- Timestamp:
- Dec 19, 2009, 1:36:27 PM (15 years ago)
- Location:
- liacs/nc/laser-pulse-shaping
- Files:
-
- 1 edited
- 2 copied
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liacs/nc/laser-pulse-shaping/Makefile
r34 r48 1 SOURCE=$(patsubst %.m,%.m.tex, $(shell ls *.m)) 2 3 include latex.mk 4 5 foo: 6 echo $(SOURCE) 7 1 8 pso.out: pso.m 2 9 @octave -q pso.m -
liacs/nc/laser-pulse-shaping/latex.mk
r45 r48 56 56 .gs.png: 57 57 $(GNUPLOT) $? 58 59 %.m.tex: %.m 60 highlight --include-style --linenumbers --no-doc \ 61 --latex --input $< --output $@ -
liacs/nc/laser-pulse-shaping/report.tex
r46 r48 22 22 \floatname{result}{Result} 23 23 24 \input{highlight.sty} 25 26 \title{The low-autocorrelation problem\\ 24 \title{Laser Pulse Shaping problem\\ 27 25 \large{Practical Assignments Natural Computing, 2009}} 28 26 \author{Rick van der Zwet\\ … … 39 37 40 38 \section{Introduction} 41 The report is focused on the so-called \emph{low-autocorrelation problem of 42 binary sequences}, is subject to actual research and is of big interest for 43 industrial applications, e.g. communications and electrical engineering. Its 44 description goes as follows. 39 The report is focused on the so-called \emph{laser pulse shaping problem}. 40 Todays lasers are also used within the range of atoms or mulecule research. 41 Using small pulses it is able to align and alter the movement of the atoms. 45 42 46 \textbf{Feasible Solutions:} Binary Sequences $\vec{y} \in \{-1,+1\}^n$ 43 The problem lies in the fact the atoms cannot be controlled by any type of 44 laser pulse. There are many parameters which could all be set to 'shape' the 45 laser pulse the way it can move the atoms. 47 46 48 \textbf{Objective Function:} 47 \section{Problem description} 48 To determine the best solution a fitness function is needed, which could be 49 found in the shape of equation~\ref{eq:fitness} 49 50 \begin{equation} 50 f(\vec{y}) = \frac{n^2}{2 \cdot E(\vec{y})} \longrightarrow maximization 51 \label{eg:fitness} 52 SHG = \int_0^T E^4(t)dt \rightlongarrow maximization 51 53 \end{equation} 52 54 53 \begin{equation}54 E(\vec{y}) = \displaystyle\sum_{k=1}^{n-1} (\sum_{i=1}^{n-k} y_i \cdot y_{i+k})^255 \end{equation}56 55 57 \section{Problem description}58 56 Due to the huge 'exploding' posibilities it is not possible to walk trough the 59 57 whole list of posibities, so we need alternative approches to tackle this
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