Random Closed Sets and Capacity Functionals -- Expectations of Random Sets -- Minkowski Addition -- Unions of Random Sets -- Random Sets and Random Functions. Appendices: Topological Spaces -- Linear Spaces -- Space of Closed Sets -- Compact Sets and the Hausdorff Metric -- Multifunctions and Continuity -- Measures and Probabilities -- Capacities -- Convex Sets -- Semigroups and Harmonic Analys…
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…
Inductive Inference -- Information -- Strict Minimum Message Length (SMML) -- Approximations to SMML -- MML: Quadratic Approximations to SMML -- MML Details in Some Interesting Cases -- Structural Models -- The Feathers on the Arrow of Time -- MML as a Descriptive Theory -- Related Work.The Minimum Message Length (MML) Principle is an information-theoretic approach to induction, hypothesis test…
Geostatistics -- The genesis of geostatistics in gold and diamond industries -- Concepts and Methods of Geostatistics -- Prediction by conditional simulation: models and algorithms -- Flow in porous media: An attempt to outline Georges Matheron’s contributions -- Over Thirty Years of Petroleum Geostatistics -- The expansion of environmental geostatistics -- Random Sets -- Random Closed Sets -…
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…
Basis Objects and Operations -- Functional Data Objects and Operations -- Linear Differential Operators and Smoothing -- Functional Registration -- Functional Linear Models -- Functional Generalized Linear Models -- Functional Principal Components -- Canonical Correlation -- Functional Cluster Analysis -- Principal Differential Analysis.S+Functional Data Analysis is the first commercial object …
La probabilità -- Rappresentazione dei fenomeni aleatori -- Calcolo elementare delle probabilità -- Calcolo delle probabilità per più variabili -- Funzioni di variabili aleatorie -- Statistica di base -- II metodo Monte Carlo -- Applicazioni del metodo Monte Carlo -- Inferenza statistica e verosimiglianza -- Minimi quadrati -- Analisi dei dati sperimentali.Il volume contiene in forma compat…
The Evolution of Type Theory until the 1940s -- Prehistory -- Type theory in Principia Mathematica -- Deramification -- Propositions as Types, Pure Type Systems, AUTOMATH -- Propositions as Types and Pure Type Systems -- The pre-PAT RTT and STT in PAT-style -- A Correspondence between RTT and the system Nuprl -- Automath -- Extensions of Pure Type Systems -- Pure Type Systems with definitions -…
Why probability and statistics? -- Outcomes, events, and probability -- Conditional probability and independence -- Discrete random variables -- Continuous random variables -- Simulation -- Expectation and variance -- Computations with random variables -- Joint distributions and independence -- Covariance and correlation -- More computations with more random variables -- The Poisson process -- …
Assessment of characteristic shear strength parameters of soil and its implication in geotechnical design -- Ambiguity of safety definition in geotechnical models -- The fuzziness and sensitivity of failure probabilities -- The mathematics of uncertainty: models, methods and interpretations -- Multi-parameter models: rules and computational methods for combining uncertainties -- Sensitivity ana…