dsotofor / Manuscrit

Commit d5c40fb1603de0971e4b57623b43424cedb5a0c5

Authored by dsotofor 2025-07-12 19:22:23 +0200

Exists in main

version all ok, corrections to do in general conclusion...

Showing 5 changed files with 39 additions and 39 deletions Side-by-side Diff

chapters/ESCBR.tex
chapters/TS.tex
main.log
main.pdf
main.synctex.gz

...	...	@@ -178,9 +178,9 @@
178	178
179	179	\begin{equation}
180	180	s_{w,j}^m=\begin{cases}
181		- s_{j,k}^m+\mathcal{N}(0,1)& si \; (\mathcal{U}_{int}(0,10))\%2=0\\
182		- s_{j,k}^m-\mathcal{N}(0,1)&sinon
183		- \end{cases}
	181	+ s_{j,k}^m+X_1& si \; (X_2)\%2=0\\
	182	+ s_{j,k}^m-X_1&sinon
	183	+ \end{cases};X_1 \sim \mathcal{N}(0,1), X_2 \sim \mathcal{U}_{int}(0,10)
184	184	\end{equation}
185	185
186	186	\begin{figure}
...	...	@@ -199,7 +199,7 @@
199	199	La fonction objectif \ref{eqOpt} établit un rapport entre la distance de la solution générée $s^m_w$ et les $x$ solutions connues $s^m_x$ avec un facteur aléatoire de \textit{drift} d'une part, et la distance entre le problème cible $p^n_w$ et les $x$ problèmes connus $p^n_x$ d'autre part. Ici, la difficulté à trouver le point optimal réside dans le fait que les points de l'espace ne peuvent pas tous convenir en tant que solution cible. La solution cible finale dépend donc des informations des solutions connues. L'objectif est d'utiliser les informations disponibles de chaque cas (problème et solution) pour valider et générer l'ensemble de solutions proposées.\\
200	200
201	201	\begin{equation}
202		-\lambda_x(p_w, s_w) = \left( \frac{d(s_w^m,(s_x^m+rn(0,d(p_w^n, p_i^n))))}{d(p_w^n,p_x^n)^2} \right)
	202	+\lambda_x(p_w, s_w) = \left( \frac{d(s_w^m,(s_x^m+X)))}{d(p_w^n,p_x^n)^2} \right); \; X \sim \mathcal{N}(0,d(p_w^n, p_x^n)
203	203	\label{eqOpt0}
204	204	\end{equation}
205	205

...	...	@@ -24,12 +24,8 @@
24	24	La famille de distributions de probabilité Beta est utilisée pour définir dynamiquement le niveau de complexité (équation \ref{eqBeta}) à proposer à l'apprenant. Cet algorithme permet de recommander des niveaux de complexité non contigus et dans lesquels des lacunes ont été détectées. Les paramètres initiaux des distributions de probabilité peuvent forcer le système à recommander des niveaux de complexité contigus (juste inférieur ou supérieur).
25	25
26	26	\begin{equation}
27		-B(x, \alpha, \beta) =
28		-\begin{cases}
29		-\frac{x^{\alpha-1}(1-x)^{\beta - 1}}{\int_0^1 u^{\alpha - 1}(1-u)^{\beta - 1}du} & si \; x \in [0, 1] \\
30		-0&sinon
31		-\end{cases}
32		-\label{eqBeta}
	27	+ Beta(\theta \| \alpha, \beta) = \frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha) \Gamma(\beta)}\theta^{\alpha-1}(1-\theta)^{\beta-1}
	28	+ \label{eqBeta}
33	29	\end{equation}
34	30
35	31	\begin{table}[!ht]

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