... approach ¹

Since 1996, software maker Mathsoft has provided with Splus 4 a menu-driven package.

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...  ^2.1

The term configuration refers to both the global construct resulting from the concatenation of the different variables and to any of the individual states. This equivocation should be dispelled by the context where the term is employed.

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... next? ^3.1

usually is employed, since most of the systems we are dealing with are probabilistic, or stochastic . Well, they may be deterministic, but because the observations may be ``stained'' with measurement errors, or because not enough variables may be recorded at the same time, researchers may not grasp the whole complexity of the process. Therefore since every recorded event is not followed exactly by the same unique event, we are then obliged to consider the sequence of events as probabilistic.

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... systems ^3.2

Markov chains also apply to continuous data, but it will not be treated here

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... \sample^4.1

To be accurate the phase space is the mathematical space of all possible values of the system. The term has come to refer to the graphical representation itself.

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...fig:fa7-stre-evol ^4.2

Produced with the S-Plus command:
> tsplot(STRE, main="Evolution of stress", xlab="Time (t)", ylab="Stress intensity", axes=T, bty="n")

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...fig:fa7-stre-tsplot ^4.3

Produced with the S-Plus command:
> TSPlot(STRE, title="Evolution of stress")

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...fig:fa7-stre-phase2D ^4.4

This graphics is produced with Splus 4.5, using the Graph Menu, 2D Plot, Scatterplot.

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...fig:fa7-stre-phase3D ^4.5

This graphics is produced with Splus 4.5, using the Graph Menu, 3D Plot, 3D Scatterplot.

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...fig:fa7-emotstre-phase2D ^4.6

This graphics is produced with Splus 4.5, using the Graph Menu, 2D Plot, Scatterplot.

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...fig:fa7-fse-phase3D ^4.7

This graphics is produced with Splus 4.5, using the Graph Menu, 3D Plot, 3D Scatterplot.

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...fig:fg9-place-tsplot ^4.8

Produced with the S-Plus command:
> tsplot(PLACE, main="Time series plot of PLACE (Subject: FG9)", xlab="Time (t)", ylab="PLACE", axes=F, bty="n")

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...fig:fa7-place-evolustrip ^4.9

Produced with the S-Plus command:
> Evolustrip(PLACE, title="Evolustrip of PLACE (Subject: FA7)")

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...fig:fg9-place-evolustrip) ^4.10

Produced with the S-Plus command:
> Evolustrip(PLACE, title="Evolustrip of PLACE (Subject: FG9)")

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...fig:fa7-allvars-evolustrip) ^4.11

Produced with the S-Plus command:
> MultiEvolustrip(FA7, title="Multivariate Evolustrip of 7 Variables")

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...fig:fa7-alldicho-evolustrip) ^4.12

Produced with the S-Plus command:
> MultiEvolustrip(BFA7, title="Multivariate Evolustrip of 7 Binary Variables")

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...fig:fa7-place-std ^4.13

Produced with the S-Plus command:
> TransitionDiagram(PLACE,Title="State transition diagram for PLACE")

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...fig:fa7-place-stdmft ^4.14

Produced with the S-Plus command:
> TransitionDiagram(PLACE,Title="State transition diagram for PLACE",mft=T)

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...fig:fa7-fes-kmap ^4.15

Produced with the S-Plus command:
> Karnaugh3(BFAM,BEMOT,BSTRE,subjectname="FA7")

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...fig:fa7-fes-kmft ^4.16

Produced with the S-Plus command:
> Karnaugh3(BFAM,BEMOT,BSTRE,subjectname="FA7",mft=T)

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...fig:fa7-fpes-kmft ^4.17

Produced with the S-Plus command:
> Karnaugh4(BFAM,BPRESS,BEMOT,BSTRE,subjectname="FA7", mft=T)

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...fig:fg9-fpes-kmft ^4.18

Produced with the S-Plus command:
> Karnaugh4(BFAM,BPRESS,BEMOT,BSTRE,subjectname="FG9", mft=T)

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...fig:xr3-fpes-kmft ^4.19

Produced with the S-Plus command:
> Karnaugh4(BFAM,BPRESS,BEMOT,BSTRE,subjectname="XR3", mft=T)

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... ^4.20

Some new blabla is put here

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...fig:random-fpes-kmft ^4.21

Produced with the S-Plus command:
> Karnaugh4(BFAM,BPRESS,BEMOT,BSTRE,subjectname="Random", mft=T)

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... command ^4.22

KarnaughAnimation3 or KarnaughAnimation4, depending on the number of variables

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...tab:binarycorrpos) ^5.1

Produced with the S-Plus command:
> BinaryAutocorrelation(matrix(c(50,25,10,40),ncol=2,byrow=T))

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...tab:binarycorrneg ^5.2

Produced with the S-Plus command:
> BinaryAutocorrelation(matrix(c(25,50,40,10),ncol=2,byrow=T))

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...tab:fa7-bstre-tfm ^5.3

Produced with the S-Plus command:
> TFM(BSTRE)

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...tab:fa7-stre6-tfmlamdba ^5.4

Produced with the S-Plus command:
> TFM(STRE)

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... statistics ^5.5

Produced with the S-Plus command:
> Lambda(STRE)

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... matrix ^5.6

Produced with the S-Plus command:
> TPM(BSTRE)

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...tab:fa7-bstre-testprop ^5.7

Produced with the S-Plus command:
> EquiprobabilityTest(TFM(BSTRE), fromstate="0", tostate="0")

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... ^5.8

Produced with the S-Plus command:
> EquiprobabilityTest(TFM(BSTRE), fromstate="1", tostate="0")

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...tab:xr3-place-equitest ^5.9

Produced with the S-Plus command:
> EquiprobabilityTest(TFM(PLACE), fromstate="Work", tostate="Home")

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...  ^5.10

Produced with the S-Plus command:
> EquiprobabilityTest(TFM(PLACE), fromstate="Work", tostate="Other")

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... ^5.11

Produced with the S-Plus command:
> EquiprobabilityTest(TFM(PLACE), fromstate="Work", tostate="Work")

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...tab:xr3-place-sackett ^5.12

Produced with the S-Plus command:
> SackettZ(PLACE,fromstate="Work",tostate="Home")

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...  ^5.13

Produced with the S-Plus command:
> SackettZ(PLACE,fromstate="Work",tostate="Other")

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...  ^5.14

Produced with the S-Plus command:
> SackettZ(PLACE,fromstate="Work",tostate="Work")

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...tab:fa7-bstre-x2res ^5.15

Produced with the S-Plus command:
> Residuals(BSTRE)

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...tab:xr3-place-x2res ^5.16

Produced with the S-Plus command:
> Residuals(PLACE)

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... scale.^6.1

There should be a constant $K$ in the equation that reflects the arbitrary choice of base, but is usually left off.

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... ^6.2

Produced with the S-Plus command:
> JointEntropy(EMOT,STRE)

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... thought.^6.3

The Pearson correlation between those two variable is $r=0.68$

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...tab:fa7-mutualinfo-fes ^6.4

Produced with the S-Plus command:
> MutualInfo(BSTRE,BEMOT)

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... ^6.5

Produced with the S-Plus command:
> MutualInfo3(BFAM,BEMOT,BSTRE)

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... get ^6.6

Produced with the S-Plus command:
> RelativeEntropy(STRE,EMOT) and RelativeEntropy(EMOT,STRE)

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... RLI ^6.7

Produced with the S-Plus command:
> RelativeLossInfo(STRE,STRE3)

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...tab:fa7-fes-ict ^6.8

Produced with the S-Plus command:
> Index(BFAM), Index(BEMOT)...

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... situations ^6.9

By the time this thesis was written the author have been told a solution was found about this upper bound problem. But no article had been found due to particular circumstances.

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...tab:fa7-stre2-stytest ^7.1

Produced with the S-Plus command:
> Omnibus(BSTRE)

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...tab:fa7-famemot-stytest) ^7.2

Produced with the S-Plus command:
> Omnibus(BEMOT) and Omnibus(BFAM)

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...tab:fa7-fes-omni) ^7.3

Produced with the S-Plus command:
> Omnibus(BSTRE, d=3)

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...fig:fa7-bstre-omni10 ^7.4

Produced with the S-Plus command:
> for (i in 2:10) bstre.omnibus[i-1] _ Omnibus(BSTRE, d=i, matrices=F)$px

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...fig:fa7-stre2-styevol) ^7.5

Produced with the S-Plus command:
> for (i in 2:10) Omnibus(BSTRE, d=i, matrices=F)$px

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...fig:fa7-stre3-styevol ^7.6

Produced with the S-Plus command:
> for (i in 2:10) Omnibus(STRE3, d=i, matrices=F)$px

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...fig:fa7-stre6-styevol ^7.7

Produced with the S-Plus command:
> for (i in 2:10) Omnibus(STRE,d=i, matrices=F)$px

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...fig:fa7-fse-movingh) ^7.8

Produced with the S-Plus command:
> for(i in 1:(261-49)) Entropy(BSTRE[i:(i+49-1)])

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...fig:fa7-fse-movingindex ^7.9

Produced with the S-Plus command:
> for(i in 1:(261-49)) Index(BSTRE[i:(i+49-1)])

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...fig:fa7-fes-autocorr ^8.1

Produced with the S-Plus command:
> BACplot(cbind(BSTRE,BEMOT,BFAM))

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