Algebraic Preliminaries -- Integration of Rational Functions -- Differential Fields -- The Order Function -- Integration of Transcendental Functions -- The Risch Differential Equation -- Parametric Problems -- The Coupled Differential System -- Structure Theorems -- Parallel Integration.This first volume in the series "Algorithms and Computation in Mathematics" is destined to become the standar…
Information Centric Optimization of Inventories in Capacitated Supply Chains: Three Illustrative Examples -- An Analysis of Advance Booking Discount Programs Between Competing Retailers -- Third Party Logistics Planning with Routing and Inventory Costs -- Optimal Investment Strategies for Flexible Resources, Considering Pricing -- Multi-Channel Supply Chain Design in B2C Electronic Commerce -- …
Sturm’s 1836 Oscillation Results Evolution of the Theory -- Sturm Oscillation and Comparison Theorems -- Charles Sturm and the Development of Sturm-Liouville Theory in the Years 1900 to 1950 -- Spectral Theory of Sturm-Liouville Operators Approximation by Regular Problems -- Spectral Theory of Sturm-Liouville Operators on Infinite Intervals: A Review of Recent Developments -- Asymptotic Metho…
Basics -- Introduction -- Linear Programming Prerequisites -- Nonlinear Programming Prerequisites -- Single-stage SLP Models -- Introduction -- Models involving Probability Functions -- Quantile Functions, Value at Risk -- Models Based on Expectation -- Models Built with Deviation Measures -- Modeling Risk and Opportunity -- Risk Measures -- Multi-stage SLP Models -- The General SLP with Recour…
Markov Models in Molecular Evolution -- to Applications of the Likelihood Function in Molecular Evolution -- to Markov Chain Monte Carlo Methods in Molecular Evolution -- Population Genetics of Molecular Evolution -- Practical Approaches for Data Analysis -- Maximum Likelihood Methods for Detecting Adaptive Protein Evolution -- HyPhy: Hypothesis Testing Using Phylogenies -- Bayesian Analysis of…
Probability Theory (i): One Random Variable -- Probability Theory (ii): Many Random Variables -- Statistics (i): An Introduction to Statistical Inference -- Stochastic Processes (i): Poisson Processes and Markov Chains -- The Analysis of One DNA Sequence -- The Analysis of Multiple DNA or Protein Sequences -- Stochastic Processes (ii): Random Walks -- Statistics (ii): Classical Estimation Theor…
Inverse Problems and Interpretation of Measurements -- Classical Regularization Methods -- Statistical Inversion Theory -- Nonstationary Inverse Problems -- Classical Methods Revisited -- Model Problems -- Case Studies.The book develops the statistical approach to inverse problems with an emphasis on modeling and computations. The framework is the Bayesian paradigm, where all variables are mode…
to residues and resultants -- Solving equations via algebras -- Symbolic-numeric methods for solving polynomial equations and applications -- An algebraist’s view on border bases -- Tools for computing primary decompositions and applications to ideals associated to Bayesian networks -- Algorithms and their complexities -- Toric resultants and applications to geometric modelling -- to numerica…
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 …