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Chillies is a novel approach for variable model transformations closing the gap between abstract architecture models, used for performance prediction, and required lowlevel details. We enable variability of transformations using chain of generators based on the HigherOrder Transformation (HOT). HOTs target different goals, such as template instantiation or transformation composition. In addition, we discuss statedependent behavior in prediction models and quality of model transformations.
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Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a nontrivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.
point projection  intersection  parametric curve  ndimensional Euclidean space  Newton’s second order method  fixed point theorem  nonlinear equations  multiple zeros  optimal iterative methods  higher order of convergence  nonlinear operator equation  Fréchet derivative  ?continuity condition  Newtonlike method  Frédholm integral equation  nonlinear equations  Padé approximation  iterative method  order of convergence  numerical experiment  fourth order iterative methods  local convergence  banach space  radius of convergence  nonlinear equation  iterative process  nondifferentiable operator  Lipschitz condition  high order  sixteenth order convergence method  local convergence  dynamics  Banach space  Newton’s method  semilocal convergence  Kantorovich hypothesis  iterative methods  Steffensen’s method  Rorder  with memory  computational efficiency  nonlinear equation  basins of attraction  optimal order  higher order method  computational order of convergence  nonlinear equations  multiple roots  Chebyshev–Halleytype  optimal iterative methods  efficiency index  Banach space  semilocal convergence  ?continuity condition  Jarratt method  error bound  Fredholm integral equation  Newton’s method  global convergence  variational inequality problem  split variational inclusion problem  multivalued quasinonexpasive mappings  Hilbert space  sixteenthorder optimal convergence  multipleroot finder  asymptotic error constant  weight function  purely imaginary extraneous fixed point  attractor basin  drazin inverse  generalized inverse  iterative methods  higher order  efficiency index  integral equation  efficiency index  nonlinear models  iterative methods  higher order  nonlinear equations  optimal iterative methods  multiple roots  efficiency index  iterative methods  nonlinear equations  Newtontype methods  smooth and nonsmooth operators  heston model  Hull–White  option pricing  PDE  finite difference (FD)  iteration scheme  Moore–Penrose  rectangular matrices  rate of convergence  efficiency index  nonlinear equations  conjugate gradient method  projection method  convex constraints  signal and image processing  nonlinear monotone equations  conjugate gradient method  projection method  signal processing  nonlinear systems  multipoint iterative methods  divided difference operator  order of convergence  Newton’s method  computational efficiency index  system of nonlinear equations  Newton method  NewtonHSS method  nonlinear HSSlike method  PicardHSS method  convexity  least square problem  accretive operators  signal processing  point projection  intersection  planar algebraic curve  Newton’s iterative method  the improved curvature circle algorithm  systems of nonlinear equations  King’s family  order of convergence  multipoint iterative methods  nonlinear equations  Potra–Pták method  optimal methods  weight function  basin of attraction  engineering applications  Kung–Traub conjecture  multipoint iterations  nonlinear equation  optimal order  basins of attraction
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As the ultimate information processing device, the brain naturally lends itself to being studied with information theory. The application of information theory to neuroscience has spurred the development of principled theories of brain function, and has led to advances in the study of consciousness, as well as to the development of analytical techniques to crack the neural code—that is, to unveil the language used by neurons to encode and process information. In particular, advances in experimental techniques enabling the precise recording and manipulation of neural activity on a large scale now enable for the first time the precise formulation and the quantitative testing of hypotheses about how the brain encodes and transmits the information used for specific functions across areas. This Special Issue presents twelve original contributions on novel approaches in neuroscience using information theory, and on the development of new information theoretic results inspired by problems in neuroscience.
neural network  Potts model  latching  recursion  functional connectome  graph theoretical analysis  eigenvector centrality  orderness  network eigenentropy  information entropy production  discrete Markov chains  spike train statistics  Gibbs measures  maximum entropy principle  pulsegating  channel capacity  neural coding  feedforward networks  neural information propagation  information theory  mutual information decomposition  synergy  redundancy  integrated information theory  integrated information  minimum information partition  submodularity  Queyranne’s algorithm  consciousness  maximum entropy  higherorder correlations  neural population coding  Ising model  brain network  complex networks  connectome  information theory  graph theory  freeenergy principle  internal model hypothesis  unconscious inference  infomax principle  independent component analysis  principal component analysis  goodness  categorical perception  perceptual magnet  information theory  perceived similarity  mutual information  synergy  redundancy  neural code  hippocampus  entorhinal cortex  navigation  neural code  representation  decoding  spiketime precision  discrimination  noise correlations  information theory  mismatched decoding  information theory  neuroscience
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For the 250th birthday of Joseph Fourier, born in 1768 in Auxerre, France, this MDPI Special Issue will explore modern topics related to Fourier Analysis and Heat Equation. Modern developments of Fourier analysis during the 20th century have explored generalizations of Fourier and Fourier–Plancherel formula for noncommutative harmonic analysis, applied to locallycompact, nonAbelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups. One should add the developments, over the last 30 years, of the applications of harmonic analysis to the description of the fascinating world of aperiodic structures in condensed matter physics. The notions of model sets, introduced by Y. Meyer, and of almost periodic functions, have revealed themselves to be extremely fruitful in this domain of natural sciences. The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, subRiemannian manifolds, and Lie groups. In parallel, in geometric mechanics, JeanMarie Souriau interpreted the temperature vector of Planck as a spacetime vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties. One last comment concerns the fundamental contributions of Fourier analysis to quantum physics: Quantum mechanics and quantum field theory. The content of this Special Issue will highlight papers exploring noncommutative Fourier harmonic analysis, spectral properties of aperiodic order, the hypoelliptic heat equation, and the relativistic heat equation in the context of Information Theory and Geometric Science of Information.
WeylHeisenberg group  affine group  Weyl quantization  Wigner function  covariant integral quantization  Fourier analysis  special functions  rigged Hilbert spaces  quantum mechanics  signal processing  nonFourier heat conduction  thermal expansion  heat pulse experiments  pseudotemperature  GuyerKrumhansl equation  higher order thermodynamics  Lie groups thermodynamics  homogeneous manifold  polysymplectic manifold  dynamical systems  nonequivariant cohomology  Lie group machine learning  SouriauFisher metric  Born–Jordan quantization  shorttime propagators  timeslicing  Van Vleck determinant  thermodynamics  symplectization  metrics  nonequilibrium processes  interconnection  discrete multivariate sine transforms  orthogonal polynomials  cubature formulas  nonequilibrium thermodynamics  variational formulation  nonholonomic constraints  irreversible processes  discrete thermodynamic systems  continuum thermodynamic systems  fourier transform  rigid body motions  partial differential equations  Lévy processes  Lie Groups  homogeneous spaces  stochastic differential equations  harmonic analysis on abstract space  heat equation on manifolds and Lie Groups
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There are many different theories of intelligence. Although these theories differ in their nuances, nearly all agree that there are multiple cognitive abilities and that they differ in the breadth of content they are typically associated with. There is much less agreement about the relative importance of cognitive abilities of differing generality for predicting important realworld outcomes, such as educational achievement, career success, job performance, and health. Some investigators believe that narrower abilities hold little predictive power once general abilities have been accounted for. Other investigators contend that specific abilities are often as—or even more—effective in forecasting many practical variables as general abilities. These disagreements often turn on differences of theory and methodology that are both subtle and complex. The five cuttingedge contributions in this volume, both empirical and theoretical, advance the conversation in this vigorous, and highly important, scientific debate.
general cognitive ability  specific cognitive abilities  academic achievement  job performance  occupational attainment  health  longevity  situational specificity  bifactor model  cognitive abilities  educational attainment  general mental ability  hierarchical factor model  higherorder factor model  intelligence  job performance  nestedfactors model  relative importance analysis  specific abilities  specific ability  second stratum abilities  academic performance  nestedfactor models  relative importance analysis  predictorcriterion bandwidth alignment  gfactor  specific abilities  scholastic performance  school grades  machine learning  curvilinear relations  ability differentiation  bifactor model  identification  bifactor(S1) model  general factor  specific factors  general intelligence (g)  nong factors  specific abilities  ability tilt  nong residuals  cognitive abilities  specific abilities  general abilities  general mental ability  relative importance  narrow abilities  subscores  intelligence  cognitive tests
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Optical microelectromechanical systems (MEMS), microoptoelectromechanical systems (MOEMS), or optical microsystems are devices or systems that interact with light through actuation or sensing at a micro or millimeter scale. Optical MEMS have had enormous commercial success in projectors, displays, and fiberoptic communications. The bestknown example is Texas Instruments’ digital micromirror devices (DMDs). The development of optical MEMS was impeded seriously by the Telecom Bubble in 2000. Fortunately, DMDs grew their market size even in that economy downturn. Meanwhile, in the last one and half decade, the optical MEMS market has been slowly but steadily recovering. During this time, the major technological change was the shift of thinfilm polysilicon microstructures to singlecrystal–silicon microsructures. Especially in the last few years, cloud data centers are demanding largeport optical cross connects (OXCs) and autonomous driving looks for miniature LiDAR, and virtual reality/augmented reality (VR/AR) demands tiny optical scanners. This is a new wave of opportunities for optical MEMS. Furthermore, several research institutes around the world have been developing MOEMS devices for extreme applications (very fine tailoring of light beam in terms of phase, intensity, or wavelength) and/or extreme environments (vacuum, cryogenic temperatures) for many years. Accordingly, this Special Issue seeks to showcase research papers, short communications, and review articles that focus on (1) novel design, fabrication, control, and modeling of optical MEMS devices based on all kinds of actuation/sensing mechanisms; and (2) new developments of applying optical MEMS devices of any kind in consumer electronics, optical communications, industry, biology, medicine, agriculture, physics, astronomy, space, or defense.
scanning micromirror  electromagnetic actuator  angle sensor  flame retardant 4 (FR4)  variable optical attenuator (VOA)  wavelength dependent loss (WDL)  polarization dependent loss (PDL)  microelectromechanical systems (MEMS)  tunable fiber laser  echelle grating  DMD chip  MEMS scanning micromirror  fringe projection  laser stripe scanning  quality map  large reflection variations  3D measurement  laser stripe width  vibration noise  MLSSP  MEMS scanning mirror  wavefront sensing  digital micromirror device  ocular aberrations  dualmode liquidcrystal (LC) device  infrared Fabry–Perot (FP) filtering  LC microlenses controlled electrically  spectrometer  infrared  digital micromirror device (DMD)  signaltonoise ratio (SNR)  stray light  programmable spectral filter  digital micromirror device  optical switch  microscanner  input shaping  openloop control  quasistatic actuation  residual oscillation  usable scan range  higherorder modes  resonant MEMS scanner  electrostatic  parametric resonance  NIR fluorescence  intraoperative microscope  2D Lissajous  fluorescence confocal  metasurface  metalens  field of view (FOV)  achromatic  Huygens’ metalens  biooptical imaging  optical coherence tomography  confocal  twophoton  spectrometer  MEMS mirror  electrothermal bimorph  Cu/W bimorph  electrothermal actuation  reliability  n/a
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Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences.
highly oscillatory  convolution quadrature rule  volterra integral equation  Bessel kernel  convergence  higher order Schwarzian derivatives  Janowski starlike function  Janowski convex function  bound on derivatives  tangent numbers  tangent polynomials  Carlitztype qtangent numbers  Carlitztype qtangent polynomials  (p,q)analogue of tangent numbers and polynomials  (p,q)analogue of tangent zeta function  symmetric identities  zeros  Lommel functions  univalent functions  starlike functions  convex functions  inclusion relationships  analytic function  Hankel determinant  exponential function  upper bound  nonlinear boundary value problems  fractionalorder differential equations  RiemannStieltjes functional integral  LiouvilleCaputo fractional derivative  infinitepoint boundary conditions  advanced and deviated arguments  existence of at least one solution  Fredholm integral equation  Schauder fixed point theorem  Hölder condition  generalized Kuramoto–Sivashinsky equation  modified Kudryashov method  exact solutions  Maple graphs  analytic function  Hadamard product (convolution)  partial sum  Srivastava–Tomovski generalization of Mittag–Leffler function  subordination  differential equation  differential inclusion  Liouville–Caputotype fractional derivative  fractional integral  existence  fixed point  Bernoulli spiral  Grandi curves  Chebyshev polynomials  pseudoChebyshev polynomials  orthogonality property  symmetric  encryption  password  hash  cryptography  PBKDF  q–Bleimann–Butzer–Hahn operators  (p,q)integers  (p,q)Bernstein operators  (p,q)Bleimann–Butzer–Hahn operators  modulus of continuity  rate of approximation  Kfunctional  HurwitzLerch zeta function  generalized functions  analytic number theory  ?generalized HurwitzLerch zeta functions  derivative properties  series representation  basic hypergeometric functions  generating functions  qpolynomials  analytic functions  Mittag–Leffler functions  starlike functions  convex functions  Hardy space  vibrating string equation  initial conditions  spectral decomposition  regular solution  the uniqueness of the solution  the existence of a solution  analytic  ?convex function  starlike function  stronglystarlike function  subordination  q Sheffer–Appell polynomials  generating relations  determinant definition  recurrence relation  q Hermite–Bernoulli polynomials  q Hermite–Euler polynomials  q Hermite–Genocchi polynomials  Volterra integral equations  highly oscillatory Bessel kernel  Hermite interpolation  direct Hermite collocation method  piecewise Hermite collocation method  differential operator  qhypergeometric functions  meromorphic function  Mittag–Leffler function  Hadamard product  differential subordination  starlike functions  Bell numbers  radius estimate  (p, q)integers  Dunkl analogue  generating functions  generalization of exponential function  Szász operator  modulus of continuity  function spaces and their duals  distributions  tempered distributions  Schwartz testing function space  generalized functions  distribution space  wavelet transform of generalized functions  Fourier transform  analytic function  subordination  Dziok–Srivastava operator  nonlinear boundary value problem  nonlocal  multipoint  multistrip  existence  Ulam stability  functions of bounded boundary and bounded radius rotations  subordination  functions with positive real part  uniformly starlike and convex functions  analytic functions  univalent functions  starlike and qstarlike functions  qderivative (or qdifference) operator  sufficient conditions  distortion theorems  Janowski functions  analytic number theory  ?generalized Hurwitz–Lerch zeta functions  derivative properties  recurrence relations  integral representations  Mellin transform  natural transform  Adomian decomposition method  Caputo fractional derivative  generalized mittagleffler function  analytic functions  Hadamard product  starlike functions  qderivative (or qdifference) operator  Hankel determinant  qstarlike functions  fuzzy volterra integrodifferential equations  fuzzy general linear method  fuzzy differential equations  generalized Hukuhara differentiability  spectrum symmetry  DCT  MFCC  audio features  anuran calls  analytic functions  convex functions  starlike functions  strongly convex functions  strongly starlike functions  uniformly convex functions  Struve functions  truncatedexponential polynomials  monomiality principle  generating functions  Apostoltype polynomials and Apostoltype numbers  Bernoulli, Euler and Genocchi polynomials  Bernoulli, Euler, and Genocchi numbers  operational methods  summation formulas  symmetric identities  Euler numbers and polynomials  qEuler numbers and polynomials  HurwitzEuler eta function  multiple HurwitzEuler eta function  higher order qEuler numbers and polynomials  (p, q)Euler numbers and polynomials of higher order  symmetric identities  symmetry of the zero
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The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.
time fractional differential equations  mixedindex problems  analytical solution  asymptotic stability  conservative problems  Hamiltonian problems  energyconserving methods  Poisson problems  Hamiltonian Boundary Value Methods  HBVMs  line integral methods  constrained Hamiltonian problems  Hamiltonian PDEs  highly oscillatory problems  boundary element method  finite difference method  floating strike Asian options  continuous geometric average  barrier options  isogeometric analysis  adaptive methods  hierarchical splines  THBsplines  local refinement  linear systems  preconditioners  Cholesky factorization  limited memory  Volterra integral equations  Volterra integro–differential equations  collocation methods  multistep methods  convergence  Bspline  optimal basis  fractional derivative  Galerkin method  collocation method  spectral (eigenvalue) and singular value distributions  generalized locally Toeplitz sequences  discretization of systems of differential equations  higherorder finite element methods  discontinuous Galerkin methods  finite difference methods  isogeometric analysis  Bsplines  curl–curl operator  time harmonic Maxwell’s equations and magnetostatic problems  low rank completion  matrix ODEs  gradient system  ordinary differential equations  Runge–Kutta  tree  stump  order  elementary differential  edgehistogram  edgepreserving smoothing  histogram specification  initial value problems  onestep methods  Hermite–Obreshkov methods  symplecticity  Bsplines  BS methods  hyperbolic partial differential equations  high order discontinuous Galerkin finite element schemes  shock waves and discontinuities  vectorization and parallelization  high performance computing  generalized Schur algorithm  nullspace  displacement rank  structured matrices  stochastic differential equations  stochastic multistep methods  stochastic Volterra integral equations  meansquare stability  asymptotic stability  numerical analysis  numerical methods  scientific computing  initial value problems  onestep methods  Hermite–Obreshkov methods  symplecticity  Bsplines  BS methods
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Inequalities appear in various fields of natural science and engineering. Classical inequalities are still being improved and/or generalized by many researchers. That is, inequalities have been actively studied by mathematicians. In this book, we selected the papers that were published as the Special Issue ‘’Inequalities’’ in the journal Mathematics (MDPI publisher). They were ordered by similar topics for readers’ convenience and to give new and interesting results in mathematical inequalities, such as the improvements in famous inequalities, the results of Frame theory, the coefficient inequalities of functions, and the kind of convex functions used for Hermite–Hadamard inequalities. The editor believes that the contents of this book will be useful to study the latest results for researchers of this field.
analytic functions  starlike functions  convex functions  FeketeSzegö inequality  Hilbert C*module  gframe  gBessel sequence  adjointable operator  analytic functions  starlike functions  convex functions  FeketeSzegö inequality  operator inequality  positive linear map  operator Kantorovich inequality  geometrically convex function  frame  weaving frame  weaving frame operator  alternate dual frame  Hilbert space  quantum estimates  HermiteHadamard type inequalities  quasiconvex  Hermite–Hadamard type inequality  strongly ?convex functions  Hölder’s inequality  Power mean inequality  Katugampola fractional integrals  Riemann–Liouville fractional integrals  Hadamard fractional integrals  Steffensen’s inequality  higher order convexity  Green functions  Montgomery identity  Fink’s identity  HermiteHadamard inequality  intervalvalued functions  (h1, h2)convex  majorization inequality  twice differentiable convex functions  refined inequality  Taylor theorem  Gronwall–Bellman inequality  proportional fractional derivative  Riemann–Liouville and Caputo proportional fractional initial value problem  convex functions  Fejér’s inequality  special means  weaving frame  weaving Kframe  Kdual  pseudoinverse  ?variation  onesided singular integral  commutator  onesided weighted Morrey space  onesided weighted Campanato space  power inequalities  exponential inequalities  trigonometric inequalities  weight function  halfdiscrete HardyHilbert’s inequality  parameter  EulerMaclaurin summation formula  reverse inequality
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Quantum information has dramatically changed information science and technology, looking at the quantum nature of the information carrier as a resource for building new information protocols, designing radically new communication and computation algorithms, and ultrasensitive measurements in metrology, with a wealth of applications. From a fundamental perspective, this new discipline has led us to regard quantum theory itself as a special theory of information, and has opened routes for exploring solutions to the tension with general relativity, based, for example, on the holographic principle, on noncausal variations of the theory, or else on the powerful algorithm of the quantum cellular automaton, which has revealed new routes for exploring quantum fields theory, both as a new microscopic mechanism on the fundamental side, and as a tool for efficient physical quantum simulations for practical purposes. In this golden age of foundations, an astonishing number of new ideas, frameworks, and results, spawned by the quantum information theory experience, have revolutionized the way we think about the subject, with a new research community emerging worldwide, including scientists from computer science and mathematics.
reconstruction of quantum theory  entanglement  monogamy  quantum nonlocality  conserved informational charges  limited information  complementarity  characterization of unitary group and state spaces  algebraic quantum theory  C*algebra  gelfand duality  classical context  bohrification  process theory  classical limit  purity  higherorder interference  generalised probabilistic theories  Euclidean Jordan algebras  Pauli exclusion principle  quantum foundations  Xray spectroscopy  underground experiment  silicon drift detector  measurement uncertainty relations  relative entropy  position  momentum  quantum mechanics  the measurement problem  collapse models  Xrays  quantum gravity  discrete spacetime  causal sets  path summation  entropic gravity  physical computing models  complexity classes  causality  blind source separation (BSS)  qubit pair  exchange coupling  entangled pure state  unentanglement criterion  probabilities in quantum measurements  independence of random quantum sources  iterant  Clifford algebra  matrix algebra  braid group  Fermion  Dirac equation  quantum information  quantum computation  semiclassical physics  quantum control  quantum genetic algorithm  samplingbased learning control (SLC)  quantum foundations  relativity  quantum gravity  cluster states  multipartite entanglement  percolation  Shannon information  quantum information  quantum measurements  consistent histories  incompatible frameworks  single framework rule  probability theory  entropy  quantum relative entropy  quantum information  quantum mechanics  inference  quantum measurement  quantum estimation  macroscopic quantum measurement  quantum annealing  adiabatic quantum computing  hard problems  Hadamard matrix  binary optimization  reconstruction of quantum mechanics  conjugate systems  Jordan algebras  quantum correlations  Gaussian states  Gaussian unitary operations  continuousvariable systems  Wignerfriend experiment  nogo theorem  quantum foundations  interpretations of quantum mechanics  subsystem  agent  conservation of information  purification  group representations  commuting subalgebras  quantum walks  Hubbard model  Thirring model  quantum information  quantum foundations  quantum theory and gravity
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