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\title{Two topics ahead membrane computing}
\author[Adam Obtu\l owicz, IMPAN, Warsaw, Poland]{Adam Obtu\l owicz\\ Institute of Mathematics, Polish Academy of Sciences\\
Warsaw, Poland}
\date{}

\begin{document}
\frame{\titlepage}

\frame{\frametitle{Two topics}

\begin{itemize}
\item[1$^\circ$]new causes and origins of \u\ with a regard on membrane
computing 

\item[2$^\circ$]western polyphony musical scores as a predecessor of an exact
(as mathematical) approach to concurrency and parallelism in computer science;
looking for (mutual) inspiration.
\end{itemize}
}

\frame{\frametitle{First topic}

Ad 1$^\circ$. New causes and origins of \u:
\begin{itemize}
\item measurement (quantum) \u\ approached by nonclassical non-Bayesian,
non-Markovian) probability theory (cf.\ e.g.\ D.~Aerst's papers),
\pause
\item indescernibility of entangled quantum states approached (in the future)
by quantum rough sets and related quantum approximation spaces,
\pause
\item (massively) parallel Monte Carlo \r\ (cf.\ A.~Obtu\l owicz's papers in
LNCS Volumes 2597, 6501) versus interactive \r\ via oracles, cf.\ S.~Arora
and B.~Barak's book (relationships to be established). 
\end{itemize}
\pause
Research proposal: searching for nonclassical probabilistic P~systems
simulating quantum massive parallelism.
}

\frame{\frametitle{Second topic}
Ad 2$^\circ$. Western polyphony from Middle Ages, through J.~S.~Bach's
(implied) polyphony, to G.~Ligeti's sound-mass music contains an exact (as
mathematical) approach to concurrency and parallelism appearing in
performance according to musical scores for many voices.
}

\frame{\frametitle{Musical score}
Writing a musical score for many simultaneously appearing voices resembles
writing a program (e.g.\ in NESTL) which respects simultaneously working
processors, where e.g.\ the restrictions for sharing an access to central
memory could correspond to counterpoint rules of polyphony.
}

\frame{\frametitle{Suggestion}
The following quotation:
\begin{quote}
\it Ligeti's goal was apparently to entangle the voices to such a degree that
they become imperceptible as individual entities \dots
\end{quote}
together with remarks about \r\ of beats in a bar according to K.~Stockhausen
from J.~J.~Iverson's Ph.D. thesis {\it Historical Memory and G.~Ligeti's
Sound-Mass Music 1958--1968\/} (Austin 2009) suggests that
\pause
\begin{itemize}
\item Ligeti's sound-mass music could serve as a metaphor for quantum massive
parallelism,
\item randomized spiking neural P systems (respecting the timing of spikes by
counting time by beats in the bars) could be mathematical models for this
metaphor. 
\end{itemize}

}
\end{document}
