text:
\section{Introduction}
Ultracold gases with dipolar interactions have been the subject of intense experimental and theoretical studies over the past few years~\cite{Lahaye:2009}.
Strong dipole-dipole interactions can be realized by using atoms with large magnetic moments such as chromium, erbium and dysprosium~\cite{Lahaye:2007,Lu:2011,Aikawa:2012} or polar molecules with electric dipole moment induced by static external field~\cite{Ni:2008,Park2015}.
Compared to systems with contact interactions, dipolar gases exhibit much richer physics both in the few-body~\cite{Wang2015} and many-body~\cite{baranov2012condensed} domains.
Even in the limit of weak interactions, their properties are highly affected by the long-range and anisotropic nature of the dipole-dipole interaction term.
In particular, for sufficiently strong dipole-dipole interactions Bogoliubov excitation spectrum of the Bose gas can contain unstable modes which drives the collapse of the condensate, observed experimentally e.g. with chromium~\cite{Lahaye2008}.

Recent experiments performed using atoms with high magnetic moments revealed the existence of new intriguing effects. When the condensate is quenched into the regime unstable from the mean field point of view, instead of collapsing the gas can form a spatially ordered structure of stable droplets with high density~\cite{Barbut2016,Wachtler2016,Kadau2016}. Stabilization of the gas in form of the droplets is due to quantum fluctuations which have crucially important contribution near the instability. These quantum droplets turn out to be stable even without the presence of an external trap, with lifetime limited only by three-body losses~\cite{Wachtler2016a,Chomaz2016,Baillie2016,Schmitt2016}.

In the regime of weak interactions the mean field description of dipolar Bose gas relies on modified Gross-Pitaevskii (GP) equation which acquires an additional nonlocal term coming from dipole-dipole interactions~\cite{Yi2001}.
Description of the droplet phase requires including beyond mean field Lee-Huang-Yang (LHY) correction which provides an additional effectively repulsive term preventing the gas from collapsing. For dipolar gases the LHY correction is strongly enhanced compared to contact interactions~\cite{Schutzhold2006,Lima2011,Lima2012}.

In the mean field theory for interacting bosons, the effective potential is given by the low energy scattering amplitude~\cite{Beliaev1958,Hugenholtz1959}. In contrast to contact interactions, for dipolar bosons it is required to include many partial waves in the scattering calculation. For weak dipole moments and away from scattering resonances Born approximation describes the scattering amplitude with good accuracy~\cite{Yi2001,Kanjilal2008,Ticknor2008,Bohn:2009,Zhang2014,Bohn2014}. However, for lanthanide atoms the validity of Born approximation can be limited as the magnetic dipole-dipole interaction becomes too strong. Furthermore, the interaction potential at short range has a complex anisotropic structure, resulting in additional coupling between partial waves. As a result, lanthanide atoms exhibit very dense structures of Feshbach resonances~\cite{Chin:2008,Petrov:2012,Baumann:2014,Frisch2014,Maier2015}. In the vicinity of a resonance Born approximation is not valid at all and one has to use numerically calculated scattering amplitude. This can modify the many-body properties of the dipolar gas~\cite{Wang2008,Huang2010}.

While the droplet model based on extended GP equation within Born and local density approximations has so far successfully described the droplet formation and their basic properties, it is worthwhile to study more elaborate models for deeper understanding of the droplet phase.
In particular, finite temperature effects can affect the size and lifetime of the droplets~\cite{Boudjemaa2016}.
Effects of the trapping potential can also be important especially when the characteristic trap lengths become comparable not only to the condensate healing length, but also to the length scales characteristic for the scattering.
Finally, strong dipolar interactions and dense resonances limit the usefulness of Born approximation for the scattering amplitude.
In this work, we concentrate on the latter point and study how the properties of dipolar Bose gas are affected by using realistic interaction potentials.
We find that the role of dipolar interactions is enhanced away from resonances and strongly suppressed in their vicinity. This has visible consequences on the many-body properties of the gas, most notably on the critical atom number needed for formation of a stable droplet.

The paper is structured as follows. In Section II we compute the scattering amplitude for a pair of magnetic atoms using a realistic interaction potential and discuss the validity of Born approximation. In Section III we briefly review the mean field theory of dipolar quantum gases and the role of beyond mean field corrections, and discuss the stability diagram of a trapped gas. These results are then used in Section IV to analyze the experimentally relevant cases of Dy atoms and weakly bound Dy$_2$ molecules. Conclusions are drawn in Section V.

\section{Scattering amplitude}
\label{sec:scater}

Providing a reasonable estimate for the low energy scattering amplitude of lanthanide atoms is a demanding task because of the complex interaction potential~\cite{Petrov:2012}. The dominating terms are isotropic van der Waals attraction $V_{\rm vdW}=-C_6/r^6$ and anisotropic dipole-dipole interaction $V_{\rm dd}=-C_3 P_2(\cos\theta)/r^3$. Other terms such as quadrupole-quadrupole and anisotropic van der Waals interaction introduce additional couplings between different partial waves and hyperfine channels. This leads to occurrence of extremely densely spaced Feshbach resonances with high partial wave character~\cite{Frisch2014}. In our model we simulate this behavior by varying the short-range boundary conditions to mimic a Feshbach resonance and we focus on the interplay of the van der Waals and dipolar interaction.

A commonly used treatment of ultracold dipolar scattering involves using a simplified potential with the dipolar term and a hard wall placed at some distance $r_0$ to set the scattering length~\cite{Kanjilal2008,Bohn:2009,Oldziejewski2016} and utilizing Born approximation to obtain the scattering amplitude. However, for magnetic atoms the length scales associated with different terms in the potential are comparable, with strong coupling between partial waves. Born approximation can be expected to break down in this case, especially in the vicinity of scattering resonances. The prominent role of the van der Waals potential can be seen e.g. by studying the adiabatic potential curves obtained by diagonalizing the angular part of the Hamiltonian in partial wave basis. Figure~\ref{fig:adpots} shows a comparison between realistic adiabatic potentials and the hard wall approximation for the case of dysprosium. It can be seen that including van der Waals interaction leads to vastly different shape and height of the centrifugal barrier. As for higher partial waves the position of the barrier moves towards the origin, the modification is even stronger in high partial wave channels.

\begin{figure}
\centering
\includegraphics[width=0.45\textwidth]{potsy.pdf}
\caption{\label{fig:adpots}Three lowest adiabatic potential curves with $m=0$ obtained for realistic dysprosium long range potential (black lines) and for the case where van der Waals interaction is replaced by a hard wall set at short distance. The length unit here $R_6=\left(2\mu C_6/\hbar^2\right)^{1/4}$, while the energy is given in units of $E_6=\hbar^2/\left(2\mu R_6 ^2\right)$.}
\end{figure}

Let us now discuss the relevant length and energy scales. In this work we will focus on strongly magnetic dysprosium atoms, for which the isotropic van der Waals coefficient takes the value $C_6=2270$ in atomic units~\cite{Lepers2016} and the dipole moment is $9.93\mu_B$ where $\mu_B$ is the Bohr magneton. One can then define characteristic van der Waals length as $R_6=\left(2\mu C_6/\hbar^2\right)^{1/4}$, which for dysprosium gives $161\,a_0$ with $a_0$ being the Bohr radius. Dipolar interactions can be characterized in a similar way by $R_{\rm dd}=2\mu d^2/ 3\hbar^2$, for Dy atoms giving $R_{\rm dd}=131\,a_0$.
We will also analyze the case of weakly bound Dy$_2$ dimers for which we take $C_6=4C_6^{\rm Dy}$ and the dipole moment is assumed to be two times larger than for Dy. This kind of molecules can be produced by making use of broad universal Feshbach resonances~\cite{Maier2015}. Weakly bound erbium molecules have been recently created and characterized~\cite{Frisch:2015}. The characteristic length scales for this case are $R_6=271.5\,a_0$ and $R_{\rm dd}=1049\,a_0$. In atomic units the dipole moments we are considering here are equivalent to $0.1-0.2\,$D. These values are easily achievable also with polar molecules placed in external electric field.

To solve the low energy scattering problem with realistic potential, we first set the boundary conditions at very short range where the van der Waals interaction dominates and coupling between partial waves is negligible. The phase of the short range wave function would then determine the scattering length for pure van der Waals interactions. Then we propagate the solution to large distances using Numerov method with collision energy set to be smaller than all characteristic energies of the problem. Dipolar interactions require including a huge number of partial waves and propagating the wave function to very large distances to obtain convergent results~\cite{Ticknor2008,Bohn:2009}. Similarly to changing the position of the hard wall, we can manipulate the short range phase to set the scattering length and simulate a Feshbach resonance (note that in contrast to contact interactions, the actual scattering length differs from the position of the hard wall as it is renormalized by dipolar interaction). The long-range nature of dipolar term which behaves as $r^{-3}$ results in increased density of near threshold bound states, so usually several resonances appear when changing the short range phase. Additional couplings can easily be included within this method.

We fit the wave function at large distances to asymptotic scattering solutions to extract the scattering amplitude
\begin{equation}
f(\mathbf{k},\mathbf{k^\prime})=4\pi\sum_{\ell m \ell^\prime m^\prime}{Y_{\ell m}^\star (\hat{k})Y_{\ell^\prime m^\prime}(\hat{k}^\prime) t_{\ell m}^{\ell^\prime m^\prime}(k)}.
\label{eq:fkk}
\end{equation}
where $t_{\ell m}^{\ell^\prime m^\prime}$ is the reduced T-matrix elements and $Y$ denote standard spherical harmonics. For bosons the summation runs only over even values of $\ell$, $\ell^\prime$.
For dipolar interactions Born approximation predicts~\cite{Yi2001,Bohn2014}
\begin{equation}
\left(t_B\right)_{\ell m}^{\ell^\prime m^\prime} = -\frac{6\pi \left<Y_{\ell, m}\right|Y_{2,0}\left|Y_{\ell^\prime, m^\prime}\right> R_{\rm dd}}{((\ell-\ell^\prime)^2-1)(\ell+\ell^\prime)(\ell+\ell^\prime+2)}
\end{equation}
for $\ell+\ell^\prime>0$. For the $t_{00}^{00}$ element one has to insert the value of the $s$-wave scattering length $a$. The total scattering amplitude within the Born approximation is then~\cite{Bohn:2009,Bohn2014}
\begin{equation}
f_B(\theta)=-a-a_{\rm dd}^{\rm Born}P_2(\cos\theta),
\label{eq:fBorn}
\end{equation}
where $\theta$ is the angle between the momentum transfer vector and the dipole axis and $a_{\rm dd}^{\rm Born}=R_{\rm dd}$. The relative strength of the dipolar interaction in the Born approximation can be characterized by $\epsilon_{\rm dd}^{\rm Born}=a_{\rm dd}^{\rm Born}/a$.

Figure~\ref{fig:fDy} shows exemplary scattering amplitudes for Dy atoms away from resonance and close to it, as well as for Er atoms and Dy$_2$ dimers away from resonance compared with Born approximation predictions. Surprisingly, in all the cases we investigated the numerically calculated scattering amplitude could be well described with the same form as in Eq.~\eqref{eq:fBorn}, but with modified $a_{\rm dd}$ parameter (from now on we will refer to the standard dipolar length as $a_{\rm dd}^{\rm Born}$ as it remains unchanged within Born approximation). This result simplifies a lot the analysis of many-body effects, since all the methods developed for dipolar bosons within Born approximation can be readily used. The next observation is that away from resonances, where scattering length is of the order of $a_{\rm dd}^{\rm Born}$, the effective $a_{\rm dd}$ turns out to be slightly larger than the actual one due to corrections arising from all partial waves. The modification turns out to be strongly energy-dependent. For Dy at 10nK collision energy the enhancement of effective dipolar length is of the order of $2\%$ and at 100nK about 10\%, while for Dy$_2$ it is about $4\%$ at 10nK. Increasing the value of the scattering length leads to a significant deviation of low $(\ell,m)$ $t$ matrix elements from Born approximation (see Fig.~~\ref{fig:res}) and results in much smaller effective $a_{\rm dd}$. Figure~\ref{fig:add} shows the dependence of the effective dipolar length on the dipolar interaction strength $\epsilon_{\rm dd}$. We see that the impact of the resonance depends on the dipole moment. For low dipole moments the dependence of $a_{\rm dd}$ on the scattering length is changed only very close to the resonance, while for highly dipolar particles the resonance has visible impact in a larger range of scattering lengths. As a result, the actual relative strength of the dipolar interaction defined as $\epsilon_{\rm dd}=a_{\rm dd}/a$ differs from $\epsilon_{\rm dd}^{\rm Born}$, being larger away from resonances and smaller in the vicinity of a resonance.

Figure~\ref{fig:res} shows an example of the dependence of the lowest $t$ matrix elements near an exemplary Feshbach resonance. Scattering length has more than one pole here due to increased density of near threshold bound states resulting from dipolar interaction. At each resonance, $t^{20}_{20}$ also diverges (whis is not clearly visible on the figure due to too low resolution of the data points and finite collision energy which suppresses the divergence) and $t^{20}_{00}$ vanishes. Within our model, channels with $m\neq 0$ are not affected by the resonance. It is possible to include additional couplings that modify scattering in higher partial wave channels. However, the phase shifts in these channels would still be dominated by universal dipolar scattering and the expected effects would be small as long as the collision energy is low enough.

\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{amplitudes2}
\caption{\label{fig:fDy}Scattering amplitude $f(\theta)$ for dysprosium atoms at scattering length $a=169\,a_0$ (upper left) and $a=1490\,a_0$ (upper right), for erbium with $a=154\,a_0$ (lower left) and for Dy$_2$ dimers with $a=185\,a_0$ (lower right). Straight black lines come from the numerical calculation, while red dashed lines show the Born approximation predictions. Note that different scale was used for Dy$_2$, where the amplitude spans a wider range due to much larger $a_{\rm dd}$ coefficient.}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{adda_razem}
\caption{\label{fig:add}Effective dipolar length as a function of $\epsilon_{\rm dd}^{\rm Born}$ for dysprosium at 10nK (blue straight line) and at 100nK (red dashed line) and Dy$_2$ (dot-dashed magenta line). Dotted black line shows the Born approximation result $a_{\rm dd}/a_{\rm dd}^{\rm Born}=1$.}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=0.3\textwidth]{Dy_matr}
\caption{\label{fig:res}Exemplary magnetic field dependencies of the lowest $t$ matrix elements near a Feshbach resonance in dysprosium. Black lines show the numerical results, while red dashed are the Born approximation results.}
\end{figure}

\section{Effective mean field theory for dipolar bosons}
Having calculated the scattering amplitude for realistic interaction potential, we will now use these results in the effective many-body theory.
The system under consideration consists of $N$ magnetic (or electric) dipolar bosons of mass m and dipole moment $d$ oriented along the $z$ direction by an external magnetic field trapped in an external potential $V_{\mathrm ext}({\mathbf r})=\frac{m}{2}\left(\omega_x^2 x^2+\omega_y^2 y^2+\omega_z^2 z^2\right)$ with $\omega_{x,y,z}$ the trapping frequencies. The second quantized Hamiltonian reads

\begin{eqnarray}
 H&=& \int\! d{\mathbf r}\,\hat\Psi^{\dag}({\mathbf r})
\left[-\frac{\hbar^2}{2m}\nabla^2+V_{\mathrm ext}({\mathbf r})\right]\hat\Psi({\mathbf r}) \nonumber\\
&\ &+\frac{1}{2}\int\! d{\mathbf r}\int\! d{\mathbf r'}
\hat\Psi^{\dag}({\mathbf r})\hat\Psi^{\dag}({\mathbf r'})
V({\mathbf r}-{\mathbf r'})\hat\Psi({\mathbf r'})\hat\Psi({\mathbf r}),
\label{h}
\end {eqnarray}

where $\hat\Psi({\mathbf r})$ and $\hat\Psi^{\dag}({\mathbf r})$ are bosonic annihilation and creation field operators respectively and $V({\mathbf r}-{\mathbf r'})$ is the interaction potential between the atoms.

The standard way to obtain the mean field Gross-Pitaevskii equation is to replace the field operators by a complex-valued function $\psi(\mathbf r,t)=\left\langle\hat\Psi(\mathbf r,t)\right\rangle$. Here we also have to include the LHY correction to the mean field equation of state.
Furthermore, the true interaction potential between the atoms $V({\mathbf r}-{\mathbf r}')$ is replaced by the effective potential $V_{\rm eff}({\mathbf r}-{\mathbf r}')$ given by the low energy scattering amplitude~\cite{Beliaev1958,Hugenholtz1959} obtained for the full potential. A general expression for an anisotropic effective potential can be given as~\cite{Yi2001}
\begin{eqnarray}
V_{\rm eff}({\mathbf r})=\frac{4\pi \hbar^2  a}{m}\delta({\mathbf r}) +\sum_{l>0, m}
\alpha_{lm} {Y_{lm}(\hat r)\over |{\mathbf r}|^{3}}, \label{veff}
\end{eqnarray}
where the first term describes the $s$-wave contribution, $Y_{lm} $ stays for standard spherical harmonic and $\alpha_{lm}$ are determined from the scattering amplitude~\cite{Yi2001}. According to the results from Section II in our case the effective potential may be written as the well-known formula consisting of a sum of the contact and dipole-dipole interactions:
 \begin{eqnarray}
V_{\rm eff}({\mathbf r}-{\mathbf r}')=\frac{4\pi \hbar^2  a}{m}\delta({\mathbf r})-\frac{4\pi \hbar^2  a_{\rm dd}}{m}{2P_{2}(cos{\theta})\over |{\mathbf r}-{\mathbf r}'|^{3}}, \label{nasz}
\end{eqnarray}
where $P_{2}(\cos{\theta})$ is the second Legendre polynomial. We remind that $a_{\rm dd}$ is an effective parameter which stems from the scattering amplitude.

The extended GP equation within the local density approximation for slowly varying spatial profile of $\psi(\mathbf r,t)$ takes the form~\cite{Wachtler2016}
\begin{eqnarray}
\ii\hbar \frac{\partial}{\partial t}\psi({\mathbf r},t) &=&  \left [ -\frac{\hbar^2}{2m}\nabla^2+V_{\rm ext}({\mathbf r})   \right\delimiter 0 \nonumber \\
 && \left\delimiter 0  +N\int d^3r'V_{\rm eff}({\mathbf r}-{\mathbf r}')|\psi({\mathbf r},t)|^2\right\delimiter 0 \nonumber \\
 && \left \delimiter 0 + g_{\rm QF}N^{3/2}|\psi({\mathbf r},t)|^{3}  \right ]      \psi({\mathbf r},t),
 \label{GPE}
\end{eqnarray}
with $\int d^3r |\psi({\mathbf r},t)|^2=1$. The last line of Eq.~\eqref{GPE} refers to the LHY correction to the equation of state. It can be intuitively understood as the zero-point motion of the Bogolibuov excitations. Primarily it was derived for a homogeneous gas with the contact interaction. However, it can be generalized to the case of dipolar interactions as well~\cite{Lima2011,Lima2012}. It turns out that the LHY contribution scales as $N^{3/2}$ for both contact and dipolar case. The magnitude of the quantum fluctuations can be described by the coefficient $g_{\mathrm QF}$. For the dipolar interaction $g_{\mathrm QF}=\frac{32}{3\sqrt{\pi}}g\sqrt{a^3}f(\epsilon_{\rm dd})$, where $f(\epsilon_{\rm dd})=\frac{1}{2}\int_0^{\pi} d\theta \sin{\theta}(1+\epsilon_{\rm dd}(3\cos^2\theta-1)) ^{5/2}$. The relative strength of the dipolar interaction is given by $\epsilon_{\rm dd}$. As we can see the LHY correction has a universal character, because it depends only on the two-body scattering length and the relative strength of the dipolar interaction. The same formula, only with effective $a_{\rm dd}$, can be used in our model.

A quite convenient way to examine the basic properties of strongly dipolar bosons such as the ground state or elementary excitations is to use a simple variational Gaussian ansatz for the wave function. Even though the system is in the Thomas-Fermi regime where the shape of the atomic cloud is far from being Gaussian, it has been shown that results obtained from this simple method are in considerable agreement with those obtained by solving numerically the Gross-Pitaevskii equation~\cite{Baillie2016,Wachtler2016a}. In the Gaussian model we take~\cite{Wachtler2016a}:

\begin{equation}
 \psi(x,y,z)=\frac{1}{\pi^{\frac{3}{4}}\left(\sigma_x \sigma_y \sigma_z\right)^{\frac{1}{2}}} \prod_{\alpha=x,y,z} {\rm e}^{-\frac{\alpha^2}{2\sigma_\alpha^2}+i\alpha^2 \eta_{\alpha}}, \label{GaussianAnsatz}
\end{equation}
where the variational parameters are the widths $\sigma_\alpha(t)$ in the $\alpha=x,y,z$ direction, and $\eta_\alpha(t)$, which determines the phase curvature along $\alpha$. We follow the notation proposed by W\"{a}chtler and Santos~\citep{Wachtler2016a,Chomaz2016}.  By straightforward calculation one can derive the energy functional corresponding to Eq.~\eqref{h} and then determine the following Euler-Lagrange equations:

\begin{equation}
\eta_\alpha=\frac{m}{2\hbar \sigma_\alpha} \frac{d\sigma_\alpha}{dt}
\end{equation}
and
\begin{equation}
\frac{d^2 \nu_\alpha}{d \tau^2}=-\frac{\partial}{\partial \nu_\alpha}U(\nu_x,\nu_y,\nu_z),
\end{equation}
where in the second equation dimensionless units $\tau=\tilde{\omega}t $, $\sigma_\alpha=\tilde{l}\nu_\alpha$, $\tilde{l}=\sqrt{\hbar/m \tilde{\omega}}$ are introduced, with $\tilde\omega=(\prod\omega_\alpha)^{1/3}$. The potential $U(\nu_x,\nu_y,\nu_z)$ for an arbitrarily chosen anisotropic potential expressed as in Eq. \eqref{veff} may be written as

\begin{eqnarray}
 U&=& \frac{1}{2}\sum_{\alpha}\left [ \nu_\alpha^{-2}+\left ( \frac{\omega_\alpha}{\tilde\omega} \right )^2\nu_\alpha^2 \right ]+\frac{2}{3}\frac{PAN^{3/2}}{\left(\prod_\alpha \nu_\alpha \right)^{\frac{3}{2}}}\nonumber \\
 &+&  \frac{PN}{\prod_\alpha \nu_\alpha}
 -\frac{1}{2}\int\int d^3r\,d^3r'\times
\nonumber \\ &\times & \sum_{l>0, m}\alpha_{lm} {Y_{lm}({\hat{\mathbf R}})\over |{\mathbf R}|^{3}}|\psi({\mathbf r},t)|^2\psi({\mathbf r'},t)|^2  ,
 \label{Energy_vi}
\end{eqnarray}
where ${\mathbf R}={\mathbf r}-{\mathbf r'}$ and the dimensionless constants $P=\sqrt{\frac{2}{\pi}}\frac{a}{\tilde{l}}$ and $A\sim \left ( \frac{a}{\tilde{l}} \right )^{3/2}$, which describes the magnitude of the LHY correction for a given effective potential $V_{\mathrm eff}$. For the effective potential described by Eq.~\eqref{nasz} the expression for $U(\nu_x,\nu_y,\nu_z)$ takes exactly the same form as in Ref.~\cite{Chomaz2016}, only with effective $a_{\rm dd}$.

In order to describe the ground state properties one has to find the minimum of $U$ that corresponds to the equilibrium widths $\nu_\alpha^{eq}$. Then the lowest excitations are fully determined by the Hessian matrix at the minimum of $U$. For spherical or cylindrical harmonic traps the three lowest excitations are characterized by the well-known 3D monopole, 3D quadrupolar and 2D quadrupolar modes~\citep{Wachtler2016a,Chomaz2016}.

To analyze stability of a self-bound droplet solution it is convenient to calculate the release energy $E_{\mathrm R}$, which is defined as the energy of the system when subtracting the energy related with the confinement, at the equilibrium widths corresponding to a droplet state~\citep{Chomaz2016}. Whenever $E_{\mathrm R}<0$ holds a self-bound solution is reached.

\section{Results}
Our goal is now to compare recent results concerning strongly interacting dipolar bosons in Ref.~\citep{Wachtler2016a,Chomaz2016,Baillie2016} with our calculations based on the effective potential  obtained from the realistic scattering amplitude described in Sec. II. In order to simplify our presentation we will describe the results as a function of $\epsilon_{\rm dd}^{\rm Born}=a_{\rm dd}^{\rm Born}/a$ and $\epsilon_{\rm dd}=a_{\rm dd}/a$. The relation between both relative dipolar strengths depends on the scattering length, as shown by~Fig.~\ref{fig:add}. We note that within Born approximation the theoretical predictions are completely universal, as the properties of the system depend only on the value of $\epsilon_{\rm dd}^{\rm Born}$. In contrast, in our treatment the dependence of $\epsilon_{\rm dd}$ on the scattering length is system specific.

\subsection{Droplet stability}
Theoretical calculations~\cite{Wachtler2016a,Chomaz2016,Baillie2016} predict the existence of stable self-bound droplets stabilized by quantum fluctuations (the LHY correction) in the region where mean-field solution predicts a collapse. In the recent experiment~\cite{Schmitt2016} the self-bound droplet has indeed been observed. However, the phase boundary (the critical atom number $N_{\rm crit}$ as a function of the scattering length) was not fully reproduced by theory. The discrepancy was explained by proposing a shift in the background scattering length from $92$ to $62.5\,a_0$. As the measurement of the critical atom number is very sensitive to the interaction parameters, the correction to the effective interaction can also significantly alter the phase diagram.

In Fig. \eqref{fig:selfDy} we show the stability diagram for Dy and Dy$_2$ with effective dipolar lengths $a_{\rm dd}$ originated from our model potential compared to the phase boundary obtained within the Born approximation. As shown previously, the self-bound solution stability only depend on the atom number $N$ and $\epsilon_{\rm dd}$~\citep{Baillie2016}. We determine the critical atom number as the value of $N$ at which the release energy $E_{\mathrm R}=0$. We plot $N_{\rm crit}$ as a function of $\epsilon_{\rm dd}^{\rm Born}$. The areas above each line correspond to stable (self-bound) solutions with $E_{\rm R}<0$ for a given system, while the areas below each line mark unstable (trap-bound) solutions with $E_{\rm R}>0$. We notice that the qualitative character of the phase diagram is the same for all of the cases, but the lines are offset relative to each other. This is obviously caused by the fact that $\epsilon_{\rm dd} \neq \epsilon_{\rm dd}^{\rm Born}$ for a given scattering length $a$. In the experimentally most interesting regime $\epsilon_{\rm dd}\gtrsim 1$, $\epsilon_{\rm dd} > \epsilon_{\rm dd}^{\rm Born}$. The drop of $\epsilon_{\rm dd}$ at large $a$ is not as relevant since in that regime the droplets do not exist. Note that for Dy$_2$ the critical line is more strongly displaced, which is in line with our findings from Sec. II and Fig. \eqref{fig:add}. These results make the observed phase boundary~\cite{Schmitt2016} more consistent with the previous measurement of the background scattering length~\cite{Maier2015}, as the measured critical atom numbers were also much lower than Born approximation predictions.

\begin{figure}[h]
\centering
\includegraphics[width=0.5\textwidth]{stability}

\caption{\label{fig:selfDy}Droplet stability diagram for Dy and Dy$_2$ with an appropriate $\tilde{a}_{\rm dd}$ as a function of $N$ and $\epsilon_{\rm dd}^{\rm Born}$ calculated using the simplified Gaussian ansatz. The lines correspond to the release energy $E_{\mathrm R}=0$ for Dy at 10nK (blue straight line) and 100nK (red dashed line), Dy$_2$ (dot-dashed magenta line) and Born solution (black dotted line). Regions below each line indicates an unstable solution ($E_{\mathrm R}>0$), whereas these above mark a stable self-bound state ($E_{\mathrm R}<0$). }
\end{figure}

\subsection{Collective modes}
In order to evaluate the three lowest lying excitations one has to calculate the Hessian matrix for the potential $U$ at the equilibrium widths $\nu_\alpha^{eq}$. In Fig. \eqref{fig:modesDy} and Fig. \eqref{fig:modesDy2} we depict the mode frequencies for Dy and Dy$_2$ respectively, both for the Born approximation and the corrected effective potential. We choose the case of a spherically symmetric trap with $N=$ 20000 atoms for two different trap frequencies $\omega=10$ and $70$ Hz.

In Fig. \eqref{fig:modesDy} we present our findings for Dy. The results for the Born approximation and our model are slightly displaced for both trapping frequencies. The reason for that is the same as in the previous subsection. The composition of the eigenstates is the same as in Ref.~\citep{Wachtler2016a}. Namely, in the mean-field regime ($\epsilon_{\rm dd}^{\rm Born}\approx 1$) the lowest excitation is given by the 2D quadrupole mode, then the second lowest mode is a 3D quadrupole mode, and the highest is a monopole mode. On the other hand, in the droplet regime ($\epsilon_{\rm dd}^{\rm Born} \gg 1$) the mode resembling 3D quadrupole mode becomes the lowest, then the second is the 2D quadrupole mode and the highest mode changes its character from 3D monopole behavior to 2D monopole mode behavior.
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{freq1_dy_10_aspectratio_1}\\
\includegraphics[width=0.5\textwidth]{freq1_dy_70_aspectratio_1}\\
\caption{\label{fig:modesDy}Comparing the lowest excitation frequencies of a spherically trapped Dy BEC with $N=20000$ atoms and $\tilde{\omega}/2\pi=10$ Hz (upper) or $\tilde{\omega}/2\pi=70$ Hz (lower) for the numerical calculation  (black straight line) and Born approximation predictions (red dashed line). In both cases the Gaussian ansatz was used. Both black and red lines exhibit anticrossings. }
\end{figure}

The results for Dy$_2$ are depicted in Fig. \eqref{fig:modesDy2}. We notice that in this case there is no significant difference between the Born approximation results and our model. The effect is more visible for a very weak trap. The qualitative difference between the results for Dy$_2$ and Dy can be explained by the fact that the collective frequencies mainly depend on the scattering length $a$ while the dipolar contribution to the Hessian matrix is rather small. As the magnetic moment of Dy$_2$ is higher than of Dy, in order to obtain a given $\epsilon_{\rm dd}^{\rm Born}$ value one needs much higher scattering lengths. Then the contact interaction part completely dominates the dipolar contribution. One can conclude that lanthanide atoms have the perfect combination of parameters for which the dipolar interaction significantly affects the collective modes.

\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{freq1_dy2_10}\\
\includegraphics[width=0.5\textwidth]{freq1_dy2_70}
\caption{\label{fig:modesDy2}Comparing the lowest excitation frequencies of a spherically trapped Dy$_2$ BEC with $N=20000$ atoms and $\tilde{\omega}/2\pi=10$ Hz (upper) or $\tilde{\omega}/2\pi=70$ Hz (lower) for the numerical calculation (black straight line) and Born approximation predictions (red dashed line). In both cases the Gaussian ansatz was used.}
\end{figure}

\section{Conclusions}
In conclusion, we studied the effects of taking into account the full scattering amplitude instead of relying on the Born approximation for the dynamics of strongly dipolar bosons gases. We demonstrated that already for lanthanide atoms one needs to use realistic interaction models. We showed that the main effect beyond the Born approximation is the emergence of effective dipolar length which replaces the standard one in the effective potential. This has strong impact on the many-body properties of the gas such as the critical atom number of the self bound droplet and to some extent on collective mode frequencies. Our results suggest that the stability boundary of the self-bound droplets is shifted to smaller atom numbers, in line with the recently reported experimental measurements~\cite{Schmitt2016}. Our findings are relevant also for recently reported Monte Carlo calculations~\cite{Saito2016,Macia2016,Cinti2016} which have used a simplified interaction potential with constant dipolar part and a hard wall, suggesting that more realistic potentials should be used there as well.

So far, the models of dipolar gases were based on local density approximation (LDA). Our treatment is no exception to that, as we calculate the scattering amplitude and the resulting effective interaction and LHY correction in free space. One subtlety in treating dipolar gases is that in order to obtain the scattering amplitude it is necessary to propagate the wave function to distances much larger than $a_{\rm dd}$, comparable to the characteristic trap length. The presence of the trap modifies the asymptotic form of the wave function at this length scale, which can potentially modify the derivation of the mean field theory. Including the trap in the derivation seems to be a challenging task. It would also be desirable to further improve the interaction model, taking into account the anisotropic van der Waals terms~\cite{Petrov:2012} and hyperfine structure details and looking for possible novel effects.

We thank Tomasz Wasak, Jan Kumlin, Hans Peter B\"{u}chler and Igor Ferrier-Barbut for fruitful discussions and comments. RO is grateful to the Stuttgart Dy team for their hospitality.

This work was supported by Alexander von Humboldt Foundation and (Polish) National Science Center Grants No. DEC- 2012/04/A/ST2/00090 and 2014/14/M/ST2/00015.

redpajama_set_name: RedPajamaArXiv


The Apple iPhone SE Space Gray arrives in an elegant finish, and sports slim dimensions of 123.8 x 58.6 x 7.6mm. This iPhone SE 64GB is outstanding in the looks department but is just as amazing when it comes to performance. It is powered by the superior A9 chip, which houses an M9 motion coprocessor that lends speed to all your actions, and facilitates fluent multitasking. This power, when combined with the fluidity of the iOS 9, makes for a stunning user interface. In addition, this device supports 4G LTE and WiFi networks, which facilitate quick access to the Internet from almost anywhere. Additionally, with up to 64GB of ROM, iPhone SE lets you stock up on all those cherished memories in the form of pictures and videos, along with the freedom to store other multimedia files.


Christine Kuglin received a Faculty Senate Teaching Excellence Award from former President Stephen Jordan at the Faculty Staff Appreciation Barbecue in May.
The Distinguished Service and Faculty Senate Teaching Excellence award winners were announced at the recent Faculty and Staff Appreciation Barbecue. Over the following weeks, we're profiling the award recipients and what goes into the making of these remarkable Roadrunner success stories.
Here's our conversation with Christine Kuglin, a former professional-in-residence in the Department of Accounting who's now pursuing a law degree at the University of Denver's Sturm College of Law. She is a 2012 graduate of the MSU Denver Master's of Professional Accountancy program.
I spent over 20 years in different forms of accounting—working as a tax accountant for small tax firms. I was also a NASA grant accountant at the University of Montana for an Earth-observing Systems project. I had various other accounting positions, but I started teaching at MSU Denver in 2013. I taught Principles of Accounting, Intermediate Accounting, and I ran the Volunteer Income Tax Assistance (VITA) program, which included undergraduate and graduate students in an integrated service learning course. We prepared tax returns for the urban Denver area for people of low and moderate means. The program was nationally recognized and won the Best Teaching paper by the Small Business Institute in 2016.
I grew up very, very poor and went to a lot of different schools. My teachers made a tremendous impact on my life. They helped me realize I could change my life's course through education and hard work. Teachers made a big difference in my life.
I think the day that one of my students—Jackie Mai—won the College of Business Student of the Year award. She had come here from Vietnam without any family and went on to earn her Master's Degree and her CPA. I had worked with Jackie in several classes. I nominated her and Dean Murphy allowed me to present Jackie with her award. I knew how much she had overcome. That was one of the best days of my life—to be a part of her journey.
It was a tremendous honor to have the validation from my peers and that they found that what I was doing was meaningful. There are so many outstanding individuals at MSU Denver who give their heart and soul to students – MSU Denver is so lucky to have so many outstanding faculty and staff. To think that what I was doing was considered special by these accomplished, hard-working people – well that is very humbling.
I think about the students. As an example, I had a student named Annie. She was a hospitality major—many students must take accounting and don't want to but they're required as part of the degree program they're in. She was dreading the class and was so stressed that she would fail. I helped her not only get through the class, she earned a B. It makes your life that much better to know that you've done something to help make a student like Annie successful. In Principles of Accounting, maybe only 10 percent of the students are accounting majors—the rest were taking it because it was required. So, to take students who may not want to take Accounting and help them be successful or maybe even grow to like it, that's pretty exciting.
I think I will always consider myself a Roadrunner. Even though I received my undergraduate from Regis and now attend the University of Denver, I received my graduate degree from MSU Denver. I have a great allegiance to MSU Denver. I came from an adverse background and MSU Denver helped me truly reach my potential. MSU Denver gives you a chance that very few places will. The faculty and the staff realize that. They help students to become the best they can be. I will always consider myself a proud Roadrunner no matter where life takes me.


A campaign of violence meted out by a squad of Iberia Parish drug deputies landed many of them in the federal pen and left the fate of Sheriff Louis Ackal in the hands of a jury, which acquitted him on civil rights charges.
Now, two years later, the scandal has resulted in convictions being dissolved for 18 people who were arrested, charged and in some cases imprisoned based on evidence drummed up by the disgraced deputies, legal advocates say.
Attorneys for the St. Mary Project, an initiative formed by private and nonprofit defense lawyers in the wake of the Iberia Parish scandal, on Monday announced the results of their work.
The group, which includes nonprofits such as the Promise of Justice Initiative and the MacArthur Justice Center, reviewed about 500 Iberia Parish cases and filed motions earlier this year to vacate convictions and sentences against 19 people.
Bofill "Bo" Duhe, the district attorney for Iberia, St. Mary and St. Martin parishes, agreed not to fight 17 of those motions. A judge granted another one, and the last one remains pending. All told, the 18 cleared defendants had served several decades of prison time on sketchy convictions, according to advocates.
The dubious arrests took place as recently as 2015 and as far back as 2008, when Ackal took office. Nearly all of the dismissed convictions came by way of guilty pleas. All but one, a burglary rap, involved a drug arrest.
The review followed an FBI investigation that led to guilty pleas from nearly a dozen former deputies for civil rights offenses. Several of them admitted to a free-swinging culture in which they beat up jail inmates and residents on the streets of New Iberia. They ran wild for years, often targeting black people and beating some just for sport, deputies testified.
Ackal, the accused ringleader, stood trial in Shreveport in late 2016. He claimed the deputies all were lying and went free. But the investigation cast doubt over the legitimacy of hundreds of arrests those deputies made over the years. Some had admitted fabricating police reports or lying in depositions to hide the abuse.
Along with those 18 tossed convictions, Duhe said he scrapped 90 additional cases that were pending when the scandal erupted.
Mark Cunningham, a partner in the Jones Walker law firm and a past president of the Louisiana State Bar Association, led the project and praised Duhe for opening his files and assigning staff to review the cases.
Mercedes Montagnes, executive director of the Promise of Justice Initiative, also cautioned that the review may be incomplete.
Ackal, 75, remains in office.


Are you looking for art classes in Ridgefield Park NJ and don't know where to look? In Demarest NJ at the Art School at Old Church in Demarest NJ, Maud Guilfoyle will be running art classes which are just what you are looking for. These art classes are suitable for all levels from beginners to the advanced and all are more than welcome. You'll develop your drawing and painting style with still life and landscape paints through Maud Guilfoyle's watercolor, oil and acrylic classes. These and other classes at the Art School have also been accepted for teachers' PDP credit.
Brilliance of color is something that watercolor painting is known for. Additionally, they are a popular choice for artists on the go, as watercolor paints are simple to pack up and set up. Through these watercolor classes Maud will direct you and assist you to hone your ability in this art so you may better create wonderful artwork of your own.
Whether you want to paint for a hobby or are looking to build a professional portfolio, these classes will give you the basics of still life and landscape painting and help you integrate art into your daily life.
Inanimate objects are the focus of still life paintings, which can use a number of objects as their subject, for example flowers, shells, stones, vases, glasses, or alternative man made or natural items. Throughout these still life art classes, you may learn to bring a realistic and beautiful still object to life in the shape of a lovely painting. Still life paintings allow much more lee way for artists by providing them with the ability to arrange objects into a composition that interests them. If you've ever been searching for still life classes in Ridgefield Park NJ, now is your chance!
Landscape painting classes will call for us delving into the natural beauty of the world like mountains, valleys, cliffs, oceans, rivers, woods, and seascapes. Bringing to life a natural scene is a wonder to behold in itself.
To find out more information and guidance on the universe of art beyond what you will learn in the classroom, check out the eBooks Maud has written. Art School Portfolio Handbook, Artist To Artist Handbook, Artists & Money Handbook and more recently, Art By Two are all eBooks that are available. Art By Two is a tribute to Maud's mother, artist Peregrine Higgins, and their relationship to each other and art itself, and features original figure drawings, landscapes, and portraits. You will find these eBooks on iBooks, Kindle, Nook, and Kobo, and are great for anyone, whether you're an artist yourself or only a lover of art. Have a look at this art class at tasoc.org for beginner to advanced artists!


text:
Mitre: Open-source code rife at DOD
"Is Linux ready for prime time"
"DISA net initiative to bridge DOD, intell data"
The use of open-source software within the Defense Department continues to gain momentum, especially in the critical area of cybersecurity, despite the fact that DOD and industry leaders have raised numerous concerns about vulnerabilities associated with the technology.
But what if open-source software applications and development were banned in DOD?
A recent study conducted by Mitre Corp. for DOD posed that hypothetical question and found that without open-source software, DOD's cybersecurity capabilities would be crippled and other areas would be severely impacted.
In open-source software, such as Linux, the source code is publicly available and gives users the right to use and change it without asking permission from any external group or person.
DOD officials asked Mitre to list the agency's open-source software applications and collect examples of how that software is being used.
A two-week e-mail survey identified 115 applications. The survey also found 251 examples of how the software is used, but the company acknowledged that actual use could be "tens of thousands of times larger than the number of examples identified."
The report, titled "Use of Free and Open-Source Software (FOSS) in the U.S. Department of Defense," was released last month to the Defense Information Systems Agency. The report found that open-source software is most important in infrastructure support, software development, security and research.
"The main conclusion of the analysis was that FOSS software plays a more critical role in the DOD than has generally been recognized," the report stated.
But the Mitre report is flawed because it is based on a question that assumes that open-source software would be banned within DOD, said Robert Kra.mer, vice president of public policy at the Computing Technology Industry Association Inc. and executive director of the Initiative for Software Choice (ISC).
"I know of no one who is saying that," Kramer said. "The ISC is not for that at all. The premise is unusual to say the least."
After receiving a working draft of the report in May, DISA solicited insights from DOD and the private sector, said Rob Walker, DISA's Net-Centric Enterprise Services program manager, in a presentation at an open-source conference in Washington, D.C., last month.
The comments collected raised three potential downsides to using open-source software:
n Exposure of system vulnerabilities.
n The introduction of Trojan software, which is hostile software covertly placed in ordinary applications.
n Conflicts with new software that incorporates "general public license" (GPL) source code. If personnel use GPL source code in the course of research and development, the entire product of that work is protected, whereas other open-source licenses are not as restrictive.
DOD officials' main concern is the licensing question, but "with reasonable care, GPL software can be used without disrupting other licenses," Walker said. He added that the introduction of unusually restrictive licenses, like some used by Microsoft Corp., "presents a more significant issue."
Open-source software is increasingly being used by government agencies, and the Mitre report proved that by saying there are thousands more applications within the Pentagon than were identified, Kramer said.
"Why do you need a policy to point to either [open-source or proprietary] software" when it is continuing to be competitive in the government marketplace? he asked.
DISA officials said that how much DOD uses open-source software in the future will largely depend on the results of the ongoing policy review.joint development Mitre Corp.'s report for the Defense Department recommended three policy-level actions to help promote use of open-source software in DOD:
n Create a "generally recognized as safe" open-source software list to provide official recognition of applications that are commercially supported, widely used and have proven track records of security and reliability.
n Develop generic policies to promote broader and more effective use of open-source software, and encourage the use of commercial products that work well with the software. A second layer of customized policies then should be created to deal with the four major use areas — infrastructure, development, security and research.
n Encourage the use of open-source software to promote diversity in systems architecture, which would reduce the cost and security risks of being fully dependent on a single software product.Related links:

redpajama_set_name: RedPajamaCommonCrawl


Rent options screen 2 deals with Early refund credit, and how many hours early. Cash drawer setup. Lookup mode.
If you enter an invalid ID# Video Deluxe will allow you to lookup the movie by name or two other ways. For total flexibility you can set Video Deluxe to manual mode and enter your own rental days and pricing.


text:
\section{Introduction}
Cassava (\textit{Manihot esculenta} Crantz) is a major subsistence crop in many parts of the world. However, in recent years cassava production in Uganda has been affected by Cassava Brown Streak Disease (CBSD) \cite{abaca2012progression,alicai2007re}.
CBSD has characteristic symptoms that appear as chlorotic leaf symptoms along the major veins and necrotic lesions on part or all of the starchy root that appear as yellow/brown \cite{alicai2007re,kawuki2019alternative}. CBSD affects the cassava root tubers which are the edible part of the cassava plant and affected, the roots are unsuitable for consumption \cite{hillocks2016disparity}.
However, there exists poor phenotypic associations between the above-ground CBSD symptoms shown in the leaves and the below-ground CBSD symptoms shown in the roots \cite{kawuki2019alternative,kaweesi2014field,valentor2018plot}. Due to this, the assessment of CBSD entirely on leaves is not sufficient enough to assess for CBSD resistance and that is why the CBSD assessment in this paper is on the roots instead of the leaves.

Efforts to breed for CBSD resistance are being put in place in the East African region \cite{ozimati2018training}. Other approaches to deal with CBSD include disease surveillance and deployment of more resistant varieties of cassava
\cite{katono2015influence,ninsiima2018automating}. Currently, the assessment of CBSD severity on cassava root cross-sections is done by visual analysis by agricultural experts. To assess a cassava root tuber for necrosis, the expert uproots a cassava plant and slices off clean discs from its root tuber and assigns a score of necrosis severity to the tuber. The characteristic symptoms in cassava root tubers are used as a measure of either resistance or tolerance to CBSD \cite{abaca2012progression}.

The current scoring approach is subjective, and moreover different authors also assign different scores for the same scale \cite{katono2015influence,ozimati2018training,rwegasira2012response} which are liable to human bias and can sometimes be erroneous. This could have several effects especially for the cassava breeders who require accurate scores when testing for CBSD resistance \cite{ninsiima2018automating,tuhaise2014pixel}.
 Therefore, there is need for automated techniques for scoring of necrosis on cassava root cross-sections.

Previous work has been proposed where computer vision techniques are used to calculate the percentage of necrosis on a cassava root infected with necrosis \cite{ninsiima2018automating,tuhaise2014pixel}. However, this relied on hand engineered features like pixel intensity along with traditional classification techniques in a controlled setting, to detect necrosis. Generally, automation of necrosis scoring is a difficult problem because the background of the root has to be segmented out first before determining the necrotized pixels in the root. Furthermore, changes in illumination of images can have a significant impact on pixel intensities of an input image. This paper introduces an approach for determining the percentage of  necrosis on a cassava root image using semantic segmentation. Semantic segmentation has been used in several applications such as phenotyping of plant diseases \cite{stewart2019quantitative}, land cover mapping \cite{kampffmeyer2016semantic} and land use classification \cite{yang2018classification} and several applications in the medical field such as segmentation of brain gliomas from MRI images \cite{cui2018automatic}.
Semantic segmentation is a challenging task in computer vision. A lot of methods have been developed to achieve this task many of which have been built using deep learning models that have shown the most noticeable performance \cite{He2017ICCV}.

The main contribution of this work is the development of a more robust approach to  necrosis scoring. The paper discusses the use of convolutional neural network, UNet model to automatically segment and classify necrotized and non-necrotized pixels of cassava root cross-sections from the input images obtained from the field. The result of which is a percentage estimate of the level of necrosis obtained from the ratio of necrotized pixels to root pixels. Images of cassava root cross-sections are annotated with the help of experts to generate a training dataset for the model. The results show that the UNet model is able to detect necrosis on input images with a high accuracy.

The rest of the paper is organised as follows: Section \ref{related_work} discusses related work. Section \ref{methods} describes the methodology used in this paper. Section \ref{model} describes the model architecture and evaluation metrics. Section \ref{experiments} provides a discussion on the experiments and the results from the experiments. Section \ref{conclusion} concludes the paper.

\section{Related Work}\label{related_work}
In this section, we discuss related approaches to necrosis detection and applications of semantic segmentation in agriculture. Current approaches to root necrosis scoring provide a qualitative score
on a scale of 1-5 \cite{hillocks2000cassava} representing how necrotized the cassava root cross-section is \cite{kaweesi2014field,kawuki2016eleven}. In this range, different authors assign different scales for necrosis \cite{katono2015influence,ozimati2018training,rwegasira2012response}. For example, authors in \cite{rwegasira2012response} give score 1 if the root is not necrotic, score 2 is 0-5\% of the root is necrotic, score 3 if 5-30\% of the root is necrotic, score 4 if 30-50\% of the root is necrotic and score 5 if $>$50\% of the root is necrotic. While the authors in \cite{katono2015influence} give score 1 if the root is not necrotic, score 2 is $<$5\% of the root is necrotic, score 3 if 5-10\% of the root is necrotic, score 4 if 10-25\% of the root is necrotic and score 5 if $>$25\% of the root is necrotic. Although they refer to the same scale, the expression of necrosis under each scale is different.

Work has been carried out to automate plant disease diagnosis and symptom measurement using image analysis techniques \cite{ramcharan2017deep,mohanty2016using,mwebaze2016prototypes}. With the successes of deep neural networks in supervised machine learning \cite{deng2013new}, convolutional neural networks have played a very significant role in image classification \cite{krizhevsky2012imagenet,simonyan2014very,szegedy2015going} and object detection \cite{redmon2016you,ren2015faster}. This has inherently driven research towards developing convolutional neural network architectures for Semantic Segmentation \cite{pathak2014fully}. Semantic Segmentation based on convolutional neural networks have outperformed other techniques and have thus been applied in many domains including Biomedical research to for identification of cell nuclei \cite{ronneberger2015u}, self-driving cars \cite{treml2016speeding} and remote sensing \cite{kampffmeyer2016semantic}.

Similarly, in agricultural research, segmentation has been applied in cotton detection \cite{li2016field} and for grape detection and tracking \cite{santos2019grape}. It was also been applied in disease detection. In \cite{singh2018deep}, semantic segmentation has been applied to phenotype plant stress. Quantitative phenotyping of the northern leaf blight virus has been successfully carried out by applying semantic segmentation to images captured by unmanned aerial vehicles \cite{stewart2019quantitative}. A different approach in \cite{wang2019segroot} has proposed a method based on neural networks to segment roots from soil background and using images of soybean roots and the results achieved a dice score of 0.64.

In the area of CBSD scoring, authors in \cite{tuhaise2014pixel} carry out analyses of necrosis in cassava root cross-sections at a pixel level using binary pixel classification with traditional classification algorithms in a controlled setting. The work in \cite{ninsiima2018automating} builds on this previous work where the analysis of necrosis is carried out on cassava root cross-sections that are captured in the field setting. Here, hand-crafted features are extracted from the input image to isolate the root from the background and two methods are applied for necrosis detection: Otsu thresholding \cite{otsu1979threshold} with blob detection and the watershed algorithm \cite{gauch1999image} with selected components based on contours present on the root cross-section.

In this paper, we utilize the ability of convolutional neural networks to automatically extract features from images beyond the pixel intensity values used by thresholding methods. This gives the model the ability to identify multiple expressions of necrosis beyond what traditional thresholding methods can do.

\section{Methodology}\label{methods}
\subsection{Data Collection}
In this experiment, 1,800 images of cassava root cross-sections were collected from the National Crop Resources Research Institute (NaCRRI), that hosts the national cassava breeding program of Uganda. Root necrosis severity was assessed on each root by slicing the root transversely 5-7 times. The cross-section with the highest visual expression of necrosis was scored by human experts on a scale of 1-5 as shown in the Table \ref{tab:valid} representing the expression of CBSD on the root  \cite{ozimati2018training}.
For each root, a picture of the cross-section that exhibited the highest score of necrosis was taken using a smartphone camera with a resolution of 1920x2520 pixels under ordinary field conditions and the corresponding CBSD score was recorded.

\begin{table}[!h]
\centering
 \caption{Scoring of Necrotized Regions on Cassava Root Cross-sections.}
 \label{tab:valid}
 \begin{tabular}{ccc}
   \hline
   Human Expert  & Expected Root  & Expected Machine \\
   Score &  Cover (\%) &  Score (\%)\\
   \hline
   1 & no necrosis & 0-2\\
   2 & $\leq$ 5 is necrotic & $\leq$ 5 \\
   3 & 6-10 is necrotic & 6-10\\
   4  & 11-25 is necrotic & 11-25\\
    5 & $>$25 is necrotic & $>$25 \\
  \hline
\end{tabular}
\end{table}

\subsection{Data Description \label{sec:datades}}
In the dataset, 1,036 images of cassava root cross-sections were necrotic while 764 were clean and did not show any necrosis.
A cross-section of a clean root is white or yellow fleshed  while a necrotic root can expresses white or brown lesions depicting CBSD.
In this data set, the manifestation of lesions on the necrotic roots is observed to fall under three main categories: (a) number of necrotic lesions - few lesions vs. many lesions, (b) size of the necrotic lesions - small lesions vs. large lesions, (c) the distribution of the necrosis - lesions at the center of the root vs. lesions at the edge of the root. A root can have necrosis presentation that falls under one of more of these categories described as shown in Figure \ref{fig:necrosis_category}.

\begin{figure}[h!]
\begin{center}
\includegraphics[width=7cm]{root-categories.png}
\end{center}
\caption{Categories of necrosis expressions on cassava roots. \textbf{(A)} many necrosis lesions, \textbf{(B)} few necrosis lesions, \textbf{(C)} large necrosis lesion, \textbf{(D)} small necrosis lesion, \textbf{(E)} necrosis lesion in the center of the root, and \textbf{(F)} necrosis lesion at the edge of the root.}\label{fig:necrosis_category}
\end{figure}

\subsection{Data Annotation}
For the segmentation task, the 1,036 images of cassava roots containing necrosis were labelled and split to create the training set with 90\% samples and the validation set with 10\% of the samples. An  additional 128 images were annotated and used as a test set. The ground truth for the segmentation task is a series of pixel-wise masks. The masks were hand-traced by volunteers with the guidance of experienced cassava breeders using the tool \textit{labelMe}\footnote{http://labelme.csail.mit.edu/Release3.0/}. During the annotation, the volunteers drew labelled polygons around two objects of interest: the root area and the necrotic area. The polygons were then converted into masks representing the necrosis lesions, the root and the background. An example of the resulting masks from the annotation are shown in Figure \ref{fig:train}.
The annotated images were saved in the PASCAL VOC format \cite{everingham2015pascal} which is a standard format for annotating images for the task of object detection and image segmentation. The main resultant files include the original image, generated mask and JSON file containing pixel coordinates.

\begin{figure}[ht!]
\centering
\includegraphics[width=\linewidth]{necrosis_labels}
\caption{Sample input images of cassava root cross-sections and the actual masks generated from annotation.}
\label{fig:train}
\end{figure}

\section{Model Architecture}\label{model}
For the semantic segmentation task, we used the UNet model \cite{ronneberger2015u}, a commonly used deep-learning architecture for performing image segmentation tasks \cite{zhao2019use}. The architecture of the UNet model is based on an encoder-decoder model with a contracting and expansive arm as shown in Figure \ref{fig:unet}. The UNet architecture has specifically proved to outperform previous methods on the task of segmentation of biomedical images. It has also has the capability of generalizing better even when trained end-to-end on very few images.

The model is composed of a linear stack of Convolutional, Batch Normalization and Rectified Linear Units (ReLu) operations followed by a max-pooling operation applied to an image with a 512x512 pixel input dimension. At each pooling layer in the encoder, spatial resolution of the feature map is reduced by 2 and number of feature channels is doubled. We keep track of the outputs of each block as we feed these high-resolution feature maps into the decoder portion.

The decoder portion is comprised of up-sampling convolutional layers together with convolutional and ReLu operations. At each block, a 2x2 up-sampling convolutional layer reduces the number of feature channels by half and the result is concatenated with the corresponding feature map from the encoder. This is followed by convolution and ReLu operations except at the final layer where a 1x1 convolution is used map the final feature map to a certain number of output classes.

\begin{figure}[ht!]
\centering
\includegraphics[width=\linewidth]{u-net-architecturez}
\caption{UNet Architecture for semantic segmentation of cassava root cross-sections.}
\label{fig:unet}
\end{figure}

For this experiment, an image with an input dimension of 256x256 pixels was used while the rest of the architecture was left unmodified as in \cite{ronneberger2015u}. The model adopts the dice coefficient as shown in equation \ref{dicecoeff} for evaluation. This calculates the ratio of the intersection of the area between the input mask and predicted mask to the sum of the total area of the input mask and the predicted mask. The dice coefficient is scored on a scale of 0-1 where scores closer to 1 imply a greater precision for the predicted mask.

    \begin{equation}
    \label{dicecoeff}
         \mathrm{DiceCoefficient} = \frac{2(R_{pred} \cap R_{inp})}{R_{pred} + R_{inp} }
    \end{equation}

    \begin{equation}
    \label{diceloss}
        \mathrm{DiceLoss} = 1 - \mathrm{DiceCoefficient}
    \end{equation}

     \begin{equation}
    \label{iou}
        \mathrm{IOU} = \frac{R_{pred} \cap R_{inp}}{R_{pred} \cup R_{inp} }
    \end{equation}

    $R_{pred}$ is the area of the predicted mask and $R_{inp}$ is the area of the input mask.

The dice loss function was used to monitor and optimize the parameters of the model during training. The dice loss was defined as the loss function and this can be calculated from the dice coefficient as shown in Equation \ref{diceloss}.
We use the mean Intersection over Union (IoU) as shown in Equation \ref{iou} \cite{milletari2016v} to evaluate how well the model classifies the necrotic and root pixels. The network predictions, which consist of generated masks have the same resolution as the input data, are processed through a SoftMax activation function which predicts which outputs the probability of each pixel belonging to the necrosis, the root or the background class.

\section{Experiments}\label{experiments}
The problem of calculating the percentage of necrotized roots is addressed as a pixel classification task where we attempt to classify the pixels covered by the necrotized region of the root against the healthy section of the root. Based on this, the severity score on the root is determined by calculating the ratio of the necrotized region to the healthy section.

\subsection{Training}
For model training, an original image is used as the input feature and the corresponding mask generated by the annotation is the label which is typical of every supervised machine learning task. All the inputs are resized to a dimension of 256x256 pixels which is the input size for the UNet model. The original label masks have a unique pixel value for the 3 regions of interest; root, necrosis and background encoded in an RB color space from 0-128. Before parsing the data for training, the color values of the mask were remapped to a new colorspace representing each of the 3 regions with a unique value in the range 0-2. In order to increase size and variations in the dataset, augmentation was done using three image transformations applied to random selections of input images and their corresponding masks; horizontal flip, rotation and width-height shifts.

The UNet model was trained using Adam \cite{kingma2014adam} optimizer with the initial learning rate set to 3e-4 and weight initialization was implemented using Xavier initialization defined by Glorot and Bengio \cite{glorot2010understanding}. We defined two callbacks; one to save training weights for best performing epoch based on the dice coefficient and another to implement early stopping if the value of the dice coefficient did not change for 20 epochs. The model was trained for a maximum for 100 epochs using Google Colab hosted environment with 12GB of memory powered by an Nvidia K80 Graphics Processing Unit (GPU).

\subsection{Predictions and Inference}
As shown in Figure \ref{fig:unet}, the output of the UNet model is an array with the same dimensions as the input image. When an image is passed into the model for inference, each of the pixels from the input is classified as being one of either two classes; the root or necrosis and everything else is the background. The pixel values of each class from the model prediction are assigned a unique value and the percentage of necrosis on the root is calculated by getting the ratio of pixels representing necrosis to the total number of pixels representing both the root and necrosis as in Equation \ref{necpercentage}.

 \begin{equation}
    \label{necpercentage}
        \mathrm{Necrosispercentage} = {\frac{P_{nec}}{(P_{nec} + P_{root}) }}  \times 100
    \end{equation}
$P_{nec}$ is the number of pixels classified as necrosis and $P_{root}$ is the number of pixels classified as the root.

In order to generate an output image, positions of pixels classified as the root and necrotic areas are extracted from the input image and a black mask with the same dimension as the input image is created. The positions of pixels in the black mask that correspond to those extracted from the input image are modified to reflect the two classes with necrotic pixels set to red and root pixels set to green as shown in Figure \ref{fig:unet_performance}.

\subsection{Performance of the UNet Model}
The UNet model showed an impressive performance with dice coefficients of 0.97 and 0.95 for the training and validation sets respectively. This implies that the model was able to correctly learn and identify the necrosis on most examples of the root with minimal mistakes. The model also managed to achieve an IOU of 0.94 and 0.90 for the training and validation sets respectively. Both the dice coefficient and IOU scores show a small difference between the training and validation sets of 0.02 and 0.04 respectively and this implies that the model is robust to effects of overfitting. By visual assessment, Figure \ref{fig:unet_performance} shows that the UNet model is able to classify the necrosis and the root with a high accuracy for the randomly selected sample of 3 images from the test set when the actual mask is compared with the predicted mask.

\begin{figure}[ht!]
\centering
\includegraphics[width=\linewidth]{paper-score.png}
\caption{Segmentation results of UNet for three image samples from the test set. The left image shows original RGB image, the middle image shows mask generated by annotation and the right image shows mask generated by prediction of the UNet model.}
\label{fig:unet_performance}
\end{figure}

\subsection{Comparison with Ground truth}
In this experiment, the performance of the UNet model\footnote{\url{http://18.221.68.135}} is compared to previous work by \cite{ninsiima2018automating} based on how well each of the approaches can estimate the percentage of necrosis on an unseen test set. Using the test set of 128 images, the ground truth percentage of necrosis for each image is generated by computing the pixel based ratio using the $\mathrm{Necrosispercentage}$ shown in Equation \ref{necpercentage}. This is calculated on the masks generated by the ground truth annotations as shown in Figure \ref{fig:train}.

The test images were then analyzed by the UNet model to generate mask predictions whose pixel ratio is used to calculate the UNet percentage of necrosis. Similarly the test images were analyzed for the Otsu predicted percentage of necrosis by running them through the CBSD analyzer\footnote{\url{http://air.ug/mcrops/?page_id=46}}, a desktop application developed by \cite{ninsiima2018automating} to house the Otsu-threshold model. Using the MSE (Mean Squared Error) and R\textsuperscript{2} as evaluation metrics, the two models were assessed to estimate how much each of the predicted percentages varies from the ground truth percentage and results are presented in Table \ref{tab:otsu_vs_unet}.
 \begin{table}[!h]
\begin{center}
 \caption{MSE, $R\textsuperscript{2}$ and $r$ scores for UNet model and Otsu-threshold model.}
 \label{tab:otsu_vs_unet}
 \begin{tabular}{m{4cm} m{1cm} m{1cm} m{1cm}}
   \hline
    & MSE & $R\textsuperscript{2}$ & $r$\\
   \hline\\
   UNet model  & 72.34 & 0.73 & 0.92\\
    Otsu-threshold model  & 273.96 & -0.03 & 0.44\\
      \hline
\end{tabular}
\end{center}
\end{table}

The predicted percentage of necrosis for the UNet and Otsu-threshold models were also plotted against the ground truth percentage in a scatter diagram Figure \ref{fig:otsu_unet_regression}. The Pearson correlation coefficient (r) was calculated to determine how close each of the model's predictions were to the ground truth. The correlation coefficients scored by the UNet model and the Otsu-threshold are 0.92 and 0.44 respectively. Visually, Figure \ref{fig:otsu_unet_regression} also shows that the UNet model (red) has a better line of best fit compared to the Otsu-model (blue).

\begin{figure}[ht!]
\centering
\includegraphics[width=\linewidth]{otsu_unet_reg}
\caption{Scatter plot for ground truth percentage against UNet predicted percentage (red) and Otsu-threshold predicted percentage (blue) with corresponding lines of best fit.}
\label{fig:otsu_unet_regression}
\end{figure}
Figure \ref{fig:otsu_unet_regression} also shows a higher correlation between the predicted necrosis percentage and the ground truth for the UNet model compared to the Otsu-threshold model.

\subsection{Discussion of Results}
In this paper, we have presented results for automatic necrosis scoring of cassava root cross-sections using semantic segmentation. The result show that necrosis scoring is a feasible task that can be accomplished with a significantly high accuracy. When compared with previous work, this paper has presented a richer test set of 128 images compared to the 20 images reported in  \cite{ninsiima2018automating}. Furthermore, the UNet model performs significantly better at the task of necrosis detection when using the annotated test dataset of 128 images as a baseline.

Unlike the Otsu-threshold model whose performance is greatly influenced by features such as the determined thresholding value and image illumination effects, the UNet model is able to learn and understand a more robust set of features from the input data and this enables it to perform well even in varying image conditions. Based on the results in Table \ref{tab:otsu_vs_unet}, both the $R\textsuperscript{2}$ and $r$ values for the UNet model show that the predictions are closer to the ground truth representation of necrosis. The results from the training experiments show that the UNet model is able to learn and predict necrosis present on cassava root cross-sections with high dice coefficients of 0.96 and 0.94 for the training and validation sets respectively and therefore this is a method that can be employed to automate the current manual approach to scoring necrosis in cassava root tubers.

\section{Conclusion and Future Work}\label{conclusion}
In this paper, we present an approach to detect necrosis in images of cassava root cross-sections using semantic segmentation. This was done with the UNet model which was trained on a dataset of 932 images and evaluated on 104 images. The experimental results show that the model is capable of identifying both the root and necrosis with a high level of accuracy as indicated by the IOU scores of 0.94 and 0.90 for the training and validation sets respectively.

Furthermore, when evaluated on a never seen set of 128 images, the UNet model performs significantly better than the previous method suggested by \cite{ninsiima2018automating} at predicting the actual percentage of necrosis over the entire test set. This shows that the UNet model learns more complex features that are able to generalize to greater variations in root cross-section images compared to methods that are using hand crafted features such as pixel value intensity.

Although the model produces very good results for necrosis detection, we observed some limitations with the analysis of results for the test set. The percentage-based comparison to the ground truth for necrosis detection is not a sufficient measure for how well the masks predicted by the models relate to the ground truth masks. As future work, we will use the IOU or dice coefficient metrics to give a more robust evaluation.

Future work will also involve investigating the performance of the UNet model for the different types of expression of necrosis discussed in Section \ref{sec:datades}. Using the segmentation results, we shall also be able to incorporate measures like size and number of lesions which could provide useful information to cassava breeding experts. We believe that this model can easily be adapted for use in similar problems like necrosis scoring detection in sweet potato root cross-sections with minimal modification.

\subsubsection*{Acknowledgments.} We would like to Dr. Robert Kawuki and the technical team from the National Crop Resources Research Institute (NaCRRI). The work is funded by Cornell University through a sub-award agreement (N0. 84941-11036) between the Makerere Artificial Intelligence Lab and Cornell University.


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text:
North Atlantic Garbage Patch
The lesser-known cousin of the Great Pacific trash island.
Trash accumulates on a Bahamas beach overlooking the Atlantic. Vagabond Shutterbug/Flickr (Creative Commons)
Left: Trash accumulates on a Bahamas beach overlooking the Atlantic. Vagabond Shutterbug/Flickr (Creative Commons)
Right: Garbage waiting to be swept out to sea in Bermuda. David Lawrence/Flickr (Creative Commons)
Garbage waiting to be swept out to sea in Bermuda. David Lawrence/Flickr (Creative Commons)
We're All Citizens of the Garbage Patch State
An Italian artist has created an imaginary homeland for all of our plastic waste.
Vittoria Traverso November 16, 2017
Guide to Islands You Don't Want to Visit, Pt.2
Shannon O'Haire August 30, 2013
As four major currents in the North Atlantic Ocean between Virginia and Cuba push rubbish through the sea, it gets absorbed into a giant marine trash island we now call the North Atlantic Garbage Patch.
Humans annually produce about 200 billion pounds of plastic and about 10% of this material ends up in the ocean. These plastics accumulate in the sea and swirl around one of five oceanic gyres - regions where currents push water (and floating debris) in an inward circular motion, trapping it in the center. The results of this swirling waste are enormous floating garbage heaps.
First documented in 1976, researchers have only recently begun to clarify the formation and motion of these artificial islands. As part of the process to understand the monstrous garbage heaps, over 7,000 students hand-picked and catalogued tens of thousands of trash pieces brought in with nets over twenty years.
Using this data, scientists estimate that the North Atlantic Garbage Patch is hundreds of kilometers in size and has a density of 200,000 pieces of trash per square kilometer in some places. Despite its enormous size and density, the patch is, more often than not, invisible to the naked eye and even satellite imaging. The photodegradable plastic that makes up the vast majority of the mass shrinks to smaller than .01 of an inch and is pushed under the surface of the water by deep waves. Unfortunately, this attribute makes it all the more likely that the plastic - and all of its pollutants - will be swallowed by aquatic creatures.
Worse yet, the potential for cleanup is largely hopeless. Marine scientists predict that a massive filter attempt would ensnare countless small marine creatures, doing more harm to the ecosystem than good.
atlantic disaster areas disasters islands water nature
http://www.wired.com/wiredscience/2010/08/atlantic-plastic/
http://news.nationalgeographic.com/news/2010/03/100302-new-ocean-trash-garbage-patch/
http://flaglerlive.com/35353/north-atlantic-garbage-patch-fg/
Somerset Bridge
Admiralty House Park
The Royal Naval Cemetery
The world's smallest drawbridge.
In Bermuda, this formal naval residence has become a go-to for cliff-jumpers and hikers.
The final resting place for Bermuda's British military, including a man who died of sunstroke.
The Abandoned Royal Navy Commander's House
The abandoned Bermudian home of a British naval leader is surrounded by crumbling sporting fields and the graves of convicts.
Hunza Nagar, Pakistan
Attabad Lake
This dazzlingly turquoise mountain lake was created in the wake of a natural disaster.
Carpello, Italy
Lake Posta Fibreno
This serene, turquoise lake in an extraordinary nature reserve showcases a rare natural phenomenon.
Chamoli, India
Skeletons of Roopkund Lake
A lake with hundreds of ancient skeletons surrounding it. The surprise is what killed them.


Security is always being challenged & the needs for protection from disaster ever present. Our most advanced solutions involve strategic planning to isolate specific parts of private networks, expand customers ability to suffer loss or expand their local office onto cloud based servers.
We provided their team with a schedule to migrate their web sites and test. Since they were already used to managing parts of their infrastructure we simply complemented their own expertise. Our team worked by their objectives and schedule, we coordinated a patching and maintenance time for their servers.
Hostek was proud to be such an asset to their team, and continue to enjoy serving them today.


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El Tesito de los Cuchillos o las Pisás de los Moros son unos petroglifos de la época romana en las Hurdes. Se ubican a mitad de camino entre las alquerías de Castillo y Erías - ambas perteneciendo al concejo hurdano de Pinofranqueado - en una elevación sobre la margen derecha del río Esperabán, junto a su confluencia con el arroyo de la Zambrana. El sitio dispone de cartel explicativo.

Los petroglifos aparecen a ras del suelo aprovechando un afloramiento de pizarra contornado por un vallado de piedra seca. Los motivos son muy variados: Podomorfos, asteriscos de líneas radiadas, armas como puñales y espadas. Junto a una de las espadas romanas aparece una inscripción latina con el texto (A)RMAMIIACAVII, que puede traducirse como "guárdate de mis armas" o "protege mis armas".

Se trata de grabados incisos y algunos piqueteados. Además aparecen también algunos repiqueteados repasados por abrasión. Dada la inscripción latina y la tipología de las espadas representadas, se puede datar el conjunto en época romana.

Notas

Petroglifos
Pinofranqueado

redpajama_set_name: RedPajamaWikipedia


About page Chelsea Modern Images. Natural light children, family, newborn and wedding photographer in Lewiston, NY. Specializes in newborn, baby, child and family photography.
I'm Chelsea Sears! I'm the owner and photographer at Chelsea Modern Images. I've been chasing people with my camera for quite a while now, and specialize in children & families. I am completely and utterly obsessed with love, the bonds between people (furry friends, too!) and am never more happy than when I can capture a genuine moment for someone to treasure.
Now that you're starting to know me, you've got to tell me all about you. We need to be comfortable with one another so that we can actually have FUN for a change at your photo shoot. I'm going to do what it takes to make you laugh - like - maybe even belly laugh - so that we can get THAT shot. You know the one, the shot you're going to want to share with everyone on Facebook & Instagram. The shot that's going to get you to actually send Christmas cards again this year. We're not just making art together, we're making memories during the session. Leave your worries at the door and the stress of getting your kids to smile to me!


A Conveyancing Solicitor arranges for the legal title of a property to move from seller to buyer.
1. Shop around. As with any major purchase or decision, the first (or cheapest) option may not be the best. Look around and compare several Conveyancing Solicitors to get a sense of what services they offer, the conveyancing fees and which conveyancer might be most suitable for you.
2. Beware of hidden costs. You'll typically need to pay for legal fees, VAT and disbursements (fees paid by the Conveyancer to third parties). At Co-op Legal Services, the conveyancing fee you are quoted for the agreed work is the conveyancing fee you pay. With your conveyancing costs agreed upfront, you know what all the costs are before any work is carried out and you don't have to worry about escalating costs.
3. Pay particular attention to 'disbursements'. There are many different costs your Conveyancing Solicitor might need to pay on top of their own fees, including stamp duty, search fees and Land Registry fees. If you see an unexpected extra fee or conveyancing cost that another conveyancer doesn't charge, query it so you're not hit with additional payments.
4. Ask what you'll still have to pay if there's no sale. Some Conveyancers, including Co-op Legal Services, offer a No Sale No Fee Guarantee service. Make sure you know and understand what this means from the outset.
5. Look out for bundled deals.Some businesses, for example, estate agents have preferred partners, such as mortgage providers and Conveyancing Solicitors. They will typically lower their own conveyancing fees if you agree to use these services. Shop around and make sure you understand what this means for you.
6. Look for relevant experience. The internet has made it easier than ever to find a legal professional at lower cost, but that doesn't mean they'll have the right expertise for your property transaction. That's why it is important to get the right advice from specialist Conveyancing Solicitors with the legal expertise and knowledge of property law.
7. Make sure they take time to listen to you. Buying a property is not a 'rubber stamp' job. You may have many questions you want to ask. A good Conveyancing Solicitor will listen to you and check out any concerns you have – as well as offering their own advice and opinions on the deal in question.
8. Make sure they are pro-active. The Conveyancer is the legal expert, not you, so they should be the one going out and negotiating with other parties and ensuring that there are no hitches. If you continually have to prompt them to do their job, it's not a good sign. You should get a good sense of how they'll approach things by looking at any customer feedback online (on review sites as well as their own websites).
9. Discuss searches. Your Conveyancing Solicitor can carry out a number of different searches to check for matters as diverse as flood risk to local regulations about upkeep of pathways around the property. They can advise you, but it's up to you to decide which to get.
10. Make no assumptions. Look at the plans for the property and check exactly what you are buying in terms of land. Don't assume that a piece of garden or side path will be included, and discuss with your Conveyancing Solicitor the implications of this.


Misses'/Miss Petite shirtdress from designer Mimi G. features working epaulets on shoulders and functional breast pockets. Design also includes side pockets and tie belt. Click "Envelope Back" directly above for more information. Mimi G Style for Simplicity. Sew along with Mimi G as you watch her video tutorial coming soon!


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The staff at hospital Accident and Emergency Departments provide vital and valuable services to the entire community. However, Emergency Department Medical Negligence claims account for almost 15% of all Medical Negligence claims. The most recent studies have shown a 50% increase in the number of reported 'clinical incidents' in emergency medicine over a four year period. Overcrowding in Emergency Departments lengthens waiting times and means staff work in increasingly difficult conditions. Here our Janet Keane, Senior Associate, examines how this can lead to Emergency Department Medical Negligence claims.
How does Emergency Department Medical Negligence arise?
Emergency department medical negligence claims can arise in the following ways:
Failure to recognise an acute condition e.g., appendicitis, meningitis, evolving stroke;
Premature discharge, transfer or step-down from an acute hospital setting;
Failure to adequately note, record or review a patient's pertinent medical history;
Failure to access timely investigative imaging e.g., MRI/CT/Ultrasound/X-ray.
Discharging a patient without the appropriate referral and/or safety netting advice regarding their health or in the event of potential deterioration.
Delayed Diagnosis or Delayed Treatment
More than 1.5 million patients attend Emergency Departments annually, with record numbers attending in 2022. The seasonal rise in the numbers attending Emergency Departments over the winter presents additional challenges to an already stretched healthcare system. Delays in ambulance response times, triage, diagnostic testing and initial diagnosis all lead to delayed treatment. This delay in providing treatment can cause further illness, deterioration in the patient's condition, poorer outcomes and even death.
The Emergency Medicine Programme for Ireland recommended an advisory target that 95% of patients should be either admitted or discharged within a 6-hour window of arrival at the ED.
The 2021 National Inpatient Experience Survey conducted by HIQA reported that of a cohort of 7239 presentations to A&E, 5135 (71%) said they waited more than the recommended 6 hours before being admitted. Of those, 305 people reported waiting more than 48 hours before they were admitted.
Even before the effects of the COVID-19 pandemic were felt by our A&E Departments the 2019 National Inpatient Experience Survey found that 70% of people reported being admitted to a ward within the target waiting time of 6 hours and 4% of over 8000 patients report they were waiting 48 hours or more before admission to a ward for appropriate treatment.
Misdiagnosis in the Emergency Department
Emergency Department Misdiagnosis is not uncommon. Patients present in often busy, overcrowded conditions to medical staff with a high workload. Overcrowding, delay and misdiagnosis are inextricably linked. Studies have shown that misdiagnosis can occur in 1 in every 9 patients admitted through the Emergency Department.
A 2021 analysis conducted by the UK Royal College of Emergency Medicine concluded that 4519 excess deaths were directly as a result of overcrowding and delays of 12 hours or longer. Adjusting these figures to reflect the population of Ireland (5 million v 68 million), 316 people a year could be dying in this country because of overcrowding, delay and misdiagnosis.
Misdiagnosis can also have severe medical implications, including the development of secondary conditions which have the obvious effect of exacerbating conditions and increasing hospital stays which lead to poorer patient outcomes.
Failure to Diagnose Acute or Underlying Conditions
When patients present at an Emergency Department they are often unable to provide clear information regarding their injury or illness. Many may be distressed or disorientated and unable to give a complete medical history.
In addition, some acute conditions require critical and prioritised care such as major trauma, acute coronary events, embolisms, an evolving stroke, meningitis, appendicitis and cauda equina syndrome. Often however the failure to appreciate these critical, time sensitive conditions arises from the fact that the patient isn't triaged properly or medically assessed in an appropriate time frame by a Doctor.
Failure to order or carry out diagnostic tests and scans
The failure to diagnose conditions is often as a result of the failure to order the appropriate investigative imaging in time or at all. This issue is often felt more acutely at the weekends and on public holidays when other imaging facilities, which patients may be sent to as alternatives, are closed. These include x-rays, MRI, CT scans and ultrasounds.
Poor follow up advice
It is essential that safety netting advice is offered to patients on discharge in the event that their condition worsens or deteriorates. The failure to offer this advice leaves the patient, who is already in a vulnerable condition, unaware of the need to re-attend when certain symptoms are felt.
Making a claim for Accident and Emergency Medical Negligence
If you believe that you have experienced inadequate medical care in and Accident and Emergency department you may be entitled to make a claim for medical negligence.
How do I make an Accident and Emergency Medical Negligence Claim?
You have two years from the date the negligence occurred, or the date that you discovered that the effect of the injury was not treated properly, because of medical negligence, to start court proceedings, with some exceptions:
Where a child has been injured as a result of negligence, court proceedings can be commenced any time before their 20th birthday.
There are no time limits to make a claim on behalf of someone who lacks the mental capacity to take their own case.
While it may be the case that you have months or even years to commence court proceedings, it is strongly advised that you engage a solicitor to investigate the injuries arising from potential negligence in the A&E Department you or a loved one visited. This will enable us to gather medical evidence such as hospital records and expert reports in support of your claim.
If you have any questions about the issues raised in this article you can contact Janet Keane in our Limerick office, or any of the members of our Medical Negligence team.


Adventure Access has teamed up with a local family in the region to provide the most authentic nomad experience available. Learn about and participate in daily nomad life through milking yaks and making cheese and butter. Learn how to setup the traditional Black Tent (where you will be sleeping). Ride horses, experience local foods, and enjoy the Yellow River region near their camp.


The capacitated multi-source Weber problem entails finding both the locations of capacitated facilities on a plane and their customer allocations. A framework that uses adaptive learning and functional representation to construct the restricted candidate list (RCL) within a greedy randomized adaptive search procedure (GRASP) is put forward. An implementation of restricted regions that forbids new facilities to be located too close to the previously found facilities is also embedded into the search to build up the RCL more efficiently. The performance of this GRASP based approach is tested on three classes of instances with constant and variable capacities. Very competitive results are obtained when compared to the best known results from the literature.