2 \immediate\closeout\minitoc
11 \@writefile{toc}{\contentsline {titlech}{\numberline {1}Distributed Average Consensus in Large Asynchronous Sensor Networks}{1}}
12 \@writefile{toc}{\authcount {1}}
13 \@writefile{toc}{\contentsline {authorch}{Jacques M. Bahi, Arnaud Giersh, Abdallah Makhoul and Ahmed Mostefaoui}{1}}
14 \@writefile{toc}{\contentsline {section}{\numberline {1.1}Introduction}{1}}
42 \@writefile{toc}{\contentsline {section}{\numberline {1.2}Overview of Averaging Problem in Sensor Networks}{3}}
45 \@writefile{toc}{\contentsline {section}{\numberline {1.3}Asynchronous Distributed Consensus with messages loss}{4}}
46 \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.1}Problem Formulation}{4}}
47 \newlabel{eqno1}{{1.1}{4}}
49 \@writefile{lot}{\contentsline {table}{\numberline {1.1}{\ignorespaces Notations}}{5}}
50 \newlabel{notations}{{1.1}{5}}
51 \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.2}Asynchronous scheme}{5}}
55 \@writefile{loa}{\contentsline {algorithm}{\numberline {1}{\ignorespaces The General Algorithm.}}{6}}
56 \newlabel{general}{{1}{6}}
57 \newlabel{x_(t+1)}{{1.2}{6}}
58 \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.3}Theoretical Analysis (Convergence)}{6}}
59 \newlabel{assump:ConnectedGraph}{{1}{6}}
60 \newlabel{Inf Assumption}{{2}{6}}
61 \newlabel{PingPong}{{3}{6}}
62 \newlabel{h5_2}{{1.3}{6}}
64 \@writefile{lof}{\contentsline {figure}{\numberline {1.1}{\ignorespaces Example of jointly connected graphs}}{7}}
65 \newlabel{fig:jointly}{{1.1}{7}}
66 \newlabel{THE}{{1}{7}}
67 \newlabel{conservation}{{1.5}{7}}
68 \newlabel{lemma:1}{{1}{7}}
69 \newlabel{Event E_1}{{1.6}{8}}
70 \newlabel{Event E_2}{{1.7}{8}}
71 \newlabel{lemma:2}{{2}{8}}
72 \newlabel{lemma:3}{{3}{8}}
73 \newlabel{lemma:4}{{4}{9}}
74 \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.4}Practical Issues}{9}}
75 \newlabel{h5_2bis}{{1.8}{10}}
76 \newlabel{h6}{{1.9}{10}}
77 \@writefile{loa}{\contentsline {algorithm}{\numberline {2}{\ignorespaces Temporally updating weights of node $i$.}}{11}}
78 \newlabel{WeightUpdate}{{2}{11}}
79 \@writefile{toc}{\contentsline {subsection}{\numberline {1.3.5}Illustrative Example}{11}}
83 \@writefile{lof}{\contentsline {figure}{\numberline {1.2}{\ignorespaces An example of a sensor network composed of four nodes with their initial measurements. }}{12}}
84 \newlabel{fig:example}{{1.2}{12}}
85 \@writefile{toc}{\contentsline {section}{\numberline {1.4}Experimental Results}{12}}
86 \newlabel{Exp}{{1.4}{12}}
88 \@writefile{toc}{\contentsline {subsection}{\numberline {1.4.1}Basic Behaviour}{13}}
89 \newlabel{BH}{{1.4.1}{13}}
90 \@writefile{lof}{\contentsline {figure}{\numberline {1.3}{\ignorespaces The Mean Error $\varepsilon $}}{14}}
91 \newlabel{Error}{{1.3}{14}}
92 \@writefile{toc}{\contentsline {subsection}{\numberline {1.4.2}Dynamic topology}{14}}
93 \@writefile{lof}{\contentsline {figure}{\numberline {1.4}{\ignorespaces Number of Iterations}}{14}}
94 \newlabel{Dynamic}{{1.4}{14}}
95 \@writefile{lof}{\contentsline {figure}{\numberline {1.5}{\ignorespaces Simulated Time}}{15}}
96 \newlabel{DynamicTime}{{1.5}{15}}
97 \@writefile{toc}{\contentsline {subsection}{\numberline {1.4.3}Larger Sensor Network}{15}}
98 \@writefile{toc}{\contentsline {section}{\numberline {1.5}Further Discussions}{15}}
99 \newlabel{DISC}{{1.5}{15}}
105 \@writefile{lof}{\contentsline {figure}{\numberline {1.6}{\ignorespaces Number of iterations}}{16}}
106 \newlabel{Density}{{1.6}{16}}
107 \@writefile{lof}{\contentsline {figure}{\numberline {1.7}{\ignorespaces Simulated Time}}{16}}
108 \newlabel{DensityTime}{{1.7}{16}}
115 \@writefile{toc}{\contentsline {section}{\numberline {1.6}Conclusion and Future Work}{17}}
116 \@writefile{toc}{\contentsline {section}{References}{17}}
117 \@mtwritefile{\contentsline {mtchap}{References}{17}}
135 \immediate\closeout\minitoc