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\markright{(BSTU Seminar - Novemver 2013)}
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\begin{document}
\begin{huge}

\clearpage  % (title) =========================================
\color{blue}
\begin{center}
{\bf Robot Navigation: \\ Two Inplimantations of State of the Arts} 
\hspace*{.5in}\\
\color{black}
\bigskip
\hspace*{1in}\\
\begin{Large}
Akira Imada  \\
\bigskip
Brest State Technical University (Belarus)
\end{Large}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf I. Navigation by Neural Network (NN)}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf (1) NN with fixed weight} \\
\bigskip
\color{black}
{\Large
A lucky dog reached a sausage avoiding cliff. \\But is he intelligent?}
\end{center}

\begin{figure}[bhtp]
\begin{center}
    \includegraphics[height=4cm]{khomshka.jpg}
\end{center}
\end{figure}






\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf (2) With weights modified during a run}\\
\bigskip 
\color{black}
{\Large  (McCullough-Pitts Neurons with Hebb rule)\\
Floreano \& Urzelai (2000) $\Rightarrow$ light seeking robot}
\end{center}
\begin{figure}[bhtp]
\begin{center}
    \includegraphics[height=4cm]{khepera.jpg}
    \includegraphics[height=4cm]{floreano.jpg}
\end{center}
\end{figure}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Hebb rule}\\
\bigskip
\color{black} 
{\Large start with random weight values $\Rightarrow$ then renewed every 100ms 
\begin{displaymath}
w_{ij}(t)=w_{ij}(t-1)+ \eta \Delta W \hspace{.5in} (0.0<\eta<1.0)
\end{displaymath}
where $\Delta W = (1-W) x y$.}
\end{center}

\begin{figure}[bhtp]
\begin{center}
    \includegraphics[height=2cm]{hebb.jpeg}
\end{center}
\end{figure}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf An example path with Hebb rule}\\
\end{center}

\begin{figure}[bhtp]
\begin{center}
    \includegraphics[height=4cm]{floreano-1.jpg}
\end{center}
\end{figure}




\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf (3) With spiking neurons\\
Rate Coding}\\ 
\bigskip
\color{black}
{\Large Floreano \& Matiussi (2001) $\Rightarrow$ also light seeking task}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Spiking neuron model} \\
\bigskip
\color{black}
{\Large
Incoming spikes can increase or decrease the membrane potential\\ 
$\Downarrow$\\
The neuron emits a spike when its membrane potential exceed threshold\\ 
$\Downarrow$\\
After firing, the membrane potential resets to a low negative voltage 
}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf An example path with rate-coding}\\
\end{center}

\begin{figure}[bhtp]
\begin{center}
    \includegraphics[height=4cm]{floreano-2.jpg}
\end{center}
\end{figure}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf (4) With spiking neurons\\
Spike Timing Dependent Plasticity (STDP)}\\ 
\bigskip
\color{black}
{\Large di Paolo (2001) $\Rightarrow$ also light seeking task}
\end{center}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf STDP}\\
\bigskip
\color{black}
{\Large Spiking neuron's vergion of Hebb rule\\
\color{black} $\Delta t = \color{blue} t_{post} \color{black} - \color{red} t_{pre}$} 
\end{center}

\begin{figure}[bhtp]
\begin{center}
    \includegraphics[height=7cm]{spike-pre-post.jpg}
\end{center}
\end{figure}



\clearpage  % =========================================
\begin{center} \color{blue}
{\bf How does STDP change weights?}
\bigskip
\color{red}
{\Large
      \begin{eqnarray*}
         W(\Delta t) = \left\{
         \begin{array}{ll}\nonumber
         \hspace{.18in}A_{+} \exp (-\Delta t/\tau_{+})
                          & \hspace{.2in}\mbox{if}\hspace{.2in}\Delta t \ge 0\\
         - A_{-} \exp (-\Delta t/\tau_{-})
                          & \hspace{.2in}\mbox{if}\hspace{.2in}\Delta t < 0\\
         \end{array}
         \right.
      \end{eqnarray*}
\color{black} where \hspace{.2in} \color{red} $\Delta t = t_{post} - t_{pre}$}
\end{center}

\begin{figure}[bhtp]
\begin{center}
    \includegraphics[height=4cm]{stdp-2.jpg}
\end{center}
\end{figure}




\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Hodgkin–Huxley model} \\
\color{black}
{\Large
\begin{displaymath}
C_M \frac{dv}{dt}=-g_{Cl}(v-E_{Cl})-g_{K}(v-E_{K})-g_{Na}(v-E_{Na})+I(t)/A
\end{displaymath}
Computationary very expensive $\Rightarrow$ possible only with a few neurons
}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Spiking Responce model} \\
\color{black}
{\Large
\begin{displaymath}
v_i(t) = \sum_{j}{w_{ji}}\sum_{f}{\epsilon_j}(t-t_{j}^{f}) + \sum_f \eta_i(t-t_i^f)
\end{displaymath}
}
\end{center}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Integrate Fire model} \\
\color{black}
{\Large
\begin{displaymath}
v_i(t) = v_r +(v_i(t - \Delta t) - v_r) \exp (- \Delta t/ \tau) + \sum_j w_{ij}f_j (t - \Delta t)
\end{displaymath}
}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Ihzkevich model} \\
\end{center}
\color{black}
{\Large
}
\begin{displaymath}
v'=0.04v^2 +5v +140 -u +I
\end{displaymath}
\begin{displaymath}
u'=a (bv -u)
\end{displaymath}

\begin{figure}[bhtp]
\begin{center}
    \includegraphics[height=5cm]{spike-01.jpg}
\end{center}
\end{figure}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf An example path with STDP}\\
\end{center}

\begin{figure}[bhtp]
\begin{center}
    \includegraphics[height=4cm]{di-paolo-path.jpg}
\end{center}
\end{figure}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf II. Brain Machine Interface}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Obama's proposal on brain science (2013)}\\

\bigskip
\color{black}
{\Large \$3 billion investment\\ to map\\ 85 to 100 billion neurons in the human brain.}

\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf H. Markram et al. in Lausanne}\\
\end{center}
\color{black}
\begin{center}
{\Large Let's create a "virtual copy of the human brain."}
\end{center}

\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Neuroscience:\\ rich in data \& poor in theory?}\\
\bigskip
\color{black}
{\Large 
\color{red}
Analyzing the brain data without a theory\\
$\Downarrow$\\
A person who does not understand how a computer works got the wiring diagram
of a computer and all snapshots of voltages at all the spots of the wires. 
Then he said "now we have data, and we need to analyze it!"\\
}
\color{black}
{\large
(J.~Weng in Connectionists Digest, Vol 335 (4) 12 March 2013)
}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Neural Dust}\\
\bigskip
\color{black}
{\Large 
$\bullet$ A concept of \color{red} human-machine interface \color{black} by D.~ Seo et al. (U.C.Berkley).\\
$\bullet$ Thousands of tiny sensors, 100 micrometers, in a human brain $\Rightarrow$ dust\\
$\bullet$ Each dust, powered by ultrasound transmissions, picks up electrical signals from nearby neurons\\
$\bullet$ They return data from the brain via ultrasound to a transceiver implanted under the skull.}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Neural Dust works like MRI and PET}\\
\bigskip
\color{black}
{\Large 
$\bullet$ It would easily monitor neurological activity for research and medical monitoring.\\
$\bullet$ We could also see this technology as a \color{red} brain-machine interfaces \color{black}.}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Navigation by Electroencephalogram (EEG)}
\end{center}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf EEG what for?}\\ 
\bigskip
\color{black}
{\Large 
$\bullet$ The most direct way to record brain activity is 
to cut open the skull and place electrodes directly onto your grey matter,\\ 
which presents other problems. \\
$\Downarrow$\\
 \color{red} Most of the research on human brain uses EEG}\\
\end{center}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Use your brain to control the world!}\\
\color{black}
{\Large 
(A promise of the brain-machine interface)\\
\bigskip
$\bullet$ It enables cursor control, brain-to-brain communication etc.\\
$\Downarrow$\\
 Farewell to smart-phone!\\
{\large (J.~Bleecker and N.~Nova at the South by Southwest Interactive conference)}}
\end{center}


\clearpage  % =========================================
\begin{center}
\color{blue}
{\bf It might sound like a Science-Fiction\\ but actually not! It's a reality.}\\
\color{black}
\bigskip
{\Large Now let's go back to a reality!}
\end{center}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Robot navigation with EEG}\\
\end{center}
\color{black}
{\Large
\begin{itemize}
\item Brain-coupled interaction for semi-autonomous navigation of an assistive robot
   \begin{itemize}
   \item[] X.~Perrin (2010)
   \end{itemize}
\item[]
\item EEG Based Brain-Machine Interfacing: Navigation of Mobile Robotic Device
   \begin{itemize}
   \item[]  M.~Mahmud et al. (2011)
   \end{itemize}
\end{itemize}
}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf A brain machine interface}\\
\color{black}
\end{center}

\begin{figure}[bhtp]
\begin{center}
   \includegraphics[height=7cm]{eeg-1.jpg}
\end{center}
\end{figure}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Spots to detect EEG signal}\\
\color{black}
\end{center}

\begin{figure}[bhtp]
\begin{center}
   \includegraphics[height=6cm]{eeg-11.jpg}
\end{center}
\end{figure}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf A cap to detect those EEG signals} \\

\color{black}
\end{center}

\begin{figure}[bhtp]
\begin{center}
   \includegraphics[height=6cm]{eeg-cap.jpg}
\end{center}
\end{figure}

\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf EEG can make a robot navigate \\just by thinking}\\ 
\end{center}

\begin{figure}[bhtp]
\begin{center}
   \includegraphics[height=4cm]{eeg-2.jpg}
   \includegraphics[height=4.2cm]{biba-robot.jpg}
\end{center}
\end{figure}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf An example path with EEG}\\
\end{center}

\begin{figure}[bhtp]
\begin{center}
    \includegraphics[height=4cm]{eeg-path.jpg}
\end{center}
\end{figure}

\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf III. Let me propose a Benchmark}
\end{center}





\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf A lucky dog who survived}\\
\end{center}

\begin{figure}[bhtp]
\begin{center}
    \includegraphics[height=8cm]{potachuk.jpg}
\end{center}
\end{figure}


\clearpage  % =========================================
\begin{center}\color{blue}
{\bf The Jeep Problem}\\
\bigskip
\color{black}
{\LARGE
The 52nd problem \\
{\Large in the} \\
{\it ``Propositiones ad acuendos inventes''} (in Latin) \\
{\Large attributed to} \\
Alcuin of York (732--804)\\
$\Downarrow$ \\
\color{red} Camel carrying grain in a desert.}
\end{center}


\clearpage  % =========================================
%%\hfill{\Large (cont'd)}
\begin{center}\color{blue}
{\bf The task in the modern version}\\
\color{black}
\bigskip
{\Large Maximize the distance a Jeep can penetrate into 1-D desert.}
\end{center}
{\Large
\begin{itemize}
\item Jeep can move a unit distance with a unit fuel.
\item Jeep can unload its fuels anywhere in the desert.
\item Fuels can be filled only at the base.
\item Jeep can go back to the base \color{red} $n$ \color{black} times to re-fill its tank.
\end{itemize}
}

\clearpage  % =========================================
\begin{center}\color{blue}
{\bf An example of a success}
\end{center}
\begin{figure}[h]
\begin{center}
\includegraphics[width=18cm,height=8cm]{jeep-1d-solution.jpg}
\end{center}
\end{figure}




%% with the task being ...
\clearpage  % =========================================
\begin{center}
\color{blue}
{\bf An extension to 2-D Desert}\\
\bigskip
\color{black}
{\Large
Goal is to \color{red} ``maximize the total distance of exploration''\\
\color{black}  with \color{red} $n$ \color{black} reserve tanks to put fuels on its path for a future usage 
}
\end{center}
{\Large
\begin{itemize}
\item[] (1) Start the base
\item[] (2) Navigate the desert
\item[] (3) Put fuels somewhere, or find the fuels to get
\item[] (4) Return to the base
\end{itemize}
}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Possible route of such a exploration}\\
\end{center}

\begin{figure}[bhtp]
\begin{center}
    \includegraphics[height=5cm]{2d-jeep.jpeg}
\end{center}
\end{figure}




\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Let's apply Turing Test! }\\
{\Large to 2D Jeep in Desert Problem} \\
\end{center}
{\Large
\begin{itemize}
\item Set the situation, like, "Explore region X \\ with being allowed 3 times return to the base"
\item The Jeep A is navigated by an artificial agent
\item The Jeep B is navigated by a human via EEG
\item Can we tell current one is by A or B?
\end{itemize}
}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Tank you for attention!}
\end{center}

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