text:
\section{Introduction}

The idea that entanglement may be used as a resource is central to the
theory of quantum communication and cryptography.
Well-known examples include teleportation \cite{BennettB+93} and the
super-dense coding of both classical and quantum data
\cite{BennettW92,BennettSST02,HarrowHL04}.
In cryptography, entanglement is used not only in some implementations
of quantum key-distribution \cite{Ekert91}, but also as a mathematical
tool in security proofs \cite{LoC99,ShorP00} of quantum
key-distribution protocols not based on entanglement (such as
\cite{BennettB84}).
In these settings it may be said that the relationship between
entanglement and other resources (in particular quantum communication,
classical communication, and private shared randomness) is reasonably
well-understood \cite{BennettDSW96,DevetakHW03}.

There are, on the other hand, settings of interest where the
properties of entanglement as a resource are very poorly understood.
One example can be found in quantum communication complexity, wherein
it is not known if prior shared entanglement ever gives an asymptotic
reduction in the number of qubits of communication required to solve
general communication problems \cite{Wolf02,Brassard03}.
A second example, which is the main focus of this paper, concerns the
power of entanglement in the multi-prover interactive proof system
model, which has been studied in several recent papers
\cite{
  KobayashiM03,
  CleveH+04,
  Wehner06,
  CleveSUU07,
  CleveGJ07,
  KempeKMTV07,
  KempeRT07}.
Bell inequalities \cite{Bell64,ClauserH+69}, and many of the
open problems concerning them \cite{Gisin07}, have a fundamental
connection to this model (although not necessarily to our main
results).

Multi-prover interactive proof systems, which were first defined by
Ben-Or, Goldwasser, Kilian, and Wigderson \cite{Ben-OrGKW88}, involve
interactions among a {\it verifier} and two or more {\it provers}.
The verifier is always assumed to be efficiently implementable, while
the provers are typically permitted to have arbitrary complexity.
The verifier and provers each receive a copy of some input string $x$,
and then engage in an interaction based on this string.
During this interaction the verifier communicates privately with
each of the provers, possibly over the course of many rounds of
communication, but the provers are forbidden from communicating
directly with one another.
The provers may, however, agree on a joint strategy before the
interaction begins.

The provers act in collaboration to convince the verifier that the
input string $x$ is a {\it yes-input} to some fixed problem, and
therefore should be {\it accepted}.
The provers are not, however, considered to be trustworthy, and
so the verifier must be defined in such a way that it {\it rejects}
strings that are {\it no-inputs} to the problem being considered.
These two conditions---that the provers can convince the verifier to
accept yes-inputs but cannot convince the verifier to accept
no-inputs---are called the {\it completeness} and {\it soundness}
conditions, respectively, and are analogous to the notions in
mathematical logic that share these names.
In contrast to the notion of a mathematical proof, however, one
typically requires only that the completeness and soundness conditions
for interactive proof systems hold with high probability (for every
fixed yes or no input string).

The study of interactive proof systems, including single-prover and
multi-prover models, has had an enormous impact on the fields of
computational complexity and theoretical cryptography
\cite{AroraB06,Goldreich01}.
In particular, multi-prover interactive proof systems, and the
characterization of their expressive power \cite{BabaiFL91}, led
to the discovery of the
{\it PCP} (or {\it Probabilistically Checkable Proof}) {\it Theorem}
\cite{AroraLMSS98,AroraS98,Dinur07}, which was a critical breakthrough
in understanding the hardness of approximation problems.

In the quantum setting, one must consider the possibility that the
provers initially share entanglement, which they might use as part of
their strategy during the interaction.
With this seemingly small change, nearly everything we know about
classical multi-prover interactive proof systems becomes invalid
within the quantum model.
The following points illustrate the effect of this change on our
current state of knowledge.

\begin{itemize}
\item
When the provers are not allowed to share prior entanglement, it is
known that the class of promise problems that have multi-prover
interactive proof systems is precisely \class{NEXP}, the class of
problems that can be solved nondeterministically in exponential time.
This holds for both classical \cite{BabaiFL91} and quantum
\cite{KobayashiM03} multi-prover interactive proofs.

\item
There are no nontrivial bounds known for the class of promise problems
having multi-prover interactive proofs when the provers initially
share entanglement, including the cases of both a classical and
quantum verifier.
At one extreme, such proof systems could have the same expressive
power as single-prover interactive proof systems, and at the other
extreme it is possible that uncomputable problems have such proof
systems.
\end{itemize}

One very basic question about multi-prover interactive proofs with
entangled provers has remained unanswered, and is closely related to
the lack of good upper bounds on their power:
{\it For a given verifier and input string, how much entanglement is
  needed for the provers to play optimally?}
To obtain an upper bound on the expressive power of multi-prover
interactive proofs with entangled provers, one seeks a general bound:
a limit on the amount of entanglement, as a function of the verifier's
description and the given input, needed for the provers to play
optimally.

Our first main result explains the difficulty in answering this
question: we prove that there exist two-prover quantum interactive
proof systems for which no finite amount of entanglement allows for an
optimal strategy on any fixed input.
In other words, there are interactive proofs such that, no matter what
entangled state the provers choose on a given input, it would always be
possible for them to do strictly better with more entanglement.
There is, therefore, no strict upper bound of the form discussed
above.
This fact has an obvious but important implication: one must consider
upper bounds on entanglement for {\it close-to-optimal} strategies if
this approach is to yield upper bounds on the power of multi-prover
quantum interactive proofs.

Our second main result concerns methods to achieve
{\it perfect completeness} of quantum interactive proof systems while
retaining small soundness error.
In the single-prover case, an efficient transformation for doing this
exists that is both simple and easy to analyze \cite{KitaevW00}.
In the multi-prover setting, an analogous result was recently obtained
by Kempe, Kobayashi, Matsumoto, and Vidick \cite{KempeKMV08} based on
a much more complicated transformation and analysis.
This more complicated transformation was designed to handle the
locality constraints imposed on multiple provers.
It turns out, however, that this complicated procedure is not needed
after all, provided one is willing to make a small sacrifice.
We prove that the simple single-prover technique can be applied in the
multi-prover case to yield a proof system with {\it near-perfect}
completeness: honest provers are able to convince the verifier to
accept yes-inputs with any probability smaller than~1 that they
desire---but they might never reach probability 1 using finite
resources.
(For instance, the provers may choose to cause the verifier to accept
yes-inputs with probability $1 - \varepsilon(n)$ where
$\varepsilon(n)$ is the reciprocal of the busy beaver function.
The implementation of such a strategy, however, could require an
enormous amount of prior shared entanglement.)

The two main results just discussed are connected by the notion of
{\it coherent state exchange}, which is discussed in the next
section.
The first main result is then proved in Section~\ref{sec:game}, while
the second is proved in Section~\ref{sec:perfect-completeness}.
The paper concludes with Section~\ref{sec:conclusion}.
Throughout the paper we assume the reader is familiar with quantum
computing and with basic aspects of classical and quantum interactive
proof systems.
Our notation and terminology are consistent with other papers on these
topics.

\section{Coherent state exchange} \label{sec:exchange}

We begin by defining {\it coherent state exchange} as follows.
Consider $m$ players $P_1,\ldots,P_m$; and suppose, for each
$i\in\{1,\ldots,m\}$, that player $P_i$ holds a quantum system whose
associated Hilbert space is denoted $\mathcal{X}^i$.
The spaces $\mathcal{X}^i$ and $\mathcal{X}^j$ need not have equal dimension for
$i\not=j$.
For two chosen pure states
$\ket{\phi},\ket{\psi}\in\mathcal{X}^1\otimes\cdots\otimes\mathcal{X}^m$,
we consider the situation in which the players wish to transform a
shared copy of $\ket{\phi}$ into $\ket{\psi}$, or vice-versa.
We require that this task is completed
{\it (1)~without communication} and
{\it (2)~by a coherent process}.

To say that a process that performs state exchange is {\it coherent}
means that it can be applied in a way that preserves superpositions.
In particular, this means that it is possible for the players to
implement a transformation of the form
\[
\alpha\ket{0^m}\ket{\gamma}
+\beta\ket{1^m}\ket{\phi}
\mapsto
\alpha\ket{0^m}\ket{\gamma}
+\beta\ket{1^m}\ket{\psi},
\]
where the first $m$ qubits represent control qubits, with one held by
each player, and where the state
$\ket{\gamma}\in\mathcal{X}^1\otimes\cdots\otimes\mathcal{X}^m$ represents an arbitrary
state shared by the players.

In the absence of additional resources, it is not possible in general
to perform this task when $m \geq 2$.
In particular, given that the players cannot create entanglement out
of thin air, the task is easily seen to be impossible when the target
state $\ket{\psi}$ has more entanglement than the initial
state~$\ket{\phi}$.
However, if we consider the situation in which the players initially
share an auxiliary quantum state, and we allow this state to be
perturbed slightly by the process, then the above impossibility
argument based on entanglement is no longer valid---and as we will show,
the task indeed becomes possible.
We note that the coherence condition requires that a process of this
sort to leave the auxiliary quantum state nearly unchanged, in essence
using it as a catalyst.
The players cannot, for instance, simply swap the input state
$\ket{\phi}$ with an initially shared copy of $\ket{\psi}$ without
losing coherence.

For the case of $m=2$, one solution to this problem can be obtained
through the use of van~Dam and Hayden's
{\it quantum state embezzlement}~\cite{vanDamH03}.
In quantum state embezzlement, two parties (Alice and Bob) perform a
transformation of the form $\ket{E_N} \mapsto \ket{E_N'}\ket{\phi}$,
for some shared entangled state $\ket{\phi}$ of their choice, where
$\{\ket{E_N}\}$ is a special family of states defined so that it
is possible to perform such a transformation in which $\ket{E_N}
\approx \ket{E_N'}$ for large $N$.
Thus, they ``embezzle'' $\ket{\phi}$ from $\ket{E_N}$, leaving little
trace of their crime.
The process for doing this described by van Dam and Hayden is coherent
and requires no communication, and can therefore be done twice (once
in reverse) to achieve coherent state exchange.
It relies, however, on a representation of two-party pure quantum
states that no longer exists for $m$-party states when $m\geq 3$.

Here, we show that coherent state exchange for any number of parties
is always possible, with near-perfect coherence.
To simplify the description of the procedure, we will assume that
$\ket{\phi}$ and $\ket{\psi}$ are orthogonal.
(The more general case where $\ket{\phi}$ and $\ket{\psi}$ are not
necessarily orthogonal is easily handled, and is discussed in the
appendix.)

Let $N$ be a positive integer, which will determine the accuracy of
the procedure.
We assume that each player $P_i$ holds $N+2$ identical registers
labelled $\reg{X}_0^{i},\ldots,\reg{X}_{N+1}^{i}$, where each register
has an associated Hilbert space that is isomorphic to $\mathcal{X}^i$.
We take the initial state of the registers
$(\reg{X}^1_1,\ldots,\reg{X}^m_1),\ldots,
(\reg{X}^1_{N+1},\ldots,\reg{X}^m_{N+1})$
to be
\begin{equation} \label{eq:shared}
\ket{E_N} = \frac{1}{\sqrt{N}}
\sum_{k = 1}^N \ket{\phi}^{\otimes k} \ket{\psi}^{\otimes (N-k+1)},
\end{equation}
and we consider the case where the initial state of the registers
$(\reg{X}^1_0,\ldots,\reg{X}^m_0)$ is the input state~$\ket{\phi}$.
Thus, the state \eqref{eq:shared} represents the entanglement
initially shared by $P_1,\ldots,P_m$.
The procedure that transforms $\ket{\phi}$ into $\ket{\psi}$ is
simple: each player $P_i$ cyclically shifts the contents of the registers
$\reg{X}^i_0,\ldots,\reg{X}^i_{N+1}$ by applying a unitary operation
defined by the action
\[
\ket{x_0}\ket{x_1}\cdots\ket{x_{N+1}} \mapsto
\ket{x_{N+1}}\ket{x_0}\cdots\ket{x_N}
\]
on standard basis states.

Let us now consider the properties of the above procedure.
It is clear that after the cyclic shift, the registers
$(\reg{X}^1_0,\ldots,\reg{X}^m_0)$ will contain a perfect copy of
$\ket{\psi}$, and the remaining registers will contain the state
\begin{equation} \label{eq:sharedafter}
\ket{E'_N} = \frac{1}{\sqrt{N}}
\sum_{k = 1}^N \ket{\phi}^{\otimes (k+1)} \ket{\psi}^{\otimes (N-k)}.
\end{equation}
Thus, the procedure transforms $\ket{\phi} \ket{E_N}$ into
$\ket{\psi} \ket{E_N'}$.
It is easily checked that $\braket{E'_N | E_N} = 1 - 1/N$, so for
large $N$ there is only a small disturbance to the shared entangled state
$\ket{E_N}$.
The procedure satisfies the coherence requirement for this reason.

In the case that the players wished instead to transform $\ket{\psi}$
to $\ket{\phi}$, so that the initial state of the registers
$(\reg{X}^1_0,\ldots,\reg{X}^m_0)$ is $\ket{\psi}$, the same state
\eqref{eq:shared} may be used, but the registers are shifted in the
opposite direction.

\subsection*{Further connections to embezzlement and other work}

A notion related to coherent state exchange, known as
{\it catalytic transformation} of pure states, was considered
by Jonathan and Plenio \cite{JonathanP99}.
In particular, they considered the situation in which two parties
transform one pure state to another (by local operations and classical
communication) using a catalyst---or a state that assists but is
left unchanged by the process.
Coherent state exchange (and embezzlement) do almost exactly this, and
without the exchange of classical information, but in the approximate
sense that the catalyst is permitted to change slightly.

As mentioned above, in the case $m=2$ one may use quantum state
embezzlement twice to implement coherent state exchange.
The family of states $\{\ket{E_N}\}$ defined in \cite{vanDamH03}
also has the added property of being {\it universal}, or independent
of the state $\ket{\phi}$ to be embezzled.
We note that it is possible  to use our method to give universal
embezzling families for all~$m$.
To define a universal embezzling family for any fixed $m$, we may
consider an $\epsilon$-net of states $\{\ket{\psi}\}$ in $N^m$
dimensions (for $\varepsilon = 1/N$, say), take
$\ket{\phi}=\ket{0^m}$, and define the embezzling state for each
$N$ to be the tensor product of all the states $\ket{E_N}$ ranging
over the $\varepsilon$-net.
The embezzlement of a particular state is then performed in the
most straightforward way.
Unlike the families of van Dam and Hayden for the case $m=2$, our
method is highly inefficient, but nevertheless establishes that
universal embezzling families exist for all~$m$.

\section{Finite entanglement is suboptimal} \label{sec:game}

The purpose of this section is to prove the first main result of the
paper, which is that there exist two-prover quantum interactive proof
systems for which no finite amount of entanglement allows for an
optimal strategy on any fixed input.
It suffices to define a two-prover quantum interactive proof system
having no dependence on the input $x$; or, in simpler terms, to
consider a cooperative game played by two players and moderated by a
referee.
This type of {\it cooperative quantum game} represents a
generalization of the {\it non-local games} model of \cite{CleveH+04},
where now the referee can send, receive, and process quantum
information.

To be more precise, and to aid in the exposition that follows, we
define two-player, one-round cooperative quantum games as follows:

\begin{enumerate}
\item
The referee prepares three quantum registers
$(\reg{R},\reg{S},\reg{T})$ in some chosen state, and then sends
$\reg{S}$ to Alice and $\reg{T}$ to Bob.

\item
Alice and Bob transform the registers $\reg{S}$ and $\reg{T}$ sent to
them however they choose, resulting in registers $\reg{A}$ and
$\reg{B}$ that are sent back to the referee.

\item
The referee performs a binary-valued measurement on the
registers $(\reg{R},\reg{A},\reg{B})$.
The outcome~1 means that Alice and Bob win, while the outcome 0 means
that they lose.
\end{enumerate}

\noindent
The restrictions on Alice and Bob are the same as for provers in a
quantum interactive proof system: they are not permitted to
communicate once the game begins, but may agree on a strategy
beforehand.
Such a strategy may include the sharing of an entangled state of their
own choosing, which they may use when transforming the registers sent
to them.
The complexity of the referee, which corresponds to the verifier in an
interactive proof system, is ignored given that we no longer consider
an input string.

\subsection*{Description of the game} \label{sec:game-description}

Consider the two-player cooperative quantum game that is determined by
the following specification of the referee:
\begin{enumerate}
\item
Let $\reg{R}$ be a qubit register and let $\reg{S}$ and
$\reg{T}$ be qutrit registers.
The referee initializes the registers $(\reg{R},\reg{S},\reg{T})$ to
the state
\[
\frac{1}{\sqrt{2}}\ket{0}\ket{00} + \frac{1}{\sqrt{2}}\ket{1}\ket{\phi}
\]
where
\[
\ket{\phi} = \frac{1}{\sqrt{2}} \ket{11} + \frac{1}{\sqrt{2}}
\ket{22}.
\]
The registers $\reg{S}$ and $\reg{T}$ are sent to Alice and Bob,
respectively.

\item
The referee receives $\reg{A}$ from Alice and $\reg{B}$ from
Bob, where $\reg{A}$ and $\reg{B}$ are both single-qubit registers.
The triple $(\reg{R},\reg{A},\reg{B})$ is measured with respect to the
projective measurement $\{\Pi_0,\Pi_1\}$, where
$\Pi_0 = I - \ket{\gamma}\bra{\gamma}$ and
$\Pi_1 = \ket{\gamma}\bra{\gamma}$,
for $\ket{\gamma} = (\ket{000} + \ket{111})\sqrt{2}$.
In accordance with the conventions stated above, the outcome 1 means
that Alice and Bob win while 0 means that they lose.
\end{enumerate}

The intuition behind this game is as follows.
Alice and Bob are presented with two possibilities, in superposition:
they receive either the unentangled state $\ket{00}$ or the entangled
state $\ket{\phi}$.
Their goal is essentially to do nothing to $\ket{00}$ and to convert
$\ket{\phi}$ to $\ket{11}$, for they want the referee to hold the
state $\ket{\gamma}$ when the final measurement is made.
These transformations must be done coherently, without measurements or
residual evidence of which of the two transformations
$\ket{00}\mapsto\ket{00}$ or $\ket{\phi} \mapsto \ket{11}$ was
performed, for otherwise the final state of the referee will not have
a large overlap with $\ket{\gamma}$.

The required transformation will be possible using coherent state
exchange, with a winning probability approaching 1.
It will be shown, however, that it is never possible for Alice and Bob
to win with certainty, provided they initially share a finite
entangled state.

\subsection*{Strategies that win with probability approaching 1}

We now present a family of strategies for Alice and Bob that win with
probability approaching~1.
In the above game, Alice receives $\reg{S}$ from the referee
and returns $\reg{A}$; and likewise for Bob with registers
$\reg{T}$ and $\reg{B}$.
Alice will begin with the qubit $\reg{A}$ initialized to $\ket{0}$, and
Bob begins with $\reg{B}$ initialized to $\ket{0}$ as well.
Let $U$ be a unitary operation, acting on a pair consisting of a qutrit
and a qubit, with the following behavior:
\[
U: \ket{0}\ket{0} \mapsto \ket{0}\ket{0},\quad\quad
U: \ket{1}\ket{0} \mapsto \ket{1}\ket{1}, \quad\quad\text{and}\quad\quad
U: \ket{2}\ket{0} \mapsto \ket{2}\ket{1}.
\]
Upon receiving $\reg{S}$, Alice applies $U$ to $(\reg{S},\reg{A})$,
and Bob does likewise to $(\reg{T}, \reg{B})$ after receiving
$\reg{T}$.
This leaves the 5-tuple $(\reg{R},\reg{A},\reg{B},\reg{S},\reg{T})$
in the state
\[
\frac{1}{\sqrt{2}} \ket{000} \ket{00} +
\frac{1}{\sqrt{2}} \ket{111} \ket{\phi}.
\]

Alice and Bob have not yet sent $\reg{A}$ and $\reg{B}$ to the
referee.
Before sending these registers, they use them as control qubits to
transform registers $\reg{S}$ and $\reg{T}$ in superposition: if
$\reg{A}$ and $\reg{B}$ are set to $0$ then nothing happens, while if
$\reg{A}$ and $\reg{B}$ are 1 they perform coherent state
exchange, transforming $\ket{\phi}$ to $\ket{00}$.
Assuming that Alice and Bob initially share the entangled state
\[
\ket{E_N} = \frac{1}{\sqrt{N}}\sum_{k = 1}^N
\ket{\phi}^{\otimes k}\ket{00}^{\otimes (N-k+1)},
\]
the resulting state is
\[
\frac{1}{\sqrt{2}} \ket{000} \ket{00}\ket{E_N} +
\frac{1}{\sqrt{2}} \ket{111} \ket{00}\ket{E_N'}
\]
for
\[
\ket{E'_N} = \frac{1}{\sqrt{N}}\sum_{k = 1}^N
\ket{\phi}^{\otimes (k+1)}\ket{00}^{\otimes (N-k)}.
\]

The registers $\reg{A}$ and $\reg{B}$ are now sent to the referee,
whose measurement results in outcome 1 with probability
\[
\norm{
\frac{1}{2} \ket{E_N} + \frac{1}{2} \ket{E_N'}}^2 = 1 - \frac{1}{2N}.
\]

\subsection*{Impossibility to win with certainty}

Now we will prove that Alice and Bob cannot win with certainty
regardless of the strategy they employ.
Without loss of generality, it may be assumed that Alice and Bob
initially share a pure entangled state $\ket{\psi}\in\mathcal{X}_A\otimes\mathcal{X}_B$,
where the spaces $\mathcal{X}_A$ and $\mathcal{X}_B$ have the same dimension $d$.
When Alice and Bob receive $\reg{S}$ and $\reg{T}$ from the referee,
the state of the entire system is given by
\[
\frac{1}{\sqrt{2}}\ket{0}\ket{00}\ket{\psi} +
\frac{1}{\sqrt{2}}\ket{1}\ket{\phi}\ket{\psi}.
\]

General quantum operations performed by Alice and Bob can be
described by linear isometries: $A$ for Alice and $B$ for Bob.
These isometries take the form
$A: \mathcal{S} \otimes \mathcal{X}_A \rightarrow \mathcal{A} \otimes \mathcal{Y}_A$ and
$B: \mathcal{T} \otimes \mathcal{X}_B \rightarrow \mathcal{B} \otimes \mathcal{Y}_B$,
where $\mathcal{S},\mathcal{T},\mathcal{A},\mathcal{B}$ are the spaces associated with the registers
$\reg{S}$, $\reg{T}$, $\reg{A}$, and $\reg{B}$, and the spaces $\mathcal{Y}_A$
and $\mathcal{Y}_B$ are arbitrary.
The state of the system immediately before the referee measures is
therefore
\[
\frac{1}{\sqrt{2}} \ket{0} (A\otimes B) \ket{00}\ket{\psi}
+\frac{1}{\sqrt{2}} \ket{1} (A\otimes B)\ket{\phi}\ket{\psi}.
\]
By defining operators $A_0,A_1\in\lin{\mathcal{S}\otimes\mathcal{X}_A,\mathcal{Y}_A}$ and
$B_0,B_1\in\lin{\mathcal{T}\otimes\mathcal{X}_B,\mathcal{Y}_B}$ as
\[
A_0 = \left(\bra{0} \otimes I\right) A, \quad
A_1 = \left(\bra{1} \otimes I\right) A, \quad
B_0 = \left(\bra{0} \otimes I\right) B,\quad
B_1 = \left(\bra{1} \otimes I\right) B,
\]
we may express the probability that Alice and Bob win as
\[
\frac{1}{4}\norm{
(A_0\otimes B_0) \ket{00}\ket{\psi}
+(A_1\otimes B_1) \ket{\phi}\ket{\psi}}^2
\leq
\frac{1}{2} + \frac{1}{2}
\abs{\bra{\phi} \bra{\psi}
\left(A_1^{\ast}A_0\otimes B_1^{\ast}B_0\right)
\ket{00} \ket{\psi}}.
\]

We have that $\norm{A_1^{\ast}A_0} \leq 1$ and
$\norm{B_1^{\ast}B_0} \leq 1$, and therefore it is possible to express
both $A_1^{\ast}A_0$ and $B_1^{\ast}B_0$ as convex combinations of
unitary operators.
By convexity, the winning probability is therefore bounded above by
\[
\frac{1}{2} + \frac{1}{2}
\abs{\bra{\phi} \bra{\psi} (U_A \otimes U_B) \ket{00} \ket{\psi}}
\]
for some choice of unitary operators $U_A$ and $U_B$.
Notice that $(U_A\otimes U_B) \ket{00}\ket{\psi}$
must have 1 e-bit of entanglement less than $\ket{\phi}\ket{\psi}$,
and so the states cannot be equal---and therefore the success
probability cannot be 1.

A quantitative bound may be proved as follows.
Using one of the Fuchs--van de Graaf inequalities \cite{FuchsvdG99}
and the monotonicity of the fidelity under partial tracing, it holds
that
\[
\abs{\braket{\phi,\psi|U_A \otimes U_B|00,\psi}}
\leq \operatorname{F}(\rho,\xi) \leq \sqrt{1 - \frac{1}{4}\norm{\rho - \xi}_1^2}
\]
for
\begin{align*}
\rho & = \operatorname{Tr}_{\mathcal{B}\otimes\mathcal{X}_B}
\left(\ket{\phi}\bra{\phi} \otimes \ket{\psi}\bra{\psi}\right),\\
\xi & = \operatorname{Tr}_{\mathcal{B}\otimes\mathcal{X}_B}
U_A
\left(\ket{00}\bra{00} \otimes \ket{\psi}\bra{\psi}\right) U_A^{\ast}.
\end{align*}
At this point we may follow precisely the analysis of
van Dam and Hayden \cite{vanDamH03} for the near-optimality of their
universal embezzling families: we have that $S(\rho)-S(\xi)=1$,
from which it follows that
$\norm{\rho - \xi}_1 \geq 1/(2\log(3d))$
by Fannes' inequality \cite{Fannes73}.
Consequently, the winning probability is bounded above by
$1 - 1/(32 \log^2 (3d))$.
The error probability therefore decreases at most quadratically in the
number of qubits that Alice and Bob initially share.

\subsection*{Consequences for entanglement assisted local quantum
  operations}

For fixed spaces $\mathcal{X}_A$, $\mathcal{X}_B$, $\mathcal{Y}_A$, and $\mathcal{Y}_B$, a quantum
operation
$\Phi: \lin{\mathcal{X}_A\otimes\mathcal{X}_B} \rightarrow \lin{\mathcal{Y}_A\otimes\mathcal{Y}_B}$
is an {\it entanglement assisted local quantum operation} if it can be
realized as illustrated in Figure~\ref{fig:ealo}; or more precisely,
if there exists some choice of spaces $\mathcal{Z}_A$ and $\mathcal{Z}_B$, a density
operator $\rho\in\density{\mathcal{Z}_A\otimes\mathcal{Z}_B}$, and admissible
super-operators $\Psi_A : \lin{\mathcal{X}_A\otimes\mathcal{Z}_A}\rightarrow\lin{\mathcal{Y}_A}$
and
$\Psi_B : \lin{\mathcal{X}_B\otimes\mathcal{Z}_B}\rightarrow\lin{\mathcal{Y}_B}$
such that
$\Phi(\xi) = (\Psi_A\otimes\Psi_B)(\rho\otimes\xi)$
for all $\xi\in\lin{\mathcal{X}_A\otimes\mathcal{X}_B}$.
Operations of this type are also known as {\it localizable}
operations \cite{BeckmanGNP01}.
\begin{figure}[t]
  \begin{center}
    \small
    \unitlength=0.65pt
    \begin{picture}(300, 200)(0,-20)
      \node[Nw=40,Nh=70,Nmr=3](A)(150,130){$\Psi_A$}
      \node[Nw=40,Nh=70,Nmr=3](B)(150,10){$\Psi_B$}
      \node[Nframe=n](rho)(100,70){$\rho$}
      \node[Nframe=n,Nw=40](xi)(-20,70){$\xi$}
      \node[Nframe=n,Nw=50](Out)(320,70){$\Phi(\xi)$}
      \drawbpedge[eyo=-10,ELpos=30](rho,90,40,A,180,40){$\mathcal{Z}_A$}
      \drawbpedge[eyo=10,ELside=r,ELpos=30](rho,-90,40,B,180,40){$\mathcal{Z}_B$}
      \drawbpedge[syo=5,eyo=10,ELpos=70](xi,0,150,A,180,150){$\mathcal{X}_A$}
      \drawbpedge[syo=-5,eyo=-10,ELside=r,ELpos=70](xi,0,150,B,180,150){$\mathcal{X}_B$}
      \drawbpedge[eyo=5,ELpos=30](A,0,150,Out,180,150){$\mathcal{Y}_A$}
      \drawbpedge[eyo=-5,ELside=r,ELpos=30](B,0,150,Out,180,150){$\mathcal{Y}_B$}
    \end{picture}
  \end{center}
  \caption{An entanglement-assisted local quantum operation~$\Phi$.
    An input state $\xi \in \density{\mathcal{X}_A\otimes\mathcal{X}_B}$ is transformed into
    the output state $\Phi(\xi)$ by means of local quantum operations
    $\Psi_A$ and $\Psi_B$, along with a shared entangled state
    $\rho\in\density{\mathcal{Z}_A\otimes\mathcal{Z}_B}$.}
  \label{fig:ealo}
\end{figure}
In addition to having an obvious relevance to two-prover quantum
interactive proof systems, this is an interesting and fundamental class
of quantum operations in its own right.

An unfortunate fact that follows from the analysis of the game
presented above is the following.
When $\mathcal{X}_A$ and $\mathcal{X}_B$ have dimension at least 3 and $\mathcal{Y}_A$ and $\mathcal{Y}_B$
have dimension at least 2, the set of entanglement-assisted local
quantum operations
$\Phi:\lin{\mathcal{X}_A\otimes\mathcal{X}_B} \rightarrow \lin{\mathcal{Y}_A\otimes\mathcal{Y}_B}$ is not
a closed set: the sequence of entanglement-assisted local quantum
operations induced by the strategies described above converges to a
valid quantum operation that is not an entanglement-assisted local quantum
operation.

\subsection*{Another connection with prior work}

We wish to point out one further connection between the above result and
some existing work.
In the exact catalytic transformation setting of Jonathan and Plenio
\cite{JonathanP99}, Daftuar and Klimesh \cite{DaftuarK01} proved the
following fact: the dimension of the catalyst required to transform
one state to another, when this is possible, cannot be bounded by any
function of the dimension of those states.
Although this fact does not have a direct implication to the
cooperative quantum games model, and is incomparable to our result as
far as we can see, there is a similarity in spirit between the results
that is worthy of note.

\section{Near-perfect completeness} \label{sec:perfect-completeness}

Kempe, Kobayashi, Matsumoto, and Vidick \cite{KempeKMV08} proved that
multi-prover quantum interactive proof systems can be efficiently
transformed to have {\it perfect completeness}, while retaining small
soundness error.
An analogous fact was previously shown to hold for single-prover
quantum interactive proof systems \cite{KitaevW00}, but the two proofs
are quite different.
The proof in \cite{KitaevW00} for the single-prover case is very
simple while the proof in \cite{KempeKMV08} for the multi-prover case
is rather complicated.
In this section we show that the use of coherent state exchange
allows the simple proof for the single-prover setting to be applied in
the multi-prover setting.

There is, however, one small caveat: whereas
Kempe, Kobayashi, Matsumoto, and Vidick achieve truly perfect
completeness (in as far as quantum operations can ever be implemented
perfectly), we must settle for {\it near-perfect} completeness:
similar to the game from the previous section, honest provers will be
able to convince the verifier to accept yes-inputs with any
probability smaller than 1 that they desire, but the probability may
not in actuality be 1.
For most intents and purposes, though, we believe that this behavior
can reasonably be viewed as representing perfect completeness.

Suppose that a verifier $V$ interacts with $m$ provers
$P_1,\ldots,P_m$ for $r$ rounds, and suppose the completeness and
soundness probabilities for this verifier are given by $c$ and $s$,
respectively (which may be functions of the input length).
Specifically, for the promise problem
$A = (A_{\text{yes}},A_{\text{no}})$ of interest, the following
conditions hold:

\begin{enumerate}
\item
  Completeness.  The verifier is convinced to accept every
  yes-input $x\in A_{\text{yes}}$ with probability at least
  $c(\abs{x})$ by the provers' strategy.

\item
  Soundness. The verifier cannot be convinced to accept any no-input
  $x\in A_{\text{no}}$ with probability exceeding $s(\abs{x})$,
  regardless of the provers' strategy.
\end{enumerate}

\noindent
As usual and without loss of generality, we may ``purify'' a given
proof system so that the verifier $V$ and provers $P_1,\ldots,P_m$ are
described by unitary operations and the provers' initial shared
entanglement is pure.
We also make two simple assumptions on the proof system and the
completeness probability $c(\abs{x})$.
First, we assume that it is possible for the provers to convince the
verifier to accept every string $x\in A_{\text{yes}}$ with probability
exactly $c(\abs{x})$.
This can be achieved, for example, by appending an extra bit to
the last message of the first prover and having the verifier reject
when this bit is 1.
Second, we assume that the value $c(\abs{x})$ is such that the
verifier can efficiently implement the rotation
\[
\ket{0} \mapsto \sqrt{1 - c(\abs{x})} \ket{0} -
\sqrt{c(\abs{x})} \ket{1},\quad\quad
\ket{1} \mapsto \sqrt{c(\abs{x})} \ket{0} +
\sqrt{1 - c(\abs{x})} \ket{1}
\]
without error.
(We also assume reversible computations incur no error.)

Now, assume that an input string
$x\in A_{\text{yes}}\cup A_{\text{no}}$ has been fixed.
(As $x$ is now fixed, we will not explicitly refer to $x$ or $\abs{x}$
when discussing quantities depending on $x$.)
Let $p$ denote the probability that the verifier accepts.
Given the purity assumption of the proof system, this means that the
final state of the entire system at the end of the interaction may be
expressed as
\[
\sqrt{1-p} \ket{0}\ket{\phi_0} + \sqrt{p} \ket{1}\ket{\phi_1},
\]
where the first qubit in this expression represents the verifier's
output qubit.
The remaining part of the state, represented by $\ket{\phi_0}$ and
$\ket{\phi_1}$, corresponds to the state of every other register in
the proof system, shared in some arbitrary way among the verifier and
provers.
For simplicity we will assume that $\ket{\phi_0}$ and $\ket{\phi_1}$
are orthogonal, which at most requires that the verifier makes a
pseudo-copy of the output qubit as its last action.

To transform the proof system to one with near-perfect completeness,
one additional round of communication is added to the end of the
protocol.
To describe what happens in this additional round of communication,
let us write $\reg{A}$ to denote the verifier's output qubit,
$\reg{V}$ to denote the register comprising all of the verifier's
memory aside from the output qubit, and $\reg{P}_1,\ldots,\reg{P}_m$
to denote registers representing the provers' memories, all
corresponding to the final state of the original protocol.

To start the additional round of communication, the verifier prepares
$m$ additional single-qubit registers $\reg{A}_1,\ldots,\reg{A}_m$ as
pseudo-copies of $\reg{A}$, so that the state of the system becomes
\[
\sqrt{1-p} \ket{0}\ket{0^m}\ket{\phi_0}
+ \sqrt{p} \ket{1}\ket{1^m}\ket{\phi_1}.
\]
The verifier then sends $\reg{V}$ to the first prover $P_1$ (which is
an arbitrary choice, but one that all provers are aware of), and sends
each register $\reg{A}_i$ to prover $P_i$.

Upon receiving these registers from the verifier, the provers perform
the following actions.
First, using the registers $(\reg{A}_1,\ldots,\reg{A}_m)$ as control
qubits, the provers perform coherent state exchange: when each
register $\reg{A}_i$ contains 0, nothing happens;
and when each register $\reg{A}_i$ contains~1, the state
$\ket{\phi_1}$ is exchanged for $\ket{\phi_0}$.
The resulting state of the entire system is
\[
\sqrt{1-p} \ket{0}\ket{0^m}\ket{\phi_0}\ket{E_N}
+ \sqrt{p} \ket{1}\ket{1^m}\ket{\phi_0}\ket{E_N'},
\]
where
\[
\ket{E_N} = \frac{1}{\sqrt{N}}
\sum_{k = 1}^N \ket{\phi_0}^{\otimes k}
\ket{\phi_1}^{\otimes (N-k+1)}
\]
is an additional shared entangled state the provers use for this
purpose, and $\ket{E_N'}$ is defined in the same way as in
Section~\ref{sec:exchange}.
(This expression of $\ket{E_N}$ makes use of the assumption that
$\ket{\phi_0}$ and $\ket{\phi_1}$ are orthogonal.
One may instead consult the discussion in the appendix, which does not
require this assumption.)
The number $N$ is the provers' choice for an accuracy parameter, which
we assume to be as large as they wish.
Once this is done, the provers return the registers
$\reg{A}_1,\ldots,\reg{A}_m$ to the verifier.

The final step is that the verifier measures the registers
$(\reg{A},\reg{A}_1,\ldots,\reg{A}_m)$ with respect to a basis
containing the state
$\sqrt{1 - c}\ket{0}\ket{0^m} + \sqrt{c}\ket{1}\ket{1^m}$,
accepting if the output matches this state.
(This is possible given our assumptions on $c$.)
In the case that $x\in A_{\text{yes}}$ the provers may take $p = c$,
and so the acceptance probability is
\[
\norm{(1 - c) \ket{E_N} + c \ket{E'_N}}^2 \geq 1 - \frac{1}{2N}.
\]
This is arbitrarily close to $1$, given that the provers may take any
value for $N$.
In the case that $x\in A_{\text{no}}$ we have $p\leq s$, from which it
is routine to show that the acceptance probability is at most
\[
\left(\sqrt{s}\sqrt{c} + \sqrt{1-s}\sqrt{1-c}\right)^2
\leq 1 - (c - s)^2.
\]

\section{Conclusion} \label{sec:conclusion}

We have discussed two applications of coherent state exchange to the
study of multi-prover quantum interactive proof systems.

The first application demonstrates that provers in a multi-prover
quantum interactive proof system may not always have an optimal
strategy when limited to finite entanglement.
We view that the primary importance of this fact is that it will serve
to better focus efforts on proving bounds on the amount of
entanglement needed for {\it close-to-optimal} provers in multi-prover
quantum interactive proofs---for such bounds can only exist in general
for close-to-optimal and not optimal success probability.

The second application is a simple proof that multi-prover quantum
interactive proof systems can be efficiently transformed to have
near-perfect completeness by adding one round of communication.
There is a trade-off between this proof and the proof of Kempe,
Kobayashi, Matsumoto, and Vidick \cite{KempeKMV08}, which is that it
is considerably simpler but cannot be said to achieve absolutely
perfect completeness.

A few other applications of coherent state exchange have also
been mentioned.
In particular, we have proved that the collection of
entanglement-assisted local quantum operations on systems of dimension
3 and higher is not a closed set, and we have proved that (highly
inefficient) universal embezzling families exist for any number of
parties.
It remains to be seen to what extent such families can be made more
efficient.

\bibliographystyle{alpha}

\newcommand{\etalchar}[1]{$^{#1}$}

redpajama_set_name: RedPajamaArXiv


Explore Delhi Street food with a chef!
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In the event of fires in underground structures, any hot, poisonous gases must be conducted away for reasons of personal safety. It must be possible to test the smoke extraction system for correct dimensioning using the Izar hot smoke test system in the structure. In the Hagerbach testing tunnel, Izar has been calibrated using pool fires.
The Izar hot smoke test system has been tested and calibrated in the tunnel system at a high level of performance. The work was scientifically monitored by the University of Edinburgh (GB).


Baldwin Hills Crenshaw is embarking on a transformational redevelopment that builds upon the significant improvements that have already been made to the mall since 2006.
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While malls are facing significant challenges nationally, with some closing altogether, our goal is to enhance the mall experience, improve walkability and transit access, and transform acres of pavement with new retail, homes, offices, green space and a hotel with banquet facilities. The plan also includes a new grand entrance at the corner of Stocker and Crenshaw that will create a stronger connection with the surrounding community.
For any questions, and to find out more about the transformation of Baldwin Hills Crenshaw, please email Community Outreach Director Jason Lombard at jlombard.bhcp@gmail.com or call 213-505-6191.
The transformation includes new mixed-income residences – consisting of both condominiums and apartments – and ground-floor retail stores.
The plan creates 961 new apartments and condominiums in the community while making the property as a whole more pedestrian-oriented by tearing down the perimeter rod iron fencing around the property, adding new community open spaces, and creating safe connections to the new Metro station and surrounding properties.
The transformational project at Baldwin Hills Crenshaw will feature a new open-air retail village.
The 330,000 square foot village will provide direct pedestrian access from Crenshaw Boulevard and create a stronger connection to the local community. We look forward to introducing new exciting entertainment options within the retail village such as a bowling alley, quality sit-down restaurants, fast-casual cafés, and attractive gathering spots connected via a landscaped promenade that leads to the existing mall.
Our goal is to continue attracting top retailers to the transformed Baldwin Hills Crenshaw to offer the amenities local residents have been asking for and which fit with the unique character of the community.
Baldwin Hills Crenshaw will continue to house many of the same service providers – including banks, a grocery store and an LAPD substation – that have made it such an important community center.
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A new 10-story office building located north of Martin Luther King Jr. Blvd. will help attract new employers and services to the region.
© 2018 Baldwin Hills Crenshaw Plaza. All Rights Reserved.


I always loved museums, pretty and historical objects and was introduced to auction houses very early on by my parents. So after having studied Art History in Amsterdam I needed to find an internship and Christie's Amsterdam was looking for one for their Impressionist department. Whilst there I fell in love with the buzz of auction and as with many who work at Christie's, stayed on.
I am the Head of Sale management for Asian Art and oversee the Chinese and Japanese auctions at Christie's. I am responsible for the finances that are involved in creating the auctions, making sure any problems are taken care of, help with the sale calendar and making sure we have enough space for our auctions, and help the team to get the sale together.
They had been looking for someone for a while and one of my colleagues who I had worked with before, who was close to the team, mentioned my name as a possible candidate. Luckily I was successful.
Working with a passionate team who are all committed to making each auction a success! It is incredible to see a piece sell in the auction, that you have been working on for a number of months. Seeing it from the beginning to the sale at the end is an incredible feeling!
Making sure that you take decisions that are both in favour of the company but also protect our client relationships. It is a fine balance.
I think it may have been a very last minute consignment, which was confirmed for sale the day before we sent our catalogue off the printer. I had to make sure the piece (which was a big sculpture) got down to London within a day, shot for our front cover and catalogued. I was able to set everything up and in the end it was one of the best front covers we had ever sold.
Most of Barbara Hepworth's sculptures – I was fortunate enough to work in the Modern British department before and the Evening sale often sold her sculptures. I would love one, although I would need a bigger flat!
Don't give up, there is an element of luck involved, but if you are really passionate about a career in the art world it is worth the wait as you will end up with a job you love in an industry you will find continually challenging and fascinating.
I would have loved to own my own bookshop – maybe an art bookshop!


Sometimes when I'm hanging out with people I discover parts of them that would make a really good trait for a character. I never mean to take pieces of people, but they just happen. Either in something they say, or something they do… I always end up taking from those around me.
When I started writing the easiest way for me to write was from my own pov (point of view). My characters were based on me or my friends in certain situations that in no way would ever happen in reality. As my writing improved so did my character development and my ability to hide the traits I took from those around me into my characters.
Now each character is a unique person in the worlds I create. Liora is a girl that is ever changing and learning in a world that has people who accept her and those that don't. Caldor has people he finds worth his time and others he will ignore for the sake of keeping his sanity.
But, there are some… and I won't say who among my characters share traits with people I know. They aren't obviously that person, but there are qualities like the way they react to bad news or how they departmentalize the situations they're in that make them part of the person I know in real life.
Where I take most from reality is conversations I hear between people, or descriptions people make about certain environmental details or emotions. These add a human touch and also helps to expand the description to something the readers may understand.
Writing for me is like a puzzle in the sense you have to take all these elements (pieces) from reality and fantasy, mix them together and see if they work. You tweak a character here. Add description over there… and eventually you get something that works.
Writing is escapism from the world around you… but in every story there are hints of reality.
Either way, I mainly find it fascinating because I have never done this. I don't see people who I want to make characters. My characters are simply… themselves. I'm not sure if that makes sense or not… I suppose that I likely put pieces of conversations, characteristics, and myself into each of my characters, but I can't honestly say that I base any of my characters on people I know.
I did the copy character when I was learning to write. It was easier to copy a person I know to learn the basics of dialogue and interactions. It was good practice to test knew styles and then I'd know if the character was in character or not. Now I've moved pass that. I rarely use people I know, but there are things certain people do that I use only because it is human or funny.
Ah! In that regard I can totally understand: finding a base line on how character interactions should go. Definitely makes sense. ^.^ I'm glad that it worked for you and that you've gotten a grasp of it. That's great progress!


text:
[rev_slider taitradio]
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Angus Tait congratulates Lew Smith at the Tait Dealer Conference December 2000
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In the accompanying photo Lew Smith accepts his award for outstanding support of Tait from Sir Angus Tait at the Tait Dealer Conference December 2000.

redpajama_set_name: RedPajamaCommonCrawl


text:
Ad Astra Takes Lift Off in Theatres, but Does it Land?
Posted on September 20, 2019 September 20, 2019 Author Ethan ShattockPosted in UncategorizedLeave a Reply
Directed by: James Gray Starring: Brad Pitt, Ruth Negga, Tommy Lee Jones, Donald Sutherland Runtime: 122 mins
Fresh off of Quentin Tarantino's Once Upon a Time in Hollywood, Brad Pitt is leaping back into theatres dressed in a spacesuit and with a mellower demeanour than his previous role involved. Like Tarantino, director James Gray boasts a lean filmography, with only a handful of feature films to his name before Ad Astra.
Pitt plays Major Roy McBride. As we are strongly and repeatedly reminded at the outset, he's the son of renowned astronaut H. Clifford McBride (Tommy Lee Jones). Clifford was a pioneering figure that drove the "Lima Project" 26 years before current events, in an amibitious and dangerous attempt to search for intelligent life elsewhere in the solar system. 10 years on from taking lift off, the Lima Project lost contact with "Space Command" while orbiting Neptune and essentially disappeared. In light of powerful but seemingly inexplicable power surges that rock the solar system, the United States Armed Forces branch in space bring in the accomplished and composed Roy and inform him that the Lima Project may be linked with the current situation. They outline that under the command of his father, the project's operations carry existential threats that could yield devastating results for the solar system. Under the veiled supervision of Clifford's former associate Colonel Pruitt (Donald Sutherland), Roy is sent on a commercial lunar flight. From the moon, he needs to go to Mars and transmit a message essentially to figure out what on earth (and elsewhere in the solar system) is happening.
One of the most striking features of Ad Astra is the self assurance with which it contextualises itself. The story is set in the future, and it's not entirely obvious exactly when. However, there's a subtle and appealling introduction here. We know that commercial flights to the moon are now a thing, and that humans are getting to grips with solar system exploration with more ease. That allows for a visually appealing but also realistic portrayal of humankind in outer space. Things seem quite commercialised, and in many ways new planets are just another space where the drudgery of labour now takes place. The manner in which the film paints the expansion of everyday human activity to new colonised planets has bleak and at times apocalyptic undertones, not unlike Apocalypse Now and even Mad Max. However normalised space travel may seem in the opening stages of the film, things appear to be spiralling out of control. Literally. An opening set piece introduces audiences to the worrying abnormalities in one of the most impressive space scenes in quite a while. In a film that demands to be seen in theatres, it's almost worth going along for this scene alone.
As the modest 2 hour running time goes on, more awe inspiring scenes unfold that shape Roy's quest to find his father. With a plot set outside the bounds of earth, it's not exactly the biggest challenge to wow audiences with cool and aesthetic effects. The concept of heading out into the unknown with our mere human feelers is fascinating in itself. It's an expansion of the human experience that delves beyond earth and perhaps explains part of the success behind franchises like Star Wars. However doable it might be, director James Gray and his team have clearly put in the work here. This effort is to be expected. When announcing Ad Astra, Gray set his ambitions high by saying he wanted "the most realistic depiction of space travel that's been put in a movie. While I can't speak to specifics with regard to scientific accuracy, I can say as an audience member that it's an incredible and immersive depiction of life (or lack thereof in some places) beyond earth. This is accompanied by a subtle but evocative soundtrack, adding a layer of sensual beauty to each scene.
An intermittent narration by Roy himself helps to compensate from an overall tight lipped demeanour from our main character. It also helps to craft the narrative, because so much of the context here is past relationships.
This is my main gripe with Ad Astra. In spite of breathtaking imagery, this seems to be a film that wants to be taken as a story that's deeply character driven. These things are often open to interpretation, but the father – son dynamic that shapes the film's story just falls flat on a number of occasions. There's a coldness and emotional impotence that affects how major scenes play out. Other relationships that are supposed to be formative to Pitt's character are just not fleshed out enough. This includes his relationship with estranged wife Eve, played by an underused Liv Tyler. It's referenced a few times that there was strain in their relationship and a lot of it had to do with Roy's life as an astronaut. This could have allowed for poignant insights that probe what exactly it is that drives so much of the anxiety and despair that undoubetdly must come with that kind of prolonged separation. This is a disappointing omission, and it may be unfair to say that the director is focusing more on special effects in favour of substance. Special effects are important in these types of films, and they're executed with superb precision here. The problem is though, much of this type of visual awe has been done already. Of course we can think back to Stanley Kubrick's 2001: A Space Odyssey, but also with Alfonso Cuarón's Gravity in 2013. In Gravity, Sandra Bullock's character brought much more to the table in terms of emotional reasonance. Another inevitable comparison is Christopher Nolan's Interstellar in 2014. Interstellar put the work in when aiming for authenticity in its portrayal of space, but boldly matched it with a deeply character driven and at times tearjerker plot. Ad Astra falls short in getting the balance right, and its disappointing in light of the talent on screen including Ireland's own Ruth Negga.
At times it seems that Gray is aiming for a frosty bleakness à la Stanley Kubrick, but the plot is so entangled in what is obviously meant to be a personal story that the tone is uncertain. While at this point it might seem like a bit of a cliché made out of low hanging fruit, this is another film that dazzles with effects as a cinematic experience, but ultimately falls short as its own story. The strained father/son drama has been done time and time again, and is typical of patriarchal themes that have dominated so many scripts in the past. It needed to do something inventive here in order to stand out, and what we get just feels underwhelming. Notwithstanding the numerous highly impressive visual scenes, the characters and the issues that plague them are underdeveloped in a way that leaves a cold chill not dissimilar from the icy surroundings of the cosmos that Roy finds himself in. It immerses you in everything, apart from the personal relationships that should be a major part of what make Ad Astra land.
About Ethan Shattock
Ethan is a popcorn-enthusiast who occasionally catches some films in between. Enjoying everything from the grandeur of the IFI, the intimacy of the Lighthouse to buzz of the small screens in the big city. Ethan has a taste for everything but tends to sink his teeth into horror in particular!
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text:
Octávio Mateus
Paleontologia- Dept. Ciências da Terra, Faculdade de Ciências e Tecnologia UNL
Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Monte de Caparica, Portugal (email)
López-Rojas, V., Mateus O., Milàn J., Wings O., Klein N., & Clemmensen L. B. (2021). A new phytosaur from the Late Triassic of Jameson Land, Greenland. 3rd Palaeontological Virtual Congress. 207.: ISBN 978-84-09-36657-6 Abstractlopez_rojas_2021_pvc3_greenland.pdf
Milàn, J., Mateus O., Mau M., Rudra A., Sanei H., & Clemmensen L. B. (2021). A possible phytosaurian (Archosauria, Pseudosuchia) coprolite from the Late Triassic Fleming Fjord Group of Jameson Land, central East Greenland. Bulletin of the Geological Society of Denmark. 69, 71-80. Abstractmilan_et_al_2021_coprolites_greenland_bull69-71-80.pdfWebsite
A large, well-preserved vertebrate coprolite was found in a lacustrine sediment in the Malmros Klint Formation of the Late Triassic Fleming Fjord Group in the Jameson Land Basin, central East Greenland. The size and internal and external morphology of the coprolite is consistent with that of crocodilian coprolites and one end of the coprolite exhibits evidence of post-egestion trampling. As the associated vertebrate fauna of the Fleming Fjord Group contains abundant remains of pseudosuchian phytosaurs, the coprolite is interpreted as being from a large phytosaur.
Clemmensen, L. B., Kent D. V., Mau M., Mateus O., & Milàn J. (2020). Triassic lithostratigraphy of the Jameson Land basin (central East Greenland), with emphasis on the new Fleming Fjord Group. Bulletin of the Geological Society of Denmark. 68, 95–132. Abstractclemmensen_et_al_2020_triassic_lithostratigraphy_of_the_jameson_land_basin.pdfWebsite
The lithostratigraphy of the Triassic deposits of the Jameson Land Basin in central East Greenland is revised. The new Scoresby Land Supergroup is now composed of the Wordie Creek, Pingo Dal, Gipsdalen and Fleming Fjord Groups. This paper only deals with the lithostratigraphy of the late Early-Late Triassic continental deposits of the latter three groups with emphasis on the vertebratebearing Fleming Fjord Group. The new Pingo Dal Group consists of three new formations, the Rødstaken, Paradigmabjerg and Klitdal Formations (all elevated from members), the new Gipsdalen Group consists of three new formations, the Kolledalen, Solfaldsdal (with the new Gråklint Member) and Kap Seaforth Formations (all elevated from members), and the new Fleming Fjord Group is subdivided into three new formations, the Edderfugledal, Malmros Klint and Ørsted Dal Formations (all elevated from members). The Edderfugledal Formation contains two cyclic bedded, lacustrine members, a lowermost Sporfjeld Member (elevated from beds), and an uppermost Pingel Dal Member (elevated from beds). The lacustrine red beds of the Malmros Klint Formation are not subdivided. The lacustrine and fluvial Ørsted Dal Formation contains three new members. In the eastern and central part of the basin, the formation is initiated by cyclic bedded, red lacustrine mudstones of the Carlsberg Fjord Member (elevated from beds), while in the northwestern part of the basin the lowermost part of the formation is composed of grey fluvial conglomerates and sandstones with subordinate red mudstones of the Bjergkronerne Member (elevated from beds). The uppermost part of the formations in most of the basin is composed of cyclic bedded, variegated lacustrine mudstones and grey to yellowish marlstones of the Tait Bjerg Member (elevated from beds). The sediments in the Fleming Fjord Group contain remains of a rich and diverse vertebrate fauna including dinosaurs, amphibians, turtles, aeotosaurs, pterosaurs, phytosaurs and mammaliaforms. Most vertebrate bones have been found in uppermost Malmros Klint Formation, and in the Carlsberg Fjord and Tait Bjerg Members. The Norian–early Rhaetian, lacustrine Fleming Fjord Group was deposited at about 41° N on the northern part of the supercontinent Pangaea. Lacustrine sedimentation was controlled by seasonal as well as longer-term (orbital) variation in precipitation. Precipitation was probably brought to the basin by southwesterly winds. The lacustrine sediments of the uppermost Fleming Fjord Group show deposition during increasingly humid conditions changing the lake environment from an ephemeral lake-steppe area to a perennial lake. This evolution of lake environment suggests a change from a winter-wet temperate climate to one with precipitation throughout the year.
Agnolin, F. L., Mateus O., Milàn J., Marzola M., Wings O., Adolfssen J. S., & Clemmensen L. B. (2018). Ceratodus tunuensis, sp. nov., a new lungfish (Sarcopterygii, Dipnoi) from the Upper Triassic of central East Greenland. Journal of Vertebrate PaleontologyJournal of Vertebrate Paleontology. e1439834., 2018: Taylor & Francis Abstractagnolin_et_al_2018_ceratodus_tunuensis_greenland.pdfWebsite
ABSTRACTThe fossil record of post-Paleozoic lungfishes in Greenland is currently restricted to a few brief reports of isolated and undetermined tooth plates coming from the uppermost Fleming Fjord Formation (late Norian) in Jameson Land, central East Greenland. Here, we describe Ceratodus tunuensis, sp. nov., a new dipnoan from a thin bed of calcareous lake mudstone from the ?rsted Dal Member of the Fleming Fjord Formation. The Ceratodus fossil record indicates that during the Late Triassic, this genus was restricted to the middle latitudes of the Northern Hemisphere. This record matches previous paleobiogeographical analyses and indicates that terrestrial biota during the Late Triassic was strongly influenced by paleolatitude.Citation for this article: Agnolin, F. L., O. Mateus, J. Milàn, M. Marzola, O. Wings, J. Schulz Adolfssen, and L. B. Clemmensen. 2018. Ceratodus tunuensis, sp. nov., a new lungfish (Sarcopterygii, Dipnoi) from the Upper Triassic of central East Greenland. Journal of Vertebrate Paleontology. DOI: 10.1080/02724634.2018.1439834.
Marzola, M., Mateus O., Milàn J., & Clemmensen L. B. (2018). A review of Palaeozoic and Mesozoic tetrapods from Greenland. Bulletin of the Geological Society of Denmark. 66, 21–46. Abstractmarzola_et_al_2018_-_review_of_greenlandic_tetrapods.pdf
This article presents a synthesis of Palaeozoic and Mesozoic fossil tetrapods from Greenland, including an updated review of the holotypes and a new photographic record of the main specimens. All fossil tetrapods found are from East Greenland, with at least 30 different known taxa: five stem tetrapods (Acanthostega gunnari, Ichthyostega eigili, I. stensioi, I. watsoni, and Ymeria denticulata) from the Late Devonian of the Aina Dal and Britta Dal Formations; four temnospondyl amphibians (Aquiloniferus kochi, Selenocara groenlandica, Stoschiosaurus nielseni, and Tupilakosaurus heilmani) from the Early Triassic of the Wordie Creek Group; two temnospondyls (Cyclotosaurus naraserluki and Gerrothorax cf. pulcherrimus), one testudinatan (cf. Proganochelys), two stagonolepids (Aetosaurus ferratus and Paratypothorax andressorum), the eudimorphodontid Arcticodactylus, undetermined archosaurs (phytosaurs and both sauropodomorph and theropod dinosaurs), the cynodont Mitredon cromptoni, and three mammals (Haramiyavia clemmenseni, Kuehneotherium, and cf. ?Brachyzostrodon), from the Late Triassic of the Fleming
Fjord Formation; one plesiosaur from the Early Jurassic of the Kap Stewart Formation; one plesiosaur and one ichthyosaur from the Late Jurassic of the Kap Leslie Formation, plus a previously unreported Late Jurassic plesiosaur from Kronprins Christian Land. Moreover, fossil tetrapod trackways are known from the Late Carboniferous (morphotype Limnopus) of the Mesters Vig Formation and at least four different morphologies (such as the crocodylomorph Brachychirotherium, the auropodomorph Eosauropus and Evazoum, and the theropodian Grallator) associated to archosaurian trackmakers are known from the Late Triassic of the Fleming Fjord Formation. The presence of rich fossiliferous tetrapod sites in East Greenland is linked to the presence of well-exposed continental and shallow marine deposits with most finds in terrestrial deposits from the Late Devonian and the Late Triassic.
Marzola, M., Mateus O., Milàn J., & Clemmensen L. B. (2017). Synrift sedimentary deposition and vertebrate fossil abundance: the tetrapod record from Greenland. Journal of Vertebrate Paleontology, Program and Abstracts. 2017, 159-160. Abstractmarzola_et_al_2017_svp_abstract_greenland.pdf
Lallensack, J. N., Klein H., Milàn J., Wings O., Mateus O., & Clemmensen L. B. (2017). Sauropodomorph dinosaur trackways from the Fleming Fjord Formation of East Greenland: Evidence for Late Triassic sauropods. Acta Palaeontologica Polonica. 62(4), 833-843. Abstractlallensack_et_al_2017_-_sauropodomorph_tracks_greenland.pdf
The Late Triassic (Norian–early Rhaetian) Fleming Fjord Formation of central East Greenland preserves a diverse fossil fauna, including both body and trace fossils. Trackways of large quadrupedal archosaurs, although already reported in 1994 and mentioned in subsequent publications, are here described and figured in detail for the first time, based on photogrammetric data collected during fieldwork in 2012. Two trackways can be referred to Eosauropus, while a third, bipedal trackway may be referred to Evazoum, both of which have been considered to represent sauropodomorph dinosaur tracks. Both the Evazoum and the Eosauropus trackways are distinctly larger than other trackways referred to the respective ichnogenera. The trackmaker of the best preserved Eosauropus trackway is constrained using a synapomorphy-based approach. The quadrupedal posture, the entaxonic pes structure, and five weight-bearing digits indicate a derived sauropodiform trackmaker. Other features exhibited by the tracks, including the semi-digitigrade pes and the laterally deflected unguals, are commonly considered synapomorphies of more exclusive clades within Sauropoda. The present trackway documents an early acquisition of a eusauropod-like pes anatomy while retaining a well-developed claw on pedal digit IV, which is reduced in eusauropods. Although unequivocal evidence for sauropod dinosaurs is no older than the Early Jurassic, the present trackway provides evidence for a possible Triassic origin of the group.
Marzola, M., Mateus O., Milàn J., & Clemmensen L. B. (2017). European affinities of the Late Triassic biota from Greenland are related to paleolatitude. 15th Annual Meeting of the European Association of Vertebrate Palaeontologists. 91, 61.: Zitteliana Abstract09._eavp_2017_-_marzola_et_al._2017._european_affinities_of_the_late_triassic_biota_from_greenland_are_related_to_paleolatitude.pdf
Marzola, M., Mateus O., Shubin N. H., & Clemmensen L. B. (2017). Cyclotosaurus naraserluki, sp. nov., a new Late Triassic cyclotosaurid (Amphibia, Temnospondyli) from the Fleming Fjord Formation of the Jameson Land Basin (East Greenland). Journal of Vertebrate Paleontology. e1303501., 2017: Taylor & Francis Abstractmarzola_et_al_2017_cyclotosaurus_greenland.pdfWebsite
ABSTRACTCyclotosaurus naraserluki, sp. nov., is a new Late Triassic capitosaurid amphibian from lacustrine deposits in the Fleming Fjord Formation of the Jameson Land Basin in Greenland. It is based on a fairly complete and well-preserved skull associated with two vertebral intercentra. Previously reported as Cyclotosaurus cf. posthumus, C. naraserluki is unique among cyclotosaurs for having the postorbitals embaying the supratemporals posteromedially. The anterior palatal vacuity presents an autapomorphic complete subdivision by a wide medial premaxillary-vomerine bony connection. The parasphenoid projects between the pterygoids and the exoccipitals, preventing a suture between the two, a primitive condition shared with Rhinesuchidae, Eryosuchus, and Kupferzellia. Within Cyclotosaurus, the Greenlandic skull has a distinctive combination of circular choanae (shared with C. ebrachensis, C. posthumus, and C. robustus) and a convex posteromedial margin of the tabulars (also present in C. ebrachensis and C. intermedius). A phylogenetic analysis indicates that C. naraserluki is the sister taxon of the middle Norian C. mordax from southern Germany, with which it shares a pair of premaxillary foramina. Cyclotosaurus is one of the most successful and diverse genera of Late Triassic temnospondyls, with at least eight species reported from middle Carnian to late Norian. Cyclotosaurus naraserluki is the largest amphibian ever reported from Greenland and one of the Late Triassic vertebrates with the highest northern paleolatitude currently known.http://zoobank.org/urn:lsid:zoobank.org:pub:43AAA541-031C-4EE1-B819-4846EBBD1BBBSUPPLEMENTAL DATA?Supplemental materials are available for this article for free at www.tandfonline.com/UJVPCitation for this article: Marzola, M., O. Mateus, N. H. Shubin, and L. B. Clemmensen. 2017. Cyclotosaurus naraserluki, sp. nov., a new Late Triassic cyclotosaurid (Amphibia, Temnospondyli) from the Fleming Fjord Formation of the Jameson Land Basin (East Greenland). Journal of Vertebrate Paleontology. DOI: 10.1080/02724634.2017.1303501.ABSTRACTCyclotosaurus naraserluki, sp. nov., is a new Late Triassic capitosaurid amphibian from lacustrine deposits in the Fleming Fjord Formation of the Jameson Land Basin in Greenland. It is based on a fairly complete and well-preserved skull associated with two vertebral intercentra. Previously reported as Cyclotosaurus cf. posthumus, C. naraserluki is unique among cyclotosaurs for having the postorbitals embaying the supratemporals posteromedially. The anterior palatal vacuity presents an autapomorphic complete subdivision by a wide medial premaxillary-vomerine bony connection. The parasphenoid projects between the pterygoids and the exoccipitals, preventing a suture between the two, a primitive condition shared with Rhinesuchidae, Eryosuchus, and Kupferzellia. Within Cyclotosaurus, the Greenlandic skull has a distinctive combination of circular choanae (shared with C. ebrachensis, C. posthumus, and C. robustus) and a convex posteromedial margin of the tabulars (also present in C. ebrachensis and C. intermedius). A phylogenetic analysis indicates that C. naraserluki is the sister taxon of the middle Norian C. mordax from southern Germany, with which it shares a pair of premaxillary foramina. Cyclotosaurus is one of the most successful and diverse genera of Late Triassic temnospondyls, with at least eight species reported from middle Carnian to late Norian. Cyclotosaurus naraserluki is the largest amphibian ever reported from Greenland and one of the Late Triassic vertebrates with the highest northern paleolatitude currently known.http://zoobank.org/urn:lsid:zoobank.org:pub:43AAA541-031C-4EE1-B819-4846EBBD1BBBSUPPLEMENTAL DATA?Supplemental materials are available for this article for free at www.tandfonline.com/UJVPCitation for this article: Marzola, M., O. Mateus, N. H. Shubin, and L. B. Clemmensen. 2017. Cyclotosaurus naraserluki, sp. nov., a new Late Triassic cyclotosaurid (Amphibia, Temnospondyli) from the Fleming Fjord Formation of the Jameson Land Basin (East Greenland). Journal of Vertebrate Paleontology. DOI: 10.1080/02724634.2017.1303501.
Marzola, M., Mateus O., Milàn J., & Clemmensen L. B. (2017). The 2016 Dinosaur Expedition to the Late Triassic of the Jameson Land Basin, East Greenland. Abstract book of the XV Encuentro de Jóvenes Investigadores en Paleontología/XV Encontro de Jovenes Investigadores em Paleontologia, Pombal, 428 pp.. 249–253. Abstract08._ejip_2017_-_marzola_et_al._2017._the_2016_dinosaur_expedition_to_the_late_triassic_of_the_jameson_land_basin_east_greenland.pdf
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Halcón (en inglés Raptor) es una novela de Gary Jennings publicada en 1992.

Personajes

Thorn: Es el protagonista hermafrodita. Sus experiencias hacen de él un muchacho aguerrido, amigo de reyes y que nunca se cansa de aprender.
Juhiza: Además del amor perdido de Wyrd, es una de las personalidades femeninas que adopta a lo largo del libro. Gracias a ella, consigue vivir un romance con Guninando, un joven de unos de los muchos pueblos que visita.
Veleda: La segunda personalidad femenina que adopta Thorn. Con ella logra ver la ciudad de Vindobona desde el punto de vista de una muchacha plebeya que se aloja en la pensión de la viuda Dengla.
Wyrd: Es un solitario, un cazador y comerciante de pieles. Thorn se lo encuentra en el bosque, tiempo después de que le expulsaran del convento. Desde ese momento, se convirtió en su maestro y amigo a pesar de la gran diferencia de edad entre ambos.

Referencias

Novelas de 1992
Libros en inglés
Novelas ambientadas en la Antigua Roma

redpajama_set_name: RedPajamaWikipedia


State Key Laboratory of Oncology in South China, Sun Yat-sen University Cancer Center, Guangzhou, GD 510060, China. Equal contributors.
this study was to analyze the expression of phosphorylated c-Src (phospho-c-Src) and its clinical significance in human cervical cancer.
to predict recurrence in CSCC. (IJCEP1304011).


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Brisbane's Most Expensive suburbs
Posted: 21 Sep, 2018
Inner city favourite New Farm is officially Brisbane's most expensive suburb, with a median house price of $1.7 million.
New figures from the Domain Group have revealed the top 20 most expensive suburbs, ranked according to median house price — and, with Brisbane's property market now in the ascent as the best performing capital city in Australia, it paints a strong picture of where the city's wealthiest residents are willing to park their cash.
New Farm topped the list with its $1.7 million median house price, followed by neighbouring Teneriffe with a median of $1.65 million.
Acreage hot spot Chandler, in Brisbane's eastern suburbs, took out third place with a median house price of $1.585 million.
Old money favourites Ascot ($1.5 million median price) and Hamilton ($1.421 million median price) were closely followed by the inner eastern riverfront precinct of Bulimba, which had a median of $1,307,500.
Other suburbs that made the top 20 most expensive list included Hawthorne, where Gina Rinehart's $18 million estate fronts the Brisbane River; Clayfield (median price $1.125 million) and Kangaroo Point (median $1.03 million) – home to the most expensive house ever sold in Brisbane: a clifftop mansion worth $18.48 million.
As well as taking out the title of Brisbane's most expensive suburb, New Farm was also recently revealed as Brisbane's best performing suburb for capital growth, with prices having soared nearly 90 per cent in the past five years.
New Farm's remarkable success came as no surprise to local Ray White agent Matt Lancashire, who described it as the "Brisbane suburb for everyone".
"There's just so much in New Farm amenity-wise. New Farm is always the first place to boom and the last to cool off," he said.
"My open numbers at the moment are huge. There's such a strong desire to be in this suburb and I see that only continuing in the future years as Brisbane gets incredible new amenities like Howard Smith Wharves."
In Ascot, long-term resident Jenny Richardson has listed her house at 7 Bale Street for sale but she's not moving far — she's already bought a new property only a couple of streets away.
Ms Richardson has lived in Ascot since 2000 and said she wanted to stay because of the lifestyle it offered.
"Ascot has just got that lovely family feel about it, it really is such a wonderful community," she said.
"It's so quiet it's got that suburban feel but with the proximity to the city and everything else — the Gasworks, Portside and James Street — and that means it's the best of both worlds."
Fourteen kilometres southeast of the CBD, the acreage suburb of Chandler consistently rates as one of Brisbane's most expensive suburbs. Home to enviable land sizes ranging from a hectare to four hectares, it's sought after for its proximity to Manly, as well as its peaceful treed surroundings.
Local Remax agent Deborah Evans explained the "acreage precinct" of Chandler, Gumdale and Belmont was in high demand, although Chandler's higher median house price of $1.585 million was partly due to its status as an acreage-only suburb.
"Every property in Chandler is an acreage property so naturally that will keep the median price high," she said.
"Neighbouring Gumdale actually has more demand but its median is brought down by the non-acreage houses that sit on regular-sized residential blocks of land."
She said demand always outstripped supply in the area and prices were rising — she recently sold a one-hectare acre block on Formosa Road for $1.6 million for land value only.
Ms Richardson's Bale Street home is a four-bedroom, three-bathroom contemporary residence set on one of Ascot's most sought-after streets and — even more importantly — in the Ascot State School catchment.
"I've loved living here; I've got wonderful views out to the hills and the house is functional and quite timeless," she said.
"I think Ascot is one of those suburbs people are always going to want to live in. It's got such a wonderful feel."
Brisbane's top 20 most expensive suburbs:
Source: Domain
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Kurtis replaces Kenny - Rea out.
A last minute change of heart by Honda has denied Jonathan Rea the chance to make his MotoGP debut at this weekend's British Grand Prix - in which Kurtis Roberts will now be Team KR's sole rider.
Rea, who recently won the Suzuka 300km endurance race and took his first BSB win at Mondello Park on Sunday, was due to ride the second Honda-powered KR212V machine alongside Kenny Jr at Donington Park - but the 20-year-old's packed schedule, which includes the Suzuka 8 Hours as well as BSB, has led to a 'change of strategy' by Honda.
"It's unfortunate Jonathan won't be able to compete with us at Donington," said Team Roberts team manager Chuck Aksland. "The whole team was looking forward to working with him. He's had a good run lately and Honda have decided that it is best for him to stick with his current priorities which obviously lie in the British Superbike Championship and Suzuka 8 hour event. Hopefully we can find another opportunity to get him aboard our MotoGP bike in the near future."
As of Sunday night, Rea still expected to ride at Donington - and had planned to visit the Team Roberts headquarters this (Monday) morning - although he also described the hectic schedule that has now, at the very least, delayed his MotoGP debut.
"I've got a very early boat trip to get to the Roberts factory in Banbury on Monday morning, to set up my levers," Rea told Crash.net Radio on Sunday evening at Mondello Park. "Then, to give you a little insight into my schedule, Tuesday I'm doing a chat show; Wednesday and Thursday I'm Superbike testing at Cadwell; Friday, Saturday and Sunday is MotoGP; Sunday night I fly to Japan for two days testing and then I'll arrive at Knockhill on Thursday night at 11pm. The next two weeks are pretty hard, but hopefully I'll be alright..."
Rea's omission isn't the only news at Team Roberts, which will now revert back to a one rider team for the British Grand Prix - having run both Kurtis and Kenny Jr for the last two rounds - but with former world champion Kenny Jr, the team's original rider, standing down until a new chassis is complete.
"It's been a difficult start to the season for all of us. We have found some areas that we hope can improve the chassis side of things, but unfortunately it takes time to design and manufacture the components," explained Aksland. "From Kenny Jr's side, it has been very frustrating, as the fundamentals of the machine seemed fine since we started testing. However, competitive lap times have not been there. He is the same rider that put our bike on the podium twice last year and we thought heading into this season we could do better. For whatever reason we have not.
"There have been a lot of changes, engine, tyre rules, etc. It took some time for us to get the 990 right and we are confident we can bring the 800 around as well. We just need some more time. All we can focus on is what we can control and that is to make the chassis better. Kenny Jr has ridden the current spec enough and we decided the best time for him to come back would be when there are new parts available to get the KR212V closer to the front. This next step is targeted for the USGP at Laguna Seca.
"Kurtis has done a good job for us during the last two races and he is improving each time he gets on the bike. Unlike the previous races, he now will have two machines available which will help him gain additional track time," he concluded.
Team Roberts has scored just four points from the first seven races of the 2007 season.
Preview - British Grand Prix.
Donington D-day for hopeful Hayden.


This superb purple variety is finer tasting than green varieties. It's as ornamental as it is edible, and is ideal for a variety of situations, and is loved by bees, butterflies and other pollinating insects. Harvest May-June (year 2).
HEALTH BENEFITS: A good source of protein and fibre.
CULINARY TIPS: Delicious pickled small and marinated in good oil, with lemon juice and vinegar, seasoned with chilli or mustard.
Great in salads with seasonal vegetables such as aubergine, with pecorino or even pizza.