Screen space directional occlusion (SSDO) is a computer graphics technique enhancing screen space ambient occlusion (SSAO) by taking direction into account to sample the ambient light (both the light coming directly at an object, as well as the light reflected off of the object directly behind it), to better approximate global illumination. SSDO was introduced by Tobias Ritschel, Thorsten Grosch, and Hans-Peter Seidel in their 2009 ACM Symposium on Interactive 3D Graphics and Games paper Approximating dynamic global illumination in image space, which describes it as extending SSAO to directional occlusion with one diffuse indirect bounce of light; later literature notes that SSDO still suffers from common screen-space artifacts such as noise and banding. == Method == The original SSDO paper describes a two-pass screen-space approach, with one pass for direct lighting and a second pass for indirect bounces. Later literature describes SSDO as assuming a general shadowing direction that allows color bleeding and a single light bounce.
SPL notation
SPL (Sentence Plan Language) is an abstract notation representing the semantics of a sentence in natural language. In a classical Natural Language Generation (NLG) workflow, an initial text plan (hierarchically or sequentially organized factoids, often modelled in accordance with Rhetorical Structure Theory) is transformed by a sentence planner (generator) component to a sequence of sentence plans modelled in a Sentence Plan Language. A surface generator can be used to transform the SPL notation into natural language sentences. Probably the most widely used SPL language used today (2022) is AMR (Abstract Meaning Representation, see there for further references), but is owes parts of its popularity to its application to NLP problems other than NLG, e.g., machine translation and semantic parsing.
Rifts (role-playing game)
Rifts is a multi-genre role-playing game created by Kevin Siembieda in August 1990 and published continuously by Palladium Books since then. It takes place in a post-apocalyptic future, deriving elements from cyberpunk, science fiction, fantasy, horror, western, mythology and many other genres. Rifts serves as a cross-over environment for a variety of other Palladium games with different universes connected through "rifts" on Earth that lead to different spaces, times, and realities that Palladium calls the "Rifts Megaverse". Rifts describes itself as an "advanced" role-playing game and not an introduction for those new to the concept. Palladium continues to publish books for the Rifts series, with about 80 books published between 1990 and 2011. Rifts Ultimate Edition was released in August 2005 and designed to update the game with Palladium's incremental changes to its system, changes in the game world, and additional information and character types. The web site is quick to point out that this is not a second edition but an improvement and expansion of the original role playing game. == Background == The RPG had the tentative title Boomers, named after the original name for the Glitter Boy power armor until Kevin Siembieda changed the name after finding out it was in use for Bubblegum Crisis. == Setting == The Rifts world is Earth, but hundreds of years into the future. Ley lines, lines of magic energy, criss-cross the earth forming supernatural geographic areas such as the Bermuda Triangle. Points where Ley Lines intersect, called a nexus, are places of powerful magic, such as the Pyramids of Giza and Stonehenge. If a Ley Line nexus energy surges or is purposely activated, the fabric of space and time can be torn, creating a rift - a hole in space-time leading to another place, time, or dimension. Ley lines contain magical energy called Potential Psychic Energy (PPE), which is found in various places, objects, and animals and is particularly strong in children. An adult's level of PPE can vary based on other factors. PPE also allows Psionics which uses energy known as Inner Strength Points or ISP. Psychic phenomenon (more commonly called psionics) can also vary from individuals, ranging from none at all to Master level abilities. Psychic abilities can manifest in virtually any way imaginable. Some psychics develop differently, such as psi-stalkers; human mutants that feed on psychic energy. === Earth === Rifts begins with two future-historical premises: first, a golden age of humanity occurs, with tremendous advances in science, technology, military, and society. Humanity as a whole is at peace as a majority of Earth's nations decide to cease world war and begin to share ideas and technology freely. Much of the Solar System is conquered, humanity's wars will end, and harmony will reign. This golden age is followed by an unknown cause near the winter solstice and a rare planetary alignment, causing a disaster that cascades into tremendous destruction via a ripple effect. The cataclysm begins with unprecedented storms, earthquakes, tsunamis, and volcanic eruptions, which kill millions of people. The Ley Line networks that crisscross the globe are energized, causing rifts to open both on Earth and throughout the Megaverse. For hundreds of years after the holocaust, many creatures, both mythical beasts and aliens, come through the Rifts to wreak havoc. The old world gone, a new Dark Age dawns and humanity's shrinking population is reduced, due to catastrophe and domestic failure, immeasurably. This period is covered in Palladium's Rifts Chaos Earth spin-off series. Rifts initially takes place in 101 P.A. (equivalent to the year 2387) 289 years after this event. The "Post-Apocalypse" calendar was established by the formation of the Coalition States in 2286. By this time, most of the disasters have quieted down, though Earth is still bathed in PPE. The planet's mystical energy has attracted aliens from other dimensions, who continue to arrive through the Rifts both accidentally and deliberately. The humanoid creatures that arrive on Earth are referred to as Dimensional Beings (called D-Bees). Some resemble familiar fantasy races, such as elves and dwarfs, while others were created specifically for the game setting. Non-humanoid creatures have also arrived, including monstrous creatures and mystical demons. To cope with these natural, supernatural, and alien menaces, the human race has adapted in a variety of ways, many of them borrowed from the technological developments of the lost Golden Age. Powered armor suits and giant vehicles are frequently used to combat the dangers of Rifts, but more invasive augmentation is common. This has three basic categories: "Juicers" augment themselves chemically, the "Borgs" augment themselves mechanically, and "Crazies" use performance-enhancing brain implants. All such augmentations boost strength, speed, endurance, and dexterity to superhuman levels. However, all come at great cost. Chemicals cause the body to wear out faster, decreasing life span to a few years. Mechanical Borg augmentation causes a loss of humanity when those with multiple limb and organ replacements become more machine than human. Brain implants cause mental instability ranging from mild phobias to crippling neurosis or psychosis. ==== North America ==== The strongest power in North America is the Coalition States (CS), which is based in the arcological city of Chi-Town and lays claim to northern Illinois, all of Iowa, the Texas Panhandle, Missouri, and the eastern half of Ontario, Canada. The second greatest power is Free Quebec, a former Coalition State that seceded following a civil war with the other Coalition States. Mexico is ruled by a group of vampire kingdoms, who treat humans as little more than food. North of the Rio Grande, west of Texas and roaming most of the American Southwest are large nomadic bands/tribes of bandits who collectively form the Pecos Empire, consisting of El Paso, Los Alamos, and Houstown. Much of the western United States has more or less willingly reverted to a mix of modern and past technology akin to the Wild West. The Royal Canadian Mounted Police managed to survive the great cataclysm, though Canada itself did not. The Mounties have become an independent law enforcement force called the Tundra Rangers, patrolling the northern wilderness. The Midwest, both upper and central, is home to most of North America's population. The Manistique Imperium and Northern Gun in Michigan's Upper Peninsula, both Coalition allies, are among the largest weapons manufacturing areas on the continent. New Lazlo is one of the largest cities in Michigan's southern portion. Chillicothe in Missouri is a large supplier of Coalition food processing and growing. Missouri's southern half, home to the city-states of Whykin (Poplar Bluff) and Kingsdale (West Plains) are in constant opposition to the CS and claim independence. Arkansas is home to the independent CS ally El Dorado. Southern Illinois and the Ohio Valley is home to the Federation of Magic. Also in the Ohio Valley is Psyscape, a city-state founded by psychics. Tolkeen was a major city in the former Minneapolis region in early Rifts books; the city welcomed users of magic. A military campaign made by the Coalition States (which is the primary event of 109 PA) resulted in the magic-user kingdom being wiped off the map. In the Northeast, the city-state of Lazlo, named after supernatural researcher and writer Victor Lazlo, was built upon the ruins of Toronto. This major center of civilization is well known as a melting pot of humans, D-Bees and other beings, and is the home of Techno-Wizardry. Mad Haven is the name given to the ruins of Manhattan; tectonic forces during the cataclysm have moved it into the coast, creating a peninsula. It is seen by most denizens of Rifts Earth as a refuge of demons and madness. ==== South America ==== The return of Atlantis caused the Amazon River basin to flood most of western South America, giving it the nickname The Land of a Thousand Islands. The Empire of the Sun, consisting of Cuzco, Nazca, Arequipa and Lima, created a wide range of technology and magic, including magic derived from the Nazca lines. In Argentina, the Silver River Republics of Cordoba (the South American Chi-Town), Santiago (one of the most tolerant human nations on Rifts Earth), Achilles (a nation founded by mutants), and New Babylon, a nation where humans and aliens coexist) have thrived and created nations whose strength rivals that of the CS. In Bolivia, freed Human and D-Bees formed the Megaversal Legion: a mercenary company with one of the highest levels of technology on Rifts Earth. ==== Europe ==== England has become a vast wilderness again, broken up by the occasional giant Millennium Tree or feudal kingdom, complete with a New Camelot and a new King Arthur, partially being manipulated by an alien intelligence disguised as Merlin. Also the magic of
ICAART
The International Conference on Agents and Artificial Intelligence (ICAART) is a meeting point for researchers (among others) with interest in the areas of Agents and Artificial Intelligence. There are 2 tracks in ICAART, one related to Agents and Distributed AI in general and the other one focused in topics related to Intelligent Systems and Computational Intelligence. The conference program is composed of several different kind of sessions like technical sessions, poster sessions, keynote lectures, tutorials, special sessions, doctoral consortiums, panels and industrial tracks. The papers presented in the conference are made available at the SCITEPRESS digital library, published in the conference proceedings and some of the best papers are invited to a post-publication with Springer. ICAART's first edition was in 2009 counting with several keynote speakers like Marco Dorigo, Edward H. Shortliffe and Eduard Hovy. Since then, the conference had several other invited speakers like Katia Sycara, Nick Jennings, Robert Kowalski, Boi Faltings and Tim Finin. Bart Selman is one of the names confirmed for the next edition of this conference. Since 2012 the conference is held in conjunction with 2 other conferences: the International Conference on Operations Research and Enterprise Systems (ICORES) and the International Conference on Pattern Recognition Applications and Methods (ICPRAM). == Areas == === Agents === Agent communication languages Cooperation and Coordination Distributed Problem Solving Economic Agent Models Emotional Intelligence Group Decision Making Intelligent Auctions and Markets Mobile Agents Multi-agent systems Negotiation and Interaction Protocols Nep News Detection Agent Models and Architectures Physical Agents at Work Privacy, Safety and Security Programming Environments and Languages Robot and Multi-Robot Systems Self Organizing Systems Semantic Web Simulation Swarm Intelligence Task Planning and Execution Transparency and Ethical Issues Agent-Oriented Software Engineering Web Intelligence Agent Platforms and Interoperability Autonomous systems Cloud Computing and Its Impact Cognitive robotics Collective Intelligence Conversational Agents === Artificial intelligence === AI and Creativity Deep Learning Evolutionary Computing Fuzzy Systems Hybrid Intelligent Systems Industrial Applications of AI Intelligence and Cybersecurity Intelligent User Interfaces Knowledge Representation and Reasoning Knowledge-Based Systems Ambient Intelligence Machine learning Model-Based Reasoning Natural Language Processing Neural Networks Ontologies Planning and Scheduling Social Network Analysis Soft Computing State Space Search Bayesian Networks Uncertainty in AI Vision and Perception Visualization Big Data Case-Based Reasoning Cognitive Systems Constraint Satisfaction Data Mining Data Science == Editions == === ICAART 2023 – Lisbon, Portugal === === ICAART 2020 – Valletta, Malta === === ICAART 2019 – Prague, Czech Republic === Proceedings - Proceedings of the 11th International Conference on Web Information Systems and Technologies - Volume 1. ISBN 978-989-758-350-6 Proceedings - Proceedings of the 11th International Conference on Web Information Systems and Technologies - Volume 2. ISBN 978-989-758-350-6 === ICAART 2018 – Funchal, Madeira, Portugal === Proceedings - Proceedings of the 10th International Conference on Web Information Systems and Technologies - Volume 1. ISBN 978-989-758-275-2 Proceedings - Proceedings of the 10th International Conference on Web Information Systems and Technologies - Volume 2. ISBN 978-989-758-275-2 === ICAART 2017 – Porto, Portugal === Proceedings - Proceedings of the 9th International Conference on Web Information Systems and Technologies - Volume 1. ISBN 978-989-758-219-6 Proceedings - Proceedings of the 9th International Conference on Web Information Systems and Technologies - Volume 2. ISBN 978-989-758-220-2 === ICAART 2016 – Rome, Italy === Proceedings - Proceedings of the 8th International Conference on Web Information Systems and Technologies - Volume 1. ISBN 978-989-758-172-4 Proceedings - Proceedings of the 8th International Conference on Web Information Systems and Technologies - Volume 2. ISBN 978-989-758-172-4 === ICAART 2015 – Lisbon, Portugal === Proceedings - Proceedings of the 7th International Conference on Web Information Systems and Technologies - Volume 1. ISBN 978-989-758-073-4 Proceedings - Proceedings of the 7th International Conference on Web Information Systems and Technologies - Volume 2. ISBN 978-989-758-074-1 === ICAART 2014 – ESEO, Angers, Loire Valley, France === Proceedings - Proceedings of the 6th International Conference on Web Information Systems and Technologies - Volume 1. ISBN 978-989-758-015-4 Proceedings - Proceedings of the 6th International Conference on Web Information Systems and Technologies - Volume 2. ISBN 978-989-758-016-1 === ICAART 2013 – Barcelona, Spain === Proceedings - Proceedings of the 5th International Conference on Web Information Systems and Technologies - Volume 1. ISBN 978-989-8565-38-9 Proceedings - Proceedings of the 5th International Conference on Web Information Systems and Technologies - Volume 2. ISBN 978-989-8565-39-6 === ICAART 2012 – Vilamoura, Algarve, Portugal === Proceedings - Proceedings of the 4th International Conference on Web Information Systems and Technologies - Volume 1. ISBN 978-989-8425-95-9 Proceedings - Proceedings of the 4th International Conference on Web Information Systems and Technologies - Volume 2. ISBN 978-989-8425-96-6 === ICAART 2011 – Rome, Italy === Proceedings - Proceedings of the 3rd International Conference on Web Information Systems and Technologies - Volume 1. ISBN 978-989-8425-40-9 Proceedings - Proceedings of the 3rd International Conference on Web Information Systems and Technologies - Volume 2. ISBN 978-989-8425-41-6 === ICAART 2010 – Valencia, Spain === Proceedings - Proceedings of the 2nd International Conference on Web Information Systems and Technologies - Volume 1. ISBN 978-989-674-021-4 Proceedings - Proceedings of the 2nd International Conference on Web Information Systems and Technologies - Volume 2. ISBN 978-989-674-022-1 === ICAART 2009 – Porto, Portugal === Proceedings - Proceedings of the 1st International Conference on Web Information Systems and Technologies. ISBN 978-989-8111-66-1
The Fractal Prince
The Fractal Prince is the second science fiction novel by Hannu Rajaniemi and the second novel to feature the post-human gentleman thief Jean le Flambeur. It was published in Britain by Gollancz in September 2012, and by Tor in the same year in the US. The novel is the second in the trilogy, following The Quantum Thief (2010) and preceding The Causal Angel (2014). == Plot summary == After the events of The Quantum Thief, Jean le Flambeur and Mieli are on their way to Earth. Jean is trying to open the Schrödinger's Box he retrieved from the memory palace on the Oubliette. After making little progress, he is prodded by the ship Perhonen to talk to Mieli, who turns out to be possessed by the pellegrini again. This time, Jean identifies Mieli's employer as a Sobornost Founder, Joséphine Pellegrini, and gets her to reveal how he got captured, thereby picking up the clues to make plans for his next heist. No sooner is that done than an attack comes from the Hunter. The ship and crew barely survived that, and Jean realizes that he has to find a better way to open the Box - fast. Mieli has been very quiet after they left Mars. She has given up almost everything to the pellegrini, even her identity, as she has promised to let the pellegrini make gogols of her in exchange for rescuing the thief. Yet, having to work with the thief is testing her, especially when the thief eventually does something even more unforgivable than stealing Sydän's jewel from her. In the city of Sirr, on an Earth ravaged by wildcode, Tawaddud and Dunyazad are sisters and members of the powerful Gomelez family. Tawaddud is the black sheep of the family, having run away from her husband and consorted with a notorious jinn, a disembodied intelligence from the wildcode desert. Now Cassar Gomelez, her father, hopes to get her to curry favor with a gogol merchant, Abu Nuwas, so that he has enough votes in the Council for the upcoming decision to renegotiate the Cry of Wrath Accords with the Sobornost. Soon, Tawaddud is embroiled in an investigation with a Sobornost envoy into the murder that triggered the need for her father to forge a new alliance in the first place, and forced to confront old secrets that will change Sirr forever. Somewhere else, in a bookshop and on a beach, a young boy is at play. His mother has told him not to talk to strangers, but there has never been anyone here before. Until now. Should he talk to them? == Influences == In the acknowledgments, Rajaniemi cites the influence of "Andy Clark, Douglas Hofstadter, Maurice Leblanc, Jan Potocki and [...] The Arabian Nights." === Self-loops === In the novel, the idea that the mind is a self-loop may have been influenced by the theories of the Professor of Philosophy, Andy Clark, and the book I Am a Strange Loop by Douglas Hofstadter. === Frame stories === The novel uses frame stories rather extensively, a feature also of The Arabian Nights and Jan Potocki's The Manuscript Found in Saragossa. Several characters in Sirr are the namesakes of characters in these two earlier works as well. The events in The Quantum Thief are also retold at least once by Jean le Flambeur in the course of the events in this novel. == Reception == The novel has received generally positive reviews. However, criticisms of the novel still revolve around Rajaniemi's uncompromising "show, don't tell" style. For example, Amy Goldschlager, writing for the Los Angeles Review of Books, suggested that "[a] bit more explication of the physics involved (“surfing the deficit angle”?) would really be helpful, more helpful than the description of the Schrödinger’s Cat problem given earlier in the book".
Class activation mapping
Class activation mapping methods are explainable AI (XAI) techniques used to visualize the regions of an input image that are the most relevant for a particular task, especially image classification, in convolutional neural networks (CNNs). These methods generate heatmaps by weighting the feature maps from a convolutional layer according to their relevance to the target class. In the field of artificial intelligence, generically defined as "the effort to automate intellectual tasks normally performed by humans", machine learning and deep learning were created. They both use statistical and computational methods to learn patterns from data, reducing the need for manually coded rules. Machine learning models are trained on input data and the known respective answers, learning the underlying patterns or structures present in the data. Traditional Machine learning algorithms employ manually designed feature sets, posing a direct link between machine learning designers and employed features. Deep learning is a subfield of machine learning, based on the concept of successive layers of representation, in which the data is progressively unfolded in different ways, to extract relevant and informative patterns in data analysis. Deep learning algorithms are defined as feature learning algorithms automatically learning hierarchical feature representations from raw data, extracting increasingly abstract features through multiple layers. CNNs are a specific architecture of deep learning models, designed to process spatially structured data, such as images, exploiting a series of convolution, non-linear activation and pooling operations to extract relevant features, contained in the so-called feature maps from input data. CNNs have demonstrated to be highly effective in a variety of computer vision and image processing tasks. CNNs (and deep learning models more broadly) are described as black boxes due to their complex and non-transparent internal layers of representation. The need for clearer indications on its internal working and decision-making process gave birth to XAI techniques. Among the proposed XAI techniques for computer vision tasks, Class activation mapping methods can show which pixels in an input image are important to the predicted logit for a class of interest, in a classification task. Class activation mapping methods were originally developed for class-discriminative scenarios to visualize which parts of the input image influenced the classification decision, namely to visually highlight the regions of those feature maps that contribute most strongly to the prediction of a given class. More advanced versions of these methods are not limited to image classification tasks, but have been extended also to several vision-related tasks, such as object detection, image captioning, visual question answering and image segmentation. == Background == The following methods laid the groundwork for the class activation maps approaches, forming the conceptual basis of using gradients to highlight class-discriminative regions. === Class model visualization and saliency maps for convolutional neural networks === The class model visualization and image-specific saliency maps approaches have been presented in the foundational work "Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps" by Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman and it generalizes the deconvnet method by Zeiler and Fergus. Class model visualization synthesizes an artificial input image that strongly activates the output neurons associated with a target class. Given a trained, fixed model, this method starts with a zero-initialized image, backpropagates the gradients from the class score to the image pixels, updates the image pixels increasing the specific class scores and it repeats the pixel updating process, showing an encoded (idealized version) prototype of the class of interest. Image-specific class saliency visualization method provides a visual explanation by highlighting the most relevant pixels in an image for predicting a certain class C of interest. This is done by computing the gradient of the class score with respect to the input image, I 0 , {\displaystyle I_{0},} w = ∂ S C ∂ I | I 0 {\displaystyle w=\left.{\frac {\partial S_{C}}{\partial I}}\right|_{I_{0}}} approximating the model locally (around I 0 {\displaystyle I_{0}} ) as linear, using a first-order Taylor expansion: S C ( I ) ≈ w C T I + b {\displaystyle S_{C}(I)\approx w_{C}^{T}I+b} . The magnitude of w C {\displaystyle w_{C}} , the gradient, indicates the importancy of the pixels: larger gradients suggest greater influence on the prediction. Once the gradient is known, the saliency map is defined as the maximum absolute gradient across the color channels: M i j = m a x C | ∂ S C ∂ I i j C | {\displaystyle M_{ij}=max_{C}\left|{\frac {\partial S_{C}}{\partial I_{ij}^{C}}}\right|} resulting in an saliency map (i.e. heatmap). === Guided backpropagation === The concept of guided backpropagation can be traced for the first time in the paper by Springenberg et al. "Striving For Simplicity: The All Convolutional Net" and also this method builds upon the work by Zeiler and Fergus "Visualizing and Understanding Convolutional Networks". Guided backpropagation core is to understand what a CNN is learning, by visualizing the patterns that activate more strongly individual neurons (or filters), in architectures which do not rely on max-pooling layer. When propagating gradients back through a rectified linear unit (ReLU), guided backpropagation passes the gradient if and only if the input to the ReLU was positive (forward pass) and the output gradient is positive (backward signal), tackling both inactive neurons, negative gradients and suppressing the noise. The result displays sharper, high-resolution visualizations of what each neuron is responding to. Guided backpropagation represents a simple and practical method for model interpretability, helping understand how and where neural networks detect semantic concepts across layers. Moreover, it can be applied to any network architecture, due to its working principle. == Base versions == Class activation mapping and gradient-weighted class activation mapping are the original and most widely used methods for visual explanations in convolutional neural networks. These methods serve as the foundation for many later developments in explainable AI. Notation: In this article, the symbols i and j represent integer indices that disappear inside sums or averages, while x and y are the continuous (or up-sampled integer) coordinates of the final heat-map that is plotted. === Class activation mapping (CAM) === Class activation mapping (CAM) was the first, and the original, version of CAM methods, and it gave the name to the whole category. The approach was firstly introduced by Zhou et al. in their seminal work "Learning Deep Features for Discriminative Localization". This approach achieves class-specific heatmaps by modifying image classification CNN architectures, replacing fully-connected layers with convolutional layers and a final global average pooling layer. Its main scope is to localize and highlight discriminative regions of an input image that a CNN uses to identify a particular class, without needing explicit bounding box annotations. ==== Global average pooling (GAP) ==== Global average pooling (GAP) represents the key element in the original CAM approach. It is a dimensionality reduction technique and, similarly to other pooling layers, it allows the downsampling of the feature maps, calculating representative values for a specific region of the feature map. The particularity of GAP is that it calculates a single value for an entire feature map, significantly reducing the model dimensions. ==== Mathematical description ==== The mathematical description considers as its key the combination of convolutional and GAP layers. In CAM, it is mandatory to have the GAP layer after the last convolutional layer and before the final linear classifier layer. This last element of the architecture connects the output logits (the network predictions) y C {\displaystyle y^{C}} , to the GAP values, with its respective fine-tuned weights, w k C {\displaystyle w_{k}^{C}} . Considering A k {\displaystyle A^{k}} as the last feature maps of the last convolutional layer, GAP produces one value for each feature map, by averaging all the matrix elements (i, j) of the feature map: F k = 1 m n ∑ i = 1 m ∑ j = 1 n A i j k {\displaystyle F^{k}={\frac {1}{mn}}\sum _{i=1}^{m}\sum _{j=1}^{n}A_{ij}^{k}} with A k = [ A 11 k A 12 k ⋯ A 1 n k A 21 k A 22 k ⋯ A 2 n k ⋮ ⋮ ⋱ ⋮ A m 1 k A m 2 k ⋯ A m n k ] = { A i j k ∣ 1 ≤ i ≤ m , 1 ≤ j ≤ n } {\displaystyle A^{k}={\begin{bmatrix}A_{11}^{k}&A_{12}^{k}&\cdots &A_{1n}^{k}\\A_{21}^{k}&A_{22}^{k}&\cdots &A_{2n}^{k}\\\vdots &\vdots &\ddots &\vdots \\A_{m1}^{k}&A_{m2}^{k}&\cdots &A_{mn}^{k}\end{bmatrix}}=\left\{A_{
Noise-based logic
Noise-based logic (NBL) is a class of multivalued deterministic logic schemes, developed in the twenty-first century, where the logic values and bits are represented by different realizations of a stochastic process. The concept of noise-based logic and its name was created by Laszlo B. Kish. In its foundation paper it is noted that the idea was inspired by the stochasticity of brain signals and by the unconventional noise-based communication schemes, such as the Kish cypher. == The noise-based logic space and hyperspace == The logic values are represented by multi-dimensional "vectors" (orthogonal functions) and their superposition, where the orthogonal basis vectors are independent noises. By the proper combination (products or set-theoretical products) of basis-noises, which are called noise-bit, a logic hyperspace can be constructed with D(N) = 2N number of dimensions, where N is the number of noise-bits. Thus N noise-bits in a single wire correspond to a system of 2N classical bits that can express 22N different logic values. Independent realizations of a stochastic process of zero mean have zero cross-correlation with each other and with other stochastic processes of zero mean. Thus the basis noise vectors are orthogonal not only to each other but they and all the noise-based logic states (superpositions) are orthogonal also to any background noises in the hardware. Therefore, the noise-based logic concept is robust against background noises, which is a property that can potentially offer a high energy-efficiency. == The types of signals used in noise-based logic == In the paper, where noise-based logic was first introduced, generic stochastic-processes with zero mean were proposed and a system of orthogonal sinusoidal signals were also proposed as a deterministic-signal version of the logic system. The mathematical analysis about statistical errors and signal energy was limited to the cases of Gaussian noises and superpositions as logic signals in the basic logic space and their products and superpositions of their products in the logic hyperspace (see also. In the subsequent brain logic scheme, the logic signals were (similarly to neural signals) unipolar spike sequences generated by a Poisson process, and set-theoretical unifications (superpositions) and intersections (products) of different spike sequences. Later, in the instantaneous noise-based logic schemes and computation works, random telegraph waves (periodic time, bipolar, with fixed absolute value of amplitude) were also utilized as one of the simplest stochastic processes available for NBL. With choosing unit amplitude and symmetric probabilities, the resulting random-telegraph wave has 0.5 probability to be in the +1 or in the −1 state which is held over the whole clock period. == The noise-based logic gates == Noise-based logic gates can be classified according to the method the input identifies the logic value at the input. The first gates analyzed the statistical correlations between the input signal and the reference noises. The advantage of these is the robustness against background noise. The disadvantage is the slow speed and higher hardware complexity. The instantaneous logic gates are fast, they have low complexity but they are not robust against background noises. With either neural spike type signals or with bipolar random-telegraph waves of unity absolute amplitude, and randomness only in the sign of the amplitude offer very simple instantaneous logic gates. Then linear or analog devices unnecessary and the scheme can operate in the digital domain. However, whenever instantaneous logic must be interfaced with classical logic schemes, the interface must use correlator-based logic gates for an error-free signal. == Universality of noise-based logic == All the noise-based logic schemes listed above have been proven universal. The papers typically produce the NOT and the AND gates to prove universality, because having both of them is a satisfactory condition for the universality of a Boolean logic. == Computation by noise-based logic == The string verification work over a slow communication channel shows a powerful computing application where the methods is inherently based on calculating the hash function. The scheme is based on random telegraph waves and it is mentioned in the paper that the authors intuitively conclude that the intelligence of the brain is using similar operations to make a reasonably good decision based on a limited amount of information. The superposition of the first D(N) = 2N integer numbers can be produced with only 2N operations, which the authors call "Achilles ankle operation" in the paper. == Computer chip realization of noise-based logic == Preliminary schemes have already been published to utilize noise-based logic in practical computers. However, it is obvious from these papers that this young field has yet a long way to go before it will be seen in everyday applications.