In a configuration where the pivot point of the pendulum is fixed in space, the equation of motion is similar to that for an uninverted pendulum. The equation of motion below assumes no friction or any other resistance to movement, a rigid massless rod, and the restriction to 2-dimensional movement. θ ¨ − g ℓ sin ⁡ θ = 0 {\displaystyle {\ddot {\theta }}-{g \over \ell }\sin \theta =0} Where θ ¨ {\displaystyle {\ddot {\theta }}} is the angular acceleration of the pendulum, g {\displaystyle g} is the standard gravity on the surface of the Earth, ℓ {\displaystyle \ell } is the length of the pendulum, and θ {\displaystyle \theta } is the angular displacement measured from the equilibrium position. When θ ¨ {\displaystyle {\ddot {\theta }}} added to both sides, it has the same sign as the angular acceleration term: θ ¨ = g ℓ sin ⁡ θ {\displaystyle {\ddot {\theta }}={g \over \ell }\sin \theta } Thus, the inverted pendulum accelerates away from the vertical unstable equilibrium in the direction initially displaced, and the acceleration is inversely proportional to the length. Tall pendulums fall more slowly than short ones. Derivation using torque and moment of inertia: The pendulum is assumed to consist of a point mass, of mass m {\displaystyle m} , affixed to the end of a massless rigid rod, of length ℓ {\displaystyle \ell } , attached to a pivot point at the end opposite the point mass. The net torque of the system must equal the moment of inertia times the angular acceleration: τ n e t = I θ ¨ {\displaystyle {\boldsymbol {\tau }}_{\mathrm {net} }=I{\ddot {\theta }}} The torque due to gravity providing the net torque: τ n e t = m g ℓ sin ⁡ θ {\displaystyle {\boldsymbol {\tau }}_{\mathrm {net} }=mg\ell \sin \theta \,\!} Where θ {\displaystyle \theta \ } is the angle measured from the inverted equilibrium position. The resulting equation: I θ ¨ = m g ℓ sin ⁡ θ {\displaystyle I{\ddot {\theta }}=mg\ell \sin \theta \,\!} The moment of inertia for a point mass: I = m R 2 {\displaystyle I=mR^{2}} In the case of the inverted pendulum the radius is the length of the rod, ℓ {\displaystyle \ell } . Substituting in I = m ℓ 2 {\displaystyle I=m\ell ^{2}} m ℓ 2 θ ¨ = m g ℓ sin ⁡ θ {\displaystyle m\ell ^{2}{\ddot {\theta }}=mg\ell \sin \theta \,\!} Mass and ℓ 2 {\displaystyle \ell ^{2}} is divided from each side resulting in: θ ¨ = g ℓ sin ⁡ θ {\displaystyle {\ddot {\theta }}={g \over \ell }\sin \theta } === Inverted pendulum on a cart === An inverted pendulum on a cart consists of a mass m {\displaystyle m} at the top of a pole of length ℓ {\displaystyle \ell } pivoted on a horizontally moving base as shown in the adjacent image. The cart is restricted to linear motion and is subject to forces resulting in or hindering motion. === Essentials of stabilization === The essentials of stabilizing the inverted pendulum can be summarized qualitatively in three steps. 1. If the tilt angle θ {\displaystyle \theta } is to the right, the cart must accelerate to the right and vice versa. 2. The position of the cart x {\displaystyle x} relative to track center is stabilized by slightly modulating the null angle (the angle error that the control system tries to null) by the position of the cart, that is, null angle = θ + k x {\displaystyle =\theta +kx} where k {\displaystyle k} is small. This makes the pole want to lean slightly toward track center and stabilize at track center where the tilt angle is exactly vertical. Any offset in the tilt sensor or track slope that would otherwise cause instability translates into a stable position offset. A further added offset gives position control. 3. A normal pendulum subject to a moving pivot point such as a load lifted by a crane, has a peaked response at the pendulum radian frequency of ω p = g / ℓ {\displaystyle \omega _{p}={\sqrt {g/\ell }}} . To prevent uncontrolled swinging, the frequency spectrum of the pivot motion should be suppressed near ω p {\displaystyle \omega _{p}} . The inverted pendulum requires the same suppression filter to achieve stability. As a consequence of the null angle modulation strategy, the position feedback is positive, that is, a sudden command to move right produces an initial cart motion to the left followed by a move right to rebalance the pendulum. The interaction of the pendulum instability and the positive position feedback instability to produce a stable system is a feature that makes the mathematical analysis an interesting and challenging problem. === From Lagrange's equations === The equations of motion c

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  Visual servoing

  Visual servoing, also known as vision-based robot control and abbreviated VS, is a technique which uses feedback information extracted from a vision sensor (visual feedback) to control the motion of a robot. One of the earliest papers that talks about visual servoing was from the SRI International Labs in 1979. == Visual servoing taxonomy == There are two fundamental configurations of the robot end-effector (hand) and the camera: Eye-in-hand, or end-point open-loop control, where the camera is attached to the moving hand and observing the relative position of the target. Eye-to-hand, or end-point closed-loop control, where the camera is fixed in the world and observing the target and the motion of the hand. Visual Servoing control techniques are broadly classified into the following types: Image-based (IBVS) Position/pose-based (PBVS) Hybrid approach IBVS was proposed by Weiss and Sanderson. The control law is based on the error between current and desired features on the image plane, and does not involve any estimate of the pose of the target. The features may be the coordinates of visual features, lines or moments of regions. IBVS has difficulties with motions very large rotations, which has come to be called camera retreat. PBVS is a model-based technique (with a single camera). This is because the pose of the object of interest is estimated with respect to the camera and then a command is issued to the robot controller, which in turn controls the robot. In this case the image features are extracted as well, but are additionally used to estimate 3D information (pose of the object in Cartesian space), hence it is servoing in 3D. Hybrid approaches use some combination of the 2D and 3D servoing. There have been a few different approaches to hybrid servoing 2-1/2-D Servoing Motion partition-based Partitioned DOF Based == Survey == The following description of the prior work is divided into 3 parts Survey of existing visual servoing methods. Various features used and their impacts on visual servoing. Error and stability analysis of visual servoing schemes. === Survey of existing visual servoing methods === Visual servo systems, also called servoing, have been around since the early 1980s , although the term visual servo itself was only coined in 1987. Visual Servoing is, in essence, a method for robot control where the sensor used is a camera (visual sensor). Servoing consists primarily of two techniques, one involves using information from the image to directly control the degrees of freedom (DOF) of the robot, thus referred to as Image Based Visual Servoing (IBVS). While the other involves the geometric interpretation of the information extracted from the camera, such as estimating the pose of the target and parameters of the camera (assuming some basic model of the target is known). Other servoing classifications exist based on the variations in each component of a servoing system , e.g. the location of the camera, the two kinds are eye-in-hand and hand–eye configurations. Based on the control loop, the two kinds are end-point-open-loop and end-point-closed-loop. Based on whether the control is applied to the joints (or DOF) directly or as a position command to a robot controller the two types are direct servoing and dynamic look-and-move. Being one of the earliest works the authors proposed a hierarchical visual servo scheme applied to image-based servoing. The technique relies on the assumption that a good set of features can be extracted from the object of interest (e.g. edges, corners and centroids) and used as a partial model along with global models of the scene and robot. The control strategy is applied to a simulation of a two and three DOF robot arm. Feddema et al. introduced the idea of generating task trajectory with respect to the feature velocity. This is to ensure that the sensors are not rendered ineffective (stopping the feedback) for any the robot motions. The authors assume that the objects are known a priori (e.g. CAD model) and all the features can be extracted from the object. The work by Espiau et al. discusses some of the basic questions in visual servoing. The discussions concentrate on modeling of the interaction matrix, camera, visual features (points, lines, etc..). In an adaptive servoing system was proposed with a look-and-move servoing architecture. The method used optical flow along with SSD to provide a confidence metric and a stochastic controller with Kalman filtering for the control scheme. The system assumes (in the examples) that the plane of the camera and the plane of the features are parallel., discusses an approach of velocity control using the Jacobian relationship s˙ = Jv˙ . In addition the author uses Kalman filtering, assuming that the extracted position of the target have inherent errors (sensor errors). A model of the target velocity is developed and used as a feed-forward input in the control loop. Also, mentions the importance of looking into kinematic discrepancy, dynamic effects, repeatability, settling time oscillations and lag in response. Corke poses a set of very critical questions on visual servoing and tries to elaborate on their implications. The paper primarily focuses the dynamics of visual servoing. The author tries to address problems like lag and stability, while also talking about feed-forward paths in the control loop. The paper also, tries to seek justification for trajectory generation, methodology of axis control and development of performance metrics. Chaumette in provides good insight into the two major problems with IBVS. One, servoing to a local minima and second, reaching a Jacobian singularity. The author show that image points alone do not make good features due to the occurrence of singularities. The paper continues, by discussing the possible additional checks to prevent singularities namely, condition numbers of J_s and Jˆ+_s, to check the null space of ˆ J_s and J^T_s . One main point that the author highlights is the relation between local minima and unrealizable image feature motions. Over the years many hybrid techniques have been developed. These involve computing partial/complete pose from Epipolar Geometry using multiple views or multiple cameras. The values are obtained by direct estimation or through a learning or a statistical scheme. While others have used a switching approach that changes between image-based and position-based on a Lyapnov function. The early hybrid techniques that used a combination of image-based and pose-based (2D and 3D information) approaches for servoing required either a full or partial model of the object in order to extract the pose information and used a variety of techniques to extract the motion information from the image. used an affine motion model from the image motion in addition to a rough polyhedral CAD model to extract the object pose with respect to the camera to be able to servo onto the object (on the lines of PBVS). 2-1/2-D visual servoing developed by Malis et al. is a well known technique that breaks down the information required for servoing into an organized fashion which decouples rotations and translations. The papers assume that the desired pose is known a priori. The rotational information is obtained from partial pose estimation, a homography, (essentially 3D information) giving an axis of rotation and the angle (by computing the eigenvalues and eigenvectors of the homography). The translational information is obtained from the image directly by tracking a set of feature points. The only conditions being that the feature points being tracked never leave the field of view and that a depth estimate be predetermined by some off-line technique. 2-1/2-D servoing has been shown to be more stable than the techniques that preceded it. Another interesting observation with this formulation is that the authors claim that the visual Jacobian will have no singularities during the motions. The hybrid technique developed by Corke and Hutchinson, popularly called portioned approach partitions the visual (or image) Jacobian into motions (both rotations and translations) relating X and Y axes and motions related to the Z axis. outlines the technique, to break out columns of the visual Jacobian that correspond to the Z axis translation and rotation (namely, the third and sixth columns). The partitioned approach is shown to handle the Chaumette Conundrum discussed in. This technique requires a good depth estimate in order to function properly. outlines a hybrid approach where the servoing task is split into two, namely main and secondary. The main task is keep the features of interest within the field of view. While the secondary task is to mark a fixation point and use it as a reference to bring the camera to the desired pose. The technique does need a depth estimate from an off-line procedure. The paper discusses two examples for which depth estimates are obtained from robot odometry and by assuming that all

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  Characteristic samples

  Characteristic samples is a concept in the field of grammatical inference, related to passive learning. In passive learning, an inference algorithm I {\displaystyle I} is given a set of pairs of strings and labels S {\displaystyle S} , and returns a representation R {\displaystyle R} that is consistent with S {\displaystyle S} . Characteristic samples consider the scenario when the goal is not only finding a representation consistent with S {\displaystyle S} , but finding a representation that recognizes a specific target language. A characteristic sample of language L {\displaystyle L} is a set of pairs of the form ( s , l ( s ) ) {\displaystyle (s,l(s))} where: l ( s ) = 1 {\displaystyle l(s)=1} if and only if s ∈ L {\displaystyle s\in L} l ( s ) = − 1 {\displaystyle l(s)=-1} if and only if s ∉ L {\displaystyle s\notin L} Given the characteristic sample S {\displaystyle S} , I {\displaystyle I} 's output on it is a representation R {\displaystyle R} , e.g. an automaton, that recognizes L {\displaystyle L} . == Formal Definition == === The Learning Paradigm associated with Characteristic Samples === There are three entities in the learning paradigm connected to characteristic samples, the adversary, the teacher and the inference algorithm. Given a class of languages C {\displaystyle \mathbb {C} } and a class of representations for the languages R {\displaystyle \mathbb {R} } , the paradigm goes as follows: The adversary A {\displaystyle A} selects a language L ∈ C {\displaystyle L\in \mathbb {C} } and reports it to the teacher The teacher T {\displaystyle T} then computes a set of strings and label them correctly according to L {\displaystyle L} , trying to make sure that the inference algorithm will compute L {\displaystyle L} The adversary can add correctly labeled words to the set in order to confuse the inference algorithm The inference algorithm I {\displaystyle I} gets the sample and computes a representation R ∈ R {\displaystyle R\in \mathbb {R} } consistent with the sample. The goal is that when the inference algorithm receives a characteristic sample for a language L {\displaystyle L} , or a sample that subsumes a characteristic sample for L {\displaystyle L} , it will return a representation that recognizes exactly the language L {\displaystyle L} . === Sample === Sample S {\displaystyle S} is a set of pairs of the form ( s , l ( s ) ) {\displaystyle (s,l(s))} such that l ( s ) ∈ { − 1 , 1 } {\displaystyle l(s)\in \{-1,1\}} ==== Sample consistent with a language ==== We say that a sample S {\displaystyle S} is consistent with language L {\displaystyle L} if for every pair ( s , l ( s ) ) {\displaystyle (s,l(s))} in S {\displaystyle S} : l ( s ) = 1 if and only if s ∈ L {\displaystyle l(s)=1{\text{ if and only if }}s\in L} l ( s ) = − 1 if and only if s ∉ L {\displaystyle l(s)=-1{\text{ if and only if }}s\notin L} === Characteristic sample === Given an inference algorithm I {\displaystyle I} and a language L {\displaystyle L} , a sample S {\displaystyle S} that is consistent with L {\displaystyle L} is called a characteristic sample of L {\displaystyle L} for I {\displaystyle I} if: I {\displaystyle I} 's output on S {\displaystyle S} is a representation R {\displaystyle R} that recognizes L {\displaystyle L} . For every sample D {\displaystyle D} that is consistent with L {\displaystyle L} and also fulfils S ⊆ D {\displaystyle S\subseteq D} , I {\displaystyle I} 's output on D {\displaystyle D} is a representation R {\displaystyle R} that recognizes L {\displaystyle L} . A Class of languages C {\displaystyle \mathbb {C} } is said to have charistaristic samples if every L ∈ C {\displaystyle L\in \mathbb {C} } has a characteristic sample. == Related Theorems == === Theorem === If equivalence is undecidable for a class C {\textstyle \mathbb {C} } over Σ {\textstyle \Sigma } of cardinality bigger than 1, then C {\textstyle \mathbb {C} } doesn't have characteristic samples. ==== Proof ==== Given a class of representations C {\textstyle \mathbb {C} } such that equivalence is undecidable, for every polynomial p ( x ) {\displaystyle p(x)} and every n ∈ N {\displaystyle n\in \mathbb {N} } , there exist two representations r 1 {\displaystyle r_{1}} and r 2 {\displaystyle r_{2}} of sizes bounded by n {\displaystyle n} , that recognize different languages but are inseparable by any string of size bounded by p ( n ) {\displaystyle p(n)} . Assuming this is not the case, we can decide if r 1 {\displaystyle r_{1}} and r 2 {\displaystyle r_{2}} are equivalent by simulating their run on all strings of size smaller than p ( n ) {\displaystyle p(n)} , contradicting the assumption that equivalence is undecidable. === Theorem === If S 1 {\displaystyle S_{1}} is a characteristic sample for L 1 {\displaystyle L_{1}} and is also consistent with L 2 {\displaystyle L_{2}} , then every characteristic sample of L 2 {\displaystyle L_{2}} , is inconsistent with L 1 {\displaystyle L_{1}} . ==== Proof ==== Given a class C {\textstyle \mathbb {C} } that has characteristic samples, let R 1 {\displaystyle R_{1}} and R 2 {\displaystyle R_{2}} be representations that recognize L 1 {\displaystyle L_{1}} and L 2 {\displaystyle L_{2}} respectively. Under the assumption that there is a characteristic sample for L 1 {\displaystyle L_{1}} , S 1 {\displaystyle S_{1}} that is also consistent with L 2 {\displaystyle L_{2}} , we'll assume falsely that there exist a characteristic sample for L 2 {\displaystyle L_{2}} , S 2 {\displaystyle S_{2}} that is consistent with L 1 {\displaystyle L_{1}} . By the definition of characteristic sample, the inference algorithm I {\displaystyle I} must return a representation which recognizes the language if given a sample that subsumes the characteristic sample itself. But for the sample S 1 ∪ S 2 {\displaystyle S_{1}\cup S_{2}} , the answer of the inferring algorithm needs to recognize both L 1 {\displaystyle L_{1}} and L 2 {\displaystyle L_{2}} , in contradiction. === Theorem === If a class is polynomially learnable by example based queries, it is learnable with characteristic samples. == Polynomialy characterizable classes == === Regular languages === The proof that DFA's are learnable using characteristic samples, relies on the fact that every regular language has a finite number of equivalence classes with respect to the right congruence relation, ∼ L {\displaystyle \sim _{L}} (where x ∼ L y {\displaystyle x\sim _{L}y} for x , y ∈ Σ ∗ {\displaystyle x,y\in \Sigma ^{}} if and only if ∀ z ∈ Σ ∗ : x z ∈ L ↔ y z ∈ L {\displaystyle \forall z\in \Sigma ^{}:xz\in L\leftrightarrow yz\in L} ). Note that if x {\displaystyle x} , y {\displaystyle y} are not congruent with respect to ∼ L {\displaystyle \sim _{L}} , there exists a string z {\displaystyle z} such that x z ∈ L {\displaystyle xz\in L} but y z ∉ L {\displaystyle yz\notin L} or vice versa, this string is called a separating suffix. ==== Constructing a characteristic sample ==== The construction of a characteristic sample for a language L {\displaystyle L} by the teacher goes as follows. Firstly, by running a depth first search on a deterministic automaton A {\displaystyle A} recognizing L {\displaystyle L} , starting from its initial state, we get a suffix closed set of words, W {\displaystyle W} , ordered in shortlex order. From the fact above, we know that for every two states in the automaton, there exists a separating suffix that separates between every two strings that the run of A {\displaystyle A} on them ends in the respective states. We refer to the set of separating suffixes as S {\displaystyle S} . The labeled set (sample) of words the teacher gives the adversary is { ( w , l ( w ) ) | w ∈ W ⋅ S ∪ W ⋅ Σ ⋅ S } {\displaystyle \{(w,l(w))|w\in W\cdot S\cup W\cdot \Sigma \cdot S\}} where l ( w ) {\displaystyle l(w)} is the correct label of w {\displaystyle w} (whether it is in L {\displaystyle L} or not). We may assume that ϵ ∈ S {\displaystyle \epsilon \in S} . ==== Constructing a deterministic automata ==== Given the sample from the adversary W {\displaystyle W} , the construction of the automaton by the inference algorithm I {\displaystyle I} starts with defining P = prefix ( W ) {\displaystyle P={\text{prefix}}(W)} and S = suffix ( W ) {\displaystyle S={\text{suffix}}(W)} , which are the set of prefixes and suffixes of W {\displaystyle W} respectively. Now the algorithm constructs a matrix M {\displaystyle M} where the elements of P {\displaystyle P} function as the rows, ordered by the shortlex order, and the elements of S {\displaystyle S} function as the columns, ordered by the shortlex order. Next, the cells in the matrix are filled in the following manner for prefix p i {\displaystyle p_{i}} and suffix s j {\displaystyle s_{j}} : If p i s j ∈ W → M i j = l ( p i s j ) {\displaystyle p_{i}s_{j}\in W\rightarrow M_{ij}=l(p_{i}s_{j})} else, M i j = 0 {\displaystyle M_{ij}=0} Now, we say row i {\displaystyle i} and t {\displaystyle t} are distinguishable if there exi

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  World Programming System

  The World Programming System, also known as WPS Analytics or WPS, is a software product developed by a company called World Programming (acquired by Altair Engineering). WPS Analytics supports users of mixed ability to access and process data and to perform data science tasks. It has interactive visual programming tools using data workflows, and it has coding tools supporting the use of the SAS language mixed with Python, R and SQL. == About == WPS can use programs written in the language of SAS without the need for translating them into any other language. In this regard WPS is compatible with the SAS system. WPS has a built-in language interpreter able to process the language of SAS and produce similar results. WPS is available to run on z/OS, Windows, macOS, Linux (x86, Armv8 64-bit, IBM Power LE, IBM Z), and AIX. On all supported platforms, programs written in the language of SAS can be executed from a WPS command line interface, often referred to as running in batch mode. WPS can also be used from a graphical user interface known as the WPS Workbench for managing, editing and running programs written in the language of SAS. The WPS Workbench user interface is based on Eclipse. WPS version 4 (released in March 2018) introduced a drag-and-drop workflow canvas providing interactive blocks for data retrieval, blending and preparation, data discovery and profiling, predictive modelling powered by machine learning algorithms, model performance validation and scorecards. WPS version 3 (released in February 2012) provided a new client/server architecture that allows the WPS Workbench GUI to execute SAS programs on remote server installations of WPS in a network or cloud. The resulting output, data sets, logs, etc., can then all be viewed and manipulated from inside the Workbench as if the workloads had been executed locally. SAS programs do not require any special language statements to use this feature. == Summary of main features == Runs on Windows, macOS, z/OS, Linux (x86, Armv8 64-bit, IBM Power LE, IBM Z), and AIX An integrated development environment based on Eclipse for Linux, macOS and Windows. Support for language of SAS elements. Support for the language of SAS Macros. Matrix Programming support using PROC IML. Support for generating band plots, bar charts, box plots, bubble plots, contour plots, dendrogram plots, ellipse plots, fringe plots, heat maps, high-low plots, histograms, loess plots, needle plots, pie charts, penalised b-spline, radar charts, reference lines, scatter plots, series plots, step plots, regression plots and vector plots. Support for statistical procedures ACECLUS, ASSOCRULES, ANOVA, BIN, BOXPLOT, CANCORR, CANDISC, CLUSTER, CORRESP, DISCRIM, DISTANCE, FACTOR, FASTCLUS, FREQ, GAM, GANNO, GENMOD, GLIMMIX, GLM, GLMMOD, GLMSELECT, ICLIFETEST, KDE, LIFEREG, LIFETEST, LOESS, LOGISTIC, MDS, MEANS, MI, MIANALYSE, MIXED, MODECLUS, NESTED, NLIN, NPAR1WAY, PHREG, PLAN, PLS, POWER, PRINCOMP, PROBIT, QUANTREG, RBF, REG, ROBUSTREG, RSREG, SCORE, SEGMENT, SIMNORMAL, STANDARD, STDSIZE, STDRATE, STEPDISC, SUMMARY, SURVEYMEANS, SURVEYSELECT, TPSPLINE, TRANSREG, TREE, TTEST, UNIVARIATE, VARCLUS, VARCOMP Support for time series procedures ARIMA, AUTOREG, ESM, EXPAND, FORECAST, LOAN, SEVERITY, SPECTRA, TIMESERIES, X12 Support for machine learning procedures DECISIONFOREST, DECISIONTREE, GMM, MLP, OPTIMALBIN, SEGMENT, SVM Support for ODS. Reads and writes SAS datasets (compressed or uncompressed). Access: Actian Matrix (previously known as ParAccel), DASD, DB2, Excel, Greenplum, Hadoop, Informix, Kognitio Archived 2012-08-24 at the Wayback Machine, MariaDB, MySQL, Netezza, ODBC, OLEDB, Oracle, PostgreSQL, SAND, Snowflake, SPSS/PSPP, SQL Server, Sybase, Sybase IQ, Teradata, VSAM, Vertica and XML. Support for SAS Tape Format. Direct output of reports to CSV, PDF and HTML. Support to connect WPS systems programmatically, remote submit parts of a program to execute on connected remote servers, upload and download data between the connected systems. Support for Hadoop Support for R Support for Python == Industry recognition == Gartner recognized World Programming in their Cool Vendors in Data Science, 2014 Report. == Lawsuit == In 2010 World Programming defended its use of the language of SAS in the High Court of England and Wales in SAS Institute Inc. v World Programming Ltd. The software was the subject of a lawsuit by SAS Institute. The EU Court of Justice ruled in favor of World Programming, stating that the copyright protection does not extend to the software functionality, the programming language used and the format of the data files used by the program. It stated that there is no copyright infringement when a company which does not have access to the source code of a program studies, observes and tests that program to create another program with the same functionality.

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  Ordination (statistics)

  Ordination or gradient analysis, in multivariate analysis, is a method complementary to data clustering, and used mainly in exploratory data analysis (rather than in hypothesis testing). In contrast to cluster analysis, ordination orders quantities in a (usually lower-dimensional) latent space. In the ordination space, quantities that are near each other share attributes (i.e., are similar to some degree), and dissimilar objects are farther from each other. Such relationships between the objects, on each of several axes or latent variables, are then characterized numerically and/or graphically in a biplot. The first ordination method, principal components analysis, was suggested by Karl Pearson in 1901. == Methods == Ordination methods can broadly be categorized in eigenvector-, algorithm-, or model-based methods. Many classical ordination techniques, including principal components analysis, correspondence analysis (CA) and its derivatives (detrended correspondence analysis, canonical correspondence analysis, and redundancy analysis, belong to the first group). The second group includes some distance-based methods such as non-metric multidimensional scaling, and machine learning methods such as T-distributed stochastic neighbor embedding and nonlinear dimensionality reduction. The third group includes model-based ordination methods, which can be considered as multivariate extensions of Generalized Linear Models. Model-based ordination methods are more flexible in their application than classical ordination methods, so that it is for example possible to include random-effects. Unlike in the aforementioned two groups, there is no (implicit or explicit) distance measure in the ordination. Instead, a distribution needs to be specified for the responses as is typical for statistical models. These and other assumptions, such as the assumed mean-variance relationship, can be validated with the use of residual diagnostics, unlike in other ordination methods. == Applications == Ordination can be used on the analysis of any set of multivariate objects. It is frequently used in several environmental or ecological sciences, particularly plant community ecology. It is also used in genetics and systems biology for microarray data analysis and in psychometrics.

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  PANGU (software)

  The PANGU (Planet and Asteroid Natural scene Generation Utility) is a computer graphics utility of which the development was funded by ESA and performed by University of Dundee. It generates scenes of planets, moons, asteroids, spacecraft and rovers. The main purpose of the tool is to test and validate navigation techniques based on the processing of images coming from on-board sensors, such as a camera or imaging LIDAR on a planetary lander.

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  Operational taxonomic unit

  An operational taxonomic unit (OTU) is an operational definition used to classify groups of closely related individuals. The term was originally introduced in 1963 by Robert R. Sokal and Peter H. A. Sneath in the context of numerical taxonomy, where an "operational taxonomic unit" is simply the group of organisms currently being studied. In this sense, an OTU is a pragmatic definition to group individuals by similarity, equivalent to but not necessarily in line with classical Linnaean taxonomy or modern evolutionary taxonomy. Nowadays, however, the term is commonly used in a different context and refers to clusters of (uncultivated or unknown) organisms, grouped by DNA sequence similarity of a specific taxonomic marker gene (originally coined as mOTU; molecular OTU). In other words, OTUs are pragmatic proxies for "species" at different taxonomic levels, in the absence of traditional systems of biological classification as are available for macroscopic organisms. For several years, OTUs have been the most commonly used units of diversity, especially when analysing small subunit 16S (for prokaryotes) or 18S rRNA (for eukaryotes) marker gene sequence datasets. == Molecular OTU by clustering of marker gene sequences == In the approach represented by DNA barcoding, a particular locus is chosen to be used as the marker gene for classification. This locus should be universally present in the scope selected, variable enough to be different among close-related species, and be flanked by conservative sequences that allow for easy amplification and detection. There are databases containing sequences for such marker genes from many different species, allowing for comparison. (Sometimes only using one locus does not provide sufficient resolution, so multiple marker genes are used. This is the case for plants, where rbcL+matK is common.) Sequences obtained this way can be clustered according to their similarity to one another, and operational taxonomic units are defined based on the similarity threshold set by the researcher. The exact threshold depends on the taxa in question and the mutational rates of the selected locus in the taxon. 97–99% are commonly used, but "it is now recognized to be somewhat arbitrary as sequence variation within and among species varies across taxa". 100% similarity (fully identical) is also common, also known as single variants. It remains debatable how well this commonly used method recapitulates true microbial species phylogeny or ecology. Although OTUs can be calculated differently when using different algorithms or thresholds, research by Schmidt et al. (2014) demonstrated that 16S-derived microbial OTUs were generally ecologically consistent across habitats and several clustering approaches. The number of OTUs defined may be inflated due to errors in DNA sequencing. === OTU clustering approaches === There are three main approaches to clustering OTUs: De novo, for which the clustering is based on similarities between sequencing reads. Closed-reference, for which the clustering is performed against a reference database of sequences. Open-reference, where clustering is first performed against a reference database of sequences, then any remaining sequences that could not be mapped to the reference are clustered de novo. Using a reference provides taxonomic context for the OTUs found. Alternatively, taxonomic context can be found after the construction of clusters by comparing representative sequences from clusters against a reference database. There are also specialized classifiers for this purpose which are much faster than naive comparison using BLAST. === OTU clustering algorithms === Hierarchical clustering algorithms (HCA): uclust & cd-hit & ESPRIT Bayesian clustering: CROP == Molecular OTU by other methods == In addition to similarity-based grouping, marker gene sequences can be sorted into OTUs using molecular phylogeny, k-mer composition, or hybrid methods combining these methods with similarity. There are also Bayesian tree-less methods and machine learning approaches. Using phylogeny often involves manually assigning terminal clades or single nodes to an OTU, so this is usually only done for refinement. Genome skimming can be used to obtain high-copy DNA without the need to choose marker genes or to design PCR primers for the chosen genes. It can provide fairly good coverage of organelle DNA and repetitive elements such as ribosomal DNA, both of which can be used like marker genes in OTU analysis. Whole-genome sequencing is more expensive and involves the production and processing of more data. By considering the entire genome, many (sometimes over 100) marker genes can be used at the same time, producing highly resolved phylogenies that correctly identify problematic taxa. It is also possible to use entire genomes for OTU assignment. For example, genomes from different bacterial species almost always have an average nucleotide identity lower than 95%, a fact that can be used to define new OTUs (and likely new species).

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  Gremlin (query language)

  Gremlin is a graph traversal language and virtual machine developed by Apache TinkerPop of the Apache Software Foundation. Gremlin works for both OLTP-based graph databases as well as OLAP-based graph processors. Gremlin's automata and functional language foundation enable Gremlin to naturally support imperative and declarative querying, host language agnosticism, user-defined domain specific languages, an extensible compiler/optimizer, single- and multi-machine execution models, and hybrid depth- and breadth-first evaluation with Turing completeness. As an explanatory analogy, Apache TinkerPop and Gremlin are to graph databases what the JDBC and SQL are to relational databases. Likewise, the Gremlin traversal machine is to graph computing as what the Java virtual machine is to general purpose computing. == History == 2009-10-30 the project is born, and immediately named "TinkerPop" 2009-12-25 v0.1 is the first release 2011-05-21 v1.0 is released 2012-05-24 v2.0 is released 2015-01-16 TinkerPop becomes an Apache Incubator project 2015-07-09 v3.0.0-incubating is released 2016-05-23 Apache TinkerPop becomes a top-level project 2016-07-18 v3.1.3 and v3.2.1 are first releases as Apache TinkerPop 2017-12-17 v3.3.1 is released 2018-05-08 v3.3.3 is released 2019-08-05 v3.4.3 is released 2020-02-20 v3.4.6 is released 2021-05-01 v3.5.0 is released 2022-04-04 v3.6.0 is released 2023-07-31 v3.7.0 is released 2025-11-12 v3.8.0 is released == Vendor integration == Gremlin is an Apache2-licensed graph traversal language that can be used by graph system vendors. There are typically two types of graph system vendors: OLTP graph databases and OLAP graph processors. The table below outlines those graph vendors that support Gremlin. == Traversal examples == The following examples of Gremlin queries and responses in a Gremlin-Groovy environment are relative to a graph representation of the MovieLens dataset. The dataset includes users who rate movies. Users each have one occupation, and each movie has one or more categories associated with it. The MovieLens graph schema is detailed below. === Simple traversals === For each vertex in the graph, emit its label, then group and count each distinct label. What year was the oldest movie made? What is Die Hard's average rating? === Projection traversals === For each category, emit a map of its name and the number of movies it represents. For each movie with at least 11 ratings, emit a map of its name and average rating. Sort the maps in decreasing order by their average rating. Emit the first 10 maps (i.e. top 10). === Declarative pattern matching traversals === Gremlin supports declarative graph pattern matching similar to SPARQL. For instance, the following query below uses Gremlin's match()-step. What 80's action movies do 30-something programmers like? Group count the movies by their name and sort the group count map in decreasing order by value. Clip the map to the top 10 and emit the map entries. === OLAP traversal === Which movies are most central in the implicit 5-stars graph? == Gremlin graph traversal machine == Gremlin is a virtual machine composed of an instruction set as well as an execution engine. An analogy is drawn between Gremlin and Java. === Gremlin steps (instruction set) === The following traversal is a Gremlin traversal in the Gremlin-Java8 dialect. The Gremlin language (i.e. the fluent-style of expressing a graph traversal) can be represented in any host language that supports function composition and function nesting. Due to this simple requirement, there exists various Gremlin dialects including Gremlin-Groovy, Gremlin-Scala, Gremlin-Clojure, etc. The above Gremlin-Java8 traversal is ultimately compiled down to a step sequence called a traversal. A string representation of the traversal above provided below. The steps are the primitives of the Gremlin graph traversal machine. They are the parameterized instructions that the machine ultimately executes. The Gremlin instruction set is approximately 30 steps. These steps are sufficient to provide general purpose computing and what is typically required to express the common motifs of any graph traversal query. Given that Gremlin is a language, an instruction set, and a virtual machine, it is possible to design another traversal language that compiles to the Gremlin traversal machine (analogous to how Scala compiles to the JVM). For instance, the popular SPARQL graph pattern match language can be compiled to execute on the Gremlin machine. The following SPARQL query would compile to In Gremlin-Java8, the SPARQL query above would be represented as below and compile to the identical Gremlin step sequence (i.e. traversal). === Gremlin Machine (virtual machine) === The Gremlin graph traversal machine can execute on a single machine or across a multi-machine compute cluster. Execution agnosticism allows Gremlin to run over both graph databases (OLTP) and graph processors (OLAP).

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  Gaussian adaptation

  Gaussian adaptation (GA), also called normal or natural adaptation (NA) is an evolutionary algorithm designed for the maximization of manufacturing yield due to statistical deviation of component values of signal processing systems. In short, GA is a stochastic adaptive process where a number of samples of an n-dimensional vector x[xT = (x1, x2, ..., xn)] are taken from a multivariate Gaussian distribution, N(m, M), having mean m and moment matrix M. The samples are tested for fail or pass. The first- and second-order moments of the Gaussian restricted to the pass samples are m and M. The outcome of x as a pass sample is determined by a function s(x), 0 < s(x) < q ≤ 1, such that s(x) is the probability that x will be selected as a pass sample. The average probability of finding pass samples (yield) is P ( m ) = ∫ s ( x ) N ( x − m ) d x {\displaystyle P(m)=\int s(x)N(x-m)\,dx} Then the theorem of GA states: For any s(x) and for any value of P < q, there always exist a Gaussian p. d. f. [ probability density function ] that is adapted for maximum dispersion. The necessary conditions for a local optimum are m = m and M proportional to M. The dual problem is also solved: P is maximized while keeping the dispersion constant (Kjellström, 1991). Proofs of the theorem may be found in the papers by Kjellström, 1970, and Kjellström & Taxén, 1981. Since dispersion is defined as the exponential of entropy/disorder/average information it immediately follows that the theorem is valid also for those concepts. Altogether, this means that Gaussian adaptation may carry out a simultaneous maximisation of yield and average information (without any need for the yield or the average information to be defined as criterion functions). The theorem is valid for all regions of acceptability and all Gaussian distributions. It may be used by cyclic repetition of random variation and selection (like the natural evolution). In every cycle a sufficiently large number of Gaussian distributed points are sampled and tested for membership in the region of acceptability. The centre of gravity of the Gaussian, m, is then moved to the centre of gravity of the approved (selected) points, m. Thus, the process converges to a state of equilibrium fulfilling the theorem. A solution is always approximate because the centre of gravity is always determined for a limited number of points. It was used for the first time in 1969 as a pure optimization algorithm making the regions of acceptability smaller and smaller (in analogy to simulated annealing, Kirkpatrick 1983). Since 1970 it has been used for both ordinary optimization and yield maximization. == Natural evolution and Gaussian adaptation == It has also been compared to the natural evolution of populations of living organisms. In this case s(x) is the probability that the individual having an array x of phenotypes will survive by giving offspring to the next generation; a definition of individual fitness given by Hartl 1981. The yield, P, is replaced by the mean fitness determined as a mean over the set of individuals in a large population. Phenotypes are often Gaussian distributed in a large population and a necessary condition for the natural evolution to be able to fulfill the theorem of Gaussian adaptation, with respect to all Gaussian quantitative characters, is that it may push the centre of gravity of the Gaussian to the centre of gravity of the selected individuals. This may be accomplished by the Hardy–Weinberg law. This is possible because the theorem of Gaussian adaptation is valid for any region of acceptability independent of the structure (Kjellström, 1996). In this case the rules of genetic variation such as crossover, inversion, transposition etcetera may be seen as random number generators for the phenotypes. So, in this sense Gaussian adaptation may be seen as a genetic algorithm. == How to climb a mountain == Mean fitness may be calculated provided that the distribution of parameters and the structure of the landscape is known. The real landscape is not known, but figure below shows a fictitious profile (blue) of a landscape along a line (x) in a room spanned by such parameters. The red curve is the mean based on the red bell curve at the bottom of figure. It is obtained by letting the bell curve slide along the x-axis, calculating the mean at every location. As can be seen, small peaks and pits are smoothed out. Thus, if evolution is started at A with a relatively small variance (the red bell curve), then climbing will take place on the red curve. The process may get stuck for millions of years at B or C, as long as the hollows to the right of these points remain, and the mutation rate is too small. If the mutation rate is sufficiently high, the disorder or variance may increase and the parameter(s) may become distributed like the green bell curve. Then the climbing will take place on the green curve, which is even more smoothed out. Because the hollows to the right of B and C have now disappeared, the process may continue up to the peaks at D. But of course the landscape puts a limit on the disorder or variability. Besides — dependent on the landscape — the process may become very jerky, and if the ratio between the time spent by the process at a local peak and the time of transition to the next peak is very high, it may as well look like a punctuated equilibrium as suggested by Gould (see Ridley). == Computer simulation of Gaussian adaptation == Thus far the theory only considers mean values of continuous distributions corresponding to an infinite number of individuals. In reality however, the number of individuals is always limited, which gives rise to an uncertainty in the estimation of m and M (the moment matrix of the Gaussian). And this may also affect the efficiency of the process. Unfortunately very little is known about this, at least theoretically. The implementation of normal adaptation on a computer is a fairly simple task. The adaptation of m may be done by one sample (individual) at a time, for example m(i + 1) = (1 – a) m(i) + ax where x is a pass sample, and a < 1 a suitable constant so that the inverse of a represents the number of individuals in the population. M may in principle be updated after every step y leading to a feasible point x = m + y according to: M(i + 1) = (1 – 2b) M(i) + 2byyT, where yT is the transpose of y and b << 1 is another suitable constant. In order to guarantee a suitable increase of average information, y should be normally distributed with moment matrix μ2M, where the scalar μ > 1 is used to increase average information (information entropy, disorder, diversity) at a suitable rate. But M will never be used in the calculations. Instead we use the matrix W defined by WWT = M. Thus, we have y = Wg, where g is normally distributed with the moment matrix μU, and U is the unit matrix. W and WT may be updated by the formulas W = (1 – b)W + bygT and WT = (1 – b)WT + bgyT because multiplication gives M = (1 – 2b)M + 2byyT, where terms including b2 have been neglected. Thus, M will be indirectly adapted with good approximation. In practice it will suffice to update W only W(i + 1) = (1 – b)W(i) + bygT. This is the formula used in a simple 2-dimensional model of a brain satisfying the Hebbian rule of associative learning; see the next section (Kjellström, 1996 and 1999). The figure below illustrates the effect of increased average information in a Gaussian p.d.f. used to climb a mountain Crest (the two lines represent the contour line). Both the red and green cluster have equal mean fitness, about 65%, but the green cluster has a much higher average information making the green process much more efficient. The effect of this adaptation is not very salient in a 2-dimensional case, but in a high-dimensional case, the efficiency of the search process may be increased by many orders of magnitude. == The evolution in the brain == In the brain the evolution of DNA-messages is supposed to be replaced by an evolution of signal patterns and the phenotypic landscape is replaced by a mental landscape, the complexity of which will hardly be second to the former. The metaphor with the mental landscape is based on the assumption that certain signal patterns give rise to a better well-being or performance. For instance, the control of a group of muscles leads to a better pronunciation of a word or performance of a piece of music. In this simple model it is assumed that the brain consists of interconnected components that may add, multiply and delay signal values. A nerve cell kernel may add signal values, a synapse may multiply with a constant and An axon may delay values. This is a basis of the theory of digital filters and neural networks consisting of components that may add, multiply and delay signalvalues and also of many brain models, Levine 1991. In the figure below the brain stem is supposed to deliver Gaussian distributed signal patterns. This may be possible since certai

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  Immediate mode (computer graphics)

  Immediate mode is an API design pattern in computer graphics libraries, in which the client calls directly cause rendering of graphics objects to the display, or in which the data to describe rendering primitives is inserted frame by frame directly from the client into a command list (in the case of immediate mode primitive rendering), without the use of extensive indirection – thus immediate – to retained resources. It does not preclude the use of double-buffering. Retained mode is an alternative approach. Historically, retained mode has been the dominant style in GUI libraries; however, both can coexist in the same library and are not necessarily exclusive in practice. == Overview == In immediate mode, the scene (complete object model of the rendering primitives) is retained in the memory space of the client, instead of the graphics library. This implies that in an immediate mode application, the lists of graphical objects to be rendered are kept by the client and are not saved by the graphics library API. The application must re-issue all drawing commands required to describe the entire scene each time a new frame is required, regardless of actual changes. This method provides on the one hand a maximum of control and flexibility to the application program, but on the other hand it also generates continuous work load on the CPU. Examples of immediate mode rendering systems include Direct2D, OpenGL and Quartz. There are some immediate mode GUIs that are particularly suitable when used in conjunction with immediate mode rendering systems. == Immediate mode primitive rendering == Primitive vertex attribute data may be inserted frame by frame into a command buffer by a rendering API. This involves significant bandwidth and processor time (especially if the graphics processing unit is on a separate bus), but may be advantageous for data generated dynamically by the CPU. It is less common since the advent of increasingly versatile shaders, with which a graphics processing unit may generate increasingly complex effects without the need for CPU intervention. == Immediate mode rendering with vertex buffers == Although drawing commands have to be re-issued for each new frame, modern systems using this method are generally able to avoid the unnecessary duplication of more memory-intensive display data by referring to that unchanging data (via indirection) (e.g. textures and vertex buffers) in the drawing commands. == Immediate mode GUI == Graphical user interfaces traditionally use retained mode-style API design, but immediate mode GUIs instead use an immediate mode-style API design, in which user code directly specifies the GUI elements to draw in the user input loop. For example, rather than having a CreateButton() function that a user would call once to instantiate a button, an immediate-mode GUI API may have a DoButton() function which should be called whenever the button should be on screen. The technique was developed by Casey Muratori in 2002. Prominent implementations include Omar Cornut's Dear ImGui in C++, Nic Barker's Clay in C and Micha Mettke's Nuklear in C.

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  Learning classifier system

  Learning classifier systems, or LCS, are a paradigm of rule-based machine learning methods that combine a discovery component (e.g. typically a genetic algorithm in evolutionary computation) with a learning component (performing either supervised learning, reinforcement learning, or unsupervised learning). Learning classifier systems seek to identify a set of context-dependent rules that collectively store and apply knowledge in a piecewise manner in order to make predictions (e.g. behavior modeling, classification, data mining, regression, function approximation, or game strategy). This approach allows complex solution spaces to be broken up into smaller, simpler parts for the reinforcement learning that is inside artificial intelligence research. The founding concepts behind learning classifier systems came from attempts to model complex adaptive systems, using rule-based agents to form an artificial cognitive system (i.e. artificial intelligence). == Methodology == The architecture and components of a given learning classifier system can be quite variable. It is useful to think of an LCS as a machine consisting of several interacting components. Components may be added or removed, or existing components modified/exchanged to suit the demands of a given problem domain (like algorithmic building blocks) or to make the algorithm flexible enough to function in many different problem domains. As a result, the LCS paradigm can be flexibly applied to many problem domains that call for machine learning. The major divisions among LCS implementations are as follows: (1) Michigan-style architecture vs. Pittsburgh-style architecture, (2) reinforcement learning vs. supervised learning, (3) incremental learning vs. batch learning, (4) online learning vs. offline learning, (5) strength-based fitness vs. accuracy-based fitness, and (6) complete action mapping vs best action mapping. These divisions are not necessarily mutually exclusive. For example, XCS, the best known and best studied LCS algorithm, is Michigan-style, was designed for reinforcement learning but can also perform supervised learning, applies incremental learning that can be either online or offline, applies accuracy-based fitness, and seeks to generate a complete action mapping. === Elements of a generic LCS algorithm === Keeping in mind that LCS is a paradigm for genetic-based machine learning rather than a specific method, the following outlines key elements of a generic, modern (i.e. post-XCS) LCS algorithm. For simplicity let us focus on Michigan-style architecture with supervised learning. See the illustrations on the right laying out the sequential steps involved in this type of generic LCS. ==== Environment ==== The environment is the source of data upon which an LCS learns. It can be an offline, finite training dataset (characteristic of a data mining, classification, or regression problem), or an online sequential stream of live training instances. Each training instance is assumed to include some number of features (also referred to as attributes, or independent variables), and a single endpoint of interest (also referred to as the class, action, phenotype, prediction, or dependent variable). Part of LCS learning can involve feature selection, therefore not all of the features in the training data need to be informative. The set of feature values of an instance is commonly referred to as the state. For simplicity let's assume an example problem domain with Boolean/binary features and a Boolean/binary class. For Michigan-style systems, one instance from the environment is trained on each learning cycle (i.e. incremental learning). Pittsburgh-style systems perform batch learning, where rule sets are evaluated in each iteration over much or all of the training data. ==== Rule/classifier/population ==== A rule is a context dependent relationship between state values and some prediction. Rules typically take the form of an {IF:THEN} expression, (e.g. {IF 'condition' THEN 'action'}, or as a more specific example, {IF 'red' AND 'octagon' THEN 'stop-sign'}). A critical concept in LCS and rule-based machine learning alike, is that an individual rule is not in itself a model, since the rule is only applicable when its condition is satisfied. Think of a rule as a "local-model" of the solution space. Rules can be represented in many different ways to handle different data types (e.g. binary, discrete-valued, ordinal, continuous-valued). Given binary data LCS traditionally applies a ternary rule representation (i.e. rules can include either a 0, 1, or '#' for each feature in the data). The 'don't care' symbol (i.e. '#') serves as a wild card within a rule's condition allowing rules, and the system as a whole to generalize relationships between features and the target endpoint to be predicted. Consider the following rule (#1###0 ~ 1) (i.e. condition ~ action). This rule can be interpreted as: IF the second feature = 1 AND the sixth feature = 0 THEN the class prediction = 1. We would say that the second and sixth features were specified in this rule, while the others were generalized. This rule, and the corresponding prediction are only applicable to an instance when the condition of the rule is satisfied by the instance. This is more commonly referred to as matching. In Michigan-style LCS, each rule has its own fitness, as well as a number of other rule-parameters associated with it that can describe the number of copies of that rule that exist (i.e. the numerosity), the age of the rule, its accuracy, or the accuracy of its reward predictions, and other descriptive or experiential statistics. A rule along with its parameters is often referred to as a classifier. In Michigan-style systems, classifiers are contained within a population [P] that has a user defined maximum number of classifiers. Unlike most stochastic search algorithms (e.g. evolutionary algorithms), LCS populations start out empty (i.e. there is no need to randomly initialize a rule population). Classifiers will instead be initially introduced to the population with a covering mechanism. In any LCS, the trained model is a set of rules/classifiers, rather than any single rule/classifier. In Michigan-style LCS, the entire trained (and optionally, compacted) classifier population forms the prediction model. ==== Matching ==== One of the most critical and often time-consuming elements of an LCS is the matching process. The first step in an LCS learning cycle takes a single training instance from the environment and passes it to [P] where matching takes place. In step two, every rule in [P] is now compared to the training instance to see which rules match (i.e. are contextually relevant to the current instance). In step three, any matching rules are moved to a match set [M]. A rule matches a training instance if all feature values specified in the rule condition are equivalent to the corresponding feature value in the training instance. For example, assuming the training instance is (001001 ~ 0), these rules would match: (###0## ~ 0), (00###1 ~ 0), (#01001 ~ 1), but these rules would not (1##### ~ 0), (000##1 ~ 0), (#0#1#0 ~ 1). Notice that in matching, the endpoint/action specified by the rule is not taken into consideration. As a result, the match set may contain classifiers that propose conflicting actions. In the fourth step, since we are performing supervised learning, [M] is divided into a correct set [C] and an incorrect set [I]. A matching rule goes into the correct set if it proposes the correct action (based on the known action of the training instance), otherwise it goes into [I]. In reinforcement learning LCS, an action set [A] would be formed here instead, since the correct action is not known. ==== Covering ==== At this point in the learning cycle, if no classifiers made it into either [M] or [C] (as would be the case when the population starts off empty), the covering mechanism is applied (fifth step). Covering is a form of online smart population initialization. Covering randomly generates a rule that matches the current training instance (and in the case of supervised learning, that rule is also generated with the correct action. Assuming the training instance is (001001 ~ 0), covering might generate any of the following rules: (#0#0## ~ 0), (001001 ~ 0), (#010## ~ 0). Covering not only ensures that each learning cycle there is at least one correct, matching rule in [C], but that any rule initialized into the population will match at least one training instance. This prevents LCS from exploring the search space of rules that do not match any training instances. ==== Parameter updates/credit assignment/learning ==== In the sixth step, the rule parameters of any rule in [M] are updated to reflect the new experience gained from the current training instance. Depending on the LCS algorithm, a number of updates can take place at this step. For supervised learning, we can simply update the accuracy/error of a

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  Jpred

  Jpred v.4 is the latest version of the JPred Protein Secondary Structure Prediction Server which provides predictions by the JNet algorithm, one of the most accurate methods for secondary structure prediction, that has existed since 1998 in different versions. In addition to protein secondary structure, JPred also makes predictions of solvent accessibility and coiled-coil regions. The JPred service runs up to 134 000 jobs per month and has carried out over 2 million predictions in total for users in 179 countries. == JPred 2 == The static HTML pages of JPred 2 are still available for reference. == JPred 3 == The JPred v3 followed on from previous versions of JPred developed and maintained by James Cuff and Jonathan Barber (see JPred References). This release added new functionality and fixed many bugs. The highlights are: New, friendlier user interface Retrained and optimised version of Jnet (v2) - mean secondary structure prediction accuracy of >81% Batch submission of jobs Better error checking of input sequences/alignments Predictions now (optionally) returned via e-mail Users may provide their own query names for each submission JPred now makes a prediction even when there are no PSI-BLAST hits to the query PS/PDF output now incorporates all the predictions == JPred 4 == The current version of JPred (v4) has the following improvements and updates incorporated: Retrained on the latest UniRef90 and SCOPe/ASTRAL version of Jnet (v2.3.1) - mean secondary structure prediction accuracy of >82%. Upgraded the Web Server to the latest technologies (Bootstrap framework, JavaScript) and updating the web pages – improving the design and usability through implementing responsive technologies. Added RESTful API and mass-submission and results retrieval scripts - resulting in peak throughput above 20,000 predictions per day. Added prediction jobs monitoring tools. Upgraded the results reporting – both, on the web-site, and through the optional email summary reports: improved batch submission, added results summary preview through Jalview results visualization summary in SVG and adding full multiple sequence alignments into the reports. Improved help-pages, incorporating tool-tips, and adding one-page step-by-step tutorials. Sequence residues are categorised or assigned to one of the secondary structure elements, such as alpha-helix, beta-sheet and coiled-coil. Jnet uses two neural networks for its prediction. The first network is fed with a window of 17 residues over each amino acid in the alignment plus a conservation number. It uses a hidden layer of nine nodes and has three output nodes, one for each secondary structure element. The second network is fed with a window of 19 residues (the result of first network) plus the conservation number. It has a hidden layer with nine nodes and has three output nodes.

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