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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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Entropies and entropylike quantities play an increasing role in modern nonlinear data analysis. Fields that benefit from this application range from biosignal analysis to econophysics and engineering. This issue is a collection of papers touching on different aspects of entropy measures in data analysis, as well as theoretical and computational analyses. The relevant topics include the difficulty to achieve adequate application of entropy measures and the acceptable parameter choices for those entropy measures, entropybased coupling, and similarity analysis, along with the utilization of entropy measures as features in automatic learning and classification. Various real data applications are given.
experiment of design  empirical mode decomposition  signal analysis  similarity indices  synchronization analysis  auditory attention  entropy measure  linear discriminant analysis (LDA)  support vector machine (SVM)  auditory attention classifier  electroencephalography (EEG)  vague entropy  distance induced vague entropy  distance  complex fuzzy set  complex vague soft set  entropy, entropy visualization  entropy balance equation  Shannontype relations  multivariate analysis  machine learning evaluation  data transformation  sample entropy  treadmill walking  center of pressure displacement  dualtasking  analog circuit  fault diagnosis  cross wavelet transform  Tsallis entropy  parametric tdistributed stochastic neighbor embedding  support vector machine  information transfer  Chinese stock sectors  effective transfer entropy  market crash  system coupling  crossvisibility graphs  image entropy  geodesic distance  DempsterShafer evidence theory  uncertainty of basic probability assignment  belief entropy  plausibility transformation  weighted Hartley entropy  Shannon entropy  learning  information  novelty detection  nonprobabilistic entropy  learning systems  permutation entropy  embedded dimension  short time records  signal classification  relevance analysis  global optimization  metaheuristic  firefly algorithm  crossentropy method  coevolution  symbolic analysis  ordinal patterns  Permutation entropy  conditional entropy of ordinal patterns  KolmogorovSinai entropy  algorithmic complexity  information entropy  particle size distribution  selfsimilar measure  simulation  data analysis  entropy  entropy measures  automatic learning
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In order to measure and quantify the complex behavior of realworld systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and nonuniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineeringoriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and antisynchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed.
multitime scale fractional stochastic differential equations  fractional Brownian motion  fractional stochastic partial differential equation  analytical solution  nonautonomous (autonomous) dynamical system  topological entropy  (asymptotical) focal entropy point  disturbation  mdimensional manifold  geometric nonlinearity  Bernoulli–Euler beam  colored noise  noise induced transitions  true chaos  Lyapunov exponents  wavelets  Lyapunov exponents  Wolf method  Rosenstein method  Kantz method  neural network method  method of synchronization  Benettin method  Fourier spectrum  Gauss wavelets  fractional calculus  Adomian decomposition  Mittag–Leffler function  descriptor fractional linear systems  regular pencils  Schur factorization  hyperchaotic system  selfsynchronous stream cipher  permutation entropy  image encryption  wavelet transform  product MValgebra  partition  Tsallis entropy  conditional Tsallis entropy  dynamical system  discrete chaos  discrete fractional calculus  hidden attractors  approximate entropy  stabilization  Information transfer  continuous flow  discrete mapping  Lorenz system  Chua’s system  deterministic chaos  random number generator  unbounded chaos  bounded chaos  phaselocked loop  Gaussian white noise  n/a
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Image analysis is a fundamental task for extracting information from images acquired across a range of different devices. Since reliable quantitative results are requested, image analysis requires highly sophisticated numerical and analytical methods—particularly for applications in medicine, security, and remote sensing, where the results of the processing may consist of vitally important data. The contributions to this book provide a good overview of the most important demands and solutions concerning this research area. In particular, the reader will find image analysis applied for feature extraction, encryption and decryption of data, color segmentation, and in the support new technologies. In all the contributions, entropy plays a pivotal role.
image retrieval  multifeature fusion  entropy  relevance feedback  chaotic system  image encryption  permutationdiffusion  SHA256 hash value  dynamic index  entropy  keyframes  Shannon’s entropy  sign languages  video summarization  video skimming  image encryption  multipleimage encryption  twodimensional chaotic economic map  security analysis  image encryption  chaotic cryptography  cryptanalysis  chosenplaintext attack  image information entropy  blind image quality assessment (BIQA)  information entropy, natural scene statistics (NSS)  Weibull statistics  discrete cosine transform (DCT)  ultrasound  hepatic steatosis  Shannon entropy  fatty liver  metabolic syndrome  multiexposure image fusion  texture information entropy  adaptive selection  patch structure decomposition  image encryption  timedelay  random insertion  information entropy  chaotic map  uncertainty assessment  deep neural network  random forest  Shannon entropy  positron emission tomography  reconstruction  field of experts  additive manufacturing  3D prints  3D scanning  image entropy  depth maps  surface quality assessment  machine vision  image analysis  Arimoto entropy  freeform deformations  normalized divergence measure  gradient distributions  nonextensive entropy  nonrigid registration  pavement  macrotexture  3D digital imaging  entropy  decay trend  discrete entropy  infrared images  low contrast  multiscale tophat transform  image encryption  DNA encoding  chaotic cryptography  cryptanalysis  image privacy  computer aided diagnostics  colonoscopy  Rényi entropies  structural entropy  spatial filling factor  binary image  Cantor set  Hénon map  Minkowski island  primeindexed primes  Ramanujan primes  Kapur’s entropy  color image segmentation  whale optimization algorithm  differential evolution  hybrid algorithm  Otsu method  image encryption  dynamic filtering  DNA computing  3D Latin cube  permutation  diffusion  fuzzy entropy  electromagnetic field optimization  chaotic strategy  color image segmentation  multilevel thresholding  contrast enhancement  sigmoid  Tsallis statistics  qexponential  qsigmoid  qGaussian  ultrasound images  person reidentification  image analysis  hash layer  quantization loss  Hamming distance  crossentropy loss  image entropy  Shannon entropy  generalized entropies  image processing  image segmentation  medical imaging  remote sensing  security
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Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group.
strongly regular graph  automorphism group  orbit matrix  binary polyhedral group  icosahedron  dodecahedron  600cell  Electric multiple unit trains  highlevel maintenance planning  time window  0–1 programming model  particle swarm algorithm  fixed point  splitquaternion  quadratic polynomial  splitoctonion  neutrosophic set  neutrosophic rough set  pessimistic (optimistic) multigranulation neutrosophic approximation operators  complete lattice  rough set  matroid  operator  attribute reduction  graded rough sets  rough intuitionistic fuzzy sets  dominance relation  logical conjunction operation  logical disjunction operation  multigranulation  planar point set  convex polygon  disjoint holes  fuzzy logic  pseudoBCI algebra  quasimaximal element  KGunion  quasialternating BCKalgebra  quality function deployment  engineering characteristics  group decision making  2tuple  metro station  emergency routes  graph partitioning  graph clustering  invariant measures  partition comparison  finite automorphism groups  graph automorphisms  Fuzzy sets  ring  normed space  fuzzy normed ring  fuzzy normed ideal  fuzzy implication  quantum Balgebra  qfilter  quotient algebra  basic implication algebra  Detour–Harary index  maximum  unicyclic  bicyclic  cacti  threeway decisions  intuitionistic fuzzy sets  multigranulation rough intuitionistic fuzzy sets  granularity importance degree  complexity  Chebyshev polynomials  gear graph  pyramid graphs  edge detection  Laplacian operation  regularization  parameter selection  performance evaluation  aggregation operator  triangular norm  ?convex set  atombond connectivity index  geometric arithmetic index  line graph  generalized bridge molecular graph  graceful labeling  edge graceful labeling  edge even graceful labeling  polar grid graph  graph  good drawing  crossing number  join product  cyclic permutation  nonlinear  synchronized  linear discrete  chaotic system  algorithm  generalized permanental polynomial  coefficient  copermanental  isoperimetric number  random graph  intersection graph  social network  Abel–Grassmann’s groupoid (AGgroupoid)  Abel–Grassmann’s group (AGgroup)  involution AGgroup  commutative group  filter  graceful labeling  edge even graceful labeling  cylinder grid graph  selective maintenance  multistate system  human reliability  optimization  genetic algorithm  hypernearring  multitransformation  embedding  distance matrix (spectrum)  distance signlees Laplacian matrix (spectrum)  (generalized) distance matrix  spectral radius  transmission regular graph  graph  good drawing  crossing number  join product  cyclic permutation  cyclic associative groupoid (CAgroupoid)  cancellative  variant CAgroupoids  decomposition theorem  construction methods
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In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: selfexcited attractors and hidden attractors. The localization of selfexcited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with nonhyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phaselocked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with selfexcited attractors and hidden attractors.
new chaotic system  multiple attractors  electronic circuit realization  SBox algorithm  chaotic systems  circuit design  parameter estimation  optimization methods  Gaussian mixture model  chaotic system  empirical mode decomposition  permutation entropy  image encryption  hidden attractors  fixed point  stability  nonlinear transport equation  stochastic (strong) entropy solution  uniqueness  existence  multiscale multivariate entropy  multistability  selfreproducing system  chaos  hidden attractor  selfexcited attractor  fractional order  spectral entropy  coexistence  multistability  chaotic flow  hidden attractor  multistable  entropy  core entropy  Thurston’s algorithm  Hubbard tree  external rays  chaos  Lyapunov exponents  multiplevalued  static memory  strange attractors  fractional discrete chaos  entropy  projective synchronization  full state hybrid projective synchronization  generalized synchronization  inverse full state hybrid projective synchronization  inverse generalized synchronization  multichannel supply chain  service game  chaos  entropy  BOPS  Hopf bifurcation  selfexcited attractors  multistability  sample entropy  PRNG  Nonequilibrium fourdimensional chaotic system  entropy measure  adaptive approximatorbased control  neural network  uncertain dynamics  synchronization  fractionalorder  complexvariable chaotic system  unknown complex parameters  chaotic map  fixed point  chaos  approximate entropy  implementation  hidden attractor  hyperchaotic system  multistability  entropy analysis  hidden attractor  complex systems  fractionalorder  entropy  chaotic maps  chaos  spatial dynamics  Bogdanov Map  chaos  laser  resonator
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This Special Issue with 35 published articles shows the significance of the topic “Signal Processing and Analysis of Electrical Circuit”. This topic has been gaining increasing attention in recent times. The presented articles can be categorized into four different areas: signal processing and analysis methods of electrical circuits; electrical measurement technology; applications of signal processing of electrical equipment; fault diagnosis of electrical circuits. It is a fact that the development of electrical systems, signal processing methods, and circuits has been accelerating. Electronics applications related to electrical circuits and signal processing methods have gained noticeable attention in recent times. The methods of signal processing and electrical circuits are widely used by engineers and scientists all over the world. The constituent papers represent a significant contribution to electronics and present applications that can be used in industry. Further improvements to the presented approaches are required for realizing their full potential.
VMD  signal analysis  ICEEMD  IMF  random noise  attenuation  commutator motor  fault diagnosis  method  technique  signal processing  acoustic  Inner and outer product  tensor  FPGA  hardware  direct digital synthesizer (DDS)  frequency tuning word (FTW)  stability  accuracy  demodulation  phaselocked loop  Chebyshev filter  measurement noise suppression  class AB operation  CMOS  current mirror  current buffer  quasi floating gate  low power  CMOS  dynamic comparator  offset calibration  high speed  low noise  low power  ADC  allpass filter  CMOS  time delay  broadband  truetimedelay  electrochemical impedance spectroscopy  FRA  multichannel acquisition  impedance spectrometry  microcontroller  intelligent vehicles  LiDAR odometry  range sensing  simultaneous localization and mapping (SLAM)  tilt sensor  sensor data fusion  complementary filters  overlapadd processing  spectral analysis  variational mode decomposition (VMD)  duffing chaotic oscillator (DCO)  permutation entropy (PE)  feature extraction  frequency characteristic  underwater acoustic signal  shipradiated noise  PM/PWM  capacitancetotime conversion  differential capacitive sensor  brickwall filter  fuzzy logic  induction motor  Shannon entropy  shortcircuit fault  APF  CNFET  polefrequency  chirality  phase angle  tuning  DC–DC converter  switched capacitor  power management integrated circuit  CMOS technology  frequency standard comparator  dual Mixing Time difference  phase difference  correlation function  chebyshev polynomial  compressed sensing  estimated sparsity  least squares solution  stochastic gradient  reconstruction probability  direct position determination  array signal processing  Doppler shifts  matrix eigenperturbation theory  system errors  Cramér–Rao bound  differential power analysis (DPA), SIMON  fault injection  double rate  power randomization  intention of movement classification  EMGSignals  Support Vector Machines  asynchronous  delay cell  passive resistor  SAR ADC  loop delay circuit  ResistancetoPeriod converter  robust readout circuits  ratiometric technique  Fresnel lens  wingbeat  insects  optoelectronics  bees  wasps  fruit flies  etraps  analogtodigital converter  successive approximation register  direct sampling  timeinterleaved  channelselectionembedded bootstrap  segmented prequantization and bypass  LVDS  highspeed serial interface  transmitter  receiver  lowpower  image fusion  multisensor fusion  night vision  hierarchical heterogeneous multiDAG workflow  multigroup scan  ultrasonic phased array  heterogeneous earliest finish time  resolver  discrete wavelet transform  singular value decomposition  automatic calibration  noise reduction  ripple voltage measurement  DAC  comparator  peakripple estimation  binary search  lowcost  secret image sharing  digital image  noutofn scheme  color palette  colluder attack  image restoration  impulse noise  ADMM  HOCTVL1  spatially adapted regularization parameter  rod electrode  electrostatic induction  method of images  induced charge  induced current  3DIC design  NILT  TSV noise coupling  RDL  chain matrix  interconnect line  n/a
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