diff --git a/code/RDGW150914.nb b/code/RDGW150914.nb
index e978b0e228a7791c66dcd994ee29e90b7e6d152e..b354ae9c811c0168548d59bbdd0ef98ab944057c 100644
--- a/code/RDGW150914.nb
+++ b/code/RDGW150914.nb
@@ -10,10 +10,10 @@
 NotebookFileLineBreakTest
 NotebookFileLineBreakTest
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-NotebookOutlinePosition[   7607559,     140561]
-CellTagsIndexPosition[   7607516,     140558]
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+CellTagsIndexPosition[   8062316,     149963]
 WindowFrame->Normal*)
 
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 Cell["\<\
 X. Jimenez, S. Bhagwat. Notebook used to generate the results of arxiv: \
@@ -46,58 +47,6 @@ X. Jimenez, S. Bhagwat. Notebook used to generate the results of arxiv: \
 
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+             AbsoluteThickness[0.1]}}}}, {Automatic, Automatic}}],
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+         Charting`ScaledTickValues[{Log, Exp}]}, {Automatic, {{0., 
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+           Directive[
+            AbsoluteThickness[0.1]]}, {2.302585092994046, 
+           Directive[
+            AbsoluteThickness[0.1]]}, {3.912023005428146, 
+           Directive[
+            AbsoluteThickness[0.1]]}, {4.605170185988092, 
+           Directive[
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+           Directive[
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+      ImageSize->Large,
+      LabelStyle->Directive[
+        GrayLevel[0], Bold, 13],
+      Method->{
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+        "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
+            (Identity[#]& )[
+             Part[#, 1]], 
+            (Exp[#]& )[
+             Part[#, 2]]}& ), "CopiedValueFunction" -> ({
+            (Identity[#]& )[
+             Part[#, 1]], 
+            (Exp[#]& )[
+             Part[#, 2]]}& )}},
+      PlotLabel->None,
+      PlotRange->NCache[{{1, 10}, {0, 
+          Log[600]}}, {{1, 10}, {0, 6.396929655216146}}],
+      PlotRangeClipping->True,
+      PlotRangePadding->{{0, 0}, {0, 0}},
+      Ticks->{Automatic, 
+        Charting`ScaledTicks[{Log, Exp}]}], Scaled[{0.5, 0.5}], Center, 
+     Scaled[{1, 1}]], InsetBox[
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+\\!\\(\\*SubscriptBox[\\(t\\), \\(0\\)]\\)=15 M\"",
+       "\"\\!\\(\\*SubscriptBox[\\(\[Rho]\\), \\(221\\)]\\): \
+\\!\\(\\*SubscriptBox[\\(t\\), \\(0\\)]\\)=10 M\"",
+       "\"\\!\\(\\*SubscriptBox[\\(\[Rho]\\), \\(210\\)]\\): \
+\\!\\(\\*SubscriptBox[\\(t\\), \\(0\\)]\\)=15 M\"",
+       "\"\\!\\(\\*SubscriptBox[\\(\[Rho]\\), \\(440\\)]\\): \
+\\!\\(\\*SubscriptBox[\\(A\\), \\(R\\)]\\)~0.1 M\""},
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+      DisplayFunction->(FormBox[
+        StyleBox[
+         StyleBox[
+          PaneBox[
+           TagBox[
+            GridBox[{{
+               TagBox[
+                GridBox[{{
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.5, 0, 0.5], 
+                    Dashing[{0, Small, Small, Small}]], {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.5, 0, 0.5], 
+                    Dashing[{0, Small, Small, Small}]], {}}}, AspectRatio -> 
+                    Full, ImageSize -> {40, 10}, PlotRangePadding -> None, 
+                    ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #}}, 
+                 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"], 
+               TagBox[
+                GridBox[{{
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
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+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.560181, 0.691569, 0.194885]], {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.560181, 0.691569, 0.194885]], {}}}, 
+                    AspectRatio -> Full, ImageSize -> {40, 10}, 
+                    PlotRangePadding -> None, ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}}, 
+                 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"], 
+               TagBox[
+                GridBox[{{
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
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+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.772079, 0.431554, 0.102387], 
+                    Dashing[{Small, Small}]], {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.772079, 0.431554, 0.102387], 
+                    Dashing[{Small, Small}]], {}}}, AspectRatio -> Full, 
+                    ImageSize -> {40, 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"], 
+               TagBox[
+                GridBox[{{
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.368417, 0.506779, 0.709798]], {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.368417, 0.506779, 0.709798]], {}}}, 
+                    AspectRatio -> Full, ImageSize -> {40, 10}, 
+                    PlotRangePadding -> None, ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}}, 
+                 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], {
+          Directive[
+           GrayLevel[0], Bold, 13], FontFamily -> "Arial"}, Background -> 
+         Automatic, StripOnInput -> False], TraditionalForm]& ),
+      Editable->True,
+      InterpretationFunction:>(RowBox[{"LineLegend", "[", 
+         RowBox[{
+           RowBox[{"{", 
+             RowBox[{
+               RowBox[{"Directive", "[", 
+                 RowBox[{
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+                   ",", 
+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
+                   InterpretationBox[
+                    ButtonBox[
+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    RGBColor[0.5, 0, 0.5], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> 
+                    RGBColor[0.33333333333333337`, 0., 0.33333333333333337`], 
+                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 
+                    1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
+                    Magnification])}]], 
+                    StyleBox[
+                    RowBox[{"RGBColor", "[", 
+                    RowBox[{"0.5`", ",", "0", ",", "0.5`"}], "]"}], 
+                    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`$ColorSelectorInitialColor = 
+                    RGBColor[0.5, 0, 0.5]; 
+                    FrontEnd`Private`$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[0.5, 0, 0.5], Editable -> False, Selectable -> 
+                    False], ",", 
+                   RowBox[{"Dashing", "[", 
+                    RowBox[{"{", 
+                    RowBox[{"0", ",", "Small", ",", "Small", ",", "Small"}], 
+                    "}"}], "]"}]}], "]"}], ",", 
+               RowBox[{"Directive", "[", 
+                 RowBox[{
+                   RowBox[{"PointSize", "[", "0.007333333333333334`", "]"}], 
+                   ",", 
+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
+                   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[{"Directive", "[", 
+                 RowBox[{
+                   RowBox[{"PointSize", "[", "0.007333333333333334`", "]"}], 
+                   ",", 
+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
+                   InterpretationBox[
+                    ButtonBox[
+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    RGBColor[0.772079, 0.431554, 0.102387], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> 
+                    RGBColor[
+                    0.5147193333333333, 0.28770266666666666`, 
+                    0.06825800000000001], FrameTicks -> None, 
+                    PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 
+                    1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
+                    Magnification])}]], 
+                    StyleBox[
+                    RowBox[{"RGBColor", "[", 
+                    RowBox[{"0.772079`", ",", "0.431554`", ",", "0.102387`"}],
+                     "]"}], 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`$ColorSelectorInitialColor = 
+                    RGBColor[0.772079, 0.431554, 0.102387]; 
+                    FrontEnd`Private`$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[0.772079, 0.431554, 0.102387], Editable -> False,
+                     Selectable -> False], ",", 
+                   RowBox[{"Dashing", "[", 
+                    RowBox[{"{", 
+                    RowBox[{"Small", ",", "Small"}], "}"}], "]"}]}], "]"}], 
+               ",", 
+               RowBox[{"Directive", "[", 
+                 RowBox[{
+                   RowBox[{"PointSize", "[", "0.007333333333333334`", "]"}], 
+                   ",", 
+                   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]}], "]"}]}], "}"}], ",", 
+           RowBox[{"{", 
+             RowBox[{#, ",", #2, ",", #3, ",", #4}], "}"}], ",", 
+           RowBox[{"LegendMarkers", "\[Rule]", 
+             RowBox[{"{", 
+               RowBox[{
+                 RowBox[{"{", 
+                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
+                 RowBox[{"{", 
+                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
+                 RowBox[{"{", 
+                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
+                 RowBox[{"{", 
+                   RowBox[{"False", ",", "Automatic"}], "}"}]}], "}"}]}], ",", 
+           RowBox[{"Joined", "\[Rule]", 
+             RowBox[{"{", 
+               RowBox[{"True", ",", "True", ",", "True", ",", "True"}], 
+               "}"}]}], ",", 
+           RowBox[{"LabelStyle", "\[Rule]", 
+             RowBox[{"Directive", "[", 
+               RowBox[{
+                 InterpretationBox[
+                  ButtonBox[
+                   TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> GrayLevel[0.], FrameTicks -> None, 
+                    PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 
+                    1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
+                    Magnification])}]], 
+                    StyleBox[
+                    RowBox[{"GrayLevel", "[", "0", "]"}], 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`$ColorSelectorInitialColor = 
+                    GrayLevel[0]; 
+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
+                    MathLink`CallFrontEnd[
+                    FrontEnd`AttachCell[Typeset`box$, 
+                    FrontEndResource["GrayLevelColorValueSelector"], {
+                    0, {Left, Bottom}}, {Left, Top}, 
+                    "ClosingActions" -> {
+                    "SelectionDeparture", "ParentChanged", 
+                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
+                   Automatic, Method -> "Preemptive"], 
+                  GrayLevel[0], Editable -> False, Selectable -> False], ",", 
+                 "Bold", ",", "13"}], "]"}]}], ",", 
+           RowBox[{"LegendLayout", "\[Rule]", 
+             RowBox[{"{", 
+               RowBox[{"\"Column\"", ",", "4"}], "}"}]}]}], "]"}]& )], 
+     Scaled[{0.53, 1.0001}], ImageScaled[{0.5, 0}],
+     BaseStyle->{FontSize -> Larger},
+     FormatType->StandardForm]},
+   AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
+   Axes->False,
+   AxesLabel->{None, None},
+   AxesOrigin->{1., 0.},
+   DisplayFunction->Identity,
+   Frame->False,
+   FrameLabel->{{
+      FormBox[
+      "\"\\!\\(\\*SubscriptBox[\\(\[Rho]\\), \\(Res\\)]\\) for \
+\\!\\(\\*SubscriptBox[\\(f\\), \\(sub\\)]\\)\"", TraditionalForm], None}, {
+      FormBox["\"q\"", TraditionalForm], None}},
+   FrameStyle->Directive[
+     GrayLevel[0], Bold, 20],
+   FrameTicks->{{
+      Charting`ScaledTicks[{Log, Exp}], 
+      Charting`ScaledFrameTicks[{Log, Exp}]}, {Automatic, Automatic}},
+   ImagePadding->All,
+   ImageSize->Large,
+   LabelStyle->Directive[
+     GrayLevel[0], Bold, 13],
+   Method->{
+    "OptimizePlotMarkers" -> True, 
+     "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
+         (Identity[#]& )[
+          Part[#, 1]], 
+         (Exp[#]& )[
+          Part[#, 2]]}& ), "CopiedValueFunction" -> ({
+         (Identity[#]& )[
+          Part[#, 1]], 
+         (Exp[#]& )[
+          Part[#, 2]]}& )}},
+   PlotLabel->None,
+   PlotRange->Automatic,
+   PlotRangeClipping->False,
+   PlotRangePadding->{{0, 0}, {0, 0}},
+   Ticks->{Automatic, 
+     Charting`ScaledTicks[{Log, Exp}]}],
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+             AbsoluteThickness[0.1]}}, {9.104979856318357, 
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+        Automatic, {{1.6094379124341003`, 
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+           Directive[
+            AbsoluteThickness[0.1]]}, {3.912023005428146, 
+           Directive[
+            AbsoluteThickness[0.1]]}, {4.605170185988092, 
+           Directive[
+            AbsoluteThickness[0.1]]}, {6.214608098422191, 
+           Directive[
+            AbsoluteThickness[0.1]]}, {6.907755278982137, 
+           Directive[
+            AbsoluteThickness[0.1]]}, {8.517193191416238, 
+           Directive[
+            AbsoluteThickness[0.1]]}}}],
+      GridLinesStyle->Directive[
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+      ImageSize->Large,
+      LabelStyle->Directive[
+        GrayLevel[0], Bold, 13],
+      Method->{
+       "OptimizePlotMarkers" -> True, 
+        "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
+            (Identity[#]& )[
+             Part[#, 1]], 
+            (Exp[#]& )[
+             Part[#, 2]]}& ), "CopiedValueFunction" -> ({
+            (Identity[#]& )[
+             Part[#, 1]], 
+            (Exp[#]& )[
+             Part[#, 2]]}& )}},
+      PlotLabel->None,
+      PlotRange->NCache[{{0.810416666666667, 10.1}, {
+          Log[3], 
+          Log[5000]}}, {{0.810416666666667, 10.1}, {1.0986122886681098`, 
+        8.517193191416238}}],
+      PlotRangeClipping->True,
+      PlotRangePadding->{{
+         Scaled[0.02], 
+         Scaled[0.02]}, {0, 0}},
+      Ticks->{Automatic, 
+        Charting`ScaledTicks[{Log, Exp}]}], Scaled[{0.5, 0.5}], Center, 
+     Scaled[{1, 1}]], InsetBox[
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+       "\"\\!\\(\\*SubscriptBox[\\(\[Rho]\\), \\(221\\)]\\): \
+\\!\\(\\*SubscriptBox[\\(t\\), \\(0\\)]\\)=10 M\"",
+       "\"\\!\\(\\*SubscriptBox[\\(\[Rho]\\), \\(210\\)]\\): \
+\\!\\(\\*SubscriptBox[\\(t\\), \\(0\\)]\\)=15 M\"",
+       "\"\\!\\(\\*SubscriptBox[\\(\[Rho]\\), \\(440\\)]\\): \
+\\!\\(\\*SubscriptBox[\\(A\\), \\(R\\)]\\)~0.1 M\""},
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+      DisplayFunction->(FormBox[
+        StyleBox[
+         StyleBox[
+          PaneBox[
+           TagBox[
+            GridBox[{{
+               TagBox[
+                GridBox[{{
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.5, 0, 0.5], 
+                    Dashing[{0, Small, Small, Small}]], {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.5, 0, 0.5], 
+                    Dashing[{0, Small, Small, Small}]], {}}}, AspectRatio -> 
+                    Full, ImageSize -> {40, 10}, PlotRangePadding -> None, 
+                    ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #}}, 
+                 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"], 
+               TagBox[
+                GridBox[{{
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
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+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.560181, 0.691569, 0.194885]], {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.560181, 0.691569, 0.194885]], {}}}, 
+                    AspectRatio -> Full, ImageSize -> {40, 10}, 
+                    PlotRangePadding -> None, ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}}, 
+                 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"], 
+               TagBox[
+                GridBox[{{
+                   GraphicsBox[{{
+                    Directive[
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+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.772079, 0.431554, 0.102387], 
+                    Dashing[{Small, Small}]], {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.772079, 0.431554, 0.102387], 
+                    Dashing[{Small, Small}]], {}}}, AspectRatio -> Full, 
+                    ImageSize -> {40, 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"], 
+               TagBox[
+                GridBox[{{
+                   GraphicsBox[{{
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.368417, 0.506779, 0.709798]], {
+                    LineBox[{{0, 10}, {40, 10}}]}}, {
+                    Directive[
+                    EdgeForm[
+                    Directive[
+                    Opacity[0.3], 
+                    GrayLevel[0]]], 
+                    PointSize[0.5], 
+                    AbsoluteThickness[1.6], 
+                    RGBColor[0.368417, 0.506779, 0.709798]], {}}}, 
+                    AspectRatio -> Full, ImageSize -> {40, 10}, 
+                    PlotRangePadding -> None, ImagePadding -> Automatic, 
+                    BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}}, 
+                 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], {
+          Directive[
+           GrayLevel[0], Bold, 13], FontFamily -> "Arial"}, Background -> 
+         Automatic, StripOnInput -> False], TraditionalForm]& ),
+      Editable->True,
+      InterpretationFunction:>(RowBox[{"LineLegend", "[", 
+         RowBox[{
+           RowBox[{"{", 
+             RowBox[{
+               RowBox[{"Directive", "[", 
+                 RowBox[{
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+                   ",", 
+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
+                   InterpretationBox[
+                    ButtonBox[
+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    RGBColor[0.5, 0, 0.5], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> 
+                    RGBColor[0.33333333333333337`, 0., 0.33333333333333337`], 
+                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 
+                    1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
+                    Magnification])}]], 
+                    StyleBox[
+                    RowBox[{"RGBColor", "[", 
+                    RowBox[{"0.5`", ",", "0", ",", "0.5`"}], "]"}], 
+                    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`$ColorSelectorInitialColor = 
+                    RGBColor[0.5, 0, 0.5]; 
+                    FrontEnd`Private`$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[0.5, 0, 0.5], Editable -> False, Selectable -> 
+                    False], ",", 
+                   RowBox[{"Dashing", "[", 
+                    RowBox[{"{", 
+                    RowBox[{"0", ",", "Small", ",", "Small", ",", "Small"}], 
+                    "}"}], "]"}]}], "]"}], ",", 
+               RowBox[{"Directive", "[", 
+                 RowBox[{
+                   RowBox[{"PointSize", "[", "0.007333333333333334`", "]"}], 
+                   ",", 
+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
+                   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[{"Directive", "[", 
+                 RowBox[{
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+                   ",", 
+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
+                   InterpretationBox[
+                    ButtonBox[
+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    RGBColor[0.772079, 0.431554, 0.102387], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> 
+                    RGBColor[
+                    0.5147193333333333, 0.28770266666666666`, 
+                    0.06825800000000001], FrameTicks -> None, 
+                    PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 
+                    1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
+                    Magnification])}]], 
+                    StyleBox[
+                    RowBox[{"RGBColor", "[", 
+                    RowBox[{"0.772079`", ",", "0.431554`", ",", "0.102387`"}],
+                     "]"}], 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`$ColorSelectorInitialColor = 
+                    RGBColor[0.772079, 0.431554, 0.102387]; 
+                    FrontEnd`Private`$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[0.772079, 0.431554, 0.102387], Editable -> False,
+                     Selectable -> False], ",", 
+                   RowBox[{"Dashing", "[", 
+                    RowBox[{"{", 
+                    RowBox[{"Small", ",", "Small"}], "}"}], "]"}]}], "]"}], 
+               ",", 
+               RowBox[{"Directive", "[", 
+                 RowBox[{
+                   RowBox[{"PointSize", "[", "0.007333333333333334`", "]"}], 
+                   ",", 
+                   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]}], "]"}]}], "}"}], ",", 
+           RowBox[{"{", 
+             RowBox[{#, ",", #2, ",", #3, ",", #4}], "}"}], ",", 
+           RowBox[{"LegendMarkers", "\[Rule]", 
+             RowBox[{"{", 
+               RowBox[{
+                 RowBox[{"{", 
+                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
+                 RowBox[{"{", 
+                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
+                 RowBox[{"{", 
+                   RowBox[{"False", ",", "Automatic"}], "}"}], ",", 
+                 RowBox[{"{", 
+                   RowBox[{"False", ",", "Automatic"}], "}"}]}], "}"}]}], ",", 
+           RowBox[{"Joined", "\[Rule]", 
+             RowBox[{"{", 
+               RowBox[{"True", ",", "True", ",", "True", ",", "True"}], 
+               "}"}]}], ",", 
+           RowBox[{"LabelStyle", "\[Rule]", 
+             RowBox[{"Directive", "[", 
+               RowBox[{
+                 InterpretationBox[
+                  ButtonBox[
+                   TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> GrayLevel[0.], FrameTicks -> None, 
+                    PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 
+                    1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
+                    Magnification])}]], 
+                    StyleBox[
+                    RowBox[{"GrayLevel", "[", "0", "]"}], 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`$ColorSelectorInitialColor = 
+                    GrayLevel[0]; 
+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
+                    MathLink`CallFrontEnd[
+                    FrontEnd`AttachCell[Typeset`box$, 
+                    FrontEndResource["GrayLevelColorValueSelector"], {
+                    0, {Left, Bottom}}, {Left, Top}, 
+                    "ClosingActions" -> {
+                    "SelectionDeparture", "ParentChanged", 
+                    "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> 
+                   Automatic, Method -> "Preemptive"], 
+                  GrayLevel[0], Editable -> False, Selectable -> False], ",", 
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+           RowBox[{"LegendLayout", "\[Rule]", 
+             RowBox[{"{", 
+               RowBox[{"\"Column\"", ",", "4"}], "}"}]}]}], "]"}]& )], 
+     Scaled[{0.53, 1.0001}], ImageScaled[{0.5, 0}],
+     BaseStyle->{FontSize -> Larger},
+     FormatType->StandardForm]},
+   AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
+   Axes->False,
+   AxesLabel->{None, None},
+   AxesOrigin->{0.810416666666667, 1.0986122886681098`},
+   DisplayFunction->Identity,
+   Frame->False,
+   FrameLabel->{{
+      FormBox[
+      "\"\\!\\(\\*SubscriptBox[\\(\[Rho]\\), \\(Res\\)]\\) for \
+\\!\\(\\*SubscriptBox[\\(\[Tau]\\), \\(sub\\)]\\)\"", TraditionalForm], 
+      None}, {
+      FormBox["\"q\"", TraditionalForm], None}},
+   FrameStyle->Directive[
+     GrayLevel[0], Bold, 20],
+   FrameTicks->{{
+      Charting`ScaledTicks[{Log, Exp}], 
+      Charting`ScaledFrameTicks[{Log, Exp}]}, {Automatic, Automatic}},
+   ImagePadding->All,
+   ImageSize->Large,
+   LabelStyle->Directive[
+     GrayLevel[0], Bold, 13],
+   Method->{
+    "OptimizePlotMarkers" -> True, 
+     "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
+         (Identity[#]& )[
+          Part[#, 1]], 
+         (Exp[#]& )[
+          Part[#, 2]]}& ), "CopiedValueFunction" -> ({
+         (Identity[#]& )[
+          Part[#, 1]], 
+         (Exp[#]& )[
+          Part[#, 2]]}& )}},
+   PlotLabel->None,
+   PlotRange->Automatic,
+   PlotRangeClipping->False,
+   PlotRangePadding->{{
+      Scaled[0.02], 
+      Scaled[0.02]}, {0, 0}},
+   Ticks->{Automatic, 
+     Charting`ScaledTicks[{Log, Exp}]}],
+  InterpretTemplate[Legended[
+    Graphics[{{}, {{{}, {}, {
+         Hue[0.67, 0.6, 0.6], 
+         Directive[
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+          AbsoluteThickness[1.6], 
+          RGBColor[0.5, 0, 0.5], 
+          Dashing[{0, Small, Small, Small}]], 
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+                    StyleBox[
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+                    DefaultBaseStyle -> {}, ButtonFunction :> 
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+                    If[
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+                    AbsoluteCurrentValue["Deployed"]], 
+                    SelectionMove[Typeset`box$, All, Expression]; 
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+                    FrontEnd`Private`$ColorSelectorInitialColor = 
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+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
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+                   RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}], ",", 
+                   InterpretationBox[
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+                    TooltipBox[
+                    GraphicsBox[{{
+                    GrayLevel[0], 
+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
+                    RGBColor[0.560181, 0.691569, 0.194885], 
+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
+                    "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, 
+                    FrameStyle -> 
+                    RGBColor[
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+                    FrameTicks -> None, PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{
+                    Automatic, 
+                    1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
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+                    RowBox[{"0.560181`", ",", "0.691569`", ",", "0.194885`"}],
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+                    BaseStyle -> {}, BaselinePosition -> Baseline, 
+                    DefaultBaseStyle -> {}, ButtonFunction :> 
+                    With[{Typeset`box$ = EvaluationBox[]}, 
+                    If[
+                    Not[
+                    AbsoluteCurrentValue["Deployed"]], 
+                    SelectionMove[Typeset`box$, All, Expression]; 
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+                    FrontEnd`Private`$ColorSelectorInitialColor = 
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+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
+                    MathLink`CallFrontEnd[
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+                    FrontEndResource["RGBColorValueSelector"], {
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+                    RectangleBox[{0, 0}]}, {
+                    GrayLevel[0], 
+                    RectangleBox[{1, -1}]}, {
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+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
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+                    FrameStyle -> 
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+                    PlotRangePadding -> None, ImageSize -> 
+                    Dynamic[{
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+                    1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[
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+                    DefaultBaseStyle -> {}, ButtonFunction :> 
+                    With[{Typeset`box$ = EvaluationBox[]}, 
+                    If[
+                    Not[
+                    AbsoluteCurrentValue["Deployed"]], 
+                    SelectionMove[Typeset`box$, All, Expression]; 
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+                    FrontEnd`Private`$ColorSelectorInitialColor = 
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+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
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+                   InterpretationBox[
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+                    RectangleBox[{0, 0}]}, {
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+                    RectangleBox[{1, -1}]}, {
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+                    RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> 
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+                    DefaultBaseStyle -> {}, ButtonFunction :> 
+                    With[{Typeset`box$ = EvaluationBox[]}, 
+                    If[
+                    Not[
+                    AbsoluteCurrentValue["Deployed"]], 
+                    SelectionMove[Typeset`box$, All, Expression]; 
+                    FrontEnd`Private`$ColorSelectorInitialAlpha = 1; 
+                    FrontEnd`Private`$ColorSelectorInitialColor = 
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+                    FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; 
+                    MathLink`CallFrontEnd[
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+                    FrontEndResource["RGBColorValueSelector"], {
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 }, Open  ]],
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 }, Open  ]],
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 }, Open  ]],
 Cell[CellGroupData[{
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 Cell[CellGroupData[{
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 }, Open  ]],
-Cell[7604645, 140470, 921, 25, 30, "Input",ExpressionUUID->"31c74185-87cf-44d0-9774-1494adec20ed"],
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 Cell[CellGroupData[{
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 }, Open  ]]
 }, Closed]]
 }, Open  ]]
diff --git a/code/mcmc.m b/code/mcmc.m
index 3e77bfa2f362aacfa32065dfade5836fda43edec..154e737f0fd74d7e45bef71b7c2b75fd7d2be65c 100755
--- a/code/mcmc.m
+++ b/code/mcmc.m
@@ -2,7 +2,7 @@
 
 (* Mathematica Package *)
 
-BeginPackage["MCMC`", {"Units`","DataFits`","BBHReduce`","NRTimeSeries`"}];
+BeginPackage["MCMC`"];
 
 MCMC::usage = "MCMC[plogexpr, paramspec, numsteps]