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This book addresses the physical phenomenon of events that seem to occur spontaneously and without any known cause. These are to be contrasted with events that happen in a (pre)determined, predictable, lawful, and causal way.All our knowledge is based on selfreflexive theorizing, as well as on operational means of empirical perception. Some of the questions that arise are the following: are these limitations reflected by our models? Under what circumstances does chance kick in? Is chance in physics merely epistemic? In other words, do we simply not know enough, or use too crude levels of description for our predictions? Or are certain events "truly", that is, irreducibly, random? The book tries to answer some of these questions by introducing intrinsic, embedded observers and provable unknowns; that is, observables and procedures which are certified (relative to the assumptions) to be unknowable or undoable. A (somewhat iconoclastic) review of quantum mechanics is presented which is inspired by quantum logic. Postulated quantum (un)knowables are reviewed. More exotic unknowns originate in the assumption of classical continua, and in finite automata and generalized urn models, which mimic complementarity and yet maintain value definiteness. Traditional conceptions of free will, miracles and dualistic interfaces are based on gaps in an otherwise deterministic universe.
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The last few years have been characterized by a tremendous development of quantum information and probability and their applications, including quantum computing, quantum cryptography, and quantum random generators. In spite of the successful development of quantum technology, its foundational basis is still not concrete and contains a few sandy and shaky slices. Quantum random generators are one of the most promising outputs of the recent quantum information revolution. Therefore, it is very important to reconsider the foundational basis of this project, starting with the notion of irreducible quantum randomness. Quantum probabilities present a powerful tool to model uncertainty. Interpretations of quantum probability and foundational meaning of its basic tools, starting with the Born rule, are among the topics which will be covered by this issue. Recently, quantum probability has started to play an important role in a few areas of research outside quantum physics—in particular, quantum probabilistic treatment of problems of theory of decision making under uncertainty. Such studies are also among the topics of this issue.
quantum logic  groups  partially defined algebras  quasigroups  viable cultures  quantum information theory  bit commitment  protocol  entropy  entanglement  orthogonality  quantum computation  Gram–Schmidt process  quantum probability  potentiality  complementarity  uncertainty relations  Copenhagen interpretation  indefiniteness  indeterminism  causation  randomness  quantum information  quantum dynamics  entanglement  algebra  causality  geometry  probability  quantum information theory  realism  reality  entropy  correlations  qubits  probability representation  Bayes’ formula  quantum entanglement  threequbit random states  entanglement classes  entanglement polytope  anisotropic invariants  quantum random number  vacuum state  maximization of quantum conditional minentropy  quantum logics  quantum probability  holistic semantics  epistemic operations  Bell inequalities  algorithmic complexity  Borel normality  Bayesian inference  model selection  random numbers  quantumlike models  operational approach  information interpretation of quantum theory  social laser  social energy  quantum information field  social atom  Bose–Einstein statistics  bandwagon effect  social thermodynamics  resonator of social laser  master equation for socioinformation excitations  quantum contextuality  Kochen–Specker sets  MMP hypergraphs  Greechie diagrams  quantum foundations  probability  irreducible randomness  random number generators  quantum technology  entanglement  quantumlike models for social stochasticity  contextuality
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This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of realworld phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems.
anomalous diffusion  complexity  magnetic resonance imaging  fractional calculus  fractional complex networks  adaptive control  pinning synchronization  timevarying delays  impulses  reaction–diffusion terms  fractional calculus  mass absorption  diffusionwave equation  Caputo derivative  harmonic impact  Laplace transform  Fourier transform  MittagLeffler function  fractional calculus  fractionalorder system  long memory  time series  Hurst exponent  fractional  control  PID  parameter  meaning  audio signal processing  linear prediction  fractional derivative  musical signal  optimal randomness  swarmbased search  cuckoo search  heavytailed distribution  global optimization
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Cryptography lies at the heart of most technologies deployed today for secure communications. At the same time, mathematics lies at the heart of cryptography, as cryptographic constructions are based on algebraic scenarios ruled by group or number theoretical laws. Understanding the involved algebraic structures is, thus, essential to design robust cryptographic schemes. This Special Issue is concerned with the interplay between group theory, symmetry and cryptography. The book highlights four exciting areas of research in which these fields intertwine: postquantum cryptography, coding theory, computational group theory and symmetric cryptography. The articles presented demonstrate the relevance of rigorously analyzing the computational hardness of the mathematical problems used as a base for cryptographic constructions. For instance, decoding problems related to algebraic codes and rewriting problems in nonabelian groups are explored with cryptographic applications in mind. New results on the algebraic properties or symmetric cryptographic tools are also presented, moving ahead in the understanding of their security properties. In addition, postquantum constructions for digital signatures and key exchange are explored in this Special Issue, exemplifying how (and how not) group theory may be used for developing robust cryptographic tools to withstand quantum attacks.
cryptography  noncommutative cryptography  oneway functions  NPCompleteness  key agreement protocol  group theory  symmetry  Engel words  alternating group  WalnutDSA  digital signatures  postquantum cryptography  cryptanalysis  braid groups  algorithms in groups  groupbased cryptography  Reed–Solomon codes  key equation  Berlekamp–Massey algorithm  Sugiyama et al. algorithm  euclidean algorithm  numerical semigroup  Weierstrass semigroup  semigroup ideal  errorcorrecting code  algebraicgeometry code  lightweight cryptography  permutation group  block cipher  generalized selfshrinking generator  tmodified selfshrinking generator  pseudorandom number generator  statistical randomness tests  cryptography  pseudorandom permutation  block cipher  ideal cipher model  beyond birthday bound  provable security  group key establishment  group theory  provable security  protocol compiler
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Entropy theory has wide applications to a range of problems in the fields of environmental and water engineering, including river hydraulic geometry, fluvial hydraulics, water monitoring network design, river flow forecasting, floods and droughts, river network analysis, infiltration, soil moisture, sediment transport, surface water and groundwater quality modeling, ecosystems modeling, water distribution networks, environmental and water resources management, and parameter estimation. Such applications have used several different entropy formulations, such as Shannon, Tsallis, Reacutenyi Burg, Kolmogorov, Kapur, configurational, and relative entropies, which can be derived in time, space, or frequency domains. More recently, entropybased concepts have been coupled with other theories, including copula and wavelets, to study various issues associated with environmental and water resources systems. Recent studies indicate the enormous scope and potential of entropy theory in advancing research in the fields of environmental and water engineering, including establishing and explaining physical connections between theory and reality. The objective of this Special Issue is to provide a platform for compiling important recent and current research on the applications of entropy theory in environmental and water engineering. The contributions to this Special Issue have addressed many aspects associated with entropy theory applications and have shown the enormous scope and potential of entropy theory in advancing research in the fields of environmental and water engineering.
complexity  streamflow  water level  composite multiscale sample entropy  trend  Poyang Lake basin  fourparameter exponential gamma distribution  principle of maximum entropy  precipitation frequency analysis  methods of moments  maximum likelihood estimation  flood frequency analysis  generalized gamma (GG) distribution  principle of maximum entropy (POME)  entropy theory  principle of maximum entropy (POME)  GB2 distribution  flood frequency analysis  nonpoint source pollution  ANN  entropy weighting method  datascarce  multievents  spatiotemporal variability  soil water content  entropy  arid region  joint entropy  NDVI  temperature  precipitation  groundwater depth  Hei River basin  turbulent flow  canopy flow  randomness  coherent structures  Shannon entropy  Kolmogorov complexity  entropy  information transfer  optimization  radar  rainfall network  water resource carrying capacity  forewarning model  entropy of information  fuzzy analytic hierarchy process  projection pursuit  accelerating genetic algorithm  entropy production  conditional entropy production  stochastic processes  scaling  climacogram  turbulence  water resources vulnerability  connection entropy  changing environment  set pair analysis  Anhui Province  crossentropy minimization  land suitability evaluation  spatial optimization  monthly streamflow forecasting  Burg entropy  configurational entropy  entropy spectral analysis time series analysis  entropy  water monitoring  network design  hydrometric network  information theory  entropy applications  hydrological risk analysis  maximum entropycopula method  uncertainty  Loess Plateau  entropy  water engineering  Tsallis entropy  principle of maximum entropy  Lagrangian function  probability distribution function  flux concentration relation  uncertainty  information  informational entropy  variation of information  continuous probability distribution functions  confidence intervals  precipitation  variability  marginal entropy  crop yield  Hexi corridor  flow duration curve  Shannon entropy  entropy parameter  modeling  spatial and dynamics characteristic  hydrology  tropical rainfall  statistical scaling  Tsallis entropy  multiplicative cascades  BetaLognormal model  rainfall forecast  cross entropy  ant colony fuzzy clustering  combined forecast  information entropy  mutual information  kernel density estimation  ENSO  nonlinear relation  scaling laws  power laws  water distribution networks  robustness  flow entropy  entropy theory  frequency analysis  hydrometeorological extremes  Bayesian technique  rainfall  entropy ensemble filter  ensemble model simulation criterion  EEF method  bootstrap aggregating  bagging  bootstrap neural networks  El Niño  ENSO  neural network forecast  sea surface temperature  tropical Pacific  entropy  cross elasticity  mean annual runoff  water resources  resilience  quaternary catchment  complement  substitute  entropy theory  complex systems  hydraulics  hydrology  water engineering  environmental engineering
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