text:
\section{Introduction}
Computers play a vital role in modern society. Since its inception in the middle of the previous century the power of digital computers has been growing exponentially with time. How long can this growth be sustained? Great interest in recent years in quantum computing is partially fuelled by the discovery that quantum computers could perform certain tasks faster than any classical computer. An example is the famous Shor factoring algorithm~\cite{Shor:97} which is polynomial, whereas the best known classical algorithm is super-polynomial. According to computational complexity, problems can be divided into two large groups. Those for which the time to find a solution grows polynomially with the size of the problem belong to the so-called P class (polynomial) and those that require polynomial time to verify the solution belong to NP (non-deterministic polynomial). Especially important subset of NP problems is called NPC (NP-complete). They have the property that any NP problem can be transformed to NPC problem in a polynomial time. Therefore, finding a polynomial algorithm for a single NPC problem would immediately provide a polynomial algorithm for all NP problems. Currently all known algorithms need exponential time to solve NPC problems. In a vague way it can be said that NPC are the hardest of NP problems.
\par
Recently a novel way of doing quantum computation via adiabatic evolution has been suggested~\cite{Farhi:00,Farhi:01}. The idea of using adiabatic evolution to do quantum computation is very simple and elegant. One starts with the system in the ground state of the initial Hamiltonian $H(0)$. Then the Hamiltonian is adiabatically slowly changed from $H(0)$ to the final $H(1)$, whose ground state encodes the solution to the problem we want to solve. The adiabatic theorem then ensures that if the changing of the Hamiltonian is sufficiently slow, we end up in the ground state of $H(1)$ at the end, thereby obtaining the solution to our problem. Numerical simulation of the adiabatic algorithm for a NPC problem called exact cover~\cite{Farhi:01} indicated that quantum adiabatic algorithm might need running time that grows only quadratically with the size of the problem. Subsequently, there have been many studies of quantum adiabatic algorithms, mostly numerical~\cite{Smelyansky:01,Childs:02,Hogg:03,Mitchell:04} but also some rigorous results are known~\cite{vanDam:01,Roland:02,Reichardt:04,Roland:04}. It has also been shown recently that adiabatic computation is polynomially equivalent to standard quantum computation~\cite{aharonov:04}. Adiabatic algorithm has also been experimentally realized on a NMR quantum computer~\cite{Steffen:03}. While numerics for number partitioning problem showed exponential scaling~\cite{Smelyansky:01} the scaling of running time in other NPC problems is still unclear. For instance, for a paradigmatic example of a NPC problem called 3-SAT  (3-satisfiability), polynomial scaling $\sim n^3$ of median cost has been found~\cite{Hogg:03}. Needless to say, the implications of having a polynomial quantum adiabatic algorithm for NPC problem would be enormous. But we have to keep in mind that the computational complexity is defined in terms of the worst case performance.
\par
 Although the studies so far focused on presumably hard instances of 3-SAT problems we will show that there exists a class of even harder 3-SAT instances not known before. We will present a clear numerical evidence for an exponential scaling of running time of quantum adiabatic algorithm for these 3-SAT instances. This finding could also be relevant for classical algorithms development, where hard instances are used in algorithm design and testing.
\par
The outline of the paper is as follows. In Section~\ref{sec:3sat} we introduce a problem studied, namely a random 3-SAT. In Section~\ref{sec:qaa} quantum adiabatic algorithm is defined and the degeneracies of the initial and final Hamiltonian are explored. In Section~\ref{sec:lz} we study the probability to successfully obtain correct result. Then in Section~\ref{sec:spec} the energy spectrum during adiabatic evolution is studied and finally in Section~\ref{sec:gap} the scaling of the energy gap and running time is presented.

\section{Random 3-SAT}
\label{sec:3sat}
In the present paper we will consider 3-SAT problem. It is a paradigmatic example of a NPC problem. 3-SAT formula is a logical statement involving $n$ boolean variables $b_i$. It consists of $m$ clauses $C_i$ in conjunction (logical AND $=\land$)
\begin{equation}
C_1 \land C_2 \land \cdots \land C_m,
\label{eq:3sat}
\end{equation}
and each clause $C_i$ is a disjunction (logical OR $=\lor$) of 3 literals, where a literal is a variable $b_i$ or its negation $\lnot b_i$ (logical NOT $=\lnot$). To illustrate, an instance of a 3-SAT formula with $n=4$ variables and $m=2$ clauses is
\begin{equation}
(b_2 \lor \lnot b_3 \lor b_4) \land (b_1 \lor b_2 \lor \lnot b_3).
\label{eq:example}
\end{equation}
The problem is to decide whether a given 3-SAT formula is satisfiable, i.e. whether there exists a prescription of variables $b_i$ such that 3-SAT formula is true. Such prescription is called a solution, the number of which will be denoted by $r$. The formula given as an example~(\ref{eq:example}) has many solutions, one being for instance $(b_4b_3b_2b_1)=1101$, where $1$ and $0$ denote true and false, respectively.
\par
Formula that is a conjunction of disjunctions is said to be in a conjunctive normal form (CNF). Any logical statement consisting of $\land$, $\lor$ and $\lnot$ operators can be rewritten in a CNF form. While 2-SAT problem (CNF formula having at most $2$ literals in each clause) belongs to P, 3-SAT is in NPC. Besides being paradigmatic example of a NPC problem it has wide range of applicability in e.g. scheduling problems, hardware verification etc... It is also directly related to deductive reasoning important in artificial intelligence. If we are given a set $\Sigma$ of facts (statements) $C_i$, $\Sigma=\cup C_i$, a new statement $C_{\rm new}$ can be deduced iff a union $\Sigma \cup \{\lnot C_{\rm new} \}$ is not satisfiable (we arrive at contradiction assuming $\lnot C_{\rm new}$), i.e. we have to solve a SAT problem.
\par
As the computational complexity is defined in terms of worst case performance, hard instances of 3-SAT have been especially intensely studied. Frequently they are obtained by randomly drawing clauses, so-called random 3-SAT. A random 3-SAT consists of $m$ different random clauses, where each clause is obtained by picking $3$ different variables $b_i$ and negating each with probability $1/2$. This is the procedure we used to obtain random instances of 3-SAT. As we were mainly interested in formulae with only one solution, we solved each instance and rejected those not having exactly one solution. In the literature on the other hand they usually study random 3-SAT formulae with an arbitrary number of solutions. In such case a phase-transition is found~\cite{Kirkpatrick:94} with the hardest instances occurring around the phase-transition point of $m/n \approx 4.2$. As we will see, random 3-SAT instances with exactly one solution and small $m/n$ will turn out to be harder than those at the phase-transition (and having arbitrary number of solutions). Correct choice of hard instances of 3-SAT is therefore absolutely essential in order to see clear exponential scaling of running time. For more information about a phase-transition in random 3-SAT see also papers in the~\cite{volumeAI} and also~\cite{monasson:99,cocco:02}. For classical SAT problem solving see e.g. collection~\cite{SAT}.

\section{Hamiltonian for adiabatic algorithm}
\label{sec:qaa}
 The construction of Hamiltonian for the 3-SAT problem is straightforward. For each variable we have to have available two states, i.e. one qubit, giving the dimension of the total Hilbert space $N=2^n$. The initial $H(0)$ is problem independent and we choose it to be a sum of one-qubit Hamiltonians $H_i$ acting on $i$-th qubit,
\begin{equation}
H(0)=\frac{1}{2}\sum_{i=1}^{n}{H_i\otimes \mathbbm{1}},\qquad H_i=\begin{pmatrix}
1 & -1 \cr
-1 & 1
\end{pmatrix}.
\label{eq:H0}
\end{equation}
The ground state $\ket{E_0(0)}$ of the initial Hamiltonian has energy $E_0=0$ and is a uniform superposition of all computational states,
\begin{equation}
\ket{E_0(0)}=\frac{1}{\sqrt{N}}\sum_{b_1,\ldots,b_n=0,1}{\ket{b_n\ldots b_1}},
\label{eq:psi0}
\end{equation}
where a label of state $\ket{b_{n}b_{n-1}\ldots b_1}=\ket{\ve{b}}$ denotes a binary expansion of the state, i.e. the value of each qubit. In fact the whole energy spectrum of the initial Hamiltonian is easily calculated. It consists of integer energies, $E_i(0)=i$, with the degeneracy of level $E_i(0)$ being equal to ${n \choose i}$. The final Hamiltonian $H(1)$ is problem dependent. We use a diagonal Hamiltonian in the computational basis, with the energy of state $\ket{\ve{b}}$ equal to the number of clauses it violates. As all states violating a given clause have the same values of $3$ variables occurring in that clause, each clause can be represented by a single 3-qubit gate. For our example (\ref{eq:example}) we would have two terms,
\begin{equation}
H(1)=\ket{010}\bra{010}_{432}\otimes \mathbbm{1} +\ket{100}\bra{100}_{321}\otimes \mathbbm{1},
\label{eq:H1example}
\end{equation}
where subscripts denote on which qubits the operator acts. Therefore, a state $\ket{\ve{b}}$ satisfying all clauses (i.e. a solution) would have energy $0$, state violating a single clause has energy $1$ and so on. Energy spectrum of $H(1)$ is therefore composed of integer values between $E_0(1)=0$ for the ground state and $E_m(1)=m$ for a state that would violate all clauses. Of course, the degeneracy $r$ of the state $E_0(1)$ of $H(1)$, i.e. the number of solutions, depends on the particular instance in question. In the thermodynamic limit, $n \to \infty$, 3-SAT formulae with $m/n$ below a ``phase transition'' point at $m/n \approx 4.2$ have many solutions, whereas formulae with $m/n>4.2$ have no solution~\cite{Kirkpatrick:94}. Whereas the spectrum of $H(0)$ is fixed, the spectrum of $H(1)$ is instance dependent. An example of spectrum of $H(0)$ and $H(1)$ for one particular 3-SAT instance having $n=14$ variables and $m=42$ clauses is shown if Fig.~\ref{fig:deg14}. From the spectrum of $H(1)$ we see for instance, that there are no states violating more than $12$ clauses and the most abundant are $3720$ states violating $5$ clauses (with energy $E=5$). There is only one state with energy $E=0$, thus there is only one solution. Throughout the work we will focus only on 3-SAT problems having exactly one solution, $r=1$. Later we will argue that such problems are expected to be the hardest.
\begin{figure}[!h]
\centerline{\includegraphics[width=3.3in]{deg14.eps}}
\caption{(Color online)~Degeneracy of the initial (left) and final Hamiltonian (right) for one 3-SAT instance with $n=14$, $m/n=3$ and exactly one solution $r=1$. Lower part of spectrum for all intermediate times $s$ is shown in Fig.~\ref{fig:test14}.}
\label{fig:deg14}
\end{figure}
\par
The interpolating Hamiltonian between $H(0)$ and $H(1)$ is chosen according to the following prescription,
\begin{equation}
H(s)=(1-s) H(0)+ s H(1),\qquad s=\frac{t}{T},
\label{eq:Hs}
\end{equation}
where $s=t/T$ is a dimensionless time and $T$ is the total running time of the adiabatic algorithm. The evolution of an arbitrary state $\ket{\psi}$ is given by a time dependent Schr\" odinger equation
\begin{equation}
\frac{1}{(dt/ds)}{\rm i} \hbar \frac{d}{ds} \ket{\psi}=H(s) \ket{\psi},
\label{eq:schrodinger}
\end{equation}
where for our choice of constant speed along the interpolating path $H(s)$ (\ref{eq:Hs}), $(dt/ds)$ is constant and equal to $T$. We set $\hbar=1$ throughout the paper.
\par
The interpolating ``path'' between $H(0)$ and $H(1)$ is quite arbitrary as well as the initial Hamiltonian $H(0)$, while the final Hamiltonian is determined by the problem in question. Instead of having uniform speed of interpolation we could vary it according to the energy gap. Such refinements are not the subject of the present paper. Trough adiabatic quantum computation hard question of computational complexity is translated into (perhaps?) easier question of the scaling of the energy gap. At least there are plenty of tools available for studying energy gaps.

\section{Failure probability}
\label{sec:lz}
In studying quantum adiabatic algorithms one usually numerically looks at the probability of successfully finding the solution for different running times $T$~\cite{Farhi:01,Smelyansky:01,Childs:02,Hogg:03}. The adiabaticity condition, guaranteeing adiabatic evolution, is usually stated as
\begin{equation}
T \gg \hbar \int_0^1{\frac{||dH/ds||}{\gamma(s)^2}ds},
\label{eq:adiabatic}
\end{equation}
where $\gamma(s)=E_1(s)-E_0(s)$ is the energy gap between the ground state and the first excited state. Adiabatic condition can also be stated locally, saying that the local inverse speed has to be larger than
\begin{equation}
\frac{dt}{ds} \gg \hbar \frac{||dH/ds||}{\gamma(s)^2}.
\end{equation}
\par
The above two adiabatic conditions~(\ref{eq:adiabatic}) give us the necessary condition for the adiabatic evolution. What would be desirable to know is also the probability of non-adiabatic transitions. This would then give us a direct way to calculate necessary running time for the desired probability to stay in the ground state at the end. For $2$ and $3$ level systems there is an exact expression. In the limit of slow evolution it is the famous Landau-Zener formula~\cite{Zener:32,Landau:58}, giving the probability of a transition in a $2$ level system, where the two eigenenergies are $E_{0,1}(s)$,
\begin{eqnarray}
P_{\uparrow}&=&\exp{\left( -\frac{T}{\tau_{\rm LZ}} \right)},\qquad \tau_{\rm LZ}=\frac{2A\hbar}{\pi \Delta^2},\nonumber \\
E_{0,1}(s)&=&\pm \frac{1}{2} \sqrt{\Delta^2+(A s)^2},
\label{eq:LZ}
\end{eqnarray}
here $\Delta$ is a minimum gap $\gamma(s)$, $T$ is a constant parameter connecting $s=t/T$ and $t$ runs from $-\infty$ to $\infty$. For a discussion of transitions in multilevel systems see~\cite{Wilkinson:00}. Landau-Zener formula has been used before~\cite{Mitchell:04} to describe adiabatic algorithm under the assumption that random matrix statistics applies to avoided crossings. Two level transition probability is also used in the adiabatic algorithm for Grover search~\cite{Roland:02}.
\par
\begin{figure}[!h]
\centerline{\includegraphics[width=3.3in]{test14Both.eps}}
\caption{(Color online)~Lower part of spectrum (lowest 18 levels out of total $N=16384$) for one instance of 3-SAT with $n=14$, $m/n=3$, the same instance as in Fig.~\ref{fig:deg14}. We can see avoided crossing at $s \approx 0.7$. Dashed line is fitted avoided crossing, i.e. line $E_1(s)-\sqrt{\Delta^2+(A s)^2}$, whose parameters are obtained by fitting parabola at the crossing.}
\label{fig:test14}
\end{figure}
Let us first have a look at the lower part of a typical spectrum of $H(s)$ to see what is the nature of transitions. To find the lowest eigenvalues we used implicitly restarted Lanczos method~\cite{arpack}, suitable for sparse eigenvalue problems. By this we could find lowest few eigenvalues for $n$ upto $20$, i.e. Hilbert space sizes $N\sim 10^6$. One particular example for $n=14$ and $m=42$ is shown in Fig.~\ref{fig:test14}. Only lowest $18$ levels out of total $N=16384$ are shown. We can see that there is {\em only one avoided crossing}, the same was the case in all other cases we have checked. The reason to have only one avoided crossing is unclear to us. It might be connected with the fact that we have a finite gap at the beginning and at the end of the algorithm. Similar behaviour has been found by other researchers~\cite{Hogg:03}. Now provided we have only one close encounter of two lowest levels, we can use degenerate perturbation theory, i.e. consider only two closest levels. Transition probability is then given simply by the Landau-Zener formula (\ref{eq:LZ}). We first checked how well the Landau-Zener formula describes the transition probability for a real 3-SAT case, such as is for example the one in Fig.~\ref{fig:test14}.
\begin{figure}[!h]
\centerline{\includegraphics[height=3.3in,angle=-90]{LZ.ps}}
\caption{(Color online)~Comparison of success probability $p({\rm ground})$ obtained with direct numerical simulation (pluses) with $P_{\uparrow}$ obtained from Landau-Zener formula (\ref{eq:LZ}). In the inset the same data is shown in a semi-log scale for longer times. All is for the same 3-SAT instance shown in Fig.~\ref{fig:test14}.}
\label{fig:LZ}
\end{figure}
To obtain probability for a transition from the ground state using Landau-Zener formula (\ref{eq:LZ}) we fitted parabola around the avoided crossing to determine two parameters, the gap $\Delta$ and the asymptotic slope $A$, needed in the Landau-Zener formula. For a case in Fig.~\ref{fig:test14} for instance, we obtain $\Delta=0.0318$ and $A=2.67$ (dashed line in Fig.~\ref{fig:test14}). Then we compared $P_{\uparrow}$ (\ref{eq:LZ}) with the result of a direct numerical simulation of a time dependent Schr\" odinger equation (\ref{eq:schrodinger}). We discretized time into small steps $dt$ (typically $dt \sim 0.1$) and then calculated one-step propagator $U(dt)=\exp{(-{\rm i} H(t) dt/\hbar)}$ by expansion in a power series. The precision has been controlled throughout the calculation. At the end of the simulation, at time $t=T$, we obtain a final state $\ket{\psi(T)}$ and then calculate the overlap with the ground state, giving us the numerical probability $p({\rm ground})$ to remain in the ground state. In Fig.~\ref{fig:LZ} we compare this numerical value with the Landau-Zener formula. One can see a very good agreement already in a regime of small $T$, where the probability to stay in the ground state is small. Therefore, the Landau-Zener formula perfectly describes the probability to stay in the ground state in all practically relevant regime (i.e. for high $p({\rm ground})$). From now on we will focus on the scaling of $\tau_{\rm LZ}$ with the size $n$ of a problem.

\section{Spectrum}
\label{sec:spec}
There are two parameters determining $\tau_{\rm LZ}$. The asymptotic slope $A$ at the avoided crossing has value of around $2$ (ground state energy changes from $0$ to $\approx 1$ at the avoided crossing and back to $0$ at $s=1$) and does not vary appreciably with $n$. The main dependence of $\tau_{\rm LZ}$ on $n$ will be therefore given by the scaling of the minimal gap $\Delta$. Heuristically one could argue that the gap $\Delta$ will be smaller when more excited levels are crowded into a region of energies between $E\approx 1$ and $E\approx 2$, where the avoided crossing takes place. The number of such levels is connected with the degeneracies of the first excited levels at the beginning and at the end of the algorithm. The degeneracy of the first excited level of $H(0)$ is fixed and equal to $n$, whereas the degeneracy of the first excited level at the end varies from instance to instance. We therefore first wanted to identify instances that have the highest number of first excited states at the end $s=1$ (remember that we always look at 3-SAT problems having exactly one solution, $r=1$). We calculated average degeneracies (averaged over $10000$ instances of random 3-SAT with $r=1$ solution) of the final hamiltonian $H(1)$ for $n=10$ and different $m$. The results are in Fig.~\ref{fig:spekter_n10}.
\begin{figure}[!h]
\centerline{\includegraphics[height=3.3in,angle=-90]{spekter_n10.ps}}
\caption{(Color online)~Degeneracies of the spectrum of final hamiltonian $H(1)$ for different ratios $m/n$. Degeneracy of the first excited state increases with decreasing $m/n$. All points are an average over $10000$ random 3-SAT instances with exactly one solution, i.e. the degeneracy of the ground state with $E=0$ is $r=1$.}
\label{fig:spekter_n10}
\end{figure}
We can see that the peak of the degeneracy moves to smaller energies with decreasing $m/n$. More importantly, the degeneracy of the first excited state (the height of the second bar) increases with decreasing $m/n$ as well. Therefore, to have as high degeneracy of the first excited state as possible, we have to have small ratio $m/n$. Note that nothing particular happens at the point of ``phase-transition'' at $m/n \approx 4-5$. From now on we will choose $m/n=3$, as such 3-SAT instances have high degeneracy of the first excited state. If this degeneracy increases exponentially with $n$ we have a fair chance that the gap $\Delta$ will also decrease exponentially. We therefore checked the scaling of the degeneracy of the first excited state of $H(1)$ with $n$ at a constant ratio $m/n=3$.
\begin{figure}[!h]
\centerline{\includegraphics[height=3.3in,angle=-90]{num_excit.ps}}
\caption{(Color online)~Degeneracy of the first excited state of the final $H(1)$ for different $n$ and $m/n$. Exponential growth can be seen for $m/n=3$, while for $m/n=5$ and $4.5$ (around the phase transition) the degeneracy is much smaller and the functional form of the growth can not be established.}
\label{fig:excit}
\end{figure}
Results are shown in Fig.~\ref{fig:excit}. We can see clear exponential growth for $m/n=3$ with the fitted exponential $\approx 8.2 e^{0.21 n}$. For larger $m/n$, i.e. around the phase transition, the growth is much slower and an exponential dependence can not be firmly established.
\par
Random 3-SAT instances with $m/n=3$ and exactly one solution are therefore our candidates for hard problems. For such instances the number of states violating only one clause (i.e. the degeneracy of the first excited state of $H(1)$) grows exponentially with $n$ and so the energy gap is expected to decrease exponentially and consequently running time to increase exponentially. What is the difficulty of such 3-SAT instances for classical algorithms? One could expect that classical algorithms will also have a hard time finding the solution as it is ``surrounded'' by exponentially many states that violate only one clause. To illustrate this we tested classical GSAT algorithm with random walk extension~\cite{Selman:92}. GSAT belongs to a group of incomplete algorithms for 3-SAT meaning that there is no a priori terminating condition. All such algorithms are variants of a local search. Concretely, in GSAT algorithm one variable is negated (flipped) at each step. The variable to negate is chosen so that the resulting state satisfies a maximum number of clauses. Note that GSAT algorithm can not prove unsatisfiability and is therefore suitable only for solvable instances.
\begin{figure}[!h]
\centerline{\includegraphics[height=3.3in,angle=-90]{gsat20.ps}}
\caption{(Color online)~Running time (number of flips) for classical GSAT algorithm solving 3-SAT instances with exactly one solution (top points) and instances with at least one solution (bottom points). All is for $n=20$ and an average over $1000$ random 3-SAT instances is performed. Error bars show standard deviation at each point.}
\label{fig:gsat20}
\end{figure}
In Fig.~\ref{fig:gsat20} we show the average number of flips needed to find a solution for $n=20$ and different number of clauses $m$. Data shown is an average over $1000$ instances having exactly one solution, $r=1$, and for comparison also for problems with at least one solution, $r\ge 1$. We can see, that for problems with at least one solution we have a characteristic phase-transition dependence~\cite{Kirkpatrick:94,volumeAI} with the hardest instances at around $m/n \approx 4.2$. On the other hand, for $r=1$ the difficulty of problems grows with decreasing $m/n$. We see that such problems are actually {\em harder} than the problems at the phase transition. The same behaviour is expected also in other local search algorithms. On the other hand there are also complete methods for solving satisfiability problems. The most widely used is the so-called DPLL~\cite{dpll} algorithm and its derivations. It searches trough a solution tree and can both prove unsatisfiability or find a solution in a finite (exponential) number of steps. Preliminary results show~\cite{unpublished} that random 3-SAT instances with one solution are harder than instances at the phase-transition also for such complete algorithms.
\par
\begin{figure}[!h]
\centerline{\includegraphics[height=3.3in,angle=-90]{prob_ground.ps}}
\caption{(Color online)~Frequency of 3-SAT formulas, i.e. the inverse probability to get such a formula, with exactly $r=1$ solution among random instances at $m/n=3$. Each point is an average over $100$ instances. Line is an exponential fit.}
\label{fig:prob_ground}
\end{figure}
Why have been such instances with one solution and small $m/n$ overlooked so far in a vast literature on phase-transition in random 3-SAT~\cite{Kirkpatrick:94,volumeAI,monasson:99,cocco:02}? The answer is very simple. They are exponentially rare among random 3-SAT instances (for small $m/n$ most have many solutions) and so they do not show up in the average behaviour that was usually studied. Nevertheless, as the computational complexity is defined in terms of a worst case performance, such problems are important. In Fig.~\ref{fig:prob_ground} we show how frequently one gets a 3-SAT problem with exactly one solution among randomly drawn 3-SAT problems at small $m/n=3$. The best fitting line in the figure is exponential $\approx 2.3 e^{0.4 n}$. The fact that 3-SAT with $r=1$ and small $m/n$ are exponentially rare makes their generation very time consuming as we have to solve very many instances before we arrive at the ``right one'' with exactly one solution.

\section{Scaling of running time}
\label{sec:gap}
Finally, after identifying 3-SAT instances that are expected to be hard for quantum adiabatic algorithm due to exponentially many states residing just above the ground state and after seeing that such instances are hard also for classical algorithms, we turn to the numerical calculation of the scaling of running time of quantum adiabatic algorithm for 3-SAT problems with $r=1$ and $m/n=3$. For each $n$ we generate $100$ such instances, find the position of the minimum of the energy gap and from the curvature at the gap determine the necessary running time according to the Landau-Zener formula (\ref{eq:LZ}).
\begin{figure}[!h]
\centerline{\includegraphics[height=3.3in,angle=-90]{gapnm3.ps}}
\caption{(Color online)~Dependence of the energy gap $\Delta$ on $n$ for 3-SAT with $m/n=3$ and $r=1$ solution. Top points are for the average gap and bottom for minimal gap (average over 100 instances). Two lines are exponential fits. For $n=16$ and $n=18$ we show the results of two independent runs to give the impression about fluctuations.}
\label{fig:gapnm3}
\end{figure}
In Fig.~\ref{fig:gapnm3} we show the dependence of the minimal gap $\Delta$ on the size $n$. Exponential fit gives dependence $\approx 0.9 e^{-0.2n}$ for the average $\Delta$ and $\approx 2 e^{-0.52 n}$ for a minimal $\Delta$ (out of $100$ instances). Clear exponential decrease can be seen over several orders of magnitude. Similar exponential behaviour can be seen also in the dependence of the running time $\tau_{\rm LZ}$ in Fig.~\ref{fig:timenm3}.
\begin{figure}[!h]
\centerline{\includegraphics[height=3.3in,angle=-90]{timenm3.ps}}
\caption{(Color online)~Dependence of running time (according to Landau-Zener formula) on $n$ for 3-SAT with $m/n=3$ and $r=1$ solution (same data as for Fig.~\ref{fig:gapnm3}). Top points are for a maximal gap, middle for the average and bottom for the median $\tau_{\rm LZ}$ (average over 100 instances). Exponential growth over $7$ orders of magnitude can be seen.}
\label{fig:timenm3}
\end{figure}
Exponential fits give scaling $\approx 1.4 e^{0.9n}$ for a maximal $\tau_{\rm LZ}$, $\approx 0.05 e^{0.9 n}$ for the average $\tau_{\rm LZ}$ and $\approx 0.2 e^{0.6 n}$ for a median time. We have therefore numerically established {\em exponential} growth of running time of the adiabatic quantum algorithm for 3-SAT with the problem size.
\par
We should mention that if one looks at the scaling of e.g. energy gap for problems with one solution at larger $m/n$, say around the phase-transition, the functional dependence can not be firmly established. It looks like a power-law $\sim n^{-0.8}$, but the exponential dependence with a very small exponent (e.g. $\sim e^{-0.05 n}$) cannot be excluded. This is in agreement with a similar behaviour of degeneracies in Fig.~\ref{fig:excit}. It might be that the asymptotic regime of exponential dependence is not yet reached for small $n\le20$ amenable to numerical study. This is probably the reason why in previous studies no clear exponential time dependence could be identified.

\section{Conclusion}
We have numerically studied quantum adiabatic algorithm for 3-SAT problem. First, we identified a class of difficult random 3-SAT instances not known previously. These are instances with exactly one solution and small number of clauses (e.g. $m/n=3$). Such 3-SAT instances are exponentially rare, which is the reason they have not been observed so far. Nevertheless, as the computational complexity is concerned with the worst case performance, they determine the complexity of the algorithm. They have exponentially many assignments of variables that violate only one clause and thereby exponentially many states just above the ground state of the final Hamiltonian. Therefore, the energy gap for such instances decreases exponentially with the size of the problem and as a consequence, running time grows exponentially. This provides a firm numerical evidence that the usual quantum adiabatic algorithm for 3-SAT has exponential complexity.
\par
In addition, such class of 3-SAT instances is expected to be difficult also for classical algorithms. In local search algorithms exponentially many ``fake'' solutions, violating only one clause, will effectively ``shadow out'' the real solution. In complete methods, like DPLL, a wrong assignment of a variable early in the search tree will cause large backtrackings. Becouse problems with small $m/n$ are under constrained, such wrong assignment will be very frequent which will make the search tree very large. As the performance of 3-SAT solving algorithms is important in many areas, further study of the behaviour of classical algorithms on this new class of 3-SAT problems in necessary.
\par
I would like to thank Toma\v z Prosen and Gregor Veble for discussions.
Financial support by the grant P1-044 of the Ministry of Education,
Science and Sports of Slovenia, and in part by the ARO grant (USA) DAAD 19-02-1-0086, as well as the Alexander von Humboldt Foundation are gratefully acknowledged.

redpajama_set_name: RedPajamaArXiv


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text:
William "Will" Raymond Smith III (* 4. Juli 1981 in Queens, New York City, New York; † 9. April 2016 in New Orleans, Louisiana) war ein US-amerikanischer American-Football-Spieler. Er spielte zehn Saisons auf der Position des Defensive End für die New Orleans Saints in der National Football League (NFL).

NFL

New Orleans Saints
Smith wurde im NFL Draft 2004 in der ersten Runde von den New Orleans Saints ausgewählt. 2006 wurde er in den Pro Bowl berufen. 2008 verlängerten die Saints seinen Vertrag um sieben Jahre. 2009 gewann er mit den Saints den Super Bowl XLIV. 2012 war er in den Bountygate-Skandal verwickelt, wofür er eine Vier-Spiele-Sperre erhielt, die jedoch aufgehoben wurde. In einem Preseason-Spiel der Saison 2013 zog er sich einen Kreuzbandriss zu, wodurch die Saison für ihn frühzeitig endete. Nach der Saison wurde er von den Saints entlassen.

Anfang Oktober 2019 gaben die Saints bekannt, Smith posthum in ihren Ring of Honor aufzunehmen.

New England Patriots
Am 5. Mai 2014 verpflichteten ihn die New England Patriots, entließen ihn jedoch am 24. August 2014 wieder.

Tod
Am 9. April 2016 war Smith in einen Autounfall verwickelt. Nach dem Unfall zog der Unfallgegner eine Waffe, erschoss Smith und verletzte dessen Frau. Smith starb im Alter von 34 Jahren noch an der Unfallstelle. Er hinterließ neben seiner Frau auch drei Kinder. Der Täter wurde von der Polizei festgenommen.

Weblinks

Einzelnachweise

American-Football-Spieler (Ohio State Buckeyes)
American-Football-Spieler (New Orleans Saints)
Kriminalfall 2016
Kriminalfall in den Vereinigten Staaten
US-Amerikaner
Geboren 1981
Gestorben 2016
Mann

redpajama_set_name: RedPajamaWikipedia


text:
The American Glavcot Rabbit Society
Join UsChevron
Officers and Bylaws
History and FAQChevron
Rarer Than Gold: The Glavcot Journey
" Becoming the Ambassador of the Fancy "
By: Tyler Tedford
Throughout history the Glavcot breed has been both tumultuous and obscure. Full of lore and mystery, this amazing breed has somehow gone from booming across the world, to extinction and back again.
Originally one variety, the Silver, was developed in the early 20th century by O. Millsum, and named by a Mr. Wesley T. Page. These silver rabbits would gain much popularity throughout the teens and twenties mostly as a fur animal. No one seems to know why the name Glavcot was chosen, adding a cryptic and almost mythical uniqueness to an already rare and remarkable breed.
The Late Meg Brown
Though never gaining recognition by the British Rabbit Council(BRC)*, the Silver Glavcot was a Dilute Steel showing no belly color rather than the traditional white belly color of an agouti. The Silver variety was imported to the United States in 1925 by Marcellus A. Meek of southern California where it gained a huge popularity with fur farms as evidenced by the author's vast collection of advertisements for them from the time period.
In addition to the popularity of the Silver variety, Glavcot fanciers would eventually add a Golden Variety to be accepted by the BRC in 1934. The breed continued for some time, until eventually falling out of favor and declining so much in popularity that both varieties became extinct in the UK and USA by 1960.
Then extinct, the endeavor of recreating them was taken on by a Mr. Joe Irons. To recreate the breed, Irons used three breeds: the brown Beveren, the Havana, and the modern day Siberian. He would go on to present the breed to the BRC at the Bradford Championship Show in Doncaster, England in January of 1976.
Original AGRS Logo Circa 2018
Silver Glavcot Wippell Print
The Golden Glavcot, as it would be called, was not popular with many fanciers but did catch the eye of a lady important to the Glavcot breed; Meg Brown of Scotland. Irons taught Meg how to carry on with the breed. It is said that Meg later crossed in European Wild Rabbits to add the agouti pattern. She carried the breed until 2002 when she was forced to give up her animals due to her poor health.
Henceforth, the breed has been thriving through a very small band of dedicated fanciers, most notably Steve Tolton. Steve has worked tirelessly to keep the breed alive by breeding and promoting the Golden Glavcot across the world.
Through Steve, the breed once again graced American shores in 2019. Through the collaboration of Steve Tolten, Samantha Sessamen, and Tyler Tedford, and with the help of Jeff Hardin, four Golden Glavcots were imported to the United States on January 23rd, 2019. These two pairs would become the foundation of the Glavcot breed's revival in the USA.
The importation was supported by the American Glavcot Rabbit Society(AGRS), which was founded by Tyler and Samantha to promote the breed prior to and after their arrival. The AGRS today accepts the breed in nine varieties. These varieties are as follows; Black, Blue, Chocolate, Lilac, White, Chocolate Chestnut, Chestnut, Opal and Lynx.
Currently the new Glavcot is thriving in the barns of over a dozen devoted fanciers here in the USA. This breed has had a tumultuous history, but today is rising from obscurity through the heart and perseverance of the fanciers dedicated to its survival.
1920's and 30's Glavcot Advertisements - USA
© 2021 American Glavcot Rabbit Society

redpajama_set_name: RedPajamaCommonCrawl


In 2012 Colornet Press was voted number one in Southern California by winning an unprecedented two Benny Awards along with three awards of Recognition. Colornet achieved the same number one position in 2011 by winning another 2 Benny awards.
WE HAVE BEEN RECOGNIZED AS THE TOP PRINTER TWO YEARS IN A ROW!
The Benny award is the highest honor in The Printing Industries of America annual competition which is the most prestigious worldwide drawing an average of 3,000 entries each year. Colornet Press has also been recognized with Benny awards in the years of 2004, 2008, 2010.


After studying art during his young adult life, film and stage actor Michael Mercurio moved from Brooklyn, New York, to Chicago to study acting. After completing an acting conservatory, he was offered a scholarship with the Chicago Actor's Studio, under the tutelage of Edward Dennis Fogell.
After studying art during his young adult life, film and stage actor Michael Mercurio moved from Brooklyn, New York, to Chicago to study acting. After completing an acting conservatory, he was offered a scholarship with the Chicago Actor's Studio, under the tutelage of Edward Dennis Fogell. Upon moving to Los Angeles, he landed a number of supporting roles in various independent films. In addition to film, Mercurio is an accomplished artist and a former member with The Actors' Gang theatre company in Los Angeles, CA.


Its high-speed linear motor powers effortlessly through thick beards with less pulling and irritation while shaving. Wet/dry technology gives the convenience of dry operation or use with foam or gel for a pampering silky-smooth shave. Round-shaped outer foils follow the contours of your face for efficient coverage and maximum comfort.


text:
##########################################################################
#
# Linux on Hyper-V and Azure Test Code, ver. 1.0.0
# Copyright (c) Microsoft Corporation
#
# All rights reserved.
# Licensed under the Apache License, Version 2.0 (the ""License"");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#     http://www.apache.org/licenses/LICENSE-2.0
#
# THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS
# OF ANY KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION
# ANY IMPLIED WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR
# PURPOSE, MERCHANTABLITY OR NON-INFRINGEMENT.
#
# See the Apache Version 2.0 License for specific language governing
# permissions and limitations under the License.
#
##########################################################################
<#
.Synopsis
    This script enables Secure Boot features of a Generation 2 VM.

.Description
    This setup script will enable the Secure Boot features of a Generation 2 VM.

.Parameter vmName
    Name of the VM.

.Parameter hvServer
    Name of the Hyper-V server hosting the VM.

.Parameter testParams
    Test data for this test case.

.Example
    setupScripts\Set-SecureBoot.ps1 -hvServer localhost -vmName NameOfVm -testParams 'rootdir=path/to/testdir;'

#>
param(
    [String] $vmName,
    [String] $hvServer,
    [String] $testParams
)

if (-not $vmName)
{
    "Error: no VMName specified"
    return $False
}

if (-not $hvServer)
{
    "Error: no hvServer specified"
    return $False
}

if (-not $testParams)
{
    "Error: no testParams specified"
    return $False
}

$error.Clear()
$vm = Get-VM -Name $vmName -ComputerName $hvServer
if ($error.Count -gt 0)
{
    "Error: Cannot find VM `"${vmName}`" "
    $error[0].Exception
    return $False
}

#
# Check if it's a Generation 2 VM
#
if ($vm.Generation -ne 2)
{
    "Error: VM `"${vmName}`" is not a Generation 2 VM"
    return $False
}

#
# Check if Secure Boot is enabled
#
$firmwareSettings = Get-VMFirmware -VMName $vm.Name -ComputerName $hvServer
if ($firmwareSettings.SecureBoot -ne "On")
{
    $error.Clear()
    Set-VMFirmware -VMName $vm.Name -EnableSecureBoot On
    if ($error.Count -gt 0)
    {
        "Error: Unable to enable secure boot!"
        $error[0].Exception
        return $False
    }
}

$error.Clear()
Set-VMFirmware -VMName $vm.Name -ComputerName $hvServer -SecureBootTemplate MicrosoftUEFICertificateAuthority
if ($error.Count -gt 0)
{
    "Error: Unable to set secure boot template!"
    $error[0].Exception
    return $False
}

Write-Host "Secure Boot: $($firmwareSettings.SecureBoot).`nSecure Boot Template: $($firmwareSettings.SecureBootTemplate) "

return $True

redpajama_set_name: RedPajamaGithub


COMING SOON, SIGN UP FOR THE WAITLIST BELOW!
SHIPPING STARTS the week of April 25th.
Our latest creation is the 4-in-1 fashion bag. It is a multi-position, high-tech, a bag for any occasion and no animals are harmed!
The bag you deserve, the only bag you need!
We are girls, we know how it feels to have a closet full of bags but still don't know which one to pick.
1) You can wear it as a purse hanging from your shoulder for your daily routine.
2) As a handbag from its rings for a more formal and sophisticated touch.
3) Attached to your waist as a belt bag for those busy days you need to be hands-free.
4) Or just take with you the wallet to that special date when you only need your essentials.
It comes with a bluetooth device with a FREE dedicated app that connects your laagam bag to your smartphone. You will always know where your bag is.
No more worries while carrying your bag!
Our integrated power bank provides convenient energy to keep your electronic devices (smartphone, tablets, ebooks, GPS, etc.) always charged.
It comes with a cable adapter for Apple and Android devices.
The bluetooth device and a the power bank are included with the purchase of our bag for free. They have specific compartments designed to fit perfectly inside.
...but better known as the leather goods capital of Europe. The quality of Ubrique's artisans is recognized worldwide and the tradition dates back to the Middle Ages.
Ubrique is the supplier to luxury International fashion houses such as Loewe, Gucci and Louis Vuitton.
Choose either golden or silvery details.
Available in black or burgundy.


text:
Дашково — название населённых пунктов:

Белоруссия
 Дашково — деревня в Бешенковичском районе Витебской области.

Грузия
 Дашково — прежнее название села Чиаури в Лагодехском муниципалитете края Кахетия.

Россия
 Дашково — деревня в Тейковском районе Ивановской области.
 Дашково — деревня в городском округе Шаховская Московской области.
 Дашково — село в Урицком районе Орловской области.
 Дашково — деревня в Себежском районе Псковской области.
 Дашково — деревня в Торопецком районе Тверской области.

Другое
 Дашково — железнодорожная станция Куйбышевской железной дороги на линии Пенза — Ряжск


How To Make A Folded Card In Word how to make a folded card in word creating your own quarter fold printable cards templates. how to make a folded card in word family tree how to make cards on the computer tutorial and download. how to make a folded card in word how to make your own place cards for free with word and picmonkey printable. How To Make A Folded Card In Word how to make a folded card in word printing your own greeting cards in word 2016 dummies. how to make a folded card in word how to make birthday cards with microsoft word 11 steps with pictures printable. how to make a folded card in word family tree how to make cards on the computer tutorial and template. How To Make A Folded Card In Word how to make a folded card in word how to make folded invitations with microsoft word microsoft free.
How To Make A Folded Card In Word how to make a folded card in word family tree how to make cards on the computer tutorial and download. how to make a folded card in word how to make your own place cards for free with word and picmonkey printable. how to make a folded card in word printing your own greeting cards in word 2016 dummies. how to make a folded card in word how to make birthday cards with microsoft word 11 steps with pictures printable. how to make a folded card in word family tree how to make cards on the computer tutorial and template.


NOVA Co. Ltd. is a communications company offering language services to a wide variety of language learners through its branches. Students want not only the opportunity to increase their proficiency in the foreign language of their choice, but also to interact with people from different cultures.
In addition to general conversation lessons, Nova offers courses for students studying for specific English tests, such as TOEIC, TOEFL and also for students studying for specific purposes, such as business or travel. Lessons are also provided for young learners through our kids programs. Join a professional team dedicated to providing quality language instruction to students of all ages.


Children are welcome at Atlanta Dermatology & Laser Surgery, and our staff is experienced in treating dermatology concerns in children of all ages. In order to make their visit as comfortable and stress-free as possible, children are invited to use the books and toys available for them in our waiting room. Atopic Dermatitis, or Eczema, is a chronic skin disorder that affects 15-20% of children in the U.S. It causes inflamed, itchy rashes that can range from minor to severe and can show up on any part of the body. The rashes can lead to infection and are sometimes associated with asthma and food allergies. Eczema is not contagious and often improves with age.
Discuss lifestyle changes that can improve your skins moisture content.
Topical treatments like ointments and shampoos.
Brown birthmarks are, as the name implies, marks on the skin that are present at birth. They are generally harmless, although large birthmarks (larger than the size of a fist) are more likely to become cancerous. Any birthmarks that appear to change in color or appearance should be checked by a doctor. Birthmarks may harm self-esteem, depending on their size and location.
These are vascular birthmarks, meaning that they consist of blood vessels close to the skin's surface. They may appear several weeks after birth and can have a spongy appearance (also known as strawberry marks).
They are pink, red, blue, or purple in color and raised above the skin. They are most often found on the head, neck or limbs. Some shrink away on their own (Rapidly Involuting), while others continue to grow as the child grows (Noninvoluting).
These vascular birthmarks are flat and consist of dilated blood capillaries. They sometimes harbor underlying tissue abnormalities, so they should always be examined by a Board Certified Dermatologist. These enlarge over time and respond most effectively to laser treatments.
One of our dermatology experts will examine the birthmark and determine if treatment is necessary. . A biopsy on brown congenital nevi may be necessary, to rule out skin cancer.


This tutorial shows how to use SendGrid to send email from an application running on a Compute Engine instance. SendGrid is a third-party email service that offers Compute Engine users a free trial with 12,000 transactional emails free each month.
Use SendGrid with Postfix on a Compute Engine instance.
Use SendGrid in Java code running on a Compute Engine instance.
Use SendGrid in Node.js code running on a Compute Engine instance.
This tutorial uses billable components of Cloud Platform including Google Compute Engine.
On the OS images tab, choose a Debian or CentOS image.
Use the Cloud Marketplace to sign up for the SendGrid Email service. Make a note of your SendGrid SMTP account credentials, which include username, password, and hostname. Your SMTP username and password are the same as what you used to sign up for the service. The SendGrid hostname is smtp.sendgrid.net.
Sign in to Sendgrid and go to Settings > API Keys.
Select the permissions for the key. At a minimum, the key will need Mail send permissions to send email.
Click Save to create the key.
SendGrid generates a new key. This is the only copy of the key so make sure to copy the key and save it for later.
Follow these steps to connect to your sendgrid-tutorial instance and run SendGrid with Postfix.
Note: The SendGrid documentation provides a set of instructions for Postfix installation and setup. If you run into issues setting up Postfix with SendGrid, review the SendGrid Postfix instructions.
If prompted, select the Local Only configuration and accept the default domain name.
Modify the Postfix configuration options.
If the following lines are in the file, comment them out.
Add the SendGrid SMTP service by adding the following line to the end of the file.
Note: You must use port 2525 because port 25 and port 587 are not allowed on Compute Engine.
Also at the end of the file, add the following lines to enforce SSL/TLS support and to configure SMTP authentication for these requests. A simple access and security layer (SASL) module handles authentication in the Postfix configuration.
Generate the SASL password map.
[YOUR_SMTP_LOGIN] is your SendGrid username.
[YOUR_SMTP_PASSWORD] is your SendGrid password.
where [YOUR_API_KEY] is the contents of an API key that you created on your SendGrid account.
[MESSAGE] is the body of the email.
[SUBJECT] is the subject of the email.
[EMAIL@EXAMPLE.COM] is the email address that you want to send a message to.
The following instructions use the SendGrid Java client library to construct and send an email message through SendGrid. You can view the full example on GitHub.
Replace YOUR-SENDGRID-API-KEY with the API key for your SendGrid account.
Replace YOUR-SENDGRID-FROM-EMAIL with the email address you you want to send mail from.
Replace DESTINATION-EMAIL with the email address you want to send mail to.
Replace <your-sendgrid-api-key> with the API key for your SendGrid account.
Replace from_email@example.com with the email address that you want to send mail from.
Replace to_email@example.com with the email address that you want to send mail to.
Click the checkbox next to your sendgrid-tutorial instance.


Julian Anthony is a fresh new DJ on the Dutch scene who is starting to turn heads. With releases lined up on Prunk's PIV, Cinthie's We_R House and Daniele Temperilli's Girasole, 2019 will be the year that Julian Anthony establishes himself as a producer.
The young artist with the characteristic afro started his musical career as a drummer. He has always been inspired by the magic that happens when drums and basslines meet. House music, a genre that came into existence by its pioneer's fascination with those elements, was a logical next step.
It was Slapfunk's Samuel Deep and Julian Alexander who taught him how to DJ with vinyl. In the years that followed he went from booking to booking with DJs requesting him to open for them. He was soon sharing line ups with Cinthie, Prunk, Benny Rodrigues, Samuel Deep and playing renowned Dutch clubs such as Toffler, Claire, Dok and Pip.
In 2019 Julian is establishing himself as a producer with his debut release on PIV reaching #30 on Beatport and more releases to announce soon.


text:
Q: MS SQL calculation query - incorrect results and/or data type (only shows integer part) I've attached picture of the problem I'm having. Basically I am supposed to be getting answer like 3.66667 for first GPA, but it's showing 3. Same for the other 2 GPAs - they have decimal parts, but its not showing. What do you think is the problem? I already tried googling, changing data type etc...
P.S. to get GPA:   divive TGP(Total Grade Points) by TCH (Total Credit Hours), however its only showing integer part...
here is the screenshot:
http://i.imgur.com/7kMF2Cj.jpg

redpajama_set_name: RedPajamaStackExchange


text:
GLENDALE, AZ - OCTOBER 30: Max McCormick #17 of the Ottawa Senators in action during the NHL game against the Arizona Coyotes at Gila River Arena on October 30, 2018 in Glendale, Arizona. The Coyotes defeated the Senators 5-1. (Photo by Christian Petersen/Getty Images)
Kraken Take Down Flames in Giordano's Return by Jonathan Amatulli
Game Preview: Preseason Game 4 vs Edmonton Oilers by Jonathan Amatulli
Seattle Kraken News
Kraken Sign Max McCormick to 1-Year Deal
by Rob Couch 3 months ago Follow @RobCouch555
The Seattle Kraken bring in Max McCormick as a depth signing to add grit to a forward group in need of a physical presence.
Max McCormick
Signed: UFA
Position: LW
Contract: 1 year remaining at $750k AAV
2020-21 Season Stats: 12GP: 2G, 1A, 3P, +3
McCormick earned the largest contract of his career in terms of average annual value (AAV) when he signed with the Kraken September 29th. He joins former linemate Morgan Geekie on the team, and looks to become more of an NHL contributor this season. McCormick spent more of last season on Carolina's taxi squad or on the injured reserve. He still managed to find a little playing time, getting into 12 games in 2020-21. In those games, he contributed two goals and one assist while only averaging 7:49 on ice time per game (ATOI).
In his career, McCormick has scored eight goals and recorded 13 points, while putting up 87 penalty minutes and 152 hits in 83 games. He has forged a respectable AHL career while he's been in the league too. Across three AHL teams, he has 168 points in 336 games.
McCormick Looks to Stick in the NHL
McCormick has spent parts of five seasons at the NHL level, jumping between there and the AHL. He has found himself as more of an AHL level player, with some fourth line upside when he does get his shot. He first broke into the league with the Ottawa Senators in 2015-16 after being drafted by them in the 6th round in 2011. Not a bad career he has carved out for himself considering most late round picks don't amount to much.
He has seen action in every year since making his NHL debut, except for the 2019-20 where he played the entire season in the AHL for the Charlotte Checkers, Carolina's affiliate. He has never been able to stick as a member of an NHL roster for an entire season to date. Injuries are great play will see McCormick up with the Kraken this season.
This is a smart depth signing by the Kraken, as Mccormick can hold his own in the NHL when he gets his chance. He will also provide value to the young players in the AHL as they develop if he sticks around. He is a good player to have in the system.
Next:Kraken Take Down Flames in Giordano's Return
Kraken Chronicle 3 monthsGame Preview: Preseason Game 4 vs Edmonton Oilers
The Big Lead 3 monthsFake Tom Brady-Bill Belichick Couples Therapy Session Fails to Yield Significant Results
Kraken Chronicle 3 monthsKraken Take Down Flames in Giordano's Return
Kraken Chronicle 3 monthsGame Preview: Preseason Game 3 at Calgary Flames
Kraken Chronicle 3 months3 Takeaways from Kraken 6-0 Preseason Loss to Oilers


text:
New Wuhan virus similar in genome to Sars, says HK infectious disease expert
The University of Hong Kong's Professor Yuen Kwok Yung (right) said the genetic sequence of the new coronavirus was "80 per cent similar" to the Sars virus found in bats, civets and human.PHOTO: AP
Jan 11, 2020, 8:08 pm SGT
https://str.sg/JqsC
Claire Huang
Hong Kong Correspondent
huangjy@sph.com.sg
HONG KONG - The new virus behind the pneumonia outbreak in the Chinese city of Wuhan has a genetic makeup largely similar to the Severe Acute Respiratory Syndrome (Sars) virus, said a leading infectious disease expert in the city.
The University of Hong Kong's Professor Yuen Kwok Yung on Saturday (Jan 11) said the genetic sequence of the new coronavirus was "80 per cent similar" to the Sars virus found in bats, civets and humans.
Speaking at a briefing, he said the difference between the two lies in the part of the virus that determines if it could "enter animal cells".
"The genetic sequence of the virus could change, and that would completely change its toxicity and infectiousness," Prof Yuen said, noting adding the genetic sequence of the Sars virus changed in 2003 and thus was able to spread among humans.
That said, the microbiologist cautioned that there was not enough information to determine if the new infection would turn into an epidemic, reminiscent of the Sars outbreak.
The Sars epidemic originated in China, infected more than 1,700 people in Hong Kong and killed nearly 300. More than 800 people, including 33 in Singapore, died from Sars in 2002 and 2003.
Prof Yuen warned that Hong Kong must continue to stay vigilant and that the tests now used by health authorities in the city were effective in screening suspected patients.
Meanwhile, the Hong Kong Hospital Authority on Saturday reported a total of 60 suspected cases of the Wuhan virus since Dec 31. All the patients had made trips to Wuhan but not to the seafood wholesale market in the city where most of the confirmed cases originated.
China reports first death in Wuhan pneumonia outbreak
Wuhan pneumonia outbreak: Hong Kong officials to get quarantine powers, masks selling out
Wuhan flu caused by new coronavirus: More about the pathogen behind the outbreak
Lessons from Sars will help Singapore tackle bug from China
More than two-thirds of the suspected cases in Hong Kong or 46 patients have been discharged and the remainder are in stable condition.
Hong Kong authorities have in recent days stepped up vigilance and public health surveillance, with the government making it mandatory to alert officials of any suspected cases.
"At the moment, everybody in Hong Kong including the general public, the healthcare workers and other stakeholders have to remain vigilant and don't take the new disease lightly because we have the painful experience of Sars. So we have to take every measure and closely monitor the situation," the Controller of the Centre for Health Protection Wong Ka Hei said at the briefing on Saturday.
In Singapore, the Ministry of Health said on Saturday that a second suspected case - a 26-year-old China national with pneumonia and travel history to Wuhan - was found not to be linked to the pneumonia cluster in Wuhan. The case has also tested negative for coronavirus.
Last week a three-year-old girl, also with a travel history to Wuhan, was kept in isolation until it was proven that she was not infected by the new virus.
Suspected cases of the Wuhan virus have also cropped up in Taiwan and South Korea.
WUHAN VIRUS


I had a period in which I was infatuated with the greatness that is Fred Astaire & Ginger Rodgers. Prior to this I often heard of them but I was occupied with later film musical of the 50's. When I checked them out for myself I got it, oh boy did I get it. When together dancing or not, Fred and Ginger are in a world of their own and everyone else ceases to exist. Just look as Night & Day (my favourite Astaire and Rodger's number), what could be more spellbinding? The Gay Divorcee is my favourite Astaire & Rodgers picture. This was their first film together as leads and yet a feel it gets everything right and I consider it a much better film than Top Hat which itself I find overrated.
I find the humour of The Gay Divorcee is more creative than that of Top Hat. Take the sequence in which Astaire finds Rodger in London by near impossible luck, then the two engage in a car chase into the countryside (how often do you get a car chase in a 30's musical), and then in a wacky races type moment he goes ahead or Rodgers and gets road closed sign out of nowhere in order to stop her. Astaire's stalker attitude could come off as creepy but he is charming enough to get away with it, making these moments morbidly funny. This whole sequence is so surreal and plays like a live-action cartoon as if the filmmakers are making fun of the film's own highly improbably mistaken identity plot. This is much more clever than the handling of the mistaken identity plot in Top Hat. I don't mean to completely undo Top Hat, I think it's a good movie, just whatever Top Hat did I can't help but feel The Gay Divorcee did much better. I've always championed Astaire's unsung abilities as a comedian. His timing and line delivery is easily on par with the likes of Cary Grant; I wish he could have appeared in some non-musical comedies. Ginger Rodgers usually had a female companion throughout the series and I think Alice Brady is the best of them all with her histrionics; the sound of her voice alone cracks me up.
The Gay Divorcee may have slipped through the recently instated production code. If not then it certainly feels like a pre-code film, with sexual tension throughout and an air of scandalousness to the whole thing.
Fred and Ginger, they were gods!


@taeyeon_ss 첫방이니까 함 달려봅시다! 힘좀 줍시다!
@taeyeon_ss 순규 떨리지만 굉장히 태연한척하고 있나봄. 놀릴거리가 생겨서 나도 씐나나봄.!
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Villa Antona Traversi è una dimora neoclassica costruita dall'architetto Leopoldo Pollack, attraverso la trasformazione dell'antecedente monastero medievale intitolato a San Vittore e si trova nel comune di Meda (provincia di Monza e della Brianza). È di proprietà della famiglia Antona Traversi.

Storia

Fondazione del monastero di San Vittore
Il complesso di Villa Antona Traversi in Meda occupa quel rilievo collinare che domina l'Alto Milanese e che fu scelto quasi dodici secoli fa per fondarvi il Monastero di San Vittore, nell'830 circa.
Sulla fondazione del Monastero esiste una leggenda, testimoniata dal codice 509 conservato nella Biblioteca Trivulziana di Milano : Aimo e Vermondo, conti di Turbigo, del casato dei Manfredingi, durante una battuta di caccia in Brianza furono inseguiti dai cinghiali fino ad un luogo in cui sorgeva una chiesa in onore di San Vittore. Qui trovarono "due lauri di meravigliosa grandezza" su cui si arrampicarono cercando la salvezza. Poiché i cinghiali continuavano a minacciarli dai piedi degli arbusti, essi fecero voto: se si fossero salvati, avrebbero fondato un monastero dedicato a S. Vittore. La Vergine esaudì le loro preghiere e Aimo e Vermondo, in segno di ringraziamento, "fondarono in onore del santo e glorioso S. Vittore Martire, un nobile monastero di Sante monache seguenti la regola di S. Benedetto".
Il Monastero è già esistente nell'anno 856: una pergamena attesta che in quell'anno la badessa Tagiperga effettua una permuta di terreni con Pietro, abate del monastero di S. Ambrogio a Milano
Il Monastero nacque già ricco e con importanti diritti feudali su Meda, Cabiate, Novedrate e Cimnago.

Medioevo
L'autorità del Monastero fu ribadita nel corso dei primi secoli, come attestano le cinque bolle papali e il diploma imperiale conservate nell'archivio . Nel 1194 il cenobio ospitò l'Imperatore Enrico VI con la sposa Costanza d'Altavilla, che sostarono a Meda durante il viaggio verso il Regno di Sicilia. Da documenti conservati nell'archivio del monastero si apprende che fino al 1252 la badessa di S. Vittore ebbe ad esercitare diritti di signoria. Il villaggio di Meda, sorto in origine come agglomerato di case alle dipendenze delle monache, venne fortificato e acquistò particolare importanza dopo l'anno Mille, quando divenne sede di un famoso mercato. Dalla fine dell'XI secolo e in coincidenza con il periodo delle lotte comunali, Meda cercò di ottenere l'affrancazione dalla signoria del monastero finché la badessa Maria da Besozzo, nell'anno 1252, rinunciò ai diritti feudali, firmando un atto di transazione con il comune e riconoscendone gli statuti, salvando però l'indipendenza del monastero e i suoi diritti ecclesiastici, in particolare il diritto di nomina del curato della chiesa di Santa Maria .

Dai Visconti a Napoleone
Meda fu attratta nell'orbita milanese e subì le stesse dominazioni signorili prima (Visconti, Sforza) e straniere poi. Nel 1496 a Meda si svolse un incontro fra l'imperatore Massimiliano d'Asburgo ed il duca di Milano Ludovico il Moro, alla presenza dei legati dei principali Stati italiani dell'epoca . Dopo il periodo spagnolo, che per il cenobio significò crescita vocazionale e consolidamento economico, più travagliato fu il periodo asburgico, in particolare durante le politiche anticlericali di Giuseppe II d'Asburgo: il monastero non fu soppresso perché la Casa delle Educande, fino ad allora riservata alle novizie in vista della monacazione, venne trasformata in una scuola aperta alle fanciulle del paese.
Dopo l'arrivo di Napoleone e la proclamazione della Repubblica Cisalpina il monastero femminile di S. Vittore il 29 maggio 1798 venne soppresso, le monache espulse e i beni venduti all'asta.

Il monastero diventa villa

L'edificio monastico fu acquistato da Giovanni Giuseppe Maunier, commerciante di Marsiglia e fornitore dell'esercito francese, che commissionò la trasformazione in villa neoclassica all'architetto Leopoldo Pollack, il quale era a Meda in quel periodo come testimoniano le relazioni e i disegni da lui lasciati riguardo al crollo del campanile della chiesa. L'architetto era discepolo di Piermarini e fu già attivo a Milano nella costruzione della Villa Reale. Nel 1836 la villa venne ceduta dagli eredi del Maunier e acquistata da Giovanni Traversi, i cui discendenti, gli Antona Traversi, la conservano tuttora.

Descrizione
Oggi Villa Antona Traversi si presenta architettonicamente in forme neoclassiche e il medesimo gusto si ritrova nelle decorazioni di affresco degli interni, ma sono presenti ancora resti sopravvissuti dell'antico Monastero, in particolare la chiesa di S. Vittore del 1520. Pollack, incaricato dal Maunier, mantenne il chiostro del monastero, che funge attualmente da cortile interno della villa, chiudendone parzialmente le arcate. La parte in cui l'intervento dell'architetto è più evidente è la facciata e il giardino. Questo fu pensato come un grande emiciclo, o "rotonda", affacciata a sud-est sulla collina dalla quale si dominava un tempo il vigneto, oggi scomparso, ed il borgo di Meda. Su tale scenografico parterre fu edificata la lunga facciata, anch'essa caratterizzata da decorazioni essenziali e linee rigorose nello stile piermariniano. La parte della chiesa riservata alle monache, gemella rispetto alla chiesa riservata ai fedeli (l'attuale chiesa di san Vittore, che si è conservata intatta), fu divisa in due parti da un tramezzo per poter essere utilizzata come granaio: l'aula inferiore, che conserva parte degli affreschi tardorinascimentali, fu trasformata in Limonera. Nell'aula superiore, detta "Sala del Coro", gli affreschi, attribuiti a Bernardino Luini e alla sua scuola, sono meglio conservati. La decorazione pittorica la ricopre interamente. Sulla volta si dipana un fitto disegno a monocromo con motivi floreali e grottesche, secondo il tipico gusto tardorinascimentale, mentre sulle pareti sono presenti tondi con sante e martiri, ed al centro un Cristo benedicente di evidente derivazione leonardesca, affiancato da S. Pietro e S. Giovanni evangelista.

All'interno della villa, l'unico ambiente a conservare decorazioni dell'antico monastero, oltre all'ex chiesa, è la sala dell'archivio, detta Sala degli Angeli, che presenta la volta affrescata dai Fiammenghini. Sono invece perfettamente conservate le raffinate decorazioni neoclassiche del periodo napoleonico nell'ottagono e nella sala delle maschere, con una volta dipinta a finti cassettoni e motivi ornamentali di derivazione classica ispirati al teatro romano.

Note

Bibliografia
 Mauri Michele, Ronzoni Domenico F., Ville della Brianza, edizioni Bellavite, collana Arte e architettura, 2003
 Guaita O., Le ville della Lombardia, Milano 1994
 Zoppa L., Per una storia di Meda: dalle origini alla fine del secolo XVIII, Meda 1971
 Binaghi Olivari M.T./ Süss F./ Bagatti Valsecchi P.F., Le ville del territorio milanese, Milano 1989

Altri progetti

Collegamenti esterni

 Sito Web di Villa Antona Traversi

Architetture di Meda
Antona Traversi
Monza


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Winner takes it all
Recent headlines were grabbed by Enas Aly, a wife who recently received an award for 100% of an asset base of £550,000 confirmed by the Court of Appeal.
The couple married in 2002 and had two children. They separated in 2011 when the husband, an anaesthetist, left the wife and moved to Bahrain. Since 2012 he failed to pay any child maintenance or spousal support.
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Judges are empowered to rearrange assets on divorce as they see fit. This case reveals that far from an exact, straight down the middle split, an outright award of everything to one party can happen in extreme circumstances. Equality is the starting point, but not the finish line. Each case turns on its own facts, and those facts may justify departing from equality.
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