LinEq}_{n,m}$ is computable
and continuous thereon by \mycite{Theorem~11}{LA}.
Now apply Lemma~\ref{l:Topology}d) to conclude 
  $\operatorname{LEV}(\operatorname{LinEq}_{n,m},d+1)\subseteq\operatorname{dom}(\operatorname{LinEq}_{n,m})\setminus(V_d\cup\cdots\cup V_0)
  =\emptyset$.
\item[b)]
Similarly to a) and in view of Theorem~\ref{t:Diag}
it suffices to show $\operatorname{Lev}(\operatorname{Diag}_d)\leq d$. 
Now, again, the set 
$V_k:=\{A:\operatorname{Card}\sigma(A)=k\}=
\{A:\operatorname{Card}\sigma(A)\geq k\}\cap\{A:\operatorname{Card}\sigma(A)\leq k\}$
of symmetric real $d\times d$-matrices $A$ with
exactly $k$ distinct eigenvalues 
is effectively open in 
$\{A:\operatorname{Card}\sigma(A)\leq k\}=\operatorname{dom}(\operatorname{Diag}_d)\setminus (V_d\cup\cdots\cup V_{k+1})$:
because $A\mapsto\operatorname{Card}\sigma(A)$ is lower-computable
and lower-continuous \mycite{Proposition~17}{LA}.
And $\operatorname{Diag}_d$ is computable and continuous on $V_k$ by
\mycite{Theorem~19}{LA}, so Lemma~\ref{l:Topology}d) yields the claim.
\item[c)]
Again,
in order to show $\operatorname{Lev}(\operatorname{EVec}_n)\leq\lfloor\log_2 n\rfloor+1$,
consider the sets
$U_k:=\big\{A\in\mathbb{R}^{n\cdot(n-1)/2}:\lfloor\log_2 m(A)\rfloor=k\big\}$,
$k=0,\ldots,\lfloor\log_2 n\rfloor$, on which
$\operatorname{EVec}_n$ is computable by Theorem~\ref{t:EV1}.
This time $\{A:\lfloor\log_2 m(A)\rfloor\leq k\}$ 
(rather than ``$\geq k$'') are,
according Observation~\ref{o:MinDim},
effectively open subsets of $\operatorname{dom}(\operatorname{EVec}_n)$.
Hence $U_k$ is relatively open in 
$\{A:\lfloor\log_2 m(A)\rfloor\geq k\}
=\mathbb{R}^{n\cdot(n-1)/2}\setminus(U_0\cup\cdots\cup U_{k-1})$:
now apply Lemma~\ref{l:Topology}d).
\qed\end{enumerate}\end{proof}
In the discrete realm, the \textsf{Church-Turing Hypothesis} is 
generally accepted and bridges the gap between computational 
practice and formal recursion theory: 
\begin{quote} \it
every function which would naturally be regarded as computable 
is computable under his definition, i.e. by one of his 
{\rm(i.e. Turing's)} machines 
\quad {\rm\cite[p.376]{Kleene}}
\end{quote}
In the real number setting, the Type-2 Machine has not attained
such universal acceptance---mostly due to its inability to
compute any discontinuous function. Hence we propose the 
following as a real counterpart to the discrete Church-Turing Hypothesis:
\begin{quote} \it
The class of real functions $f$
which would naturally be regarded as computable
coincides with those functions 
computable by a Type-2 Machine
\emph{with finite discrete advice of colour classes
in $2\text{--}\Sigma_1(\operatorname{dom} f)$}.
\end{quote}

\begin{myquestion}
\begin{enumerate}
\item[a)]
Is the rank the (up to permutation) unique
least advice rendering $\operatorname{LinEq}$ computable/continuous?
\item[b)] 
Is the number of distinct eigenvalues the (up to permutation)
unique least advice rendering $\operatorname{Diag}$ computable/continuous?
\item[c)]
More generally, what are sufficient conditions for the sets
$\operatorname{LEV}(f,i)$ ($i=1,\ldots,\operatorname{Lev}(f)$) to be the \emph{unique}
least-size partition of $\operatorname{dom}(f)$ into subsets where
$f$ is continuous?
\end{enumerate}
\end{myquestion}
Recall that in the proof of Corollary~\ref{c:Comparison2},
we have repeatedly employed Lemma~\ref{l:Topology}d) 
giving a sufficient condition for the sets $\operatorname{LEV}(f,i)$ 
to constitute a \emph{least-size} partition of $\operatorname{dom}(f)$ 
into subsets where $f$ is continuous.

Knobias - Has anyone used their news service?
Discussion in 'Trading Software' started by cwb1014, Oct 6, 2003.
Has anyone used Knobias's RAiDAR-PRO news aggregation and analysis service (see: http://www.knobias.com/institution/araidar.htm). It's received some fairly good reviews in the financial press, but I've never heard anything about it from actual users.
Any information that anyone can provide would be greatly appreciated..
Engineer, Pasteur Institute
Vérinique Villiers and Edith Gouin work together on the Rickettsia project. Listeria monocytogenes, Shigella flexneri, and Rickettisia conorii are three bacterial pathogens that are able to polymerize actin into ’comet tail’ structures and move within the cytosol of infected cells. The actin-based motilities of L. monocytogenes and S. flexneri are known to require the bacterial proteins ActA and IscA, respectively, and several mammalian cytoskeleton proteins including Arp2/3 complex and VASP (vasodilator-stimulated phosphoprotein) for L. monotyogenes and vinculin and N-WASP (the neural Wiskott-Aldrich syndrome protein) for S. flexneri.
We have previously reported that the actin tails of Rickettsia conorii, another intracellular bacterium, unlike those of Listeria of Shigella are composed of long unbranched actin filaments apparently devoid of Arp2/3 complex (J. Cell. Science, 1999).
Then, we identified a R. conorii surface protein, RickA, as a novel type of Arp2/3 activator. In vitro, RickA activates, albeit far less efficiently than ActA, the nucleating activity of Arp2/3 and its capacity to induce branch formation. In infected cells, Arp2/3 is detected on the bacterial surface but not in the Rickettsia tails, as it is the case for Listeria and Shigella tails. When expressed in mammalian cells, and targeted to the membrane, RickA induces filopodia. Thus RickA-induced actin polymerisation, which results in the generation of the long actin filaments reminiscent of those present in filopodia, appears as a powerful tool for the study of filopodia formation.New York is flooded and the city is ruled by the upper classes. Below, the mystics live in the depths, in buildings threatening to crumble into the sea. But mystics must have their powers drained for they are dangerous and a menace to society left free to do as they please. Aria is engaged to Thomas; a union that will build a bridge between two rival families. The only problem is, Aria can’t remember falling in love with him, or much about him at all. Her memory ruined by an overdose, she meets a boy in the depths; a mystic. Is he the key to unlocking her memories and will she fall in love with Thomas all over again?
What
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- Ellie
Oh, finally, something you've read that I DON'T immediately want to rush out and buy. Thanks for giving me a few days' break, haha!  review! I love dystopian books, although not so much YA. I really like a good world-building. Sounds odd indeed to stay in a flooded place if further down the country things are normal/better.The Woodland Lounge Set consists of two lounge chairs, a 2-seater, and a coffee table made with a beautifully light-coloured Akasia wood in a modern, contemporary style. The coffee table and side table are fitted with Terazzo table tops, lending a sleek and fresh look to this natural style. This unique set is the perfect size, very reasonably priced and oh-so-trendy.
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This kit has only been tested with the LCDs we sell and support, if you use another we will not be able to guarantee it works