text:
\section{Introduction}
\label{intro}

Recently, the equilibrium properties of the Ashkin-Teller neural network ({\sc
atnn}) have been studied in \cite{BK98,BK99}.
The neurons of the {\sc atnn} are described by {\it two} Ising spins
of different types. This allows the network to
store and to retrieve pairs of patterns.
Therefore, more complicated information can be stored in the {\sc atnn}
than in the Hopfield model \cite{Ho82,AGS87},
e.g., the fore- and background of a picture.
Every spin is connected to spins of the same type. In addition,
the neurons are connected to each other. The connections linking the neurons
are four-spin couplings, since they connect two pairs of spins,
one pair per neuron.
This allows the network to retrieve both patterns of a pair simultaneously.
One can think of the model as a combination of two Hopfield models,
each retrieving one of the patterns. The four-spin coupling is then a
connection between both models.
The underlying idea is that the simultaneous retrieval of a pair of patterns
is easier than the independent retrieval of the patterns in the pair.

There are various reasons for studying this model.
The Ashkin-Teller spin glass is related to disordered systems where the
disorder evolves on a time scale that can be tuned \cite{Ca94}.
The introduction of a neuron containing different types of spins
is also neurobiologicaly
motivated by the fact that areas in the brain exist which react to two
different kinds of dependent stimuli in such a way that the response to
particular combinations of these stimuli is stronger than the response
to others \cite{KI93}. Finally, in neuropsychological studies on amnesia,
it has become appreciated that
memory is composed of multiple separate systems which can store
different types of informations, e.g., information based on skills and
informations based on specific facts or data \cite{Sq93}.

In \cite{BK98,BK99}, the thermodynamic and retrieval properties of the
{\sc atnn} have been studied using replica-symmetric mean-field theory.
In the present paper, we analyse the parallel dynamics of the asymmetric
extremely diluted version of the model.
Both the way how the system evolves to its equilibrium configuration and the
properties of the equilibrium configuration itself are subjects of interest.
It is known \cite{BKS90,BJS99b} that the dynamics in symmetric architectures,
even in the diluted case, is complicated
in a non-trivial way because of correlations between the neuron states. These
correlations are caused by feedback loops and common ancestors.
In contrast to the Hopfield model, where the dynamics has been solved taking
into account all the correlations \cite{BJS98,BJS99a}, the presence
of two types of spins makes the analysis of the correlations
in the {\sc atnn} very complicated.
The underlying reason is the existence of two sources of correlations.
First, feedback loops appear due to the two-spin interaction,
as in the Hopfield model. Second,
the four-spin coupling causes correlations between
spins of different type.
Therefore, in order to arrive at a first insight in the
dynamics of the model, we limit ourselves to its asymmetric extremely diluted
version where all correlations
between the neuron states are eliminated \cite{DGZ87,BSVZ94}.

Using standard signal-to-noise analysis techniques (see, e.g, refs.
\cite{BJS99b,DGZ87,PZ91}),
we find that the local field of the asymmetrically diluted {\sc atnn}
contains only a normally distributed part, besides the signal.
As observed already for the asymmetric diluted Hopfield model
\cite{DGZ87}, the structure of the local field does not change
in time. This allows us to write down immediately
the complete time evolution of the main overlaps.

The rest of the paper is organised as follows.
In the second section, we define the model as
an extension of the Hopfield model. We
introduce parallel dynamics at arbitrary temperature, and define
the main overlaps (one for each type of spins)
as macroscopic measures for the retrieval quality. In
Section~\ref{section:dynamicsatnn},
we use signal-to-noise analysis techniques in order to
write down the evolution equations at arbitrary time.
From the evolution equations,
the fixed-point equations are obtained.
These equations lead to the dynamical capacity-temperature diagram
presented in Section~\ref{secatnn:results}. Finally, we give some
concluding remarks in Section~\ref{secatnn:concl}.

\section{The model}
\label{section:modelATNN}
The {\sc atnn}
is defined as a neural network consisting of $N$ neurons.
Each of the neuron states is described by two spins
with value $\sigma_i$ and
$s_i$ ($i=1,\dots,N$), both taken from the discrete set $\{-1,+1\}$.
For each type, the spins $i$ and $j$ are coupled by a two-spin interaction
$J_{ij}^{(1)}$
and $J_{ij}^{(2)}$ respectively, while the neurons $i$ and $j$ are
coupled by a four-spin interaction $J_{ij}^{(3)}$.
We assume no diagonal terms viz.\ $J_{ii}^{(y)}=0,~y=1,2,3$.

A configuration of an {\sc atnn} consists out of a
$\mbox{\boldmath $\sigma$}$- and ${\vec s}$-part viz.\
\begin{equation}
  \left(\mbox{\boldmath $\sigma$}(t)=\{\sigma_j(t)\},
       {\vec s}(t)    =\{s_j(t)\}\right);~j=1,\dots,N \,.
  \nonumber
\end{equation}
Given such a configuration, we define three types of local fields:
two Hopfield-like local fields which measure the incoming
signal to the spins $\sigma_i$ and $s_i$, caused by the spins of the same
type
\begin{eqnarray}
   h_{N,i}^{(1)}({\mbox{\boldmath $\sigma$}}(t))=
                \sum_{j=1}^N J_{ij}^{(1)}\sigma_j(t)
   \nonumber \\
   h_{N,i}^{(2)}({{\vec s}}(t))=
                \sum_{j=1}^N J_{ij}^{(2)}s_j(t)\,,
  \label{eq:hatnn1}
\end{eqnarray}
and, in addition,
a local field which measures the incoming signal to neuron $i$,
caused by both spins of the other neurons
\begin{eqnarray}
  h_{N,i}^{(3)}({\mbox{\boldmath $\sigma$}}(t),{{\vec s}}(t))&=&
     \sum_{j=1}^N J_{ij}^{(3)}
			\sigma_j(t)s_j(t)\,.
\label{eq:hatnn}
\end{eqnarray}
In the sequel, we write the shorthand notation
$h^{(x)}_{N,i}(t) \equiv
h_{N,i}^{(x)}({\vec S}_x(t)),~x=1,2$ with
${\vec S}_1(t)={\mbox {\boldmath $\sigma$}}(t)$, $\vec S_2(t)=\vec s(t)$,
and
$h^{(3)}_{N,i}(t) \equiv h_{N,i}^{(3)}({\mbox{\boldmath $\sigma$}}(t),
	{{\vec s}}(t))$.
The configuration $(\mbox{\boldmath $\sigma$}(0),{\vec s}(0))$ is chosen as
input.
At temperature $T=1/\beta$, all neurons are updated in parallel
according to the transition probability
\begin{eqnarray}
  &&\hspace{-.5cm}
    \Pr(\sigma_i(t+1)=\sigma|\mbox{\boldmath $\sigma$}(t),{\vec s}(t))
    	\nonumber\\
    &&=\frac12\left[ 1+\tanh\beta\sigma
	  	\left(h_{N,i}^{(1)}(t)+s_i(t)h_{N,i}^{(3)}(t)
		\right)
	    \right]
    \nonumber \\
    &&\hspace{-.5cm}
    \Pr(s_i(t+1)=s|\mbox{\boldmath $\sigma$}(t),{\vec s}(t))
  	\nonumber \\
    &&=\frac12\left[ 1+\tanh\beta s
	  	\left(h_{N,i}^{(2)}(t)+\sigma_i(t)h_{N,i}^{(3)}(t)
		\right) \right]\,.
\label{eq:upatnnstoch}
\end{eqnarray}
We assume hereby that both types of spins exhibit the same degree of
stochasticity.
At zero temperature, this dynamics becomes deterministic and is given by
\begin{eqnarray}
  S_{x,i}(t+1)&=&\mbox{\rm sign}
	  	\left(h_{N,i}^{(x)}(t)+S_{\tilde x,i}(t)h_{N,i}^{(3)}(t)
		\right)
\label{eq:upatnndet}
\end{eqnarray}
with $x,\tilde x=1,2$ and $x\neq\tilde x$.
The $\mbox{\boldmath $\sigma$}$-spins
receive at each time input from the ${\vec s}$-spins and vice versa
due to the term containing $h_{N,i}^{(3)}(t)$.

The aim of the network is to store simultaneously $p_1$ patterns
$\{\mbox{\boldmath $\xi$}^\mu\},~\mu=1,\dots,p_1$
in the $\mbox{\boldmath $\sigma$}$-part of the network and
$p_2$ patterns $\{\mbox{\boldmath $\eta$}^\mu\},~\mu=1,\dots,p_2$ in the
${\vec s}$-part. All components of the patterns $\xi_i^\mu$  and
$\eta_i^\mu$  are i.i.d.r.v.\ taken from $\{-1,+1\}$ with zero mean
$\left<\xi_i^\mu\right>=0=\left<\eta_i^\mu\right>$
and independent type by type
$\left<\xi_i^\mu\eta_j^\nu\right>=0$ ($i,j=1,\dots,N$).
In order to store these embedded patterns, the two-spin couplings are chosen
according to the Hebb rule
\begin{eqnarray}
  J_{ij}^{(1)}=\frac{J_1}{N} \sum_{\mu=1}^{p_1} \xi_i^\mu \xi_j^\mu
  \label{eq:J1} \qquad
  J_{ij}^{(2)}=\frac{J_2}{N} \sum_{\mu=1}^{p_2} \eta_i^\mu \eta_j^\mu
  	\,.
  \label{eq:J2}
\end{eqnarray}
The four-spin interaction is, also in analogy to the Hebb-rule, defined as
\cite{BK98}
\begin{eqnarray}
  J_{ij}^{(3)}&=&\frac{J_3}{N} \sum_{\mu=1}^{p_3}
  	\gamma_i^\mu \gamma_j^\mu  \,.
\label{eq:Jatnn}
\end{eqnarray}
Under the assumption of independent embedded patterns
$\mbox{\boldmath $\xi$}^\mu$
and $\mbox{\boldmath $\eta$}^\mu$, we consider the following form
\begin{equation}
  \gamma_i^\mu=\xi_i^\mu \eta_i^\mu	\,.
\nonumber
\end{equation}
The patterns $\{\mbox{\boldmath $\gamma$}^\mu\},~\mu=1,\dots,p_3$
are then a set of i.i.d.r.v.\ taken from $\{-1,+1\}$ with
zero mean. In the literature, this choice of patterns is called the linked
case \cite{BK98}.

The variables $J_y,~y=1,2,3$ are constants scaling the relative
importance of all types of couplings.
We choose in the sequel $J_1=J_2$ since
we want both types of spins interchangeable for simplicity.
The relative scale of
the temperature and coupling strengths is fixed by choosing $J_1=1$.
Finally, we define $J=J_3/J_1$ such that this quantity measures the
relative strength of the
four-spin couplings with respect to the two-spin couplings.
In the limit $J\to 0$ the {\sc atnn} becomes, at least in structure, the
equivalent of two independent Hopfield models
since $h_{N,i}^{(3)}(t)=0$ at all times.
We use the temperature $T$ and the relative coupling
strength $J$ as independent variables.

In the sequel, we take the interactions asymmetric extremely diluted
\cite{DGZ87,BSVZ94}
\begin{eqnarray}
  \tilde J_{ij}^{(y)}=c_{ij}^{(y)}~N~J_{ij}^{(y)}/c_y
  \qquad y=1,2,3
\label{eq:modJdilatnn}
\end{eqnarray}
with $c_y>0$  and $\Pr\{c_{ij}^{(y)}=a\}=(1-c_y/N)\delta_{a,0} +
(c_y/N) \delta_{a,1}$.
The variables $\{c_{ij}^{(y)}\}$ are independent for
each pair $(i,j)$ representing both the asymmetry and the dilution.
The diagonal terms are excluded $c_{ii}^{(y)}=0$.
The structure of the architecture of the network then becomes a directed
tree with an average number of incoming and outgoing connections
(type by type) both equal to $c_y$.
It is assumed that $c_y\ll N$.
The system is first diluted by taking the limit $N\to\infty$. Afterwards,
the number of incoming signals per site is made
extensive by taking the limit $c_y\to\infty$.
The probability to have feedback in the system is now zero and the
correlations are treelike.

In
principle, all couplings can be diluted independently (viz.\ $c_1\neq
c_2 \neq c_3$). For convenience, however, we dilute them in the same way,
\begin{equation}
  c_{ij}^{(1)}=c_{ij}^{(2)}=c_{ij}^{(3)}\equiv c_{ij}
  \qquad c_1=c_2=c_3\equiv c \,.
   \nonumber
\end{equation}
This means that both spins of a neuron get information from the same neurons
and that the dynamics of both types of spins can be treated analogously.
Since the number of embedded patterns is of the same order as
the number of connections a spin has with spins of the same type, we have
$p_1=p_2=p_3=\alpha c\equiv p$.
In what follows, we write, for simplicity, $J_{ij}^{(y)}$ instead of
$\tilde{J}_{ij}^{(y)}$.

At this point, we note that the capacity of the {\sc atnn} is defined as the
ratio of the number of patterns stored in the network and the number of
couplings to a neuron. In this model where we want to store $2p$ patterns
$\{\mbox{\boldmath $\xi$}^\mu,\mbox{\boldmath $\gamma$}^\mu\}$,
all neurons have in average $3c$ links to the other
neurons: $2c$ two-spin couplings and $c$ four-spin couplings.
Therefore, the capacity of the {\sc atnn} equals
\begin{equation}
  \alpha_{\rm ATNN}\equiv\frac{2p}{3c}=\frac23\alpha \,.
  \nonumber
\end{equation}

The retrieval quality of the model is measured by the Hamming distance
between the microscopic state of the network and the stored patterns
\begin{eqnarray}
  &&D^\mu_H(t)\equiv\left[\sum_{x}
  	\left(d_x({\mbox{\boldmath $\psi$}}_x^\mu,{\vec S}_x(t))\right)^2
	\right]^{\frac12}
  \label{eq:hamdistatnn1}
  \\
  &&d_x({\mbox{\boldmath $\psi$}}_x^\mu,{\vec S}_x(t))\equiv
                \frac{1}{N}
                \sum_{i=1}^N[\psi_{x,i}^\mu-S_{x,i}(t)]^2
  \label{eq:hamdistatnn}
\end{eqnarray}
where $\mu=1,\dots,p$,
$x=1,2$, ${\mbox{\boldmath$\psi$}}_1^\mu={\mbox{\boldmath$\xi$}}^\mu$
and ${\mbox{\boldmath$\psi$}}_2^\mu={\mbox{\boldmath$\eta$}}^\mu$.
This naturally introduces the main overlaps
\begin{eqnarray}
        m_{x,N}^\mu(t)=\frac{1}{N}
                \sum_{i=1}^N\psi_{x,i}^\mu S_{x,i}(t)
                \quad \mu =1,\dots,p \,.
\label{eq:matnndef}
\end{eqnarray}
In the diluted model the sum in (\ref{eq:matnndef})
has to be taken over  the tree-like structure, viz.
$\frac1N\sum_{i=1}^N \to \frac1c\sum_{i=1}^Nc_{ij}$. The expression for
the  main overlap (\ref{eq:matnndef}) then reads
\begin{eqnarray}
        m_{x,c,N}^\mu(t)=\frac{1}{c}
                \sum_{i=1}^Nc_{ij}\psi_{x,i}^\mu S_{x,i}(t)
                \quad \mu =1,\dots,p \,.
\label{eq:matnndefc}
\end{eqnarray}
We remark that both expressions (\ref{eq:matnndef}) and (\ref{eq:matnndefc})
become equal in the thermodynamic limit $c,N\to\infty$.

\section{Dynamics}
\label{section:dynamicsatnn}

In this section we construct a set of recursion equations for the main
overlap  order parameters. We use hereby signal-to-noise techniques
(see, e.g., refs. \cite{BSVZ94,PZ91}).
Finally, we write down the fixed-point equations.

Suppose an initial spin configuration
$(\mbox{\boldmath $\sigma$}(0),{\vec s}(0))$. The configurations
${\vec S}_x(0)=\{S_{x,i}(0)\},~i=1,\dots,N$
are collections of i.i.d.r.v.\ with mean
$\left<S_{x,i}(0)\right>=0$ and variance
$\left<\left(S_{x,i}(0)\right)^2\right>=1$.
Spins of different types are uncorrelated
$\left<\sigma_i(0)s_j(0)\right>=0$ ($i,j=1,\dots,N$).
Both types are correlated with only one of the stored patterns, e.g., the
first one
\begin{eqnarray}
     \left<\psi_{x,i}^\mu S_{x,j}(0)\right>=
                         \delta_{i,j}\delta_{\mu,1}m^1_{x,0}
     	\,.
\label{eq:initatnnsigma}
\end{eqnarray}
The site by site independence of spins and patterns implies by the law
of large numbers ({\sc lln}) that we get for the main overlaps
\begin{eqnarray}
   m^1_x(0)\equiv\!\lim_{c,N\to\infty}m_{x,c,N}^1(0)
     =\left<\psi_{x,i}^1S_{x,i}(0)\right>=m^1_{x,0} \,.
\label{eq:matnn(0)}
\end{eqnarray}

We now want to study how the main overlaps evolve under the parallel
dynamics specified before. For a general time step and at $T=0$, we find
from (\ref{eq:matnndefc}) and the {\sc lln} in the limit $c,N\to\infty$
\begin{eqnarray}
  \label{eq:matnn}
  m_x^1(t+1) &=&
    \left<\!\left<
      \psi_{x,i}^1 \mbox{\rm sign}
      	\left(h_i^{(x)}(t)+\psi_{\tilde x,i}(t) h_i^{(3)}(t)\right)
	\right>\!\right> \nonumber\\
  m_3^1(t+1) &=&
    \left<\!\left<
      \xi_i^1 \eta_i^1
      \mbox{\rm sign} \left(h_i^{(1)}(t)+s_i(t) h_i^{(3)}(t)\right)
      	\right.\right.\nonumber \\ &&\qquad\left.\left.
      \times\mbox{\rm sign} \left(h_i^{(2)}(t)+
                           \sigma_i(t) h_i^{(3)}(t)\right)
	\right>\!\right>
\end{eqnarray}
where $x,\tilde x=1,2;~x\neq\tilde x $.
The average  $\left<\!\left< \cdot \right>\!\right>$
denotes the average both over the distribution of the embedded patterns
$\{\xi_i^\mu\}$ and $\{\eta_i^\mu\}$ and the initial configuration
$\{\sigma_i(0),s_i(0)\}$. The average over the latter is
hidden in an average over the local fields through the updating rule
(\ref{eq:upatnnstoch}).

The equations (\ref{eq:matnn}) show that the knowledge of the
distribution of the local field at successive time steps is sufficient
in order to find the evolution equations for the order parameters.
We start with calculating the distribution of
the local field of the $\mbox{\boldmath $\sigma$}$-spins at $t=0$.
Using the definitions (\ref{eq:Jatnn}) and applying
the signal-to-noise analysis, we have
\begin{equation}
  h_{N,i}^{(1)}(0)=\xi_i^1\frac 1c \sum_{j=1}^N c_{ij}
	\xi_j^1 \sigma_j(0)
    + \frac 1c \sum_{\mu=2}^p \xi_i^\mu
	\sum_{j=1}^Nc_{ij} \xi_j^\mu \sigma_j(0)	\,.
  \label{eq:h0a}
\end{equation}
The signal term, i.e., the first term on the r.h.s.\ of (\ref{eq:h0a}),
is nothing but
the main overlap (\ref{eq:matnndefc}) multiplied by $\xi_i^1$.
In the noise part, i.e., the second term on the r.h.s.,
all terms are uncorrelated by construction such that we can apply the
central limit theorem ({\sc clt}) to find
\begin{equation}
  \lim_{c,N\to\infty} \frac{1}{\sqrt{p}}
    \sum_{\mu=2}^p \xi_i^\mu \frac{1}{\sqrt{c}}
    \sum_{j=1}^N c_{ij} \xi_j^\mu \sigma_j(0)
    \sim {\cal N}(0,1)
  \nonumber
\end{equation}
where ${\cal N}(0,1)$ represents a Gaussian random variable with mean
$0$ and variance $1$.
Therefore, in the limit $c,N\to\infty$, the local field at $t=0$ is the
sum of  two independent random variables
\begin{eqnarray}
  h_i^{(1)}(0)\equiv\lim_{c,N\to\infty}h_{N,i}^{(1)}(0)
  	=\xi_i^1 m_1^1(0) + \sqrt\alpha ~z_1(0)
  \label{eq:h100}
\end{eqnarray}
with $z_1(0)\sim{\cal N}(0,1)$. In an analogous way, we find for the local
field of the ${\vec s}$-spins
\begin{eqnarray}
  h_i^{(2)}(0)\equiv\lim_{c,N\to\infty}h_{N,i}^{(2)}(0)
  	=\eta_i^1 m_2^1(0) + \sqrt\alpha ~z_2(0)
\label{eq:hatnnsna}
\end{eqnarray}
with $z_2(0)\sim{\cal N}(0,1)$.

As in the local fields of the spins (\ref{eq:hatnn1}),
we separate in the local field (\ref{eq:hatnn}) the
terms containing the first pattern
$\mbox{\boldmath $\gamma$}^1$ from the rest
\begin{eqnarray}
  h_{N,i}^{(3)}(0)&=&\gamma_i^1\frac 1c \sum_{j=1}^N c_{ij}
	\gamma_j^1 \sigma_j(0) s_j(0)
	\nonumber \\
    &&\quad + \frac 1c \sum_{\mu=2}^p \gamma_i^\mu
	\sum_{j=1}^N c_{ij} \gamma_j^\mu \sigma_j(0)s_j(0)	\,.
\end{eqnarray}
In analogy with before, we call the first term the signal and the last
term the noise. Applying the {\sc lln} to the signal term, we get
\begin{equation}
  \lim_{c,N\to\infty}
  \frac 1c \sum_{j=1}^N c_{ij} \gamma_j^1 \sigma_j(0) s_j(0)
    = \left<\gamma_j^1 \sigma_j(0) s_j(0)\right> \,.
  \nonumber
\end{equation}
Since this term resembles strongly the main overlaps
(\ref{eq:matnndefc}), we call it also an overlap and denote
it by $m_{3}^1(0)$. In general, this overlap is defined by
\begin{equation}
        \label{eq:mdef3}
        m_{3,c,N}^\mu(t)=\frac{1}{c}
                \sum_{i=1}^N c_{ij}\gamma_i^\mu\sigma_i(t) s_i(t)
                \quad \mu =1,\dots,p \,.
\end{equation}
In the sequel, we will treat this parameter at
the same level as the other overlaps (\ref{eq:matnndefc}).
For the linked choice of patterns
$\gamma_i^\mu\equiv\xi_i^\mu \eta_i^\mu$, it follows from
(\ref{eq:initatnnsigma})
that $\left<\gamma_i^\mu\sigma_j(0)s_k(0)\right>=
\delta_{ij}\delta_{ik}\delta_{\mu1}
m^1_{1,0}m^1_{2,0}$ since the initial spin configurations
$\sigma_j(0)$ and
$s_j(0)$ are independent. Therefore, we have in the thermodynamic limit
and at $t=0$
\begin{equation}
  \label{eq:m3(0)}
  m_3^1(0)\equiv \lim_{c,N\to\infty}m_{3,c,N}^1(0)=m_1^1(0) m_2^1(0)\,.
\end{equation}
Following the same line of arguments as before, the noise term converges
again to a Gaussian random variable such that
\begin{equation}
  h_i^{(3)}(0)\equiv\lim_{c,N\to\infty}h_{N,i}^{(3)}(0)
  	= J\xi_i^1\eta_i^1 m_3^1(0) + J\sqrt\alpha ~ z_3(0)
  \label{eq:h300}
\end{equation}
with $z_3(0)\sim{\cal N}(0,1)$.
This finishes the calculation of the local fields at time $t=0$.

At a general time $t$, the local fields still consist out of a signal
term, proportional to the main overlap, and a Gaussian distributed noise
part.  This is due to the extreme dilution which eliminates all common
ancestors in the dynamics. Therefore, all variables
$\{X_j^\mu\equiv\psi_{x,i}^\mu c_{ij}\psi_{x,j}^\mu S_{x,j}(t)|
	j=1,\dots,N;~\mu=1,\dots,p\}$
are a set of i.i.d.r.v.\ and we can apply the {\sc clt} in the same way as in
eq.~(\ref{eq:h0a}). So, we find for the distribution of
the local fields a set of equations with the same structure as the
eqs.~(\ref{eq:h100}), (\ref{eq:hatnnsna}) and (\ref{eq:h300}), viz.\
\begin{eqnarray}
  h_i^{(x)}(t) &=& \psi_{x,i}^1 m_x^1(t)+\sqrt\alpha~z_x(t)
     ;~ z_x(t)\sim{\cal N}(0,1)
  \label{eq:hatnn(t)}
  \nonumber \\
  h_i^{(3)}(t) &=& J\xi_i^1 \eta_i^1 m_3^1(t)+
  	J\sqrt\alpha~z_3(t)
	;~ z_3(t)\sim{\cal N}(0,1)\,.
    \nonumber \\
\end{eqnarray}
The three Gaussian variables $z_y(t)$ are uncorrelated.

Using the distributions of the local fields (\ref{eq:hatnn(t)}) and
remarking that the joint probability of $s_i(t),\sigma_i(t),\xi_i^1$ and
$\eta_i^1$ is
obtained from the overlaps $m_y^1(t),~y=1,2,3$,
the equations (\ref{eq:matnn}) and (\ref{eq:hatnn(t)})
lead immediately to the evolution equations for the order parameters at
zero temperature
\begin{eqnarray}
  m_x^1(t+1)&=&\sum_{\sigma=\pm1}
    \frac 12 \left(1+\sigma m_{\tilde x}^1(t)\right)
    \mbox{\rm Erf}\left(\frac{m_x^1(t)+\sigma J m_3^1(t)}
    	{\sqrt{2\alpha(1+J^2)}}\right)
  \nonumber  \\
  m_3^1(t+1)&=&\sum_{\sigma,\tau=\pm1}
    \left(\sigma \tau +\sigma m_1^1(t) + \tau m_2^1(t) + m_3^1(t)\right)
    \nonumber \\ && \qquad
    \int {\cal D} z ~
    \mbox{\rm Erf}\left(\frac{\sigma m_1^1(t)+Jm_3^1(t)+J\sqrt{\alpha}z}
    		{\sqrt{2\alpha}}\right)
    \nonumber \\ &&\qquad
    \times\mbox{\rm Erf}\left(\frac{\tau m_2^1(t)
                 +J m_3^1(t)+J\sqrt{\alpha}z}{\sqrt{2\alpha}}\right)
    \label{eq:matnn(t)final}
\end{eqnarray}
where $x,\tilde x=1,2,~ x\neq\tilde x $.

After some time $t$ the dynamics reaches the point where the spins
macroscopically equilibrate. This means that the main overlap becomes
stationary, viz.\ $m^1_y(t+1)=m^1_y(t)$.
Since the expressions for the local fields do not
change their structure, the corresponding fixed-point equations are
easily obtained from
eq.~(\ref{eq:matnn(t)final}) by replacing the time dependent quantities
by  their equilibrium value $m_y^1\equiv\lim_{t\to\infty}m_y^1(t)$.
In the limit $J\to0$, the equations (\ref{eq:matnn(t)final}) are
consistent  with the evolution equations of \cite{DGZ87}.

At non-zero temperature $T=1/\beta$ the main overlaps at time~$t$ read
\begin{eqnarray}
  m_x^1(t+1)&=&\left<\!\left<
      \psi_{x,i}^1 \left< S_{x,i}(t+1)\right>_\beta
    \right>\!\right>
  \nonumber \\
  m_3^1(t+1)&=&\left<\!\left<
      \xi_i^1 \eta_i^1 \left< \sigma_i(t+1)\right>_\beta
		       \left< s_i(t+1)\right>_\beta
    \right>\!\right> \,.
\label{eq:matnnstoch(t)}
\end{eqnarray}
The thermal averages are defined by the updating rule
(\ref{eq:upatnnstoch}) and can be written as
\begin{eqnarray}
  \hspace{-.6cm}
  \left< S_{x,i}(t+1)\right>_\beta&=&
    \tanh\left[\beta\left(h_i^{(x)}(t)+
    	S_{\tilde x,i}(t)h_i^{(3)}(t)\right)\right]\,.
\label{eq:thermaverageatnn}
\end{eqnarray}
The stochasticity in the dynamics does not modify the local spin
correlations when compared with the deterministic dynamics.
Therefore, the local fields are still distributed according to
(\ref{eq:hatnn(t)}) and we get for the order parameters
\begin{eqnarray}
  m_x^1(t+1)&=&\sum_{\sigma=\pm1} \frac12
  	\left(1+\sigma m_{\tilde x}^1(t)\right)
    \nonumber \\ && \hspace{-1.8cm} \times
    \int \!{\cal D} y  \tanh \beta
	\left( m_x^1(t) + \sigma J m_3^1(t) + \sqrt{\alpha(1+J^2)}y
	\right)
  \nonumber \\
  \nonumber \\
  m_3^1(t+1)&=&\sum_{\sigma,\tau=\pm1}
    \frac14 \left(\sigma\tau +\sigma m_1^1(t)+ \tau m_2^1(t)
              + m_3^1(t)\right)
                            \nonumber \\
    && \hspace{-1.8cm} \times
    \int \!{\cal D} z\!\int \!{\cal D} x  \tanh \beta
	\left( \sigma m_1^1(t) + J m_3^1(t) + \sqrt{\alpha}x
	+ J\sqrt{\alpha}z \right)
    \nonumber \\ && \hspace{-1.8cm} \times
 	      \int \!{\cal D} y  \tanh \beta
	\left( \tau m_2^1(t) + J m_3^1(t) + \sqrt{\alpha}y
	+ J\sqrt{\alpha}z \right)\,.
\label{eq:matnn(t)stoch}
\end{eqnarray}
The fixed-point equations are read off from (\ref{eq:matnn(t)stoch}) by
using again $m_y^1=\lim_{t\to\infty}m_y^1(t)$, $y=1,2,3$. In
the zero-temperature limit $\beta\to\infty$, the equations above
reduce to (\ref{eq:matnn(t)final}).
Moreover, in the limit $J\to0$, they are consistent with the ones
obtained for the asymmetric
extremely diluted Hopfield model in \cite{DGZ87}.

\section{Results}
\label{secatnn:results}
In this section, we discuss the numerical results for the {\sc atnn}
obtained from the
fixed-point equations derived in the previous section. We present the
capacity-temperature diagram indicating the regions of retrieval as a
function of the capacity $\alpha_{\rm ATNN}$ and the temperature $T$, and
some representative figures illustrating the main features of
the model.

\begin{figure}
\epsfxsize=7.5cm
\centerline{\hspace{-.5cm}
	\rotate[r]{\epsfbox{fasediag.eps}}}
\caption{Capacity-temperature diagram for the {\sc atnn} for J=0.0 (full
line),  $J=0.3$ (dotted line), $J=1.0$ (dashed line), $J=2.0$ (long
dashed  line) and $J=3.0$ (dot-dashed line).}
\label{figatnn:phasediag}
\end{figure}

Due to the choice $J_1=J_2=1$ and due to the condition that both types
of spins  have a finite initial overlap with one condensed pattern, it
turns  out that the overlaps $m_1(t)$ and $m_2(t)$ always converge to
the same  equilibrium values, independent of the size of the initial
overlaps.  (We forget about the superscript $1$). Therefore we can
restrict  ourselves to the case $m_1=m_2$.

The resulting capacity-temperature diagram is pre\-sen\-ted in
Fig.~\ref{figatnn:phasediag}.
First, we consider the special case $J=0$. At $T=0$
a non-zero solution for the fixed-point equations exists as long as
$\alpha<2/\pi$,
indicating a transition from the retrieval to the non-retrieval regime
at $\alpha_{\rm ATNN}=4/3\pi$. When the temperature
increases, the critical capacity decreases to become zero at $T=1$.
The resulting transition line in the capacity-temperature
diagram is similar to the one of the Hopfield model
\cite{DGZ87} up to a rescaling of the capacity. This is not surprising
since the structure of the equations of the {\sc atnn}
for $J=0$ is consistent with those of the
Hopfield model. The transition is always continuous, and
the main overlap decreases when $\alpha_{\rm ATNN}$ increases.
This indicates
that the more embedded patterns, the harder the retrieval and the worse
the retrieval quality.

\begin{figure*}
\epsfxsize=6.cm
\centerline{\rotate[r]{\epsfbox{overlap.eps}}}
\caption{Overlaps $m_1$ (full line) and $m_3$ (broken line) at the critical
capacity as a function of the temperature,
for $a$) J=0.3, $b$) J=1.0 and $c$) J=3.0.}
\label{figatnn:overlap}
\end{figure*}

When the four-spin coupling is non-zero, things become different. A larger
four-spin coupling makes retrieval possible at higher temperature and
decreases  the critical capacity at low temperature.

For finite loading ($\alpha_{\rm ATNN}=0$), a continuous transition occurs
for $J\leq1/3$ at $T=1$. For larger $J$, the transition becomes
discontinuous  and the critical temperature becomes larger. This
indicates that  a model with non-zero  four-spin couplings can perform
better  in the presence of noise in the dynamics.
This corresponds with the results in \cite{BK98}. The overlap $m_1$
at the critical temperature
increases up to $J=2$, meaning that the larger $J$ the better the retrieval
quality. From $J=2$ onwards, the increasing noise in the
dynamics at the transition line results in a slowly decreasing
overlap $m_1$. We note that we always observe $m_3=(m_1)^2$ when
$\alpha_{{\rm ATNN}}=0$.

At zero temperature ($T=0$),
increasing $J$ implies decreasing the critical capacity. The
transition is always first order, except for $J=0$. The
main overlap $m_1$ at the transition line first increases with $J$, but
starts to decrease from $J=2.0$ onwards. At larger $J$, it starts
increasing  again. The overlap $m_3$, however,
always increases and becomes larger than $m_1$ for $J\geq4.2$.
The critical capacity for $J=1$ is equal to $0.3131$, which is higher
than  that of the fully connected {\sc atnn} ($\alpha_c=0.1839$)
\cite{BK99}.  This is consistent with the results obtained by comparing
the  asymmetric extremely
diluted with the fully connected Hopfield model \cite{AGS87,DGZ87}.

For non-zero temperature and infinite loading, the transition is
partially continuous as long as $J\in[0,1/3]$.
The larger $J$, the larger the temperature is where a
continuous transition occurs. As an example, we have drawn the value of the
overlaps at the critical capacity for $J=0.3$
(Fig.~\ref{figatnn:overlap}$a$) where the transition is continuous for
$T\geq0.88$.
When $J\geq1/3$, the transition is discontinuous for all temperature. In
Fig.~\ref{figatnn:overlap}$b$ and Fig.~\ref{figatnn:overlap}$c$,
we have drawn the overlaps at the critical capacity for $J=1$ and $J=3$.
The overlap $m_1$ exhibits a maximum at $T=0.32$ and $T=0.86$ respectively
while $m_3$ is always decreasing.

\section{Concluding remarks}
\label{secatnn:concl}

In this article, we have studied
the parallel dynamics of the asymmetric extremely diluted {\sc atnn}
with linked patterns at arbitrary temperature.
Because of the absence of correlations between the neurons, we have found
that the noise of the local field at all time steps is normally
distributed.
Hence, the dynamical equations for the order parameters are obtained
immediately. Furthermore, the dynamical capacity-temperature diagram is
discussed.

In the presence of the four-coupling term, the dynamics can
exhibit more noise without disturbing the retrieval process completely.
Moreover, the transition from the retrieval to the non-retrieval regime
becomes first order. This implies that the Hamming
distance becomes smaller, even at the transition line.
So in general, we can say that the four-coupling term enhances the
retrieval  quality of the network.

\begin{acknowledgement}
The authors are indebted to L.~Bianchi for some contributions at the
initial stages of this work and to P.~Koz\l owski for constructive
discussions. One of us (D.B.) thanks the Fund for Scientific
Research - Flanders  (Belgium) for financial support.
\end{acknowledgement}

redpajama_set_name: RedPajamaArXiv


SPRINGFIELD, Mass. (AP) — A luxurious Massachusetts resort has been sued by a lady with a nut allergy who landed within the hospital after being served a veggie burger containing cashews.
The Berkshire Eagle reviews that the swimsuit filed in federal courtroom in Springfield this week towards Canyon Ranch Wellness Resort in Lenox alleges negligence, breach of guarantee, breach of contract and intentional and negligent infliction of emotional misery. It seeks unspecified damages.
Kristin Chu Good, of New York Metropolis, says she and her mom paid $3,000 for a weekend on the resort in December 2017.
Good says she knowledgeable quite a few workers on the resort, together with her server, she was allergic to nuts and was assured there have been none in her meals.
A Canyon Ranch spokeswoman stated she couldn't touch upon pending litigation.
Get the newest breaking information despatched on to your cellphone. Obtain our free app.


Owners may feel like they owe their dog free-range of as much square-footage as possible, even when alone, in order to imitate the most "natural" condition. "Cage-free" is a popular concept. The modern American dog, however, lives in an extraordinarily complicated and unnatural condition. Maximizing freedom of movement is not always safe or stress-free. In our society a crate-trained dog gets to go more places and spend more time with her favorite people.
At home, a crate can provide the dog a safe place to wait out unwanted (by the dog) visitors. Visiting children can be especially stressful for dogs who are not used to quick movements and handling by strangers. In the car, crating can protect dogs in the event of a crash and keep them out of your hair (literally) while you drive.
Behaviors like barking, whining, chewing, aggression, fence-climbing and house-soiling develop and become habits when a dog is left unsupervised in a house or yard. If the dog must be deprived of the company of its "pack", a kennel or crate is a safer and more manageable area of responsibility, especially for dogs under a year old. Young dogs frequently require surgery from swallowing pieces of string, fabric, plastic, wood or metal while unsupervised. Many die before owners realize that a blocked intestine is causing lethal harm.
In order to get the dog to recognize how safe the crate is, you first have to get him into it by making it a rewarding place. Throw food into the back of the open crate every time you walk past it and give the dog his regular meals in the crate.
For the initial 30-50 treats, don't shut the door of the crate when the dog is in it. Get your dog to linger in the crate by throwing a second and third treat in the back while she's still collecting the first treat. If you have some communication skills already installed in your dog, you can suggest that she try lying down or waiting in the crate and praise and/or reward that behavior when it occurs. Practice swinging the door in to shut it, poke a few treats through the wire, and then open it again. Don't pet or praise on exiting the crate. You want the dog to notice that being in the crate is full of interest and rewards, while outside of the crate is ho-hum. Don't force the dog into the crate or block her exit.
Once the dog feels comfortable waiting a few minutes in the crate for additional treats, door open or shut, give her a favorite chew-food (rib bone, KONG or rawhide) and shut the door. Stay where she can see you if she's an anxious type. Open the crate door a little before the dog finishes with the bone. Repeat the next day, leaving the crate door shut for a little longer.
At any point if the dog whines or barks, give no sign of noticing. Stay nearby and wait for an opportunity to release the dog once it quiets. NEVER RELEASE A WHINING DOG, even if it takes hours for her to stop. Wait until 30 seconds after her last sound.
Avoid violating your dog's "safe area" by reaching into the crate to drag him out, letting children crawl in with him, or banging on the top. For training purposes, the crate should be located somewhere where you and the dog can interface with it regularly throughout the day, such as the living room.
If your training gets short circuited and you have to put your dog in the crate before he is completely desensitized and content there, expect your dog to vocalize long and hard before giving up. Being noisy has been his strategy since birth to get attention so he's not going to give it up easily. It's nice to be far away, possibly across town, when this happens. Never, ever release, cajole, or feed a barking dog. Delay any interaction with the dog until he is completely quiet for at least 15 seconds. Also be careful in the early stages that you don't throw a party she wants to go to while she's locked in there. Don't wait until after the doorbell rings to try to stuff her in.
Avoid the Walmart-type crate with clips on the sides to hold the top and bottom together (like the one on the right). These are made of more flexible plastic and I see a lot of these crates with cracks in the upper shell and missing clips. Screw-fastened crates or heavy-duty clipped crates are sturdier. If you start with a folding wire crate, cover the sides with a blanket for a more den-like feel.
Most dogs like car rides enough that they are happy to get in a crate in the car. In fact, that's one way to get your dog familiar with the crate: make it a condition of going on car-rides. However, if your dog is more car-phobic you will need to take the time to reward him for being in the crate, in the car. If you plan on shipping your dog by an airline, make sure you do lots of car-crate conditioning before the trip and invest in an airline-approved crate from the start.
Use a hard-sided crate for initial training. Once the dog is settling promptly and reliably in the crate, a folding canvas crate is super convenient for travel. I have 2 that I use all the time, one is a sturdy canvas if I'm leaving my dog on a porch for an hour or two and the other is a very thin pop up crate that I can flatten or open with one hand.
Skipping these steps is a sure way to make a crate-complainer. The dog has to be conditioned to recognize the crate as a supremely safe and rewarding place, so that as soon as he steps into that familiar space, the dopamine and happy thoughts will involuntarily start to flow.


text:
Barbus acuticeps är en fiskart som beskrevs av Matthes, 1959. Barbus acuticeps ingår i släktet Barbus och familjen karpfiskar. IUCN kategoriserar arten globalt som starkt hotad. Inga underarter finns listade.

Källor

Karpfiskar
acuticeps

redpajama_set_name: RedPajamaWikipedia


text:
Q: Homework: finding Big-Oh for code fragments To be up front with everyone, this is for a homework assignment.  I don't expect anyone to provide out and out answers for me, this is more to check that I'm understanding things correctly or to figure out what I'm doing wrong.
I've been given some fragments of code to determine what Big-Oh would be of them.  Each is dealing with for loops, however the last two that we were given are throwing me off a bit.  The first:
   sum = 0;
      for (i = 0; i < n; i++) //1
         for (j = 0; j < i * i; j++) //2
            for (k = 0; k < j; k++) //3
               sum++;

I think that Big-Oh of this would be O(n^4).  #1 will run n times, #2 will run n^2 times, and #3 will run n times, giving me n^4.  However, when I write this properly in C++ and give n values of 10, 100 and 1000 (per my assignment), n = 10 returns 7524 (good, less than 10,000) n = 100 returns a value of 975,002,490 while the upper bound would be 100,000,000.  Obviously, I'm off somewhere in my analysis of the loops, but I'm not quite sure where.  Not sure what n = 1000 will return, since my computer has been crunching away at it for a while and doesn't appear to be ready to give me an answer yet.
The second fragment is as follows:
   sum = 0;
      for (i = 0; i < n; i++) //1
         for (j = 0; j < i * i; j++) //2
            if (j % i == 0) //3
               for (k = 0; k < j; k++) //4
                  sum++;

I believe I can safely ignore the if statement since its runtime would be the running time of the test plus its contents, meaning I would again come up with O(n^4).

A: Well Im not a big O expert but I know for loops and some maths so I will try help you a bit.
When you consider your statement " #1 will run n times, #2 will run n^2 times, and #3 will run n times, giving me n^4" it is only partially correct.. Yes the numbers is almost correct if you run the loops separatly. But consider an example of n = 4... First #1 will run 4 times, but for each iteration of loop number #1 loops number #2 will run i*i times... so..
First when i = 0 #2 will run 0 times.. (j < 0*0)
Then when i = 1 #2 will run 1 time (j < 1*1)
Then when i = 2 #2 loop will run 4 times (j < 2*2)
and when i = 3 #2 will run 9 times  (j < 3*3)
so in total #2 will run 14 times. (0 + 1 + 4 + 9 ) and 4^4 is not 14. And this also escalates to the #3 loops.
As you said that you are not interested in a direct answer I hope this helps you understand the for loops a bit better.

redpajama_set_name: RedPajamaStackExchange


text:
SC Refuses Anticipatory Bail To Chidambaram, ED May Arrest Him
In a massive blow to former finance minister P Chidambaram, the Supreme Court on Thursday rejected anticipatory bail in the Enforcement Directorate case. Chidambaram won't be shown all the materials collected by the ED at this stage and the ED doesn't need to produce the transcripts of Chidambaram's questioning in the court, said the Supreme Court. Watch the full report.
Updated : 05 September 2019, 11:01 AM

redpajama_set_name: RedPajamaCommonCrawl


Further encourage activities by incorporating supplies into the kitchen. Keep pens, crayons, markers, paper, et cetera handy. If computers are a focus in your life then consider adding a small portable laptop computer to your kitchen and getting a wi-fi connection. Avoid the computer hutch as it usually faces away from the action and doesn't encourage interactivity. Also, if you have little ones with limited computer access and you're diligent enough to monitor their activity, letting them surf the net while you're hovering nearby is usually a win/win situation.
Take the focus off of food. It may feel a little weird at first, but try to think of your kitchen as something other than a food place. Remove food pictures and other items you have lying around that focus on eating. If you're going to have snacks out in the open, make them healthy ones. You don't want your family to hang out in the kitchen, only to give them weight problems, you want them to hang out there and feel comfortable not eating.
And finally, encourage people to be interested in what you're doing. Have cooking utensils (obviously not knives) in a place where little ones can get at them and feel like they're a part of the meal making process or in the clean up.
Overall, create a family-centric kitchen by giving everyone a comfortable place to sit and work or play. Encourage others to help with kitchen tasks, but don't make that the entire focus; bring in items that support other activities as well. Be creative in your decorating and redecorating so that every person is considered and feels welcome spending time together in the kitchen.


Adjunct professor of the American College, Curtis Cloke, RICP says there are 18 to 20 retirement risk factors that may need to be addressed when designing your retirement plan. It's a daunting task to design a retirement plan that covers every one of those items and that's why you need a retirement expert to assist you. Here are the top ten retirement risks.
Medical Health (Frailty): Medicare and supplement plans can help with healthcare costs, but catastrophic events could overwhelm your budget and your emotions.
Long Term Care: For most retirees it is an inevitable event that consumes assets in the later years of life that can leave you living off of Social Security only.
Financial Elder Abuse: Scams, unethical advisers and strangers prey upon unprotected seniors, but the vast amount of thefts are from family and friends.
Sequence of Returns: Withdrawing monthly income from your portfolio can be dangerous in a down market and can inadvertently quickly reduce your portfolio's size.
Inflation: Real inflation can rob the purchasing power of your retirement dollar for the commodities you need to live on in retirement.
Liquidity Risk: Life happens. Whether you need to pay deductibles for unforeseen auto, home and medical events, repairs or maintenance, you need cash at the ready.
Forced Retirement: Sometimes you're forced to retire earlier than you planned on by an employer, an injury or becoming a caregiver to a family member.
Loss of Spouse: When a spouse dies income may be reduced, taxes may increase and the loss of companionship can cause great personal hardship for the survivor.
Unexpected Financial Responsibility: Children can return home or suddenly you're raising your grandchildren after a divorce or death of your child.
Regulatory Risk: The government has, and more than likely will, change the tax code, other rules and regulations that can significantly impact your retirement plan.
These risks can devastate the financial lifestyle of retirees and leave their vision of the golden years in ruins. Defending against these risks is vital in order to insure, as much as is humanly possible, an enjoyable retirement.


Splash on over to the city's floating food truck.
The food is "very straighforward," Schwartzman said. They're selling $6 dogs "just like your downtown street-meat-style hot dogs," including pork and Kosher beef and veggie dogs and bratwurst, served on Franz buns. There's "every kind of classic condiment you can think of, including the requisite cream cheese and sriracha." Rice is the grill chef and "likes to get a nice caramelization and char" on the dogs, while Schwartzman handles toppings. Drinks are $2 standard sodas; think Coke, Fresca, root beer.
With those resumes, wouldn't we expect them to be cooking mini-Kurobuta-Mangalitsa "haute dogs" on hand-kneaded wild-caught-yeast buns, or something?
I had thought that Summer Dog was the first "floating food truck" in town, but Joanna Iverson wrote to alert me that she and her brother had operated "Coqui Cabana" on Lake Union and Lake Washington for three years, enjoying "the best customers and a fabulous time" before "mediocre summers and unobtainable liquor permits" led them to seek other adventures. (It took the health department two years to figure out how to permit them, she said — they wish Summer Dog well and are glad to have paved the way.) My apologies to Joanna — clearly I need to get out on the water more myself.
Corrected Aug. 21 to add mention of Coqui Cabana and remove reference to Summer Dog as the city's first floating food truck.


text:
Paul Merson makes prediction about Chelsea FC this season
Sky Sports pundit Paul Merson is backing Chelsea FC to challenge for the title this season
Friday 11 September 2020, 08:00 UK
Arsenal legend Paul Merson (Photo: Sky Sports)
Paul Merson believes Chelsea FC can challenge for the Premier League title this season thanks to Frank Lampard's shrewd signings in the 2020 summer transfer window.
The Blues legend led Chelsea FC to a fourth-placed finish in the Premier League last term after Lampard took over the reins from Maurizio Sarri last summer.
Lampard's side struggled for consistency throughout his debut campaign in charge of the west London outfit, conceding more goals than any other team in the top 10.
The Chelsea FC manager has bolstered his attacking options with the signing of Ajax winger Hakim Ziyech, RB Leipzig striker Timo Werner and Bayer Leverkusen playmaker Kai Havertz in deals worth in excess of £150m.
Lampard has also attempted to address the west London side's defensive problems by signing experienced Paris Saint-Germain defender Thiago Silva and Leicester City left-back Ben Chilwell.
The Blues snapped up Nice defender Malang Sarr on a free transfer, while Chelsea FC have one eye on the future with the addition of Xavier Mbuyamba from FC Barcelona.
Chelsea FC finished 33 points adrift of Premier League champions Liverpool FC last season to highlight the gap between the two sides.
However, Sky Sports pundit Merson believes Chelsea FC can challenge Liverpool FC and Manchester City for the Premier League title this season.
"Chelsea have bought brilliantly," Merson told Sky Sports.
"Ben Chilwell is a great signing. Yes, Marcos Alonso delivered goals, but Chelsea were weak down the left last season and needed a full-back to defend.
"Thiago Silva looks a shrewd piece of business, he a proper centre-half. If Chelsea can get a good year out of him, they have a chance.
"People highlight the fact that he's 35-years-old, but football is about now, not four or five years down the line.
"Managers haven't got four or five years, there is no point in them going out and buying a player for the future.
"If they do that, they will be watching that player from the TV after getting the sack!"
Chelsea FC missed out on their first trophy under Lampard last season after a 2-1 defeat by Arsenal in the FA Cup final.
The Blues will start the 2020-21 Premier League season with a trip to Brighton and Hove Albion at the Amex Stadium on Monday night.
Michael Owen states his prediction for Brighton v Chelsea FC
Paul Merson sends warning to Liverpool FC about potential weakness


text:
Tax credit task force postpones hearing after Norcross sues
By Mike CataliniAssociated Press
The judge presiding over the lawsuit asked that Tuesday's hearing and the release of a report on tax credits be delayed, and the panel agreed, according to a statement released by the task force.
TRENTON — A New Jersey task force that raised questions about how businesses tied to Democratic political powerbroker George Norcross got millions in tax incentives said Friday that it's delaying its next hearing in response to his lawsuit.
Norcross is suing Democratic Gov. Phil Murphy over the task force he empaneled in January, arguing that it unlawfully used subpoena powers and unfairly singled out firms tied to him. In a court document filed on Thursday Norcross wrote that the task force was damaging his reputation and "inflicting irreparable harm" upon him and his co-plaintiffs.
Norcross is an executive at insurance brokerage Conner Strong & Buckelew, of Evesham, and chairs the board at Cooper University Health Care. Those organizations are also plaintiffs in the suit against Murphy, along with the Michaels Organization and law firm Parker McCay, of Mount Laurel. Norcross is also a former Camden County Democratic chairman, a noted fundraiser for the party, as well as a friend of Senate President Steve Sweeney, D-3rd of West Deptford, and brother of U.S. Rep. Donald Norcross, D-1st of Camden.
Friday's postponement is just the latest in a high-tension, politically fraught fight over tax credits.
Murphy pledged earlier this year to overhaul the state's current crop of tax incentives, which were enacted under Republican Chris Christie and expire July 1. A key rationale for enacting a new program was a state comptroller report that the Economic Development Authority, which oversees the credits, couldn't verify whether all obligations had been met for credits to be awarded. Murphy is instead seeking a capped tax credit program, as opposed to the uncapped one enacted under his predecessor.
Murphy's push chafed lawmakers, many of whom had either voted for or helped write the expiring program, but the tensions worsened when at a May meeting in Newark, the task force publicized documents questioning whether Norcross-linked firms met requirements to get credits.
The task force, for example, presented emails showing that Cooper said it had initially no intention of leaving New Jersey but then later said it was considering a move to Philadelphia, which the EDA cited as a factor in awarding the credits. Supporters of Norcross have said that it wasn't necessary under the law to show that a company was considering moving out of state if a firm was going to Camden.
Cooper received $40 million over 10 years, with about $13 million already paid out.
There have been other developments, though, that raised questions, including reports by The New York Times and WNYC and ProPublica.
The Times reported that a lobbyist with Parker McCay helped write the legislation. WNYC and ProPublica reported that Camden got about four times as many tax breaks as other cities, among other findings.
The task force also made an unspecified criminal referral.
Late last month, Norcross filed suit against Murphy in Superior Court in Mercer County. He also did critical interviews in the media. In one he compared Murphy to the King of England, prompting the first-term governor to say that was "very hard" for someone with Irish roots to hear.
A hearing in the lawsuit is set for June 17. A new date for the task force meeting was not specified.


text:
Catastrophic Collapse of the Larval Trematode Component Community in Charlie's Pond (North Carolina)
Russell, Collin, Casson, Tina, Sump, Courtney, Luth, Kyle, Zimmermann, Michael, Negovetich, Nicholas, Esch, Gerald
The Journal of parasitology 2015 v.101 no.1 pp. 116-120
Echinoparyphium, Halipegus, Helisoma, Physa, Plagiorchis, Posthodiplostomum, cercariae, larvae, parasites, snails, species diversity, summer, vegetation, North Carolina
In 1984, work on the parasite population and community ecology in the pulmonate snail, Helisoma anceps, was initiated in Charlie's Pond (North Carolina). Similar research on Physa gyrina was started in 1986. When study in the pond began in 1984, 8 species of larval trematodes were being shed from Hel. anceps. By far, the dominant species was Halipegus occidualis, with prevalences generally ∼60%, except during midsummer, when older snails were dying. For the other 7 trematode species being shed, prevalences were consistently less than 4%. By 2006, 18 species had been identified in Hel. anceps at one time or another. In 1986, Hal. eccentricus was discovered in P. gyrina, with a prevalence of ∼49%. Through 2006, 7 trematodes were found to be shedding cercariae from P. gyrina. Halipegus eccentricus disappeared from the pond in 1998. From March through November of 2012 and 2013, 1,292 Hel. anceps and 716 P. gyrina were collected, using collection protocols that were identical to those used from 1984 through 2006. In 2012, 5 trematode species, including Hal. occidualis, were present in Hel. anceps at one time or another. During the last part of the 2012 collecting season cercariae of just 2 species were being shed from Hel. anceps (and 1 from P. gyrina). In 2013, only cercariae of Haematoloechus longiplexus and Uvulifer ambloplitis were observed from Hel. anceps. The latter species was lost by 2014, and an echinostome was present (2.1%); a single snail was infected with Haem. longiplexus. Four species were being shed from P. gyrina, i.e., Echinoparyphium sp. (7.9%), Glypthelmins sp. (1.5%), Plagiorchis sp. (4.9%), and Posthodiplostomum sp. (7.4%). Rarefaction curves were generated for Hel. anceps shedding in 1984, 1988, 1989, 2002, 2006, and August of 2014. The data clearly indicate that species diversity was constantly declining over the 31-yr period. We did not include P. gyrina in the analysis since data for this snail species were not acquired until 1991–1992. At present, we have no definitive explanation for the decrease in diversity, although circumstantial evidence suggests that it might be related to periodic declines in water level that negatively affected the colonization and maintenance of emergent vegetation within the pond.
http://dx.doi.org/10.1645%2F14-549.1
DOI: 10.1645/14-549.1
Find in a library http://dx.doi.org/10.1645%2F14-549.1 Download RIS File Export to Zotero


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text:
using System;
using System.Globalization;
using System.Windows.Data;
using tweetz5.Utilities.System;

namespace tweetz5.Utilities
{
    public class Win7FontFamilyConverter : IValueConverter
    {
        public object Convert(object value, Type targetType, object parameter, CultureInfo culture)
        {
            return (BuildInfo.IsWindows8OrNewer) ? "Segoe UI Symbol" : "FontAwesome";
        }

        public object ConvertBack(object value, Type targetType, object parameter, CultureInfo culture)
        {
            throw new NotImplementedException();
        }
    }
}

redpajama_set_name: RedPajamaGithub


text:
A Look Inside Copper Branch's First Atlantic Canadian Location In Dieppe
by Huddle Staff
From left to right: Dr. Valerie Maher-Laporte, Rene Couture, and Carolyn Ross. Image: Submitted
DIEPPE – Montreal-based fast-casual vegan restaurant Copper Branch opened its first Atlantic Canadian location on 200 Champlain St. in Dieppe last week.
"We tried the food in Montreal and couldn't believe how good it was or that it was vegan," says franchisee Carolyn Ross in a press release. "That's when we started looking into opening a franchise in New Brunswick because we knew if we liked it, others would too."
Dr. Valerie Maher-Laporte and Rene Couture are her co-franchisees.
"What attracted us to Copper Branch was, of course, the food," Couture said. "But also a unique opportunity to expose people to good tasting, high quality, plant-based eating."
The menu will be the same as other Copper Branch locations, which includes power bowls, sandwiches, burgers, chilli and soups, desserts, smoothies, and organic teas and coffees, among others. It serves an entirely plant-based and vegan food that isn't processed. The average price of meals ranges between $13 to $15, including main items like a $9 burger or a $10 bowl, a side and a beverage.
RELATED: Vegan Restaurant Chain Opening Dieppe Location
The 1900 square-foot restaurant in Dieppe is the first of several stores planned for the region.
Twin Oaks Management, the Moncton-based company hired to develop the Atlantic Canada franchises, are expected to open locations in Halifax, Fredericton, Saint John, and St. John's in the coming months.
Copper Branch currently has more than 45 locations across Canada and is setting itself up in the U.S. and Europe.
Here's a look inside the Dieppe restaurant:
Images: Submitted
Copper Branch Dieppe Vegan
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text:
Q: Categories Fibered in Groupoids and Yoneda My question refers to an article of Aaron Mazel-Gee about fibered categories in grupoids where the author introduces in a quite strange way a new category $\{X_0/X_1\}$ providing a functor $p: \{X_0/X_1\} \to  C$ making $\{X_0/X_1\}$ into a category fibered in groupoids: https://etale.site/writing/stax-seminar-talk.pdf
We have following construction:
We start with a fixed category $C$ and consider the pair $(X_0,X_1)$ of two objects $X_1, X_1 \in C$ satisfying identities between maps $s, t , \epsilon, i $ and $m$ as described in the article. Here the excerpt:

Then comes the cruical point:
We take a $U \in C$ and define a category $\{X_0(U)/X_1(U)\}$.
The objects are defined via $ob(\{X_0(U)/X_1(U)\}):= X_0(U)$.
And exactly this is the problem: What is exactly $X_0(U)$? Especially how $X_0$ "acts" on $U \in C$.
Some days ago I asked a similar question and got two answers from @Victoria M and @Kevin Carlson. But up to now I'm quite not sure if I understood the explanations correctly. Here the link: Fibered Categories in Groupoids
Now I would like to try to explain how I understood it and I would be glad if anybody could look thought my interpretation attempts and take corrections if there is some point which I totally misunderstood:
In the setting as above the $X_i \in C$ themselves form a groupoid $(X_0,X_1)$ by definition iff they satisfy the identities between $s, t, \epsilon, i ,m$ (in sense of "internal groupoid").
For arbitrary $U \in C$ the only meaning for $X_i(U)$ seems logically to me comes with a "double interpretation" of the $X_i$:
as roughly elements of $C$ and as functors $X_i: C \to Grp$ given formally concretely via the $Hom$ functor $C(-, X_i)$.
Seems reasonable in light of Yoneda-lemma or more precisely Yoneda embedding. Then the expresion $X_0(U)$ is identified with $C(U, X_0)$. Seems plausible.
But is this interpretation of the category $X_0/X_1$ and $X_0(U)$ exacly that what the author meant or a failable attemp to find a interpretation?


text:
Return to Sports Offered
Turf Flag Football *NEW*
Sport Info
*NEW* for Fall 2019 we've added Outdoor Flag Football!
Down, set, HUT! Come try KSSC Flag Football! Making passes, catching balls, scoring touchdowns!
Flag Football is a popular twist on the grid iron game. Played 7-on-7, this league provides football that is fun and open to everyone.
Come on out and catch the pigskin!
Fall 2019 Details:
Tuesday: Starts Tuesday, September 10 and ends on Tuesday, October 15.
# of Weeks
6 weeks (4 regular season games + 2 playoff games).
Estimated Game Times
Rotating Start times of 6:00pm and 7:30pm.
Game are 90 minutes.
Please note: Every effort is made to equalize the start times across the league.
Registration Options & Price
Team registration: $385 + HST
After checkout, send your teammates roster invites through the website (under "My Team" player list) so they can accept the waiver and access the schedule and standings once it is posted.
Individual registration: $55 + HST.
You will be placed on a roster of individuals by end of day Wednesday, September 4. For ease of communication with our office, teams must select a captain and co-captain on our website to represent your individuals team. Click here to learn more about Individual teams.
Bye Dates
There are no bye dates.
Individual Teams and Equipment
Individual registrants: After Wednesday, September 4, we ask individual players to contact their teammates through our website (you can log in, click on "My Team", then "Player List") to confirm the following:
Team Captains & Co-Captain
Jersey Colour
Who will place the deposit for the required equipment.
Once confirmed, please have the team captain email the above information to info@kssc.ca, and have the individual placing the deposit on equipment to call our office (613-544-8326 x 122) to ensure your equipment will be ready for your first game.
See "Sport Info" tab for equipment requirements for your league.
Equipment, Newsletter & Member Key Tags: Will be provided to you at your first game by the onsite KSSC representative. Only the teams who have placed the deposit will receive the equipment.
Please do not attend the Individual meet & greet on September 12, which is for indoor sport registrants.
Rosters & Schedules
Individual team rosters and schedules will be posted online on Wednesday, September 4.
Ready to Play?? Great! Decide on your night of the week & skill level from the grid below!
Looking to play with a friend or two? Don't worry! You'll be telling us after you've registered and paid!
**Click here for our Refund Policy
Skill Level Sun Mon Tue Wed Thu Fri Sat
Intermediate/ Recreational :
close Intermediate/ Recreational: Players who have some experience at an organized level of the sport. Players should be average to above average in all aspects of the game. The percentage of the team suggested to fit this description is 65%
Add Team
to Cart : $385.00
Add Individual
to Cart : $55.00
- Click the skill description for more info!
- Prices listed are before taxes
- Review the Refund Policy
- After the posted registration deadline, late fees will apply.
Is the class/league/night/skill division you are interested in sold out?
Please send an email with your name, phone number and desired sport to info@kssc.ca and we will add you to the wait list! We will contact you if/when a spot opens up.
What you need to know about Flag Football!
# of People on Court
7 players (minimum 2 males and 2 females).
Suggested Roster
9-12 players.
Teams are required to have their own NFL regulation size ball, cones, and flag belts.
If you do not want to bring your own, a Flag Football kit (Football + flags) is available to rent from KSSC. A $75 refundable deposit is required and payable online through the website (in shopping cart). Equipment will be provided to you at your first game.
Teams should bring both light and dark coloured shirts to each game.
Additional League Information
All teams receive:
KSSC key tag which will get your team discounts from KSSC partners. Click here for details.
Championship winning teams receive:
Coveted KSSC Champion Team T-Shirts!
Download the rules here: KSSC_Flag_Football_Rules.pdf
Flag_Football_Diagram.pdf
Sport & Social Club General Rules
Score & Spirit Point Reporting
Game Scores (account for 75% of total points): Team captains are responsible for reporting the scores after your game by logging into your player profile and clicking on 'My Team' tab and selecting 'Report Score/Spirit Points'. Teams have a 48 hour window to report scores after the completion of the game. Please be timely with your score reporting so league standings can remain updated for playoff positioning.
Spirit Points (account for 25% of total points): Spirit points are awarded to a team from their opponent after each game to encourage sportsmanship, honesty, integrity and fair play. For more information and how to properly award spirit points, please see our section 'All About Spirit Points'.
Standings/Schedules
Players can view league standings & schedules by logging into your player profile and clicking on 'Standings/Schedule'.
Player Eligibility
All players must be added to the team roster by the team captain. This process confirms that all players have electronically agreed (checked the box) to our policies and online waiver.
Substitute players are allowed, however they must be added to the roster (check the online waiver). Adding a substitute player from another team in the same league is allowed, however, regular/consistent use of a substitute player in the same league is considered unsportsmanlike and not encouraged.
For a player to be eligible for a playoff game, the following criteria must be met or the team will default the game:
Be on the SSC online team roster.
Play a minimum of two regular season games in a 6-10 week season, or three regular season games in an 11-14 week season.
Play for only one team per league/pool in playoff games. If a player plays for two teams, the second game will be defaulted.
A default will occur if a team cannot field a squad by 15 minutes after the official start time. If a team does not meet the standard eligibility requirements, team captains must confirm the outcome prior to starting the game. Captains may agree to waive the rules regarding minimum players. IF IT IS AGREED THAT THE GAME COUNTS, IT COUNTS! In the event there is a default dispute and the game was played, the SSC ruling is that the game counts.
In the event of inclement weather, follow your sport specific foul weather policy below. To view our general foul weather policy click here.
Rough Play & Player Conduct
It is recognized that incidental contact between players is inevitable – however, all players should go out of their way to avoid creating unsafe play.
Any unsportsmanlike conduct may result in immediate expulsion from the league. This includes, physical or rough play, verbal abuse, damage to facility property and/or loss of facility permit. Fighting will result in immediate expulsion from the league. To view our Unsportsmanlike Conduct policy click here.
Drinking alcoholic beverages, use of drugs and smoking at your game site before, during, or after your game is strictly prohibited. Offenders will be asked to leave the league without refund. No Exceptions.
Game Coordinator (GC) On-site SSC Staff
A GC presence is dependent on sport, season, and/or facility locations. They are not referees, as all games are self-officiated. They are on-site to be a neutral supporter of both teams, clarify rules, manage equipment, start/stop games, and to inform players of league news.
Game Coordinators may stop a game before the full time has expired due to overly aggressive play, persistent unsportsmanlike conduct or a general violation of the rules of the game.
SSC Official Flag Football Rules – Coed 7-on-7
Flag football is a version of Canadian football where the basic rules of the game are similar to those of the mainstream game (often called "tackle football" for contrast), but instead of tackling players to the ground, the defensive team must remove a flag or flag belt from the ball carrier ("deflagging") to end a down.
Game Length & Foul Weather Guidelines
Games are 90 minutes in length including a 5 minute halftime midway through the game (unless otherwise indicated in your schedule).
Games start and end according to your online SSC schedule.
If games start late, games must finish at the scheduled time (e.g. 6:15pm-7:30pm).
Games are played rain or shine.
If a game is stopped due to lightning, games played until half time will constitute a complete game.
If one team shows up during foul weather to play and the other team is missing, or if one team leaves mid-game and there is an opportunity to continue play - it is an automatic win for the present team.
Equipment (Mandatory)
Teams are required to bring an NFL size Football, six (6) pylons, and a set of ten (10) flag belts (with 2 flags each) for every game.
This equipment is available to rent through SSC. A $75 refundable deposit is required for the equipment, payable through online registration.
Teams should bring both light & dark coloured t-shirts to help distinguish opponents.
Please wear shorts/pants with NO pockets. This will reduce finger injuries when trying to grab the flags.
Only flags with Velcro attachments to the belt are permitted.
Metal cleats are not allowed.
Players on Field and Gender Ratio
Teams are comprised of 7 players on the field.
Teams must play with a minimum of 2 males and 2 females on the field at all times.
A team can play with a minimum of 5 people, as long as the gender requirements are met.
Captains may agree to waive the rules regarding minimum players and gender ratio before the game starts.
Field & Player Set-Up
Team captains should meet before the start of the game to set-up the field with the required pylons.
Please check the online SSC schedule for a specific map of the facility and field orientation (when available).
To view a diagram of a flag football field set-up, click on the pdf document in the rules section.
The field set-up includes:
Total field length (60 paces)
Between the end zones (50 paces)
End zones (5 paces)
Total field width (35 paces)
A pace is approximately 3 heel-to-toe steps.
Flags should be placed on the hips of each player at the outset of each play. The flag must be on top of all clothing and cannot be folded over such that the Velcro attachment is on the inside or hidden.
To start the game, teams can decide who gets 'first ball' by either a coin toss or playing a game of rock, paper-scissors.
Teams should switch sides at half time.
Teams are responsible for keeping score & time.
A game can end in a tie during the regular season.
A point is scored when a player catches any legal pass or runs the ball into the defensive end zone prior to having one of their flags stripped.
To score a player must step over the line in the end zone (it is not enough to have the "plain of the end zone" broken by the ball).
Teams receive one (1) point for each touchdown.
There are no conversions.
Game Start & General Rules
The kicking team will kick-off from their own end zone line. All players on the team must line-up behind the kicker and can only start to run downfield once the ball has been kicked. If the ball is kicked out of bounds, the offensive team will start their drive at the spot where the ball left the playing area – there is not an option to ask for a re-kick.
From the time the ball is placed on the line of scrimmage, the offense has 30 "steamboats" to start the next play. Running down the clock with an unnecessarily long huddle is not an acceptable strategy.
If a defending team sacks the quarterback (or any offensive player with the ball) in the offensive end zone, the ball is turned over at midfield to the defending team.
If an interception occurs in the end-zone and the player is flagged down, a touchback will occur, and the intercepting team will gain possession on the 10-yard line.
If the ball is kicked through the end zone on either a punt or kick-off (or kicked into the end zone and the receiving team elects not to run the ball out by letting the ball go), the offensive team will start their drive 10 paces out from their end zone, in the centre of the field. If the receiving team elects to catch the ball in the end zone (or runs back into the end zone after catching the ball), the receiver is in play and runs the risk of being tackled in his/her own end zone.
Teams may call a one (1) minute time-out per half if needed except during the last 10 minutes of play.
Ending the Half or Game - With three minutes to go in the half (game), there are 5 plays left in the half (game). A kick-off after a touchdown is not considered a play.
Offense, Quarterback and Receiving
The offensive team has four (4) downs to cover the entire field. If the offensive team fails to score on the 4th down, the ball is turned over and the new offensive team starts their drive from the position where the last play ended.
The offensive team may punt on the 4th down, and does not need to notify the defense of their intentions to do so.
The Quarterback may only run the football past the line of scrimmage when/if any defensive player crosses the line of scrimmage at the end of the 5 "steamboats". If a defensive player does not cross the line of scrimmage, the Quarterback cannot run the ball.
To start an offensive play, the ball must be snapped by the offensive Center, from the point of scrimmage to the Quarterback. There is no minimal distance required by the Quarterback who can be either up close to the Center or in a shot-gun formation. The Quarterback cannot self-snap.
Spinning - An offensive player CAN turn their bodies from side to side, but cannot spin 360 degrees. This prevents defensive players from injuring their fingers. If a player spins, the ball is dead at the point where the spin occurred.
Offensive players may not block or otherwise obstruct any defensive players.
Offensive players cannot protect/cover/hide/block his/her flag. If the person with the ball blocks the defenders hand from grabbing their flag, the play is dead where the block occurred.
An offensive player can dive or jump to catch a ball, but once in possession he/she cannot leave their feet at any time. This includes all forms of jumping and diving. If the ball carrier breaks this rule, the play is dead at the point where the player stood before the infraction.
If a flag inadvertently falls off the ball carrier, or if a player attempts to grab a flag and there is not one on the hip of the offensive player, the play is stopped at that location.
First point of contact: A receiver is determined to be "in" or "out" based on their first point of contact with the ground. If a player lands first with one foot in-bounds, and then the other foot touches down out-of-bounds, it IS a legal catch, but the play ends where they touched the out of bounds line. If a player catches the ball, but is straddling or lands straddling the sideline, it is NOT a catch. Only a one foot landing is needed - as long as that foot touches down in-bounds.
The defense must loudly count five (5) "steamboats" before rushing the quarterback.
While counting, the defense must line up at or behind the line of scrimmage.
Steamboats should be counted as follows: "one...steam...boat".
Once the ball has come in contact with a 2nd offensive player (Quarterback hand-off or throw to receiver), the defending players can cross over the line of scrimmage before the end of the 5 "steamboats" and engage with the offensive players.
A defender may not step in front of the ball carrier or block a running lane if it has the potential to create an unsafe play. Likewise an offensive player should not run with their head down, in an attempt to run through the defenders. In other words, incidental contact is inevitable, but players should not be run over. Please use your best judgment.
Dead Play
If a player carrying the ball slips/falls and one knee touches the ground, the play is dead and the defense does not have to remove a flag for the play to stop. Please observe this rules carefully as it helps to promote safer play.
If the football touches the ground for any reason (kick-offs, fumbles, handoffs, etc) the ball is dead and the play is over. The next play is started at the spot where the ball hit the ground.
Violations & Making Calls
The offending player should call their own infractions, however any players involved with the infraction can also make a call.
Players not on the field at the time of any incident cannot make a call at any time.
Fouls (including picks) that are called by the offence or defence will lead to a re-down (the play starting over from the line of scrimmage). Once a foul is called, the play must stop and the play is started over. If the offence/defence is fouled, they can choose not to call a foul if it is an advantage to do so. Example - A receiver is fouled as they catch the ball and continues to run the ball in for a touchdown.
All games are self-refereed. Disputes about a possible infraction are to be discussed amongst the people involved in the play. If an agreement cannot be reached, simply redo the down. Please play safely and with good spirit.
Playoff games should be 80 minutes in length in anticipation of needing the extra time to settle a tie.
A game can end in a tie during the regular season. In the playoffs, if regulation time expires and the score is tied, the game continues until a team has scored to break the tie.
Team Playoff Position: Ties in the standings will be broken first on head-to-head play. If there are more than 2 teams that are tied, all the teams must have played each other in order for the results to go to head-to-head. Otherwise, least points against, then +/-, then most points for will determine the placement in that order.
The SSC office will update the playoff schedule once all scores have been submitted and after the last regular season game. Please do not assume the time/location of your playoff game until team names have been posted into the schedule.
Remember… Always have fun!
All games will be played within 20KM of the downtown core.
KSSC Flag Football will be played at either of the following locations. Once confirm, this page will be updated.
Invista Centre - Caraco Field
Machin Turf Field


text:
from setuptools import setup

setup(
    name="nycodex", version="0.0.0", author="ADI Foundry", packages=["nycodex"]
)


text:
enum WakeReason
{
	// Indicates that another thread has requested that the paging thread change
	// states, such as shutting down to exit the process.
	EWR_ChangeStatus,

	// Indicates that the state of one or more resources has changed, and the
	// worker thread should reprioritize the resources and perform more paging work.
	EWR_Submission,

	// Indicates that the graphics kernel has changed this process's memory budget,
	// and the worker thread may need to react accordingly. If the budget has
	// increased, the worker thread may retry failed paging operations (such as
	// prefetching) that failed because the operaiton would bring the process
	// over budget. If the budget has decreased, the paging thread must trim
	// resources to remain under the budget.
	EWR_BudgetNotification,

	_EWR_COUNT
};

//
// The current status of the worker thread.
//
enum WorkerThreadStatus
{
	EWTS_Suspended,
	EWTS_Running,
	EWTS_Shutdown,

	_EWTS_COUNT
};

//
// The paging worker thread is the powerhouse behind all paging and texture streaming
// for the sample.
//
// The worker thread's primary goal is to stream texture data for the rendering pipeline
// asynchronously, and prioritize video memory based on the new budgetting information
// present in DXGI.
//
class PagingWorkerThread
{
private:
	friend class DX12Framework;

	DX12Framework* m_pFramework;

	WorkerThreadStatus m_CurrentStatus;
	WorkerThreadStatus m_RequestedStatus;

	//
	// Thread management
	//
	HANDLE m_hThread;
	HANDLE m_hWakeEvents[_EWR_COUNT];
	HANDLE m_hStatusChangeEvent;
	DWORD m_BudgetNotificationCookie;

	// Lock for accessing the prioritization list head, which is accessed by both
	// the rendering and paging threads.
	CRITICAL_SECTION m_PrioritizationListLock;

	// A list of unprioritized resources. A resource must be prioritized before
	// any paging operations can occur, so that the paging thread knows how to process
	// the resource.
	LIST_ENTRY m_PrioritizationListHead;

	// An array of priority-ordered linked list heads. The worker thread will process
	// resources in these arrays in strict order.
	LIST_ENTRY m_PriorityQueues[_ERP_COUNT];

private:
	PagingWorkerThread(DX12Framework* pFramework);
	~PagingWorkerThread();

	HRESULT Init();

	void Flush();
	void DiscardPendingWork();
	DWORD Run();

	void EnqueueResource(Resource* pResource);
	void ReprioritizeResources();
	void PrioritizeResource(Resource* pResource);
	Resource* SelectResource();

	void ProcessStatusChangeRequest();
	void ProcessSubmission(bool* pMoreWork);
	void ProcessBudgetChangeNotification();

	void SetStatus(WorkerThreadStatus Status);

	static DWORD CALLBACK ThreadEntry(void* pArg);
};

//
// A paging frame does not have any special state.
//
struct PagingFrame : Frame
{
};

//
// The paging context is a specialization of the Context object that creates a
// unique D3D12 command queue and set of frames for paging operations. The command
// queue is created as a copy command queue, which can map to paging engines on
// the graphics hardware. In addition to the scheduling granularity offered by
// the graphics kernel scheduler, being mapped to a hardware paging engine allows
// the paging operations to run completely in parallel with 3D graphics work
// submitted on the 3D engines.
//
class PagingContext : public Context
{
public:
	PagingContext(DX12Framework* pFramework);
	~PagingContext();

	HRESULT CreateDeviceDependentState();
	void DestroyDeviceDependentState();

	inline PagingFrame* GetCurrentFrame() const
	{
		return static_cast<PagingFrame*>(m_pCurrentFrame);
	}
};


alexallright – Page 2 – All right, let's automate something.
This tutorial covers animation and rigging tools from "Rig Tools" window.
01:15 – Bake to anim asset.
03:54 – Bake to rig.
07:15 – Root motion animation.
11:42 – Update from source.
17:25 – Isolate selected controllers.
01:03 – Face rig data.
03:16 – Face table controller.
09:30 – Custom controllers for face.
10:20 – Post parent controllers.
10:46 – !!!!ATTENTION!!!! you need to set controller GROUPS as CHILD controllers instead of controllers itself!!!!
00:42 – Create animation blueprint.
I'm very happy to announce that Allright Rig 2.0 has been released on Unreal Engine Marketplace! Thank you to Epic Games, my Early Access clients and everyone who supported me and encouraged me throughout this entire process! Special thank to Egor Tomskiy, Ilgar Lunin, Kirill Tokarev, Lina Halper, Coverop, Niko Skipz, Michael Ricks and my wonderful wife Jessie !
Added: Bake all anim instance (morph target and material) curves to anim asset.
Added: "Simplify Curve" filter – removes redundant keys from curve depending on tolerance value.
Added: Update all sequencer subsequence tracks during baking animation to anim asset.
Added: "OnUpdateRig" event for RigModular class. Runs right after the rig was updated (runs during baking process as well).
Added: "AddCurveValue" function – lets you set morph or material values, that can be updated and baked in "ModularRig" class.
Added: Refresh presets list after reopening "RigTools" window.
Added: Optimize (simplify and remove static) float curves after baking to anim asset.
Fixed: Bake morph target animation to anim asset in UE 4.20.
Fixed: Duplicated "Select" buttons in "Anim Tools" window.
Allright Rig Example Project Released!


text:
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