X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/ThesisAli.git/blobdiff_plain/a5b27a679ef2809581fb27959ecfcf348dcbbe39..b191d9759ebf18d2e624b3b4704485e1187621b2:/SlidesAli/These.tex

diff --git a/SlidesAli/These.tex b/SlidesAli/These.tex
index 94c4bef..272a409 100644
--- a/SlidesAli/These.tex
+++ b/SlidesAli/These.tex
@@ -98,7 +98,7 @@
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 02    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame} {Problem Definition, Solution, and Objectives}
+\begin{frame} {Problem definition and solution}
  \vspace{-3.5em}
  \begin{figure}
    \includegraphics[width=0.495\textwidth]{Figures/6}
@@ -110,7 +110,7 @@
 %   \includegraphics[width=0.475\textwidth]{Figures/13}
 \end{figure}
 
- \begin{block}{\textcolor{white}{ MAIN QUESTION?}}
+ \begin{block}{\textcolor{white}{MAIN QUESTION}}
   		\textcolor{black}{How to minimize the energy consumption and extend the network lifetime when covering a certain area?}
 \end{block}
  \end{frame}
@@ -119,12 +119,15 @@
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 03    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{Problem Definition, Solution, and Objectives}
+\begin{frame}{Problem definition and solution}
 
-\begin{block}{\textcolor{white}{OUR SOLUTION: distributed optimization process}}
-\bf \textcolor{black}{Division into subregions}\\
-\bf \textcolor{black}{For each subregion:}
+\begin{block}{\textcolor{white}{OUR SOLUTION $\blacktriangleright$ Distributed optimization process}}
+\begin{enumerate} [i)]
+\item \bf \textcolor{black}{Division into subregions}
+\item \bf \textcolor{black}{For each subregion}
   	
+\end{enumerate}
+
  \begin{itemize}
          \item \bf \textcolor{magenta}{Leader election}
          \item \bf \textcolor{magenta}{Activity Scheduling based optimization}
@@ -213,7 +216,7 @@
     \begin{femtoBlock}	
 	{Sensor \\}
 		 \begin{itemize}
-  			\item  Electronic low-cost tiny device
+  			\item Electronic low-cost tiny device
   			\item Sense, process and transmit data
   			\item Limited energy, memory and processing capabilities
   		\end{itemize}
@@ -286,8 +289,8 @@
 
      \includegraphics[height = 5cm]{Figures/WSN-M.pdf}
  \end{figure} 
- 
- \bf \textcolor{blue} {Our approach: includes cluster architecture and scheduling schemes}
+ \vspace{-1.0em}
+ \bf \textcolor{blue} {Our approach includes cluster architecture and scheduling schemes}
 \end{frame}
 
 %\begin{frame}{Energy-Efficient Mechanisms of a working WSN}
@@ -303,15 +306,15 @@
 %%%%%%%%%%%%%%%%%%%%
 \begin{frame}{Network lifetime}
 \vspace{-1.5em}
-\begin{block}{\textcolor{white} {Some definitions:}}
+\begin{block}{\textcolor{white} {Some definitions}}
 \small
 \begin{enumerate}[i)]
-\item \textcolor{black} {Time spent until death of the first sensor (or cluster head).}
-\item \textcolor{black} {Time spent until death of all wireless sensor nodes in WSN.}
-\item  \textcolor{black} {Time spent by WSN in covering each target by at least one sensor.}
-\item  \textcolor{black} {Time during which the area of interest is covered by at least k nodes.}
-\item \textcolor{black} {Elapsed time until losing the connectivity or the coverage.}
-\item \bf \textcolor{red} {Time elapsed until the coverage ratio becomes less than a predetermined threshold $\alpha$.}
+\item \textcolor{black} {Time spent until death of the first sensor (or cluster head)}
+\item \textcolor{black} {Time spent until death of all wireless sensor nodes in WSN}
+\item  \textcolor{black} {Time spent by WSN in covering each target by at least one sensor}
+\item  \textcolor{black} {Time during which the area of interest is covered by at least k nodes}
+\item \textcolor{black} {Elapsed time until losing the connectivity or the coverage}
+\item \bf \textcolor{red} {Time elapsed until the coverage ratio becomes less than a predetermined threshold $\alpha$}
 \end{enumerate}
 \end{block}
 
@@ -327,18 +330,18 @@
 %%%%%%%%%%%%%%%%%%%%
 \begin{frame}{Coverage in Wireless Sensor Networks}
  
-\begin{block} <1-> {\textcolor{white} {Coverage definition:}} 
-\textcolor{blue} {Coverage} reflects how well a sensor field is monitored efficiently using as less energy as possible.
+\begin{block} <1-> {\textcolor{white} {Coverage definition}} 
+\textcolor{blue} {Coverage} reflects how well a sensor field is monitored efficiently using as less energy as possible
 \end{block}
  
 
  
-\begin{block} <2-> {\textcolor{white} {Coverage types:}} 
+\begin{block} <2-> {\textcolor{white} {Coverage types}} 
 \begin{enumerate}[i)]
-\item \small  \textcolor{red} {Area coverage: every point inside an area has to be monitored.}
-\item  \textcolor{blue} {Target coverage:} only a finite number of discrete points called targets have to be monitored.
+\item \small  \textcolor{red} {Area coverage $\blacktriangleright$ every point inside an area has to be monitored}
+\item  \textcolor{blue} {Target coverage} $\blacktriangleright$ only a finite number of discrete points called targets have to be monitored
 
-\item  \textcolor{blue} {Barrier coverage:} detection of targets as they cross a barrier such as in intrusion detection and border surveillance applications.
+\item  \textcolor{blue} {Barrier coverage} $\blacktriangleright$ detection of targets as they cross a barrier such as in intrusion detection and border surveillance applications
 \end{enumerate}
 \end{block}
  
@@ -355,7 +358,7 @@
 %%%%%%%%%%%%%%%%%%%% 
 \begin{frame}{Existing works}
 \vspace{-0.3em}
-\begin{block}  {\textcolor{white} {Coverage approaches:}} 
+\begin{block}  {\textcolor{white} {Coverage approaches}} 
 %Most existing coverage approaches in literature classified into
 \begin{enumerate}[i)]
 \item \textcolor{blue} { Full centralized coverage algorithms}
@@ -388,7 +391,7 @@
 
 \end{frame}
 
-\begin{frame}{Existing works: DESK algorithm (Vu et al.)}
+\begin{frame}{Existing works $\blacktriangleright$ DESK algorithm (Vu et al.)}
 \vspace{-1.5em}
 \begin{figure}[!t]
 	   \includegraphics[height = 4.0cm]{Figures/DESK.eps}
@@ -397,9 +400,9 @@
      
      \begin{itemize}
        \item Requires only one-hop neighbor information (fully distributed)
-       \item Each sensor decides its status (Active or Sleep) based on the perimeter coverage model without optimization
+       \item Each sensor decides its status (Active or Sleep) based on the perimeter coverage model, without optimization
               
-     \end{itemize}
+\end{itemize}
 
 
 %\tiny \bf \textcolor{blue}{DESK is chosen for comparison because it works into rounds fashion similar to our approaches, as well as DESK is a full distributed coverage approach.}
@@ -407,7 +410,7 @@
 
 \end{frame}
 
-\begin{frame}{Existing works: GAF algorithm (Xu et al.)}
+\begin{frame}{Existing works $\blacktriangleright$ GAF algorithm (Xu et al.)}
 
 \vspace{-3.3em}
  \begin{columns}[c]
@@ -428,7 +431,7 @@
 	\begin{itemize}
 	\item Distributed energy-based scheduling approach
   	\item Uses geographic location information to divide the area into a fixed square grids
-  	\item Nodes are in one of three sates: discovery, active, or sleep
+  	\item Nodes are in one of three sates $\blacktriangleright$ discovery, active, or sleep
   	\item  Only one node staying active in grid
   	\item  The fixed grid is square with r units on a side
   	 \item  Nodes cooperate within each grid to choose the active node
@@ -460,26 +463,26 @@
 \vspace{-0.1cm}
 
 \begin{enumerate} [$\divideontimes$]
-  		    \item  Static wireless sensor, homogeneous in terms of: 
+  		    \item  Static wireless sensor, homogeneous in terms of  
              \begin{itemize}
              \item Sensing, communication, and processing capabilities
              \end{itemize}
   			\item  Heterogeneous initial energy
   			\item  High density uniform deployment 
-  			 \item Its $R_c\geq 2R_s$  for imply connectivity among active nodes during complete coverage (hypothesis proved by Zhang and Zhou)
+  			 \item $R_c\geq 2R_s$   complete coverage $\Rightarrow$ connectivity (proved by Zhang and Zhou)
 
   			 \item  Multi-hop communication
-  			 \item  Known location by:
+  			 \item  Known location by 
     \begin{itemize}
      \item Embedded GPS  or location discovery algorithm          
     \end{itemize}
     
-    \item Using two kinds of packets: 
+    \item Using two kinds of packets  
         \begin{itemize}    	
     	   \item INFO packet
     	   \item ActiveSleep packet
         \end{itemize}
-        \item Five status for each node:
+        \item Five status for each node 
         \begin{itemize}    	
     	   \item  \small LISTENING, ACTIVE, SLEEP, COMPUTATION, and COMMUNICATION
         \end{itemize}
@@ -500,21 +503,21 @@
 
 
 
-\begin{frame}{Our general scheme}
+\begin{frame}{General scheme}
 \vspace{-0.2cm}
 \begin{figure}[ht!]
  \includegraphics[width=110mm]{Figures/GeneralModel.jpg}
  \end{figure} 
  
 \begin{itemize}
-\item DiLCO and PeCO  $\blacktriangleright$ use one round sensing ($T=1$)
-\item MuDiLCO $\blacktriangleright$ uses multiple rounds sensing ($T=1\cdots T$)
+\item DiLCO and PeCO  $\blacktriangleright$ one round sensing ($T=1$)
+\item MuDiLCO $\blacktriangleright$ multiple rounds sensing ($T=1\cdots T$)
 \end{itemize}
 
 \end{frame}
 
 
-\begin{frame}{Our general scheme}
+\begin{frame}{General scheme}
   \vspace{-0.2cm}
 \begin{enumerate} [i)]
 \item \textcolor{blue}{\textbf{INFORMATION EXCHANGE}} $\blacktriangleright$ Sensors exchange through multi-hop communication, their
@@ -561,7 +564,7 @@
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 15    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small DiLCO Protocol $\blacktriangleright$ Coverage Problem Formulation}
+\begin{frame}{\small DiLCO protocol $\blacktriangleright$ Coverage problem formulation}
 \vspace{0.2cm}
 \centering
 \includegraphics[height = 7.2cm]{Figures/modell1.pdf}
@@ -572,7 +575,7 @@
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 16    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small DiLCO Protocol $\blacktriangleright$ DiLCO Protocol Algorithm}
+\begin{frame}{\small DiLCO protocol $\blacktriangleright$ DiLCO protocol algorithm}
 %\begin{femtoBlock} {}
 \centering
 %\includegraphics[height = 7.2cm]{Figures/algo.jpeg}
@@ -587,11 +590,11 @@
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 18    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small DiLCO Protocol $\blacktriangleright$ Simulation Framework}
+\begin{frame}{\small DiLCO protocol $\blacktriangleright$ Simulation framework}
 \vspace{-0.8cm}
 \small
 \begin{table}[ht]
-\caption{Relevant parameters for simulation.}
+\caption{Relevant parameters for simulation}
 \centering
 \begin{tabular}{c|c}
 \hline
@@ -619,9 +622,9 @@ Network Simulator & Discrete Event Simulator OMNeT++
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 19    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small DiLCO Protocol $\blacktriangleright$ Energy Model \& Performance Metrics }
+\begin{frame}{\small DiLCO protocol $\blacktriangleright$ Energy model \& performance metrics }
 %\vspace{-1.8cm}
-\begin{femtoBlock} {Energy Consumption Model}
+\begin{femtoBlock} {Energy consumption model}
 \vspace{-1.0cm}
 \begin{table}[h]
 %\centering
@@ -644,14 +647,14 @@ Network Simulator & Discrete Event Simulator OMNeT++
 
 \end{femtoBlock}
 \vspace{-0.5cm}
-\begin{femtoBlock} {Performance Metrics}
+\begin{femtoBlock} {Performance metrics}
 \small
-\begin{enumerate}[$\mapsto$]
+\begin{enumerate}[$\blacktriangleright$]
 
 \item {{\bf Coverage Ratio (CR)}}
-\item{{\bf Number of Active Sensors Ratio (ASR)}}
-\item {{\bf  Energy Consumption}}
-\item {{\bf Network Lifetime}}
+\item {{\bf Number of Active Sensors Ratio (ASR)}}
+\item {{\bf Energy consumption}}
+\item {{\bf Network lifetime}}
 %\item {{\bf Execution Time}}
 %\item {{\bf Stopped Simulation Runs}}
 
@@ -664,7 +667,7 @@ Network Simulator & Discrete Event Simulator OMNeT++
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 20    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{ \small DiLCO Protocol $\blacktriangleright$ Performance Comparison}
+\begin{frame}{ \small DiLCO protocol $\blacktriangleright$ Performance comparison}
 
 \vspace{-0.5cm}
 \begin{figure}[h!]
@@ -683,7 +686,7 @@ Network Simulator & Discrete Event Simulator OMNeT++
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 20    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{ \small DiLCO Protocol $\blacktriangleright$ Performance Comparison}
+\begin{frame}{ \small DiLCO protocol $\blacktriangleright$ Performance comparison}
 \vspace{-0.5cm}
 
 \begin{figure}[h!]
@@ -712,7 +715,7 @@ Network Simulator & Discrete Event Simulator OMNeT++
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 22    %%
 %%%%%%%%%%%%%%%%%%%%
-\begin{frame}{ \small DiLCO Protocol $\blacktriangleright$ Performance Comparison}
+\begin{frame}{ \small DiLCO protocol $\blacktriangleright$ Performance comparison}
 \vspace{-0.5cm}
 \begin{figure}%[h!]
 \begin{columns}[c]
@@ -734,7 +737,7 @@ Network Simulator & Discrete Event Simulator OMNeT++
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 23    %%
 %%%%%%%%%%%%%%%%%%%%
-\begin{frame}{ \small DiLCO Protocol $\blacktriangleright$ Performance Comparison}
+\begin{frame}{ \small DiLCO protocol $\blacktriangleright$ Performance comparison}
 \vspace{-0.5cm}
 \begin{figure}%[h!]
 \begin{columns}[c]
@@ -778,7 +781,7 @@ Network Simulator & Discrete Event Simulator OMNeT++
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 29    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small MuDiLCO Protocol $\blacktriangleright$  Multiround Coverage Problem Formulation}
+\begin{frame}{\small MuDiLCO protocol $\blacktriangleright$  Multiround coverage problem Formulation}
 \vspace{0.2cm}
 
 \centering
@@ -801,7 +804,7 @@ Network Simulator & Discrete Event Simulator OMNeT++
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 31    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small MuDiLCO Protocol $\blacktriangleright$ Results Analysis and Comparison}
+\begin{frame}{\small MuDiLCO protocol $\blacktriangleright$ Results analysis and comparison}
 \vspace{-0.5cm}
 \begin{figure}[h!]
 \centering
@@ -815,7 +818,7 @@ Network Simulator & Discrete Event Simulator OMNeT++
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 32    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small MuDiLCO Protocol $\blacktriangleright$ Results Analysis and Comparison}
+\begin{frame}{\small MuDiLCO protocol $\blacktriangleright$ Results analysis and comparison}
 \vspace{-0.5cm}
 \begin{figure}[h!]
 \centering
@@ -856,7 +859,7 @@ Network Simulator & Discrete Event Simulator OMNeT++
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 35    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small MuDiLCO Protocol $\blacktriangleright$ Results Analysis and Comparison}
+\begin{frame}{\small MuDiLCO protocol $\blacktriangleright$ Results analysis and comparison}
 \vspace{-0.5cm}
 \begin{figure}%[h!]
 \begin{columns}[c]
@@ -876,7 +879,7 @@ Network Simulator & Discrete Event Simulator OMNeT++
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 36    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small MuDiLCO Protocol $\blacktriangleright$ Results Analysis and Comparison}
+\begin{frame}{\small MuDiLCO protocol $\blacktriangleright$ Results analysis and comparison}
 \vspace{-0.5cm}
 \begin{figure}%[h!]
 \begin{columns}[c]
@@ -902,7 +905,7 @@ Network Simulator & Discrete Event Simulator OMNeT++
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 45    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small PeCO Protocol $\blacktriangleright$ Assumptions and Models}
+\begin{frame}{\small PeCO protocol $\blacktriangleright$ Assumptions and models}
 
 \vspace{-0.5cm}
 \begin{figure}%[h!]
@@ -926,22 +929,27 @@ $$\alpha =  \arccos \left(\dfrac{Dist(u,v)}{2R_s}
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 46    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small PeCO Protocol $\blacktriangleright$ Assumptions and Models}
+\begin{frame}{\small PeCO protocol $\blacktriangleright$ Assumptions and models}
 
-\vspace{-0.5cm}
+\vspace{-1.2cm}
 \begin{figure}%[h!]
-\begin{columns}[c]
-	\column{.50\textwidth}
-\includegraphics[scale=0.33]{Figures/ch6/expcm2.jpg}  
-\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~(a)\\	
-\column{.50\textwidth}
-\includegraphics[scale=0.38]{Figures/tbl.jpeg} 
-\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~(b)	\\
-\end{columns}
-\caption{(a) Maximum coverage levels for perimeter of sensor node $0$. and (b) Coverage intervals and contributing sensors for sensor node 0.}
-  \label{pcm2sensors}
+%\begin{columns}[c]
+%	\column{.50\textwidth}
+\includegraphics[scale=0.6]{Figures/ch6/expcm2.jpg}  
+%\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~(a)\\	
+%\column{.50\textwidth}
+%\includegraphics[scale=0.38]{Figures/tbl.jpeg} 
+%\footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~(b)	\\
+%\end{columns}
+%\caption{(a) Maximum coverage levels for perimeter of sensor node $0$. and (b) Coverage intervals and contributing sensors for sensor node 0.}
+%  \label{pcm2sensors}
 \end{figure}
 
+\vspace{-0.9cm}
+\textcolor {red} {Set of sensors involved in coverage interval of sensor 0 between 3R to 4R $\Rightarrow$ [0,1,2,4]\\
+Maximum coverage level: 4 
+}%$a^0_{i0}= 1$
+%For example, the interval between 3R to 4R is covered by 4 sensors (0,1,2,4), it means the coverage level is 4
 
 \end{frame}
 
@@ -950,7 +958,7 @@ $$\alpha =  \arccos \left(\dfrac{Dist(u,v)}{2R_s}
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 47    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small PeCO Protocol $\blacktriangleright$ PeCO Protocol Algorithm}
+\begin{frame}{\small PeCO protocol $\blacktriangleright$ PeCO protocol algorithm}
 \vspace{-0.7cm}
 %\includegraphics[height = 7.2cm]{Figures/algo6.jpeg}
 
@@ -964,12 +972,12 @@ $$\alpha =  \arccos \left(\dfrac{Dist(u,v)}{2R_s}
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE 48    %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small PeCO Protocol $\blacktriangleright$ Perimeter-based Coverage Problem Formulation}
-\vspace{-0.7cm}
+\begin{frame}{\small PeCO protocol $\blacktriangleright$ Perimeter-based coverage problem formulation}
+\vspace{-0.72cm}
 
 \begin{figure}[h!]
 \centering
-\includegraphics[scale=0.49]{Figures/modell3.pdf}  
+\includegraphics[scale=0.5]{Figures/modell3.pdf}  
 \end{figure} 
 
 \end{frame}
@@ -979,7 +987,7 @@ $$\alpha =  \arccos \left(\dfrac{Dist(u,v)}{2R_s}
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE     %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small PeCO Protocol $\blacktriangleright$ Performance Evaluation and Analysis}
+\begin{frame}{\small PeCO protocol $\blacktriangleright$ Performance evaluation and analysis}
 \vspace{-0.5cm}
 \begin{figure}[h!]
 \centering
@@ -994,7 +1002,7 @@ $$\alpha =  \arccos \left(\dfrac{Dist(u,v)}{2R_s}
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE     %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small PeCO Protocol $\blacktriangleright$ Performance Evaluation and Analysis}
+\begin{frame}{\small PeCO protocol $\blacktriangleright$ Performance evaluation and analysis}
 \vspace{-0.5cm}
 \begin{figure}[h!]
 \centering
@@ -1008,7 +1016,7 @@ $$\alpha =  \arccos \left(\dfrac{Dist(u,v)}{2R_s}
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE     %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small PeCO Protocol $\blacktriangleright$ Performance Evaluation and Analysis}
+\begin{frame}{\small PeCO protocol $\blacktriangleright$ Performance evaluation and analysis}
 \vspace{-0.5cm}
 \begin{figure}%[h!]
 \begin{columns}[c]
@@ -1029,7 +1037,7 @@ $$\alpha =  \arccos \left(\dfrac{Dist(u,v)}{2R_s}
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE     %%
 %%%%%%%%%%%%%%%%%%%% 
-\begin{frame}{\small PeCO Protocol $\blacktriangleright$ Performance Evaluation and Analysis}
+\begin{frame}{\small PeCO protocol $\blacktriangleright$ Performance evaluation and analysis}
 \vspace{-0.5cm}
 \begin{figure}%[h!]
 \begin{columns}[c]
@@ -1040,7 +1048,7 @@ $$\alpha =  \arccos \left(\dfrac{Dist(u,v)}{2R_s}
 \includegraphics[scale=0.35]{Figures/ch6/R/LT50.eps} 
 \footnotesize \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(b)	\\
 \end{columns}
-\caption{Network Lifetime for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
+\caption{Network lifetime for (a)~$Lifetime_{95}$ and (b)~$Lifetime_{50}$.}
   \label{fig3LT}
 \end{figure}
 
@@ -1063,7 +1071,7 @@ $$\alpha =  \arccos \left(\dfrac{Dist(u,v)}{2R_s}
 %%%%%%%%%%%%%%%%%%%%
 %%    SLIDE     %%
 %%%%%%%%%%%%%%%%%%%% 
-\section{\small {Conclusion and Perspectives}}
+\section{\small {Conclusion and perspectives}}
 
 
 %%%%%%%%%%%%%%%%%%%%
@@ -1074,20 +1082,19 @@ $$\alpha =  \arccos \left(\dfrac{Dist(u,v)}{2R_s}
 
 \item  Two-step approaches are proposed to optimize both coverage and lifetime performances, where:
 \begin{itemize}
-\item Sensing field is divided into smaller subregions using divide-and-conquer method.
-\item One of the proposed optimization protocols is applied in each subregion in a distributed parallel way.
+\item Sensing field is divided into smaller subregions using divide-and-conquer method
+\item One of the proposed optimization protocols is applied in each subregion in a distributed parallel way
 \end{itemize}
-\item The proposed protocols (DiLCO, MuDiLCO, PeCO) combine two efficient mechanisms: 
+\item The proposed protocols (DiLCO, MuDiLCO, PeCO) combine two efficient mechanisms 
 \begin{itemize}
 \item Network leader election, and
-\item Sensor activity scheduling based optimization.
+\item Sensor activity scheduling based optimization
 \end{itemize}
-\item Our protocols are periodic where each period consists of 4
-phases:
+\item Our protocols are periodic where each period consists of 4 phases
 \begin{itemize}
-\item Information exchange,
-\item Network leader election, 
-\item Decision based optimization, 
+\item Information exchange
+\item Network leader election
+\item Decision based optimization 
 \item Sensing.
 \end{itemize}
 \end{enumerate}
@@ -1104,16 +1111,16 @@ phases:
 \begin{frame}{Conclusion}
 \begin{enumerate} [$\blacktriangleright$]
 
-\item DiLCO and PeCO provide a schedule for one round per period.
-\item MuDiLCO provides a schedule for multiple rounds per period.
-\item Comparison results show that DiLCO, MuDiLCO, and PeCO protocols:
+\item DiLCO and PeCO provide a schedule for one round per period
+\item MuDiLCO provides a schedule for multiple rounds per period
+\item Comparison results show that DiLCO, MuDiLCO, and PeCO protocols
 \begin{itemize}
- \item maintain the coverage for a larger number of rounds.
- \item use less active nodes to save energy efficiently during sensing.
- \item are more powerful against network disconnections.
- \item perform the optimization with suitable execution times.
- \item consume less energy.
- \item prolong the network lifetime.
+ \item Maintain the coverage for a larger number of rounds
+ \item Use less active nodes to save energy efficiently during sensing
+ \item Are more powerful against network disconnections
+ \item Perform the optimization with suitable execution times
+ \item Consume less energy
+ \item Prolong the network lifetime
 
 \end{itemize}
 \end{enumerate}
@@ -1153,12 +1160,11 @@ Coverage and lifetime optimization in heterogeneous energy wireless sensor netwo
 %%%%%%%%%%%%%%%%%%%% 
 \begin{frame}{Perspectives}
 \begin{enumerate} [$\blacktriangleright$]
-\item Investigate the optimal number of subregions.
-\item Design a heterogeneous integrated optimization protocol to integrate coverage, routing, and data aggregation protocols.
-\item Extend PeCO protocol so that the schedules are planned for multiple
-sensing periods.
-\item Consider particle swarm optimization or evolutionary algorithms to obtain quickly near optimal solutions.
-\item Improve our mathematical models to take into account heterogeneous sensors from both energy and node characteristics point of views. 
+\item Investigate the optimal number of subregions
+\item Design a heterogeneous integrated optimization protocol to integrate coverage, routing, and data aggregation protocols
+\item Extend PeCO protocol so that the schedules are planned for multiple sensing periods
+\item Consider particle swarm optimization or evolutionary algorithms to obtain quickly near optimal solutions
+\item Improve our mathematical models to take into account heterogeneous sensors from both energy and node characteristics point of views
 %\item The cluster head will be selected in a distributed way and based on local information.
 \end{enumerate}
 
