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A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations
Artificial neural networks (ANNs) have very successfully been used in numerical simulations for a series of computational problems
ranging from image classification/image recognition, speech recognition, time series analysis, game intelligence, and computational
advertising to numerical approximations of partial differential equations (PDEs). Such numerical simulations suggest that ANNs have the
capacity to very efficiently approximate high-dimensional functions and, especially, indicate that ANNs seem to admit the fundamental
power to overcome the curse of dimensionality when approximating the high-dimensional functions appearing in the above named
computational problems. There are a series of rigorous mathematical approximation results for ANNs in the scientific literature. Some of
them prove convergence without convergence rates and some of these mathematical results even rigorously establish convergence rates but
there are only a few special cases where mathematical results can rigorously explain the empirical success of ANNs when approximating
high-dimensional functions. The key contribution of this article is to disclose that ANNs can efficiently approximate high-dimensional
functions in the case of numerical approximations of Black-Scholes PDEs. More precisely, this work reveals that the number of required
parameters of an ANN to approximate the solution of the Black-Scholes PDE grows at most polynomially in both the reciprocal of the
prescribed approximation accuracy
eBook
The Future of Artificial Neural Networks
This book is a compilation of eleven quality articles exploring a variety of aspects on applications of ANN. Various authors of the articles from India and abroad have presented their work around the applications of ANN in healthcare and self-medication behaviour, Stock Market Analytics, ANN integrated application for industries including regulatory complaining aspect in Banking Industry, Deep Learning Framework in Medical Diagnosis, Face Recognition, Mobile Learning in Medical Education, Process and Applications of ANN using MATLAB, etc.
eBook
Applications of nature-inspired computing in renewable energy systems
\"This book discusses the latest research on nature-inspired computing approaches applied to the design and development of renewable energy systems and provides new solutions to the renewable energy domain such as microgrids, wind power, and artificial neural networks\"-- Provided by publisher.
Book
Swarm intelligence and bio-inspired computation : theory and applications
Swarm Intelligence and bio-inspired computation have become increasing popular in the last two decades.Bio-inspired algorithms such as ant colony algorithms, bat algorithms, bee algorithms, firefly algorithms, cuckoo search and particle swarm optimization have been applied in almost every area of science and engineering with a dramatic increase.
eBook
Neural network world : international journal on neural and mass-parallel computing and information systems
Mezinárodní časopis o problematice neuronových a paralelních výpočetních a informačních systémů
Journal
Informatic Capabilities of Translation and Its Implications for the Origins of Life
The ability to encode and convert heritable information into molecular function is a defining feature of life as we know it. The conversion of information into molecular function is performed by the translation process, in which triplets of nucleotides in a nucleic acid polymer (mRNA) encode specific amino acids in a protein polymer that folds into a three-dimensional structure. The folded protein then performs one or more molecular activities, often as one part of a complex and coordinated physiological network. Prebiotic systems, lacking the ability to explicitly translate information between genotype and phenotype, would have depended upon either chemosynthetic pathways to generate its components—constraining its complexity and evolvability— or on the ambivalence of RNA as both carrier of information and of catalytic functions—a possibility which is still supported by a very limited set of catalytic RNAs. Thus, the emergence of translation during early evolutionary history may have allowed life to unmoor from the setting of its origin. The origin of translation machinery also represents an entirely novel and distinct threshold of behavior for which there is no abiotic counterpart—it could be the only known example of computing that emerged naturally at the chemical level. Here we describe translation machinery’s decoding system as the basis of cellular translation’s information-processing capabilities, and the four operation types that find parallels in computer systems engineering that this biological machinery exhibits.
Journal Article
Artificial Intelligence for Developers in Easy Steps
Artificial Intelligence for Developers in easy steps is for coders who want to enhance their skillset quickly and easily. Artificial Intelligence (AI) is here to stay, and this guide reveals how AI works and illustrates how to build AI applications. It even covers no-code AI tools. This primer comes with free downloadable source code to get you started straightaway. Topics covered include:Creating a chatbot.Building an expert system. Understanding the flatworld, fuzzy logic, and subsumption architecture. Genetic algorithms, neural networks, generative AI, and low code. Aimed at aspiring developers and students who are familiar with Python and now want to master AI concepts and build intelligent AI solutions. AI programming is mainstream now. Update your coding skills and stay on top!
eBook
Between Fiction, Reality, and Ideality: Virtual Objects as Computationally Grounded Intentional Objects
Virtual objects, such as online shops, the elements that go to make up virtual life in computer games, virtual maps, e-books, avatars, cryptocurrencies, chatbots, holograms, etc., are a phenomenon we now encounter at every turn: they have become a part of our life and our world. Philosophers—and ontologists in particular—have sought to answer the question of what, exactly, they are. They fall into two camps: some, pointing to the chimerical character of virtuality, hold that virtual objects are like dreams, illusions and fictions, while others, citing the real impact of virtuality on our world, take them to be real—an actual part of the real world, just like other real objects. In this article, we defend the thesis that both sides are wrong. Using Roman Ingarden’s phenomenological ontology, we advocate a position according to which a virtual object is a computationally grounded intentional object that has its existential foundation in computational processes, which are compliant with a certain model of computation. We point out that virtuality is framed by some kind of ideal mathematical objects: i.e., mathematical models of computation, which in turn fall, each of them, under their respective ideas. We also refer to the idea of natural computation, which in conjunction with the ontological analysis carried out leads to the thesis that an object can be more or less virtual.
Journal Article