From fbfe2db366a7b2fb13483a76e8032897c4a29f23 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Wed, 12 Feb 2020 09:12:37 -0500
Subject: analysis of new data

---
 tempering_analysis.nb | 6543 +++++++++++++++++++++++++++++++------------------
 1 file changed, 4138 insertions(+), 2405 deletions(-)

diff --git a/tempering_analysis.nb b/tempering_analysis.nb
index b9596a4..c0b147a 100644
--- a/tempering_analysis.nb
+++ b/tempering_analysis.nb
@@ -10,10 +10,10 @@
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+NotebookOptionsPosition[    340951,       6692]
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+CellTagsIndexPosition[    341242,       6704]
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-        Scaled[0.02]}, {
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-        Scaled[0.02]}}, Ticks -> {Automatic, Automatic}}],FormBox[
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+        "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
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+           (Identity[#]& )[
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                     ImagePadding -> Automatic, 
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+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}}, 
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+     FrameLabel -> {{None, None}, {None, None}}, 
+     FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, 
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+          "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
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+            "freeformCursorMode" -> True, 
+             "placement" -> {"x" -> "All", "y" -> "None"}}}}, 
+       "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> 
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+        Scaled[0.02]}, {
+        Scaled[0.02], 
+        Scaled[0.02]}}, Ticks -> {Automatic, Automatic}}],FormBox[
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+       RowBox[{"n", "\[LongEqual]", "12"}], "None", 
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+                   GraphicsBox[{{
+                    Directive[
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+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    AbsoluteThickness[1.6], 
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+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.368417, 0.506779, 0.709798]], {}}}, 
+                    AspectRatio -> Full, ImageSize -> {20, 10}, 
+                    PlotRangePadding -> None, ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.880722, 0.611041, 0.142051]], {
+                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.880722, 0.611041, 0.142051]], {}}}, 
+                    AspectRatio -> Full, ImageSize -> {20, 10}, 
+                    PlotRangePadding -> None, ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, {
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.560181, 0.691569, 0.194885]], {
+                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    Opacity[1.], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.560181, 0.691569, 0.194885]], {}}}, 
+                    AspectRatio -> Full, ImageSize -> {20, 10}, 
+                    PlotRangePadding -> None, ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #5}}, 
+                 GridBoxAlignment -> {
+                  "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, 
+                 AutoDelete -> False, 
+                 GridBoxDividers -> {
+                  "Columns" -> {{False}}, "Rows" -> {{False}}}, 
+                 GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
+                  GridBoxSpacings -> {
+                  "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, 
+             GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, 
+             AutoDelete -> False, 
+             GridBoxItemSize -> {
+              "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, 
+             GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], 
+            "Grid"], Alignment -> Left, AppearanceElements -> None, 
+           ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> 
+           "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
+         FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> 
+         False], TraditionalForm]& ), 
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+         RowBox[{
+           RowBox[{"{", 
+             RowBox[{
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+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
+                   InterpretationBox[
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+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    RGBColor[0.368417, 0.506779, 0.709798], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
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+                    FrameStyle -> 
+                    RGBColor[
+                    0.24561133333333335`, 0.3378526666666667, 
+                    0.4731986666666667], FrameTicks -> None, PlotRangePadding -> 
+                    None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
+                    AbsoluteCurrentValue[Magnification]}]], 
+                    StyleBox[
+                    RowBox[{"RGBColor", "[", 
+                    RowBox[{"0.368417`", ",", "0.506779`", ",", "0.709798`"}],
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+                    BaseStyle -> {}, BaselinePosition -> Baseline, 
+                    DefaultBaseStyle -> {}, ButtonFunction :> 
+                    With[{Typeset`box$ = EvaluationBox[]}, 
+                    If[
+                    Not[
+                    AbsoluteCurrentValue["Deployed"]], 
+                    SelectionMove[Typeset`box$, All, Expression]; 
+                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
+                    FrontEnd`Private`$ColorSelectorInitialColor = 
+                    RGBColor[0.368417, 0.506779, 0.709798]; 
+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
+                    MathLink`CallFrontEnd[
+                    FrontEnd`AttachCell[Typeset`box$, 
+                    FrontEndResource["RGBColorValueSelector"], {
+                    0, {Left, Bottom}}, {Left, Top}, 
+                    "ClosingActions" -> {
+                    "SelectionDeparture", "ParentChanged", 
+                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
+                    Automatic, Method -> "Preemptive"], 
+                    RGBColor[0.368417, 0.506779, 0.709798], Editable -> False,
+                     Selectable -> False]}], "]"}], ",", 
+               RowBox[{"Directive", "[", 
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+                   RowBox[{"Opacity", "[", "1.`", "]"}], ",", 
+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
+                   InterpretationBox[
+                    ButtonBox[
+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    RGBColor[0.368417, 0.506779, 0.709798], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> 
+                    RGBColor[
+                    0.24561133333333335`, 0.3378526666666667, 
+                    0.4731986666666667], FrameTicks -> None, PlotRangePadding -> 
+                    None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
+                    AbsoluteCurrentValue[Magnification]}]], 
+                    StyleBox[
+                    RowBox[{"RGBColor", "[", 
+                    RowBox[{"0.368417`", ",", "0.506779`", ",", "0.709798`"}],
+                     "]"}], NumberMarks -> False]], Appearance -> None, 
+                    BaseStyle -> {}, BaselinePosition -> Baseline, 
+                    DefaultBaseStyle -> {}, ButtonFunction :> 
+                    With[{Typeset`box$ = EvaluationBox[]}, 
+                    If[
+                    Not[
+                    AbsoluteCurrentValue["Deployed"]], 
+                    SelectionMove[Typeset`box$, All, Expression]; 
+                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
+                    FrontEnd`Private`$ColorSelectorInitialColor = 
+                    RGBColor[0.368417, 0.506779, 0.709798]; 
+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
+                    MathLink`CallFrontEnd[
+                    FrontEnd`AttachCell[Typeset`box$, 
+                    FrontEndResource["RGBColorValueSelector"], {
+                    0, {Left, Bottom}}, {Left, Top}, 
+                    "ClosingActions" -> {
+                    "SelectionDeparture", "ParentChanged", 
+                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
+                    Automatic, Method -> "Preemptive"], 
+                    RGBColor[0.368417, 0.506779, 0.709798], Editable -> False,
+                     Selectable -> False]}], "]"}], ",", 
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+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
+                   InterpretationBox[
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+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    RGBColor[0.880722, 0.611041, 0.142051], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> 
+                    RGBColor[
+                    0.587148, 0.40736066666666665`, 0.09470066666666668], 
+                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
+                    AbsoluteCurrentValue[Magnification]}]], 
+                    StyleBox[
+                    RowBox[{"RGBColor", "[", 
+                    RowBox[{"0.880722`", ",", "0.611041`", ",", "0.142051`"}],
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+     Identity, DisplayFunction -> Identity, DisplayFunction -> Identity, 
+     DisplayFunction -> Identity, AspectRatio -> 
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+     AxesLabel -> {
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+     DisplayFunction :> Identity, Frame -> {{False, False}, {False, False}}, 
+     FrameLabel -> {{None, None}, {None, None}}, FrameTicks -> {{
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+        Charting`ScaledFrameTicks[{Log, Exp}]}, {Automatic, Automatic}}, 
+     GridLines -> {None, None}, GridLinesStyle -> Directive[
+       GrayLevel[0.5, 0.4]], 
+     Method -> {
+      "OptimizePlotMarkers" -> True, 
+       "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
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+            Part[#, 1]], 
+           (Exp[#]& )[
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+           (Identity[#]& )[
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+           (Exp[#]& )[
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+     PlotRange -> {{0, 10}, {-9.210340371976182, -0.6931471805599453}}, 
+     PlotRangeClipping -> True, PlotRangePadding -> {{0, 0}, {0, 0}}, 
+     Ticks -> {Automatic, 
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+       RowBox[{"n", "\[LongEqual]", "12"}], 
+       RowBox[{"n", "\[LongEqual]", "16"}]}, "PointLegend", 
+      DisplayFunction -> (FormBox[
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+         StyleBox[
+          PaneBox[
+           TagBox[
+            GridBox[{{
+               TagBox[
+                GridBox[{{
+                   GraphicsBox[{{
+                    Directive[
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+                    Directive[
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+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    RGBColor[0.368417, 0.506779, 0.709798], 
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+                    Directive[
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+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    RGBColor[0.368417, 0.506779, 0.709798], 
+                    AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, 
+                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
+                    ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    RGBColor[0.880722, 0.611041, 0.142051], 
+                    AbsoluteThickness[1.6]], {
+                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
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+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    RGBColor[0.880722, 0.611041, 0.142051], 
+                    AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, 
+                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
+                    ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    RGBColor[0.560181, 0.691569, 0.194885], 
+                    AbsoluteThickness[1.6]], {
+                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    RGBColor[0.560181, 0.691569, 0.194885], 
+                    AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, 
+                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
+                    ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}}, 
+                 GridBoxAlignment -> {
+                  "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, 
+                 AutoDelete -> False, 
+                 GridBoxDividers -> {
+                  "Columns" -> {{False}}, "Rows" -> {{False}}}, 
+                 GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
+                  GridBoxSpacings -> {
+                  "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, 
+             GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, 
+             AutoDelete -> False, 
+             GridBoxItemSize -> {
+              "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, 
+             GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], 
+            "Grid"], Alignment -> Left, AppearanceElements -> None, 
+           ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> 
+           "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
+         FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> 
+         False], TraditionalForm]& ), 
+      InterpretationFunction :> (RowBox[{"PointLegend", "[", 
+         RowBox[{
+           RowBox[{"{", 
+             RowBox[{
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+                 RowBox[{
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+                   ",", 
+                   InterpretationBox[
+                    ButtonBox[
+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    RGBColor[0.368417, 0.506779, 0.709798], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> 
+                    RGBColor[
+                    0.24561133333333335`, 0.3378526666666667, 
+                    0.4731986666666667], FrameTicks -> None, PlotRangePadding -> 
+                    None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
+                    AbsoluteCurrentValue[Magnification]}]], 
+                    StyleBox[
+                    RowBox[{"RGBColor", "[", 
+                    RowBox[{"0.368417`", ",", "0.506779`", ",", "0.709798`"}],
+                     "]"}], NumberMarks -> False]], Appearance -> None, 
+                    BaseStyle -> {}, BaselinePosition -> Baseline, 
+                    DefaultBaseStyle -> {}, ButtonFunction :> 
+                    With[{Typeset`box$ = EvaluationBox[]}, 
+                    If[
+                    Not[
+                    AbsoluteCurrentValue["Deployed"]], 
+                    SelectionMove[Typeset`box$, All, Expression]; 
+                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
+                    FrontEnd`Private`$ColorSelectorInitialColor = 
+                    RGBColor[0.368417, 0.506779, 0.709798]; 
+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
+                    MathLink`CallFrontEnd[
+                    FrontEnd`AttachCell[Typeset`box$, 
+                    FrontEndResource["RGBColorValueSelector"], {
+                    0, {Left, Bottom}}, {Left, Top}, 
+                    "ClosingActions" -> {
+                    "SelectionDeparture", "ParentChanged", 
+                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
+                    Automatic, Method -> "Preemptive"], 
+                    RGBColor[0.368417, 0.506779, 0.709798], Editable -> False,
+                     Selectable -> False], ",", 
+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], 
+               ",", 
+               RowBox[{"Directive", "[", 
+                 RowBox[{
+                   RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}], 
+                   ",", 
+                   InterpretationBox[
+                    ButtonBox[
+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    RGBColor[0.880722, 0.611041, 0.142051], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> 
+                    RGBColor[
+                    0.587148, 0.40736066666666665`, 0.09470066666666668], 
+                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
+                    AbsoluteCurrentValue[Magnification]}]], 
+                    StyleBox[
+                    RowBox[{"RGBColor", "[", 
+                    RowBox[{"0.880722`", ",", "0.611041`", ",", "0.142051`"}],
+                     "]"}], NumberMarks -> False]], Appearance -> None, 
+                    BaseStyle -> {}, BaselinePosition -> Baseline, 
+                    DefaultBaseStyle -> {}, ButtonFunction :> 
+                    With[{Typeset`box$ = EvaluationBox[]}, 
+                    If[
+                    Not[
+                    AbsoluteCurrentValue["Deployed"]], 
+                    SelectionMove[Typeset`box$, All, Expression]; 
+                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
+                    FrontEnd`Private`$ColorSelectorInitialColor = 
+                    RGBColor[0.880722, 0.611041, 0.142051]; 
+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
+                    MathLink`CallFrontEnd[
+                    FrontEnd`AttachCell[Typeset`box$, 
+                    FrontEndResource["RGBColorValueSelector"], {
+                    0, {Left, Bottom}}, {Left, Top}, 
+                    "ClosingActions" -> {
+                    "SelectionDeparture", "ParentChanged", 
+                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
+                    Automatic, Method -> "Preemptive"], 
+                    RGBColor[0.880722, 0.611041, 0.142051], Editable -> False,
+                     Selectable -> False], ",", 
+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], 
+               ",", 
+               RowBox[{"Directive", "[", 
+                 RowBox[{
+                   RowBox[{"PointSize", "[", "0.009166666666666668`", "]"}], 
+                   ",", 
+                   InterpretationBox[
+                    ButtonBox[
+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    RGBColor[0.560181, 0.691569, 0.194885], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> 
+                    RGBColor[
+                    0.37345400000000006`, 0.461046, 0.12992333333333334`], 
+                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
+                    AbsoluteCurrentValue[Magnification]}]], 
+                    StyleBox[
+                    RowBox[{"RGBColor", "[", 
+                    RowBox[{"0.560181`", ",", "0.691569`", ",", "0.194885`"}],
+                     "]"}], NumberMarks -> False]], Appearance -> None, 
+                    BaseStyle -> {}, BaselinePosition -> Baseline, 
+                    DefaultBaseStyle -> {}, ButtonFunction :> 
+                    With[{Typeset`box$ = EvaluationBox[]}, 
+                    If[
+                    Not[
+                    AbsoluteCurrentValue["Deployed"]], 
+                    SelectionMove[Typeset`box$, All, Expression]; 
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+         RGBColor[0.368417, 0.506779, 0.709798], 
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+         RGBColor[0.880722, 0.611041, 0.142051], 
+         AbsoluteThickness[1.6]]}, {
+        Directive[
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+         RGBColor[0.560181, 0.691569, 0.194885], 
+         AbsoluteThickness[1.6]]}}, {{
+        Directive[
+         PointSize[0.007333333333333334], 
+         RGBColor[0.368417, 0.506779, 0.709798], 
+         AbsoluteThickness[1.6]]}, {
+        Directive[
+         PointSize[0.007333333333333334], 
+         RGBColor[0.880722, 0.611041, 0.142051], 
+         AbsoluteThickness[1.6]]}, {
+        Directive[
+         PointSize[0.007333333333333334], 
+         RGBColor[0.560181, 0.691569, 0.194885], 
+         AbsoluteThickness[1.6]]}, {}, {}, {}, {}, {}, {}, {}}, {{
+        Directive[
+         PointSize[0.007333333333333334], 
+         RGBColor[0.368417, 0.506779, 0.709798], 
+         AbsoluteThickness[1.6]]}, {
+        Directive[
+         PointSize[0.007333333333333334], 
+         RGBColor[0.880722, 0.611041, 0.142051], 
+         AbsoluteThickness[1.6]]}, {
+        Directive[
+         PointSize[0.007333333333333334], 
+         RGBColor[0.560181, 0.691569, 0.194885], 
+         AbsoluteThickness[1.6]]}, {}, {}, {}, {}, {}, {}, {}}}, {{}, {}}}, {
+    DisplayFunction -> Identity, DisplayFunction -> Identity, AspectRatio -> 
+     NCache[GoldenRatio^(-1), 0.6180339887498948], Axes -> {True, True}, 
+     AxesLabel -> {
+       FormBox["\[Beta]", TraditionalForm], 
+       FormBox[
+        RowBox[{"e", "(", "\[Beta]", ")"}], TraditionalForm]}, 
+     AxesOrigin -> {0, -0.8046567982253087}, DisplayFunction :> Identity, 
+     Frame -> {{False, False}, {False, False}}, 
+     FrameLabel -> {{None, None}, {None, None}}, 
+     FrameTicks -> {{Automatic, Automatic}, {Automatic, Automatic}}, 
+     GridLines -> {None, None}, GridLinesStyle -> Directive[
+       GrayLevel[0.5, 0.4]], 
+     Method -> {
+      "OptimizePlotMarkers" -> True, 
+       "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
+           (Identity[#]& )[
+            Part[#, 1]], 
+           (Identity[#]& )[
+            Part[#, 2]]}& ), "CopiedValueFunction" -> ({
+           (Identity[#]& )[
+            Part[#, 1]], 
+           (Identity[#]& )[
+            Part[#, 2]]}& )}}, 
+     PlotRange -> {{0, 10}, {-0.9956235625, -0.8147076805555554}}, 
+     PlotRangeClipping -> True, PlotRangePadding -> {{0, 0}, {
+        Scaled[0.05], 
+        Scaled[0.05]}}, Ticks -> {Automatic, Automatic}}],FormBox[
+    FormBox[
+     TemplateBox[{
+       RowBox[{"n", "\[LongEqual]", "8"}], 
+       RowBox[{"n", "\[LongEqual]", "12"}], 
+       RowBox[{"n", "\[LongEqual]", "16"}]}, "PointLegend", 
+      DisplayFunction -> (FormBox[
+        StyleBox[
+         StyleBox[
+          PaneBox[
+           TagBox[
+            GridBox[{{
+               TagBox[
+                GridBox[{{
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    RGBColor[0.368417, 0.506779, 0.709798], 
+                    AbsoluteThickness[1.6]], {
+                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    RGBColor[0.368417, 0.506779, 0.709798], 
+                    AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, 
+                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
+                    ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, {
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    RGBColor[0.880722, 0.611041, 0.142051], 
+                    AbsoluteThickness[1.6]], {
+                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    RGBColor[0.880722, 0.611041, 0.142051], 
+                    AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, 
+                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
+                    ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, {
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    RGBColor[0.560181, 0.691569, 0.194885], 
+                    AbsoluteThickness[1.6]], {
+                    LineBox[{{0, 10}, {20, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    RGBColor[0.560181, 0.691569, 0.194885], 
+                    AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, 
+                    ImageSize -> {20, 10}, PlotRangePadding -> None, 
+                    ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}}, 
+                 GridBoxAlignment -> {
+                  "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, 
+                 AutoDelete -> False, 
+                 GridBoxDividers -> {
+                  "Columns" -> {{False}}, "Rows" -> {{False}}}, 
+                 GridBoxItemSize -> {"Columns" -> {{All}}, "Rows" -> {{All}}},
+                  GridBoxSpacings -> {
+                  "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, 
+             GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, 
+             AutoDelete -> False, 
+             GridBoxItemSize -> {
+              "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, 
+             GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], 
+            "Grid"], Alignment -> Left, AppearanceElements -> None, 
+           ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> 
+           "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], {
+         FontFamily -> "Arial"}, Background -> Automatic, StripOnInput -> 
+         False], TraditionalForm]& ), 
+      InterpretationFunction :> (RowBox[{"PointLegend", "[", 
+         RowBox[{
+           RowBox[{"{", 
+             RowBox[{
+               RowBox[{"Directive", "[", 
+                 RowBox[{
+                   RowBox[{"PointSize", "[", "0.007333333333333334`", "]"}], 
+                   ",", 
+                   InterpretationBox[
+                    ButtonBox[
+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    RGBColor[0.368417, 0.506779, 0.709798], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> 
+                    RGBColor[
+                    0.24561133333333335`, 0.3378526666666667, 
+                    0.4731986666666667], FrameTicks -> None, PlotRangePadding -> 
+                    None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
+                    AbsoluteCurrentValue[Magnification]}]], 
+                    StyleBox[
+                    RowBox[{"RGBColor", "[", 
+                    RowBox[{"0.368417`", ",", "0.506779`", ",", "0.709798`"}],
+                     "]"}], NumberMarks -> False]], Appearance -> None, 
+                    BaseStyle -> {}, BaselinePosition -> Baseline, 
+                    DefaultBaseStyle -> {}, ButtonFunction :> 
+                    With[{Typeset`box$ = EvaluationBox[]}, 
+                    If[
+                    Not[
+                    AbsoluteCurrentValue["Deployed"]], 
+                    SelectionMove[Typeset`box$, All, Expression]; 
+                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
+                    FrontEnd`Private`$ColorSelectorInitialColor = 
+                    RGBColor[0.368417, 0.506779, 0.709798]; 
+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
+                    MathLink`CallFrontEnd[
+                    FrontEnd`AttachCell[Typeset`box$, 
+                    FrontEndResource["RGBColorValueSelector"], {
+                    0, {Left, Bottom}}, {Left, Top}, 
+                    "ClosingActions" -> {
+                    "SelectionDeparture", "ParentChanged", 
+                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
+                    Automatic, Method -> "Preemptive"], 
+                    RGBColor[0.368417, 0.506779, 0.709798], Editable -> False,
+                     Selectable -> False], ",", 
+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], 
+               ",", 
+               RowBox[{"Directive", "[", 
+                 RowBox[{
+                   RowBox[{"PointSize", "[", "0.007333333333333334`", "]"}], 
+                   ",", 
+                   InterpretationBox[
+                    ButtonBox[
+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    RGBColor[0.880722, 0.611041, 0.142051], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> 
+                    RGBColor[
+                    0.587148, 0.40736066666666665`, 0.09470066666666668], 
+                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
+                    AbsoluteCurrentValue[Magnification]}]], 
+                    StyleBox[
+                    RowBox[{"RGBColor", "[", 
+                    RowBox[{"0.880722`", ",", "0.611041`", ",", "0.142051`"}],
+                     "]"}], NumberMarks -> False]], Appearance -> None, 
+                    BaseStyle -> {}, BaselinePosition -> Baseline, 
+                    DefaultBaseStyle -> {}, ButtonFunction :> 
+                    With[{Typeset`box$ = EvaluationBox[]}, 
+                    If[
+                    Not[
+                    AbsoluteCurrentValue["Deployed"]], 
+                    SelectionMove[Typeset`box$, All, Expression]; 
+                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
+                    FrontEnd`Private`$ColorSelectorInitialColor = 
+                    RGBColor[0.880722, 0.611041, 0.142051]; 
+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
+                    MathLink`CallFrontEnd[
+                    FrontEnd`AttachCell[Typeset`box$, 
+                    FrontEndResource["RGBColorValueSelector"], {
+                    0, {Left, Bottom}}, {Left, Top}, 
+                    "ClosingActions" -> {
+                    "SelectionDeparture", "ParentChanged", 
+                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
+                    Automatic, Method -> "Preemptive"], 
+                    RGBColor[0.880722, 0.611041, 0.142051], Editable -> False,
+                     Selectable -> False], ",", 
+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], 
+               ",", 
+               RowBox[{"Directive", "[", 
+                 RowBox[{
+                   RowBox[{"PointSize", "[", "0.007333333333333334`", "]"}], 
+                   ",", 
+                   InterpretationBox[
+                    ButtonBox[
+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    RGBColor[0.560181, 0.691569, 0.194885], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> 
+                    RGBColor[
+                    0.37345400000000006`, 0.461046, 0.12992333333333334`], 
+                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 1.35 CurrentValue["FontCapHeight"]/
+                    AbsoluteCurrentValue[Magnification]}]], 
+                    StyleBox[
+                    RowBox[{"RGBColor", "[", 
+                    RowBox[{"0.560181`", ",", "0.691569`", ",", "0.194885`"}],
+                     "]"}], NumberMarks -> False]], Appearance -> None, 
+                    BaseStyle -> {}, BaselinePosition -> Baseline, 
+                    DefaultBaseStyle -> {}, ButtonFunction :> 
+                    With[{Typeset`box$ = EvaluationBox[]}, 
+                    If[
+                    Not[
+                    AbsoluteCurrentValue["Deployed"]], 
+                    SelectionMove[Typeset`box$, All, Expression]; 
+                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
+                    FrontEnd`Private`$ColorSelectorInitialColor = 
+                    RGBColor[0.560181, 0.691569, 0.194885]; 
+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
+                    MathLink`CallFrontEnd[
+                    FrontEnd`AttachCell[Typeset`box$, 
+                    FrontEndResource["RGBColorValueSelector"], {
+                    0, {Left, Bottom}}, {Left, Top}, 
+                    "ClosingActions" -> {
+                    "SelectionDeparture", "ParentChanged", 
+                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
+                    Automatic, Method -> "Preemptive"], 
+                    RGBColor[0.560181, 0.691569, 0.194885], Editable -> False,
+                     Selectable -> False], ",", 
+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}]}],
+              "}"}], ",", 
+           RowBox[{"{", 
+             RowBox[{#, ",", #2, ",", #3}], "}"}], ",", 
+           RowBox[{"LegendMarkers", "\[Rule]", 
+             RowBox[{"{", 
+               RowBox[{
+                 RowBox[{"{", 
+                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
+                 RowBox[{"{", 
+                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
+                 RowBox[{"{", 
+                   RowBox[{"False", ",", "Automatic"}], "}"}]}], "}"}]}], ",", 
+           RowBox[{"Joined", "\[Rule]", 
+             RowBox[{"{", 
+               RowBox[{"True", ",", "True", ",", "True"}], "}"}]}], ",", 
+           RowBox[{"LabelStyle", "\[Rule]", 
+             RowBox[{"{", "}"}]}], ",", 
+           RowBox[{"LegendLayout", "\[Rule]", "\"Column\""}]}], "]"}]& ), 
+      Editable -> True], TraditionalForm], TraditionalForm]},
+  "Legended",
+  DisplayFunction->(GridBox[{{
+      TagBox[
+       ItemBox[
+        PaneBox[
+         TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, 
+         BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], 
+       "SkipImageSizeLevel"], 
+      ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, 
+    GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, 
+    AutoDelete -> False, GridBoxItemSize -> Automatic, 
+    BaselinePosition -> {1, 1}]& ),
+  Editable->True,
+  InterpretationFunction->(RowBox[{"Legended", "[", 
+     RowBox[{#, ",", 
+       RowBox[{"Placed", "[", 
+         RowBox[{#2, ",", "After"}], "]"}]}], "]"}]& )]], "Output",
+ CellChangeTimes->{{3.790501975959618*^9, 3.7905020568911247`*^9}, {
+   3.790502162871426*^9, 3.790502197077286*^9}, 3.7905024866172*^9, {
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  CellLabel->
-  "Out[119]=",ExpressionUUID->"8859f4d2-839c-4aad-be80-f128e6490cbc"]
+  "Out[269]=",ExpressionUUID->"011cfe76-5e46-4695-9c02-f9b1d9e2513f"]
 }, Open  ]],
 
 Cell[CellGroupData[{
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   3.78986147356671*^9, 3.789861534004075*^9}, {3.7898617800836077`*^9, 
   3.789861835680109*^9}},
- CellLabel->"In[41]:=",ExpressionUUID->"6bf8aea7-b7b9-4d5b-a161-210bee9bd86a"],
+ CellLabel->
+  "In[177]:=",ExpressionUUID->"6bf8aea7-b7b9-4d5b-a161-210bee9bd86a"],
 
 Cell[BoxData[
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-     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.007333333333333334],
-       AbsoluteThickness[1.6], LineBox[CompressedData["
+     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
+      0.0055000000000000005`], AbsoluteThickness[1.6], LineBox[CompressedData["
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-- 
cgit v1.2.3-54-g00ecf