New in 9.0: Mathematics & Algorithms

Mathematica 9 adds major extensions and integration across the system. Probability and statistics adds survival and reliability analysis as well as a unified treatment for all random processes. Graphs and networks adds network flows, social network analysis, and major performance enhancements. Control systems adds PID autotuning as well as full support for descriptor and delay systems. Numerical differential equations now includes hybrid systems and parametric systems, as well as advanced support for differential algebraic equations.

(OrangeLink[Descriptive Statistics – Dependency Measures », paclet:guide/DescriptiveStatistics])

(RefLink[SpearmanRho, paclet:ref/SpearmanRho]) — Spearman's rank correlation for data and distributions

(RefLink[KendallTau, paclet:ref/KendallTau]) — Kendall's rank correlation for data and distributions

(OrangeLink[Hypothesis Tests – Independence Tests », paclet:guide/HypothesisTests])

(RefLink[IndependenceTest, paclet:ref/IndependenceTest]) — test whether two vectors are independent

(RefLink[CorrelationTest, paclet:ref/CorrelationTest]) — test whether two vectors are uncorrelated

New Parametric Distributions

(RefLink[HypoexponentialDistribution, paclet:ref/HypoexponentialDistribution]) — hypoexponential distribution

(RefLink[VarianceGammaDistribution, paclet:ref/VarianceGammaDistribution]) — variance gamma distribution

(OrangeLink[Derived Distributions », paclet:guide/DerivedDistributions])

(RefLink[SplicedDistribution, paclet:ref/SplicedDistribution]) — splicing several distributions such as different body and tail

(RefLink[CompoundPoissonDistribution, paclet:ref/CompoundPoissonDistribution]) — Poisson distribution with given jump size distribution

(RefLink[OrderDistribution, paclet:ref/OrderDistribution]) — generalized to different and multivariate distributions

New Data Models

(RefLink[EventData, paclet:ref/EventData]) — censored (left, right, interval) and truncated data

(RefLink[WeightedData, paclet:ref/WeightedData]) — weighted data

(RefLink[Mean, paclet:ref/Mean]) — descriptive statistics works for censored and weighted data

(RefLink[EstimatedDistribution, paclet:ref/EstimatedDistribution]) — parametric distribution estimation from censored data

(RefLink[EmpiricalDistribution, paclet:ref/EmpiricalDistribution]) — nonparametric distributions from censored data

(OrangeLink[Survival Analysis », paclet:guide/SurvivalAnalysis])

(RefLink[SurvivalModelFit, paclet:ref/SurvivalModelFit]) — survival functions with confidence bands from censored data

(RefLink[CoxModelFit, paclet:ref/CoxModelFit]) — Cox proportional hazards model from censored data

(RefLink[LogRankTest, paclet:ref/LogRankTest]) — hypothesis test for equal hazard rates

(OrangeLink[Reliability Modeling and Analysis », paclet:guide/Reliability])

(RefLink[ReliabilityDistribution, paclet:ref/ReliabilityDistribution]) — reliability block diagram model for a system

(RefLink[FailureDistribution, paclet:ref/FailureDistribution]) — fault tree model for a system

(RefLink[StandbyDistribution, paclet:ref/StandbyDistribution]) — standby reliability distribution (cold, hot, ...)

(RefLink[BirnbaumImportance, paclet:ref/BirnbaumImportance]) — measure to pinpoint subsystem to improve for reliability

(OrangeLink[Random Processes », paclet:guide/RandomProcesses])

(RefLink[RandomFunction, paclet:ref/RandomFunction]) — simulate a random process

(RefLink[TemporalData, paclet:ref/TemporalData]) — represent one or several time series data

(RefLink[EstimatedProcess, paclet:ref/EstimatedProcess]) — process estimated from time series data

(RefLink[SliceDistribution, paclet:ref/SliceDistribution]) — distribution for a time slice of a random process

(OrangeLink[Parametric Processes », paclet:guide/ParametricRandomProcesses])

(OrangeLink[Finite Markov Processes », paclet:guide/MarkovProcesses])

(OrangeLink[Queueing Processes », paclet:guide/QueueingProcesses])

(OrangeLink[Time Series Processes », paclet:guide/TimeSeriesProcesses])

(OrangeLink[Stochastic Differential Equation Processes », paclet:guide/StochasticDifferentialEquationProcesses])

(OrangeLink[Differential Equations with Events », paclet:guide/DifferentialEquationsWithEvents])

(RefLink[WhenEvent, paclet:ref/WhenEvent]) — discrete actions in differential equations when an event occurs

(RefLink[NDSolve, paclet:ref/NDSolve]) — now supports differential equations with events

Differential Equations with Parameters

(RefLink[ParametricNDSolveValue, paclet:ref/ParametricNDSolveValue]) — solve differential equations depending on parameters

Differential Algebraic Equations

(RefLink[NDSolve, paclet:ref/NDSolve]) — can now solve high-index DAEs

(OrangeLink[Graphs & Networks », paclet:guide/GraphsAndNetworks])

(RefLink[FindPostmanTour, paclet:ref/FindPostmanTour]) — find a tour that traverses each edge at least once

(OrangeLink[Social Network Analysis », paclet:guide/SocialNetworks])

(RefLink[FindGraphCommunities, paclet:ref/FindGraphCommunities]) — find communities within a graph

(RefLink[GlobalClusteringCoefficient, paclet:ref/GlobalClusteringCoefficient]) — compute the global clustering coefficient

(OrangeLink[Network Flows and Cuts », paclet:guide/GraphPathsCyclesAndFlows])

(RefLink[FindMaximumFlow, paclet:ref/FindMaximumFlow]) — find the maximum flow from a source vertex to a target vertex

(RefLink[FindMinimumCostFlow, paclet:ref/FindMinimumCostFlow]) — find the minimum cost flows

(RefLink[FindMinimumCut, paclet:ref/FindMinimumCut]) — find the minimum cut for a graph

(OrangeLink[Random Graphs », paclet:guide/RandomGraphs])

(RefLink[GraphPropertyDistribution, paclet:ref/GraphPropertyDistribution]) — automatically compute properties of random graphs

(RefLink[SpatialGraphDistribution, paclet:ref/SpatialGraphDistribution]) — higher-performance random graph generation

Control Systems

(RefLink[PIDTune, paclet:ref/PIDTune]) — automatic design of PID controllers

(OrangeLink[Models with Time Delays », paclet:guide/DelayControlSystems])

(RefLink[SystemsModelDelay, paclet:ref/SystemsModelDelay]) — represent delays in state-space and transfer-function models

(OrangeLink[Models with Algebraic Constraints », paclet:guide/DescriptorControlSystems])

(RefLink[DescriptorStateSpace, paclet:ref/DescriptorStateSpace]) — whether to use descriptor state-space representation

Fast Symbolic Linear and Polynomial Algebra

(RefLink[LinearSolve, paclet:ref/LinearSolve]) — fast methods for sparse symbolic and exact systems

(RefLink[Expand, paclet:ref/Expand]) — fast methods for polynomials with numeric coefficients

New Polynomial Functions

New Matrix Functions

(RefLink[MatrixLog, paclet:ref/MatrixLog]) — matrix log function

(RefLink[MatrixFunction, paclet:ref/MatrixFunction]) — matrix function for a general function

New Algebraic Numbers

(RefLink[CubeRoot, paclet:ref/CubeRoot]) — real cube root

(RefLink[Surd, paclet:ref/Surd]) — real n(^th) root

(OrangeLink[Vector Calculus », paclet:guide/VectorAnalysis])

Coordinate Systems

(RefLink[CoordinateChartData, paclet:ref/CoordinateChartData]) — properties of coordinate systems

(RefLink[TransformedField, paclet:ref/TransformedField]) — transform a field between coordinate systems

(OrangeLink[Symbolic Tensor Algebra », paclet:guide/SymbolicTensors])

(RefLink[Arrays, paclet:ref/Arrays]) — domain of arrays with given properties

Symmetries and Symmetrized Arrays

(RefLink[SymmetrizedArray, paclet:ref/SymmetrizedArray]) — compact representation of arrays with symmetry