Chaotic cryptology is the application of mathematical chaos theory to the practice of cryptography, the study or techniques used to privately and securely transmit information with the presence of a third-party or adversary. Since first being investigated by Robert Matthews in 1989, the use of chaos in cryptography has attracted much interest. However, long-standing concerns about its security and implementation speed continue to limit its implementation. Chaotic cryptology consists of two opposite processes: Chaotic cryptography and Chaotic cryptanalysis. Cryptography refers to encrypting information for secure transmission, whereas cryptanalysis refers to decrypting and deciphering encoded encrypted messages. In order to use chaos theory efficiently in cryptography, the chaotic maps are implemented such that the entropy generated by the map can produce required Confusion and diffusion. Properties in chaotic systems and cryptographic primitives share unique characteristics that allow for the chaotic systems to be applied to cryptography. If chaotic parameters, as well as cryptographic keys, can be mapped symmetrically or mapped to produce acceptable and functional outputs, it will make it next to impossible for an adversary to find the outputs without any knowledge of the initial values. Since chaotic maps in a real life scenario require a set of numbers that are limited, they may, in fact, have no real purpose in a cryptosystem if the chaotic behavior can be predicted. One of the most important issues for any cryptographic primitive is the security of the system. However, in numerous cases, chaos-based cryptography algorithms are proved insecure. The main issue in many of the cryptanalyzed algorithms is the inadequacy of the chaotic maps implemented in the system. == Types == Chaos-based cryptography has been divided into two major groups: Symmetric chaos cryptography, where the same secret key is used by sender and receiver. Asymmetric chaos cryptography, where one key of the cryptosystem is public. Some of the few proposed systems have been broken. The majority of chaos-based cryptographic algorithms are symmetric. Many use discrete chaotic maps in their process. == Applications == === Image encryption === Bourbakis and Alexopoulos in 1991 proposed supposedly the earliest fully intended digital image encryption scheme which was based on SCAN language. Later on, with the emergence of chaos-based cryptography hundreds of new image encryption algorithms, all with the aim of improving the security of digital images were proposed. However, there were three main aspects of the design of an image encryption that was usually modified in different algorithms (chaotic map, application of the map and structure of algorithm). The initial and perhaps most crucial point was the chaotic map applied in the design of the algorithms. The speed of the cryptosystem is always an important parameter in the evaluation of the efficiency of a cryptography algorithm, therefore, the designers were initially interested in using simple chaotic maps such as tent map, and the logistic map. However, in 2006 and 2007, the new image encryption algorithms based on more sophisticated chaotic maps proved that application of chaotic map with higher dimension could improve the quality and security of the cryptosystems. === Hash function === Chaotic behavior can generate hash functions, such as applying the Chirikov/Julia 3D trajectory translation into a SHA-512 hash. === Random number generation === The unpredictable behavior of the chaotic maps can be used in the generation of random numbers. Some of the earliest chaos-based random number generators tried to directly generate random numbers from the logistic map. Many more recent works did so using the numerical solutions of hyperchaotic systems of differential equations, either at the integer-order, or the fractional-order.
Non-separable wavelet
Non-separable wavelets are multi-dimensional wavelets that are not directly implemented as tensor products of wavelets on some lower-dimensional space. They have been studied since 1992. They offer a few important advantages. Notably, using non-separable filters leads to more parameters in design, and consequently better filters. The main difference, when compared to the one-dimensional wavelets, is that multi-dimensional sampling requires the use of lattices (e.g., the quincunx lattice). The wavelet filters themselves can be separable or non-separable regardless of the sampling lattice. Thus, in some cases, the non-separable wavelets can be implemented in a separable fashion. Unlike separable wavelet, the non-separable wavelets are capable of detecting structures that are not only horizontal, vertical or diagonal (show less anisotropy). == Examples == Red-black wavelets Contourlets Shearlets Directionlets Steerable pyramids Non-separable schemes for tensor-product wavelets
Klaus-Robert Müller
Klaus-Robert Müller (born 1964 in Karlsruhe, West Germany) is a German computer scientist and physicist, most noted for his work in machine learning and brain–computer interfaces. == Career == Klaus-Robert Müller received his Diplom in mathematical physics and PhD in theoretical computer science from the University of Karlsruhe. Following his Ph.D. he went to Berlin as a postdoctoral fellow at GMD (German National Research Center for Computer Science) Berlin (now part of Fraunhofer Institute for Open Communication Systems), where he started building up the Intelligent Data Analysis (IDA) group. From 1994 to 1995 he was a research fellow at Shun'ichi Amari's lab at the University of Tokyo. 1999 Müller became an associate professor for neuroinformatics at the University of Potsdam, transitioning to the full professorship for Neural Networks and Time Series Analysis in 2003. Since 2006 he holds the chair for Machine Learning at Technische Universität Berlin. Since 2012 he holds a distinguished professorship at Korea University in Seoul. He co-founded and is co-director of the Berlin Big Data Center (BBDC) of TU Berlin. As of 2017, 29 former doctoral or postdoctoral researchers of Klaus-Robert Müller have become full professors themselves. Bernhard Schölkopf and Alexander J. Smola were supervised by him as members of his research group. Since 2020 he is director of the Berlin Institute for the Foundations of Learning and Data (BIFOLD), a German National AI Competence Center, and director of the European Laboratory for Learning and Intelligent Systems (ELLIS) unit Berlin. In 2020/2021 he spent his sabbatical at Google Brain as a principal scientist. == Research == Müller has contributed extensively to several major interests of machine learning, including support vector machines (SVMs) and kernel methods, and artificial neural networks. He pioneered applying new methods of pattern recognition in domains like brain–computer interfaces, using them for patients with Locked-in syndrome. He is one of the leading computer scientists affiliated with Germany. His current research interests include: Statistical learning theory (Support Vector Machines, Deep Neural Networks, Boosting) Learning of non-stationarity data Fusion of structured heterogeneous multi-modal data, co-adaptation Applications: MEG, EEG, NIRS, ECoG, EMG, Brain Computer Interfaces, computational neuroscience, computer vision, genomic data analysis, computational chemistry and atomistic simulations, digital pathology == Honours and awards == Klaus-Robert Müller was elected a fellow of the German National Academy of Sciences Leopoldina in 2012. In 2017 he was elected member of the Berlin-Brandenburg Academy of Sciences and Humanities and also external scientific member of the Max Planck Society. In 2021 he was elected member of the German Academy of Science and Engineering. His work was honoured with several awards, including: 2026 Gottfried Wilhelm Leibniz Prize 2025 IEEE Neural Network Pioneer Award 2024 Feynman Prize in Nanotechnology 2023 Hector Fellow 2025, 2024, 2023, 2022, 2021, 2020, and 2019 Clarivate Highly Cited Researcher 2017 Vodafone Innovations Award 2017 2014 Science Prize of Berlin 2014 by the Governing Mayor of Berlin 2014 European Research Council Panel Consolidator Grants 2009 Best Paper award by IEEE Engineering in Medicine and Biology Society EMBS 2006 SEL-ALCATEL Research Prize for Technical Communication 1999 Olympus Award for Pattern Recognition == Books == with Holzinger, Andreas; et al., eds. (2022). xxAI – Beyond Explainable Artificial Intelligence. Lecture Notes in Computer Science. Vol. 13200. Springer Cham. doi:10.1007/978-3-031-04083-2. ISBN 978-3-031-04082-5. with Schütt, Kristof T.; et al., eds. (2020). Machine Learning Meets Quantum Physics. Lecture Notes in Physics. Vol. 968. Springer Cham. doi:10.1007/978-3-030-40245-7. ISBN 978-3-030-40244-0. S2CID 242406994. with Samek, Wojciech; et al., eds. (2019). Explainable AI: Interpreting, Explaining and Visualizing Deep Learning. Lecture Notes in Computer Science. Vol. 11700. Springer Cham. doi:10.1007/978-3-030-28954-6. ISBN 978-3-030-28953-9. with Montavon, Grégoire; et al., eds. (2012). Neural Networks: Tricks of the Trade. Lecture Notes in Computer Science. Vol. 7700 (2nd ed.). Springer Berlin, Heidelberg. doi:10.1007/978-3-642-35289-8. ISBN 978-3-642-35288-1. S2CID 39578794.
Best AI Bug Finders in 2026
In search of the best AI bug finder? An AI bug finder is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI bug finder slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
Node2vec
node2vec is an algorithm to generate vector representations of nodes on a graph. The node2vec framework learns low-dimensional representations for nodes in a graph through the use of random walks through a graph starting at a target node. It is useful for a variety of machine learning applications. node2vec follows the intuition that random walks through a graph can be treated like sentences in a corpus. Each node in a graph is treated like an individual word, and a random walk is treated as a sentence. By feeding these "sentences" into a skip-gram, or by using the continuous bag of words model, paths found by random walks can be treated as sentences, and traditional data-mining techniques for documents can be used. The algorithm generalizes prior work which is based on rigid notions of network neighborhoods, and argues that the added flexibility in exploring neighborhoods is the key to learning richer representations of nodes in graphs. The algorithm is considered one of the best graph classifiers.
Dave's Redistricting
Dave's Redistricting App (DRA) is an online web app originally created by Dave Bradlee that allows anyone to simulate redistricting a U.S. state's congressional and legislative districts. == Purpose == According to Bradlee, the software was designed to "put power in people's hands," and so that they "can see how the process works, so it's a little less mysterious than it was 10 years ago." Bradlee has noticed that many citizens are taking this process seriously and using his app to create legitimate redistricting maps that could be put in place. Some websites have called Bradlee the pioneer and cause of the rise of do-it-yourself redistricting. States such as Montana in 2021 allowed the general population to use it to submit redistricting proposals following the 2020 United States Census. Dave's Redistricting has frequently been mentioned as a resource that can be used to combat gerrymandering, given that the public has free access to it. Political science firms such as FiveThirtyEight have used the website to draw examples of gerrymandered districts, including on their famous Atlas of Redistricting. Dave Bradlee built the first generation of DRA. DRA 2020 is built by a small team of volunteers—Dave Bradlee, Terry Crowley, Alec Ramsay, and David Rinn—all with a shared passion for technology & democracy and all Microsoft veterans. Their mission is to empower civic organizations and citizen activists to advocate for fair congressional and legislative districts and increased transparency in the redistricting process. == Functions == Users can redraw the congressional and state legislative districts for all 50 states, the District of Columbia, and Puerto Rico using a variety of census and election datasets including Cook PVI. Maps can be optimized for different criteria. DRA 2020 added several major features to the first generation app: Sharing & collaborative editing of maps, like Google Docs Multiple statewide elections for all 50 states including the ability to import your own data Comprehensive analytics for evaluating and comparing maps Custom overlays, and Block-level editing DRA remains free to use. == Versions == 2.2: This uses Bing Maps, an outdated software that projects the districts of a single state onto a map of the United States. 2.5: After Bing Maps announced that it would no longer be updating for the foreseen future, the U.S. Map feature was removed. DRA 2020: At the end of 2018, a beta version of 2020 was released. This version that did not require Microsoft Silverlight and could be used in any web browser. DRA 2020 has been under continuous development since and is built using React (JavaScript library), Mapbox, OpenStreetMap, TypeScript, Node.js, Amazon Web Services, as well as many open source components, tools, and icons.
Comparison of machine translation applications
Machine translation is an algorithm which attempts to translate text or speech from one natural language to another. == General information == Basic general information for popular machine translation applications. == Languages features comparison == The following table compares the number of languages which the following machine translation programs can translate between. (Moses and Moses for Mere Mortals allow you to train translation models for any language pair, though collections of translated texts (parallel corpus) need to be provided by the user. The Moses site provides links to training corpora.) This is not an all-encompassing list. Some applications have many more language pairs than those listed below. This is a general comparison of key languages only. A full and accurate list of language pairs supported by each product should be found on each of the product's websites. === Multi-pair translations === === Paired translations ===