From 3ff2fc630fffffa04ff28f495a3095d760e5036f Mon Sep 17 00:00:00 2001 From: zeefaad Date: Tue, 5 May 2026 21:20:38 +0200 Subject: [PATCH] =?UTF-8?q?avanc=C3=A9e?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- composants.typ | 502 ++ main.pdf | 10186 ++++++++++++++++++++++++++++++++ main.typ | 363 ++ pres.md | 17 + presentation.pdf | 8966 +++++++++++++++++++++------- presentation.typ | 414 -- src/athena_fidus.jpg | Bin 0 -> 325934 bytes src/athena_fidus.png | Bin 0 -> 12085436 bytes src/athena_fidus_no_text.jpg | Bin 0 -> 314718 bytes src/athena_fidus_not_text.png | Bin 0 -> 9052547 bytes src/construction.jpg | Bin 0 -> 129179 bytes src/construction.png | Bin 0 -> 2430867 bytes src/runcamfpv.png | Bin 0 -> 1123199 bytes src/runcamfpv2.png | Bin 0 -> 285553 bytes 14 files changed, 17847 insertions(+), 2601 deletions(-) create mode 100644 composants.typ create mode 100644 main.pdf create mode 100644 main.typ delete mode 100644 presentation.typ create mode 100644 src/athena_fidus.jpg create mode 100644 src/athena_fidus.png create mode 100644 src/athena_fidus_no_text.jpg create mode 100644 src/athena_fidus_not_text.png create mode 100644 src/construction.jpg create mode 100644 src/construction.png create mode 100644 src/runcamfpv.png create mode 100644 src/runcamfpv2.png diff --git a/composants.typ b/composants.typ new file mode 100644 index 0000000..d0c283f --- /dev/null +++ b/composants.typ @@ -0,0 +1,502 @@ +#import "@preview/polylux:0.4.0": * +#import "@preview/cetz:0.5.0" +#import "@preview/cetz-plot:0.1.3": plot + +#set math.mat(delim: "[") + +// Infos +#let auteur = "Anthony PERRONI" +#let numero = "49871" +#let titre = "Codes LDPC" +#let annee = "2025 - 2026" + +// Template +#let myslide(partie, contenu) = slide[ + // Header + #block(width: 100%, fill: black, inset: (top: 0.6cm, bottom: 0.6cm, left: 1.5cm, right: 1.5cm))[ + #set text(fill: white, size: 28pt, weight: "bold") + #partie + ] + // Contenu + #pad(x: 1.5cm, top: 0.2cm)[ + #set text(size: 20pt) + #contenu + ] + + // Footer + #v(1fr) + #context { + // let cur = counter(page).get().first() + // let tot = counter(page).final().first() + let cur = counter("logical-slide").get().first() + let tot = counter("logical-slide").final().first() + + if cur > 1 { + block(width: 100%, fill: black, inset: (top: 0.2cm, bottom: 0.2cm, left: 1.5cm, right: 1.5cm))[ + #set text(fill: white, size: 12pt, weight: "bold") + #grid( + columns: (1.5fr, 2fr, 1fr, auto), + align: (left, center, center, right), + [#auteur n°#numero], [#titre], [#annee], [#(cur - 1) / #(tot - 1)], + ) + ] + } + } +] + +// Plan +#let design_plan(items) = { + let r = 6pt + let epaisseur = 2pt + let hauteur_ligne = 2.5em + let espace_vertical = 20pt + + pad(left: 1cm, top: 1cm)[ + #block[ + #place(dx: r, dy: hauteur_ligne / 2)[ + #line( + length: (items.len() - 1) * (hauteur_ligne + espace_vertical), + angle: 90deg, + stroke: epaisseur + black, + ) + ] + + #grid( + columns: (2 * r, auto), + column-gutter: 20pt, + row-gutter: espace_vertical, + ..items + .map(item => ( + box(height: hauteur_ligne, align(center + horizon)[ + #circle(radius: r, fill: white, stroke: epaisseur + black) + ]), + box(height: hauteur_ligne, align(left + horizon)[ + #text(weight: "bold", size: 1.1em)[#item] + ]), + )) + .flatten() + ) + ] + ] +} + +// Graphe de Tanner en filigrane +#let graphe_tanner_fond(taille, spread) = { + cetz.canvas(length: taille, { + import cetz.draw: * + + let n_var = 18 + let n_chk = 9 + let var_y = 11 + let chk_y = -8 + + // Calcul automatique pour que le graphe soit centré sur X=0 + let dist_v = (n_var - 1) * spread + let v_start = -dist_v / 2 + let vpos = range(n_var).map(i => (v_start + i * spread, var_y)) + + let spread_c = dist_v / (n_chk - 1) + let c_start = -dist_v / 2 + let cpos = range(n_chk).map(i => (c_start + i * spread_c, chk_y)) + + let edges = ( + (0, 0), + (0, 4), + (0, 8), + (1, 1), + (1, 5), + (1, 0), + (2, 2), + (2, 6), + (2, 1), + (3, 3), + (3, 7), + (3, 2), + (4, 4), + (4, 8), + (4, 3), + (5, 5), + (5, 0), + (5, 4), + (6, 6), + (6, 1), + (6, 5), + (7, 7), + (7, 2), + (7, 6), + (8, 8), + (8, 3), + (8, 7), + (9, 0), + (9, 3), + (9, 6), + (10, 1), + (10, 4), + (10, 7), + (11, 2), + (11, 5), + (11, 8), + (12, 0), + (12, 5), + (12, 7), + (13, 1), + (13, 3), + (13, 8), + (14, 2), + (14, 4), + (14, 6), + (15, 0), + (15, 4), + (15, 7), + (16, 1), + (16, 5), + (16, 8), + (17, 2), + (17, 3), + (17, 6), + ) + + for e in edges { + let vp = vpos.at(e.at(0)) + let cp = cpos.at(e.at(1)) + line((vp.at(0), vp.at(1)), (cp.at(0), cp.at(1)), stroke: 0.45pt + rgb("#e0e0e0")) + } + + for p in vpos { + circle((p.at(0), p.at(1)), radius: 0.25, fill: white, stroke: 0.8pt + rgb("#cccccc")) + } + + for p in cpos { + let (x, y) = p + rect((x - 0.25, y - 0.25), (x + 0.25, y + 0.25), fill: white, stroke: 0.8pt + rgb("#cccccc")) + } + }) +} + +// Schema Shannon +#let canal_shannon_intro() = { + cetz.canvas({ + import cetz.draw: * + + // Styles + let s = (stroke: 2pt + black) + let s_fleche = (stroke: 2pt + black) + let pointe_pleine = (end: "stealth", fill: black) + + let espacement = 5.5 + + // Blocs + content((0, 0), [Source], name: "src", frame: "rect", ..s, padding: .3) + content((espacement, 0), [Emetteur], name: "em", frame: "rect", ..s, padding: .3) + content((espacement * 2, 0), [Canal], name: "chan", frame: "rect", ..s, padding: .3) + content((espacement * 3, 0), [Récepteur], name: "rec", frame: "rect", ..s, padding: .3) + content((espacement * 4, 0), [Destinataire], name: "dest", frame: "rect", ..s, padding: .3) + + // Bruit + content((rel: (0, 1.8), to: "chan"), [Bruit], name: "bruit", frame: "rect", ..s, padding: .3) + + // Codage / Décodage + content((rel: (0, 1), to: "em"), [*Codage*]) + content((rel: (0, 1), to: "rec"), [*Décodage*]) + + // Flèches (On utilise s_fleche et pointe_pleine) + line("src.east", "em.west", mark: pointe_pleine, ..s_fleche) + line("em.east", "chan.west", mark: pointe_pleine, ..s_fleche) + line("chan.east", "rec.west", mark: pointe_pleine, ..s_fleche) + line("rec.east", "dest.west", mark: pointe_pleine, ..s_fleche) + line("bruit.south", "chan.north", mark: pointe_pleine, ..s_fleche) + + // Annotation + let note-style = (size: 0.75em, style: "italic") + content((espacement * 0.5, -0.5), text(..note-style)[Message]) + content((espacement * 1.5, -0.5), text(..note-style)[Signal]) + content((espacement * 2.5, -0.5), text(..note-style)[Signal]) + content((espacement * 3.5, -0.5), text(..note-style)[Message]) + }) +} + +#let plongement_schema() = { + cetz.canvas(length: 1.5cm, { + import cetz.draw: * + + // Styles + let style-pointille = (stroke: (paint: black, thickness: 1.2pt, dash: "dashed")) + let style-point = (fill: black, stroke: none) + let rayon-point = 0.08 + let pointe-fleche = (end: "stealth", fill: black) + + let m = ( + p00: (-4, 0), + p01: (-2, 0), + p11: (-2, -2), + p10: (-4, -2), + ) + + // Arêtes pointillés + line(m.p00, m.p01, m.p11, m.p10, close: true, ..style-pointille) + + // Points sur les sommets + circle(m.p00, radius: rayon-point, ..style-point) + circle(m.p01, radius: rayon-point, ..style-point) + circle(m.p11, radius: rayon-point, ..style-point) + circle(m.p10, radius: rayon-point, ..style-point) + + // Étiquettes + content(m.p00, [00], anchor: "south-east", padding: .2) + content(m.p01, [01], anchor: "south-west", padding: .2) + content(m.p11, [11], anchor: "north-west", padding: .2) + content(m.p10, [10], anchor: "north-east", padding: .2) + + content((-3, -2.6), [$FF_2^2$]) + + line((-1.2, -1), (1.2, -1), mark: pointe-fleche, stroke: 1.5pt + black) + content((0, -0.6), [*Plongement*]) + + // Sommets face arrière + let cb = (p000: (2.5, 0), p001: (4.5, 0), p011: (4.5, -2), p010: (2.5, -2)) + // Sommets face avant (décalés) + let cf = (p100: (3.5, 1), p101: (5.5, 1), p111: (5.5, -1), p110: (3.5, -1)) + + // Arêtes pointillés du cube + line(cb.p000, cb.p001, cb.p011, cb.p010, close: true, ..style-pointille) // Face arrière + line(cf.p100, cf.p101, cf.p111, cf.p110, close: true, ..style-pointille) // Face avant + line(cb.p000, cf.p100, ..style-pointille) // Liaisons + line(cb.p001, cf.p101, ..style-pointille) + line(cb.p011, cf.p111, ..style-pointille) + line(cb.p010, cf.p110, ..style-pointille) + + // Points sur les sommets du cube + circle(cb.p000, radius: rayon-point, ..style-point) + circle(cb.p001, radius: rayon-point, ..style-point) + circle(cb.p011, radius: rayon-point, ..style-point) + circle(cb.p010, radius: rayon-point, ..style-point) + circle(cf.p100, radius: rayon-point, ..style-point) + circle(cf.p101, radius: rayon-point, ..style-point) + circle(cf.p111, radius: rayon-point, ..style-point) + circle(cf.p110, radius: rayon-point, ..style-point) + + // Étiquettes du cube + content(cb.p000, [000], anchor: "south-east", padding: .2) + // content(cb.p001, [001], anchor: "south-west", padding: .2) + content((rel: (-0.85, 0.1), to: cb.p001), [001], anchor: "south-west", padding: .2) + content(cb.p011, [011], anchor: "north-west", padding: .2) + content(cb.p010, [010], anchor: "north-east", padding: .2) + content(cf.p100, [100], anchor: "south-east", padding: .2) + content(cf.p101, [101], anchor: "south-west", padding: .2) + content(cf.p111, [111], anchor: "north-west", padding: .2) + // content(cf.p110, [110], anchor: "north-east", padding: .2) + content((rel: (0.85, -0.1), to: cf.p110), [110], anchor: "north-east", padding: .2) + + content((4, -2.6), [$FF_2^3$]) + }) +} + +#let definition( + titre: "Définition", + accent: black, + titre_taille: 1.13em, + corps_taille: 1.2em, + contenu, +) = { + block( + width: 100%, + fill: rgb("#f8f9fa"), + stroke: 0.5pt + gray.lighten(60%), + radius: 8pt, + clip: true, + + grid( + columns: (5pt, 1fr), + rows: auto, + fill: (col, row) => if col == 0 { accent }, + [], + block( + width: 100%, + inset: (x: 16pt, y: 15pt), + { + { + set text(fill: accent, weight: 800, size: titre_taille, tracking: 0.5pt) + show math.equation: set text(weight: 700, size: 1.05em) + titre + } + v(18pt, weak: true) + { + set text(size: corps_taille) + set par(leading: 0.7em, justify: false) + contenu + } + }, + ), + ), + ) +} + +#let limite_shannon_graphique() = { + let col-shannon = red.darken(10%) + let col-code-long = blue.darken(20%) + let col-code-short = gray.lighten(10%) + set text(size: 11pt) + + move(dx: -5pt, dy: 0pt)[ + #cetz.canvas({ + import cetz.draw: * + + plot.plot( + size: (23, 15), + + // 1. On grossit les labels d'axes (15pt) + x-label: pad(bottom: 30pt)[#move(dy: 80pt)[#text(size: 18pt)[$E_b/N_0$ (dB)]]], + y-label: move(dx: -20pt, dy: -10pt)[#text(size: 18pt)[Bit Error Rate (BER)]], + + x-min: 0, + x-max: 10, + y-min: -8.5, + y-max: 0.2, + x-tick-step: 1, + y-tick-step: 2, + + // Axis + x-format: x => move(dy: 14pt)[#text(size: 16pt)[#x]], + y-format: y => move(dx: -5pt)[#text(size: 16pt)[$10^(#y)$]], + + x-grid: true, + y-grid: true, + + // Légende positionnée en bas. + legend: "north-east", + legend-style: ( + stroke: 0.5pt + gray, + fill: white, + padding: 0.2, + offset: (-161.4pt, -45.1pt), + ), + { + // 1. Limite de Shannon (Asymptote) + plot.add( + ((1.5, -8.5), (1.5, 0.2)), + style: (stroke: (paint: col-shannon, thickness: 2pt, dash: "dashed")), + label: [Limite de Shannon], + ) + + // 2. Petit bloc linéaire (n ≈ 100) - Ultra-densifié (smooth) + plot.add( + ( + (0.0, 0.00), + (0.2, -0.01), + (0.4, -0.03), + (0.6, -0.05), + (0.8, -0.07), + (1.0, -0.10), + (1.2, -0.13), + (1.4, -0.17), + (1.6, -0.21), + (1.8, -0.25), + (2.0, -0.30), + (2.2, -0.36), + (2.4, -0.43), + (2.6, -0.51), + (2.8, -0.60), + (3.0, -0.70), + (3.2, -0.80), + (3.4, -0.91), + (3.6, -1.03), + (3.8, -1.16), + (4.0, -1.30), + (4.2, -1.44), + (4.4, -1.59), + (4.6, -1.75), + (4.8, -1.92), + (5.0, -2.10), + (5.2, -2.28), + (5.4, -2.47), + (5.6, -2.67), + (5.8, -2.88), + (6.0, -3.10), + (6.2, -3.32), + (6.4, -3.55), + (6.6, -3.79), + (6.8, -4.04), + (7.0, -4.30), + (7.2, -4.56), + (7.4, -4.83), + (7.6, -5.11), + (7.8, -5.40), + (8.0, -5.70), + (8.2, -6.00), + (8.4, -6.31), + (8.6, -6.63), + (8.8, -6.96), + (9.0, -7.30), + (9.2, -7.62), + (9.4, -7.95), + (9.6, -8.29), + (9.8, -8.64), + (10.0, -9.00), + ), + style: (stroke: (paint: col-code-short, thickness: 1.5pt)), + label: [Code court ($n approx 100$)], + ) + + // 3. Grand bloc linéaire (n = 64 800) - Ultra-densifié (smooth & waterfall net) + plot.add( + ( + (0.0, 0.0), + (0.2, -0.005), + (0.4, -0.01), + (0.6, -0.02), + (0.8, -0.035), + (1.0, -0.05), + (1.1, -0.07), + (1.2, -0.10), + (1.3, -0.14), + (1.4, -0.20), + (1.45, -0.28), + (1.50, -0.40), + (1.52, -0.45), + (1.54, -0.52), + (1.56, -0.60), + (1.58, -0.69), + (1.60, -0.80), + (1.62, -0.92), + (1.64, -1.05), + (1.66, -1.19), + (1.68, -1.34), + (1.70, -1.50), + (1.72, -1.69), + (1.74, -1.89), + (1.76, -2.11), + (1.78, -2.35), + (1.80, -2.60), + (1.82, -2.88), + (1.84, -3.18), + (1.86, -3.50), + (1.88, -3.84), + (1.90, -4.20), + (1.92, -4.52), + (1.94, -4.86), + (1.96, -5.22), + (1.98, -5.60), + (2.00, -6.00), + (2.02, -6.32), + (2.04, -6.64), + (2.06, -6.94), + (2.08, -7.23), + (2.10, -7.50), + (2.12, -7.66), + (2.14, -7.81), + (2.16, -7.95), + (2.18, -8.08), + (2.20, -8.20), + (2.22, -8.32), + (2.24, -8.44), + (2.25, -8.50), + ), + style: (stroke: (paint: col-code-long, thickness: 3.5pt)), + label: [Code long ($n = 64\,800$)], + ) + }, + ) + }) + ] +} + diff --git a/main.pdf b/main.pdf new file mode 100644 index 0000000..013a1f0 --- /dev/null +++ b/main.pdf @@ -0,0 +1,10186 @@ +%PDF-1.7 +% + +1 0 obj +<< + /Type /Pages + /Count 25 + /Kids [515 0 R 517 0 R 519 0 R 523 0 R 525 0 R 527 0 R 529 0 R 531 0 R 533 0 R 535 0 R 537 0 R 539 0 R 541 0 R 543 0 R 545 0 R 547 0 R 549 0 R 551 0 R 553 0 R 555 0 R 557 0 R 559 0 R 561 0 R 563 0 R 565 0 R] +>> +endobj + +2 0 obj +<< + /Type /StructTreeRoot + /RoleMap << + /Datetime /Span + /Terms /Part + /Title /P + /Strong /Span + /Em /Span + >> + /K [28 0 R] + /ParentTree << + /Nums [0 3 0 R 1 4 0 R 2 5 0 R 3 432 0 R 4 426 0 R 5 6 0 R 6 7 0 R 7 8 0 R 8 9 0 R 9 10 0 R 10 11 0 R 11 12 0 R 12 13 0 R 13 14 0 R 14 15 0 R 15 16 0 R 16 17 0 R 17 18 0 R 18 19 0 R 19 20 0 R 20 21 0 R 21 22 0 R 22 23 0 R 23 24 0 R 24 25 0 R 25 26 0 R 26 27 0 R] + >> + /ParentTreeNextKey 27 +>> +endobj + +3 0 obj +[480 0 R 479 0 R 478 0 R 477 0 R] +endobj + +4 0 obj 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100644 index 74bc37e..0000000 --- a/presentation.typ +++ /dev/null @@ -1,414 +0,0 @@ -#import "@preview/polylux:0.4.0": * -#import "@preview/cetz:0.5.0" - -#set page( - paper: "presentation-4-3", - margin: 0cm, -) - -// Font -#set text( - font: "New Computer Modern", - size: 20pt, - fill: black, -) - -// Infos -#let auteur = "Anthony PERRONI" -#let numero = "49871" -#let titre = "Codes LDPC" -#let annee = "2025 - 2026" - -// Template -#let myslide(partie, contenu) = slide[ - // Header - #block(width: 100%, fill: black, inset: (top: 0.6cm, bottom: 0.6cm, left: 1.5cm, right: 1.5cm))[ - #set text(fill: white, size: 28pt, weight: "bold") - #partie - ] - - // Contenu - #pad(x: 1.5cm, top: 0.2cm)[ - #set text(size: 20pt) - #contenu - ] - - // Footer - #v(1fr) - #context { - let cur = counter(page).get().first() - let tot = counter(page).final().first() - - if cur > 1 { - block(width: 100%, fill: black, inset: (top: 0.2cm, bottom: 0.2cm, left: 1.5cm, right: 1.5cm))[ - #set text(fill: white, size: 12pt, weight: "bold") - #grid( - columns: (1.5fr, 2fr, 1fr, auto), - align: (left, center, center, right), - [#auteur n°#numero], [#titre], [#annee], [#(cur - 1) / #(tot - 1)], - ) - ] - } - } -] - -// Plan -// Plan -#let design_plan(items) = { - let r = 6pt - let epaisseur = 2pt - let hauteur_ligne = 2.5em - let espace_vertical = 20pt - - pad(left: 1cm, top: 1cm)[ - #block[ - #place(dx: r, dy: hauteur_ligne / 2)[ - #line( - length: (items.len() - 1) * (hauteur_ligne + espace_vertical), - angle: 90deg, - stroke: epaisseur + black, - ) - ] - - #grid( - columns: (2 * r, auto), - column-gutter: 20pt, - row-gutter: espace_vertical, // On applique la variable ici - ..items - .map(item => ( - box(height: hauteur_ligne, align(center + horizon)[ - #circle(radius: r, fill: white, stroke: epaisseur + black) - ]), - box(height: hauteur_ligne, align(left + horizon)[ - #text(weight: "bold", size: 1.1em)[#item] - ]), - )) - .flatten() - ) - ] - ] -} - -// Page de garde -#slide[ - #v(1fr) - #align(center)[ - #pad(x: 1.5cm)[ - #text(size: 3em, weight: "bold")[#titre] - #v(0cm) - #text(size: 1.4em)[*#auteur n°#numero*] \ - #v(1cm) - #text(size: 1.1em)[#annee] - ] - ] - #v(1fr) -] - -#myslide("Plan")[ - #design_plan(( - [Introduction], - [Codes linéaires], - [LDPC], - [Codage], - [Décodage], - [Analyse], - )) -] - - -#myslide("Introduction : transmission numérique")[ - // Schema Shannon - #align(center + horizon)[ - #cetz.canvas({ - import cetz.draw: * - - // Styles - let s = (stroke: 2pt + black) - let s_fleche = (stroke: 2pt + black) - let pointe_pleine = (end: "stealth", fill: black) - - let espacement = 5.5 - - // Blocs - content((0, 0), [Source], name: "src", frame: "rect", ..s, padding: .3) - content((espacement, 0), [Emetteur], name: "em", frame: "rect", ..s, padding: .3) - content((espacement * 2, 0), [Canal], name: "chan", frame: "rect", ..s, padding: .3) - content((espacement * 3, 0), [Récepteur], name: "rec", frame: "rect", ..s, padding: .3) - content((espacement * 4, 0), [Destinataire], name: "dest", frame: "rect", ..s, padding: .3) - - // Bruit - content((rel: (0, 1.8), to: "chan"), [Bruit], name: "bruit", frame: "rect", ..s, padding: .3) - - // Codage / Décodage - content((rel: (0, 1), to: "em"), [*Codage*]) - content((rel: (0, 1), to: "rec"), [*Décodage*]) - - // Flèches (On utilise s_fleche et pointe_pleine) - line("src.east", "em.west", mark: pointe_pleine, ..s_fleche) - line("em.east", "chan.west", mark: pointe_pleine, ..s_fleche) - line("chan.east", "rec.west", mark: pointe_pleine, ..s_fleche) - line("rec.east", "dest.west", mark: pointe_pleine, ..s_fleche) - line("bruit.south", "chan.north", mark: pointe_pleine, ..s_fleche) - - // Annotation - let note-style = (size: 0.75em, style: "italic") - content((espacement * 0.5, -0.5), text(..note-style)[Message]) - content((espacement * 1.5, -0.5), text(..note-style)[Signal]) - content((espacement * 2.5, -0.5), text(..note-style)[Signal]) - content((espacement * 3.5, -0.5), text(..note-style)[Message]) - }) - ] - #v(5cm) - image de mon drone FPV, 5G -] - -#myslide("Problématique")[ - #align(center)[ - Comment utiliser les codes LDPC pour garantir la fiabilité d'une transmission en présence de - bruit ? - ] -] - -#myslide("Définition : Codes Linéaires")[ - $cal(C)$ de paramètres $(n, k) in NN^2$, ($n > k$) - - // $Phi : & FF_2^k --> FF_2^n \ - // & x arrow.long.bar Phi(x) = c$ - // $Phi : #box(baseline: 1.6em)[$ cases( - // delim: "|", - // bb(F)_2^k & arrow bb(F)_2^n, - // x & arrow.long.bar Phi(x) - // ) $]$ - - // $Phi$ linéaire et injective - - Espace des messages : $FF_2^k$\ - Espace des mots transmis :$FF_2^n$ - - Redondance de $n - k$ bits - - Rendement $display(R = k / n)$ - - #align(center)[ - #cetz.canvas(length: 1.5cm, { - import cetz.draw: * - - // Styles - let style-pointille = (stroke: (paint: black, thickness: 1.2pt, dash: "dashed")) - let style-point = (fill: black, stroke: none) - let rayon-point = 0.08 - let pointe-fleche = (end: "stealth", fill: black) - - let m = ( - p00: (-4, 0), - p01: (-2, 0), - p11: (-2, -2), - p10: (-4, -2), - ) - - // Arêtes pointillés - line(m.p00, m.p01, m.p11, m.p10, close: true, ..style-pointille) - - // Points sur les sommets - circle(m.p00, radius: rayon-point, ..style-point) - circle(m.p01, radius: rayon-point, ..style-point) - circle(m.p11, radius: rayon-point, ..style-point) - circle(m.p10, radius: rayon-point, ..style-point) - - // Étiquettes - content(m.p00, [00], anchor: "south-east", padding: .2) - content(m.p01, [01], anchor: "south-west", padding: .2) - content(m.p11, [11], anchor: "north-west", padding: .2) - content(m.p10, [10], anchor: "north-east", padding: .2) - - content((-3, -3), [$FF_2^2$]) - - line((-1.2, -1), (1.2, -1), mark: pointe-fleche, stroke: 1.5pt + black) - content((0, -0.6), [*Plongement*]) - - // Sommets face arrière - let cb = (p000: (2.5, 0), p001: (4.5, 0), p011: (4.5, -2), p010: (2.5, -2)) - // Sommets face avant (décalés) - let cf = (p100: (3.5, 1), p101: (5.5, 1), p111: (5.5, -1), p110: (3.5, -1)) - - // Arêtes pointillés du cube - line(cb.p000, cb.p001, cb.p011, cb.p010, close: true, ..style-pointille) // Face arrière - line(cf.p100, cf.p101, cf.p111, cf.p110, close: true, ..style-pointille) // Face avant - line(cb.p000, cf.p100, ..style-pointille) // Liaisons - line(cb.p001, cf.p101, ..style-pointille) - line(cb.p011, cf.p111, ..style-pointille) - line(cb.p010, cf.p110, ..style-pointille) - - // Points sur les sommets du cube - circle(cb.p000, radius: rayon-point, ..style-point) - circle(cb.p001, radius: rayon-point, ..style-point) - circle(cb.p011, radius: rayon-point, ..style-point) - circle(cb.p010, radius: rayon-point, ..style-point) - circle(cf.p100, radius: rayon-point, ..style-point) - circle(cf.p101, radius: rayon-point, ..style-point) - circle(cf.p111, radius: rayon-point, ..style-point) - circle(cf.p110, radius: rayon-point, ..style-point) - - // Étiquettes du cube - content(cb.p000, [000], anchor: "south-east", padding: .2) - content(cb.p001, [001], anchor: "south-west", padding: .2) - content(cb.p011, [011], anchor: "north-west", padding: .2) - content(cb.p010, [010], anchor: "north-east", padding: .2) - content(cf.p100, [100], anchor: "south-east", padding: .2) - content(cf.p101, [101], anchor: "south-west", padding: .2) - content(cf.p111, [111], anchor: "north-west", padding: .2) - content(cf.p110, [110], anchor: "north-east", padding: .2) - - content((4, -3), [$FF_2^3$]) - }) - ] - -] - -// #myslide("Définition : Codes Linéaires")[ -// // Matrice génératrice : $op("Mat")_cal(B)(Phi) = G in cal(M)_(k, n)(FF_2)$, $op("rg")(G) = k$ -// -// // $cal(C) = op("Im")(Phi) = {x G | x in FF_2^k}$ -// -// Forme bilinéaire symétrique : -// $forall x, y in FF_2^n, space (x|y)_(FF_2^n) = display(sum_(i=0)^n x_i y_i)$ -// -// Encodage : -// $Phi : #box(baseline: 1.6em)[$ cases( -// delim: "|", -// FF_2^k & -> FF_2^n, -// x & arrow.long.bar Phi(x) -// ) $]$ -// -// $Phi in cal(L)(FF_2^k, FF_2^n)$, $op("rg")(Phi) = k$, $Phi$ injective -// -// $cal(C) = op("Im")(Phi)$ -// -// $G = op("Mat")_cal(B)(Phi) in cal(M)_(k,n)(FF_2)$ -// Pour $x in FF_2^k, Phi(x) = x G$ -// -// $Phi$ admet un unique adjoint $Phi^*$, -// $ -// forall x in FF_2^k, forall y in FF_2^n, (Phi(x) | y)_(FF_2^n) = (x, Phi(y)^*)_(FF_2^k) -// $ -// de plus $cal(C)^bot = op("Im")(Phi)^bot = ker(Phi^*)$ et $dim(cal(C)^bot) = n - k$ -// -// Equation du code dual : $y in cal(C^bot) <==> Phi(y)^* = 0 <==> y G^T = 0$ -// -// De plus $display((cal(C)^bot)^bot) = cal(C)$ (car non dégénérée) -// -// -// ] -// -// #myslide("Définition : Codes Linéaires")[ -// -// $(h_1, ..., h_(n-k))$ base de $cal(C)^bot$ -// Définisson $H in cal(M)_(n-k, n)(FF_2)$ avec les $h_i$ comme lignes -// $H$ : matrice de contrôle de parité -// -// $forall c in FF_2^n, c in cal(C) <==> c H^T = 0$ -// -// $S : #box(baseline: 1.6em)[$ cases( -// delim: "|", -// FF_2^n & -> FF_2^(n-k), -// y & arrow.long.bar y H^T -// ) $]$ -// et $ker(S) = cal(C)$ ... -// -// ] - -#myslide("Définition : Codes Linéaires")[ - faire un truc plus theoriques... -] - -#myslide("Définition : Codes Linéaires")[ - - Matrice génératrice - - $G in cal(M)_(k,n)(FF_2)$ - - - Encodage : $m in FF_2^k, c = m dot.o G$ - - - Forme systématique : $G = [I_k | P]$ avec $P$ matrice de parité - - - Matrice de contrôle de parité $H = [- P^top | I_(n-k)]$ - $c in FF_2^n$ est un mot de code valide $<==>$ $c^top dot.o H = 0$ - - De plus $G dot.o H^T = 0$ -] - -#myslide("Définition : Codes Linéaires")[ - Reception de $r = c + e$ avec $c in cal(C), e in FF_2^n$ - $r^top dot.o H = s$ le syndrome - - $(c + e)^top H = c^top H + e^top H = e^top H$ -] - -#myslide("Redondance et limite théorique")[ - Graphique waterfall avec n = 100 et n = 64800 avec limite de Shannon, $display(R = k /n) < 1$, $m = n - k$ - - Bande passante... - - Il existe $C$ pour un canal tel que pour $R < C$ on peut atteindre une probabilité d'erreur nulle. - $=>$ gros bloc (moyenne du bruit aléatoire) -] - -#myslide("Décodage par Maximum de Vraisemblance")[ - Trouver le message envoyer le + probable sachant le message recu : NP-COMPLET (Max) - Decodage par syndrome d'une code lin'aire général est NP-Complet - Complexité $O(2^k)$ -] - -#myslide("LDPC")[ - Matrice $H$ clairsemée(low density) donc complexité mointre, pas de produit de matrice mais algorithme itératif efficace quasi linéaire - Graphique d'un H très grand clairesemée avec plein de 0, généré en rust par exemple où les 1 sont des points noir et le reste du blanc - Défniition avec (w_r,w_c) -] - -#myslide("Graphe de Tanner")[ - Il existe un isomorphisme entre H et le Graphe de Tanner - Graphe de tanner (cetz) - Contrainte de somme nulle -] - -#myslide("Encodage")[ -] - -#myslide("Décodage")[ - Canal d'étude (AWGN) analogique, tension etc, ce qui se passe en radio dans les cables etc -] - -#myslide("Hard decoding")[ - Nul (0 ou 1) - transition perte d'information -] - -#myslide("Implementation")[ - -] - -#myslide("Soft decoding")[ - belief propagation, log ou virgule fixe, explication resultat meilleur -] - -#myslide("Implementation")[ - -] - -#myslide("Test")[ - Irl hackrf, test de diff de debit avec des paquets -] - -#myslide("Image")[ - Test de transmission d'image avec différent ldpc non opti et opti (le H) -] - -#myslide("Annexe")[ - Annexe -] - -#myslide("Théorie deriere la définition des codes linaires")[ - Poser les notations algebriques -] -#myslide("Unicité de l'adjoint")[ - Unicité de l'adjoint pour une forme bilinéaire symétrique non dégénérée. -] diff --git a/src/athena_fidus.jpg b/src/athena_fidus.jpg new file mode 100644 index 0000000000000000000000000000000000000000..bc20727c88d5beb81d5c60490418871e414d018c GIT binary patch literal 325934 zcmb5WcU)6V*EYHdL5d>1BSuIB5{lBR2BalO3lKUgy-4pU8c>uj1Oif(P6&u}sUl5^ z^dcZ|3(~=cV8M2F(EEL!_nhtF%VCUrFWE0@w<`EJUfQf0M#1IHE6BYF{nwQO;oi3T%*?5FzMtb-q2iVv} z*WXFbE2LCXTnVlH%_Yw>%P2+Eo6raf35kh_8KO{zMc#JaMgQ0Iy8~cjI7VRDp`{T9 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Modern", + size: 20pt, + fill: black, +) +#set math.mat(delim: "[") + +// Page de garde +#slide[ + #place(center + horizon)[ + #graphe_tanner_fond(1cm, 1.5) + ] + #v(1fr) + #align(center + horizon)[ + #pad(x: 2cm)[ + #text(size: 3em, weight: "bold", fill: black)[#titre] + + #text(size: 1.2em, weight: "bold", fill: black)[#auteur] + + #h(0.5em) + + #text(size: 1.2em, fill: black)[n°#numero] + + #text(size: 0.95em, fill: black)[#annee] + ] + ] + #v(1fr) +] + +#myslide("Plan")[ + #design_plan(( + [Introduction], + [Codes linéaires], + [LDPC], + [Codage], + [Décodage], + [Analyse], + )) +] + +#myslide("Introduction : Transmission Numérique")[ + #align(center + horizon)[ + #canal_shannon_intro() + ] +] + +#myslide("Introduction : Utilisation")[ + #align(center + horizon)[ + #grid( + columns: (1.5fr, 1.5fr), + gutter: 1.5cm, + align: center + horizon, + [ + #box(width: 80%)[ + #stack( + dir: ttb, + spacing: -0.5em, + image("src/athena_fidus_no_text.jpg", width: 100%), + align(left)[ + #box( + inset: (x: 5pt, y: 0pt), + text(size: 0.45em, fill: white)[* https://gallery.ariane.group *], + ) + ], + ) + ] + #v(0.5em) + Athena-Fidus + ], + [ + #box(width: 80%)[ + #stack( + dir: ttb, + spacing: -0.5em, + image("src/runcamfpv2.png", width: 100%), + align(left)[ + #box( + inset: (x: 5pt, y: 0pt), + text(size: 0.45em, fill: white)[* https://www.runcam.com/ *], + ) + ], + ) + ] + #v(0.5em) + Module OpenIPC + ], + ) + ] +] + +#myslide("Problématique")[ + #place(center + horizon, dy: 8.1cm)[#graphe_tanner_fond(0.9cm, 1.75)] + #place(center + horizon, dy: 7.7cm)[ + #block(width: 100%)[ + #text(size: 1.2em, weight: "bold", fill: black)[ + Comment utiliser les codes LDPC pour garantir la fiabilité d'une transmission en présence de bruit ? + ] + ] + ] +] + +#myslide("Définition : Codes Linéaires en Bloc")[ + #definition(titre: [Code $display((n,k) in NN^2)$])[ + $cal(C)$ sous-espace vectoriel de dimension $k$ de $FF_2^n$ + ] + + #[ + #set text(size: 1.1em) + - $k$ : longueur du message original + - $n$ : longueur du mot de code + - $m = n - k$ : nombre de bits de parités + ] + + #definition(titre: "Encodage")[ + $Phi : FF_2^k & -> FF_2^n in cal(L)(FF_2^k, FF_2^n)$ + ] + + #v(-1.3em) + + #uncover(2)[ + #align(center + horizon)[ + #plongement_schema() + ] + ] +] + +#myslide("Définition: Matrice Génératrice")[ + #definition(titre: "Matrice Génératrice")[ + $G in cal(M)_(k,n)(FF_2)$ dont les lignes sont une base de $cal(C)$ + ] + + #definition(titre: "Encodage")[ + Pour un message $u in FF_2^k$ le mot de code $c in cal(C)$ est : + $ + c = Phi(u) = u dot.o G + $ + ] + + #definition(titre: "Forme systématique")[ + $ + G = mat( + I_k, P; + augment: #1, + delim: "[", + ) + $ + ] + + #[ + #set text(size: 1.2em) + - Pour $u in FF_2^k, space display(u dot.o G = mat(u, u dot.o P; augment: #1, delim: "[",))$ + + - $P in cal(M)_(k ,(n-k))(FF_2)$ matrice de parité\ + ] +] + +#myslide("Défniition: Matrice de Contrôle")[ + #definition(titre: "Matrice de Contrôle")[ + $ + H = mat( + P^top, I_(n-k); + augment: #1, + delim: "[", + ) + $ + ] + #[ + #set text(size: 1.2em) + - $cal(C) = ker(H) = {v in FF_2^n | H dot.o v^top = 0}$ + + - $display(G dot.o H^top = 0)$ + ] + + #definition(titre: "Syndrome")[ + Pour un vecteur reçu $r = c + e, space s in FF_2^(n - k)$ + $ + s = H r^top = H c^top + H e^top = 0 + H e^top + $ + ] + #[ + #set text(size: 1.2em) + - Si $s = 0, space r$ est un mot de code valide + - Sinon s donne la signature de l'erreur $e$ + ] + // Possible décodage par syndrome +] + +#myslide("Exemple d'un code linéaire")[ + #[ + #set text(size: 1.1em) + #let col-u = blue + #let col-p = orange + + + #underline(offset: 3pt)[Exemple d'un code $(5,2)$] + + + - On choisit la matrice de parité $P$ : + $ + P = #math.mat( + (text(fill: col-p)[1], text(fill: col-p)[1], text(fill: col-p)[0]), + (text(fill: col-p)[0], text(fill: col-p)[1], text(fill: col-p)[1]), + ) + $ + + - Alors la matrice génératrice $G$ est : + $ + G = #math.mat( + (text(fill: col-u)[1], text(fill: col-u)[0], text(fill: col-p)[1], text(fill: col-p)[1], text(fill: col-p)[0]), + (text(fill: col-u)[0], text(fill: col-u)[1], text(fill: col-p)[0], text(fill: col-p)[1], text(fill: col-p)[1]), + augment: 2, + ) + $ + + - Message $display(u = #math.mat((text(fill: col-u)[1], text(fill: col-u)[1])))$ + + - Mot de code $c = u G$ : + $ + c = #math.mat((text(fill: col-u)[1], text(fill: col-u)[1])) + #math.mat( + (text(fill: col-u)[1], text(fill: col-u)[0], text(fill: col-p)[1], text(fill: col-p)[1], text(fill: col-p)[0]), + (text(fill: col-u)[0], text(fill: col-u)[1], text(fill: col-p)[0], text(fill: col-p)[1], text(fill: col-p)[1]), + augment: 2, + ) + = + #math.mat(( + text(fill: col-u)[1], + text(fill: col-u)[1], + text(fill: col-p)[1], + text(fill: col-p)[0], + text(fill: col-p)[1], + )) + $ + ] +] + +#myslide("Exemple d'une code linéaire")[ + #[ + #set math.mat(delim: "[") + #let colu = blue + #let colp = orange + + #v(0.5em) + + #set text(size: 1.1em) + Enfin + + $ + H = #math.mat( + (text(fill: colp)[1], text(fill: colp)[0], 1, 0, 0), + (text(fill: colp)[1], text(fill: colp)[1], 0, 1, 0), + (text(fill: colp)[0], text(fill: colp)[1], 0, 0, 1), + augment: 2, + ) + $ + + #v(0.8em) + + Vérification du mot de code $display(c = mat(#text(fill: colu)[1], #text(fill: colu)[1], #text(fill: colp)[1], #text(fill: colp)[0], #text(fill: colp)[1]))$ + + #v(0.8em) + + $ + H c^top = mat( + 1, 0, 1, 0, 0; + 1, 1, 0, 1, 0; + 0, 1, 0, 0, 1 + ) mat(#text(fill: colu)[1], #text(fill: colu)[1], #text(fill: colp)[1], #text(fill: colp)[0], #text(fill: colp)[1])^top + = mat( + 1 plus.o 0 plus.o 1 plus.o 0 plus.o 0; + 1 plus.o 1 plus.o 0 plus.o 0 plus.o 0; + 0 plus.o 1 plus.o 0 plus.o 0 plus.o 1 + ) + = mat(0; 0; 0) + $ + ] +] + +// A REMPLACER AVEC DE VRAI DONNE SUR DE VRAI CODE LDPC ET HAMMING PAR EXEMPLE +#myslide("Approcher la Limite de Shannon")[ + #limite_shannon_graphique() + +] + +// #myslide("Redondance et limite théorique")[ +// Graphique waterfall avec n = 100 et n = 64800 avec limite de Shannon, $display(R = k /n) < 1$, $m = n - k$ +// +// Bande passante... +// +// Il existe $C$ pour un canal tel que pour $R < C$ on peut atteindre une probabilité d'erreur nulle. +// $=>$ gros bloc (moyenne du bruit aléatoire) +// ] + +#myslide("Décodage par Maximum de Vraisemblance")[ + Trouver le message envoyer le + probable sachant le message recu : NP-COMPLET (Max) + Decodage par syndrome d'une code lin'aire général est NP-Complet + Complexité $O(2^k)$ +] + +#myslide("LDPC")[ + Matrice $H$ clairsemée(low density) donc complexité mointre, pas de produit de matrice mais algorithme itératif efficace quasi linéaire + Graphique d'un H très grand clairesemée avec plein de 0, généré en rust par exemple où les 1 sont des points noir et le reste du blanc + Défniition avec (w_r,w_c) +] + +#myslide("Graphe de Tanner")[ + Il existe un isomorphisme entre H et le Graphe de Tanner + Graphe de tanner (cetz) + Contrainte de somme nulle +] + +#myslide("Encodage")[ +] + +#myslide("Décodage")[ + Canal d'étude (AWGN) analogique, tension etc, ce qui se passe en radio dans les cables etc +] + +#myslide("Hard decoding")[ + Nul (0 ou 1) + transition perte d'information +] + +#myslide("Implementation")[ + +] + +#myslide("Soft decoding")[ + belief propagation, log ou virgule fixe, explication resultat meilleur +] + +#myslide("Implementation")[ + +] + +#myslide("Test")[ + Irl hackrf, test de diff de debit avec des paquets +] + +#myslide("Image")[ + Test de transmission d'image avec différent ldpc non opti et opti (le H) +] + +#myslide("Annexe")[ + #align(center + horizon)[ + Annexe + ] + #align(center + horizon)[ + #image("src/construction.jpg", width: 80%) + ] +] + +#myslide("Théorie deriere la définition des codes linaires")[ + Poser les notations algebriques etc... +] diff --git a/pres.md b/pres.md index be20203..eb221f3 100644 --- a/pres.md +++ b/pres.md @@ -36,6 +36,23 @@ Linéarité => decodage par syndrome Ajouter de la redondance coûte cher en débit, c'est ce que l'on appelle l'overhead. Pour garder un débit élevé tout en corrigeant beaucoup d'erreurs, la solution est d'utiliser des codes de très grande taille. En augmentant la longueur du bloc N, nous permettons au décodeur de traiter l'information de manière statistique et de nous approcher très près de la capacité limite du canal. ## 2 La correction d'erreur n'est pas gratuite : elle se paie en débit. Pour ne pas gaspiller de bande passante tout en restant fiable, la théorie de Shannon nous montre qu'il faut utiliser des codes de très grande taille. Un bloc long permet de mieux diluer l'impact du bruit. C'est pour cette raison que les standards modernes (5G, Wi-Fi) utilisent des codes LDPC massifs : ils offrent le meilleur ratio 'correction / sacrifice de débit' possible à ce jour. +## 3 +Pourquoi des codes “longs” ? +• Moyennage du bruit : Plus le +bloc est grand, plus le bruit +aléatoire du canal se rapproche de +sa moyenne statistique (Loi des +Grands Nombres). +• Phénomène de Waterfall : Pour +les grands 𝑛, on observe une chute +brutale de la probabilité d’erreur à +un seuil précis. +• Convergence : Shannon a prouvé +que la capacité 𝐶 n’est atteinte +que lorsque 𝑛⟶∞. +• Standard DVB-S2 : Utilise 𝑛= +64, 800 pour être à moins de 1 dB +de la limite théorique. # MDL ## 1 diff --git a/presentation.pdf b/presentation.pdf index 523c727..be2671f 100644 --- a/presentation.pdf +++ b/presentation.pdf @@ -4,8 +4,8 @@ 1 0 obj << /Type /Pages - /Count 23 - /Kids [362 0 R 364 0 R 366 0 R 368 0 R 370 0 R 372 0 R 374 0 R 376 0 R 378 0 R 380 0 R 382 0 R 384 0 R 386 0 R 388 0 R 390 0 R 392 0 R 394 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180 0 R 180 0 R 180 0 R 179 0 R 179 0 R 179 0 R 178 0 R 178 0 R 178 0 R 177 0 R 177 0 R 177 0 R 176 0 R 176 0 R 176 0 R 176 0 R 176 0 R 175 0 R 175 0 R 174 0 R 174 0 R 174 0 R 174 0 R 174 0 R 174 0 R 174 0 R 174 0 R 173 0 R 172 0 R 170 0 R 168 0 R 166 0 R] endobj 15 0 obj -[136 0 R 135 0 R 133 0 R 131 0 R 129 0 R] +[163 0 R 163 0 R 163 0 R 163 0 R 162 0 R 162 0 R 162 0 R 162 0 R 162 0 R 161 0 R 159 0 R 157 0 R 155 0 R] endobj 16 0 obj -[126 0 R 126 0 R 126 0 R 125 0 R 123 0 R 121 0 R 119 0 R] +[152 0 R 152 0 R 151 0 R 150 0 R 150 0 R 150 0 R 150 0 R 149 0 R 147 0 R 145 0 R 143 0 R] endobj 17 0 obj -[116 0 R 116 0 R 115 0 R 113 0 R 111 0 R 109 0 R] +[140 0 R 140 0 R 140 0 R 139 0 R 137 0 R 135 0 R 133 0 R] endobj 18 0 obj -[106 0 R 105 0 R 103 0 R 101 0 R 99 0 R] +[130 0 R 129 0 R 127 0 R 125 0 R 123 0 R] endobj 19 0 obj -[96 0 R 96 0 R 95 0 R 93 0 R 91 0 R 89 0 R] +[120 0 R 120 0 R 120 0 R 119 0 R 117 0 R 115 0 R 113 0 R] endobj 20 0 obj -[86 0 R 85 0 R 83 0 R 81 0 R 79 0 R] +[110 0 R 110 0 R 109 0 R 107 0 R 105 0 R 103 0 R] endobj 21 0 obj -[76 0 R 76 0 R 75 0 R 73 0 R 71 0 R 69 0 R] +[100 0 R 99 0 R 97 0 R 95 0 R 93 0 R] endobj 22 0 obj -[66 0 R 66 0 R 65 0 R 63 0 R 61 0 R 59 0 R] +[90 0 R 90 0 R 89 0 R 87 0 R 85 0 R 83 0 R] endobj 23 0 obj -[56 0 R 56 0 R 55 0 R 53 0 R 51 0 R 49 0 R] +[80 0 R 79 0 R 77 0 R 75 0 R 73 0 R] endobj 24 0 obj -[46 0 R 46 0 R 45 0 R 43 0 R 41 0 R 39 0 R] +[70 0 R 70 0 R 69 0 R 67 0 R 65 0 R 63 0 R] endobj 25 0 obj -[36 0 R 36 0 R 35 0 R 33 0 R 31 0 R 29 0 R] +[60 0 R 60 0 R 59 0 R 57 0 R 55 0 R 53 0 R] endobj 26 0 obj -<< - /Type /StructElem - /S /Document - /P 2 0 R - /K [335 0 R 333 0 R 332 0 R 331 0 R 312 0 R 303 0 R 302 0 R 301 0 R 300 0 R 299 0 R 290 0 R 289 0 R 288 0 R 279 0 R 278 0 R 274 0 R 271 0 R 269 0 R 267 0 R 266 0 R 265 0 R 264 0 R 263 0 R 262 0 R 253 0 R 252 0 R 243 0 R 242 0 R 238 0 R 236 0 R 219 0 R 215 0 R 213 0 R 204 0 R 203 0 R 199 0 R 197 0 R 188 0 R 187 0 R 184 0 R 183 0 R 179 0 R 170 0 R 169 0 R 168 0 R 159 0 R 158 0 R 157 0 R 156 0 R 147 0 R 146 0 R 137 0 R 136 0 R 127 0 R 126 0 R 117 0 R 116 0 R 107 0 R 106 0 R 97 0 R 96 0 R 87 0 R 86 0 R 77 0 R 76 0 R 67 0 R 66 0 R 57 0 R 56 0 R 47 0 R 46 0 R 37 0 R 36 0 R 27 0 R] ->> +[50 0 R 49 0 R 48 0 R 47 0 R 45 0 R 43 0 R 41 0 R] endobj 27 0 obj -<< - /Type /StructElem - /S /Div - /P 26 0 R - /K [34 0 R 32 0 R 30 0 R 28 0 R] ->> +[38 0 R 38 0 R 37 0 R 35 0 R 33 0 R 31 0 R] endobj 28 0 obj << /Type /StructElem - /S /Div - /P 27 0 R - /K [29 0 R] + /S /Document + /P 2 0 R + /K [476 0 R 457 0 R 448 0 R 447 0 R 446 0 R 445 0 R 436 0 R 435 0 R 422 0 R 413 0 R 412 0 R 403 0 R 402 0 R 393 0 R 380 0 R 374 0 R 365 0 R 364 0 R 355 0 R 342 0 R 336 0 R 335 0 R 334 0 R 333 0 R 332 0 R 331 0 R 322 0 R 321 0 R 314 0 R 306 0 R 301 0 R 290 0 R 281 0 R 280 0 R 275 0 R 264 0 R 257 0 R 248 0 R 239 0 R 238 0 R 234 0 R 229 0 R 228 0 R 223 0 R 222 0 R 211 0 R 210 0 R 201 0 R 200 0 R 199 0 R 198 0 R 196 0 R 195 0 R 186 0 R 185 0 R 184 0 R 183 0 R 182 0 R 181 0 R 180 0 R 179 0 R 178 0 R 177 0 R 176 0 R 175 0 R 174 0 R 173 0 R 164 0 R 163 0 R 162 0 R 153 0 R 152 0 R 151 0 R 150 0 R 141 0 R 140 0 R 131 0 R 130 0 R 121 0 R 120 0 R 111 0 R 110 0 R 101 0 R 100 0 R 91 0 R 90 0 R 81 0 R 80 0 R 71 0 R 70 0 R 61 0 R 60 0 R 51 0 R 50 0 R 49 0 R 48 0 R 39 0 R 38 0 R 29 0 R] >> endobj 29 0 obj << /Type /StructElem - /S /Span + /S /Div /P 28 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [5] - /Pg 406 0 R + /K [36 0 R 34 0 R 32 0 R 30 0 R] >> endobj @@ -164,7 +149,7 @@ endobj << /Type /StructElem /S /Div - /P 27 0 R + /P 29 0 R /K [31 0 R] >> endobj @@ -178,8 +163,8 @@ endobj /O /Layout /Placement /Block >>] - /K [4] - /Pg 406 0 R + /K [5] + /Pg 561 0 R >> endobj @@ -187,7 +172,7 @@ endobj << /Type /StructElem /S /Div - /P 27 0 R + /P 29 0 R /K [33 0 R] >> endobj @@ -201,8 +186,8 @@ endobj /O /Layout /Placement /Block >>] - /K [3] - /Pg 406 0 R + /K [4] + /Pg 561 0 R >> endobj @@ -210,7 +195,7 @@ endobj << /Type /StructElem /S /Div - /P 27 0 R + /P 29 0 R /K [35 0 R] >> endobj @@ -224,54 +209,54 @@ endobj /O /Layout /Placement /Block >>] - /K [2] - /Pg 406 0 R + /K [3] + /Pg 561 0 R >> endobj 36 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0 1] - /Pg 406 0 R + /S /Div + /P 29 0 R + /K [37 0 R] >> endobj 37 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [44 0 R 42 0 R 40 0 R 38 0 R] + /S /Span + /P 36 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [2] + /Pg 561 0 R >> endobj 38 0 obj << /Type /StructElem - /S /Div - /P 37 0 R - /K [39 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0 1] + /Pg 561 0 R >> endobj 39 0 obj << /Type /StructElem - /S /Span - /P 38 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [5] - /Pg 404 0 R + /S /Div + /P 28 0 R + /K [46 0 R 44 0 R 42 0 R 40 0 R] >> endobj @@ -279,7 +264,7 @@ endobj << /Type /StructElem /S /Div - /P 37 0 R + /P 39 0 R /K [41 0 R] >> endobj @@ -293,8 +278,8 @@ endobj /O /Layout /Placement /Block >>] - /K [4] - /Pg 404 0 R + /K [6] + /Pg 559 0 R >> endobj @@ -302,7 +287,7 @@ endobj << /Type /StructElem /S /Div - /P 37 0 R + /P 39 0 R /K [43 0 R] >> endobj @@ -316,8 +301,8 @@ endobj /O /Layout /Placement /Block >>] - /K [3] - /Pg 404 0 R + /K [5] + /Pg 559 0 R >> endobj @@ -325,7 +310,7 @@ endobj << /Type /StructElem /S /Div - /P 37 0 R + /P 39 0 R /K [45 0 R] >> endobj @@ -339,77 +324,78 @@ endobj /O /Layout /Placement /Block >>] - /K [2] - /Pg 404 0 R + /K [4] + /Pg 559 0 R >> endobj 46 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0 1] - /Pg 404 0 R + /S /Div + /P 39 0 R + /K [47 0 R] >> endobj 47 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [54 0 R 52 0 R 50 0 R 48 0 R] + /S /Span + /P 46 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [3] + /Pg 559 0 R >> endobj 48 0 obj << /Type /StructElem - /S /Div - /P 47 0 R - /K [49 0 R] + /S /Figure + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [2] + /Pg 559 0 R >> endobj 49 0 obj << /Type /StructElem - /S /Span - /P 48 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [5] - /Pg 402 0 R + /S /P + /P 28 0 R + /K [1] + /Pg 559 0 R >> endobj 50 0 obj << /Type /StructElem - /S /Div - /P 47 0 R - /K [51 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0] + /Pg 559 0 R >> endobj 51 0 obj << /Type /StructElem - /S /Span - /P 50 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [4] - /Pg 402 0 R + /S /Div + /P 28 0 R + /K [58 0 R 56 0 R 54 0 R 52 0 R] >> endobj @@ -417,7 +403,7 @@ endobj << /Type /StructElem /S /Div - /P 47 0 R + /P 51 0 R /K [53 0 R] >> endobj @@ -431,8 +417,8 @@ endobj /O /Layout /Placement /Block >>] - /K [3] - /Pg 402 0 R + /K [5] + /Pg 557 0 R >> endobj @@ -440,7 +426,7 @@ endobj << /Type /StructElem /S /Div - /P 47 0 R + /P 51 0 R /K [55 0 R] >> endobj @@ -454,31 +440,31 @@ endobj /O /Layout /Placement /Block >>] - /K [2] - /Pg 402 0 R + /K [4] + /Pg 557 0 R >> endobj 56 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0 1] - /Pg 402 0 R + /S /Div + /P 51 0 R + /K [57 0 R] >> endobj 57 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [64 0 R 62 0 R 60 0 R 58 0 R] + /S /Span + /P 56 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [3] + /Pg 557 0 R >> endobj @@ -486,7 +472,7 @@ endobj << /Type /StructElem /S /Div - /P 57 0 R + /P 51 0 R /K [59 0 R] >> endobj @@ -500,31 +486,31 @@ endobj /O /Layout /Placement /Block >>] - /K [5] - /Pg 400 0 R + /K [2] + /Pg 557 0 R >> endobj 60 0 obj << /Type /StructElem - /S /Div - /P 57 0 R - /K [61 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0 1] + /Pg 557 0 R >> endobj 61 0 obj << /Type /StructElem - /S /Span - /P 60 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [4] - /Pg 400 0 R + /S /Div + /P 28 0 R + /K [68 0 R 66 0 R 64 0 R 62 0 R] >> endobj @@ -532,7 +518,7 @@ endobj << /Type /StructElem /S /Div - /P 57 0 R + /P 61 0 R /K [63 0 R] >> endobj @@ -546,8 +532,8 @@ endobj /O /Layout /Placement /Block >>] - /K [3] - /Pg 400 0 R + /K [5] + /Pg 555 0 R >> endobj @@ -555,7 +541,7 @@ endobj << /Type /StructElem /S /Div - /P 57 0 R + /P 61 0 R /K [65 0 R] >> endobj @@ -569,31 +555,31 @@ endobj /O /Layout /Placement /Block >>] - /K [2] - /Pg 400 0 R + /K [4] + /Pg 555 0 R >> endobj 66 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0 1] - /Pg 400 0 R + /S /Div + /P 61 0 R + /K [67 0 R] >> endobj 67 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [74 0 R 72 0 R 70 0 R 68 0 R] + /S /Span + /P 66 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [3] + /Pg 555 0 R >> endobj @@ -601,7 +587,7 @@ endobj << /Type /StructElem /S /Div - /P 67 0 R + /P 61 0 R /K [69 0 R] >> endobj @@ -615,31 +601,31 @@ endobj /O /Layout /Placement /Block >>] - /K [5] - /Pg 398 0 R + /K [2] + /Pg 555 0 R >> endobj 70 0 obj << /Type /StructElem - /S /Div - /P 67 0 R - /K [71 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0 1] + /Pg 555 0 R >> endobj 71 0 obj << /Type /StructElem - /S /Span - /P 70 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [4] - /Pg 398 0 R + /S /Div + /P 28 0 R + /K [78 0 R 76 0 R 74 0 R 72 0 R] >> endobj @@ -647,7 +633,7 @@ endobj << /Type /StructElem /S /Div - /P 67 0 R + /P 71 0 R /K [73 0 R] >> endobj @@ -661,8 +647,8 @@ endobj /O /Layout /Placement /Block >>] - /K [3] - /Pg 398 0 R + /K [4] + /Pg 553 0 R >> endobj @@ -670,7 +656,7 @@ endobj << /Type /StructElem /S /Div - /P 67 0 R + /P 71 0 R /K [75 0 R] >> endobj @@ -684,31 +670,31 @@ endobj /O /Layout /Placement /Block >>] - /K [2] - /Pg 398 0 R + /K [3] + /Pg 553 0 R >> endobj 76 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0 1] - /Pg 398 0 R + /S /Div + /P 71 0 R + /K [77 0 R] >> endobj 77 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [84 0 R 82 0 R 80 0 R 78 0 R] + /S /Span + /P 76 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [2] + /Pg 553 0 R >> endobj @@ -716,7 +702,7 @@ endobj << /Type /StructElem /S /Div - /P 77 0 R + /P 71 0 R /K [79 0 R] >> endobj @@ -730,31 +716,31 @@ endobj /O /Layout /Placement /Block >>] - /K [4] - /Pg 396 0 R + /K [1] + /Pg 553 0 R >> endobj 80 0 obj << /Type /StructElem - /S /Div - /P 77 0 R - /K [81 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0] + /Pg 553 0 R >> endobj 81 0 obj << /Type /StructElem - /S /Span - /P 80 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [3] - /Pg 396 0 R + /S /Div + /P 28 0 R + /K [88 0 R 86 0 R 84 0 R 82 0 R] >> endobj @@ -762,7 +748,7 @@ endobj << /Type /StructElem /S /Div - /P 77 0 R + /P 81 0 R /K [83 0 R] >> endobj @@ -776,8 +762,8 @@ endobj /O /Layout /Placement /Block >>] - /K [2] - /Pg 396 0 R + /K [5] + /Pg 551 0 R >> endobj @@ -785,7 +771,7 @@ endobj << /Type /StructElem /S /Div - /P 77 0 R + /P 81 0 R /K [85 0 R] >> endobj @@ -799,31 +785,31 @@ endobj /O /Layout /Placement /Block >>] - /K [1] - /Pg 396 0 R + /K [4] + /Pg 551 0 R >> endobj 86 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0] - /Pg 396 0 R + /S /Div + /P 81 0 R + /K [87 0 R] >> endobj 87 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [94 0 R 92 0 R 90 0 R 88 0 R] + /S /Span + /P 86 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [3] + /Pg 551 0 R >> endobj @@ -831,7 +817,7 @@ endobj << /Type /StructElem /S /Div - /P 87 0 R + /P 81 0 R /K [89 0 R] >> endobj @@ -845,31 +831,31 @@ endobj /O /Layout /Placement /Block >>] - /K [5] - /Pg 394 0 R + /K [2] + /Pg 551 0 R >> endobj 90 0 obj << /Type /StructElem - /S /Div - /P 87 0 R - /K [91 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0 1] + /Pg 551 0 R >> endobj 91 0 obj << /Type /StructElem - /S /Span - /P 90 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [4] - /Pg 394 0 R + /S /Div + /P 28 0 R + /K [98 0 R 96 0 R 94 0 R 92 0 R] >> endobj @@ -877,7 +863,7 @@ endobj << /Type /StructElem /S /Div - /P 87 0 R + /P 91 0 R /K [93 0 R] >> endobj @@ -891,8 +877,8 @@ endobj /O /Layout /Placement /Block >>] - /K [3] - /Pg 394 0 R + /K [4] + /Pg 549 0 R >> endobj @@ -900,7 +886,7 @@ endobj << /Type /StructElem /S /Div - /P 87 0 R + /P 91 0 R /K [95 0 R] >> endobj @@ -914,31 +900,31 @@ endobj /O /Layout /Placement /Block >>] - /K [2] - /Pg 394 0 R + /K [3] + /Pg 549 0 R >> endobj 96 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0 1] - /Pg 394 0 R + /S /Div + /P 91 0 R + /K [97 0 R] >> endobj 97 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [104 0 R 102 0 R 100 0 R 98 0 R] + /S /Span + /P 96 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [2] + /Pg 549 0 R >> endobj @@ -946,7 +932,7 @@ endobj << /Type /StructElem /S /Div - /P 97 0 R + /P 91 0 R /K [99 0 R] >> endobj @@ -960,31 +946,31 @@ endobj /O /Layout /Placement /Block >>] - /K [4] - /Pg 392 0 R + /K [1] + /Pg 549 0 R >> endobj 100 0 obj << /Type /StructElem - /S /Div - /P 97 0 R - /K [101 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0] + /Pg 549 0 R >> endobj 101 0 obj << /Type /StructElem - /S /Span - /P 100 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [3] - /Pg 392 0 R + /S /Div + /P 28 0 R + /K [108 0 R 106 0 R 104 0 R 102 0 R] >> endobj @@ -992,7 +978,7 @@ endobj << /Type /StructElem /S /Div - /P 97 0 R + /P 101 0 R /K [103 0 R] >> endobj @@ -1006,8 +992,8 @@ endobj /O /Layout /Placement /Block >>] - /K [2] - /Pg 392 0 R + /K [5] + /Pg 547 0 R >> endobj @@ -1015,7 +1001,7 @@ endobj << /Type /StructElem /S /Div - /P 97 0 R + /P 101 0 R /K [105 0 R] >> endobj @@ -1029,31 +1015,31 @@ endobj /O /Layout /Placement /Block >>] - /K [1] - /Pg 392 0 R + /K [4] + /Pg 547 0 R >> endobj 106 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0] - /Pg 392 0 R + /S /Div + /P 101 0 R + /K [107 0 R] >> endobj 107 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [114 0 R 112 0 R 110 0 R 108 0 R] + /S /Span + /P 106 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [3] + /Pg 547 0 R >> endobj @@ -1061,7 +1047,7 @@ endobj << /Type /StructElem /S /Div - /P 107 0 R + /P 101 0 R /K [109 0 R] >> endobj @@ -1075,31 +1061,31 @@ endobj /O /Layout /Placement /Block >>] - /K [5] - /Pg 390 0 R + /K [2] + /Pg 547 0 R >> endobj 110 0 obj << /Type /StructElem - /S /Div - /P 107 0 R - /K [111 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0 1] + /Pg 547 0 R >> endobj 111 0 obj << /Type /StructElem - /S /Span - /P 110 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [4] - /Pg 390 0 R + /S /Div + /P 28 0 R + /K [118 0 R 116 0 R 114 0 R 112 0 R] >> endobj @@ -1107,7 +1093,7 @@ endobj << /Type /StructElem /S /Div - /P 107 0 R + /P 111 0 R /K [113 0 R] >> endobj @@ -1121,8 +1107,8 @@ endobj /O /Layout /Placement /Block >>] - /K [3] - /Pg 390 0 R + /K [6] + /Pg 545 0 R >> endobj @@ -1130,7 +1116,7 @@ endobj << /Type /StructElem /S /Div - /P 107 0 R + /P 111 0 R /K [115 0 R] >> endobj @@ -1144,31 +1130,31 @@ endobj /O /Layout /Placement /Block >>] - /K [2] - /Pg 390 0 R + /K [5] + /Pg 545 0 R >> endobj 116 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0 1] - /Pg 390 0 R + /S /Div + /P 111 0 R + /K [117 0 R] >> endobj 117 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [124 0 R 122 0 R 120 0 R 118 0 R] + /S /Span + /P 116 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [4] + /Pg 545 0 R >> endobj @@ -1176,7 +1162,7 @@ endobj << /Type /StructElem /S /Div - /P 117 0 R + /P 111 0 R /K [119 0 R] >> endobj @@ -1190,31 +1176,31 @@ endobj /O /Layout /Placement /Block >>] - /K [6] - /Pg 388 0 R + /K [3] + /Pg 545 0 R >> endobj 120 0 obj << /Type /StructElem - /S /Div - /P 117 0 R - /K [121 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0 1 2] + /Pg 545 0 R >> endobj 121 0 obj << /Type /StructElem - /S /Span - /P 120 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [5] - /Pg 388 0 R + /S /Div + /P 28 0 R + /K [128 0 R 126 0 R 124 0 R 122 0 R] >> endobj @@ -1222,7 +1208,7 @@ endobj << /Type /StructElem /S /Div - /P 117 0 R + /P 121 0 R /K [123 0 R] >> endobj @@ -1237,7 +1223,7 @@ endobj /Placement /Block >>] /K [4] - /Pg 388 0 R + /Pg 543 0 R >> endobj @@ -1245,7 +1231,7 @@ endobj << /Type /StructElem /S /Div - /P 117 0 R + /P 121 0 R /K [125 0 R] >> endobj @@ -1260,30 +1246,30 @@ endobj /Placement /Block >>] /K [3] - /Pg 388 0 R + /Pg 543 0 R >> endobj 126 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0 1 2] - /Pg 388 0 R + /S /Div + /P 121 0 R + /K [127 0 R] >> endobj 127 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [134 0 R 132 0 R 130 0 R 128 0 R] + /S /Span + /P 126 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [2] + /Pg 543 0 R >> endobj @@ -1291,7 +1277,7 @@ endobj << /Type /StructElem /S /Div - /P 127 0 R + /P 121 0 R /K [129 0 R] >> endobj @@ -1305,31 +1291,31 @@ endobj /O /Layout /Placement /Block >>] - /K [4] - /Pg 386 0 R + /K [1] + /Pg 543 0 R >> endobj 130 0 obj << /Type /StructElem - /S /Div - /P 127 0 R - /K [131 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0] + /Pg 543 0 R >> endobj 131 0 obj << /Type /StructElem - /S /Span - /P 130 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [3] - /Pg 386 0 R + /S /Div + /P 28 0 R + /K [138 0 R 136 0 R 134 0 R 132 0 R] >> endobj @@ -1337,7 +1323,7 @@ endobj << /Type /StructElem /S /Div - /P 127 0 R + /P 131 0 R /K [133 0 R] >> endobj @@ -1351,8 +1337,8 @@ endobj /O /Layout /Placement /Block >>] - /K [2] - /Pg 386 0 R + /K [6] + /Pg 541 0 R >> endobj @@ -1360,7 +1346,7 @@ endobj << /Type /StructElem /S /Div - /P 127 0 R + /P 131 0 R /K [135 0 R] >> endobj @@ -1374,31 +1360,31 @@ endobj /O /Layout /Placement /Block >>] - /K [1] - /Pg 386 0 R + /K [5] + /Pg 541 0 R >> endobj 136 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0] - /Pg 386 0 R + /S /Div + /P 131 0 R + /K [137 0 R] >> endobj 137 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [144 0 R 142 0 R 140 0 R 138 0 R] + /S /Span + /P 136 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [4] + /Pg 541 0 R >> endobj @@ -1406,7 +1392,7 @@ endobj << /Type /StructElem /S /Div - /P 137 0 R + /P 131 0 R /K [139 0 R] >> endobj @@ -1420,31 +1406,31 @@ endobj /O /Layout /Placement /Block >>] - /K [6] - /Pg 384 0 R + /K [3] + /Pg 541 0 R >> endobj 140 0 obj << /Type /StructElem - /S /Div - /P 137 0 R - /K [141 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0 1 2] + /Pg 541 0 R >> endobj 141 0 obj << /Type /StructElem - /S /Span - /P 140 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [5] - /Pg 384 0 R + /S /Div + /P 28 0 R + /K [148 0 R 146 0 R 144 0 R 142 0 R] >> endobj @@ -1452,7 +1438,7 @@ endobj << /Type /StructElem /S /Div - /P 137 0 R + /P 141 0 R /K [143 0 R] >> endobj @@ -1466,8 +1452,8 @@ endobj /O /Layout /Placement /Block >>] - /K [4] - /Pg 384 0 R + /K [10] + /Pg 539 0 R >> endobj @@ -1475,7 +1461,7 @@ endobj << /Type /StructElem /S /Div - /P 137 0 R + /P 141 0 R /K [145 0 R] >> endobj @@ -1489,31 +1475,31 @@ endobj /O /Layout /Placement /Block >>] - /K [3] - /Pg 384 0 R + /K [9] + /Pg 539 0 R >> endobj 146 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0 1 2] - /Pg 384 0 R + /S /Div + /P 141 0 R + /K [147 0 R] >> endobj 147 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [154 0 R 152 0 R 150 0 R 148 0 R] + /S /Span + /P 146 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [8] + /Pg 539 0 R >> endobj @@ -1521,7 +1507,7 @@ endobj << /Type /StructElem /S /Div - /P 147 0 R + /P 141 0 R /K [149 0 R] >> endobj @@ -1535,54 +1521,59 @@ endobj /O /Layout /Placement /Block >>] - /K [10] - /Pg 382 0 R + /K [7] + /Pg 539 0 R >> endobj 150 0 obj << /Type /StructElem - /S /Div - /P 147 0 R - /K [151 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [3 4 5 6] + /Pg 539 0 R >> endobj 151 0 obj << /Type /StructElem - /S /Span - /P 150 0 R + /S /Formula + /P 28 0 R /A [<< /O /Layout /Placement /Block >>] - /K [9] - /Pg 382 0 R + /K [2] + /Pg 539 0 R >> endobj 152 0 obj << /Type /StructElem - /S /Div - /P 147 0 R - /K [153 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0 1] + /Pg 539 0 R >> endobj 153 0 obj << /Type /StructElem - /S /Span - /P 152 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [8] - /Pg 382 0 R + /S /Div + /P 28 0 R + /K [160 0 R 158 0 R 156 0 R 154 0 R] >> endobj @@ -1590,7 +1581,7 @@ endobj << /Type /StructElem /S /Div - /P 147 0 R + /P 153 0 R /K [155 0 R] >> endobj @@ -1604,59 +1595,54 @@ endobj /O /Layout /Placement /Block >>] - /K [7] - /Pg 382 0 R + /K [12] + /Pg 537 0 R >> endobj 156 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [3 4 5 6] - /Pg 382 0 R + /S /Div + /P 153 0 R + /K [157 0 R] >> endobj 157 0 obj << /Type /StructElem - /S /Formula - /P 26 0 R + /S /Span + /P 156 0 R /A [<< /O /Layout /Placement /Block >>] - /K [2] - /Pg 382 0 R + /K [11] + /Pg 537 0 R >> endobj 158 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0 1] - /Pg 382 0 R + /S /Div + /P 153 0 R + /K [159 0 R] >> endobj 159 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [166 0 R 164 0 R 162 0 R 160 0 R] + /S /Span + /P 158 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [10] + /Pg 537 0 R >> endobj @@ -1664,7 +1650,7 @@ endobj << /Type /StructElem /S /Div - /P 159 0 R + /P 153 0 R /K [161 0 R] >> endobj @@ -1678,17 +1664,22 @@ endobj /O /Layout /Placement /Block >>] - /K [12] - /Pg 380 0 R + /K [9] + /Pg 537 0 R >> endobj 162 0 obj << /Type /StructElem - /S /Div - /P 159 0 R - /K [163 0 R] + /S /Formula + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [4 5 6 7 8] + /Pg 537 0 R >> endobj @@ -1696,13 +1687,13 @@ endobj << /Type /StructElem /S /Span - /P 162 0 R + /P 28 0 R /A [<< /O /Layout /Placement /Block >>] - /K [11] - /Pg 380 0 R + /K [0 1 2 3] + /Pg 537 0 R >> endobj @@ -1710,82 +1701,77 @@ endobj << /Type /StructElem /S /Div - /P 159 0 R - /K [165 0 R] + /P 28 0 R + /K [171 0 R 169 0 R 167 0 R 165 0 R] >> endobj 165 0 obj << /Type /StructElem - /S /Span + /S /Div /P 164 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [10] - /Pg 380 0 R + /K [166 0 R] >> endobj 166 0 obj << /Type /StructElem - /S /Div - /P 159 0 R - /K [167 0 R] + /S /Span + /P 165 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [54] + /Pg 535 0 R >> endobj 167 0 obj << /Type /StructElem - /S /Span - /P 166 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [9] - /Pg 380 0 R + /S /Div + /P 164 0 R + /K [168 0 R] >> endobj 168 0 obj << /Type /StructElem - /S /Formula - /P 26 0 R + /S /Span + /P 167 0 R /A [<< /O /Layout /Placement /Block >>] - /K [4 5 6 7 8] - /Pg 380 0 R + /K [53] + /Pg 535 0 R >> endobj 169 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0 1 2 3] - /Pg 380 0 R + /S /Div + /P 164 0 R + /K [170 0 R] >> endobj 170 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [177 0 R 175 0 R 173 0 R 171 0 R] + /S /Span + /P 169 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [52] + /Pg 535 0 R >> endobj @@ -1793,7 +1779,7 @@ endobj << /Type /StructElem /S /Div - /P 170 0 R + /P 164 0 R /K [172 0 R] >> endobj @@ -1807,87 +1793,106 @@ endobj /O /Layout /Placement /Block >>] - /K [28] - /Pg 378 0 R + /K [51] + /Pg 535 0 R >> endobj 173 0 obj << /Type /StructElem - /S /Div - /P 170 0 R - /K [174 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [50] + /Pg 535 0 R >> endobj 174 0 obj << /Type /StructElem - /S /Span - /P 173 0 R + /S /Formula + /P 28 0 R /A [<< /O /Layout /Placement /Block >>] - /K [27] - /Pg 378 0 R + /K [42 43 44 45 46 47 48 49] + /Pg 535 0 R >> endobj 175 0 obj << /Type /StructElem - /S /Div - /P 170 0 R - /K [176 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [40 41] + /Pg 535 0 R >> endobj 176 0 obj << /Type /StructElem - /S /Span - /P 175 0 R + /S /Formula + /P 28 0 R /A [<< /O /Layout /Placement /Block >>] - /K [26] - /Pg 378 0 R + /K [35 36 37 38 39] + /Pg 535 0 R >> endobj 177 0 obj << /Type /StructElem - /S /Div - /P 170 0 R - /K [178 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [32 33 34] + /Pg 535 0 R >> endobj 178 0 obj << /Type /StructElem - /S /Span - /P 177 0 R + /S /Formula + /P 28 0 R /A [<< /O /Layout /Placement /Block >>] - /K [25] - /Pg 378 0 R + /K [29 30 31] + /Pg 535 0 R >> endobj 179 0 obj << /Type /StructElem - /S /P - /P 26 0 R - /K [15 182 0 R 17 181 0 R 21 22 180 0 R 24] - /Pg 378 0 R + /S /Formula + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [26 27 28] + /Pg 535 0 R >> endobj @@ -1895,9 +1900,13 @@ endobj << /Type /StructElem /S /Formula - /P 179 0 R - /K [23] - /Pg 378 0 R + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [23 24 25] + /Pg 535 0 R >> endobj @@ -1905,9 +1914,13 @@ endobj << /Type /StructElem /S /Formula - /P 179 0 R - /K [18 19 20] - /Pg 378 0 R + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [20 21 22] + /Pg 535 0 R >> endobj @@ -1915,72 +1928,87 @@ endobj << /Type /StructElem /S /Formula - /P 179 0 R - /K [16] - /Pg 378 0 R + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [17 18 19] + /Pg 535 0 R >> endobj 183 0 obj << /Type /StructElem - /S /P - /P 26 0 R - /K [14] - /Pg 378 0 R + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [16] + /Pg 535 0 R >> endobj 184 0 obj << /Type /StructElem - /S /P - /P 26 0 R - /K [1 186 0 R 8 185 0 R] - /Pg 378 0 R + /S /Formula + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [12 13 14 15] + /Pg 535 0 R >> endobj 185 0 obj << /Type /StructElem - /S /Formula - /P 184 0 R - /K [9 10 11 12 13] - /Pg 378 0 R + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0 1 2 3 4 5 6 7 8 9 10 11] + /Pg 535 0 R >> endobj 186 0 obj << /Type /StructElem - /S /Formula - /P 184 0 R - /K [2 3 4 5 6 7] - /Pg 378 0 R + /S /Div + /P 28 0 R + /K [193 0 R 191 0 R 189 0 R 187 0 R] >> endobj 187 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0] - /Pg 378 0 R + /S /Div + /P 186 0 R + /K [188 0 R] >> endobj 188 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [195 0 R 193 0 R 191 0 R 189 0 R] + /S /Span + /P 187 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [99] + /Pg 533 0 R >> endobj @@ -1988,7 +2016,7 @@ endobj << /Type /StructElem /S /Div - /P 188 0 R + /P 186 0 R /K [190 0 R] >> endobj @@ -2002,8 +2030,8 @@ endobj /O /Layout /Placement /Block >>] - /K [47] - /Pg 376 0 R + /K [98] + /Pg 533 0 R >> endobj @@ -2011,7 +2039,7 @@ endobj << /Type /StructElem /S /Div - /P 188 0 R + /P 186 0 R /K [192 0 R] >> endobj @@ -2025,8 +2053,8 @@ endobj /O /Layout /Placement /Block >>] - /K [46] - /Pg 376 0 R + /K [97] + /Pg 533 0 R >> endobj @@ -2034,7 +2062,7 @@ endobj << /Type /StructElem /S /Div - /P 188 0 R + /P 186 0 R /K [194 0 R] >> endobj @@ -2048,40 +2076,42 @@ endobj /O /Layout /Placement /Block >>] - /K [45] - /Pg 376 0 R + /K [96] + /Pg 533 0 R >> endobj 195 0 obj << /Type /StructElem - /S /Div - /P 188 0 R - /K [196 0 R] + /S /Formula + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95] + /Pg 533 0 R >> endobj 196 0 obj << /Type /StructElem - /S /Span - /P 195 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [44] - /Pg 376 0 R + /S /P + /P 28 0 R + /K [21 197 0 R] + /Pg 533 0 R >> endobj 197 0 obj << /Type /StructElem - /S /P - /P 26 0 R - /K [198 0 R] + /S /Formula + /P 196 0 R + /K [22 23 24 25 26 27 28 29 30] + /Pg 533 0 R >> endobj @@ -2089,9 +2119,13 @@ endobj << /Type /StructElem /S /Formula - /P 197 0 R - /K [25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43] - /Pg 376 0 R + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20] + /Pg 533 0 R >> endobj @@ -2099,39 +2133,41 @@ endobj << /Type /StructElem /S /P - /P 26 0 R - /K [1 202 0 R 7 201 0 R 17 200 0 R 24] - /Pg 376 0 R + /P 28 0 R + /K [1] + /Pg 533 0 R >> endobj 200 0 obj << /Type /StructElem - /S /Formula - /P 199 0 R - /K [18 19 20 21 22 23] - /Pg 376 0 R + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0] + /Pg 533 0 R >> endobj 201 0 obj << /Type /StructElem - /S /Formula - /P 199 0 R - /K [8 9 10 11 12 13 14 15 16] - /Pg 376 0 R + /S /Div + /P 28 0 R + /K [208 0 R 206 0 R 204 0 R 202 0 R] >> endobj 202 0 obj << /Type /StructElem - /S /Formula - /P 199 0 R - /K [2 3 4 5 6] - /Pg 376 0 R + /S /Div + /P 201 0 R + /K [203 0 R] >> endobj @@ -2139,13 +2175,13 @@ endobj << /Type /StructElem /S /Span - /P 26 0 R + /P 202 0 R /A [<< /O /Layout /Placement /Block >>] - /K [0] - /Pg 376 0 R + /K [83] + /Pg 531 0 R >> endobj @@ -2153,249 +2189,257 @@ endobj << /Type /StructElem /S /Div - /P 26 0 R - /K [211 0 R 209 0 R 207 0 R 205 0 R] + /P 201 0 R + /K [205 0 R] >> endobj 205 0 obj << /Type /StructElem - /S /Div + /S /Span /P 204 0 R - /K [206 0 R] + /A [<< + /O /Layout + /Placement /Block + >>] + /K [82] + /Pg 531 0 R >> endobj 206 0 obj << /Type /StructElem - /S /Span - /P 205 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [77] - /Pg 374 0 R + /S /Div + /P 201 0 R + /K [207 0 R] >> endobj 207 0 obj << /Type /StructElem - /S /Div - /P 204 0 R - /K [208 0 R] + /S /Span + /P 206 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [81] + /Pg 531 0 R >> endobj 208 0 obj << /Type /StructElem - /S /Span - /P 207 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [76] - /Pg 374 0 R + /S /Div + /P 201 0 R + /K [209 0 R] >> endobj 209 0 obj << /Type /StructElem - /S /Div - /P 204 0 R - /K [210 0 R] + /S /Span + /P 208 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [80] + /Pg 531 0 R >> endobj 210 0 obj << /Type /StructElem - /S /Span - /P 209 0 R + /S /Formula + /P 28 0 R /A [<< /O /Layout /Placement /Block >>] - /K [75] - /Pg 374 0 R + /K [54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79] + /Pg 531 0 R >> endobj 211 0 obj << /Type /StructElem - /S /Div - /P 204 0 R - /K [212 0 R] + /S /L + /P 28 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [217 0 R 212 0 R] >> endobj 212 0 obj << /Type /StructElem - /S /Span + /S /LI /P 211 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [74] - /Pg 374 0 R + /K [216 0 R 213 0 R] >> endobj 213 0 obj << /Type /StructElem - /S /P - /P 26 0 R - /K [67 214 0 R] - /Pg 374 0 R + /S /LBody + /P 212 0 R + /K [214 0 R] >> endobj 214 0 obj << /Type /StructElem - /S /Formula + /S /P /P 213 0 R - /K [68 69 70 71 72 73] - /Pg 374 0 R + /K [48 215 0 R 53] + /Pg 531 0 R >> endobj 215 0 obj << /Type /StructElem - /S /P - /P 26 0 R - /K [218 0 R 58 217 0 R 60 216 0 R] - /Pg 374 0 R + /S /Formula + /P 214 0 R + /K [49 50 51 52] + /Pg 531 0 R >> endobj 216 0 obj << /Type /StructElem - /S /Formula - /P 215 0 R - /K [61 62 63 64 65 66] - /Pg 374 0 R + /S /Lbl + /P 212 0 R + /K [47] + /Pg 531 0 R >> endobj 217 0 obj << /Type /StructElem - /S /Formula - /P 215 0 R - /K [59] - /Pg 374 0 R + /S /LI + /P 211 0 R + /K [221 0 R 218 0 R] >> endobj 218 0 obj << /Type /StructElem - /S /Formula - /P 215 0 R - /K [53 54 55 56 57] - /Pg 374 0 R + /S /LBody + /P 217 0 R + /K [219 0 R] >> endobj 219 0 obj << /Type /StructElem - /S /L - /P 26 0 R - /A [<< - /O /List - /ListNumbering /Circle - >>] - /K [231 0 R 225 0 R 220 0 R] + /S /P + /P 218 0 R + /K [40 220 0 R] + /Pg 531 0 R >> endobj 220 0 obj << /Type /StructElem - /S /LI + /S /Formula /P 219 0 R - /K [224 0 R 221 0 R] + /K [41 42 43 44 45 46] + /Pg 531 0 R >> endobj 221 0 obj << /Type /StructElem - /S /LBody - /P 220 0 R - /K [222 0 R] + /S /Lbl + /P 217 0 R + /K [39] + /Pg 531 0 R >> endobj 222 0 obj << /Type /StructElem - /S /P - /P 221 0 R - /K [40 223 0 R] - /Pg 374 0 R + /S /Formula + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [25 26 27 28 29 30 31 32 33 34 35 36 37 38] + /Pg 531 0 R >> endobj 223 0 obj << /Type /StructElem - /S /Formula - /P 222 0 R - /K [41 42 43 44 45 46 47 48 49 50 51 52] - /Pg 374 0 R + /S /L + /P 28 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [224 0 R] >> endobj 224 0 obj << /Type /StructElem - /S /Lbl - /P 220 0 R - /K [39] - /Pg 374 0 R + /S /LI + /P 223 0 R + /K [227 0 R 225 0 R] >> endobj 225 0 obj << /Type /StructElem - /S /LI - /P 219 0 R - /K [230 0 R 226 0 R] + /S /LBody + /P 224 0 R + /K [22 226 0 R 24] + /Pg 531 0 R >> endobj 226 0 obj << /Type /StructElem - /S /LBody + /S /Formula /P 225 0 R - /K [227 0 R] + /K [23] + /Pg 531 0 R >> endobj 227 0 obj << /Type /StructElem - /S /P - /P 226 0 R - /K [27 229 0 R 36 228 0 R 38] - /Pg 374 0 R + /S /Lbl + /P 224 0 R + /K [21] + /Pg 531 0 R >> endobj @@ -2403,161 +2447,180 @@ endobj << /Type /StructElem /S /Formula - /P 227 0 R - /K [37] - /Pg 374 0 R + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [11 12 13 14 15 16 17 18 19 20] + /Pg 531 0 R >> endobj 229 0 obj << /Type /StructElem - /S /Formula - /P 227 0 R - /K [28 29 30 31 32 33 34 35] - /Pg 374 0 R + /S /L + /P 28 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [230 0 R] >> endobj 230 0 obj << /Type /StructElem - /S /Lbl - /P 225 0 R - /K [26] - /Pg 374 0 R + /S /LI + /P 229 0 R + /K [233 0 R 231 0 R] >> endobj 231 0 obj << /Type /StructElem - /S /LI - /P 219 0 R - /K [235 0 R 232 0 R] + /S /LBody + /P 230 0 R + /K [8 232 0 R 10] + /Pg 531 0 R >> endobj 232 0 obj << /Type /StructElem - /S /LBody + /S /Formula /P 231 0 R - /K [233 0 R] + /K [9] + /Pg 531 0 R >> endobj 233 0 obj << /Type /StructElem - /S /P - /P 232 0 R - /K [14 234 0 R] - /Pg 374 0 R + /S /Lbl + /P 230 0 R + /K [7] + /Pg 531 0 R >> endobj 234 0 obj << /Type /StructElem - /S /Formula - /P 233 0 R - /K [15 16 17 18 19 20 21 22 23 24 25] - /Pg 374 0 R + /S /P + /P 28 0 R + /K [237 0 R 235 0 R] >> endobj 235 0 obj << /Type /StructElem - /S /Lbl - /P 231 0 R - /K [13] - /Pg 374 0 R + /S /Formula + /P 234 0 R + /K [236 0 R] >> endobj 236 0 obj << /Type /StructElem - /S /P - /P 26 0 R - /K [237 0 R] + /S /Span + /P 235 0 R + /A [<< + /O /Layout + /TextDecorationType /Underline + >>] + /K [2 3 4 5 6] + /Pg 531 0 R >> endobj 237 0 obj << /Type /StructElem - /S /Formula - /P 236 0 R - /K [3 4 5 6 7 8 9 10 11 12] - /Pg 374 0 R + /S /Span + /P 234 0 R + /A [<< + /O /Layout + /TextDecorationType /Underline + >>] + /K [1] + /Pg 531 0 R >> endobj 238 0 obj << /Type /StructElem - /S /L - /P 26 0 R + /S /Span + /P 28 0 R /A [<< - /O /List - /ListNumbering /Circle + /O /Layout + /Placement /Block >>] - /K [239 0 R] + /K [0] + /Pg 531 0 R >> endobj 239 0 obj << /Type /StructElem - /S /LI - /P 238 0 R - /K [241 0 R 240 0 R] + /S /Div + /P 28 0 R + /K [246 0 R 244 0 R 242 0 R 240 0 R] >> endobj 240 0 obj << /Type /StructElem - /S /LBody + /S /Div /P 239 0 R - /K [2] - /Pg 374 0 R + /K [241 0 R] >> endobj 241 0 obj << /Type /StructElem - /S /Lbl - /P 239 0 R - /K [1] - /Pg 374 0 R + /S /Span + /P 240 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [91] + /Pg 529 0 R >> endobj 242 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0] - /Pg 374 0 R + /S /Div + /P 239 0 R + /K [243 0 R] >> endobj 243 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [250 0 R 248 0 R 246 0 R 244 0 R] + /S /Span + /P 242 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [90] + /Pg 529 0 R >> endobj @@ -2565,7 +2628,7 @@ endobj << /Type /StructElem /S /Div - /P 243 0 R + /P 239 0 R /K [245 0 R] >> endobj @@ -2579,8 +2642,8 @@ endobj /O /Layout /Placement /Block >>] - /K [5] - /Pg 372 0 R + /K [89] + /Pg 529 0 R >> endobj @@ -2588,7 +2651,7 @@ endobj << /Type /StructElem /S /Div - /P 243 0 R + /P 239 0 R /K [247 0 R] >> endobj @@ -2602,123 +2665,108 @@ endobj /O /Layout /Placement /Block >>] - /K [4] - /Pg 372 0 R + /K [88] + /Pg 529 0 R >> endobj 248 0 obj << /Type /StructElem - /S /Div - /P 243 0 R - /K [249 0 R] + /S /L + /P 28 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [253 0 R 249 0 R] >> endobj 249 0 obj << /Type /StructElem - /S /Span + /S /LI /P 248 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [3] - /Pg 372 0 R + /K [252 0 R 250 0 R] >> endobj 250 0 obj << /Type /StructElem - /S /Div - /P 243 0 R - /K [251 0 R] + /S /LBody + /P 249 0 R + /K [86 251 0 R] + /Pg 529 0 R >> endobj 251 0 obj << /Type /StructElem - /S /Span + /S /Formula /P 250 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [2] - /Pg 372 0 R + /K [87] + /Pg 529 0 R >> endobj 252 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0 1] - /Pg 372 0 R + /S /Lbl + /P 249 0 R + /K [85] + /Pg 529 0 R >> endobj 253 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [260 0 R 258 0 R 256 0 R 254 0 R] + /S /LI + /P 248 0 R + /K [256 0 R 254 0 R] >> endobj 254 0 obj << /Type /StructElem - /S /Div + /S /LBody /P 253 0 R - /K [255 0 R] + /K [77 255 0 R 84] + /Pg 529 0 R >> endobj 255 0 obj << /Type /StructElem - /S /Span + /S /Formula /P 254 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [56] - /Pg 370 0 R + /K [78 79 80 81 82 83] + /Pg 529 0 R >> endobj 256 0 obj << /Type /StructElem - /S /Div + /S /Lbl /P 253 0 R - /K [257 0 R] + /K [76] + /Pg 529 0 R >> endobj 257 0 obj << /Type /StructElem - /S /Span - /P 256 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [55] - /Pg 370 0 R + /S /Div + /P 28 0 R + /K [263 0 R 258 0 R] >> endobj @@ -2726,115 +2774,92 @@ endobj << /Type /StructElem /S /Div - /P 253 0 R - /K [259 0 R] + /P 257 0 R + /K [262 0 R 260 0 R 259 0 R] >> endobj 259 0 obj << /Type /StructElem - /S /Span + /S /Formula /P 258 0 R /A [<< /O /Layout /Placement /Block >>] - /K [54] - /Pg 370 0 R + /K [57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75] + /Pg 529 0 R >> endobj 260 0 obj << /Type /StructElem - /S /Div - /P 253 0 R - /K [261 0 R] + /S /P + /P 258 0 R + /K [42 261 0 R] + /Pg 529 0 R >> endobj 261 0 obj << /Type /StructElem - /S /Span + /S /Formula /P 260 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [53] - /Pg 370 0 R + /K [43 44 45 46 47 48 49 50 51 52 53 54 55 56] + /Pg 529 0 R >> endobj 262 0 obj << /Type /StructElem - /S /Formula - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [50 51 52] - /Pg 370 0 R + /S /P + /P 258 0 R + /K [41] + /Pg 529 0 R >> endobj 263 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [42 43 44 45 46 47 48 49] - /Pg 370 0 R + /S /Div + /P 257 0 R + /K [] >> endobj 264 0 obj << /Type /StructElem - /S /Strong - /P 26 0 R + /S /L + /P 28 0 R /A [<< - /O /Layout - /Placement /Block + /O /List + /ListNumbering /Circle >>] - /K [41] - /Pg 370 0 R + /K [270 0 R 265 0 R] >> endobj 265 0 obj << /Type /StructElem - /S /Formula - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [38 39 40] - /Pg 370 0 R + /S /LI + /P 264 0 R + /K [269 0 R 266 0 R] >> endobj 266 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [34 35 36 37] - /Pg 370 0 R + /S /LBody + /P 265 0 R + /K [267 0 R] >> endobj @@ -2842,9 +2867,8 @@ endobj << /Type /StructElem /S /P - /P 26 0 R - /K [29 268 0 R] - /Pg 370 0 R + /P 266 0 R + /K [268 0 R] >> endobj @@ -2853,48 +2877,45 @@ endobj /Type /StructElem /S /Formula /P 267 0 R - /K [30 31 32 33] - /Pg 370 0 R + /K [35 36 37 38 39 40] + /Pg 529 0 R >> endobj 269 0 obj << /Type /StructElem - /S /P - /P 26 0 R - /K [24 270 0 R 28] - /Pg 370 0 R + /S /Lbl + /P 265 0 R + /K [34] + /Pg 529 0 R >> endobj 270 0 obj << /Type /StructElem - /S /Formula - /P 269 0 R - /K [25 26 27] - /Pg 370 0 R + /S /LI + /P 264 0 R + /K [274 0 R 271 0 R] >> endobj 271 0 obj << /Type /StructElem - /S /P - /P 26 0 R - /K [16 273 0 R 20 272 0 R] - /Pg 370 0 R + /S /LBody + /P 270 0 R + /K [272 0 R] >> endobj 272 0 obj << /Type /StructElem - /S /Formula + /S /P /P 271 0 R - /K [21 22 23] - /Pg 370 0 R + /K [273 0 R] >> endobj @@ -2902,39 +2923,37 @@ endobj << /Type /StructElem /S /Formula - /P 271 0 R - /K [17 18 19] - /Pg 370 0 R + /P 272 0 R + /K [13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33] + /Pg 529 0 R >> endobj 274 0 obj << /Type /StructElem - /S /P - /P 26 0 R - /K [277 0 R 2 276 0 R 11 275 0 R 15] - /Pg 370 0 R + /S /Lbl + /P 270 0 R + /K [12] + /Pg 529 0 R >> endobj 275 0 obj << /Type /StructElem - /S /Formula - /P 274 0 R - /K [12 13 14] - /Pg 370 0 R + /S /Div + /P 28 0 R + /K [279 0 R 276 0 R] >> endobj 276 0 obj << /Type /StructElem - /S /Formula - /P 274 0 R - /K [3 4 5 6 7 8 9 10] - /Pg 370 0 R + /S /Div + /P 275 0 R + /K [278 0 R 277 0 R] >> endobj @@ -2942,23 +2961,23 @@ endobj << /Type /StructElem /S /Formula - /P 274 0 R - /K [1] - /Pg 370 0 R + /P 276 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [2 3 4 5 6 7 8 9 10 11] + /Pg 529 0 R >> endobj 278 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0] - /Pg 370 0 R + /S /P + /P 276 0 R + /K [1] + /Pg 529 0 R >> endobj @@ -2966,31 +2985,31 @@ endobj << /Type /StructElem /S /Div - /P 26 0 R - /K [286 0 R 284 0 R 282 0 R 280 0 R] + /P 275 0 R + /K [] >> endobj 280 0 obj << /Type /StructElem - /S /Div - /P 279 0 R - /K [281 0 R] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0] + /Pg 529 0 R >> endobj 281 0 obj << /Type /StructElem - /S /Span - /P 280 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [6] - /Pg 368 0 R + /S /Div + /P 28 0 R + /K [288 0 R 286 0 R 284 0 R 282 0 R] >> endobj @@ -2998,7 +3017,7 @@ endobj << /Type /StructElem /S /Div - /P 279 0 R + /P 281 0 R /K [283 0 R] >> endobj @@ -3012,8 +3031,8 @@ endobj /O /Layout /Placement /Block >>] - /K [5] - /Pg 368 0 R + /K [82] + /Pg 527 0 R >> endobj @@ -3021,7 +3040,7 @@ endobj << /Type /StructElem /S /Div - /P 279 0 R + /P 281 0 R /K [285 0 R] >> endobj @@ -3035,8 +3054,8 @@ endobj /O /Layout /Placement /Block >>] - /K [4] - /Pg 368 0 R + /K [81] + /Pg 527 0 R >> endobj @@ -3044,7 +3063,7 @@ endobj << /Type /StructElem /S /Div - /P 279 0 R + /P 281 0 R /K [287 0 R] >> endobj @@ -3058,18 +3077,17 @@ endobj /O /Layout /Placement /Block >>] - /K [3] - /Pg 368 0 R + /K [80] + /Pg 527 0 R >> endobj 288 0 obj << /Type /StructElem - /S /P - /P 26 0 R - /K [1 2] - /Pg 368 0 R + /S /Div + /P 281 0 R + /K [289 0 R] >> endobj @@ -3077,99 +3095,91 @@ endobj << /Type /StructElem /S /Span - /P 26 0 R + /P 288 0 R /A [<< /O /Layout /Placement /Block >>] - /K [0] - /Pg 368 0 R + /K [79] + /Pg 527 0 R >> endobj 290 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [297 0 R 295 0 R 293 0 R 291 0 R] + /S /L + /P 28 0 R + /A [<< + /O /List + /ListNumbering /Circle + >>] + /K [296 0 R 291 0 R] >> endobj 291 0 obj << /Type /StructElem - /S /Div + /S /LI /P 290 0 R - /K [292 0 R] + /K [295 0 R 292 0 R] >> endobj 292 0 obj << /Type /StructElem - /S /Span + /S /LBody /P 291 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [17] - /Pg 366 0 R + /K [293 0 R] >> endobj 293 0 obj << /Type /StructElem - /S /Div - /P 290 0 R - /K [294 0 R] + /S /P + /P 292 0 R + /K [294 0 R 78] + /Pg 527 0 R >> endobj 294 0 obj << /Type /StructElem - /S /Span + /S /Formula /P 293 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [16] - /Pg 366 0 R + /K [64 65 66 67 68 69 70 71 72 73 74 75 76 77] + /Pg 527 0 R >> endobj 295 0 obj << /Type /StructElem - /S /Div - /P 290 0 R - /K [296 0 R] + /S /Lbl + /P 291 0 R + /K [63] + /Pg 527 0 R >> endobj 296 0 obj << /Type /StructElem - /S /Span - /P 295 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [15] - /Pg 366 0 R + /S /LI + /P 290 0 R + /K [300 0 R 297 0 R] >> endobj 297 0 obj << /Type /StructElem - /S /Div - /P 290 0 R + /S /LBody + /P 296 0 R /K [298 0 R] >> endobj @@ -3177,98 +3187,81 @@ endobj 298 0 obj << /Type /StructElem - /S /Span + /S /P /P 297 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [14] - /Pg 366 0 R + /K [45 299 0 R] + /Pg 527 0 R >> endobj 299 0 obj << /Type /StructElem - /S /P - /P 26 0 R - /K [13] - /Pg 366 0 R + /S /Formula + /P 298 0 R + /K [46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62] + /Pg 527 0 R >> endobj 300 0 obj << /Type /StructElem - /S /Span - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [0 1 2 3 4 5 6 9 10 11 12] - /Pg 366 0 R + /S /Lbl + /P 296 0 R + /K [44] + /Pg 527 0 R >> endobj 301 0 obj << /Type /StructElem - /S /Strong - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [8] - /Pg 366 0 R + /S /Div + /P 28 0 R + /K [305 0 R 302 0 R] >> endobj 302 0 obj << /Type /StructElem - /S /Strong - /P 26 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [7] - /Pg 366 0 R + /S /Div + /P 301 0 R + /K [304 0 R 303 0 R] >> endobj 303 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [310 0 R 308 0 R 306 0 R 304 0 R] + /S /Formula + /P 302 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [37 38 39 40 41 42 43] + /Pg 527 0 R >> endobj 304 0 obj << /Type /StructElem - /S /Div - /P 303 0 R - /K [305 0 R] + /S /P + /P 302 0 R + /K [36] + /Pg 527 0 R >> endobj 305 0 obj << /Type /StructElem - /S /Span - /P 304 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [10] - /Pg 364 0 R + /S /Div + /P 301 0 R + /K [] >> endobj @@ -3276,77 +3269,71 @@ endobj << /Type /StructElem /S /Div - /P 303 0 R - /K [307 0 R] + /P 28 0 R + /K [313 0 R 307 0 R] >> endobj 307 0 obj << /Type /StructElem - /S /Span + /S /Div /P 306 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [9] - /Pg 364 0 R + /K [312 0 R 309 0 R 308 0 R] >> endobj 308 0 obj << /Type /StructElem - /S /Div - /P 303 0 R - /K [309 0 R] + /S /Formula + /P 307 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [26 27 28 29 30 31 32 33 34 35] + /Pg 527 0 R >> endobj 309 0 obj << /Type /StructElem - /S /Span - /P 308 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [8] - /Pg 364 0 R + /S /P + /P 307 0 R + /K [15 311 0 R 21 310 0 R 25] + /Pg 527 0 R >> endobj 310 0 obj << /Type /StructElem - /S /Div - /P 303 0 R - /K [311 0 R] + /S /Formula + /P 309 0 R + /K [22 23 24] + /Pg 527 0 R >> endobj 311 0 obj << /Type /StructElem - /S /Span - /P 310 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [7] - /Pg 364 0 R + /S /Formula + /P 309 0 R + /K [16 17 18 19 20] + /Pg 527 0 R >> endobj 312 0 obj << /Type /StructElem - /S /Div - /P 26 0 R - /K [330 0 R 328 0 R 327 0 R 325 0 R 324 0 R 322 0 R 321 0 R 319 0 R 318 0 R 316 0 R 315 0 R 313 0 R] + /S /P + /P 307 0 R + /K [14] + /Pg 527 0 R >> endobj @@ -3354,22 +3341,17 @@ endobj << /Type /StructElem /S /Div - /P 312 0 R - /K [314 0 R] + /P 306 0 R + /K [] >> endobj 314 0 obj << /Type /StructElem - /S /Span - /P 313 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [6] - /Pg 364 0 R + /S /Div + /P 28 0 R + /K [320 0 R 315 0 R] >> endobj @@ -3377,72 +3359,71 @@ endobj << /Type /StructElem /S /Div - /P 312 0 R - /K [] + /P 314 0 R + /K [319 0 R 316 0 R] >> endobj 316 0 obj << /Type /StructElem - /S /Div - /P 312 0 R - /K [317 0 R] + /S /P + /P 315 0 R + /K [318 0 R 12 317 0 R] + /Pg 527 0 R >> endobj 317 0 obj << /Type /StructElem - /S /Span + /S /Formula /P 316 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [5] - /Pg 364 0 R + /K [13] + /Pg 527 0 R >> endobj 318 0 obj << /Type /StructElem - /S /Div - /P 312 0 R - /K [] + /S /Formula + /P 316 0 R + /K [2 3 4 5 6 7 8 9 10 11] + /Pg 527 0 R >> endobj 319 0 obj << /Type /StructElem - /S /Div - /P 312 0 R - /K [320 0 R] + /S /P + /P 315 0 R + /K [1] + /Pg 527 0 R >> endobj 320 0 obj << /Type /StructElem - /S /Span - /P 319 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [4] - /Pg 364 0 R + /S /Div + /P 314 0 R + /K [] >> endobj 321 0 obj << /Type /StructElem - /S /Div - /P 312 0 R - /K [] + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [0] + /Pg 527 0 R >> endobj @@ -3450,31 +3431,31 @@ endobj << /Type /StructElem /S /Div - /P 312 0 R - /K [323 0 R] + /P 28 0 R + /K [329 0 R 327 0 R 325 0 R 323 0 R] >> endobj 323 0 obj << /Type /StructElem - /S /Span + /S /Div /P 322 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [3] - /Pg 364 0 R + /K [324 0 R] >> endobj 324 0 obj << /Type /StructElem - /S /Div - /P 312 0 R - /K [] + /S /Span + /P 323 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [73] + /Pg 525 0 R >> endobj @@ -3482,7 +3463,7 @@ endobj << /Type /StructElem /S /Div - /P 312 0 R + /P 322 0 R /K [326 0 R] >> endobj @@ -3496,8 +3477,8 @@ endobj /O /Layout /Placement /Block >>] - /K [2] - /Pg 364 0 R + /K [72] + /Pg 525 0 R >> endobj @@ -3505,152 +3486,1681 @@ endobj << /Type /StructElem /S /Div - /P 312 0 R - /K [] + /P 322 0 R + /K [328 0 R] >> endobj 328 0 obj << /Type /StructElem - /S /Div - /P 312 0 R - /K [329 0 R] + /S /Span + /P 327 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [71] + /Pg 525 0 R >> endobj 329 0 obj << /Type /StructElem - /S /Span - /P 328 0 R - /A [<< - /O /Layout - /Placement /Block - >>] - /K [1] - /Pg 364 0 R + /S /Div + /P 322 0 R + /K [330 0 R] >> endobj 330 0 obj << /Type /StructElem - /S /Div - /P 312 0 R - /K [] + /S /Span + /P 329 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [70] + /Pg 525 0 R >> endobj 331 0 obj << /Type /StructElem - /S /Span - /P 26 0 R + /S /Formula + /P 28 0 R /A [<< /O /Layout /Placement /Block >>] - /K [0] - /Pg 364 0 R + /K [67 68 69] + /Pg 525 0 R >> endobj 332 0 obj << /Type /StructElem - /S /P - /P 26 0 R - /K [2] - /Pg 362 0 R + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [59 60 61 62 63 64 65 66] + /Pg 525 0 R >> endobj 333 0 obj << /Type /StructElem - /S /P - /P 26 0 R - /K [334 0 R] + /S /Strong + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [58] + /Pg 525 0 R >> endobj 334 0 obj << /Type /StructElem - /S /Strong - /P 333 0 R - /K [1] - /Pg 362 0 R + /S /Formula + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [55 56 57] + /Pg 525 0 R >> endobj 335 0 obj << /Type /StructElem - /S /P - /P 26 0 R - /K [0] - /Pg 362 0 R + /S /Span + /P 28 0 R + /A [<< + /O /Layout + /Placement /Block + >>] + /K [51 52 53 54] + /Pg 525 0 R >> endobj 336 0 obj << - /Type /Font - 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