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

Vertebrates develop with respect to anterior-posterior axis in head-to-tail manner~\cite{benazeraf2013formation}.
First, formation of the \textit{primitive streak} at posterior and its extension towards anterior breaks radial symmetry of the embryo and sets anterior-posterior axis\cite{stern2004gastrulation}.
The anterior tip of primitive streak is defined as an organizer center called \textit{Hensen}'\textit{s node} in avian embryos.
Gastrulation, the organization of three germ layers called \textit{ectoderm}, \textit{mesoderm} and \textit{endoderm}, takes place at the level of primitive streak.
Cells from dorsal layer, \textit{epiblast}, undergo epithelial-to-mesenchymal transition (EMT)~\cite{hay1995overview} and migrate ventrally through the streak to form endoderm and mesoderm; the remaining cells in epiblast form ectoderm.

Gastrulation is accompanied by the elongation of anterior-posterior body axis.
As body axis elongates, Hensen's node regresses posteriorly and progressively induces the patterning of surrounding tissues~\cite{spratt1947regression}.
Cells located posteriorly to the node, in the streak and its derivatives, continue to gastrulate and ingress into embryonic mesoderm.  Once in mesoderm, they progressively differentiate into mature tissues anteriorly. For instance, ingressing cells from the anterior part of the primitive streak first form presomitic mesoderm (PSM) which later segments into somites, precursors of the future vertebraes~\cite{benazeraf2013formation}.
This process of maturation occurs anteriorly while new immature cells are continuously added at the posterior part of the tissue contributing to its elongation.
Regression of the node and sequential anterior-posterior patterning of PSM are sketched in Fig.~\ref{fig:model} (A).

\begin{figure}[h]
  \centering \setlength{\fboxsep}{0pt}%
  \setlength{\fboxrule}{0pt}%
  \includegraphics[width=\textwidth]{figs/Fig1.eps}
  \caption{Modelling the elongation of avian embryo.
  (A). Schematic representation of embryo elongation accompanied by regression of Hensen's node.
  Arrow indicates direction of regression.
  Surrounding node is the presomitic mesoderm
  with cell motility and density gradient of characteristic length L.
  \textit{Inset:} Single PSM cell is approximated through an elastic soft disc.
  Hard core radius R corresponds to cell's excluded volume.
  A shell of thickness $\delta$ defines the extent of cell's deformation due to inter-cellular interactions.
 (B). Model embryo as a collection of elastic soft discs.
 PSM tissue is modelled as a mixture of two types of cells: anterior and posterior.
 Both types have the same hard core radii R.
 Shell thickness $\delta_{A}$ and $ \delta_{P}$ for anterior and posterior cells
 are chosen such that PSM cell number density roughly follows the experimental observations~\cite{benazeraf2010random}.
}
  \label{fig:model}
\end{figure}

A steady regression of Hensen's node implies an existence of a force directed from anterior to posterior.
B{\'e}naz{\'e}raf et al.~\cite{benazeraf2010random} performed set of experiments to identify its origins and nature.
Their works demonstrate that caudal PSM plays a key role in the posterior body axis elongation.
PSM lies laterally on both sides of embryonic midline (Fig.~\ref{fig:model} (A)).
As Hensen's node regresses towards posterior,
PSM cells left behind change their packing and motile properties and form progressively dense and less motile mesoderm~\cite{benazeraf2010random}.
The latter eventually forms somites by condensation and epithelization of mesenchymal cells (mesenchymal-to-epithelial transition)~\cite{christ1995early}.

Cells are capable to actively change their shapes by modulating cortical forces~\cite{rauzi20114}. Collectively, such cell shape changes can result in tissue elongation through convergence-extension~\cite{keller2000mechanisms}.

The analysis of PSM cell movements relative to extracellular matrix (ECM)
showed no directional bias~\cite{benazeraf2010random}.
Individual cells perform random diffusive-like motions, much like colloidal particles~\cite{berg1993random}.
At the same time overall motion of PSM tissue is biased towards posterior.
Significant lateral convergence that accompanies anterior-posterior elongation during convergence-extension is not observed in posterior PSM tissue elongation, which rules out convergence-extension mechanism of the elongation.

How random unbiased motions of individual cells translate to a directional motion of the entire tissue?

Collective cell movements may impose overall directionality on tissue motion~\cite{vicsek1995novel}. Cells are known to exhibit high degree of coherence at the most posterior region of the embryo, tailbud. This effect, however, is less prominent in presomitic mesoderm~\cite{lawton2013regulated}.

Another mechanism for directional tissue motion was proposed by Cai et al. in the context of neuron cell migration~\cite{cai2006modelling}.
Their modelling works of neural tissue explants suggest that presence of a gradient of motogenic signalling molecules imposes a directionality on intrinsically unbiased cellular motions.
Indeed, in the absence of motogenic substances cells spreads away from the center of the explant in a symmetric fashion.
Introducing motility promotor (inhibitor) substance to a cell population biases directionality of cell spreading towards (away) from the source of the substance~\cite{cai2006modelling, benazeraf2010random}.

Molecules of Fibroblast Growth Factor family (FGF) are known to control the motility of PSM cells in avian embryos~\cite{delfini2005control}.
Specifically, gradient of FGF8 originates around Hensen's node and establishes a decreasing gradient of PSM cell motilities in posterior-anterior direction.
Thus, FGFs can potentially act as motogenic molecules in embryos.
This gives rise to the hypothesis that directional motion of PSM tissue is an emergent property of the graded motility inflicted on PSM cells by FGFs~\cite{benazeraf2010random}.

The spread of cells in neural explants is triggered by initial inhomogeneity in cell population density imposed on the system by the nature of the experiment.
Similarly, one can assume that stationary regression of node in embryos requires the formation and maintenance of inhomogeneous PSM density throughout the regression. Mechanisms responsible for establishment of stationary gradient of cell density leading to directional motion in embryos are not well understood.

Flux of new PSM cells is another important contributor to embryonic body development.
EMT and ingression of new cells into mesoderm is a necessary process to initiate limb budding~\cite{gros2014vertebrate}.
Suppressing the ingression of cells into PSM severely truncates the elongation of body axis in mice~\cite{boulet2012signaling}.
It is not clear how ingressed cells contribute to the regression of the node specifically in the context of motogenic hypothesis.

In this paper we employ computational methods to address these questions above.
We start by developing a single cell based stochastic model for the elongating embryo.
Individual treatment of cells allows to manipulate their motile, packing and growth properties on a single cell level.
It also allows to quantify the extent to which a specific mechanism influences the regression of the node.

Our simulations predict causality between the influx rate of PSM cells and the regression rate of the node.
Higher PSM influx rates correspond to higher regression rate of the node.
Interestingly, based on our results, the steepness of cell density gradient affects the influx rate of PSM cells the most.
Simulated systems with sharper density gradients have higher influx of cells added to the system.
Systems that lacked density gradient display lesser extent of node regression
even though cellular motilities were graded.
Based on our findings we propose and numerically validate the following mechanism for regression of Hensen's node.
The ability of cells to pack into more compact structures in anterior promotes the influx of the cells from posterior to anterior.
The regression of the node is then driven by excluded volume effects.
Cell motility gradient further aids node's regression by prohibiting tissue expansion towards less motile anterior and biasing it towards more motile posterior.

\section{Model and Methods}
\label{sec:model}

Experimentally observed diffusive-like motion of individual cells
has long served as a base for development of simple models,
where cells are treated as colloidal particles~\cite{anderson2007single}.
One such model was originally proposed by Drasdo et al.~\cite{drasdo1995monte},
Briefly, a cell is approximated through a spherical particle with a hard core of radius R and a shell of thickness $\delta$ as shown in Fig.~\ref{fig:model} (\textit{Inset})).
The former corresponds to the excluded volume of cell
while the latter determines the extent of cell's ability to deform.

Our model is developed based on analogous cell representation.
Essentially flat structure of the embryo allows to employ a two dimensional framework and model elongating embryo as a collection of two-dimensional elastic discs as described above performing a Brownian motion.
Since caudal PSM affects regression of the node the most, we limit our model to explicitly considering Hensen's node and surrounding PSM cells.
PSM cells are embedded into extracellular matrix (ECM). It has been shown that ECM tissue motion closely follows the motion of PSM cells~\cite{benazeraf2010random}. Based on these observations, we do not consider ECM explicitly and assume its motion is mediated by PSM cells.
The system is further simplified by disregarding any structural details of the node and considering it to be a Brownian particle of a larger size.

Below we present the set of model assumptions.

\subsection*{Cell Phenotypes.}

PSM cells in wild type embryos display different packing and motile properties depending on their position along anterior-posterior axis~\cite{benazeraf2010random}.
Moreover, set of experiments on single cells extracted from anterior and posterior sections of PSM tissue showed distinct differences in cellular behavior outside of tissue context (unpublished data by B{\'e}naz{\'e}raf and Pourqui\'e).  Based on these observations we propose a phenomenological model where PSM consists of two types of cells
with different physical properties.
The existence of distinct cell ``physical phenotypes" in mesenchyme was earlier considered in limb morphogenesis (see e.g.~\cite{damon2008limb}).
Cells in limb bud expressed higher cellular cohesivity and cell number density compared to flank mesoderm.
The gastrulation movements in Drosophila embryo requires existence of cells with different mechanical properties~\cite{rauzi2015embryo}.
We assume that anterior and posterior PSM cells are distinct physical phenotypes of PSM with different physical properties, such as size and motility.
To account for packing differences in anterior vs posterior, posterior cells are assigned larger radii and higher diffusion coefficients compared to anterior cells (Fig.~\ref{fig:model} (B)).

In avian embryos Hensen's node acts as an organizer of embryonic development.
We capture gradual change in PSM packing and motility by assigning a cell one of the two types based on its relative position with respect to the node according to the probability

\begin{equation}\label{eq:prob}
		 \phi_{A} = \left \{ \begin{array} {ll}
			0 &\mbox{if $x_{cell}\geq x_{node}$} \\
			1 & \mbox{if $x_{cell}\leq x_{node}-L$}\\
			\sim(x_{node}-x_{cell})& \mbox{if $x_{node}-L < x_{cell}<x_{node}$}
			\end{array} \right.
 \end{equation}

Here, $\phi_{A}$ is the probability of a cell being of an anterior type,
$x_{cell}$ and $x_{node}$ are positions of the cell and the node along the anterior-posterior axis,
and L is the characteristic length of the density gradient (see Fig.~\ref{fig:model} (B)).

\subsection*{Cell-cell interactions.}

Motions of cells inside tissue are influenced by their interactions with neighbouring cells.
Cells in vicinity may form adhesive bonds to maintain the integrity of the tissue.
They exert elastic repulsive forces on neighbour cells as a response to compression.
Drasdo et al.~\cite{drasdo2007role} explored several variants of interaction potentials between cells
and found that the exact form of potentials does not affect qualitative description of developmental processes.
For simplicity, we model cell-cell repulsion and adhesion with linear spring-like forces.
Caudal PSM cells are only loosely connected within tissue.
Anterior PSM cells, on the other hand,
change their adhesive and migratory properties and eventually condense into somites~\cite{gossler1997somitogenesis}.
With the above,
we assume that a pair of anterior and posterior
or two posterior cells interact solely through repulsive elastic forces
modelled by linear springs.
To facilitate the tendency of anterior cells to condense,
in addition to the elastic repulsion, we also consider weak cell-cell adhesion force between two anterior cells in vicinity.
Detailed description of inter-cellular forces and the choice of the interaction parameters is presented in Sec. \nameref{sec:forces} and ~\nameref{sec:params} correspondingly.

\subsection*{Addition of New Cells.}

Influx of new PSM cells is maintained by ingression of cells from epiblast as well as by cell proliferation in PSM.
Understanding origins and nature of newly added PSM cells is beyond the scope of this paper.
Here, we are only concerned about the fact that there is an ongoing addition of mass (new cells) to the system.
As such, we do not distinguish between processes of ingression and cell proliferation and model the
addition of new cells to the system via growth and division of the existing ones.
Cells grow by means of small stochastic increments of their radii.
Once cell's area is doubled, it is divided through randomly oriented division line.
During the division, cell is replaced by two daughter cells
of same type and physical properties as their parent.

Caudal PSM has the most prominent effect on regression of the Hensen's node.
For computational efficiency,
we neglect the proliferation outside of caudal PSM
assuming it has only a small influence on regression.
The region where new cells are added is defined relative to the instantaneous positions of the node.
In anterior, cells within a distance $GR_{A}$=L (same as characteristic distance of density gradient)
from Hensen's node grow,
provided their local number density does not exceed a threshold value $\rho_{thres}$.
The latter requirement makes sure that the growth of the cell is suppressed in the crowded environments, reducing the unrealistic overlap of cells in the system.

Similarly, in the posterior,
cells that are within $GR_{P}$ distance from the node are candidates for the growth.
Adding new cells in posterior is necessary to maintain the existence of tissue posterior to the node throughout simulations. From a biological point of view, this posterior growth regions may be considered as the portion of the primitive streak that contributes to the influx of PSM cells into the system.

\subsection*{System Dynamics.}

Langevin equation of motion for the \textit{i}-th cell takes form

 \begin{equation}\label{eq:motion}
		 \begin{array}{l}
		  	m_i\cdot\frac{\vec{r_i}}{dt}=\vec{F_{i}}/\gamma_i+\sqrt{D_i}\cdot\vec{\eta_i}
    	 \end{array}
   \end{equation}

Here, $m_{i}$ and $\vec{r_i}$ are the mass and the position of the cell,
$\vec{F_{i}}=\sum\limits_{j}\vec{F}_{ij}^{HC}+\sum\limits_{j}\vec{F}_{ij}^{SC}+\sum\limits_{j}\vec{F}_{ij}^{Attr}$ is the total inter-cellular force acting on a given cell,
and $\eta_i$ is the Gaussian noise.
Similar to thermal systems, damping and diffusion coefficients  $\gamma_i$  and $D_{i}$ in cellular systems relate as $D=F_{T}/\gamma$, where $F_{T}$ is the analogue of the thermal energy $K_{BT}$~\cite{drasdo1995monte}.
We consider cell type dependent diffusion coefficients to reflect differences in anterior and posterior cell motilities.

\subsection*{Simulation Procedure.}

We follow time evolution of the system by solving the system of equations of motions (Eq.~\ref{eq:motion}) with the molecular dynamics simulation methods.
Cells are placed in simulation box with elastic boundaries mimicking lateral and anterior-posterior boundaries of embryo. If cell moves outside of the boundary box, a linear spring-like force directed towards the simulation box acts on it.
We define lateral boundaries to be stiffer than the anterior/posterior boundaries.
The choice of boundaries is motivated by
a relatively unrestricted extension of the embryo in the anterior-posterior direction.
The existence of lateral plates, on the other hand, prevents expansion of embryo in the lateral direction.
The choice of the position and the strength of lateral boundaries is arbitrary. We find that our system does not display strong dependence on the boundary conditions (See \nameref{S3_Fig}).

Our simulations start from 500 cells
that are assigned types according to the probability as defined in Eq.(~\ref{eq:prob}).
At each time step we identify cells that are candidates for growth as described in previous section. Radii of growing cells are increased at random
which introduces asynchrony in cell cycles.
Every $T_{div}$ steps we check cells' areas and the ones with the doubled area are replaced by two cells of the same type as their parent.
Such division algorithm may create an overlap of daughter cells, however the system is equilibrated within few time steps.

Cell types depend on their relative positions from the node.
At fixed time steps $T_{type}$ we estimate the position of the node on anterior-posterior axis
and re-evaluate the probability distribution of cell types.
Cells are then assigned new types according to the updated probability.

Following this procedure, we grow systems of up to few thousand cells (See \nameref{S1_Movie},  \nameref{S2_Movie} and  \nameref{S3_Movie})

Due to the spherical symmetry of model cells anterior-most and posterior-most regions show a high degree of order, which is not observed in experiments. This is an artefact of the model since cells in real tissues constantly change their shapes as a response to changing environment which we do not consider here.
To ensure this artificial ordering does not have prominent effect on regression of the node,
we introduces a disorder in the packing of cells in by varying hard core radii of the cells.
Indeed, variability of cells' sizes did result in the less ordered packing of cells in system,
and the qualitative behaviour of the model system remained the same (See \nameref{S2_Fig} and \nameref{S7_Movie},  \nameref{S8_Movie}, \nameref{S9_Movie}).

\subsection*{Parametrization.}

We discuss detailed parametrization and the choice of numerical values for model and simulation parameters in Sec. \nameref{sec:params}.
Briefly, our model is dimensionless where cell's mass, hard core radius and metabolic energy are set to unity of mass, length and energy accordingly. All results  are reported in reduced units.
Corresponding real values can be estimated once the appropriate conversion base between reduced and real units is established.
We choose real values for the mass of eukaryotic cell (m=10\textsuperscript{-12} kg), cell's metabolic energy (E=10\textsuperscript{-16} J~\cite{drasdo2007role}) and the characteristic length of PSM density gradient (L=500$\mu$m~\cite{benazeraf2010random}) as a conversion base.
Then, time unit is evaluated as $[t]=\sqrt{[m][l]^2/[E]}$. This leads to following real values for the base conversion units: [m]=10\textsuperscript{-12} kg, [l]=20$\mu$m and [t]=10\textsuperscript{-3}sec.
To get a better insight into the quantitative differences between the model and real system we compare estimated real values of model parameters with the appropriate experimentally measurable quantities.
Comparison reveals that model cells are roughly two times larger than the real cells and that for computational efficiently the dynamics of the system is accelerated by a factor of 10\textsuperscript{6}. Such scaling allows us to keep the size of simulated system and the simulation times relatively small.

\section{Results}
\label{sec:results}

\subsection*{Trajectories, Motility and Packing of Model Cells.}

We start by examining cell motions and their packing densities for three biologically relevant PSM phenotypes expressing different FGF concentration profiles.
Wild type embryos are characterized by a gradient of FGF with the source located at Hensen's node.
FGF gain-of-function (loss-of-function) phenotypes over-express (block) FGF signalling in PSM cells.
We consider FGF implicitly through appropriately chosen distribution of cell types in the model.
Wild type embryos are modelled by considering a system
that consists of a mixture of anterior and posterior cells.
Model gain-of-function phenotypes consist of entirely posterior, more motile and loosely packed cells, whereas loss-of-function phenotypes consist of less motile and densely packed anterior cells.
Simulated elongation of wild type, FGF gain-of-function and FGF loss-of-function phenotype embryos are shown in \nameref{S1_Movie}, \nameref{S2_Movie} and \nameref{S3_Movie} correspondingly.

First, we compare model cell movements with experimentally observed PSM deformation~\cite{benazeraf2010random}.
Simulated trajectories of few cells picked at random are shown in Fig.~\ref{fig:traj}.

\begin{figure}[h]
 \centering \setlength{\fboxsep}{0pt}%
  \setlength{\fboxrule}{0pt}%
  \includegraphics[width=\textwidth]{figs/Fig2.eps}
 \caption{Trajectories of selected cells for three simulated phenotypes.
  Presented are (A) wild type, (B) FGF gain-of-function and (C) FGF loss-of-function model systems.
  Tissue is subdivided into sections along anterior-posterior axes. Different sections are color coded.
  Cells are selected at random and their initial positions are marked with asterisk.
 The trajectory of Hensen's node (red) is also shown for the reference.
 Cell trajectories are estimated over different time intervals.
}
  \label{fig:traj}
\end{figure}

We notice that our model captures the key features of cell trajectories in different phenotypes.
Simulated wild type embryos (Fig.~\ref{fig:traj} (A)) exhibit distinct regions where cell motions have different directionality.
Cells around and immediately anterior to the node move predominately towards posterior.
More anteriorly, we observed regions where cells do not seem to move in any apparent direction and regions where cellular motions are biased towards anterior.
Our results are analogous to experimentally observed trajectories of cells from various sections of PSM in wild type embryos~\cite{benazeraf2010random}.
Trajectories acquired from different simulation time intervals confirm
that this behaviour persists throughout the entire simulation.

Consistently with experiments, simulations of FGF gain-of-function system (Fig.~\ref{fig:traj} (B)) show little difference between motility of the cells in the anterior and posterior regions of tissue.
Moreover, the extent of the posterior cells' displacements is noticeably smaller.
Finally, we do not observe any significant displacements of cells in simulated FGF loss-of-function case (Fig.~\ref{fig:traj} (C)), similar to experiments.

Next, we quantify the anterior-posterior profile for cell motilities inside the tissue.
Analogous to the experimental procedure~\cite{benazeraf2010random},
we first estimate cell motions relative to the tissue deformation
by subtracting total displacement of tissue
from the displacement of individual cells.
Afterwards, the mean squared displacements (MSD) of cells are estimated.
Time intervals over which MSD is calculated are taken small enough to ensure cells mostly stay within the same region relative to the node.
The results are averaged over all cells in the given section for the given time interval and are shown in Fig.~\ref{fig:msd}.

\begin{figure}[h]
 \centering \setlength{\fboxsep}{0pt}%
  \setlength{\fboxrule}{0pt}%
  \includegraphics[width=\textwidth]{figs/Fig3.eps}
  \caption{ Mean square displacements of cells for three simulated phenotypes (log-log plot).
  Mean square displacements are estimated for  (A) wild type, (B) FGF gain-of-function and (C) FGF loss-of-function model embryos.
  Data taken from the different sections of the tissue along anterior-posterior axis are color coded.
  Total displacement of a given section is subtracted from the displacements of individual cells prior to the estimation of cells mean square displacements.
  Time intervals over which MSD are estimated are taken small enough
  to ensure cells stay within the same section.
  While there are some variations in the MSD for all three phenotypes,
  wild type model system exhibits steeper decrease of cell motility in posterior-to-anterior direction.
  }
  \label{fig:msd}
\end{figure}

All three cases demonstrate variability in MSD,
with more anterior regions having lesser degree of cellular motility.
However, wild type embryo displays steeper gradient of motility compared to the other two cases
as observed in experiments.

Another experimentally observed difference between three tissues expressing different levels of FGF is the packing densities of cells in anterior vs posterior.
To estimate cell number densities,
simulated tissue is divided  into square grid
and number of model cells in each grid cell is calculated.
The results are then smoothed out by linear interpolation.
As one can see from Fig.~\ref{fig:dens},

\begin{figure}[h]
 \centering \setlength{\fboxsep}{0pt}%
  \setlength{\fboxrule}{0pt}%
  \includegraphics[width=\textwidth]{figs/Fig4.eps}
  \caption{ Cellular number density of three simulated phenotypes.
  Cell number densities for (A) wild type, (B) FGF gain-of-function and (C) FGF loss-of-function model systems are estimated at different time points.
  Simulated wild type tissue qualitatively reproduces the gradient of cell packing density
  in anterior-posterior direction.
  FGF gain-of-function phenotype and FGF loss-of-function phenotypes
  both display relatively uniform cells packing.
  The approximate positions of the Hensen's node are marked by red.
  }
  \label{fig:dens}
\end{figure}

Consistent with experiments, our model reproduces the gradient of cellular number density for wild type embryos.
FGF gain-of-function as well as FGF loss-of-function phenotypes feature relatively uniform packing,
with overall higher packing densities in loss-of-function case, compared to gain-of-function case.

Finally, evaluating density and motility gradient profiles at different time intervals reveals that they remain relatively stable throughout simulations (See Figs.~\ref{fig:msd},~\ref{fig:dens}). Thus, our model provides a mechanism to maintain inhomogeneous density of PSM cells throughout embryo elongation (See \nameref{S4_Movie}, \nameref{S5_Movie} and \nameref{S6_Movie}).

\subsection*{The Graded Motility and Density of PSM Cells Along With the Influx of PSM Cells is Sufficient to Account For the Regression of Hensen's Node.}

As we have demonstrated in the previous section, our two-type cell model is sufficient to
qualitatively reproduce characteristic density and motility profiles as well as the individual cell motions of avian PSM tissues.

In this section we quantify displacements of Hensen's node for the three phenotype tissues.
Experimental observations show that extent of node's regression is most notable in the wild type embryos.
Both FGF gain-of-function and loss-of-function phenotypes have significantly slower regression rates.
We tracked the displacement of the node by recording its  position along the anterior-posterior axis at fixed time steps for three simulated phenotypes.
The results are shown in Fig.~\ref{fig:ap_node}.

\begin{figure}[h]
  \centering \setlength{\fboxsep}{0pt}%
  \setlength{\fboxrule}{0pt}%
  \includegraphics[width=\textwidth]{figs/Fig5.eps}
  \caption{ Causality between cells added to system and anterior-posterior displacement of Hensen's node. (A) Anterio-posterior displacement of the node.
 Wild type embryo exhibits the highest motility of the node.
 Simulations reproduce decrease in the regression of the node for both FGF gain-of-function
 and FGF loss-of-function cases. Error bars correspond to the standard deviation of node's displacement over 1000 simulation time steps.
 (B) The extent of Hensen's node displacement correlates with the increase of the total number of cells in simulated system.
 The rates are which cells are added to the system are higher in the wild type embryos,
 followed by FGF gain-of-function and FGF loss-of-function phenotypes.
  }
  \label{fig:ap_node}
\end{figure}

Similar to experiments, wild type embryos demonstrate the fastest regression rates, whereas
both FGF gain-of-function and FGF loss-of-function have lesser degree of regression of Hensen's node.
We estimated the regression rate of the model node in the wild type embryos to be about $30\mu m/hr$,
which differs from the experimentally observed regression rates of the node by factor of three.
Provided cell physical properties in our model are defined up to an order of magnitude, we find that our model matches the experimental observations of the extent of node's regression quite well.
Moreover, as we show in \nameref{S4_Fig}, node's regression rate can be easily tuned  by changing the influx rates of cells.

Our findings reinforce the earlier proposed importance of the gradient profiles and the influx of PSM cells and suggests that these mechanisms alone might be sufficient to explain the observed regression of the node.

\subsection*{The Extent of the Hensen's Node Regression Correlates With the Steepness of the Cell Density Gradient.}

Interestingly, there is a causality between the addition of new cells and the extent of the Hensen's node displacement (Fig.~\ref{fig:ap_node}).
Both FGF gain- and loss-of-function model phenotypes display reduced growth rates compared to model wild type embryos.
The difference between model wild type embryos and the FGF phenotypes lies in the existence of gradients in cell packing density and motility,
which suggests that graded profile of the density and/or motility promotes growth (influx) of cells in system.
To confirm out assumption we gradually decrease the difference between anterior and posterior
cell radii and observe the changes in the displacement of the node and the total number of cells in the system (Fig.~\ref{fig:vary_size}).

\begin{figure}[h]
 \centering \setlength{\fboxsep}{0pt}%
  \setlength{\fboxrule}{0pt}%
  \includegraphics[width=\textwidth]{figs/Fig6.eps}
  \caption{ Relation between the difference in anterior and posterior cells sizes,
  the anterior-posterior displacement of Hensen's node and the total number of cells in the system.
    (A) The increase in the differences between anterior and posterior cells sizes correlates with the increase of the displacement of Hensen's node. Error bars correspond to the standard deviation of node's displacement over 1000 simulation time steps.
     (B) The increase in the differences between anterior and posterior cells sizes correlates with the increase of the total number of cells in the system.
     Data for different ratios between anterior and posterior cell radii are colour coded as follows:
   $R_{Tot}^{A}$=0.56, $R_{Tot}^{P}$=0.9 (green),
   $R_{Tot}^{A}$=0.6, $R_{Tot}^{P}$=0.9 (purple),
    $R_{Tot}^{A}$=0.7, $R_{Tot}^{P}$=0.9 (yellow),
    $R_{Tot}^{A}=0.8$, $R_{Tot}^{P}$=0.9 (red),
    $R_{Tot}^{A}$=0.9, $R_{Tot}^{P}$=0.9 (blue).
  }
  \label{fig:vary_size}
\end{figure}

As seen in Fig.~\ref{fig:vary_size} the greater difference between the anterior and posterior cell sizes promotes the growth rate of the system
and, consequently, the faster anterior-posterior displacement of  Hensen's node.

To investigate the influence of explicit diffusion gradient on Hensen's node displacement,
we considered a system that consists of posterior cells that are assigned diffusion coefficients $D_A$ and $D_P$ based on the probability~(\ref{eq:prob}).
Such system lacks density gradient observed in wild type embryos but has an explicitly introduced gradient of cell motilities as in wild type embryos.
We then compared the node's regression in the above-mentioned system with
simulations of wild type embryos (both density
and motility gradients are explicitly considered) and FGF gain-of-function (density gradient is absent and all cells are assigned same motility).
As we can see from Fig.~\ref{fig:grad_effect}, introducing cell motility gradient to otherwise uniform system contributes positively to regression of the node.
However, the increase in the node's regression rate is relatively small.
Introducing the density gradient along with motility gradient significantly increases regression rate.

\begin{figure}[h]
  \centering \setlength{\fboxsep}{0pt}%
  \setlength{\fboxrule}{0pt}%
  \includegraphics[width=0.7\textwidth]{figs/Fig7.eps}
  \caption{ The effect of the explicit diffusion gradient on the displacement of Hensen's node.
  The anterior-posterior displacements of the node in the system that has same cell sizes and explicitly introduced motility gradient analogous to wild type embryo (referred as graded motility) is compared to the FGF gain-of-function (referred as uniform motility) and wild type embryos.
Introducing explicit gradient of motility shifts the displacement of the node towards posterior.
This shift is more prominent when density gradient is introduced as well.
  }
  \label{fig:grad_effect}
\end{figure}

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

Recent experimental works identify presomitic mesoderm as a key player in the elongation of anterior-posterior body axis and regression of Hensen's node in avian embryos.
Tracking of individual cell motions couples gradient of cell motilities to the rate of regression\cite{benazeraf2010random}.

In the attempt to understand how cells movements induce regression we have developed a single cell based model that accounts for graded density and motility of PSM tissue and incorporates influx of new cells.  Based on our studies, we proposed regression mechanism which is summarized in Fig.~\ref{fig:scheme}.

In wild type embryos (Fig.~\ref{fig:scheme} (A)) the existence of two types of cells with different packing and motile properties establishes gradients of motility and density (Figs. ~\ref{fig:msd} (A) and ~\ref{fig:dens} (A)).
As demonstrated by simulations,
gradient of cell packing density influences cell proliferation.
Embryos featuring steeper density gradients have higher rates of cell addition(Fig.~\ref{fig:vary_size}).
From a physical point of view, the ability of cells to pack into denser configurations in anterior can effectively decrease cell density in posterior and create space for addition of new cells via ingression or cell proliferation.
As new cells are added to the system, regions anterior to the node become increasingly more crowded which eventually leads to the expansion of the tissue through excluded volume effects.

Cell motility counteracts crowding effects and creates favourable conditions for tissue expansion.
In wild type embryos motility of cells decreases from posterior to anterior biasing
motion of PSM tissue along with Hensen's node towards more motile posterior, by effectively prohibiting the expansion of the tissue in anterior direction (Fig.~\ref{fig:grad_effect}).
After assuming its new position along anterior-posterior axis,
Hensen's node re-establishes the gradients of cell motility and density (Fig.~\ref{fig:ap_node} (A)).

Both gain-of-function (Fig.~\ref{fig:scheme} (B)) and loss-of-function (Fig.~\ref{fig:scheme} (C)) model phenotypes
flatten density and motility gradients. The absence of cell density gradients decreases the rate of cell addition reducing regression and elongation rates in both phenotypes.

Further difference between regression rates of FGF gain-of-function and FGF loss-of-function phenotypes lies in the difference of their cell motilities. High cells motilities everywhere in FGF gain-of-function phenotypes counteract cell crowding effects and promote tissue expansion in both anterior and posterior directions. This eliminates the bias of PSM tissue motion towards posterior due to motility gradient and further reduces regression rate of the node.
Due to low cell motilities in FGF loss-of-function embryos cells form crowded environment early in simulations which severely reduces addition of new cells and, hence, regression rates of the elongation and regression.

\begin{figure}[h]
  \centering \setlength{\fboxsep}{0pt}%
  \setlength{\fboxrule}{0pt}%
  \includegraphics[width=\textwidth]{figs/Fig8.eps}
  \caption{Proposed mechanism for stationary regression of Hensen's node.
  Solid arrows specify positive feedback. Blunt arrows specify negative feedback with the higher strength of the feedback indicated by darker color. Dashed arrow specifies re-establishment of cell types based on their updated positions relative to the node.
  (A) In wild type embryos existence of two cell types establishes cell density gradient which has a positive contribution to addition of new cells.
  Addition of new cells increases cell crowding in PSM tissue anterior to node which leads to its expansion. Motility of cells counteracts cell crowding effects and creates favourable conditions for tissue expansion. Due to gradient of cells motilities in wild type embryos the expansion of tissue and regression of node are biased towards more motile posterior.
(B) In the FGF gain-of-function embryos the absence of density gradient reduces cell addition rates. Higher cell motilities everywhere aid to tissue expansion in both anterior and posterior directions and eliminate bias in cell movements towards posterior observed in wild type embryos. These two factors lead to a reduction in node's regression rate.
(C) FGF loss-of-function embryos, in addition to the absence of gradients of cell motility and density,
have also a reduced motility of all cells.
In contrast to FGF gain-of-function embryos,
where high cell diffusion rates of cells counteract the crowding effects,
cells with low motilities stay clustered. High local cell densities penalize cell proliferation rates,
which further decreases the regression rate of the node.
}
  \label{fig:scheme}
\end{figure}

Within the scope of our hypothesis we were able to reproduce regression rates of Hensen's node in wild type, FGF gain-of-function and FGF loss-of-function phenotypes up to an order of magnitude. Regression rates in the model depend on physical properties of PSM tissue, such as difference between cell sizes in anterior and posterior, influx rates of new cells into PSM, etc. Due to the lack of precise experimental values, numerical values of model parameters are defined up to an order of magnitude. Future experimental measurements of relevant PSM properties as well as careful estimates of PSM cell proliferation and ingression will aid to more accurate estimates of node's regression rate.

While a flat structure of chick embryo allows to develop a two-dimensional model, more accurate quantitate description of the system would require to extend it to three-dimensional case.  The key physical drivers described here  (gradient of density and motility) would still remain in three dimensions, so that the main interest of 3D simulations would be to study   elongation of the embryo in the context of multiple interacting tissues. The extension is in principle straightforward by including  an approximation of a single cell through an elastic spherical particle. While such model would provide better insight into regression, it would also be much more computationally expensive, and two dimensional simulations are better suited to identify first principles.

We have used here a molecular dynamics approach to describe cell motion and  tissue elongation. Such cellular models allow for direct comparison to experimentally measured features (such as cell trajectories, mean square deviations, cellular density), corresponding to a ``microscopic'' scale .  Control of the microscopic features by a morphogen gradient then gives rise to a complex ``macroscopic'' emergent behaviour. The interplay of the microscopic/macroscopic scales is not trivial since presumably many different microscopic mechanisms could give rise to some macroscopic elongation. Simulations of mutants and of microscopic features allow for a better biological understanding of the origin of embryonic physics. Insights from this approach can later give rise to more continuous and biologically realistic description, that would be necessary to scale-up simulations of embryogenesis.

\clearpage
\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


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Mogg, Elizabeth
Area: Somerset - West
View records on the VWML website for Mogg, Elizabeth
Elizabeth Mogg at Holford (1830-1921): age 74, 8 songs (includes two versions of 'Waly Waly') Aug 1904: Elizabeth's life is difficult to reconstruct because she called herself both Mogg and Moggridge. It is the same woman, same location and family round her, just different surnames in different censuses.
She was baptised 'Elizabeth Mogg', daughter of William & Mary Mogg on 3/10/1830 in Over Stowey church. Her father William was a labourer and they lived at Bincombe, a part of Over Stowey parish. Her mother Mary died and was buried at Over Stowey church on 25/10/1844, when Elizabeth was only 14. In 1851 William Mogg was therefore a widower, an agricultural labourer with two daughters Charlotte (26) and Elizabeth (19), neither of whom had an occupation. According to a later census (1911), Elizabeth was 'crippled from birth', so she may have found it difficult to work.
Elizabeth then had an illegitimate child Mary Ann (baptised Fiddington church 23/11/1851). Elizabeth's older sister Charlotte also had 2 illegitimate children by a labourer Henry Chilcott and they married in 1861. In 1861, now that her sister Charlotte had moved out, Elizabeth, aged 27 with young daughter Mary 9, was living with her widowed father William Mogg at Bincombe. In 1871 census Elizabeth now called herself Moggridge - she was 36 and a dressmaker. By this time she had had a second illegitimate child, a son William (age 7 in the census). She later told Sharp that she had indeed had 2 children out of wedlock. In 1881 Elizabeth reverted to the name Mogg and she was still a dressmaker and William was 17, an agricultural labourer. They were living at Lime Street, Nether Stowey. By 1891 Elizabeth had moved in with her brother-in-law Henry Chilcott and her older sister Charlotte, who were living at Dodington (ref is RG12 piece 1866 f25 p3). She was 60 by now, still a dressmaker.
Also in the same house was James Squires, aged 19. James was the son of Charlotte's daughter Elizabeth. So, Elizabeth Mogg, the singer was the great aunt of Jim Squires, the singer! In 1901 Elizabeth ('Moggridge'), aged 70, was still with Henry & Charlotte Chilcott in Dodington. By 1911 Elizabeth ('Mogg'), aged 81, was living with her bereaved son-in-law William Dinham, who had married her daughter Mary Ann back in 1873 at Holford church. They had had 9 children, 2 of whom were still at home in 1911. However, Mary Ann had died in March 1909 and Elizabeth perhaps wanted to help son-in-law William with the children but it is reported that her final years were dogged by ill-health and poor mobility. She died at Holford in 1921 aged 91.

redpajama_set_name: RedPajamaCommonCrawl


The AU Carry Handle Mount for Trijicon MRO red dot sights fits all M16/M4/AR15 A1/A2 and similar detachable carry handles. The mount features an iron sight see-through allowing you to utilize your iron sights shall the need arise. A rugged, lightweight design with an oversized bolt for secure mounting and easy installation.


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Q: Accessing an F# Map from inside C# code Is there any simple way to access an F# Map from inside C# code?
I mean, both C# and F# lists are enumerable so I can iterate an F# list from inside C# code just through that interface, like explained in this post.
Suppose I've declared such a Map inside a F# module called module.fs:
let MyMap : Map<string,T>>

I would like to access the map from inside C# this way:
Map m = module.MyMap;

Is possible to do something like this without performing conversions?

A: Map is called FSharpMap when accessed outside F#. You could use var to avoid the awkward type name (in your example). However, most F#-specific types implement interfaces that play well across language boundaries. For instance, Map implements IDictionary<_,_>. In APIs that will be used outside F#, the recommended solution is to expose those interfaces instead.
Check out the Component Design Guidelines for more recommendations.
Having said that, you can use FSharpMap from C# without any trouble. It just looks weird and doesn't lend itself to idiomatic C# code.

redpajama_set_name: RedPajamaStackExchange


Knowledgeable, Responsive & Dedicated to Your Buying Experience!
Buying a home may very well be the biggest investment you will ever make. Buyer representation is typically at no cost to you, so why not demand the best agent to guide you through this complex transaction? Whether you're buying a starter home, your dream home or an investment property, take advantage of our experience as a top Cincinnati real estate team & local market expert to make the most informed purchase decision you can. Let's get started today!
That is, your financial reserves plus your borrowing capacity. If you give us some basic information about your available savings, income and current debt, we can refer you to lenders best qualified to help you.
Sometimes the property you are seeking is available but not actively advertised in the market. Rest assured we'll investigate to find all available properties on your behalf.
We have access to a variety of informational resources and can provide local community information on utilities, zoning, schools, etc. There are two things you'll want to know: First, will the property provide the environment I want for a home or investment? Second, will the property have resale value when I am ready to sell? We'll help you figure that out.
There are many negotiating factors, including but not limited to price, financing, terms, date of possession and often the inclusion or exclusion of repairs and furnishings or appliances. The purchase agreement should allow time for you to complete appropriate inspections and investigations of the property before you are bound to complete the purchase. We will advise you as to which investigations and inspections are recommended or required.
Depending on the area and property, this could include inspections for termites, dry rot, asbestos, faulty structure, roof condition, septic tank and well tests, just to name a few. We will help you find qualified, responsible professionals to do most of these investigations and provide you with written reports.
You will want to see a preliminary report on the property title. Title indicates ownership of property and can be mired in confusing status of past owners or rights of access. The title to most properties will have some limitations; for example, easements (access rights) for utilities.
We will help you understand different financing options and identify qualified lenders.
We will guide you through the closing process and make sure everything flows together smoothly.
Want a House You're Proud To Call Home?
There is nothing that is so complex that it can't be easily explained. Just because you don't apply for a thirty year mortgage once a week doesn't mean you have to take the first one that comes along. You'll need to learn some new terms, apply some new concepts and take the time to understand what you're getting into.
If, at any point, something happens that doesn't make sense to you, simply demand a full and complete explanation. If it still doesn't make sense, seek help from someone you trust like your CPA or your loan officer.
In the world of real estate sales, YOU are the most important person.
The purchase process can be a roller coaster and more than frustrating at times.
But the truth is that you are the one person in the transaction that makes it all happen.
We're here to help you approach home buying with intelligence and confidence.


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June 14, 2012 - Gama Aviation Awarded Scottish Air Ambulance Contract Again - AINonline
Gama Aviation announced today that the Scottish Ambulance Service has again selected the company to be its dedicated provider of air ambulance services, extending its contract for seven more years, to 2020. Gama's Scottish fleet includes a Beechcraft King Air 200C at both Aberdeen and Glasgow Airports and a Eurocopter EC135T2 at both Glasgow and Inverness. The two EC135s will be replaced with two new EC145T2s next year. Two Eurocopter Super Pumas in Shetland and Aberdeen are also on standby.
Gama Aviation Awarded Scottish Air Ambulance Contract Agai1.pdf


The YMCA at Knightdale Station offers summer parent and child swim classes for babies and toddlers ages 18 to 36 months.
Registration opens on April 1 for YMCA Members and April 15 for Program Participants. Click on the attachment below for the 2019 swim lesson schedule at Knightdale Station.
For questions about the program, contact Jeff.Little@YMCATriangle.org.


Our signature Yoga Sculpt class is based on the Law of Attraction infused with positive affirmations, sweat, squats, a bomb playlist, weights. Raise your frequency while aligning to your highest self!
Let go of emotional + physical weight.
Take your Power back & Transform!
You get your own personal trainer & life coach for way less money!
Guaranteed to change your body, mind, and your frequency.


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Richland County History
July 14, 2019 December 9, 2020 timothy brian mckee
Safety Town: Mansfield's Gift to Children of the World
Mansfield has been known for a lot of different things throughout American History, and the world has come to know our name by way of a countless variety of people, companies, products, works of literature, pop music, celebrities, and events of historic proportion.
But our town's chief contribution to aid in the evolution of civilization on the planet has been one particular export: Safety Town.
Children in places all over the country and around the world are more likely to make it to adulthood because they learned to live more safely at an early age; and Mansfield is a part of that equation.
All those kids—in Louisiana, in Illinois, in Germany or Indonesia—are imprinted with basic principles of safety by their own teachers in their own communities; but the system of education by which they are taught can be traced back to one place on the Earth and one particular time in history: Prospect Park in Mansfield on August 6, 1937.
That was when kids first waited till the light changed at Safety Town.
It began as an experiment and was inspired by a book.
The experiment was conceived and implemented by Patrolman Frend Boals as a method to teach fundamentals of traffic cooperation; and was sparked by a book of children's stories written by the supervisor of Mansfield primary schools, Mildred Miles Roberts.
Her 1930 book was called Safety Town Stories, and the cover is emblematic of the entire Safety Town concept: kids and a traffic light.
Patrolman Frend Boals (1904-1958) and the book by Mildred Roberts that inspired him.
From the very first day when children crossed at the corners of make believe streets, and learned to pay attention to traffic lights like it was a game, everyone knew the 'experiment' was a success.
Within a week there were representatives on site from the national AAA office in Washington DC reporting back to the National Safety Department. Within two weeks there were film crews in town from Chicago hoping to get footage for news reels.
Over the next few years the Safety Town story with pictures of Mansfield kids appeared in newspapers and magazines across the nation. The American Automobile Association adopted it as part of their permanent pedestrian safety program.
From there the idea took off like it was always meant to be a part of American life.
They say nothing is more difficult to stop than an idea whose time has come. The Safety Town idea arrived right on time. In 1937 there were dozens of Depression era WPA programs entirely focused on safety issues. Every city had a "Safety Council;" Mansfield had several "Safety Week" events during the year; for drivers, for workers, and for homemakers.
So when Officer Fred Boals took the ABCs of safety to the preschool kids of Mansfield he was already riding a societal wave of interest. Making it kid-friendly was his genius.
He turned it into a game. He wanted it to be so fun the kids would be singing their lessons.
He built kid-sized streets with stop signs that were only as tall as a 6-year old. He got the firemen of Station 1 to build wooden sidewalks and a kid-sized traffic light. A sign painter named Roy Gale made kid-sized houses to put in the neighborhoods of Safety Town; and in 1938 Boals talked the Richland County Automobile Club into buying 25 bright red toy cars for kids to pedal around the streets.
The first class in 1937 graduated 40 youngsters. In 1938 there were 300.
When Frend Boals joined the Mansfield Police Department they were still riding horses to traffic jams; and he eventually rose to hold the position of Mansfield Traffic Commissioner. Here he directs traffic at Safety Town in 1939.
The original fleet of Safety Town vehicles were bright red chain-driven cars that kids pedaled around Prospect Park. In the 1940s they were upgraded to blue and white models.
In those first few seasons, Safety Town was a portable village sponsored by the City Recreation Department that moved every other week to a different part of the city. It was established at Woodland School, Hedges, West First Street, West Fifth Street and Western Avenue Schools; Johns Park, North Lake Park and Liberty Park. It even emigrated to Shelby for two weeks.
Since that beginning, Safety Town has been in continuous habitation except for a 5 year hiatus during WWII. In the 1970s there was talk of discontinuing it when enrollment dropped to rock bottom numbers, but someone always stepped in to spring for new materials.
From the very earliest years there was always talk of building a permanent Safety Town in Mansfield, but different generations and different decades found the kid's burg settling wherever it could. For many years its most permanent location was at the old Brinkerhoff School on Marion Avenue.
In 1953 it was replanted at the new Brinkerhoff School on Euclid Avenue and a sign was posted to establish its official latitude and longitude.
In recent years it could also be found at Woodland or Raemelton Schools.
The original 1937 instructional model at Safety Town had participating children divided into two groups — the drivers and the pedestrians — in order to engender cooperation and mutual concern.
When the new Brinkerhoff elementary school was built in 1950 on Euclid Avenue the playground was laid out with Safety Town in mind.
Photo documentation indicates that there have been at least three sets of buildings at Safety Town since 1937. This is how they looked in 1993.
In the summer of 2009 the streets of Safety Town were laid out at Raemelton School.
The whole concept of Safety Town was sound and ingenious: plant the seed of sanity in little minds when they are at that age when everything makes an indelible impression.
So does it work? The proof is easy to find: there are many dozens of grown, mature (old) folks in Mansfield who can still sing their Safety Town songs.
Singing has always been an integral element of Safety Town education. The music and lyrics have evolved through the generations, but for the first 40 years all the kids in Mansfield learned 'Songs of Safety' from a 1939 record.
Safety Town is a very intensely personal Mansfield thing. If you didn't grow up here its not likely you'll get it unless you grew up somewhere else where there is a Safety Town.
That is the genius of it, because everywhere that Safety Town exists they feel the exact same way: like it belongs to them.
Go to Shreveport LA and you'll find they own Safety Town. For generations they have been nurturing their young with the same toy houses on little lined streets with short stop signs.
Go to Troy MI and talk with old folks whose kids went to Safety Town; whose grandkids went to Safety Town, and you'll hear what a uniquely Troy experience it is.
It is also a Naperville IL tradition that the community owns and loves, as well as Paris TX, and Salem OR.
Safety Town class of 1953 at Brinkerhoff School.
This photo by Jeff Sprang was taken in the summer of 1977 when attendance at Safety Town was so low there was talk of abandoning the project.
Mansfield tried to establish itself in the 1950s as a sort of official Safety Town resource clearing house, but that function ultimately wound up in Cleveland as the National Safety Town Center.
There are Safety Town programs indoors and outdoors in 3500 communities in the US, and in 38 countries outside our borders. They all—each of them—feel it is their own legacy.
Most of them—nearly all of them—have little sense of what they owe to Mansfield. That is really the best kind of fame.
There are some really spectacular Safety Town permanent parks in America that look like little Disney towns. They make your heart warm.
Mansfield's most permanent Safety Town is found in the hearts of kids and parents who remember cops and firemen and bikes and stoplights in the eternal summer of our souls since 1937.
Speaking of Safety Town in 1937 Patrolman Frend Boals said, "The fruits of our labor now in Mansfield education will be reaped in 20 years when those tots of today become the motorists of tomorrow."
It is 80 years later and the fruits are untold, worldwide and continually seeding themselves to future generations.
Many of the photos of Safety Town through the years were taken on Graduation Day: this one was in 1960.
The streets of Safety Town are full of grown ups every Graduation Day, along with friendly representatives from MPD and MFD.
One of the most important elements of Safety Town is establishing a congenial and trusting relationship between young citizens and the police by redefining "law enforcement" as the "safety force." Officer Hurlow, seen here in 1993, had more friends in town than anyone.
Brinkerhoff School
Frend Boals
Mansfield OH
Mansfield Police Department
Marion Avenue
Mildred Roberts
Prospect School
Published by timothy brian mckee
View all posts by timothy brian mckee
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Boston College QB Jurkovec will return for senior season
(AP Photo/Mary Schwalm)
BOSTON (AP) Boston College quarterback Phil Jurkovec said on Monday that he will return for his senior season rather than enter the NFL draft.
"I will be returning to Chestnut Hill in 2022 to complete my economics degree, improve all facets of my game, and compete nationally," he said in a statement issued by the school. "Let's win!"
Jurkovec threw for 2,558 yards and 17 touchdowns in the pandemic-shortened 2020 season. This year, he injured his right (throwing) wrist in Week 2 and missed six games before returning on Nov. 11.
The Eagles went 4-2 in his starts in 2021 and are 10-6 in his career. He is fifth in school history with six 300-yard passing games in just 16 games played.
More AP college football: https://apnews.com/hub/college-football and https://twitter.com/AP-Top25 Sign up for the AP's college football newsletter: https://apnews.com/cfbtop25


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Reading comics and playing with toys so you don't have to.
Spider-Men: When Peter Met Miles
Posted on January 3, 2013 by Chris
Peter Parker has had a rough couple of weeks, with switching bodies with Doctor Octopus and dying and such. Spider-Men is a glimpse to a more lighthearted adventure, with him entering the Ultimate Universe and meeting the Spider-Man of that reality.
The only thing that I really wasn't too keen on this story was how Peter winds up getting into the Ultimate Universe. Longtime illusionist and lame villain Mysterio has acquired some sort of trans-dimensional gateway that Peter accidentally activated, sending him to another reality where he meets Miles. Mysterio now has the opportunity to kill the two Spider-Men.
While dodging Mysterio's robot avatars and such, the two bond. Miles really looks up to Peter, who himself is amazed on how respected the alternate version of himself was by the people of Ultimate New York. Knowing that he doesn't belong, the Ultimates agree to help find a way to send Peter home.
The best parts of Brian Bendis' story are when Peter meets up with this world's version of Aunt May and Gwen Stacy, both of them who are still mourning the loss of their Peter. Things are also odd for Peter, as he's talking to a version of a girl he was deeply in love with, but whose life was cut short in his reality.
This really was really made the book for me were these exchanges. Peter and Miles could have not punched a whole thing through it; the story was fine without any action. There was plenty; the Spidey's and the Ultimates team up to stop Mysterio. The ending is a little odd; Mysterio learned a lot about Peter Parker's secret identity and such by watching him through his device, and the Ultimates wound up imprisoning him in their world to keep Peter's secrets safe. But mostly it's important for Miles and the Aunt May and Gwen that he knows; they were able to get closure knowing that somewhere there is a Peter very close to the one that they knew who is living a wonderful life.
When that Peter got home he Googled Miles, and we don't know what he found online. But between that and Mysterio stuck in the Ultimate world there are two plot points to pick up at a later date.
The art on this was by Sara Pichelli, whose work is really growing on me. I read that she does most of her work on a Wacom tablet and I'm amazed about how thin her line work is. It's very clean and looks great.
Getting back to Spider-Men, I give it a glowing recommendation It's more a Miles than a Peter story, but it doesn't matter which Spider-Man you prefer. It's a great Spider-Man story all around.
This entry was posted in Uncategorized and tagged brian bendis, crossover, marvel, miles morales, peter parker, spider-man, ultimate by Chris. Bookmark the permalink.
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Q: Forcing optimal solution for FindShortestTour I use FindShortestTour as explained here and it works nicely for a small number of cities. However when I try this with as little as 16 cities, the given tour isn't optimal anymore. I've tried using different Methods but none of them gave me the optimal tour (solutions within a 5% to 400% range of the optimal solution).
How can I force Mathematica to give me the optimal solution?
Edit:
This is my code (pretty much copy-paste from the link above as I'm very new to Mathematica)
dim = 16;
max = 100;

(* create symmetric matrix with random integers *)
d = RandomInteger[max, {dim, dim}];
d = Table[If[i > j, d[[i, j]], d[[j, i]]], {i, 1, Length[d[[1]]]}, {j, 1,Length[d[[1]]]}];
(d[[#, #]] = Infinity) & /@ Range[dim];
d // Grid

(* find tour *)
{len, tour} = FindShortestTour[Range[dim], DistanceFunction -> (d[[#1, #2]] &),
  Method -> "TwoOpt"]

(* display tour *)
HighlightGraph[ WeightedAdjacencyGraph[d, DirectedEdges -> False,
  GraphStyle -> "SmallNetwork", EdgeLabels -> "EdgeWeight"],
 Style[UndirectedEdge[#1, #2], Thickness[.01], Red] & @@@ Partition[tour, 2, 1, 1]]

A: Daniel Lichtblau has confirmed that this is a problem with the integer linear programming code. Moreover, a bug report has been filed and the problem will be addressed in a future version.


Returns true if the first argument is greater than or equal to the second argument. Equivalent to the >= operator.
Output: Keeps all rows in which the value in the myValue column is greater than or equal to the value in minLimit.


Ob Hospitalist Group (OBHG) would like to congratulate our nineteen Partner Hospitals Named to the US News and World Report 2013 Best Hospitals List. This is the 24th year U.S. News and World Report has compiled its hospital rankings. Hospitals were rated on their performance in areas including patient survival rates and patient safety information.
OBHG would like to congratulate the OB/GYN department at our partner hospital, Halifax Health for being voted Department of the Year! Each year, graduating residents vote on several superlatives and this year they chose the Halifax OB/GYN department as the department of the year. They made special mention of OBHG hospitalists, particularly recognizing their excellence in teaching and sincere commitment to providing high quality of care to their patients. Dr. Brian Bogdanowicz, graduating resident summed up his experience thusly, "OBHG is instrumental in the obstetric education for the Halifax Family Residency Program. They are available 24 hours per day and are eager to teach residents and integrate them into the daily care of the patients on the floor. Their consistent presence and knowledgebase have improved the educational experience for me and my fellow residents."
Congratulations to the team, OBHG hospitalists and especially to the graduating residents!
Click here to read more about Halifax Health.
Louisville, KY - Ob Hospitalist Group(OBHG) is Proud to Announce Our 47th Hospital Partner, Norton Hospital – Downtown, in Louisville, KY.
Norton Hospital - Downtown opened their new Obstetrical Emergency Department (OBED) June 18, 2013. This new service is a result of a partnership between Norton Healthcare and OBHG that ensures highly-skilled, Board Certified OB/GYN physicians (hospitalists) are on-site at Norton Hospital 24 hours a day, 365 days a year. This is the first of the two Norton Healthcare programs that OBHG will be opening this year.
As the founder of Ob Hospitalist Group (OBHG), the leading OB/GYN hospitalist provider in the nation, I'm frequently asked to describe the event that led me to its creation. However, it wasn't just one event, but a series of compounding issues and strains I experienced as a private practicing OB/GYN that led me to realize there were some significant voids in women's health care – in both hospitals and private practices.Those voids were most evident in the high-stress situations of trying to be in two places at once – seeing a patient in the office while a laboring patient experiences an unforeseen emergency at the hospital. They were also apparent during nights filled with phone calls or during a child's ballgame with a beeper going off right before their big moment.
We've all had the experience of showing up for our first day of work, eager, prepared but not quite sure what to expect. The following is a brief synopsis of Dr. Debbie Bredestege's first day at one of Ob Hospitalist Group's (OBHG) newest hospitalist programs at Cox South in Missouri.
Early in Dr. Bredestege's first shift, a young female patient arrived by EMS after being discovered unconscious by a family member. She was evaluated by the Emergency Department physician who called Dr. Bredestege upon discerning a positive pregnancy test in addition to hypotension and tachycardia. Even before Dr. Bredestege saw the patient, she suspected an ectopic pregnancy.
Ob Hospitalist Group (OBHG) is committed to our mission of elevating the quality and safety of women's healthcare. OBHG hospitalists provide on-site support and coverage 24 hours a day, 365 days a year- adding many levels of value to a hospital program. The presence of an OB/GYN Hospitalist provides peace of mind for patients who are given the unique advantage of being assessed by a physician upon each visit, reduced risk for hospitals and much needed support not only for the physicians, but for the nursing staff as well. In an effort to better understand and support the nursing staff in our nearly 50 partner hospitals, OBHG recently interviewed some of those nurses to gain their perspective on the benefits of the program. We wanted to share with you some of their thoughts on their individual OBHG hospitalist programs and the changes they have made in their lives and that of their patients.
DAYTONA BEACH, FLA. – (June 14, 2013) – The obstetrical team at Halifax Health – Center for Women & Infant Health has earned the 2013 MOREOB Recognition Award for outstanding performance in the application of knowledge, communication and teamwork in order to make patient safety the priority and everyone's responsibility. The award is presented based on the team's yearly achievement toward meeting the goals of the MOREOB Program.
Springfield, MO – OBHG is proud to introduce our 46th Dedicated OB/GYN 24-hour Obstetric Emergency Department (OBED) at Cox South, A member of the CoxHealth medical system in Springfield, MO. This is our first program in Missouri, expanding OBHG's presence to 20 states.
About CoxHealth: CoxHealth is the only locally owned, not-for-profit health system based in Springfield, MO. It is accredited by The Joint Commission, distinguished as one of the nation's Top 100 Integrated Healthcare Systems (2006-2012) and recognized as a U.S. News & World Report Best Regional Hospital.
About Cox South: Cox South is the jewel of the medical mile. Located on the southern edge of Springfield, MO this full-service facility has been serving physicians and their patients since 1985. The growing campus of Cox South includes many physician offices, a Level I Trauma Center and numerous other special services.


It was impossible to ask a father who is/was an engineer a simple question, because he had to calculate everything before answering. And he would look up at the ceiling, chin in hand, arms across chest, frowning, till he found the right answer. My father didn't need computers. He was a computer. I felt like I was being raised by a computer. To make matters worse, I was raised in a single parent family. Just my father. The Engineer. Egads.
After all, no other way of thinking is encouraged. So what will we cook for dinner? First, we have to go down to the basement and get a level, that tool with the nifty bubbles that have to line up if everything is equally level. And ascertain (that word again) that the stove is absolutely level before attempting to cook. Wait!!! You cannot cook if the frying pan handle is in anyway loose. Must tighten that screw. Where's your toolbox? I grew up with toolboxes, not sewing machines. After all, I'm the Daughter of an Engineer, and I have a reputation to live up to. Or surpass. But first I must speak at least 5 languages fluently, and try aiming for a Master's or Ph.D. But I digress. Cook we must for we have to eat. To live.
Here he goes again, "But what is the precise dimension of the frying pan? Don't dare make fun of me! If the circumference of the frying pan is not vast enough to accommodate the sausages...and they have to be German, or at least Polish, the sausages...Wait! Stop! We can not eat pork. It's too fatty and will increase our chances of dying prematurely by heart disease, which statistics say is the number one killer. And is that smoke I smell? There will be no smoking in this house! Punishable by a sentence to hard labour in Siberia!"
"Dad, uh, where is Siberia? I'm really hungry. And I'm about to devour all the cookies as this Ph.D. level discourse on useful fats versus hazardous fats reigns on."
Dad replies, "You think I am joking? This is serious. We are Slavic here. We must eat sausages in the mathematically correct frying pan, on the right stove element, not too big, agh! That would utilize unnecessary electricity...."


What distinguishes U.S. policy on Russia under Donald Trump from other U.S. presidents?
"While the Clinton, Bush, and Obama resets didn't last, they provided periods of respite in the historically tense ties and allowed both sides to achieve important policy goals," according to the analysis by Robert E. Hamilton, an Associate Professor of Eurasian Studies at the U.S. Army War College.
Hamilton argues that the Trump's own affinity for Putin, as demonstrated by his refusal to criticize the Russian president and inability to acknowledge Russian interference in the election, explains much of his failure. The latest example of this affinity was Trump's muted reaction to the Russian seizure of three Ukrainian ships in the Kerch Strait.
"Congress imposed sanctions on Russia and restricted Trump's ability to lift them. The Departments of Defense and State convinced the White House to sell advanced Javelin anti-tank missiles to Georgia and Ukraine despite Trump's reluctance to go ahead with the sale. Trump was similarly reluctant to expel Russian diplomats from the U.S. as punishment for the use of a nerve agent in the United Kingdom, but was apparently convinced to do so by senior advisors," the analysis reads.
The assessment concludes on a pessimistic note: Until the Trump presidency ends, a reset is impossible, and the personal relationship between presidents will remain mostly irrelevant.


text:
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Who do you want to replace Mary Berry?
The Bake Off dream is over! Love Productions' decision to sell the rights of the iconic show to Channel 4 has been met with national outrage, becoming known as simply 'Bakexit'. The decision has also seen the stars of the show fall like a poorly secured gingerbread structure leaving social media awash with 'expensive tent' jokes.
The binge-watching life
In 2015 Collins English Dictionary's announced that their 'Word of the Year' was in "Binge-Watching". This decision was largely due to the staggering 200% increase in usage of the term that year. To me, this increase in the use of the word is not that surprising.
The greatest reality TV moments
The 'wrong Miss Universe' blunder at last year's tournament has been named the most memorable reality TV moment of all time. The epic fail was witnessed by a TV audience of 7.6million and went viral on social media. Miss Colombia Ariadna Gutierrez was crowned for a full two minutes...
The reality TV habit
In light of the current explosive series of Celebrity Big Brother, which has had millions of viewers tuning in to the daily drama, OnePoll polled 2000 UK adults to discover what makes us so engrossed in reality TV. Nearly 4 in 10 of us watch some form of reality TV... we wanted to understand what draws us to reality tv shows.
Is poetry a dying art form or just evolving?
OnePoll conducted two nationally representative surveys, which found that 22% of Brits don't even know who Robert Burns is, and less than half know that the great Bard of Ayrshire wrote Auld Lang Syne. 14% said they didn't know a single word of the song – apparently not even realising that the title features in the lyrics ...
Call Me Caitlyn
Social media has recently been abuzz with the transformation of Bruce Jenner into Caitlyn Jenner. We ran a quick snap poll, asking 1000 respondents how they felt about the transformation.
The portrayal of women in film and TV
It is a common conception that women are misrepresented in TV & film. Often the female characters function only to serve the male lead, or are gender stereotyped as the dumb/ unintelligent character or just there for their looks.
57% of Brits still don't know what ALS stands for. Here's what we really know about the ice bucket challenge.
The ice bucket challenge is the new big thing to take over most of our social media feeds, and, as the name slightly gives away, it involves chucking an ice cold bucket of water over yourself, filming it, and sticking it on social media. This is all done with the aim of raising awareness and donations for ALS/MND.
What is it like to live in London?
For a lot of people, London is the ultimate goal. Those following their dreams will often end up in London. OnePoll surveyed 1000 people living in London about the excitement, fun and downsides to living in the Capital.
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My project for Day 22 was Abecedarian Summer Schoolhouse from With Thy Needle and Thread. I fell in love with this project as soon as I saw it last summer. The fact that it is stitched over one thread was an added bonus. I am using the called for overdyed flosses, a mixture of Weeks Dye Works and The Gentle Arts threads on the called for fabric! That doesn't happen often!
The main change I am making is that I decided to stitch it as one long piece, instead of as separate pillows. One of the reasons for this is that I have never done a pillow finish, so I'm a bit intimidated, and of course, I no longer own a sewing machine!
I mentioned my plans in my Stitch with Me video, and one of my commenters mentioned someone on Instagram who was doing just that. I found the post by Skye Coote, @scottycoo on IG, and got her permission to share it here. She did have to make some changes to the pattern to make them the same height. I may or may not do that. I will decide when I get to the other pieces. But isn't it stunning all worked together as one piece!
I am only on part 1 of this 4 part series. It's been a while since I worked on this, and this is what I had done.
Have I mentioned that I adore this piece! Look at those tiny stitches! Love it!
I got the roof completed and a nice chunk done on the side of the house, so that's where I leave it till the next time.
On to the next project! Lizzie Kate's Snowman '10!


text:
extern "C" IMAGE_DOS_HEADER __ImageBase;

namespace base {

bool PathProviderWin(int key, FilePath* result) {

  // We need to go compute the value. It would be nice to support paths with
  // names longer than MAX_PATH, but the system functions don't seem to be
  // designed for it either, with the exception of GetTempPath (but other
  // things will surely break if the temp path is too long, so we don't bother
  // handling it.
  wchar_t system_buffer[MAX_PATH];
  system_buffer[0] = 0;

  FilePath cur;
  switch (key) {
    case base::FILE_EXE:
      GetModuleFileName(NULL, system_buffer, MAX_PATH);
      cur = FilePath(system_buffer);
      break;
    case base::FILE_MODULE: {
      // the resource containing module is assumed to be the one that
      // this code lives in, whether that's a dll or exe
      HMODULE this_module = reinterpret_cast<HMODULE>(&__ImageBase);
      GetModuleFileName(this_module, system_buffer, MAX_PATH);
      cur = FilePath(system_buffer);
      break;
    }
    case base::DIR_WINDOWS:
      GetWindowsDirectory(system_buffer, MAX_PATH);
      cur = FilePath(system_buffer);
      break;
    case base::DIR_SYSTEM:
      GetSystemDirectory(system_buffer, MAX_PATH);
      cur = FilePath(system_buffer);
      break;
    case base::DIR_PROGRAM_FILESX86:
      if (base::win::OSInfo::GetInstance()->architecture() !=
          base::win::OSInfo::X86_ARCHITECTURE) {
        if (FAILED(SHGetFolderPath(NULL, CSIDL_PROGRAM_FILESX86, NULL,
                                   SHGFP_TYPE_CURRENT, system_buffer)))
          return false;
        cur = FilePath(system_buffer);
        break;
      }
      // Fall through to base::DIR_PROGRAM_FILES if we're on an X86 machine.
    case base::DIR_PROGRAM_FILES:
      if (FAILED(SHGetFolderPath(NULL, CSIDL_PROGRAM_FILES, NULL,
                                 SHGFP_TYPE_CURRENT, system_buffer)))
        return false;
      cur = FilePath(system_buffer);
      break;
    case base::DIR_IE_INTERNET_CACHE:
      if (FAILED(SHGetFolderPath(NULL, CSIDL_INTERNET_CACHE, NULL,
                                 SHGFP_TYPE_CURRENT, system_buffer)))
        return false;
      cur = FilePath(system_buffer);
      break;
    case base::DIR_COMMON_START_MENU:
      if (FAILED(SHGetFolderPath(NULL, CSIDL_COMMON_PROGRAMS, NULL,
                                 SHGFP_TYPE_CURRENT, system_buffer)))
        return false;
      cur = FilePath(system_buffer);
      break;
    case base::DIR_START_MENU:
      if (FAILED(SHGetFolderPath(NULL, CSIDL_PROGRAMS, NULL,
                                 SHGFP_TYPE_CURRENT, system_buffer)))
        return false;
      cur = FilePath(system_buffer);
      break;
    case base::DIR_APP_DATA:
      if (FAILED(SHGetFolderPath(NULL, CSIDL_APPDATA, NULL, SHGFP_TYPE_CURRENT,
                                 system_buffer)))
        return false;
      cur = FilePath(system_buffer);
      break;
    case base::DIR_PROFILE:
      if (FAILED(SHGetFolderPath(NULL, CSIDL_PROFILE, NULL, SHGFP_TYPE_CURRENT,
                                 system_buffer)))
        return false;
      cur = FilePath(system_buffer);
      break;
    case base::DIR_LOCAL_APP_DATA_LOW:
      if (win::GetVersion() < win::VERSION_VISTA) {
        return false;
      }
      // TODO(nsylvain): We should use SHGetKnownFolderPath instead. Bug 1281128
      if (FAILED(SHGetFolderPath(NULL, CSIDL_APPDATA, NULL, SHGFP_TYPE_CURRENT,
                                 system_buffer)))
        return false;
      cur = FilePath(system_buffer).DirName().AppendASCII("LocalLow");
      break;
    case base::DIR_LOCAL_APP_DATA:
      if (FAILED(SHGetFolderPath(NULL, CSIDL_LOCAL_APPDATA, NULL,
                                 SHGFP_TYPE_CURRENT, system_buffer)))
        return false;
      cur = FilePath(system_buffer);
      break;
    case base::DIR_SOURCE_ROOT: {
      FilePath executableDir;
      // On Windows, unit tests execute two levels deep from the source root.
      // For example:  chrome/{Debug|Release}/ui_tests.exe
      PathService::Get(base::DIR_EXE, &executableDir);
      cur = executableDir.DirName().DirName();
      FilePath checkedPath =
          cur.Append(FILE_PATH_LITERAL("base/base_paths_win.cc"));
      if (!file_util::PathExists(checkedPath)) {
        // Check for WebKit-only checkout. Executable files are put into
        // WebKit/Source/WebKit/chromium/{Debug|Relese}, and we should return
        // WebKit/Source/WebKit/chromium.
        cur = executableDir.DirName();
      }
      break;
    }
    default:
      return false;
  }

  *result = cur;
  return true;
}

}  // namespace base

redpajama_set_name: RedPajamaGithub


text:
Mollie Beattie
April 27, 1947 (age 49)
Glen Cove, New York , United States
In 2009, she was designated a Women"s History Month Honoree by the National Women"s History Project. From 1985 to 1989, she was Vermont commissioner of forests, parks and recreation. From 1989 to 1990, she was deputy secretary for Vermont"s Agency of Natural Resources. From 1993 to 1996, she served as the first woman director of the United States. Fish & Wildlife Service. She oversaw the successful reintroduction of the gray wolf into northern Rocky Mountains. She died on June 27, 1996, in Townshend, Vermont. The Mollie Beattie Wilderness in Arctic National Wildlife Refuge is named after her. In the long term, the economy and the environment are the same thing. If it"s unenvironmental it is uneconomical. That is the rule of nature. -- Mollie Beattie.
Ben Manilla
Shyam Benegal
Jean-Pierre Jeunet
Ajith Nair
John Klima
Valentin Sapcariu
Mollie Beattie Edit Profile
Mollie H. Beattie was an American conservationist, and director of the United States Fish and Wildlife Service.
She was born on April 27, 1947, in Glen Cove, New New York
She graduated from Marymount College, Tarrytown with bachelor"s degree in philosophy in 1968, and from the University of Vermont with a master"s degree in forestry in 1979, and from Harvard University with a master"s degree in public administration in 1991.
In 2009, she was designated a Women"s History Month Honoree by the National Women"s History Project. From 1985 to 1989, she was Vermont commissioner of forests, parks and recreation. From 1989 to 1990, she was deputy secretary for Vermont"s Agency of Natural Resources.
From 1993 to 1996, she served as the first woman director of the United States. Fish & Wildlife Service.
She oversaw the successful reintroduction of the gray wolf into northern Rocky Mountains. She died on June 27, 1996, in Townshend, Vermont.
The Mollie Beattie Wilderness in Arctic National Wildlife Refuge is named after her. In the long term, the economy and the environment are the same thing.
If it"s unenvironmental it is uneconomical.
That is the rule of nature. -- Mollie Beattie.
June 27, 1996 (aged 49)
Glen Cove, Long Island