text:
\section{Introduction}
The Yukawa pair potential has been used to model a wide variety of different phenomena in physics~\cite{Rowlinson1989}. Named after Hideki Yukawa who used this potential in his meson theory~\cite{Yukawa1935}, Debye and H{\"u}ckel~\cite{Debye1923} had in fact used it earlier to describe the interactions between ions in solutions. The Yukawa pair potential, which is also referred to as the screened Coulomb potential, has the form

\begin{equation}\label{eq:y_debyuehuckel}
  \upsilon(r) = \dfrac{Q^2}{r} \,\, \exp\left(-r/\lambda\right)\,.
\end{equation}
Here $Q$ is the particle charge in the Gaussian unit system and $\lambda$ the so-called screening length. Although Debye-H{\"u}ckel theory was devised for describing the behavior of dilute ionic solutions, the Yukawa potential has proven useful also in the description of charge carriers that are much larger than those of the surrounding medium. This is the case for instance in suspensions of charge-stabilized colloids or in dusty plasmas, compare, e.g. the DLVO theory~\cite{Derjaguin1941, VerweyOverbeek} in which the interaction between the surfaces of two colloids is described by a potential of the Yukawa form. The colloid particles are often modeled with a potential that adds a hard-core repulsion, but the low-temperature part of the phase diagram of this ``hard-core'' Yukawa potential can be mapped onto the phase diagram of the Yukawa pair potential~\cite{Hynninen2003}.

Besides electrons and ions, dusty plasmas contain small solid particles that are charged. In dusty plasmas the distance between the solid particles is usually large compared to the size of the particles, and their interaction can therefore be modeled using the (point) Yukawa potential of Eq. (\ref{eq:y_debyuehuckel}). A more involved potential consisting of a sum of Yukawa terms is sometimes used to capture phenomena like plasma production and loss balance~\cite{Khrapak2010}. The physics of dusty plasmas is not only of interest for industrial applications where such plasmas are formed, but also in astrophysics for the understanding of stellar materials and planet formation~\cite{Fortov2005, Morfill2009}.

In 1986 it was found that colloids in suspension can form crystal lattices~\cite{Pusey1986} and it was predicted that this should also be possible in dusty plasmas~\cite{Ikezi1986}. This created a renewed interest in the phase diagram of the Yukawa system~\cite{Robbins1988, Meijer1991, Farouki1992}. It was later found in experiments that plasma crystals indeed do exist~\cite{chu1994, Thomas1994}. If $\rho$ is the number density of particles, in the field of dusty plasmas the phase diagram is usually presented in terms of the following two dimensionless parameters ~\cite{Dzhumagulova2013, Yazdi2014}: the screening parameter
\begin{equation}\label{scr}
\kappa\equiv\frac{\rho^{-1/3}}{\lambda}
\end{equation}
and the coupling parameter
\begin{equation}\label{coup}
\Gamma\equiv \frac{Q^2\,\rho^{1/3}}{k_BT}\,.
\end{equation}
Physically, the screening parameter is much larger than unity whenever the screening length is much smaller than the average interparticle distance -- this characterizes the part of the thermodynamic phase diagram where the exponential damping term dominates over the Coulomb term. In the other limit, $\kappa\ll 1$, the exponential damping term plays little role and the system behaves as a single-component repulsive Coulomb system, the so-called one-component plasma (OCP), with an ill-defined thermodynamic limit due to the infinite screening length. The case $\Gamma\gg 1$ corresponds to the potential energy from the individual pair interactions being much larger than the thermal energy; this favors crystallization, depending on the value of $\kappa$, see below. In the opposite limit, $\Gamma\ll 1$, the system approaches an ideal gas. Care must be taken when comparing $\kappa$ or $\Gamma$ values in the literature, because they often include in their definition further multiplicative constants. For instance, in the above definitions of the screening and coupling parameters the term $\rho^{-1/3}$ is often replaced by the Wigner-Seitz radius $a=[3/(4\pi\rho)]^{1/3}$.

The Yukawa system's phase diagram is well understood with its two solid phases and a fluid phase~\cite{Ikezi1986, Robbins1988, Meijer1991, Farouki1992}. At high $\kappa$ the Yukawa fluid crystallizes into an face-centered cubic (FCC) lattice, while at low $\kappa$ it crystallizes into a body-centered cubic (BCC) lattice. The triple point separating fluid, FCC, and BCC phases is located at $\kappa\cong 6.90, \Gamma \cong 3.47\times 10^3$~\cite{Hamaguchi1997}. Vaulina et al.~\cite{Vaulina2000, Vaulina2002} derived an expression for the melting line from the pair potential using the Lindemann melting criterion \cite{Lindemann1910, Gilvarry1956}. This expression is confirmed below, where it is derived from the isomorph theory. This theory applies to the class of systems (dense liquids and classical crystals) termed \emph{Roskilde-simple} -- or just \emph{Roskilde} (\emph{R}) -- systems~\cite{Ingebrigtsen2012c, Dyre2014}. As documented below, the Yukawa system exhibits the strong correlations between equilibrium virial and potential-energy fluctuations required for a system to belong this class.

Over the years, investigations of the dynamics of the Yukawa system have mostly focused on the self-diffusion coefficient and the viscosity~\cite{Robbins1988, Kremer1987, Lowen1993, Rosenfeld2000, Rosenfeld2001, Ohta2000, Daligault2012, Khrapak2012, Dzhumagulova2013, Faussurier2014}. In the present publication we derive some of the previously reported scaling properties of the Yukawa system's transport coefficients from the general isomorph theory.

\begin{figure}
  \centering
  \includegraphics[width=\figwidth]{y_UWscatter.eps}
  \caption{Scatter plot (red symbols) demonstrating strong correlations between the instantaneous values of the virial $W$ and the potential energy $U$ during an equilibrium $NVT$ simulation of the Yukawa system at $\rho = 3\times 10^{-3}$ and $T=5.3608\times 10^{-5}$ ($\kappa=6.934$ and $\Gamma=2690$). The dashed line is the standard linear regression with slope $\gamma$.}\label{fig:UWscatter}
\end{figure}

The isomorph theory initiated from the observation that some model liquids have strongly correlated fluctuations of their energy and pressure~\cite{Pedersen2008b}. More precisely, the correlations are between the {\it configurational} parts of these quantities. If one for a system of $N$ particles splits energy and pressure into ideal-gas terms, which depend only on the particle momenta, and configurational terms depending only on the particle positions as follows
\begin{align}
  E  &= K(\vect{p}_1, \ldots, \vect{p}_N) + U(\vect{r}_1, \ldots, \vect{r}_N)\,,\label{eq4}\\
  pV &= N k_B T(\vect{p}_1, \ldots, \vect{p}_N) + W(\vect{r}_1, \ldots, \vect{r}_N)\,,\label{eq5}
\end{align}
strong correlations between the potential energy $U$ and virial $W$ constant-volume thermal-equilibrium fluctuations are found for a number of systems~\cite{Pedersen2008}. An illustration of such strong virial potential-energy correlations is shown in \fig{fig:UWscatter} that plots the instantaneous values of $W$ versus those of $U$ during an $NVT$ equilibrium simulation of the Yukawa system. The correlations are quantified by the standard Pearson correlation coefficient~\cite{paper1}
\begin{equation}\label{eq:R}
  R = \frac{\left\langle \Delta W \Delta U \right\rangle}
           {\sqrt{\left\langle(\Delta W)^2\right\rangle \left\langle(\Delta U)^2\right\rangle}}\,.
\end{equation}
As \fig{fig:UWscatter} shows, $R$ is high for the Yukawa system. A system is generally considered to have strong $U,W$ correlation whenever $R>0.9$~\cite{paper1}, a convenient but also somewhat arbitrary criterion. Many model systems have been shown to exhibit strong $U,W$ correlations~\cite{paper1, Veldhorst2012, Bacher2014}, including the Lennard-Jones (LJ) system and other simple liquids, molecular liquid models~\cite{Ingebrigtsen2012b, Veldhorst2014}, liquids under shear~\cite{Separdar2013}, and crystals~\cite{Albrechtsen2014}. These systems were initially called ``strongly correlating'', but that repeatedly led to confusion with strongly correlated quantum systems, and they are now instead referred to as Roskilde-simple or just Roskilde (R) systems~\cite{Malins2013, Abramson2014, Henao2014, Pieprzyk2014, Prasad2014, Schmelzer2015, Buchenau2015, Heyes2015}. The isomorph theory has also been applied to nano-confined liquids~\cite{Ingebrigtsen2013b, Ingebrigtsen2014} and, e.g., to derive density-scaling invariants for zero-temperature plastic flow properties of glasses~\cite{Lerner2014}.

\begin{figure}
  \centering
  \includegraphics[width=\figwidth]{y_smallstep1.eps}
  \caption{The radial distribution function (left) and the mean square displacement (right) in reduced units for four different state points, two of which are isomorphic to each other. The initial state point (black line) has $\rho_1=3\times 10^{-3}, T_1=5.361\times 10^{-5}$, while the isomorphic state point (dashed, red line) has $\rho_2=3.3\times 10^{-3}, T_2=6.553\times 10^{-5}$. The method used to identify the state point ($\rho_2,T_2$) as being  isomorphic to state point ($\rho_1,T_1$) is given below in Sec.~\ref{ssec:dic}.
The two isomorphic state points are seen to have identical structure and dynamics to a very good approximation. The effects of either changing density or temperature (green and blue dashed lines) are shown for comparison. The insets show enlarged views of the same data.}\label{fig:smallstep}
\end{figure}

In 2009 it was found that R liquids have ``isomorphic'' curves in their thermodynamic phase diagram~\cite{paper4}. Isomorphs are curves along which all properties derived from structure or dynamics are invariant in properly reduced units, making the phase diagram effectively one dimensional with respect to many properties~\cite{paper4}. An example of this is shown in \fig{fig:smallstep}, where the Yukawa fluid is shown to have -- to a very good approximation -- identical radial distribution functions ($g(r)$) and mean square displacements at two state points that are isomorphic to each other.

Having its origins in the field of organic, glass-forming liquids, the isomorph theory has been applied to explain certain empirical scalings in that field. These include the so-called density scaling, according to which the dynamics is a function of $\rho^\gamma/T$~\cite{Roland2005}. This is an approximation to the isomorph theory that applies when fairly small changes in density are considered, as in most experiments ~\cite{paper4, Bohling2012}. Because both the excess entropy, $S_{\rm ex}\equiv S-S_{ideal}$ ($S_{ideal}$ being the entropy of the ideal gas at same temperature and density), and the reduced-unit dynamics are invariant along isomorphs, the isomorph theory also predicts that R liquids obey Rosenfeld's excess entropy scaling, which states that the reduced transport coefficients are functions of $S_{ex}$~\cite{Rosenfeld1977}. Not predicted by the isomorph theory, but nevertheless found to apply to R liquids~\cite{Ingebrigtsen2013}, is the Rosenfeld-Tarazona relation~\cite{Rosenfeld1998} that gives expressions for the constant-density temperature dependence of the isochoric specific heat ($c_V\propto T^{-2/5}$). For a more comprehensive overview of the isomorph theory the reader is referred to a recently published Feature article~\cite{Dyre2014}.

The fact that the Yukawa system has strong $UW$ correlations shows that it belongs to the class of R liquids. This is consistent with the long-known facts that the Yukawa system~\cite{Rosenfeld2000, Sanbonmatsu2001} and the OCP~\cite{Daligault2006} obey excess entropy scaling as well as the above-mentioned Rosenfeld-Tarazona relation for the specific heat's temperature dependence~\cite{Rosenfeld1998}.  The implication is that the isomorph theory applies also to systems that are not conventional liquids, such as colloidal suspensions and dusty plasmas. In fact, the findings presented below confirm a recently derived theory of quasiuniversality according to which the Yukawa system is in the so-called \emph{EXP} quasiuniversality class of simple, monatomic, pair-potential  systems, a class that includes also, e.g., the inverse-power-law (IPL) and Lennard-Jones systems~\cite{Bacher2014a}.

In the following we first give a short overview of the isomorph theory and the computer simulation procedures used in the paper (Secs.~\ref{sec:theory} and~\ref{sec:simulations}). We proceed to show how to construct isomorphs using two different methods in Sec.~\ref{sec:isomorphs}. Sec.~\ref{sec:results} then shows that the isomorphs generated by these methods are very close to one another and confirms the predicted isomorph invariance of structure and dynamics. Finally, Sec.~\ref{sec:discussion} gives a brief discussion.

\section{Isomorphs in Roskilde-simple systems: A brief review\label{sec:theory}}

The isomorph theory uses so-called reduced units in which quantities are made dimensionless via units based on the thermodynamic quantities density and temperature, {\it not} the length and energy of the microscopic potential that are often used in reporting simulation results. Thus one uses the unit $l_0\equiv\rho^{-1/3}$ for length, $e_0\equiv k_BT$ for energy, and $t_0\equiv\rho^{-1/3}/\sqrt{k_BT/m}$ for time with $m$ being the particle mass (for Brownian dynamics a different time unit is used) \cite{paper4}. For instance, the collective position of the system's particles, $\vect{R} \equiv (\vect{r}_1, \ldots, \vect{r}_N)$, is expressed in reduced units as

\begin{equation}\label{eq:reduced_conf}
  \tilde{\vect{R}} \equiv \rho^{1/3} \vect{R}\,,
\end{equation}
where the tilde here and henceforth denotes a reduced quantity.

The isomorph theory is conveniently summarized in the expression~\cite{Dyre2014}
\begin{equation}\label{eq:hidden_scale_invariance}
U(\vect{R}) \cong h(\rho) \tilde{\Phi}(\tilde{\vect{R}}) + g(\rho)\,.
\end{equation}
Here $\tilde{\Phi}$ is a dimensionless, state-point independent function of the reduced configurations $\tilde{\vect{R}}$; the term $\tilde{\Phi}(\tilde{\vect{R}})$ controls the structure and dynamics in reduced units, but notably it contains no length or energy scales. The functions $h(\rho)$ and $g(\rho)$ both have units of energy. The physics of Eq. (\ref{eq:hidden_scale_invariance}) is that upon changing the density of a system, the potential-energy surface to a good approximation merely undergoes a linear, affine rescaling. We proceed to show how \eq{eq:hidden_scale_invariance} is used to derive the most important properties of R systems, their strong virial energy correlations and the existence of isomorphs. Before doing so we note that the isomorph theory was recently generalized by defining a Roskilde-simple system by the property that the order of potential energies is maintained for uniform scaling of configurations, i.e., by the condition $U(\vect{R}_a)<U(\vect{R}_b)\Rightarrow U(\lambda\vect{R}_a)<U(\lambda\vect{R}_b)$~\cite{Schroder2014}. This leads to slightly modified predictions, but overall the new isomorph theory is close to the original, which is the one used below.

The microscopic virial of Eq. (\ref{eq5}) is defined by~\cite{AllenTildesley}
\begin{equation}\label{eq:Wdef}
W(\vect{R})\equiv -\frac{1}{3}\,\vect{R}\cdot\nabla U(\vect{R})\,.
\end{equation}
It is easy to show that $W(\vect{R})$ characterizes the change of potential energy for a uniform scaling of space (i.e., leaving $\tilde{\vect{R}}$ intact) as follows \cite{Dyre2013b}

\begin{equation}
  W(\vect{R}) = \left(\frac{\partial U(\vect{R})}{\partial\ln\rho} \right)_{\tilde{\vect{R}}}\,.
\end{equation}
Combining this with \eq{eq:hidden_scale_invariance} and eliminating $\tilde{\Phi}(\tilde{\vect{R}})$ one finds that

\begin{equation}\label{eq:gamma3}
  W(\vect{R}) \cong \gamma(\rho) U(\vect{R}) + \phi(\rho)\,.
\end{equation}
Here

\begin{equation}\label{eq:gamma_hrho}
  \gamma(\rho) \equiv \dfrac {\ud \ln h(\rho)} {\ud\ln\rho}
\end{equation}
and $\phi(\rho) = \ud g(\rho)/\ud\ln\rho - g(\rho)\gamma(\rho)$. From \eq{eq:gamma3} it follows that at constant density the fluctuations in $W$ and $U$ are correlated with linear-regression slope $\gamma$ given by

\begin{equation}\label{eq:gamma-fluctuations}
  \gamma \equiv \frac {\left<\Delta W \Delta U\right>} {\left<(\Delta U)^2\right>}\,.
\end{equation}
As shown in \fig{fig:UWscatter}(a) the Yukawa system indeed has strong $WU$ correlations (with slope $\gamma=2.14$ at the state point studied here).

We proceed to show that \eq{eq:hidden_scale_invariance} implies the existence of isomorphs. First these curves in the thermodynamic phase diagram need to be defined. Consider two densities, $\rho_1$ and $\rho_2$, and two configuration $\vect{R}_1$ and $\vect{R}_2$ at these densities, respectively, with the same reduced coordinates, i.e., $\rho_1^{1/3}\vect{R}_1 = \rho_2^{1/3}\vect{R}_2 \equiv \tilde{\vect{R}}$. Applying \eq{eq:hidden_scale_invariance} to $U(\vect{R}_1)$ and $U(\vect{R}_2)$ and eliminating the common factor $\tilde{\Phi}(\tilde{\vect{R}})$ we find $\left[U(\vect{R}_1) -g(\rho_1)\right]/h(\rho_1) = \left[U(\vect{R}_2) -g(\rho_2)\right]/h(\rho_2)$. Define now two temperatures by $k_BT_1\equiv Kh(\rho_1)$ and $k_BT_2\equiv Kh(\rho_2)$ with the same proportionality constant $K$. This gives

\begin{equation}\label{eq:isomorphDef_log}
  \dfrac{U(\vect{R}_1)}{k_BT_1} \cong \dfrac{U(\vect{R}_2)}{k_BT_2} + B_{12}\,,
\end{equation}
where the constant $B_{12}$ depends only the two state points, not on the configurations. This can be rewritten as

\begin{equation}\label{eq:isomorphDef}
  \exp\left(-\dfrac{U(\vect{R}_1)}{k_B T_1}\right) \cong C_{12} \exp\left(-\dfrac{U(\vect{R}_2)}{k_B T_2}\right)\,.
\end{equation}
This equation implies identical canonical probabilities of configurations with the same reduced coordinates. When this is obeyed to a good approximation for most of the physically relevant configurations, the two state points $(\rho_1,T_1)$ and $(\rho_2,T_2)$ are by definition {\it isomorphic} to one another~\cite{paper4}. This defines a mathematical equivalence relation in the thermodynamic phase diagram, and an isomorph is then defined as a curve along which all pairs of state points are isomorphic.

From the isomorph definition \eq{eq:isomorphDef} it follows that many properties of the system are invariant between isomorphic state points~\cite{paper4}. Isomorph invariants include thermodynamic quantities such as the excess entropy and the isochoric specific heat, as well as the reduced-unit dynamics and structure. Not all quantities are invariant even in reduced units, for instance the free energy and its volume derivatives like pressure or compressibility.

Because the temperature is proportional to $h(\rho)$ along an isomorph with the same proportionality constant, isomorphs are described by

\begin{equation}\label{eq:T_hrho_isomorph}
  \frac{h(\rho)}{T}={\rm Const.}
\end{equation}
Since moreover the excess entropy per particle $s_{ex}$ is constant on an isomorph (because the Boltzmann probabilities of scaled configurations are), the temperature of an R system, i.e., one with isomorphs, separates as follows~\cite{Ingebrigtsen2012}

\begin{equation}\label{eq:factorization}
  k_BT = f(s_{ex})h(\rho)\,.
\end{equation}
It can be shown that this separation property is mathematically equivalent to the thermal average of \eq{eq:gamma3}, which is simply the configurational Gr{\"u}neisen equation of state $W\cong\gamma(\rho) U+\phi(\rho)$~\cite{Ingebrigtsen2012}.

The isomorph theory is approximate for all realistic systems. In fact, Eqs.(\ref{eq:hidden_scale_invariance}) and (\ref{eq:isomorphDef}) are only exact for systems that have an Euler-homogeneous potential-energy function. The most important example of such systems are those with an inverse-power-law (IPL) pair potential ($\upsilon(r) \propto r^{-n}$). IPL systems are easily shown to be characterized by $h(\rho)\propto \rho^\gamma$, and it follows from \eq{eq:Wdef} that $\gamma$ is related to the exponent $n$ of the IPL pair potential by

\begin{equation}\label{eq:gamma_ipl_exponent}
  \gamma = \frac{n}{3}\,.
\end{equation}
The applicability of the isomorph theory for simple atomic systems may be understood physically from the fact that, in the region of the first peak of the radial distribution function, the interatomic potential is well fitted by an IPL term plus a linear term, the so-called extended IPL (eIPL) pair potential~\cite{paper2}. This provides an intuitive explanation why many non-IPL liquids obey the isomorph theory. Notably, the linear term contributes little to the fluctuations in the energy or the virial. The reason for this is that when a particle moves, interparticle distance decrease on one side while increasing on the other side. The sum of the interparticle distances stays approximately the same. ~\cite{paper2}

\section{Simulation procedure\label{sec:simulations}}

Our simulations used the ``Roskilde University Molecular Dynamics'' (RUMD) code, which is optimized for GPU computing~\cite{RUMD}. All simulations were performed in the $NVT$ ensemble with a standard Nos{\'e}-Hoover thermostat. A state point is characterized by two parameters: the density $\rho$, reported below in the unit system defined by the screening length $\lambda$ of \eq{eq:y_debyuehuckel}, and the temperature $T$ reported in the unit system defined by the unit $Q^2/(\lambda k_B)$. Equivalently, a state point may be characterized by the two dimensionless numbers the screening parameter $\kappa$ of \eq{scr} and the coupling parameter $\Gamma$ of \eq{coup}. For maximum clarity the simulation results are presented both in terms of $\rho$ and $T$, and in terms of $\kappa$ and $\Gamma$. In practice the simulations were performed directly in reduced units, i.e., density and temperature were set equal to unity, changing instead the length and energy parameters of the potential in order to investigate different state points in the thermodynamic phase diagram.

In reduced units the integration time step $\Delta \tilde{t}$ was decreased at low screening lengths ($\kappa\gg 1$) because the potential here becomes very steep. We used a shifted-force cutoff~\cite{Toxvaerd2011} for the potential, with a (reduced) cutoff $r_{cut}$ that varied with the state point because longer cutoffs are needed at low $\kappa$ values. Wherever necessary we increased the number of particles $N$ to allow for larger cutoffs. It should be noted that this cutoff method does not yield accurate values of the potential energy, especially at high densities close to the OCP limit. The accurate calculation of the potential energy of the OCP hase been discussed elsewhere~\cite{Hansen1973, Ng1974, Slattery1980}, and is beyond the scope of this investigation. Table~\ref{tab:y_simdetails} summarizes the simulation parameters used.

\begin{table}
  \centering
  \setlength{\tabcolsep}{6pt}
  \begin{tabular}{l|crr|l}
     & \multicolumn{1}{c}{$N$} &  \multicolumn{1}{c}{$\tilde{r}_{cut}$} & \multicolumn{1}{c|}{$\Delta\tilde{t}$ } & \\
    \hline
    $  \qquad\quad\;\! \rho < 0.01$ & 2048 & 4.3  & 0.0010 & $\;\;\:  5 < \kappa$       \\
    $0.01    \leqslant \rho < 0.5$  & 2048 & 5.2  & 0.0025 & $      1.5 < \kappa < 5$   \\
    $0.5\;\: \leqslant \rho$        & 8192 & 10.0 & 0.0025 & $\qquad\:\:\,\kappa < 1.5$ \\
    \hline
  \end{tabular}
  \caption{The parameters used in the simulations. Depending on the density $\rho$ the number of particles in the system $N$ was changed to allow for a larger reduced cutoff radius $\tilde{r}_{cut}$. The reduced time step $\Delta\tilde{t}$ was decreased at the lowest densities.}
  \label{tab:y_simdetails}
\end{table}

\section{Two methods for identifying the isomorphs\label{sec:isomorphs}}

This section details two methods for mapping out an isomorph in the thermodynamic phase diagram. The first one is numerical; it is accurate for small density variations, but not well suited for studies involving large density variation. Here a recently proposed approximate analytical method is more handy. This method estimates the isomorph from the pair potential by using \eq{eq:T_hrho_isomorph} in conjunction with an analytical expression for $h(\rho)$. This has been shown to work well for the Lennard-Jones system and two systems with pair potentials that are sums of two, respectively three IPL terms~\cite{Bohling2014}.

\subsection{The direct isomorph check: A numerical method\label{ssec:dic}}

Equation (\ref{eq:isomorphDef_log}) can be rewritten as
\begin{equation}\label{eq:dic}
  U(\vect{R}_2) \cong \dfrac{T_2}{T_1}U(\vect{R}_1) + D_{12}\,.
\end{equation}
This shows that the potential energies of configurations at density $\rho_1$ and the same ones scaled to density $\rho_2$ are predicted to be linearly related. If the configurations are taken from an equilibrium simulation at state point $(\rho_1,T_1)$, the slope is the ratio $T_2/T_1$, where $T_2$ is the temperature for which state point $(\rho_2,T_2)$ is isomorphic to state point $(\rho_1,T_1)$. This can be used to find state points that are isomorphic to each other. This procedure is termed the direct isomorph check because it is based directly on the isomorph definition \eq{eq:isomorphDef}~\cite{paper4}.

\begin{figure}
  \centering
  \includegraphics[width=\figwidth]{y_UUscatter.eps}
  \caption{The Yukawa system simulated at $\rho_1 = 3\times 10^{-3}$ ($\kappa=6.93$) and $T_1=5.361\times 10^{-5}$ ($\Gamma=2690$). The potential energies $U_1\equiv U(\vect{R_1})$ of configurations were plotted versus the potential energies $U_2\equiv U(\vect{R_2})$ of the same configurations scaled to a 10\% higher density denoted $\rho_2$ (green symbols). The two energies are highly correlated, indicating that the Yukawa system obeys the isomorph definition (\eq{eq:isomorphDef_log}). By simple linear regression (dashed line) we find the slope $T_2/T_1$ (see \eq{eq:dic}), which means that for the state point at $\rho_1$ to be isomorphic to the one at $\rho_2$, the temperature of the latter should be $T_2=1.2224\times T_1=6.553\times 10^{-5}$ ($\Gamma=2272$).}
  \label{fig:UUscatter}
\end{figure}

The direct-isomorph-check procedure is illustrated in \fig{fig:UUscatter}. Here a number of configurations $\vect{R}_1$ with potential energy denoted by $U_1$ were sampled from an equilibrium simulation of the Yukawa fluid at density $\rho_1$. Each configuration was then scaled to the higher density $\rho_2=1.1\times\rho_1$, at which the new potential energy $U_2$ was calculated. The figure shows that the potential energies $U_1$ and $U_2$ are highly correlated. The standard linear-regression slope is $1.2224$. According to \eq{eq:dic} this number is the ratio $T_2/T_1$, which allows for determining $T_2$ such that the state point $(\rho_2,T_2)$ is isomorphic to $(\rho_1,T_1)$. We see that along the isomorph through $(\rho_1,T_1)$ a density increase of 10\% implies a 22.2\% increase in temperature.

The structure and dynamics of the two isomorphic state points are shown to be the same in \fig{fig:smallstep}, indicating that the direct isomorph check works well for density changes of 10\%. However, it should be noted that the change in density cannot be huge, because the isomorph theory is only approximate (except for IPL systems), which implies that direct-isomorph-check plots give relatively poor correlations for large density jumps. To avoid this problem, we used in this work always a density change of merely 10\% for direct isomorph checks, corresponding to changing $\kappa$ by less than 4\%. In the simulations presented in section~\ref{sec:results} we used the direct isomorph check to create an isomorph by doing a simulation at the initial state point $(\rho,T) = (10^{-3},3\times 10^{-6})$, scaling configurations to a new density, and finding the temperature of the new isomorphic state point. This was repeated at the new state point to obtain a third one, etc. In this way we obtained altogether a set of 32 prospective isomorphic state points in the range $3\times 10^{-4}\leqslant\rho\leqslant 3.6\times 10^{-3}$ ($6.5\leqslant\kappa\leqslant 14.9$). These state points are referred to here as ``prospective'' because they will be compared to other sets of prospective isomorphic state points generated in different ways.

\subsection{Predicting the isomorph analytically from the pair potential}

In this section we aim to construct an isomorph by obtaining an expression for the function $h(\rho)$ of \eq{eq:hidden_scale_invariance}. For pair potentials that are a sum of IPLs, $h(\rho)$ can be determined from a single simulation at a reference state point~\cite{Ingebrigtsen2012, Bohling2012}. For other potentials such as the Yukawa this is not possible. Nevertheless, B{\o}hling {\it et al.}~\cite{Bohling2014} have recently shown that $h(\rho)$ can be estimated from the potential. We briefly review these findings before applying this method to the Yukawa potential.

\begin{figure}
  \centering
  \includegraphics[width = \figwidth]{y_n2.eps}
  \caption{Estimates of the effective IPL exponent $n^{(p)}(r)$ for the Yukawa potential using \eq{eq:n_general}.}
  \label{fig:y_n2-r}
\end{figure}

As mentioned earlier, for an IPL pair potential $\propto r^{-n}$ it is known that $\gamma=n/3$ (\eq{eq:gamma_ipl_exponent}). For other potentials an effective $r$-dependent IPL exponent can be estimated using ratios of derivatives of the potential~\cite{paper2} as follows:
\begin{equation}\label{eq:n_general}
  n^{(p)}(r) \equiv -r\frac{\upsilon^{(p+1)}(r)}{\upsilon^{(p)}(r)} -p\,,
\end{equation}
where $\upsilon^{(p)}$ denotes the $p$th derivative of the potential. For an IPL pair potential, $n^{(p)}(r)$ is constant and gives the correct exponent for all $p$. For other potentials, the effective exponent depends on both $p$ and $r$, meaning that the ``softness'' of the particles depends on the separation between the particles. We show this in \fig{fig:y_n2-r} for the Yukawa potential. It is known that in the OCP limit the potential reduces to a Coulomb interaction, for which $n=1$. This corresponds to small interparticle distances and we see indeed that in the limit of $r\rightarrow 0$ one finds $n^{(p)}(r)\rightarrow 1$ for every $p$.

Recall that potentials that obey the isomorph theory have been found to be well fitted by an extended IPL potential, i.e., an IPL potential plus a linear term~\cite{paper2}.
An obvious choice for $p$ is thus 2, since this would ignore the linear contribution to the extended IPL potential:
\begin{equation}\label{eq:n2}
  n^{(2)}(r) \equiv -r\frac{\upsilon'''(r)}{\upsilon''(r)} -2\,.
\end{equation}
The next question is at which distance to evaluate $n^{(2)}(r)$. Since the physics of R liquids has been shown to be governed by the interactions in the first coordination shell~\cite{Ingebrigtsen2012c}, the nearest neighbor distance is an obvious choice. Since any distance scales with density as $r\propto\rho^{-1/3}$, we can write the nearest-neighbor distance as $\Lambda\rho^{-1/3}$, where $\Lambda$ is a number close to unity. By combining \eq{eq:n2} and \eq{eq:gamma_ipl_exponent} one finds~\cite{Bohling2014}
\begin{equation}\label{eq:gamma_potential2}
  \gamma(\rho) = \left.\dfrac{n^{(2)}(r)}{3}\right|_{r=\Lambda\rho^{-1/3}}\,.
\end{equation}
 As noted by B{\o}hling {\it et al.}~\cite{Bohling2014}, $\Lambda$ is not expected to be the same for all state points. However, because structure in reduced units is predicted to be invariant along an isomorph, $\Lambda$ must also be an isomorph invariant. By comparing with simulation results of different pair potentials, they indeed find that $\gamma(\rho)$ does not predict the density-scaling exponent equally well for different isomorphs if $\Lambda$ is isomorph independent, although the prediction is qualitatively correct. Instead, an isomorph dependent (and thus excess entropy  dependent) nearest-neighbor distance $\Lambda(s_{ex})\rho^{-1/3}$ was able to estimate the isomorph more precisely, giving~\cite{Bohling2014}
\begin{equation}\label{eq:gamma_potential}
  \gamma(\rho,s_{ex}) = \left.\dfrac{n^{(2)}(r)}{3}\right|_{r=\Lambda(s_{ex})\rho^{-1/3}}\,.
\end{equation}

It is possible to rewrite \eq{eq:n2} as $n^{(2)}(r) \equiv \ud \ln[r^2\upsilon''(r)] / \ud \ln r$. This can be combined with \eq{eq:gamma_hrho} to find~\cite{Bohling2014}
\begin{equation}\label{eq:hrho_potential}
  h(\rho,s_{ex}) = \left.Ar^2\upsilon''(r)\right|_{r=\Lambda(s_{ex})\rho^{-1/3}}\,,
\end{equation}
where $A$ is an arbitrary constant. This can now be used to find an isomorph in the phase diagram using the facts that $h(\rho,s_{ex})/T={\rm Const.}$ (\eq{eq:T_hrho_isomorph}) and $s_{ex}$ is an isomorph invariant.

Applying this method to the Yukawa potential, we find using \eq{eq:hrho_potential} after straightforward calculations
\begin{equation}\label{eq:y_hrho}
  h(\rho,s_{ex}) = A\exp^{-\Lambda\rho^{-1/3}} \left[\Lambda\rho^{-1/3} + 2 + 2\Lambda^{-1}\rho^{1/3}\right]\,.
\end{equation}
If we express $h(\rho,s_{ex})$ in terms of the Yukawa parameters $\kappa$ and $\Gamma$, we find
\begin{equation}\label{eq:Gamma-k}
  \Gamma = \Gamma_0 \dfrac{2e^{\Lambda\kappa}}{(\Lambda\kappa)^2 + 2\Lambda\kappa + 2}\,
\end{equation}
where $\Gamma_0=\Lambda/(2A)$ is the value of $\Gamma$ in the OCP limit ($\kappa=0$). Vaulina {\it et al.}~\cite{Vaulina2000} found that a curve of this shape with $\Lambda=1$ and $\Gamma_0=106.6$ gives a good description of the melting line as found by Hamaguchi {\it et al.}~\cite{Hamaguchi1997}, and also of the melting line of dissipative Yukawa systems~\cite{Vaulina2002}. Their findings are fully consistent with the isomorph theory and now placed in a more general setting: The melting line is predicted to be an isomorph~\cite{paper4} since if an isomorph were to cross the melting line this would mean \eq{eq:isomorphDef} should be obeyed for a pair of liquid and solid state points. This cannot be the case, because the relative Boltzmann probabilities for liquid and solid configurations are clearly different at these two state points. Vaulina {\it et al.} used Lindemann's melting criterion which states that melting happens when the root mean square displacement is 10\% of the crystal's nearest neighbor distance~\cite{Gilvarry1956}. Since both structure and dynamics are invariant on the isomorph, they should also be so at the melting line. Lindemann's melting criterion is thus consistent with the isomorph theory~\cite{paper4}. It should also be noted that Yazdi {\it et al.}~\cite{Yazdi2014} recently showed that \eq{eq:Gamma-k} with $\Gamma_0=368$ and $\Lambda=1$ gives a good description of the ideal glass transition of mode-coupling theory; apparently this line is an isomorph which makes sense since isomorphs are lines of identical physics (in reduced units). A consequence of the melting line being an isomorph is also that the temperature $T$ on an isomorph scaled by the melting temperature $T_m$ is an isomorph invariant if isomorphs have the same shape (i.e., their shape is given by $h(\rho)$ instead of $h(\rho,s_{ex}))$. Thus so-called melting temperature scaling methods that have found that dynamic and/or thermodynamic properties of the Yukawa system~\cite{Rosenfeld2000, Rosenfeld2001, Khrapak2015a, Khrapak2015b} and the OCP~\cite{Rosenfeld2000, Rosenfeld2001, Khrapak2013} are functions only of $T/T_m$, are saying that these properties are isomorph invariants.

In addition to the direct isomorph check described in section~\ref{ssec:dic} we used \eq{eq:y_hrho} to obtain two sets of isomorphic state points. For this it is necessary to know the relevant reduced interparticle distance $\Lambda$. Because Vaulina {\it et al.}~\cite{Vaulina2000} found \eq{eq:Gamma-k} with $\Lambda=1$ to be a good description of the melting line and the melting line is an isomorph, we test if \eq{eq:y_hrho} with $\Lambda=1$ is the correct description of an isomorph. The prospective isomorph with $\Lambda=1$ that we have tested is characterized by $A=6.347\times 10^{-3}$ ($\Gamma_0 = 78.78$).

We also tried to calculate a more accurate value of $\Lambda$. Previously, B{\o}hling {\it et al.}~\cite{Bohling2014} used the most probable nearest neighbor distance for $\Lambda$, which they determined from the position of the first peak in $r^2g(r)$, with $g(r)$ being the radial distribution function. They found for the potentials they tested at different state points that $0.975\leqslant\Lambda\leqslant 1.065$. We below use the different method to determine $\Lambda$ from the $U,W$ fluctuations published earlier by Bailey {\it et al.}~\cite{Bailey2013}. First, we derive the expression for $\gamma(\rho,s_{ex}) = \partial \ln h(\rho,s_{ex})/\partial \ln \rho$ (\eq{eq:gamma_hrho}) for the Yukawa potential using \eq{eq:y_hrho}:
\begin{equation}\label{eq:y_gamma_rho_isomorph}
  \gamma(\rho,s_{ex}) = \dfrac {\Lambda^3} {3\Lambda^2\rho^{1/3} + 6\Lambda\rho^{2/3} + \rho} + \dfrac{1}{3}\,.
\end{equation}
We then did a simulation at an initial state point ($\rho=0.005$ and $T=0.00015$). At this state point $\gamma$ was found from the fluctuations to be 1.78 using \eq{eq:gamma-fluctuations}. From \eq{eq:y_gamma_rho_isomorph} it then follows that $\Lambda=1.03$ is the relevant reduced nearest-neighbor distance at that state point. The third prospective isomorph is thus identified by \eq{eq:y_hrho} with $\Lambda=1.03$ and $A=7.414\times 10^{-3}$ ($\Gamma_0=69.46$) to obtain a set of state points with the same densities as the points generated for the $\Lambda=1$ prospective isomorph.

\section{Comparing the three prospective isomorphs\label{sec:results}}
\begin{figure}
  \centering
  \includegraphics[width=\figwidth]{y_im_RhoT.eps}
  \caption{Prospective isomorphs in the (a) $\rho,T$ phase diagram and the (b) $\kappa,\Gamma$ phase diagram generated in the three different ways described in Sec. IV. Comparing the two estimates of $h(\rho)$ from the pair potential, there is a visible difference in the slope at low density (high $\kappa$). The isomorphs are approximately parallel to the expressions of the melting line~\cite{Vaulina2000} and the ideal MCT glass transition~\cite{Yazdi2014} (dashed lines), showing that these lines are both isomorphs. This is what one expects from the fact that the physics is invariant along the isomorphs. Sets of isothermal and iso-$\Gamma$ state points have also been included in the figure because these are used later in this section.}\label{fig:y_im_RhoT}
\end{figure}

This section compares the three sets of prospective isomorphic state points generated as described in the previous section. The three prospective isomorphs are shown in \fig{fig:y_im_RhoT} plotted both in the $\rho,T$ and the $\kappa,\Gamma$ plane. The isomorphs are parallel to the expression for the melting line~\cite{Vaulina2000} and the ideal glass transition line from mode coupling theory~\cite{Yazdi2014}. The three prospective isomorphs are slightly different, but overall close to one another. It is therefore not surprising that they have similar invariance properties. The remainder of this section focuses on illuminating the minor differences.

\begin{figure}
  \centering
  \includegraphics[width=\figwidth]{y_im_Rgamma.eps}
  \caption{The virial potential-energy correlation coefficient $R$ (top), and the so-called density-scaling coefficient $\gamma$ (bottom) plotted versus density (left) and the screening parameter $\kappa$ (right). The Yukawa fluid is Roskilde-simple at all simulated state points. We find that $\gamma$ varies significantly, reflecting a dramatic change in steepness of the Yukawa potential with density.}\label{fig:y_im_Rgamma}
\end{figure}

Figures \ref{fig:y_im_Rgamma}(a) and (b) verify that the strong correlations between the virial and the potential-energy $NVT$ equilibrium fluctuations are present over the entire range of densities studied. Whereas models of conventional liquids are usually not strongly correlating at low densities and temperatures due to the large contribution of the attractive term in the potential, the Yukawa system is in fact strongly correlating with correlation coefficient $R>0.99$ (\eq{eq:R}) at all tested state points. The values $R>0.99$ are very high, especially when compared to those of other models that, as mentioned, are considered Roskilde liquids if they  obey $R>0.90$~\cite{paper1, paper2, Veldhorst2012, Ingebrigtsen2012b}. Recently, the ten-bead rigid-bond flexible Lennard-Jones chain was even demonstrated to have excellent isomorphs despite having $R\approx 0.86$~\cite{Veldhorst2014}.

Figures \ref{fig:y_im_Rgamma}(c) and (d) show the density-scaling coefficient $\gamma$ calculated using \eq{eq:gamma-fluctuations}.
In the OCP limit we find that $\gamma$ goes to $1/3$ as expected for an IPL with $n=1$. At lower densities the behavior of $\gamma$ is influenced by the exponential term, for which the estimated $\gamma(\rho)$ has also been shown for comparison. Due to the increase in the steepness of the potential, $\gamma$ increases from $1/3$ to 5 in the density range shown. The lowest correlation coefficient is found in the crossover region of densities marking the region where the effects of both the exponential and Coulomb terms are important.

\begin{figure}
  \centering
  \includegraphics[width=\figwidth]{y_im2_im3_gamma-diff.eps}
  \caption{Relative difference between the estimated $\gamma(\rho)$ (\eq{eq:y_gamma_rho_isomorph}) and $\gamma$ calculated from the fluctuations via \eq{eq:gamma-fluctuations} (denoted in the figure by $\gamma_f$). The prediction $\gamma(\rho)_{\Lambda=1.03}$ is generally in best agreement with the values from the equilibrium fluctuations.}
  \label{fig:im23_gamma-diff}
\end{figure}

There is a slight difference between the values of $\gamma$ calculated from the fluctuations and those predicted for $\gamma(\rho,s_{ex})$ from \eq{eq:y_gamma_rho_isomorph} with $\Lambda=1$ (black dashed line). To investigate this further we plot in \fig{fig:im23_gamma-diff} the relative difference between the two estimated functions $\gamma(\rho,s_{ex})$ for $\Lambda=1$ and $\Lambda=1.03$ and the values of $\gamma$ calculated from the fluctuations. Both predictions are too low at high density (small $\kappa$). Unsurprisingly, the prediction with $\Lambda=1.03$, a number that was identified using the value of $\gamma$ from the energy and virial fluctuations at a reference state point with $\rho=0.005$ ($\kappa=5.85$), is more accurate at low densities (large $\kappa$).

\begin{figure}
  \centering
  \includegraphics[width=\figwidth]{y_im8_Fs_msd.eps}
  \caption{(a) The reduced mean-square displacement and (b) the self intermediate scattering function plotted as functions of the reduced time on the isomorph generated using the direct isomorph check. The dynamics collapse almost perfectly. The $q$ vector is kept constant in reduced units as $q=\rho^{1/3}\tilde{q}$ with $\tilde{q}=7$.}\label{fig:im8_dynamics}
\end{figure}

\begin{figure}
  \centering
  \includegraphics[width=\figwidth]{y_im2_im3_Fs_msd.eps}
  \caption{(a) and (c) The reduced mean-square displacements (left); (b) and (d) intermediate scattering functions (right) along the two isomorphs obtained from \eq{eq:y_hrho} for $\Lambda=1$ (top) and $\Lambda=1.03$ (bottom). Both sets of state points show almost invariant dynamics, although for $\Lambda=1.03$, the collapse is slightly worse than for $\Lambda=1$. The reduced scattering vector was again $\tilde{q}=7$.}\label{fig:im23_dynamics}
\end{figure}

We proceed to check to which degree the three sets of prospective isomorphic state points exhibit the invariance of dynamics and structure predicted for isomorphs.
We test the invariance of the dynamics in \fig{fig:im8_dynamics} for the isomorph generated by the direct-isomorph-check method and in \fig{fig:im23_dynamics} for the two isomorphs generated from the estimates of $h(\rho)$. The figures show the mean-square displacements and the intermediate scattering functions in reduced units. For all three sets of prospective isomorphic state points both measures of the dynamics collapse nicely onto a single curve.

\begin{figure}
  \centering
  \includegraphics[width=\figwidth]{y_im_D.eps}
  \caption{The reduced diffusion coefficient along the three prospective isomorphs, calculated from linear regression of the part of the mean-square displacement above unity. The diffusion coefficients of the state points obtained with the direct isomorph check are constant in the tested range of densities. The two estimates from \eq{eq:Gamma-k} have been tested in much larger range, and show a larger deviation from isomorph invariance, especially the estimate with $\Lambda=1.03$ at high density. Overall, the dynamics on either of the three prospective isomorphs are much more invariant, however, than on the curves of constant temperature or constant $\Gamma$.}\label{fig:diffusion}
\end{figure}

There are only minor differences in how invariant the dynamics are on the three prospective  isomorphs. To amplify these differences we calculated the reduced diffusion coefficient from the mean-square displacement at all investigated state points. The results are shown in \fig{fig:diffusion}, and compared with the diffusion coefficient along an isotherm and a curve of constant $\Gamma$. In view of the large density range simulated there is  little variation in the diffusion coefficient along the isomorph. The isomorph obtained with the direct-isomorph-check method only covers part of the phase diagram (because of the time-consuming nature of obtaining these state points). The reduced diffusion coefficients are virtually constant over the range simulated by this method. The results for the isomorph estimated from the pair potential with $\Lambda=1.03$ collapse with those of the isomorph from the direct isomorph check. Interestingly, the range where the diffusion coefficients are almost invariant coincides with the range where agreement between the estimated and the fluctuation $\gamma$ is best. We also note that although $\Lambda=1$ leads to a worse prediction for $\gamma$, it gives a more invariant diffusion coefficient when the whole phase diagram is considered. We attribute this to some cancellation of errors, rather than reflecting that $\Lambda=1$ gives a more precise value of the relevant interparticle distance. Note also that the invariance of the dynamics, and thus the isomorphs seems to continue all the way to the OCP limit. As mentioned earlier, also the melting line is an isomorph, so our results indicate that also the melting line continues to the OCP limit, indicating the existence of a phase transition in the OCP~\cite{Stishov1998}, at least from a dynamical point of view.

\begin{figure}
  \centering
  \includegraphics[width=\figwidth]{y_im8_rdf.eps}
  \caption{The reduced radial distribution function $g(\tilde{r})$ at isomorphic state points obtained with the direct isomorph check (a). Although the change in density is an entire decade, the reduced-unit structure does not change significantly along the isomorph. The invariance is especially striking when compared to the reduced radial distribution functions of isothermal state points (b), especially considering the smaller density range for the isotherm.}\label{fig:y_im8_structure}
\end{figure}

\begin{figure}
  \centering
  \includegraphics[width=\figwidth]{y_im2_im3_rdf_sq.eps}
  \caption{The radial distribution functions (left) and static structure factors (right) for state points obtained from \eq{eq:y_hrho} for two values of $\Lambda$. The structure is not completely invariant on the isomorph; both the height and the position of the first peak vary somewhat.}\label{fig:y_im23_rdf}
\end{figure}

We proceed now to testing the isomorph invariance of structure as quantified via the radial distribution function $g(\tilde{r})$ and the static structure factor $S(\tilde{q})$ (both in reduced units). Results for the prospective isomorphic state points obtained using the direct isomorph check are shown in \fig{fig:y_im8_structure}; results for state points of the two estimates of $h(\rho)$ with $\Lambda=1$ and $\Lambda=1.03$ are plotted in \fig{fig:y_im23_rdf}. Overall, the structure is invariant on the three prospective isomorphs when compared to the change in $g(\tilde{r})$ along the isotherm. This is especially impressive considering the density on the isotherm changes by a factor of 4.4, while on the isomorphs it changes by a factor of 10 (\fig{fig:y_im8_structure}(a)) and $10^4$ (\fig{fig:y_im8_structure}).

Whereas the 10\% density change applied in \fig{fig:smallstep} resulted in invariance of the structure, the large density changes applied here (a factor of 10 and $10^4$ respectively) \emph{do} lead to systematic changes in the structure along the proposed isomorph, especially in the region of the first peak of $g(\tilde{r})$. This is not unexpected, because the increase in the steepness of the potential with decreasing density (see \fig{fig:y_im_Rgamma}) makes close encounters between particles less probable. This results in a steeper initial slope of $g(\tilde{r})$ and thus a higher first peak if the total number of nearest neighbors is unchanged ~\cite{Bohling2014}. Taking into account that the direct-isomorph-check isomorph ``only'' involves densities variations covering a single decade, we note that the deviation from isomorphic invariance is smallest for the state points obtained using $\Lambda=1$.

Not only the height of the peak, but also its position changes somewhat along the prospective isomorphs. This is an effect of the large change in the effective steepness of the potential (i.e., relative to $k_BT$). The Yukawa potential has for instance both a BCC and an FCC solid phase with the triple point at $\kappa=6.90$~\cite{Hamaguchi1997}. These two crystal structures have different reduced nearest-neighbor distances, and it is not surprising that some of these structural differences continue to exist in the liquid state. The change of the nearest-neighbor distance with density,  however, indicates that a single value for $\Lambda$ is not enough for accurately  tracing out the isomorph.

\vspace{1cm}

\section{Discussion\label{sec:discussion}}

We have shown that the Yukawa system is Roskilde simple. This was shown from the strong correlations between equilibrium virial and potential-energy fluctuations and by the fact that the Yukawa system has isomorphs in its phase diagram. An isomorph is a curve of constant excess entropy, but the curve can also be estimated directly from the pair potential. We have verified that the dynamics are invariant on the isomorphs as predicted by the theory. The structure of the fluid as characterized by the radial distribution function was found to be invariant to a lesser degree, in part because the position of the first peak shifts slightly. Our estimate of the isomorph shape from the pair potential uses the nearest-neighbor distance. Consequently, \eq{eq:y_gamma_rho_isomorph} with a constant $\Lambda$ can \emph{not} give an exact description of the density dependence of $\gamma$ along an isomorph. In view of the invariant dynamics shown in \fig{fig:im23_dynamics}(a) and (b), however, \eq{eq:y_hrho} with $\Lambda=1$ must be said to give a rather good description of the isomorph shape.

In summary, we have shown that the isomorph theory provides a simple and general framework for understanding previous findings for the Yukawa system. Thus our results explain the previously identified expression of the melting line of Yukawa systems~\cite{Vaulina2000, Vaulina2002}, which here follows from the fact that the melting line is an isomorph~\cite{paper4}. Likewise, the isomorph theory~\cite{Robbins1988, Rosenfeld2000, Rosenfeld2001} explains the observation that the transport coefficients of the Yukawa fluid collapse when plotted versus temperature scaled by the melting temperature (compare \eq{eq:T_hrho_isomorph}), as well as the recently proposed expression for the ideal glass transition line of mode coupling theory~\cite{Yazdi2014}.Finally, we point out that the Yukawa system belongs to the ``exponential'' class of quasiuniversal systems~\cite{Bacher2014a}.

\acknowledgments{
The centre for viscous liquid dynamics ``Glass and Time'' is sponsored by the Danish National Research Foundation via Grant No. DNRF61.
}

redpajama_set_name: RedPajamaArXiv


text:
using System;
using System.Collections.Generic;
using System.Drawing;
using System.Drawing.Drawing2D;
using System.Globalization;
using System.Linq;
using System.Windows.Forms;

// ReSharper disable once CheckNamespace
namespace RegulatedNoise
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				tb_uicolor.Text = ApplicationContext.RegulatedNoiseSettings.UiColour;
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        protected void DrawCalibrationPoints(IEnumerable<Point> calibration)
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                return;

            Form1.OcrCalibrator.CalibrationBoxes[_selCalibrationPoint.Id] = _selCalibrationPoint;

            AlignCalibrationBoxesWhereRelevant(Form1.OcrCalibrator.CalibrationBoxes);

            FillRawData();

            pb_calibratorBox.Refresh();

            Form1.OcrCalibrator.SaveCalibration();
        }

        private static void AlignCalibrationBoxesWhereRelevant(List<CalibrationPoint> calibrationBoxes )
        {
            for (int i = 3; i < 11; i++)
                calibrationBoxes[i] = new CalibrationPoint
                    (i,new Point(calibrationBoxes[i].Position.X,
                            calibrationBoxes[2].Position.Y));

            calibrationBoxes[11] = new CalibrationPoint
                (11,new Point(calibrationBoxes[2].Position.X,
                    calibrationBoxes[11].Position.Y));

            calibrationBoxes[1] = new CalibrationPoint
                (1,new Point(calibrationBoxes[5].Position.X,
                        calibrationBoxes[1].Position.Y));
        }

        private void Pb_calibratorBox_MouseMove(object sender, MouseEventArgs e)
        {
            if (Form1.OcrCalibrator.CalibrationBoxes == null)
                return;

            if (_isMouseDown)
            {
                _selCalibrationPoint.SetPosition(new Point(e.X - _selCalibrationPoint.Offset.X, e.Y - _selCalibrationPoint.Offset.X));

                if (_selCalibrationPoint.Hitbox.Right > pb_calibratorBox.Width)
                {
                    _selCalibrationPoint.SetX(pb_calibratorBox.Width - _selCalibrationPoint.Hitbox.Width);
                }
                if (_selCalibrationPoint.Hitbox.Top < 0)
                {
                    _selCalibrationPoint.SetY(0);
                }
                if (_selCalibrationPoint.Hitbox.Left < 0)
                {
                    _selCalibrationPoint.SetX(0);
                }
                if (_selCalibrationPoint.Hitbox.Bottom > pb_calibratorBox.Height)
                {
                    _selCalibrationPoint.SetY(pb_calibratorBox.Height - _selCalibrationPoint.Hitbox.Height);
                }
                pb_calibratorBox.Refresh();
            }
            //255,162
            if (pb_calibratorMagnifier.Image != null)
                pb_calibratorMagnifier.Image.Dispose();

            if (pb_calibratorBox.Image != null && _refbmp != null)
                pb_calibratorMagnifier.Image = Crop(_refbmp, new Rectangle(e.X - 25, e.Y - 17, 50, 31));
        }

        // call me lazy if you will - this is copied from OCR.cs
        public Bitmap Crop(Bitmap b, Rectangle r)
        {
            // From http://stackoverflow.com/questions/734930/how-to-crop-an-image-using-c

            var nb = new Bitmap(r.Width, r.Height);
            var g = Graphics.FromImage(nb);
            g.InterpolationMode = InterpolationMode.NearestNeighbor;
            g.DrawImage(b, -r.X, -r.Y);
            g.ScaleTransform(4f,4f);
            return nb;
        }

        private void Pb_calibratorMagnifier_Paint(object sender, PaintEventArgs e)
        {
            if (pb_calibratorMagnifier.Image != null)
            {
                e.Graphics.DrawLine(new Pen(Color.LightGray), pb_calibratorMagnifier.Width/2, 0,
                    pb_calibratorMagnifier.Width/2, pb_calibratorMagnifier.Height);
                e.Graphics.DrawLine(new Pen(Color.LightGray), 0, pb_calibratorMagnifier.Height / 2,
                    pb_calibratorMagnifier.Width, pb_calibratorMagnifier.Height/2);

            }
        }

        private void Tb_uicolor_TextChanged(object sender, EventArgs e)
        {
            try
            {
                var red = int.Parse(tb_uicolor.Text.Substring(1, 2),NumberStyles.HexNumber);
                var green = int.Parse(tb_uicolor.Text.Substring(3, 2), NumberStyles.HexNumber);
                var blue = int.Parse(tb_uicolor.Text.Substring(5, 2), NumberStyles.HexNumber);

                pb_uicolor.BackColor = Color.FromArgb(red, green, blue);

					 ApplicationContext.RegulatedNoiseSettings.UiColour = tb_uicolor.Text;
            }
// ReSharper disable once EmptyGeneralCatchClause
            catch
            {
            }

        }

        private void Btn_calibration_reset_Click(object sender, EventArgs e)
        {
            if (Form1.GameSettings.Display != null)
            {
                var calibrations = Form1.OcrCalibrator.GetCalculatedCalibrationPoints(Form1.GameSettings.Display.Resolution);
                DrawCalibrationPoints(calibrations);
                FillRawData();
                pb_calibratorBox.Refresh();
                Form1.OcrCalibrator.SaveCalibration();
                return;
            }

            MessageBox.Show("Unable to calibrate automatically, please calibrate manually...");
        }

    }
}

redpajama_set_name: RedPajamaGithub


text:
Pentagon says troops at US border to cost about $210 million
Posted 7:23 pm, November 20, 2018, by AP Wire
WASHINGTON — Using thousands of military troops to help secure the Southwest border will cost an estimated $210 million under current plans, the Pentagon told Congress on Tuesday, even as questions arose about the scope and duration of the controversial mission.
The total includes $72 million for approximately 5,900 active-duty troops providing support to Customs and Border Protection, plus $138 million so far for 2,100 National Guard troops who have been performing a separate border mission since April, according to a report sent to Congress on Tuesday but not released by the Pentagon.
A copy of the report was obtained by The Associated Press. After the AP published its story the Pentagon released a statement confirming the active-duty portion of the deployments is estimated at $72 million. It did not mention the $138 million in National Guard costs.
The total would grow beyond the current combined estimate of $210 million if the active-duty mission is extended beyond the current completion date of Dec. 15. Officials said an extension appeared likely but had not yet been agreed upon.
The Pentagon also was working on a potential adjustment to the mission that would give the active-duty troops who are operating in Texas, Arizona and California the authority to defend Customs and Border Protection personnel if necessary. The troops, who include military police, are currently authorized to defend themselves.
About 2,800 of the active-duty troops are in South Texas, far from the main migrant caravan in Tijuana, Mexico, south of California. The movement of the Central American migrants into Mexico in October was the stated reason that President Donald Trump ordered the military to provide support for Customs and Border Protection.
Trump, who called the migrant caravan an "invasion," has been accused by critics, including some retired military officers, of using the military deployment as a political tool in the run-up to the Nov. 6 midterm elections.
Sen. Dianne Feinstein, a California Democrat, said Tuesday the Pentagon's cost report shows the mission was a "charade."
"These soldiers spent weeks away from home and the Pentagon wasted millions of taxpayer dollars so President Trump could stoke fears of asylum seekers and try to influence election results," she said. "Using our military men and women as political pawns to support an anti-immigrant agenda is a low point, even for this president."
On Tuesday, Trump said he was sure the troops are happy to be on the border mission, even though it means being away from home over Thanksgiving.
"Don't worry about the Thanksgiving. These are tough people," Trump told reporters before flying to Florida for the holiday. "They know what they're doing and they're great and they've done a great job. You're so worried about the Thanksgiving holiday for them. They are so proud to be representing our country on the border where if you look at what's happening, Mexico, the people from Tijuana are saying, wow these are tough people. They're fighting us."
If, as expected, the mission is extended beyond Dec. 14, at least some of the troops are likely also to be away for Christmas.
Defense Secretary Jim Mattis has declined to publicly discuss cost estimates for the border mission, saying as recently as last week that he had little confidence in the accuracy of figures he had seen thus far.
"We can estimate costs all we want, I'd prefer to give you real costs. Right now, I can't give that to you," Mattis told reporters last Wednesday when he flew to Texas to see the military's work. "It's the cost of deploying them, it's the cost of transferring their equipment to the border, it's fuel costs, it's all those kinds of costs. So, I just don't want to get into something I can't give you what I believe confidently is accurate."
In its report to Congress on Tuesday, the Pentagon said it expects the deployment of 5,900 active-duty troops through Dec. 15 to cost $72 million, while adding that the mission, which is now three weeks old, is still being refined. The cost includes $19 million for personnel, $20 million for transportation of personnel, equipment and supplies, $28 in operating expenses and $5 million for concertina wire and other border barrier materials.
"The total cost of the operation has yet to be determined and will depend on the total size, duration and scope," the report said.
It said that as of Nov. 14, about $14 million in actual payments for expenses such as travel, supplies and transportation had been reported by the units involved.
The National Guard's border mission, which is being conducted by troops for numerous states, has cost an estimated $138 million as of Tuesday, the Pentagon report said. That mission, involving about 2,100 troops, began in April.
House approves $1.4 trillion spending deal to avert shutdown amid impeachment push
President Trump says aim of killing Iranian general was to 'stop a war,' not start one
'All is well,' President Trump tweets after Iran fires missiles at Iraqi base housing US troops
Iran strikes back at United States with missile attack at air base
Pentagon identifies two service members killed in roadside bombing in Afghanistan
US Army warns about fake text messages about military draft
Two US service members died in a helicopter crash in Afghanistan
Trump issues pardons for 3 war crime cases, including one soldier in Ft. Leavenworth prison
Gender reveal stunt led to plane crash in Texas
British troops help relocate more than a dozen endangered black rhinos
President Trump doubles down on striking cultural sites in Iran
US pulling out of northern Syria; full withdrawal possible
Trump administration preparing to announce long-anticipated reduction of US troops in Afghanistan

redpajama_set_name: RedPajamaCommonCrawl


text:
int main(int argc, char* argv[])
{
	unsigned int playerNumber = 0;
	signed int chosenNumber = 0;

	unsigned int cpuNumber = 200;

	printf("Please enter a number less than 100:");

	if(scanf("%d", &chosenNumber))
	{
		if(chosenNumber > 99)
		{
			printf("That's not below 100!  You lose!\n");
		}
		else
		{
			playerNumber += chosenNumber;
			if(chosenNumber > cpuNumber)
			{
				printf("You win!");
				printf("Scores: %x, %x", cpuNumber, playerNumber);
			}
			else
			{
				printf("You Lose!");
			}
		}
	}
	else
	{
		printf("That's not a number silly!");
	}
	return 0;
}


you got knowledge in the field of recommender systems.
In particular, what types of recommender systems exist?
We were talking a little bit on the subject of Recommender System comparison.
Is one Recommender System better than another?
It is exactly the subject of this video.
I'm going to explain to you how to evaluate Recommender Systems.
When you build recommender service you have some objectives in mind.
you would like to positively surprise your users with interesting recommendations.
Or you may want to always recommend relevant new items.
about new books about Spark as soon as they are published.
to spend as much time as possible on your website, and so on.
This is called a long-term objective.
the example of the metric that you can use to track customer lifetime value.
and r is a retention rate.
who continue to use your service after a fixed period of time.
You have a long-term objective.
How does it help to choose between several recommended system algorithms?
You can have two versions of your service and compare them over a period of time.
what AB testing stands for.
Because it will help you to compare algorithms online.
then you will spend the whole month to compare your algorithms.
it is like writing websites on pure HTML language.
I bet you know better ways of time killing.
That is why people usually use short-term process.
For example, you can use click through rate method, or CTR for short.
how many times they clicked on it.
to have a high correlation with the long term objective, LTV in our case.
will be using it in the future.
doesn't necessarily lead to optimization of a long-term objective.
it can increase the value of CTR.
your target audience in the long term.
And second, you can compare your algorithms way more faster.
Experimenting on real service customers is risky.
Consider a music streaming recommender service.
or dance music for quite a while, then you risk to lose a customer.
Saves your time and efforts and attract good customers.
So running an experiment is not for free.
How can you limit or overcome probable negative impressions?
The answer is, use your studies.
You setup an experimental service.
the least of hypotheses you would like to validate.
If you manage to do it physically, drop me a line how you did it.
The experiments at top has to be as close to the real world conditions as possible.
After you have made a decision, the chosen algorithm has to be validated online.
But is there even a faster way to run experiments?
Yes, you can compare the whole set of different algorithms offline.
you can use historical events to design experiments.
chosen for user case studies and online experiments.
high correlation with online experiments.
on the last ACF RecSys conference in 2016.
by the correlation optimization during experiments for some recommender services.
The field of offline metrics is well studied in academia.
please look through the available literature.
Time to go back to the math and other black magic.
such as MAE and RMSE.
estimate users' preference with high precision and confidence.
predictions, there are several ways to measure these metrics.
The obvious one is to use global metrics, for example GMAE.
prediction, and average over all the available values.
The other one, which is also widely used in production, is CMAE.
Which stands for Customer MAE.
You calculate MAE per each customer, and only then average those values.
diversity in the amount of feedback provided by different users.
Similar to CMAE, you can calculate item-oriented MAE.
But I personally haven't seen this variant of metric being used a lot.
us, and how to calculate it.
Given a user item metrics, how do you run cross validation?
you can assign each user item right into a cross validation split at random.
In this case, you don't need to think about anything.
as other cross validation approaches.
You can split data set by users or items.
Remember CMIE, here we go.
also called query, is used to build a user's profile if necessary.
The third approach is the most precise one.
at random is that we have intentionally used the information from the future.
In the introductory video I told you that a user item metrics has three dimensions.
The third dimension is time.
All the events from our service can be ordered by time stamps.
We split our data set by the time.
Train algorithms on all the available data before this time.
And evaluate them on the data after it.
also called retrained from scratch on every cross validation iteration.
See Wikipedia to get more information about incremental learning.
the peculiarities of the recommender system evaluation.
There are books and online courses dedicated to this topic.
that we are going to use in assignments.
Mean absolute error, and root mean squared error.
Please bear in mind that these methods I would further rate in production task.
But, are not so relevant for the top and recommendation task.
which doesn't correspond to the optimum in terms of MRR and DCG-like methods.
Summary of this video is the following.
correlation of user studies offline and online experiments.
You can explain where and when to use them.
And you can explain why it is so important to properly choose offline metric.
algorithm on MIE and RMSE for each of these scenarios.
Enjoy your lessons, and see you soon.


The Dual Enrollment program (formerly known as Move On When Ready/ACCEL) is a state-funded program for high school (public, private, and approved home-study) students that provides dual enrollment tuition assistance in Georgia. The program offers the opportunity to earn dual credit, satisfying high school and college Required High School Curriculum. provides opportunities for eligible high school students to enroll at East Georgia State College* and earn both high school and college credit via part-time or full-time enrollment. When satisfactorily completed, such courses will count both toward high school graduation and college credit. Student must remain in good academic standing with a 2.0 GPA or higher to remain eligible for the program. Students can enroll only in courses approved by the high school counselor and those listed in the Course Directory published by the Georgia Student Finance Commission. There is no residency or citizenship requirement to participate in the Dual Enrollment program.
Attend a Dual Enrollment day! Potential Dual Enrollment students will have the opportunity to visit campus and get started on the Admissions process for becoming a Dual Enrollment student. They will be able to complete the admissions application, submit transcripts and other paperwork, as well as test with the Accuplacer if required. The student will leave the day understanding if they are eligible for the program and what the next steps are to become an EGSC Dual Enrollment student.
The Dual Enrollment program covers 100% of tuition for approved courses, all mandatory, non-course related fees, and textbooks for approved courses. Students may incur expenses for course-related fees and supplies required for a particular course, or optional fees.
Please be aware that the program does not cover course related fees or outside reading texts. Students taking a science with a lab will be responsible for a science lab fee.
Optional, supplemental or suggested textbooks are not covered by the Dual Enrollment program and are the responsibility of the student.
Attend a Dual Enrollment participating school public or private secondary educational institution within the State of Georgia. Ask your guidance counselor to be sure your school is approved to participate.
* Using the College Board concordance tables, the new SAT scores will be converted to the old SAT equivalents to determine the combined Critical Reading + Math score required for admission. The combined, converted Critical Reading and Math score must total 970 in addition to meeting the individual score requirements. You can reference the new concordance tables online.
** If Reading score is 75 or higher, WritePlacer is not required. To be eligible for College Algebra, students must have a score of 79 or higher in Elementary Algebra or a score of 266 or higher in Quantitative Reasoning, Algebra, and Statistics.
Effective Summer 2018, USG placement guidelines have changed. Please see chart below to review your scoring placement.
**We can only make a decision based on the highest scores that we receive. Please make sure that scores are up-to-date. If you submit scores and then take the test again, then you may submit the new scores for us to review. We will reassess your file based on the updated scores.
Step 1 : Discuss your plan to apply for Dual Enrollment with your parents and high school counselor. Work with your high school counselor to ensure you meet the Dual Enrollment requirements (i.e. HOPE, GPA, test scores, etc.) Your high school counselor will assist you in selecting your high school classes and the Dual Enrollment coordinator will assist you in selecting your college classes.
Step 2 : Submit an application for admission to East Georgia State College ($20 application fee is waived) via GAfutures. Your high counselor will be able to assist you with setting up your GAfutures account. If you wish to speak to an EGSC counselor to get more information before applying, please feel free to stop by any of our office locations (Swainsboro, Statesboro or Augusta), call us at (478) 289-2017 or email us.
Step 3 : Review your Admissions Checklist and submit transcripts, test scores, and your Immunization Records along with the Medical Entrance form.
Step 4 : Complete the GAfutures Dual Enrollment Program Funding Application. Your high counselor will be able to assist you with setting up your GAfutures account. Students attending a home study program or do not have a Social Security number must complete the paper Dual Enrollment program funding application. As a part of your Dual Enrollment application process, your parents must give permission for you to participate in the Dual Enrollment program. After completing the Dual Enrollment application, you need to meet with your high school counselor to discuss approved courses and submit the Dual Enrollment agreement form, which must be completed and submitted prior to the first day of classes at East Georgia State College. Please note this application goes directly to the Georgia Student Finance Commission and NOT East Georgia State College.
Step 5 : Submit a completed Dual Enrollment Student Participation Agreement. Please print this form and complete it fully with your guidance counselor and parent/guardian after discussing the courses to enroll in. It should be returned to Student Affairs by the student or guidance counselor in order for an admission decision to be made. The form can be submitted via email (documents@ega.edu) or faxed to 478-289-2353.
For additional information regarding Dual Enrollment, please see program information and regulations.
Step 1 : Make an appointment with the Dual Enrollment Coordinator. Please note that some college courses may have pre-requisites and you may not be eligible for those courses. Sign up for your registration appointment by clicking on the campus you will be attending.
IMPORTANT: If you make any changes to your course schedule after your Dual Enrollment application has been approved, you must complete a new Dual Enrollment agreement form and have the new course(s) approved by both your high school counselor and the Dual Enrollment coordinator. Students are also not permitted to withdraw from a currently enrolled course without prior approval from their high school counselor verifying if the course will affect their high school graduation requirements.
Step 2 : Log-in and activate your myEGSC account. Click here for instructions on how to obtain your login and password information. Prior to attending Orientation, you must submit a photo for your student ID online here.
Step 3 : Take a copy of your official college schedule to your high school counselor prior to the beginning of the semester to ensure that your high school class schedule is appropriately adjusted. This can be printed from your myEGSC account.
Step 4 : Attend a Dual Enrollment Orientation. All first-time EGSC Dual Enrollment students are required to attend Orientation as it provides students and their families with a more informed understanding of resources, policies, and new student expectations. Key elements of the program include a sequence of informational sessions for students and parents, training on myEGSC and its applications. Since students have the ability to take their Dual Enrollment classes at their high school or at either the Swainsboro or Statesboro campus, we strongly encourage students to attend the Orientation session most convenient for them. Orientation registration is required and the registration link will be emailed to students that will include the date, time, and location. Parents are also highly encouraged to attend. Both students and parents will be given information about the Dual Enrollment program and East Georgia State College.
I'm a Returning Dual Enrollment student, what's next?
Complete an online Dual Enrollment application. This is required prior to each term you want to take classes, not just prior to your first term.


Are you ready to have hours of fun?
Here at Russell Up, we have a great selection of high quality bouncy castles that can be enjoyed by all ages at any event.
Pick from the following themes - Peppa Pig / Sponge Bob / Disco Party / Clown / Mickey & Minnie Mouse / Pirate / Princess / Frozen / Super Hero / Disco Dome / Dinosaur / Pop/Rock Star / Princess Carriage.
Russell-Up Entertainments specialise in all your event needs!!!
We cover all areas of London, Essex, Hertfordshire and some parts of Kent.
BOUNCY CASTLES for hire / Popcorn & Candy Floss + more 5 out of 5, 1 based on 1 ratings 1 user reviews.
What a great company. I would not hesitate to recommend and I will definitely use again. This last event of mine had the hardest crowd, 300 16/17 year olds and I could not have got better than Russel, his patience, service, price, product would be hard to beat.


WorkPoint Express settings – Welcome! How can we help?
The behaviour of WorkPoint Express (WPE) is controlled by the settings. Some of these are managed by the users, some are managed by system administrators. Below is a guide to the usage.
To get to the settings. go to WPE and click on the three dots at the top. From here select "Settings".
The settings page will look somewhat like this.
This opens WPE in windows such as emails - i.e. when you create a new mail, WPE sidebar opens in the mail window.
When you want to see properties (e.g. on a document), you can have it displayed in WPE or in a separate pop up window.
If you often need to edit properties you can check this so properties always are displayed when you select an item, e.g. a document. It will grey out if 3 is checked.
If you have more views than on document lists, this setting determines whether default view always is displayed first.
When opening WorkPoint Express in for example an email window, this setting determines how it opens. If it is unchecked, both entity and detail window in WorkPoint Express is open, if checked the entity detail window is hidden.
When you drag and drop an email to WPE, it will by default create a copy. If this checkbox is checked, it will be moved to WPE (hence deleted from your inbox).
Force the use of WebDAV technology for edit document. As it is old technology do only use this if you have to. WorkPoint does not provide support for this.
This setting determines what happens when you double click on a document in WPE.
This setting determines if the property window should open after upload of a document to a document list.
This setting determines if the property window should open after upload of an email to an email list.
This setting applies to Email Manager: It determines if the Email Manager property window should open after upload of an email.
By default SharePoint overwrites created date when a document is uploaded to SharePoint. This setting allows for setting created and modified properties on uploaded documents to preserve the original created date. More information here.
Chooses the language of WPE - "Default" selects the MS Office language in use.
This setting opens a pop up after an email is sent. The floating pop up makes it easier to drag and drop the sent email to WPE. Alternatively you must find the email in your "sent items" folder to journalise it.
When 17 is selected, you can also drag documents to the related document list via the pop-up window using this setting.
Tags emails in your inbox when they are journalised in WorkPoint.
Determines the speed the content loads in WPE when connected to SharePoint.
as 20, when connected to WorkPoint Server (on-premise).
as 20 when connected to WorkPoint365.
When selected this setting hides any lists on the site that are not present in the WorkPoint tab web part.
This tab is where you can manage the behaviour of the WorkPoint modules.
Check the business modules you want displayed in WPE and change the order of appeareance.
For each business module check what to show and whether the content should be expanded or not and change the order of appeareance.
This setting applies to Email Manager. The system can provide suggestions for where an email should be journalised. You can adjust the suggestions weight here. Note: Only for WorkPoint On-premises, not supported in WorkPoint365.
This setting manages the connection to the WPE datastore.
Settings on the system page is mainly for administrators and configurators and requires system knowledge.
Access control tab is used to set the access rights via an Active Directory Group.
Here you can determine and map the fields on the email lists on the sites. Map the email fields to the fields in SharePoint (WorkPoint).
Same as 2, but for Outlook contact cards, allowing the user to drag and drop contact cards to create WorkPoint contacts.
Smart file handling allows large files to be streamed to a network drive instead of stored in the database.
Use this setting to create smart custom links to use when right-clicking on a business module site.
These settings are for Email Manager. Indstillingerne. "Show auto journalize allowed toggle button" and "Show all e-mails button" are determining if these buttons should be displayed in "E-mail Overview". For "Show all e-mails button" you can with "Only for members of Active Directory group" settings control access to the button.
These settings are for Email Manager. "Smart journalization after sent" activates the feature. If this mail is a reply to a mail (parent) and the parent is journalized in EMM, then this feature will journalize the mail the same place as the parent. "Number of lines shown in the journals row" sets the amount of lines displayed in the journal view in the emails. "Ask for archiving e-mails with bcc addresses after sent" allows Email Manager to store emails sent to bcc recipients (hence reveals bcc email addresses).
Selfexplanatory. Value for "Maximum number of items shown in document list" must be between 10 and 100. Value for "Journal Page Size" must be between 10 and 10000. Value for "Maximum number of e-mails shown in search all journals" must between 10 og 1000.
This setting is used when a solution contains lists with many lookup fields. These can slow performance. Set the value as high as possible. If the value is set too high, the system will be unable to retrieve the list.
This setting controls the interface for SharePoint managed metadata. If a managed metadata field contains a lot of values, a flat view is recommended for better performance. When using a flat view, the user must type in a search to retrieve metadata. If a flat view is not used, metadata terms will be displayed in a tree structure.
These settings controls the system timeout. Only to use if some system service starts responding very slowly.
This setting is only relevant if WorkPoint Journalise flag is installed. The setting controls how often the flags are updated. Generally the higher value the lesser stress on the system.
This setting is used when you have root sites common for all users. The setting can filter user access, so only users that are members of a certain Azure AD group can access the root site in question. To do this, the URL to the Active Directory i Azure must be set here.
Check this to use uri schemes for opening MS Office documents. This is recommened.
These settings are made for optimising performance when uploading documents. If de-selected, upload performance is increased.
When checking "Set title", uploaded documents will have the metadata "Title" set by the system. "Preserve version number" is only relevant when uploading to document lists with version control activated. This setting will maintain correct versioning when uploading documents. If it is unchecked, the version will jump two numbers when uploading, provided there is versioning enabled on the list and other metadata are set during uploads.


text:
'use strict';

var _ = require('lodash');

module.exports = {

  /**
   * @param req
   */
  buildCallbackNextUrl: function buildCallbackNextUrl(req) {
    var url = req.query.next;
    var includeToken = req.query.includeToken;
    var accessToken = _.get(req, 'session.tokens.accessToken');

    if (includeToken && accessToken) {
      return url + '?access_token=' + accessToken;
    } else {
      return url;
    }
  }
};


Backed by a team of knowledgeable professionals, we are an identified firm in the market for providing an extensive range of Use and Throw Ball Pen Making Machine.
Established in the year 2016, Mondal Trading Corporation is the leading Manufacturer, Trader and Exporter of Ball Pen Making Machine, Plastic Ballpoint Pen, Pen Accessories and much more. We are a quality-conscious firm and continuously struggle hard to bring forth only premium quality products to our prestigious patrons at reasonable rates.


text:
Paul Arling
Paul Arling, Chairman and Chief Executive Officer, joined UEI in 1996 as Chief Financial Officer. He was named Director in 1996, President and COO in 1998, CEO in 2000 and Chairman in 2001.
Paul earned a BS and an MBA from the Wharton School at the University of Pennsylvania.