Two Classical Optimization Problems -- Gauss’ Question -- What Does Solution Mean? -- Network Design Problems -- A New Challenge: The Phylogeny -- An Analysis of Steiner’s Problem in Phylogenetic Spaces -- Tree Building Algorithms.The problem of "Shortest Connectivity" has a long and convoluted history: given a finite set of points in a metric space, search for a network that connects these…
The Implied Volatility Surface -- Smile Consistent Volatility Models -- Smoothing Techniques -- Dimension-Reduced Modeling -- Conclusion and Outlook.The implied volatility surface is a key financial variable for the pricing and the risk management of plain vanilla and exotic options portfolios alike. Consequently, statistical models of the implied volatility surface are of immediate importance …
Classical Techniques -- Integer Programming -- Genetic Algorithms -- Genetic Programming -- Tabu Search -- Simulated Annealing -- Variable Neighborhood Search -- Constraint Programming -- Multi-Objective Optimization -- Complexity Theory and the No Free Lunch Theorem -- Machine Learning -- Artificial Immune Systems -- Swarm Intelligence -- Fuzzy Reasoning -- Rough Set Based Decision Support -- …
Methods of Solving Ill-Posed Problems -- One-Dimensional Inverse Scattering and Spectral Problems -- Inverse Obstacle Scattering -- Stability of the Solutions to 3D Inverse Scattering Problems with Fixed-Energy Data -- Non-Uniqueness and Uniqueness Results -- Inverse Problems of Potential Theory and Other Inverse Source Problems -- Non-Overdetermined Inverse Problems -- Low-Frequency Inversion …
On Existence of Solutions of Semilinear Impulsive Functional Differential Equations with Nonlocal Conditions -- On Banach-Lie Algebras, Spectral Decompositions and Complex Polarizations -- Commuting Triples of Subnormal Operators and Related Moment Problems -- The Equality of the Reduced and the Full C*-Algebras and the Amenability of a Topological Groupoid -- ?-Numerical Radius in Banach Space…
Inverse Scattering with Rational Scattering Coefficients and Wave Propagation in Nonhomogeneous Media -- Aluthge Transforms and the Convex Hull of the Spectrum of a Hilbert Space Operator -- Maximal Nevanlinna-Pick Interpolation for Points in the Open Unit Disc -- On the Numerical Solution of a Nonlinear Integral Equation of Prandtl’s Type -- Fourier Integral Operators and Gelfand-Shilov Spac…
Modeling Text Databases -- An Overview of Probabilistic and Time Series Models in Finance -- Stereological Estimation of the Rose of Directions from the Rose of Intersections -- Approximations for Multiple Scan Statistics -- Krawtchouk Polynomials and Krawtchouk Matrices -- An Elementary Rigorous Introduction to Exact Sampling -- On the Different Extensions of the Ergodic Theorem of Information…
Inroduction -- Rogers-Ramanujan Continued Fraction and Its Modular Properties -- Explicit Evaluations of the Rogers-Ramanujan Continued Fraction -- A Fragment on the Rogers-Ramanujan and Cubic Continued Fractions -- The Rogers-Ramanujan Continued Fraction and Its Connections with Partitions and Lambert Series -- Finite Rogers-Ramanujan Continued Fractions -- Other q-continued Fractions -- Asymp…
Lévy Processes in Euclidean Spaces and Groups -- Locally Compact Quantum Groups -- Quantum Stochastic Analysis - an Introduction -- Dilations, Cocycles and Product Systems.This volume is the first of two volumes containing the revised and completed notes lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Al…
to Quantum Trajectories -- The Bohmian Route to the Hydrodynamic Equations -- The Phase Space Route to the Hydrodynamic Equations -- The Dynamics and Properties of Quantum Trajectories -- Function and Derivative Approximation on Unstructured Grids -- Applications of the Quantum Trajectory Method -- Adaptive Methods for Trajectory Dynamics -- Quantum Trajectories for Multidimensional Dynamics --…