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  Color histogram

  In image processing and photography, a color histogram is a representation of the distribution of colors in an image. For digital images, a color histogram represents the number of pixels that have colors in each of a fixed list of color ranges that span the image's color space (the set of all possible colors). A color histogram can be built for any kind of color space, although the term is more often used for three-dimensional spaces such as RGB or HSV. For monochromatic images, the term intensity histogram may be used instead. For multi-spectral images, where each pixel is represented by an arbitrary number of measurements (for example, beyond the three measurements in RGB), a color histogram is N-dimensional, with N being the number of measurements taken. Each measurement has its own wavelength range of the light spectrum, some of which may be outside the visible spectrum. If the set of possible color values is sufficiently small, each of those colors may be placed on a range by itself; then the histogram is merely the count of pixels that have each possible color. Most often, the space is divided into an appropriate number of ranges, often arranged as a regular grid, each containing many similar color values. A color histogram may also be represented and displayed as a smooth function defined over the color space that approximates the pixel counts. Like other kinds of histograms, a color histogram is a statistic that can be viewed as an approximation of an underlying continuous distribution of color values. == Overview == Color histograms are flexible constructs that can be built from images in various color spaces, whether RGB, rg chromaticity or any other color space of any dimension. A histogram of an image is produced first by discretization of the colors in the image into a number of bins, and counting the number of image pixels in each bin. For example, a red–blue chromaticity histogram can be formed by first normalizing color pixel values by dividing RGB values by R+G+B, then quantizing the normalized R and B coordinates into N bins each. A two-dimensional histogram of red–blue chromaticity divided into four bins (N=4) may yield a histogram similar to this table: A histogram can be N-dimensional. Although harder to display, a three-dimensional color histogram for the above example could be thought of as four separate red–blue histograms, where each of the four histograms contains the red–blue values for a bin of green (0–63, 64–127, 128–191, and 192–255). The histogram provides a compact summarization of the distribution of data in an image. A color histogram of an image is relatively invariant with translation and rotation about the viewing axis, and varies only slowly with the angle of view. By comparing histogram signatures of two images and matching the color content of one image with the other, a color histogram is particularly well suited for the problem of recognizing an object of unknown position and rotation within a scene. Importantly, translation of an RGB image into the illumination invariant rg-chromaticity space allows the histogram to operate well in varying light levels. 1. What is a histogram? A histogram is a graphical representation of the number of pixels in an image. In a more simple way to explain, a histogram is a bar graph, whose X-axis represents the tonal scale (black at the left and white at the right), and Y-axis represents the number of pixels in an image in a certain area of the tonal scale. For example, the graph of a luminance histogram shows the number of pixels for each brightness level (from black to white), and when there are more pixels, the peak at the certain luminance level is higher. 2. What is a color histogram? A color histogram of an image represents the distribution of the composition of colors in the image. It shows different types of colors appeared and the number of pixels in each type of the colors appeared. The relation between a color histogram and a luminance histogram is that a color histogram can be also expressed as “three luminance histograms”, each of which shows the brightness distribution of each individual red/green/blue color channel. == Characteristics of a color histogram == A color histogram focuses only on the proportion of the number of different types of colors, regardless of the spatial location of the colors. The values of a color histogram are from statistics. They show the statistical distribution of colors and the essential tone of an image. In general, as the color distributions of the foreground and background in an image are different, there might be a bimodal distribution in the histogram. For the luminance histogram alone, there is no perfect histogram and in general, the histogram can tell whether it is over-exposure or not, but there are times when you might think the image is over exposed by viewing the histogram; however, in reality it is not. == Principles of the formation of a color histogram == The formation of a color histogram is rather simple. From the definition above, we can simply count the number of pixels for each 256 scales in each of the 3 RGB channel, and plot them on 3 individual bar graphs. In general, a color histogram is based on a certain color space, such as RGB or HSV. When we compute the pixels of different colors in an image, if the color space is large, then we can first divide the color space into certain numbers of small intervals. Each of the intervals is called a bin. This process is called color quantization. Then, by counting the number of pixels in each of the bins, we get a color histogram of the image. The concrete steps of the principles can be viewed in Example 1. == Examples == === Example 1 === Given the following image of a cat (an original version and a version that has been reduced to 256 colors for easy histogram purposes), the following data represents a color histogram in the RGB color space, using four bins. Bin 0 corresponds to intensities 0–63 Bin 1 is 64–127 Bin 2 is 128–191 and Bin 3 is 192–255. === Example 2 === Application in camera: Nowadays, some cameras have the ability to show the 3 color histograms when we take photos. We can examine clips (spikes on either the black or white side of the scale) in each of the 3 RGB color histograms. If we find one or more clipping on a channel of the 3 RGB channels, then this would result in a loss of detail for that color. To illustrate this, consider this example: We know that each of the three R, G, B channels has a range of values from 0 to 255 (8 bit). So consider a photo that has a luminance range of 0–255. Assume the photo we take is made of 4 blocks that are adjacent to each other and we set the luminance scale for each of the 4 blocks of original photo to be 10, 100, 205, 245. Thus, the image looks like the topmost figure on the right. Then, we overexpose the photo a little, say, the luminance scale of each block is increased by 10. Thus, the luminance scale for each of the 4 blocks of new photo is 20, 110, 215, 255. Then, the image looks like the second figure on the right. There is not much difference between both figures, all we can see is that the whole image becomes brighter (the contrast for each of the blocks remain the same). Now, we overexpose the original photo again, this time the luminance scale of each block is increased by 50. Thus, the luminance scale for each of the 4 blocks of the new photo is 60, 150, 255, 255. The new image now looks like the third figure on the right. Note that the scale for the last block is 255 instead of 295, for 255 is the top scale and thus the last block has clipped. When this happens, we lose the contrast of the last 2 blocks, and thus we cannot recover the image no matter how we adjust it. To conclude, when taking photos with a camera that displays histograms, always keep the brightest tone in the image below the largest scale 255 on the histogram in order to avoid losing details. == Drawbacks and other approaches == The main drawback of histograms for classification is that the representation is dependent on the color of the object being studied, ignoring its shape and texture. Color histograms can potentially be identical for two images with different object content which happens to share color information. Conversely, without spatial or shape information, similar objects of different color may be indistinguishable based solely on color histogram comparisons. There is no way to distinguish a red and white cup from a red and white plate. Put it another way: histogram-based algorithms have no concept of a generic 'cup', and a model of a red and white cup is no use when given an otherwise identical blue and white cup. Another problem is that color histograms have high sensitivity to noisy interference such as lighting intensity changes and quantization errors. High dimensionality (bins) color histograms are also another issue. Some color histogram feature spaces often occupy more than one hundred di

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  Baum–Welch algorithm

  In electrical engineering, statistical computing and bioinformatics, the Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm to compute the statistics for the expectation step. The Baum–Welch algorithm, the primary method for inference in hidden Markov models, is numerically unstable due to its recursive calculation of joint probabilities. As the number of variables grows, these joint probabilities become increasingly small, leading to the forward recursions rapidly approaching values below machine precision. == History == The Baum–Welch algorithm was named after its inventors Leonard E. Baum and Lloyd R. Welch. The algorithm and the Hidden Markov models were first described in a series of articles by Baum and his peers at the IDA Center for Communications Research, Princeton in the late 1960s and early 1970s. One of the first major applications of HMMs was to the field of speech processing. In the 1980s, HMMs were emerging as a useful tool in the analysis of biological systems and information, and in particular genetic information. They have since become an important tool in the probabilistic modeling of genomic sequences. == Description == A hidden Markov model describes the joint probability of a collection of "hidden" and observed discrete random variables. It relies on the assumption that the i-th hidden variable given the (i − 1)-th hidden variable is independent of previous hidden variables, and the current observation variables depend only on the current hidden state. The Baum–Welch algorithm uses the well known EM algorithm to find the maximum likelihood estimate of the parameters of a hidden Markov model given a set of observed feature vectors. Let X t {\displaystyle X_{t}} be a discrete hidden random variable with N {\displaystyle N} possible values (i.e. We assume there are N {\displaystyle N} states in total). We assume the P ( X t ∣ X t − 1 ) {\displaystyle P(X_{t}\mid X_{t-1})} is independent of time t {\displaystyle t} , which leads to the definition of the time-independent stochastic transition matrix A = { a i j } = P ( X t = j ∣ X t − 1 = i ) . {\displaystyle A=\{a_{ij}\}=P(X_{t}=j\mid X_{t-1}=i).} The initial state distribution (i.e. when t = 1 {\displaystyle t=1} ) is given by π i = P ( X 1 = i ) . {\displaystyle \pi _{i}=P(X_{1}=i).} The observation variables Y t {\displaystyle Y_{t}} can take one of K {\displaystyle K} possible values. We also assume the observation given the "hidden" state is time independent. The probability of a certain observation y i {\displaystyle y_{i}} at time t {\displaystyle t} for state X t = j {\displaystyle X_{t}=j} is given by b j ( y i ) = P ( Y t = y i ∣ X t = j ) . {\displaystyle b_{j}(y_{i})=P(Y_{t}=y_{i}\mid X_{t}=j).} Taking into account all the possible values of Y t {\displaystyle Y_{t}} and X t {\displaystyle X_{t}} , we obtain the N × K {\displaystyle N\times K} matrix B = { b j ( y i ) } {\displaystyle B=\{b_{j}(y_{i})\}} where b j {\displaystyle b_{j}} belongs to all the possible states and y i {\displaystyle y_{i}} belongs to all the observations. An observation sequence is given by Y = ( Y 1 = y 1 , Y 2 = y 2 , … , Y T = y T ) {\displaystyle Y=(Y_{1}=y_{1},Y_{2}=y_{2},\ldots ,Y_{T}=y_{T})} . Thus we can describe a hidden Markov chain by θ = ( A , B , π ) {\displaystyle \theta =(A,B,\pi )} . The Baum–Welch algorithm finds a local maximum for θ ∗ = a r g m a x θ ⁡ P ( Y ∣ θ ) {\displaystyle \theta ^{}=\operatorname {arg\,max} _{\theta }P(Y\mid \theta )} (i.e. the HMM parameters θ {\displaystyle \theta } that maximize the probability of the observation). === Algorithm === Set θ = ( A , B , π ) {\displaystyle \theta =(A,B,\pi )} with random initial conditions. They can also be set using prior information about the parameters if it is available; this can speed up the algorithm and also steer it toward the desired local maximum. ==== Forward procedure ==== Let α i ( t ) = P ( Y 1 = y 1 , … , Y t = y t , X t = i ∣ θ ) {\displaystyle \alpha _{i}(t)=P(Y_{1}=y_{1},\ldots ,Y_{t}=y_{t},X_{t}=i\mid \theta )} , the probability of seeing the observations y 1 , y 2 , … , y t {\displaystyle y_{1},y_{2},\ldots ,y_{t}} and being in state i {\displaystyle i} at time t {\displaystyle t} . This is found recursively: α i ( 1 ) = π i b i ( y 1 ) , {\displaystyle \alpha _{i}(1)=\pi _{i}b_{i}(y_{1}),} α i ( t + 1 ) = b i ( y t + 1 ) ∑ j = 1 N α j ( t ) a j i . {\displaystyle \alpha _{i}(t+1)=b_{i}(y_{t+1})\sum _{j=1}^{N}\alpha _{j}(t)a_{ji}.} Since this series converges exponentially to zero, the algorithm will numerically underflow for longer sequences. However, this can be avoided in a slightly modified algorithm by scaling α {\displaystyle \alpha } in the forward and β {\displaystyle \beta } in the backward procedure below. ==== Backward procedure ==== Let β i ( t ) = P ( Y t + 1 = y t + 1 , … , Y T = y T ∣ X t = i , θ ) {\displaystyle \beta _{i}(t)=P(Y_{t+1}=y_{t+1},\ldots ,Y_{T}=y_{T}\mid X_{t}=i,\theta )} that is the probability of the ending partial sequence y t + 1 , … , y T {\displaystyle y_{t+1},\ldots ,y_{T}} given starting state i {\displaystyle i} at time t {\displaystyle t} . We calculate β i ( t ) {\displaystyle \beta _{i}(t)} as, β i ( T ) = 1 , {\displaystyle \beta _{i}(T)=1,} β i ( t ) = ∑ j = 1 N β j ( t + 1 ) a i j b j ( y t + 1 ) . {\displaystyle \beta _{i}(t)=\sum _{j=1}^{N}\beta _{j}(t+1)a_{ij}b_{j}(y_{t+1}).} ==== Update ==== We can now calculate the temporary variables, according to Bayes' theorem: γ i ( t ) = P ( X t = i ∣ Y , θ ) = P ( X t = i , Y ∣ θ ) P ( Y ∣ θ ) = α i ( t ) β i ( t ) ∑ j = 1 N α j ( t ) β j ( t ) , {\displaystyle \gamma _{i}(t)=P(X_{t}=i\mid Y,\theta )={\frac {P(X_{t}=i,Y\mid \theta )}{P(Y\mid \theta )}}={\frac {\alpha _{i}(t)\beta _{i}(t)}{\sum _{j=1}^{N}\alpha _{j}(t)\beta _{j}(t)}},} which is the probability of being in state i {\displaystyle i} at time t {\displaystyle t} given the observed sequence Y {\displaystyle Y} and the parameters θ {\displaystyle \theta } ξ i j ( t ) = P ( X t = i , X t + 1 = j ∣ Y , θ ) = P ( X t = i , X t + 1 = j , Y ∣ θ ) P ( Y ∣ θ ) = α i ( t ) a i j β j ( t + 1 ) b j ( y t + 1 ) ∑ k = 1 N ∑ w = 1 N α k ( t ) a k w β w ( t + 1 ) b w ( y t + 1 ) , {\displaystyle \xi _{ij}(t)=P(X_{t}=i,X_{t+1}=j\mid Y,\theta )={\frac {P(X_{t}=i,X_{t+1}=j,Y\mid \theta )}{P(Y\mid \theta )}}={\frac {\alpha _{i}(t)a_{ij}\beta _{j}(t+1)b_{j}(y_{t+1})}{\sum _{k=1}^{N}\sum _{w=1}^{N}\alpha _{k}(t)a_{kw}\beta _{w}(t+1)b_{w}(y_{t+1})}},} which is the probability of being in state i {\displaystyle i} and j {\displaystyle j} at times t {\displaystyle t} and t + 1 {\displaystyle t+1} respectively given the observed sequence Y {\displaystyle Y} and parameters θ {\displaystyle \theta } . The denominators of γ i ( t ) {\displaystyle \gamma _{i}(t)} and ξ i j ( t ) {\displaystyle \xi _{ij}(t)} are the same ; they represent the probability of making the observation Y {\displaystyle Y} given the parameters θ {\displaystyle \theta } . The parameters of the hidden Markov model θ {\displaystyle \theta } can now be updated: π i ∗ = γ i ( 1 ) , {\displaystyle \pi _{i}^{}=\gamma _{i}(1),} which is the expected frequency spent in state i {\displaystyle i} at time 1 {\displaystyle 1} . a i j ∗ = ∑ t = 1 T − 1 ξ i j ( t ) ∑ t = 1 T − 1 γ i ( t ) , {\displaystyle a_{ij}^{}={\frac {\sum _{t=1}^{T-1}\xi _{ij}(t)}{\sum _{t=1}^{T-1}\gamma _{i}(t)}},} which is the expected number of transitions from state i to state j compared to the expected total number of transitions starting in state i, including from state i to itself. The number of transitions starting in state i is equivalent to the number of times state i is observed in the sequence from t = 1 to t = T − 1. b i ∗ ( v k ) = ∑ t = 1 T 1 y t = v k γ i ( t ) ∑ t = 1 T γ i ( t ) , {\displaystyle b_{i}^{}(v_{k})={\frac {\sum _{t=1}^{T}1_{y_{t}=v_{k}}\gamma _{i}(t)}{\sum _{t=1}^{T}\gamma _{i}(t)}},} where 1 y t = v k = { 1 if y t = v k , 0 otherwise {\displaystyle 1_{y_{t}=v_{k}}={\begin{cases}1&{\text{if }}y_{t}=v_{k},\\0&{\text{otherwise}}\end{cases}}} is an indicator function, and b i ∗ ( v k ) {\displaystyle b_{i}^{}(v_{k})} is the expected number of times the output observations have been equal to v k {\displaystyle v_{k}} while in state i {\displaystyle i} over the expected total number of times in state i {\displaystyle i} . These steps are now repeated iteratively until a desired level of convergence. Note: It is possible to over-fit a particular data set. That is, P ( Y ∣ θ final ) > P ( Y ∣ θ true ) {\displaystyle P(Y\mid \theta _{\text{final}})>P(Y\mid \theta _{\text{true}})} . The algorithm also does not guarantee a global maximum. ==== Multiple sequences ==== The algorithm described thus far assumes a single observed sequence Y = y 1 , … , y T {\displaystyle Y=y_{1},\ldots ,y_{T}} . However, in many situations, there are several sequences observed: Y 1 ,

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  Kristian Kersting

  Kristian Kersting (born November 28, 1973, in Cuxhaven, Germany) is a German computer scientist. He is Professor of Artificial intelligence and Machine Learning at the Department of Computer Science at the Technische Universität Darmstadt, Head of the Artificial Intelligence and Machine Learning Lab (AIML) and Co-Director of hessian.AI, the Hessian Center for Artificial Intelligence. He is known for his research on statistical relational artificial intelligence, probabilistic programming, and deep probabilistic learning. == Life == Kersting studied computer science at the University of Freiburg, where he received his Ph.D. in 2006. At the university he attended a course on artificial intelligence given by Bernhard Nebel and became interested in the topic. He was a visiting postdoctoral researcher at the KU Leuven and a postdoctoral associate at the Massachusetts Institute of Technology (MIT). His advisor at MIT was Leslie Pack Kaelbling. From 2008 to 2012, he led a research group at the Fraunhofer Institute for Intelligent Analysis and Information Systems (IAIS). He then became a Juniorprofessor at the University of Bonn and associate Professor at the computer science department of the Technical University of Dortmund. From 2017 to 2019, he was professor of machine Learning and since 2019 professor of artificial intelligence and machine learning at the department of computer science of the Technische Universität Darmstadt. He is also a researcher at ATHENE, the largest research institute for IT security in Europe and leads a research department at the German Research Centre for Artificial Intelligence (DFKI). Kristian Kersting is the co-spokesperson of Cluster of Excellence "Reasonable Artificial Intelligence", RAI (2026-32). == Awards == In 2006, he received the AI Dissertation Award of the European Association for Artificial Intelligence. In 2008, he received the Fraunhofer Attract research grant with a budget of 2.5 million euros over five years. He was appointed Fellow of the European Association for Artificial Intelligence (EurAI) and Fellow of the European Laboratory for Learning and Intelligent Systems (ELLIS) in 2019. In 2019 he received the "Deutscher KI-Preis" ("German AI Award"), endowed with 100,000 euros, for his outstanding scientific achievements in the field of artificial intelligence. He was elected an AAAI Fellow in 2024. == Publications == De Raedt L., Kersting K. (2008) Probabilistic Inductive Logic Programming. In: De Raedt L., Frasconi P., Kersting K., Muggleton S. (eds) Probabilistic Inductive Logic Programming. Lecture Notes in Computer Science, vol 4911. Springer, Berlin, Heidelberg. ISBN 978-3-540-78651-1 Luc De Raedt, Kristian Kersting, Sriraam Natarajan and David Poole, "Statistical Relational Artificial Intelligence: Logic, Probability, and Computation", Synthesis Lectures on Artificial Intelligence and Machine Learning" Morgan & Claypool, March 2016 ISBN 9781627058414.

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  Abeba Birhane

  Abeba Birhane is an Ethiopian-born cognitive scientist who works at the intersection of complex adaptive systems, machine learning, algorithmic bias, and critical race studies. Birhane's work with Vinay Prabhu uncovered that large-scale image datasets commonly used to develop AI systems, including ImageNet and 80 Million Tiny Images, carried racist and misogynistic labels and offensive images. She has been recognized by VentureBeat as a top innovator in computer vision and named as one of the 100 most influential persons in AI 2023 by TIME magazine. == Early life and education == Birhane was born in Ethiopia. She received her Bachelors of Science in Psychology and a Bachelors of Arts in Philosophy from The Open University. In 2015, she completed her Master of Science in Cognitive Science and, in 2021, her Ph.D. at the Complex Software Lab in the School of Computer Science at University College Dublin. == Career and research == Birhane studied the impacts of emerging AI technologies and how they shape individuals and local communities. She found that AI algorithms tend to disproportionately impact vulnerable groups such as older workers, trans people, immigrants, and children. Her research on relational ethics won the best paper award at NeurIPS’s Black in AI workshop in 2019. She has also studied and written about algorithmic colonization driven by corporate agendas. Her work in decolonizing computational sciences addressed the inherited oppressions in current systems especially towards women of color. In 2020, Birhane and Vinay Prabhu, principal machine learning scientist at UnifyID, published a paper examining the problematic data collection, labelling, classification, and consequences of large image datasets. These datasets, including ImageNet and MIT's 80 Million Tiny Images, have been used to develop thousands of AI algorithms and systems. Birhane and Prabhu found that they contained many racist and misogynistic labels and slurs as well as offensive images. This resulted in MIT voluntarily and formally taking down the 80 Million Tiny Images dataset. More recently, Birhane has worked with Rediet Abebe, George Obaido, and Sekou Remy on researching the barriers to data sharing in Africa. They found that power imbalances are significant in the data sharing process, even when the data comes from Africa. Their research was published at the ACM Conference on Fairness, Accountability, and Transparency. In 2024, Birhane established the AI Accountability Lab research group at Trinity College Dublin. == Selected awards == 2019 NeurIPS Black in AI Workshop Best Paper Award 2020 Venture Beat AI Innovations Award in the category Computer Vision Innovation (received with Vinay Prabhu) 2021 100 Brilliant Women in AI Ethics Hall of Fame Honoree 2022 Lero Director’s Prize for PhD/PostDoctoral Contribution. 2023 100 Most Influential People in AI by TIME magazine

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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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  Arthur Zimek

  Arthur Zimek is a professor in data mining, data science and machine learning at the University of Southern Denmark in Odense, Denmark. He graduated from LMU Munich in Germany, where he worked with Prof. Hans-Peter Kriegel. His dissertation on "Correlation Clustering" was awarded the "SIGKDD Doctoral Dissertation Award 2009 Runner-up" by the Association for Computing Machinery. He is well known for his work on outlier detection, density-based clustering, correlation clustering, and the curse of dimensionality. He is one of the founders and core developers of the open-source ELKI data mining framework.

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  Leslie P. Kaelbling

  Leslie Pack Kaelbling is an American roboticist and the Panasonic Professor of Computer Science and Engineering at the Massachusetts Institute of Technology. She is widely recognized for adapting partially observable Markov decision processes from operations research for application in artificial intelligence and robotics. Kaelbling received the IJCAI Computers and Thought Award in 1997 for applying reinforcement learning to embedded control systems and developing programming tools for robot navigation. In 2000, she was elected as a Fellow of the Association for the Advancement of Artificial Intelligence. == Career == Kaelbling received an A. B. in Philosophy in 1983 and a Ph.D. in Computer Science in 1990, both from Stanford University. During this time she was also affiliated with the Center for the Study of Language and Information. She then worked at SRI International and the affiliated robotics spin-off Teleos Research before joining the faculty at Brown University. She left Brown in 1999 to join the faculty at MIT. Her research focuses on decision-making under uncertainty, machine learning, and sensing with applications to robotics. == Journal of Machine Learning Research == In the spring of 2000, she and two-thirds of the editorial board of the Kluwer-owned journal Machine Learning resigned in protest to its pay-to-access archives with simultaneously limited financial compensation for authors. Kaelbling co-founded and served as the first editor-in-chief of the Journal of Machine Learning Research, a peer-reviewed open access journal on the same topics which allows researchers to publish articles for free and retain copyright with its archives freely available online. In response to the mass resignation, Kluwer changed their publishing policy to allow authors to self-archive their papers online after peer-review. Kaelbling responded that this policy was reasonable and would have made the creation of an alternative journal unnecessary, but the editorial board members had made it clear they wanted such a policy and it was only after the threat of resignations and the actual founding of JMLR that the publishing policy finally changed. == Selected works == Reinforcement Learning: A Survey (LP Kaelbling, ML Littman, AW Moore). Journal of Artificial Intelligence Research (JAIR) 4 (1996) 237-285. A highly cited survey on the field of reinforcement learning. Planning and acting in partially observable stochastic domains (LP Kaelbling, ML Littman, AR Cassandra). Artificial Intelligence 101 (1), 99-134. Acting under uncertainty: Discrete Bayesian models for mobile-robot navigation (AR Cassandra, LP Kaelbling, JA Kurien). Intelligent Robots and Systems (2) 963-972. The synthesis of digital machines with provable epistemic properties (SJ Rosenschein, LP Kaelbling). Proceedings of the 1986 Conference on Theoretical Aspects of Reasoning about Knowledge, 83-98. Practical reinforcement learning in continuous spaces (WD Smart, LP Kaelbling). 2000 International Conference on Machine Learning (ICML), 903-910. Hierarchical task and motion planning in the now (LP Kaelbling, T Lozano-Pérez). 2011 IEEE International Conference on Robotics and Automation (ICRA), 1470-1477.

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  AI Avatar Generators Reviews: What Actually Works in 2026

  Shopping for the best AI avatar generator? An AI avatar generator is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI avatar generator slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

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  Sarpa (snakebite app)

  Sarpa or SARPA (Snake Awareness, Rescue and Protection app) is a snakebite app, an application for mobile devices developed in India to provide rapid, life-saving help for victims of snakebite, which kill an estimated 58,000 people a year in India. The app provides information about snakes, gets fast aid for people bitten, and helps in the development of antivenoms. Similar systems developed in India include SnakeHub, Snake Lens, Snakepedia, Serpent and the Big Four Mapping Project. The apps provide rapid response to snakebite incidents, often in remote areas, using a network of volunteers managed by local wildlife departments; their use can save human lives by providing rapid medical care, and also snakes, by helping to avoid interaction between the species. In 2026, it was announced that the app had plans to offer real-time contact from doctors directly from the app to provide users with decision-making advice.

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  AI Video Editors Reviews: What Actually Works in 2026

  Curious about the best AI video editor? An AI video editor is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI video editor slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.

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  Amebis

  Amebis from Kamnik is a company in Slovenia in the field of language technologies. The company has published several electronic dictionaries and encyclopedic dictionaries (e.g. ASP (32) dictionaries) and developed spell checkers, grammar checker Besana, hyphenators and lemmatizers for Slovene, Serbian and Albanian languages. The company maintains and edits the largest Slovenian dictionary portal Termania, which contains more than 135 dictionaries. The most used terminological dictionary on Termania is the Slovenian medical dictionary. In co-operation with company Alpineon and the Jožef Stefan Institute they have developed a speech synthesizer and screen reader Govorec (Speaker). They have also provided technical support for the largest text corpus of Slovene, called FidaPLUS, Fran and Franček. Amebis also developed the system of machine translation Amebis Presis, which incorporates the Slovenian language. On 11 October 2023 Amebis received award of the Father Stanislav Škrabec Foundation for special achievements in Slovene linguistics.

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  Mirella Lapata

  Mirella Lapata is a computer scientist and Professor in the School of Informatics at the University of Edinburgh. Working on the general problem of extracting semantic information from large bodies of text, Lapata develops computer algorithms and models in the field of natural language processing (NLP). == Education == Lapata obtained a Master of Arts (MA) degree from Carnegie Mellon University and subsequently earned a doctorate from the University of Edinburgh. Lapata's doctoral research investigated the acquisition of information from polysemous linguistic units using probabilistic methods supervised by Alex Lascarides, Chris Brew and Steve Finch. == Career and research == After her doctorate, Lapata assumed academic positions at Saarland University and at the Department of Computer Science at the University of Sheffield. At the University of Edinburgh she became a reader in the School of Informatics where she is a full Professor and holds a personal chair in natural language processing. Lapata is a member of the Human Communication Research Center and Institute for Language, Cognition and Computation, both in Edinburgh. Between 2015 and 2017, Lapata served as a member of the Royal Society Machine Learning Working Group. Recently Lapata was granted a European Research Council (ERC) Consolidator Grant worth €1.9M to fund five years of her project, TransModal: Translating from Multiple Modalities into Text. === Awards and honours === In 2009 Lapata became the first recipient of the Microsoft British Computer Society (BCS)/BCS IRSG Karen Spärck Jones Award. The award recognises achievement in furthering the progress in information retrieval and natural language processing; the award commemorates the life and work of Karen Spärck Jones. In 2012 Lapata won an Empirical Methods in Natural Language Processing (EMNLP)-CoNLL 2012 Best Reviewer Award. In 2018 Lapata was awarded, alongside Li Dong, an Association for Computational Linguistics (ACL) Best Paper Honorable Mention. In 2019 Lapata was elected a Fellow of the Royal Society of Edinburgh In 2020 Lapata was elected to the Academia Europaea. In 2025 Lapata was awarded the BCS Lovelace Medal for Computing Research.

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  Molecular graphics

  Molecular graphics is the discipline and philosophy of studying molecules and their properties through graphical representation. IUPAC limits the definition to representations on a "graphical display device". Ever since Dalton's atoms and Kekulé's benzene, there has been a rich history of hand-drawn atoms and molecules, and these representations have had an important influence on modern molecular graphics. Colour molecular graphics are often used on chemistry journal covers artistically. == History == Prior to the use of computer graphics in representing molecular structure, Robert Corey and Linus Pauling developed a system for representing atoms or groups of atoms from hard wood on a scale of 1 inch = 1 angstrom connected by a clamping device to maintain the molecular configuration. These early models also established the CPK coloring scheme that is still used today to differentiate the different types of atoms in molecular models (e.g. carbon = black, oxygen = red, nitrogen = blue, etc). This early model was improved upon in 1966 by W.L. Koltun and are now known as Corey-Pauling-Koltun (CPK) models. The earliest efforts to produce models of molecular structure was done by Project MAC using wire-frame models displayed on a cathode ray tube in the mid 1960s. In 1965, Carroll Johnson distributed the Oak Ridge thermal ellipsoid plot (ORTEP) that visualized molecules as a ball-and-stick model with lines representing the bonds between atoms and ellipsoids to represent the probability of thermal motion. Thermal ellipsoid plots quickly became the de facto standard used in the display of X-ray crystallography data, and are still in wide use today. The first practical use of molecular graphics was a simple display of the protein myoglobin using a wireframe representation in 1966 by Cyrus Levinthal and Robert Langridge working at Project MAC. Among the milestones in high-performance molecular graphics was the work of Nelson Max in "realistic" rendering of macromolecules using reflecting spheres. Initially much of the technology concentrated on high-performance 3D graphics. During the 1970s, methods for displaying 3D graphics using cathode ray tubes were developed using continuous tone computer graphics in combination with electro-optic shutter viewing devices. The first devices used an active shutter 3D system, generating different perspective views for the left and right channel to provide the illusion of three-dimensional viewing. Stereoscopic viewing glasses were designed using lead lanthanum zirconate titanate (PLZT) ceramics as electronically controlled shutter elements. Active 3D glasses require batteries and work in concert with the display to actively change the presentation by the lenses to the wearer's eyes. Many modern 3D glasses use a passive, polarized 3D system that enables the wearer to visualize 3D effects based on their own perception. Passive 3D glasses are more common today since they are less expensive. The requirements of macromolecular crystallography also drove molecular graphics because the traditional techniques of physical model-building could not scale. The first two protein structures solved by molecular graphics without the aid of the Richards' Box were built with Stan Swanson's program FIT on the Vector General graphics display in the laboratory of Edgar Meyer at Texas A&M University: First Marge Legg in Al Cotton's lab at A&M solved a second, higher-resolution structure of staph. nuclease (1975) and then Jim Hogle solved the structure of monoclinic lysozyme in 1976. A full year passed before other graphics systems were used to replace the Richards' Box for modelling into density in 3-D. Alwyn Jones' FRODO program (and later "O") were developed to overlay the molecular electron density determined from X-ray crystallography and the hypothetical molecular structure. === Timeline === == Types == === Ball-and-stick models === In the ball-and-stick model, atoms are drawn as small sphered connected by rods representing the chemical bonds between them. === Space-filling models === In the space-filling model, atoms are drawn as solid spheres to suggest the space they occupy, in proportion to their van der Waals radii. Atoms that share a bond overlap with each other. === Surfaces === In some models, the surface of the molecule is approximated and shaded to represent a physical property of the molecule, such as electronic charge density. === Ribbon diagrams === Ribbon diagrams are schematic representations of protein structure and are one of the most common methods of protein depiction used today. The ribbon shows the overall path and organization of the protein backbone in 3D, and serves as a visual framework on which to hang details of the full atomic structure, such as the balls for the oxygen atoms bound to the active site of myoglobin in the adjacent image. Ribbon diagrams are generated by interpolating a smooth curve through the polypeptide backbone. α-helices are shown as coiled ribbons or thick tubes, β-strands as arrows, and non-repetitive coils or loops as lines or thin tubes. The direction of the polypeptide chain is shown locally by the arrows, and may be indicated overall by a colour ramp along the length of the ribbon.

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  Semiautomaton

  In mathematics and theoretical computer science, a semiautomaton is a deterministic finite automaton having inputs but no output. It consists of a set Q of states, a set Σ called the input alphabet, and a function T: Q × Σ → Q called the transition function. Associated with any semiautomaton is a monoid called the characteristic monoid, input monoid, transition monoid or transition system of the semiautomaton, which acts on the set of states Q. This may be viewed either as an action of the free monoid of strings in the input alphabet Σ, or as the induced transformation semigroup of Q. In older books like Clifford and Preston (1967) semigroup actions are called "operands". In category theory, semiautomata essentially are functors. == Transformation semigroups and monoid acts == A transformation semigroup or transformation monoid is a pair ( M , Q ) {\displaystyle (M,Q)} consisting of a set Q (often called the "set of states") and a semigroup or monoid M of functions, or "transformations", mapping Q to itself. They are functions in the sense that every element m of M is a map m : Q → Q {\displaystyle m\colon Q\to Q} . If s and t are two functions of the transformation semigroup, their semigroup product is defined as their function composition ( s t ) ( q ) = ( s ∘ t ) ( q ) = s ( t ( q ) ) {\displaystyle (st)(q)=(s\circ t)(q)=s(t(q))} . Some authors regard "semigroup" and "monoid" as synonyms. Here a semigroup need not have an identity element; a monoid is a semigroup with an identity element (also called "unit"). Since the notion of functions acting on a set always includes the notion of an identity function, which when applied to the set does nothing, a transformation semigroup can be made into a monoid by adding the identity function. === M-acts === Let M be a monoid and Q be a non-empty set. If there exists a multiplicative operation μ : Q × M → Q {\displaystyle \mu \colon Q\times M\to Q} ( q , m ) ↦ q m = μ ( q , m ) {\displaystyle (q,m)\mapsto qm=\mu (q,m)} which satisfies the properties q 1 = q {\displaystyle q1=q} for 1 the unit of the monoid, and q ( s t ) = ( q s ) t {\displaystyle q(st)=(qs)t} for all q ∈ Q {\displaystyle q\in Q} and s , t ∈ M {\displaystyle s,t\in M} , then the triple ( Q , M , μ ) {\displaystyle (Q,M,\mu )} is called a right M-act or simply a right act. In long-hand, μ {\displaystyle \mu } is the right multiplication of elements of Q by elements of M. The right act is often written as Q M {\displaystyle Q_{M}} . A left act is defined similarly, with μ : M × Q → Q {\displaystyle \mu \colon M\times Q\to Q} ( m , q ) ↦ m q = μ ( m , q ) {\displaystyle (m,q)\mapsto mq=\mu (m,q)} and is often denoted as M Q {\displaystyle \,_{M}Q} . An M-act is closely related to a transformation monoid. However the elements of M need not be functions per se, they are just elements of some monoid. Therefore, one must demand that the action of μ {\displaystyle \mu } be consistent with multiplication in the monoid (i.e. μ ( q , s t ) = μ ( μ ( q , s ) , t ) {\displaystyle \mu (q,st)=\mu (\mu (q,s),t)} ), as, in general, this might not hold for some arbitrary μ {\displaystyle \mu } , in the way that it does for function composition. Once one makes this demand, it is completely safe to drop all parenthesis, as the monoid product and the action of the monoid on the set are completely associative. In particular, this allows elements of the monoid to be represented as strings of letters, in the computer-science sense of the word "string". This abstraction then allows one to talk about string operations in general, and eventually leads to the concept of formal languages as being composed of strings of letters. Another difference between an M-act and a transformation monoid is that for an M-act Q, two distinct elements of the monoid may determine the same transformation of Q. If we demand that this does not happen, then an M-act is essentially the same as a transformation monoid. === M-homomorphism === For two M-acts Q M {\displaystyle Q_{M}} and B M {\displaystyle B_{M}} sharing the same monoid M {\displaystyle M} , an M-homomorphism f : Q M → B M {\displaystyle f\colon Q_{M}\to B_{M}} is a map f : Q → B {\displaystyle f\colon Q\to B} such that f ( q m ) = f ( q ) m {\displaystyle f(qm)=f(q)m} for all q ∈ Q M {\displaystyle q\in Q_{M}} and m ∈ M {\displaystyle m\in M} . The set of all M-homomorphisms is commonly written as H o m ( Q M , B M ) {\displaystyle \mathrm {Hom} (Q_{M},B_{M})} or H o m M ( Q , B ) {\displaystyle \mathrm {Hom} _{M}(Q,B)} . The M-acts and M-homomorphisms together form a category called M-Act. == Semiautomata == A semiautomaton is a triple ( Q , Σ , T ) {\displaystyle (Q,\Sigma ,T)} where Σ {\displaystyle \Sigma } is a non-empty set, called the input alphabet, Q is a non-empty set, called the set of states, and T is the transition function T : Q × Σ → Q . {\displaystyle T\colon Q\times \Sigma \to Q.} When the set of states Q is a finite set—it need not be—, a semiautomaton may be thought of as a deterministic finite automaton ( Q , Σ , T , q 0 , A ) {\displaystyle (Q,\Sigma ,T,q_{0},A)} , but without the initial state q 0 {\displaystyle q_{0}} or set of accept states A. Alternately, it is a finite-state machine that has no output, and only an input. Any semiautomaton induces an act of a monoid in the following way. Let Σ ∗ {\displaystyle \Sigma ^{}} be the free monoid generated by the alphabet Σ {\displaystyle \Sigma } (so that the superscript is understood to be the Kleene star); it is the set of all finite-length strings composed of the letters in Σ {\displaystyle \Sigma } . For every word w in Σ ∗ {\displaystyle \Sigma ^{}} , let T w : Q → Q {\displaystyle T_{w}\colon Q\to Q} be the function, defined recursively, as follows, for all q in Q: If w = ε {\displaystyle w=\varepsilon } , then T ε ( q ) = q {\displaystyle T_{\varepsilon }(q)=q} , so that the empty word ε {\displaystyle \varepsilon } does not change the state. If w = σ {\displaystyle w=\sigma } is a letter in Σ {\displaystyle \Sigma } , then T σ ( q ) = T ( q , σ ) {\displaystyle T_{\sigma }(q)=T(q,\sigma )} . If w = σ v {\displaystyle w=\sigma v} for σ ∈ Σ {\displaystyle \sigma \in \Sigma } and v ∈ Σ ∗ {\displaystyle v\in \Sigma ^{}} , then T w ( q ) = T v ( T σ ( q ) ) {\displaystyle T_{w}(q)=T_{v}(T_{\sigma }(q))} . Let M ( Q , Σ , T ) {\displaystyle M(Q,\Sigma ,T)} be the set M ( Q , Σ , T ) = { T w | w ∈ Σ ∗ } . {\displaystyle M(Q,\Sigma ,T)=\{T_{w}\vert w\in \Sigma ^{}\}.} The set M ( Q , Σ , T ) {\displaystyle M(Q,\Sigma ,T)} is closed under function composition; that is, for all v , w ∈ Σ ∗ {\displaystyle v,w\in \Sigma ^{}} , one has T w ∘ T v = T v w {\displaystyle T_{w}\circ T_{v}=T_{vw}} . It also contains T ε {\displaystyle T_{\varepsilon }} , which is the identity function on Q. Since function composition is associative, the set M ( Q , Σ , T ) {\displaystyle M(Q,\Sigma ,T)} is a monoid: it is called the input monoid, characteristic monoid, characteristic semigroup or transition monoid of the semiautomaton ( Q , Σ , T ) {\displaystyle (Q,\Sigma ,T)} . == Properties == If the set of states Q is finite, then the transition functions are commonly represented as state transition tables. The structure of all possible transitions driven by strings in the free monoid has a graphical depiction as a de Bruijn graph. The set of states Q need not be finite, or even countable. As an example, semiautomata underpin the concept of quantum finite automata. There, the set of states Q are given by the complex projective space C P n {\displaystyle \mathbb {C} P^{n}} , and individual states are referred to as n-state qubits. State transitions are given by unitary n×n matrices. The input alphabet Σ {\displaystyle \Sigma } remains finite, and other typical concerns of automata theory remain in play. Thus, the quantum semiautomaton may be simply defined as the triple ( C P n , Σ , { U σ 1 , U σ 2 , … , U σ p } ) {\displaystyle (\mathbb {C} P^{n},\Sigma ,\{U_{\sigma _{1}},U_{\sigma _{2}},\dotsc ,U_{\sigma _{p}}\})} when the alphabet Σ {\displaystyle \Sigma } has p letters, so that there is one unitary matrix U σ {\displaystyle U_{\sigma }} for each letter σ ∈ Σ {\displaystyle \sigma \in \Sigma } . Stated in this way, the quantum semiautomaton has many geometrical generalizations. Thus, for example, one may take a Riemannian symmetric space in place of C P n {\displaystyle \mathbb {C} P^{n}} , and selections from its group of isometries as transition functions. The syntactic monoid of a regular language is isomorphic to the transition monoid of the minimal automaton accepting the language. == Literature == A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups. American Mathematical Society, volume 2 (1967), ISBN 978-0-8218-0272-4. F. Gecseg and I. Peak, Algebraic Theory of Automata (1972), Akademiai Kiado, Budapest. W. M. L. Holcombe, Algebraic Automata Theory (1982), Cambridge University Press J. M. Howie, Automata and Languages, (1991), Cla

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  Top 10 AI Bug Finders Compared (2026)

  Trying to pick the best AI bug finder? An AI bug finder is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI bug finder slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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