From 43a783d2eb0197a84a88ae871a8cbeb3505077b4 Mon Sep 17 00:00:00 2001 From: kilian Date: Wed, 4 Nov 2026 09:59:15 +0100 Subject: [PATCH] =?UTF-8?q?Korrektur=20Normalisierung=20der=20Werte=20in?= =?UTF-8?q?=20ILP=20Hypergraph=20und=20Ort=20Eigenst=C3=A4ndigkeitserkl?= =?UTF-8?q?=C3=A4rung?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Report/Masterarbeit_Kilian_Seng.pdf | Bin 2981481 -> 2981610 bytes Report/Masterarbeit_Kilian_Seng.tex | 60 ++++++++++++++-------------- 2 files changed, 30 insertions(+), 30 deletions(-) diff --git a/Report/Masterarbeit_Kilian_Seng.pdf b/Report/Masterarbeit_Kilian_Seng.pdf index f2933112c0198942c35645ce68935800a9b6cc00..5e8c9a2fff59dd0f16f4c6acf210b4bb9b5f999e 100644 GIT binary patch delta 34425 zcmX8YV{j%-*8t$yw#|)g+qP|+cWm3(*tR#=*tYGB`R4h)A6M0>n(jVzrn`E2X3joZ zfX_c$fa`gofW?yepqK%?PBLS(CWLMEyVJAtLeK}Q!5ZZqaf6-_0>x@JgaV1bQ&4t> z{pJ3>03yrewn`w=o+naFFDPGW2c#-?S}_|wKFqBae?_ub}HzfK@#zV zg7BG|fcGMslqGDKv{G_#0jFLCD1KQx#*ct$u&IDjz zf5j+1y5~JdjpS%sTar2Nj=b8tXD>nzzeJQAFqv=r_zf8tV9mxGa4J=*Euoic+^|Q}bwB$~2>=#oCLTVYd}Hi_z8CcUfmt<5+*_ z4o<6Aj#!H?Xz%k)_g89crMm+98%cot7f%EC$vWA-J>EPkp ziTO(gs3$251^u>=L0Yz{ocU=R)rY*zAaB+?H*!$n(-okn8W#W1eGfy`9zUUx+(QOP zkP5pdA{XABZaU9kF+Koj|8T;?Z7MZ6woJo6T6J0VZMm+}$LOyKHR)MKUC!F)3CAQh zyO&twdh{I~J1VNsOVjsb#03LCxF$bO2Dyksn~EgogF8@=Q79_ME?rHz{<(>eHpKO* zpCfm$EN~BXTm<2bDKF}*INLzOK%7l@gK9CBS8f+U92_v;BU@N_Irw~e5shk++=GhWlCGI!vgvVdjwHvPtDQ4v^Vhc`Wa6~w zpN)O({bL8Vd$qUhoAO7CqRgWPKZ9rZO81SO?3UA4)l3YKZ^Fs<%@S4D_H*2?71Wll7jiFPn*q2RCx$%DS1VN1G5#K(r0g-1#1NdilU z$^f$7C<1{7F>9zu1$_=#Mt{>~#yMGjz%m4TZ7fZxvNXj>!MTr2%0ZToFGoGq_!cq| zV^fFJ(j#oraPPSXD6N1J4rC+yYGKM!f4^BMiu|_C! zHIEO-41Ek6dGEq^r(d%8!1>}7bG-HkOq@#l6<$61eK88B^#q72-yp1JcA$e_Gl388 zxJ&_nzP>P83K$lPp8I3I2G^Q2!)}dnMc9Nw!z5}6|A@@s(M#U^>w5=_D_Y>}pCB&v zYVx>d$?_D^cNT1ZZM;guJDdq&*CQjtT!vu9eg7^GA|U=`KxlVFB%S{BVE3;SZ?k+) z!-9AYj04)5sgPo)375c~jjDBDTX$_K>AL}ptKUfbwFSKQOazS@GH>VDviX?UPa4X3 zu;<_mcokp&&BPv568|GEt(U=q0bM77&9Tmc@Zi#UHW1X+J)ORsnNyTXQK2z(3p}8? zaP?iNyR>D`vAL>5n#^u4lH&|rGP_m{s_LWRv<8jyPCO9t5jOwt6h2`+14{r%85LD( zl>I|Jbh^GGfpQ$rS4A0`gdn%mGn0^S{i@2atM(Gy``+3^Jh*}tRRQbpkH_%?ByJuO zu;nhD$ym~&`p0j_KmVTIE&=7QAL&B*olqM1Vo4iRZw&7Y8;~*f&Ph*Y9H8JHg3lpwnvn+Z6^1_Skf|`qUG??#@2pz|Lwht3GTk0`()T} z)k$3oD=!zF_14Gu%jXSet*%zpqZMDAM}NmDz-Og?h!FwCXJcjhNoc-E`$?|i#xU;p zWQ)V*Zt2a7WfIes(FRDDPmq}+i)Y2t5I`SoPe>^=vimMr!A`%8aZ*4{2k=2GN9o4hrX!wluO`XY?3w> zgaa(k?Y$@N>Myj8%mc?59U+ia0>fZda>0DJm1D6|hn%8AI`SWs7*o!Aw}ap|9p}Iu zeqQ#rUdeWQ8$-9y>Ng1+j-XjxKKmhP*?oS zNL>A-H_osB%fu-A8`(0Z>t=O+D`6zdP(d*1ow&j_CzOaes`9oXJ^1Lo9xAwSShNRY zQ~i#bij}O0R1RJ4f{FJ2nuq6mZG}sBf?rhF(KfrwgxaV4Yxo*17&PyNBmHDMP)j

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zenU}<^?u|FiVj=vXL}X3T3^Gkq9fL~szety-g_?U*x17nibo@qz7e7F=?IC< z2=x^an!XXC_1*~WZiM9bB6RFxRy&;|kR2+$S)?SC85W{P=m5nKWbU=e6rz%s~y%RpO8R>2y$0<={?djmGX z7Ptzu2SXcAw4>(+*a0`eEubwKcfc;-#eX`wx4kj0KFvG-G&?lXY%@p~f+A21c>AA@ z12zYx*|m{on?{-~0BJU|q}jQWW=l|-JwWLMr~z!rNV6>87hvm9n(YH=_6wxhAdv0@{eTTaX?6&u jhiu@^PokUtV6*f8Tm4p7m%x54APO}zHwq;sMNdWwqiQ~q diff --git a/Report/Masterarbeit_Kilian_Seng.tex b/Report/Masterarbeit_Kilian_Seng.tex index 64e0ecd..89afc73 100644 --- a/Report/Masterarbeit_Kilian_Seng.tex +++ b/Report/Masterarbeit_Kilian_Seng.tex @@ -1201,7 +1201,7 @@ 3-Methylxanthin & 0.08 & 0.11\\ 7-Methylxanthin & 0.16 & 0.12\\ Theophylline & 0.11 & 0.09\\ - Paraxanthin & 0.19 & 0.1\\ + Paraxanthin & 0.19 & 0.10\\ Theobromin & 0.07 & 0.18\\ Koffein & 0.19 & 0.17\\ \hline @@ -1224,7 +1224,7 @@ p-Coumarsäure & 0.25 & 0.29\\ m-Coumarsäure & 0.08 & 0.08\\ Benzaldehyd & 0.06 & 0.12\\ - Kaffeesäure & 0.22 & 0.1\\ + Kaffeesäure & 0.22 & 0.10\\ 3-Hydroxybenzaldehyd & 0.01 & 0.02\\ 4-Hydroxybenzaldehyd & 0.22 & 0.17\\ 3,4-Dihydroxybenzaldehyd & 0.11 & 0.11\\ @@ -1234,7 +1234,7 @@ \end{table} \FloatBarrier \section{ILP: Ein-Molekül-Reaktionen} - Der Hypergraph der komplett explorierten Synthese wurde an Gurobi übergeben und um eine Kante, die in das Startmolekül hineinfließt und aus dem Zielmolekül herausfließt, erweitert. Die Wahrscheinlichkeiten wurden als konstante Werte $p_{i,e}$ den Kanten $e$ des Hypergraphen zugeordnet. Die Wahrscheinlichkeit des Moleküls wurde den Kanten zugeordnet, welche in den Knoten fließen. Die Kante 4 von Zimtsäure zu Benzaldehyd hat also die Wahrscheinlichkeit $p_{1,4} = 0.09$, dass diese Reaktion dem ersten Referenzspektrum mit p-Coumarsäure entspricht. + Der Hypergraph der komplett explorierten Synthese wurde an Gurobi übergeben und um eine Kante, die in das Startmolekül hineinfließt und aus dem Zielmolekül herausfließt, erweitert. Die Wahrscheinlichkeiten wurden als konstante Werte $p_{i,e}$ den Kanten $e$ des Hypergraphen zugeordnet. Die Wahrscheinlichkeit des Moleküls wurde den Kanten zugeordnet, welche in den Knoten fließen. Die Kante 4 von Zimtsäure zu Benzaldehyd hat also die Wahrscheinlichkeit $p_{1,4} = 0.06$, dass diese Reaktion dem ersten Referenzspektrum mit p-Coumarsäure entspricht. Für jede Kante werden vier ganzzahlige Variablen $x_{e}$, $b_{e}$, $n_{1,e}$ und $n_{2,e}$ definiert. Die Variable $b_{e}$ ist dabei eine Wahrheitsvariable die definiert, ob eine Kante verwendet wird. Die Variable $x_{e}$ beschreibt wie oft die selbe Kante verwendet wird. Die Variablen $n_{1,e}$ und $n_{2,e}$ sind ebenfalls Wahrheitsvariablen und legen fest, welche zwei Reaktionen den Referenz NMR-Spektren entsprechen und deswegen zu der Zielfunktion dazuzählen. Dabei ist $n_{1,e}$ die Zuordnungsvariable zu dem ersten Referenzspektrum mit 7-Methylxanthin oder p-Coumarsäure und $n_{2,e}$ die Zuordnungsvariable zu dem zweiten Referenzspektrum mit 3,7-Methylxanthin oder 4-Hydroxybenzaldehyd. Die Variablen unterliegen den Beschränkungen, dass: \begin{itemize} @@ -1263,19 +1263,19 @@ \label{hypergraphcaffsynth} Index & Edukt & Produkt & $n_{\text{7-Methylxanthin},e}$ & $n_{\text{3,7-Dimethylxanthin},e}$\\ \hline - 1 & & Xanthin & 0.12 & 0.25\\ - 2 &Xanthin & 1-Methylxanthin & 0.18 & 0.16\\ - 3 &Xanthin & 3-Methylxanthin & 0.12 & 0.2\\ - 4 &Xanthin & 7-Methylxanthin & 0.25 & 0.21\\ - 5 &1-Methylxanthin & Theophyllin & 0.18 & 0.16\\ - 6 &1-Methylxanthin & Paraxanthin & 0.3 & 0.18\\ - 7 &3-Methylxanthin & Theophyllin & 0.18 & 0.16\\ - 8 &3-Methylxanthin & Theobromin & 0.1 & 0.31\\ - 9 &7-Methylxanthin & Paraxanthin & 0.3 & 0.18\\ - 10 &7-Methylxanthin & Theobromin & 0.1 & 0.31\\ - 11 &Theophyllin & Koffein & 0.3 & 0.29\\ - 12 &Paraxanthin & Koffein & 0.3 & 0.29\\ - 13 &Theobromin & Koffein & 0.3 & 0.29\\ + 1 & & Xanthin & 0.08 & 0.14\\ + 2 &Xanthin & 1-Methylxanthin & 0.11 & 0.09\\ + 3 &Xanthin & 3-Methylxanthin & 0.08 & 0.11\\ + 4 &Xanthin & 7-Methylxanthin & 0.16 & 0.12\\ + 5 &1-Methylxanthin & Theophyllin & 0.11 & 0.09\\ + 6 &1-Methylxanthin & Paraxanthin & 0.19 & 0.10\\ + 7 &3-Methylxanthin & Theophyllin & 0.11 & 0.09\\ + 8 &3-Methylxanthin & Theobromin & 0.07 & 0.18\\ + 9 &7-Methylxanthin & Paraxanthin & 0.19 & 0.10\\ + 10 &7-Methylxanthin & Theobromin & 0.07 & 0.18\\ + 11 &Theophyllin & Koffein & 0.19 & 0.17\\ + 12 &Paraxanthin & Koffein & 0.19 & 0.17\\ + 13 &Theobromin & Koffein & 0.19 & 0.17\\ 14 &Koffein & & 0.0 & 0.0\\ \hline \end{tabular} @@ -1319,19 +1319,19 @@ \label{hypergraphvanilsynth} Index & Edukt & Produkt & $n_{\text{p-Coumarsäure},e}$ & $n_{\text{4-Hydroxybenzaldehyd},e}$\\ \hline - 1 & & Zimtsäure & 0.09 & 0.17\\ - 2 &Zimtsäure & p-Coumarsäure & 0.38 & 0.44\\ - 3 &Zimtsäure & m-Coumarsäure & 0.12 & 0.12\\ - 4 &Zimtsäure & Benzaldehyd & 0.09 & 0.18\\ - 5 &p-Coumarsäure & Kaffeesäure & 0.34 & 0.15\\ - 6 &p-Coumarsäure & 4-Hydroxybenzaldehyd & 0.34 & 0.26\\ - 7 &m-Coumarsäure & Kaffeesäure & 0.34 & 0.15\\ - 8 &m-Coumarsäure & 3-Hydroxybenzaldehyd & 0.02 & 0.03\\ - 9 &Benzaldehyd & 3-Hydroxybenzaldehyd & 0.02 & 0.03\\ - 10 &Benzaldehyd & 4-Hydroxybenzaldehyd & 0.1 & 0.31\\ - 11 &Kaffeesäure & 3,4-Dihydroxybenzaldehyd & 0.17 & 0.17\\ - 12 &3-Hydroxybenzaldehyd & 3,4-Dihydroxybenzaldehyd & 0.17 & 0.17\\ - 13 &4-Hydroxybenzaldehyd & 3,4-Dihydroxybenzaldehyd & 0.17 & 0.17\\ + 1 & & Zimtsäure & 0.06 & 0.11\\ + 2 &Zimtsäure & p-Coumarsäure & 0.25 & 0.29\\ + 3 &Zimtsäure & m-Coumarsäure & 0.08 & 0.08\\ + 4 &Zimtsäure & Benzaldehyd & 0.06 & 0.12\\ + 5 &p-Coumarsäure & Kaffeesäure & 0.22 & 0.10\\ + 6 &p-Coumarsäure & 4-Hydroxybenzaldehyd & 0.22 & 0.17\\ + 7 &m-Coumarsäure & Kaffeesäure & 0.22 & 0.10\\ + 8 &m-Coumarsäure & 3-Hydroxybenzaldehyd & 0.01 & 0.02\\ + 9 &Benzaldehyd & 3-Hydroxybenzaldehyd & 0.01 & 0.02\\ + 10 &Benzaldehyd & 4-Hydroxybenzaldehyd & 0.22 & 0.17\\ + 11 &Kaffeesäure & 3,4-Dihydroxybenzaldehyd & 0.11 & 0.11\\ + 12 &3-Hydroxybenzaldehyd & 3,4-Dihydroxybenzaldehyd & 0.11 & 0.11\\ + 13 &4-Hydroxybenzaldehyd & 3,4-Dihydroxybenzaldehyd & 0.11 & 0.11\\ 14 &3,4-Dihydroxybenzaldehyd & & 0.0 & 0.0\\ \hline \end{tabular} @@ -1700,7 +1700,7 @@ \begin{tabular}{lp{12em}l} - Bielefeld, \today && \hspace{4cm} \\\cline{1-1}\cline{3-3} \\ + Detmold, \today && \hspace{4cm} \\\cline{1-1}\cline{3-3} \\ \end{tabular} \vspace{-0.5 cm}