/* start paper.css */
.ptmr8t-x-x-144{font-size:144%;}
.ptmb8t-x-x-144{font-size:144%;  font-weight: bold;}
.ptmb8t-x-x-144{  font-weight: bold;}
.ptmb8t-x-x-144{  font-weight: bold;}
.ptmr8t-x-x-120{font-size:120%;}
.ptmri8t-x-x-120{font-size:120%;font-style: italic;}
.ptmri8t-x-x-120{font-style: italic;}
.ptmb8t-x-x-120{font-size:120%;  font-weight: bold;}
.ptmb8t-x-x-120{  font-weight: bold;}
.ptmb8t-x-x-120{  font-weight: bold;}
.ptmri8t-{font-style: italic;}
.ptmri8t-{font-style: italic;}
.cmtt-10{font-family: monospace,monospace;}
.cmtt-10{font-family: monospace,monospace;}
.ptmr8t-x-x-90{font-size:90%;}
.cmtt-9{font-size:90%;font-family: monospace,monospace;}
.cmtt-9{font-family: monospace,monospace;}
.ptmb8t-{  font-weight: bold;}
.ptmb8t-{  font-weight: bold;}
.ptmb8t-{  font-weight: bold;}
p{margin-top:0;margin-bottom:0}
p.indent{text-indent:0;}
p + p{margin-top:1em;}
p + div, p + pre {margin-top:1em;}
div + p, pre + p {margin-top:1em;}
a { overflow-wrap: break-word; word-wrap: break-word; word-break: break-word; hyphens: auto; }
@media print {div.crosslinks {visibility:hidden;}}
a img { border-top: 0; border-left: 0; border-right: 0; }
center { margin-top:1em; margin-bottom:1em; }
td center { margin-top:0em; margin-bottom:0em; }
.Canvas { position:relative; }
img.math{vertical-align:middle;}
div.par-math-display, div.math-display{text-align:center;}
li p.indent { text-indent: 0em }
li p:first-child{ margin-top:0em; }
li p:last-child, li div:last-child { margin-bottom:0.5em; }
li p~ul:last-child, li p~ol:last-child{ margin-bottom:0.5em; }
.enumerate1 {list-style-type:decimal;}
.enumerate2 {list-style-type:lower-alpha;}
.enumerate3 {list-style-type:lower-roman;}
.enumerate4 {list-style-type:upper-alpha;}
div.newtheorem { margin-bottom: 2em; margin-top: 2em;}
.obeylines-h,.obeylines-v {white-space: nowrap; }
div.obeylines-v p { margin-top:0; margin-bottom:0; }
.overline{ text-decoration:overline; }
.overline img{ border-top: 1px solid black; }
td.displaylines {text-align:center; white-space:nowrap;}
.centerline {text-align:center;}
.rightline {text-align:right;}
pre.verbatim {font-family: monospace,monospace; text-align:left; clear:both; }
.fbox {padding-left:3.0pt; padding-right:3.0pt; text-indent:0pt; border:solid black 0.4pt; }
div.fbox {display:table}
div.center div.fbox {text-align:center; clear:both; padding-left:3.0pt; padding-right:3.0pt; text-indent:0pt; border:solid black 0.4pt; }
div.minipage{width:100%;}
div.center, div.center div.center {text-align: center; margin-left:1em; margin-right:1em;}
div.center div {text-align: left;}
div.flushright, div.flushright div.flushright {text-align: right;}
div.flushright div {text-align: left;}
div.flushleft {text-align: left;}
.underline{ text-decoration:underline; }
.underline img{ border-bottom: 1px solid black; margin-bottom:1pt; }
.framebox-c, .framebox-l, .framebox-r { padding-left:3.0pt; padding-right:3.0pt; text-indent:0pt; border:solid black 0.4pt; }
.framebox-c {text-align:center;}
.framebox-l {text-align:left;}
.framebox-r {text-align:right;}
span.thank-mark{ vertical-align: super }
span.footnote-mark sup.textsuperscript, span.footnote-mark a sup.textsuperscript{ font-size:80%; }
div.tabular, div.center div.tabular {text-align: center; margin-top:0.5em; margin-bottom:0.5em; }
table.tabular td p{margin-top:0em;}
table.tabular {margin-left: auto; margin-right: auto;}
td p:first-child{ margin-top:0em; }
td p:last-child{ margin-bottom:0em; }
div.td00{ margin-left:0pt; margin-right:0pt; }
div.td01{ margin-left:0pt; margin-right:5pt; }
div.td10{ margin-left:5pt; margin-right:0pt; }
div.td11{ margin-left:5pt; margin-right:5pt; }
table[rules] {border-left:solid black 0.4pt; border-right:solid black 0.4pt; }
td.td00{ padding-left:0pt; padding-right:0pt; }
td.td01{ padding-left:0pt; padding-right:5pt; }
td.td10{ padding-left:5pt; padding-right:0pt; }
td.td11{ padding-left:5pt; padding-right:5pt; }
table[rules] {border-left:solid black 0.4pt; border-right:solid black 0.4pt; }
.hline hr, .cline hr{ height : 0px; margin:0px; }
.hline td, .cline td{ padding: 0; }
.hline hr, .cline hr{border:none;border-top:1px solid black;}
.tabbing-right {text-align:right;}
/* div.float, div.figure {margin-left: auto; margin-right: auto;}
div.float img {text-align:center;}
div.figure img {text-align:center;} */
.marginpar,.reversemarginpar {width:20%; float:right; text-align:left; margin-left:auto; margin-top:0.5em; font-size:85%; text-decoration:underline;}
.marginpar p,.reversemarginpar p{margin-top:0.4em; margin-bottom:0.4em;}
.reversemarginpar{float:left;}
table.equation {width:100%;}
.equation td{text-align:center; }
td.equation { margin-top:1em; margin-bottom:1em; }
td.equation-label { width:5%; text-align:center; }
td.eqnarray4 { width:5%; white-space: normal; }
td.eqnarray2 { width:5%; }
table.eqnarray-star, table.eqnarray {width:100%;}
div.eqnarray{text-align:center;}
div.array {text-align:center;}
div.pmatrix {text-align:center;}
table.pmatrix {width:100%;}
span.pmatrix img{vertical-align:middle;}
div.pmatrix {text-align:center;}
table.pmatrix {width:100%;}
span.bar-css {text-decoration:overline;}
table.tabular{border-collapse: collapse; border-spacing: 0;}
img.cdots{vertical-align:middle;}
.partToc a, .partToc, .likepartToc a, .likepartToc {line-height: 200%; font-weight:bold; font-size:110%;}
.chapterToc a, .chapterToc, .likechapterToc a, .likechapterToc, .appendixToc a, .appendixToc {line-height: 200%; font-weight:bold;}
.index-item, .index-subitem, .index-subsubitem {display:block}
div.caption {text-indent:-2em; margin-left:3em; margin-right:1em; text-align:left;}
div.caption span.id{font-weight: bold; white-space: nowrap; }
h1.partHead{text-align: center}
p.bibitem { text-indent: -2em; margin-left: 2em; margin-top:0.6em; margin-bottom:0.6em; }
p.bibitem-p { text-indent: 0em; margin-left: 2em; margin-top:0.6em; margin-bottom:0.6em; }
.paragraphHead, .likeparagraphHead { margin-top:2em; font-weight: bold;}
.subparagraphHead, .likesubparagraphHead { font-weight: bold;}
.verse{white-space:nowrap; margin-left:2em}
div.maketitle {text-align:center;}
h1.titleHead{text-align:center;}
div.maketitle{ margin-bottom: 2em; }
div.author, div.date {text-align:center;}
div.thanks{text-align:left; margin-left:10%; font-size:85%; font-style:italic; }
div.author{white-space: nowrap;}
div.abstract p {margin-left:5%; margin-right:5%;}
div.abstract {width:100%;}
.abstracttitle{text-align:center;margin-bottom:1em;}
/* figure.float, div.figure {margin-left: auto; margin-right: auto;}
figure.float img, figure.figure img {display: block; margin-left: auto; margin-right: auto;}
figure.figure > p {text-align:center;} */
/* figcaption.caption {text-indent:-2em; margin-left:3em; margin-right:1em; text-align:center;}
figcaption.caption span.id{font-weight: bold; white-space: nowrap; } */
.abstract{margin:1em;}
.rotatebox{display: inline-block;}
div.tabular, div.center div.tabular {text-align: center; margin-top:0.5em; margin-bottom:0.5em; }
table.tabular td p{margin-top:0em;}
table.tabular {margin-left: auto; margin-right: auto;}
td p:first-child{ margin-top:0em; }
td p:last-child{ margin-bottom:0em; }
div.td00{ margin-left:0pt; margin-right:0pt; }
div.td01{ margin-left:0pt; margin-right:5pt; }
div.td10{ margin-left:5pt; margin-right:0pt; }
div.td11{ margin-left:5pt; margin-right:5pt; }
table[rules] {border-left:solid black 0.4pt; border-right:solid black 0.4pt; }
td.td00{ padding-left:0pt; padding-right:0pt; }
td.td01{ padding-left:0pt; padding-right:5pt; }
td.td10{ padding-left:5pt; padding-right:0pt; }
td.td11{ padding-left:5pt; padding-right:5pt; }
table[rules] {border-left:solid black 0.4pt; border-right:solid black 0.4pt; }
.hline hr, .cline hr{ height : 0px; margin:0px; }
.hline td, .cline td{ padding: 0; }
.hline hr, .cline hr{border:none;border-top:1px solid black;}
div.array {text-align:center;}
dt.enumerate-enumitem{float:left; clear:left; margin-left:1em; margin-right:1em;}
.uline{ text-decoration:underline; }
.uuline{ text-decoration:underline; }
span.sout {text-decoration: line-through }
span.xout {text-decoration: line-through }
span.uwave {text-decoration:underline }
.lstlisting .label{margin-right:0.5em; }
div.lstlisting{font-family: monospace,monospace; white-space: nowrap; margin-top:0.5em; margin-bottom:0.5em; }
div.lstinputlisting{ font-family: monospace,monospace; white-space: nowrap; }
.lstinputlisting .label{margin-right:0.5em;}
div.algorithmic span.algorithmic{white-space:pre}
div.algorithm table.caption { border-bottom: 1px solid black; margin-bottom:1pt; }
#TBL-2 colgroup{border-left: 1px solid black;border-right:1px solid black;}
#TBL-2{border-collapse:collapse;}
#TBL-2 colgroup{border-left: 1px solid black;border-right:1px solid black;}
#TBL-2{border-collapse:collapse;}
#TBL-2 colgroup{border-left: 1px solid black;border-right:1px solid black;}
#TBL-2{border-collapse:collapse;}
#TBL-2 colgroup{border-left: 1px solid black;border-right:1px solid black;}
#TBL-2{border-collapse:collapse;}
#TBL-2--{vertical-align:top;}
#TBL-2--{vertical-align:top;}
#TBL-2--{vertical-align:top;}
#TBL-2--{vertical-align:top;}
#TBL-2--{vertical-align:top;}
tr#TBL-4-1- td{border-top:0.112em solid}
tr#TBL-4-1- td{border-bottom:0.06999em solid}
tr#TBL-4-11- td{border-bottom:0.112em solid}
/* end paper.css */

/* This CSS is based on: view-source:https://www.bamsoftware.com/papers/thesis/index.html */

.titleHead {
    font-size: 28px;
    font-weight: bold;
    margin-bottom: 40px;
    justify-content: center;
    color: #3F3F3F;
}

.authors {
    display: flex;
    flex-wrap: wrap;
    width: 90%;
    justify-content: center;
    margin-left: auto;
    margin-right: auto;
    margin-bottom: 10px;
}

.author {
    font-weight: normal;
    margin: 0 10px 30px;
}

.author-name {
    font-size: 22px;
    font-weight: bold;
    margin-bottom: 5px;
    color: #3F3F3F;
}

.author-affiliation {
    font-size: 14px;
    font-weight: normal;
    color: #7F7F7F;
}


a {
    text-decoration: none;
    color: dodgerblue;
}
a:visited {
    color: midnightblue;
}
a:hover {
    background-color: lavender;
}

h1, h2, h3 {
    color: #444;
}
h1 a, h2 a, h3 a {
    color: inherit;
    text-decoration: none;
}
h1 a:visited, h2 a:visited, h3 a:visited {
    color: inherit;
}
h1 a:hover, h2 a:hover, h3 a:hover {
    background-color: inherit;
}

hr {
    width: 80%;
}

article {
    width: 75%;
    max-width: 48em;
    font-family: sohne, "Helvetica Neue", Helvetica, Arial, sans-serif;
    text-rendering: optimizeLegibility;
    -webkit-font-smoothing: antialiased;
    /* padding-left: 40px;     */
}
section {
    margin-top: 6em;
}
section section{
    margin-top: 3em;
}
nav {
    margin-top: 0em;
}
section h1, section h2, section h3 {
    font-size: 200%;
}
section section h1, section section h2, section section h3 {
    font-size: 150%;
}
section section section h1, section section section h2, section section section h3 {
    font-size: 100%;
}

/* https://edwardtufte.github.io/tufte-css/ */
aside {
    float: right;
    clear: right;
    width: 20vw;
    margin-right: -22.5vw;

    font-size: 0.8rem;
    padding: 0.5em;
    border-radius: 0 0.4em 0.4em;
    overflow: auto;
}
aside p {
    margin: 0;
}
aside p + p {
    margin-top: 0.5em;
}
.note {
    background-color: powderblue;
}
.erratum {
    background-color: lightcoral;
}

@media(max-width: 620px) {
    body {
        margin-left: 0em;
        margin-right: 0em;
    }
    h1, h2, h3 {
        margin-left: 0em;
    }
    article {
        width: 100%;
    }
    aside {
        float: none;
        clear: none;
        width: auto;
        margin-right: 0;
    }
}

nav ul {
    padding-left: 0;
}
nav ul ul {
    padding-left: 2em;
}
nav li {
    font-weight: bold;
    list-style-type: none;
    margin-top: 0.5em;
}
nav li li {
    font-weight: normal;
    margin-top: 0;
}

dt {
    font-weight: bold;
}
#bibliography dt {
    font-weight: normal;
}

pre {
    background-color: whitesmoke;
    padding: 0.2em;
    overflow: auto;
}

header {
    text-align: center;
}
#titlepage p {
    margin-top: 1em;
}
#abstract h1, #contents h1 {
    font-size: 100%;
}
#abstract header {
    margin-bottom: 2em;
}
#bibliography dt::before {
    content: "[";
}
#bibliography dt::after {
    content: "]";
}
#bibliography dt {
    float: left;
    clear: left;
    width: 3em;
    text-align: right;
}
#bibliography dd {
    margin-left: 4em;
}
#bibliography dt, #bibliography dd {
    padding: 0.4em;
}
#bibliography dt:target + dd {
    background-color: lavender;
}

#index-container {
    display: flex;
    flex-direction: row;
    flex-wrap: wrap;
    align-items: flex-start;
    font-size: 90%;
}
#index-container div {
    flex: 1;
    min-width: 15em;
    padding-right: 1em;
}
#index-container ul {
    padding-left: 2em;
    text-indent: -2em;
}
#index-container li {
    list-style-type: none;
}

td {
    vertical-align: top;
    padding: 0 0.2em;
}

figure img {
    display: block;
    margin-left: auto;
    margin-right: auto;
    max-width: 48em;
    object-fit: contain;
}

@media (min-width: 768px) {
    .figure-img {
        width: 75%; /* Default to 75% for bigger screens */
    }
}

@media (max-width: 768px) {
    .figure-img {
        width: 100%; /* 100% width for screens smaller than 768px */
    }
}



figure table {
    margin: auto;
}
figure.midsize img {
    max-height: 22em;
}
figcaption {
    margin-top: 0.5em;
    font-size: 90%;
}

.lalign {
    text-align: left;
}
.calign {
    text-align: center;
}
.ralign {
    text-align: right;
}
.subdued {
    color: gray;
}
.mbox {
    white-space: nowrap;
}

.cnref {
    font-family: sans-serif;
}

.swatch {
    display: inline-block;
    width: 1em;
    height: 1em;
}

    /* [21] style list numbering as is typical for citation numbering. */
.citation-numbering {
    list-style: citation-numbering-counter-style;
}
@counter-style citation-numbering-counter-style {
    system: extends decimal;
    prefix: "[";
    suffix: "]  ";
}

/* paper */
img {
    width: 100%;
}
th {
    white-space: nowrap;
    background-color: lightgray;
    text-align: center;
}
th, td {
    padding: 0 0.25em;
    border: 1px solid;
    text-align: center;
    vertical-align: middle;
}
table {
    display: inline-block;
    overflow: auto;
    text-align: center;
}
    video {
    max-width: 100%;
    max-height: 100%;
}


img.svg {
    width: auto;
}

.figure {
    width: 100%;
}

.table-container {
    display: inline-block;
    width: 100%; /* Adjust to fit the container */
    overflow-x: auto; /* Enables horizontal scroll */
    overflow-y: hidden; /* Prevent vertical scroll (optional) */
}
.tabular {
    width: auto; /* Adjust to fit the container */
    overflow: auto; /* Enables horizontal scroll */
    /* center the tabular */
    margin-left: auto;
    margin-right: auto;
}
table {
    width: auto; /* Allows the table to size itself based on content */
    margin: 0 auto; /* Centers the table horizontally */
}

.label {
    user-select: none; /* Disable text selection */
    -webkit-user-select: none; /* Safari */
    -moz-user-select: none; /* Firefox */
    -ms-user-select: none; /* Internet Explorer/Edge */
}

.h2 {
    display: block;
}