The Town Clerk's Office is in motion with processing the annual town census which is mandated by the Commonwealth. Thank you to those who have already completed and returned this year's form. All residents, regardless of voter registration or citizenship, are required to confirm or correct the census form. The Town Clerk's Office has also added a new feature for residents who are new to town or may have lost their original form. With this, you have the capacity to respond electronically or via mail.


Prior to joining UCSF, Barry was the CEO of Threshold Pharmaceuticals, a fully integrated oncology drug discovery/clinical development company that he led as CEO from its Series A financing through IPO to its eventual sale in 2017. He was also a Venture Partner at Sofinnova Ventures from June 2002 until July 2007. Prior to Threshold, Barry co-founded and was CEO and Chairman of Camitro, a venture capital backed drug discovery technology company with teams in California and Cambridge, UK, which was acquired 2 years after its founding. Before Camitro, Barry was at Affymax Research Institute, which was acquired by Glaxo Wellcome, plc as its drug discovery technology development center and where Barry was Vice President of Research, responsible for technology development and drug discovery. Prior to Affymax, Barry was at Protein Design Labs (PDL) and Anergen. As a bench scientist at PDL, he co-invented the technology underlying fully humanized antibody therapeutics and applied that to daclizumab (Zenapax), the first FDA-approved fully humanized antibody therapeutic, that was licensed to and commercialized by Roche for the prevention of kidney transplant rejection. This technology has contributed to more than 15 FDA approved therapeutics with cumulative revenues in excess of $200B. Throughout his career, Barry has been a member of the Boards of Directors of a dozen both early stage venture capital-backed as well as public biotech companies and Chairman and/or Lead Director of 9 of those.
With a BA in Biophysics and PhD in Biology from the University of Pennsylvania, Barry was a Damon Runyan-Walter Winchell Cancer Fund Fellow as well as a Senior Fellow of the American Cancer Society at UCSF.


text:
ATLANTA, Ga.,
Three-Time Former Hungarian National Champion Signs For Team Novo Nordisk
For everyone, a diabetes diagnosis is a terrifying moment that comes with a lot of uncertainty. Life changes in an instant and it is a condition that immediately affects the entire family. I'm proud that our organization could give Peter hope through those first days when he struggled and his entire family was fearful of his future. While we never wish anyone to be diagnosed with type 1 diabetes, we are eager to welcome Peter into our family,
Phil Southerland, CEO & Co-Founder of Team Novo Nordisk
Follow me on Twitter (opens in new window)
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Team Novo Nordisk is proud to announce that Olympian Peter Kusztor will join its 2019 roster
Peter_006
For the first time since launching in late 2012, Team Novo Nordisk is adding a new rider to its professional roster from outside of its development pipeline. Team Novo Nordisk is proud to announce that Hungarian Peter Kusztor will join its 2019 roster. The Olympian was recently diagnosed with type 1 diabetes and will bring depth and experience to the world's first all-diabetes professional cycling team.
Peter is a very experienced rider as an Olympian and former multi-national champion. That exposure and level of experience will bolster our overall performance in 2019, and we are all looking forward to welcoming him to the team,
Vassili Davidenko, General Manager of Team Novo Nordisk
"For everyone, a diabetes diagnosis is a terrifying moment that comes with a lot of uncertainty. Life changes in an instant and it is a condition that immediately affects the entire family," Team Novo Nordisk CEO and Co-Founder Phil Southerland said. "I'm proud that our organization could give Peter hope through those first days when he struggled and his entire family was fearful of his future. While we never wish anyone to be diagnosed with type 1 diabetes, we are eager to welcome Peter into our family."
While racing for MyBike Stevens on Stage 3 of the Czech Cycling Tour, Kusztor broke his collarbone (August 2018). Before going in for surgery, doctors checked his fasting blood glucose levels, which were elevated. Initially, doctors believed he had type 2 diabetes and hospitalized him to bring down his blood glucose. He did not respond to medication, and eventually endocrinologists ran a series of new tests that lead to his type 1 diagnosis.
The diagnosis and lifestyle changes were difficult for Kusztor, and he couldn't imagine racing professionally while managing the condition. Yet the Hungarian had raced against Team Novo Nordisk over the years and knew that all riders on the team competed with type 1 diabetes.
"Over the years, I've always admired the riders at Team Novo Nordisk and the way they raced while managing such a serious condition. I knew about their unique mission, which has become my own personal mission," Kusztor said. "In Hungary, people still don't believe that you can race at the top level with diabetes and I'm motivated to overcome these judgments and prove that it is still possible to race with diabetes."
Not wanting to give up his career and dream, Kusztor reached out to Team Novo Nordisk to receive information on nutrition and training advice for someone newly diagnosed with diabetes. After several conversations, the team offered him a spot on the 2019 squad.
"Peter is a very experienced rider as an Olympian and former multi-national champion," Team Novo Nordisk General Manager Vassili Davidenko explained. "That exposure and level of experience will bolster our overall performance in 2019, and we are all looking forward to welcoming him to the team."
Throughout Kusztor's career, accolades include representing Hungary at the 2008 Beijing Olympic Games, two-time Hungary national road race champion (2010, 2012), Hungary national time trial champion (2010), winner overall at the Tour of Bretagne (2011), second overall at Gemenc GP (2017) and lining up for four UCI Road World Championships (2008, 2009, 2012, 2013).
"Moving up to Team Novo Nordisk means that a very big and old dream of mine is finally coming true. While I fully believe I have the ability to race at this level, I've never had the chance to move up," Kusztor said. "My primary goal for the 2019 season is to get to know Team Novo Nordisk and learn how to train and race with diabetes at this top level. Additionally, I recognize that I still have a lot to learn around racing at this level."
Outside of Italian Andrea Peron, Kusztor is the only rider on Team Novo Nordisk's 2019 roster who didn't come through the organization's pipeline.
"It's invigorating to add a rider with this level of experience from outside the team to our roster," Southerland said. "His intense hunger and fight are very palpable and I'm eager to see how this drive will motivate all our riders."
The 33-year-old went professional in 2005 with P-nivo Betonexpressz 2000 and has raced the past 13 seasons with continental squads including Atlas Personal, Utensilnord, Amplatz-BMC, and MyBike Stevens.
"I'm excited for next year's program and believe it will be well suited for me. The professional continental calendar is more balanced, and I'm motivated to achieve my best results, but first and foremost, I want to fit into this program and work with my new teammates to earn our best results together," Kusztor concluded.
Off the bike, Kusztor is married and has two daughters. His family lives outside of Budapest in Páty where he and his wife also run an amateur cycling team.
About Team Novo Nordisk – Racing to Change Diabetes
Team Novo Nordisk is a global all-diabetes sports team of cyclists spearheaded by the world's first all-diabetes UCI Professional Continental cycling team. In 2012, Phil Southerland, co-founder and CEO of the team, and global healthcare company Novo Nordisk, came together to create Team Novo Nordisk, based on a shared vision to inspire, educate and empower people around the world affected by diabetes.
For more information, go to www.teamnovonordisk.com.
Fitzalan Crowe
Vice President of Marketing and Sponsorship
fitzalan.crowe@teamnovonordisk.com
BACK TO PRESSROOM
Team Novo Nordisk Switching Over to Shimano Disc Brakes for 2020 Season
Benhamouda Runner-Up on Stage 5 of Tour of China
Charles Planet Extends Contract with Team Novo Nordisk for 2020
Kiwi Hamish Beadle Moves Up to Team Novo Nordisk Pro Squad
University Diabetes Experts Share Innovative Research into Professional Cycling Team

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: What are the priors in Bayesian Neural Network? So I have knowledge of Bayesian statistics/econometrics, but I only recently found out about Bayesian Neural Networks. I was wondering what the priors are in a Bayesian Neural Network?
And is it possible to give an importance weight to different input features? Or have the ability to shrink features with a prior?
Basically, I am trying to see if Neural Networks can be used in a setting where the number of observations is not very large by performing feature selection. However, instead of feature selection I thought about including all features and give prior weights to the features based on the outcomes of the feature selection step. Is this possible?

redpajama_set_name: RedPajamaStackExchange


text:
\section{Introduction}

Fluid membranes occur in a wide variety of physical, chemical, and
biological systems
\cite{amphiphiles,bilayers,biomembranes,lipo-mann95}.  Examples
include surfactant films, uni-lamellar and multi-lamellar vesicles,
and lipid bilayer membranes, such as those in biological cells.
Increased attention has been paid to the properties of multi-component
bilayer membranes.  There are at least two important reasons for this.
On the one hand, biological cell membranes naturally involve mixtures
of several different lipid and protein components
\cite{biomembranes,lipo-mann95}.
Processes such as budding, shape and textural transformations, and
raft formation are believed to involve local inhomogeneities in these
mixtures
\cite{farge92,Dobe+93,SackFede95,mcconnell99a,farge00,crowe01,webb03,keller02,keller03,keller04,munro03,edidin_rev03,gaus03a}.
On the other hand, lipid mixtures have been shown to play an important
role in the formation of stable vesicles for a variety of potential
biomedical applications such as controlled gene and drug delivery
\cite{lipogenes97,lipomedicine98}.

The additional internal degrees of freedom that accompany the presence
of two or more components within a fluid membrane can lead to a rich
set of different membrane properties.  The understanding of the
effects of composition variations on membrane properties is important,
as it may shed light on the behavior of cell membranes, and also
enable rational control of synthetic membrane structure and function.
The compositional degrees of freedom in a multi-component membrane can
dramatically influence both its morphology and phase behavior.  For
instance, phase separation within the membrane can occur, analogous to
phase separation of ordinary fluids.  However, such two-dimensional
phase separation within a membrane is expected to be closely linked
with the three-dimensional shape of the membrane.  This is because, at
a microscopic level, the curvature properties, and especially the
spontaneous curvature, are largely dictated by the structure of the
constituent molecules~\cite{israelachvili}.  Thus, regions of
different composition will often have different curvature properties.
In such cases, the formation of a domain of one phase within a matrix
of another phase can lead to a localized deformation of the membrane.
This deformation can be enhanced by finite line tension between
domains, which when sufficiently large can drive budding (the
formation and subsequent separation of a small vesicle).  Experimental
studies of model two and three component systems have examined domain
formation~\cite{farge92,SackFede95,farge00,mcconnell99a,crowe01,webb03,keller02,keller03,keller04}
and its role in the process of membrane shape
transformations~\cite{webb03,keller03} and
budding~\cite{farge92,SackFede95}.

Many theoretical studies have examined the interplay between internal
degrees of freedom and membrane shape in two-component fluid
membranes~\cite{leibler86,leibler87,safranpinc90,safranpinc91,AKK92,Lipo92b,MackSafr93,Seif93,JuliLipo93,Kawa+93,Tani+94,
HardMack94,JuliLipo96, kumar99,gozdz01}.  In theoretical studies of
phase-separated bilayer vesicles, it was found that budding can occur
in the limit of large line tension between the two
phases~\cite{Lipo92b,JuliLipo93,JuliLipo96}.  However, when surface
tension is relevant, phase separation can lead to stable, modulated
phases of flat films and
vesicles
\cite{leibler87,AKK92,Kawa+93,Tani+94,HardMack94,JuliLipo96,kumar99,gozdz01}.
Indeed, equilibrium modulated morphologies have been observed in
several recent studies of phase-separated multi-component bilayer
vesicles~\cite{webb03,keller03}.  On the other hand, the deformation
of homogeneously mixed two-component fluid membranes may induce
in-plane phase separation\cite{Seif93}.

For a mixed monolayer, the deformation of the film due to phase
separation of two components with differing spontaneous curvature is
an immediate consequence of the different molecular architectures of
the two components.  For a bilayer membrane, however, the coupling of
composition to curvature is somewhat more subtle because of symmetry
considerations.  Phase separation can take two different forms within
a bilayer membrane.
As shown in Fig.~\ref{pics}(a), a symmetric domain of one component
can develop within a matrix of another phase.  In Fig.~\ref{pics}(b),
an asymmetric domain is shown, in which the two halves of the bilayer
have different compositions.  As illustrated in the figure, these
effects can influence the shapes and phase behavior of membranes in
different ways.  In the symmetric case [Fig.~\ref{pics}(a)], the
domain can remain flat \cite{Lipo92b} although the domain can be more
or less rigid than the surrounding membrane, a situation reminiscent
of rafts in biological membranes.  However, composition
inhomogeneities can give rise to deformation of a bilayer membrane if
there is an asymmetric distribution of the lipid constituents across
the bilayer, as shown in Fig.~\ref{pics}(b) \cite{gebhardt77}.  Such
lipid asymmetry has been clearly demonstrated experimentally in
biological membranes \cite{opdenkamp79,verklejj}.  This broken
symmetry of the bilayer can either arise spontaneously
\cite{MackSafr93} or as a result of different environments on the
inside and outside of a vesicle.  In the latter case, we must also
consider the possibility of a non-zero surface tension due to an
osmotic pressure difference between the inside and outside.

\begin{figure}[ht]
\displaywidth\columnwidth
\includegraphics[scale=0.35]{./figures/Fig1.eps}
\caption{
(a) Flat symmetric phase-separated membrane, and (b) curved,
asymmetric phase-separated membrane.}
\label{pics}
\end{figure}

In this paper, we examine the stability and equilibrium shapes of
domains in asymptotically flat fluid films (or giant vesicles with
dimensions much larger than the domain sizes).  We focus on domains of
constituents with finite effective spontaneous curvature, embedded in
a matrix of membrane material with zero spontaneous curvature.  These
domains can either be due to phase separation of two or more
components in a mixed membrane, or to the inclusion of an ``impurity''
in the film (such as a membrane protein or a surface adsorbed
macromolecule) \cite{Sens2004}.  We show that for membranes under
tension, stable protruding circular domains (we call these \emph{caplets}, as in Refs.\ \cite{gozdz01,HardMack94}) similar to
those observed for mixtures of lecithin and phosphatitic acid
\cite{gebhardt77} can occur at low concentrations of the minority
component or impurity.  We illustrate the structure of such circular
\emph{caplet} domains in Fig.~\ref{shapes}.
\begin{figure}
\includegraphics[width=2.8truein]{./figures/NewCap1.eps}
\includegraphics[width=2.8truein]{./figures/NewSlug1gray.eps}
\includegraphics[width=2.8truein]{./figures/NewBud1gray.eps}
\caption{
  Schematic representation of phase-separated circular (top) and
  stripe (middle) domains and a bud (bottom) of the $B$ component,
  with induced deformations.}
\label{shapes}
\end{figure}
We also demonstrate the possibility of a phase transition from a
mesophase of circular caplets to a mesophase of protruding stripe
domains either with increasing area fraction of the minority component
or with increasing tension.  We illustrate these
stripe domains in Fig.~\ref{shapes}.

In both cases, the domains are shown to be stable with respect to
complete phase separation in a flat membrane.  In
Section~\ref{sec:model} we present our model and briefly discuss our
analysis in the Monge gauge treatment. In Section~\ref{sec:eqns}, we
provide the resulting Euler-Lagrange equations and boundary conditions
used in our Monge gauge calculations.  In Section~\ref{sec:regimes} we
present Monge limit results in the dilute and concentrated regimes,
and discuss the extent to which the limiting approximations of Ref.
\cite{HardMack94} apply. In Section~\ref{sec:num} we present the
results of a numerical calculation of the budding transition beyond
the Monge approximation, and we conclude in Section~\ref{sec:yadayada}
with a summary and discussion.

\section{Model (Monge Gauge)}\label{sec:model}

We consider a single idealized two-component membrane consisting of
incompatible amphiphiles $A$ and $B$.  Furthermore, we consider asymmetric
bilayers, in which phase separation occurs in only one leaflet of the
bilayer, as shown in Fig.~\ref{pics}(b).  This applies, for instance,
to the case of phase separation in an asymmetric bilayer vesicle or
biomembrane.  Such domains can also be induced by the adsorption of
macroions on the inside or outside of a bilayer vesicle, as in the
experiments of Refs.~\cite{Baek+95,SackFede95}.  We assume that the
binary liquid mixture is far from its critical point, implying that
there are sharp interfaces between the domains of $A$ and $B$, and that
the membrane consists of a fluid minority phase $B$ surrounded by an
asymptotically flat fluid majority phase $A$.

We investigate the properties of two prototypical domain morphologies
(see Fig.~\ref{domains}), which are idealizations of actual
structures that may exhibit disordered textures of polydisperse,
irregular domains:
\begin{itemize}
\item[i)] Quasi-one-dimensional domains of ${\rm B}$ (stripes),
  with an impurity phase of width $2 x_0$ embedded inside a majority
  stripe with total with $2X_0$. The stripe length (system dimension)
  is $L$, and the projected area of an element (minority plus majority
  repeat unit) is $S_{A,\perp}+S_{B,\perp}=2 X_0L$.
\item[ii)] Monodisperse circular domains of ${\rm B}$ (caplets).
  For caplets we take a circular Wigner-Seitz cells with impurity
  radius $r_0$ and total radius $R_0$.  The circular Wigner-Seitz cell
  approximation leads to a lower bound for the free energy of a less
  symmetric structure, such as a hexagonal array.  The projected area
  of an element is $S_{A,\perp}+S_{B\,\perp}=\pi R_0^2$.
\end{itemize}
Below we will typically scale these dimensions by the spontaneous
curvature $c_0$, thus defining $\rho_0=r_0c_0$, $\bar{R}_0=R_0c_0$, $\xi_0=x_0c_0$, $\Xi_0=X_0c_0$.

\begin{figure}[ht]
\includegraphics[scale=1.0]{figures/DomainPics.eps}
\caption{
  A sketch of the stripe and caplet morphologies.  Fig.~(a) shows a
  linear array of ${\rm B}$-phase stripes of width $2 x_0$ (black) in a
  matrix of phase ${\rm A}$ (grey).  Fig.~(b) shows a hexagonal array
  of ${\rm B}$-phase circular caplets of radius $r_0$ (black) in a
  matrix of phase ${\rm A}$ (grey).  The dashed lines in each figure
  show the appropriate Wigner-Seitz cell boundaries, while the
  membrane displacement profile of an appropriate unit cell cross
  section is shown above each figure.}
\label{domains}
\end{figure}
For given material parameters, we obtain minimum energy height
profiles $h({\rm\bf r})$ (within a linearized Monge gauge
description), where ${\rm\bf r}$ is the position in the plane, and
minimize the resulting free energy over the domain dimensions. We
consider the background ${\rm A}$ phase to be flat and restrict our
attention to the simplified case of equal bending moduli $\kappa_{{\rm
    A}}=\kappa_{\rm B} \equiv\kappa$.

For phase separated membranes under tension,
the free energy of a single domain (stripe or caplet)  has the form
\begin{equation}
G_0=F_l + F_s + F_b
\label{Eq1}
\end{equation}
where $F_l$, $F_{s}$, and $F_b$ are the energy contributions from the
interfacial (line) tension between the two phases, the membrane frame
(surface) tension, and the bending elasticity.  To lowest order in the
Monge representation (see Appendix \ref{app:a}), valid for nearly flat
membranes, these contributions relative to a flat reference state are
given as follows.
\begin{widetext}
The bending energy is
\begin{equation}
F_b=\frac12\kappa\left\{
\int_{S_{\rm A}} \left(\nabla^2 h\right)^2 dS_{\perp}
+\int_{S_{\rm B}} \left[ \left(\nabla^2 h\right)^2
-2c_0\nabla^2 h + c_0^2\left(\nabla h\right)^2\right] dS_{\perp}
\right\},
\label{Eq4}
\end{equation}
where $dS_{\perp}$ is the (flat) area measure in the plane, $S_i$
denotes the projected area occupied by phase $i$, $h({\rm\bf r})$ is
the height profile above some flat reference plane, $\nabla$ is a
two-dimensional gradient operator, $\kappa$ is the bending modulus,
and $c_0$ is the spontaneous curvature of the ${\rm B}$ phase.  The
line tension energy is
\begin{align}
F_l &= \lambda \oint_{\partial S_{\rm B}}dl =
\left\{
\begin{array}{ll}
\lambda\, 2\pi r_0 N& \qquad\hbox{(caplets)}\\
\noalign{\vskip5truept}
\lambda\, 2 L N& \qquad\hbox{(stripes)}\\
\end{array}
\right.
\label{Eq2}
\end{align}
where $N$ is the number of domains, $\partial S_{\rm B}$ denotes the
boundary of the impurity region, and $\lambda$ is the line tension.
The work done by the membrane in deforming relative to the flat state
is
\begin{equation}
F_{s}= \frac12\left\{
\sigma\int_{S_{\rm A}} \left|\boldsymbol{\nabla} h\right|^2 dS_{\perp}
+ (\sigma+\mu)\int_{S_{\rm B}} \left|\boldsymbol{\nabla}
  h \right|^2
dS_{\perp}\right\},
\label{Eq3}
\end{equation}
\end{widetext}
where $\sigma$ is the frame tension, and the Lagrange multiplier (or
exchange chemical potential per unit area) $\mu$ controls the amount
of impurity phase. We assume a fixed area per molecule in the
membrane, and thus ignore stretching energies.

It will be convenient to define a renormalized chemical potential
$\tilde{\mu}$, by
\begin{align} \tilde{\mu}&=\mu + \kappa c_0^2, \label{eq:3}
\end{align}
where $\kappa c_0^2$ arose in Eq.~(\ref{eq:3}) from keeping all terms
to second order in the height field \cite{gozdz01}. This
renormalization, neglected in \cite{HardMack94}, is typically very
small: $\kappa c_0^2$ is of order $k_BT$ divided by a curvature radius
squared of order $(100\textrm{nm})^2$, while $\sigma\sim k_BT$ divided
by a length squared of order $\textrm{nm}^2$.  In fact, we will find
that this renormalization does not change the phase boundaries if only
one phase has a non-zero spontaneous curvature; see \cite{gozdz01} for
a different example.

Stationarity of Eq.~(\ref{Eq1}) with respect to height variations
leads to Euler-Lagrange (E-L) equations for the height profiles in
regions ${\rm A}$ and ${\rm B}$.  The detailed derivation of the these
equations are presented in Appendix~\ref{app:a}.  To calculate the phase
behavior we must  minimize the free energy $G$ of an array of domains,
\begin{equation}
G(\mu,\sigma,\lambda) = N
G_0(\mu,\sigma,\lambda),
\end{equation}
where
\begin{equation}
N = \frac{S_{fr}}{S_{A,\perp}+S_{B\,\perp}}
\end{equation}
is the number of domains and $S_{fr}$ is the frame area, which without
loss of generality we consider to be fixed. The free energy must also
be minimized over the dimensions of the ${\rm A}$ and ${\rm B}$
domains, $x_0$ and $X_0$ for the stripes and $r_0$ and $R_0$ for the
caplets:
\begin{subequations}
\label{ELequations}
  \begin{align}
    \frac{\partial G}{\partial x_0}&=0,&\
    \frac{\partial G}{\partial X_0}&=0,&\textrm{(stripes)}\label{ELS}\\
    \frac{\partial G}{\partial r_0}&=0,&\
    \frac{\partial G}{\partial R_0}&=0,&\textrm{(caplets)}.\label{ELC}
  \end{align}
\end{subequations}
Physically, minimization over the inner length ($x_0$ or $r_0$) is
equivalent to allowing exchange of $B$ for $A$ species, while minimization
over the outer length ($X_0$ or $R_0$) is equivalent to allowing more
or less total area into the system, doing work against the frame
tension.

Phase coexistence is found by equating  chemical potentials,
\begin{equation}
  \label{eq:1}
  \mu_{\rm stripes}=\mu_{\rm caplets}.
\end{equation}
In the dilute limit, where all the impurity is in a single domain, we
must minimize the free energy per impurity,
\begin{equation}
g(\mu,\sigma,\lambda) =
\frac{G_0(\mu,\sigma,\lambda)}{A^{\perp}_{\rm B}}
\end{equation}
over the impurity domain size. In using the projected area of the
${\rm B}$ phase we have kept terms consistent with the Monge gauge
calculation (and hence ignored a term of order $h^2$ in the
denominator).

Following \cite{HardMack94}, we will use \emph{hatted} variables for
dimensionless quantities $\hat\lambda, \hat\sigma, \hat\mu$
(introduced below and Appendix~\ref{app:a}) scaled by $\kappa$ and
appropriate powers of $c_0$, and unadorned variables for physical
quantities. This differs from the more recent work of \cite{gozdz01}
in which dimensional quantities were hatted and dimensionless
quantities were not hatted.

For simplicity, we have also assumed that all bending moduli are the
same in the different phases.  Different mean curvature moduli
$\kappa$ will obviously shift the phase boundary in favor of the phase
with a lower curvature modulus, while a difference in Gaussian
curvature moduli would lead to a shape-dependent line tension that
will shift the phase boundaries \cite{JuliLipo96}.
\section{Euler-Lagrange equations and boundary conditions}\label{sec:eqns}
Variation of $G_0(\mu,\sigma,\lambda)$ with respect to $h({\rm\bf r})$
gives the Euler-Lagrange equations for the height profile. To
calculate the free energy we only need the slope $\eta=dh/dx$ (stripe)
or $\eta=dh/dr$ (caplet).  As shown in
Appendix~\ref{app:a}, the slopes in regions $A$ and $B$ ($i={\rm A},{\rm
  B}$) satisfy
\begin{subequations}
\begin{align}
\frac{d^2\eta}{d\xi^2}- {\zeta_i}^2\eta=0&\qquad\hbox{(stripes)}
\label{Eq5}\\
\frac{d^2\eta}{d\rho^2} + \frac{1}{\rho}\frac{d\eta}{d\rho} -
\left( {\zeta_i}^2+\frac{1}{\rho^2}\right)\eta=0 &
\qquad\hbox{(caplets)}
\label{Eq6}
\end{align}
\end{subequations}
where we have introduced dimensionless variables,
\begin{subequations}
\begin{eqnarray}
\xi &=& c_0 x \\
\rho &=& c_0 r\\
{\zeta}_{\rm B}^2 &=& \hat{\sigma}+\hat{\mu} \label{eq:24}\\
{\zeta}_{\rm A}^2 &=& \hat{\sigma} \\
\hat\sigma &=& \frac{\sigma}{\kappa c_0^2} \\
\hat{\mu} &=& \frac{\tilde{\mu}}{\kappa c_0^2} + 1 \\
{\hat{\lambda}} &=& \frac{\lambda}{\kappa c_0}.
\end{eqnarray}
\end{subequations}
Note that the renormalization of $\mu$ due to $\kappa c_0^2$ is
identical in both stripe and caplet phases, and will thus play no role
in determining coexistence, \textit{i.e.}, in Eq.~(\ref{eq:1}).

Symmetry of $\eta$ at the domain centers implies
\begin{equation}
\eta(0) = \eta''(0) = 0.
\label{eq:h2a}
\end{equation}
where primes denote derivatives with respect to either $\rho$ or
$\xi$. Another condition may be supplied by requiring a well-defined
energy.  A discontinuity in $\eta$ would imply singular curvature at
the boundary, leading to a non-physical curvature energy in the region
of the interface $\partial_{S_B}$ between $A$ and $B$ phases.  Hence
we must have
\begin{equation}
\left[\eta_{\rm A}- \eta_{\rm B}\right]_{\partial_{S_B}}=0.
\label{eq:h4a}
\end{equation}
The final boundary conditions follow from the variation of the height
profile, and are derived in Appendix~\ref{app:a}. In the dilute limit,
\begin{align}
\left[{c}_{\rm B} - {c}_{\rm A}\right]_{\partial_{S_B}} &= c_0
&&\textrm{(torque)}
\label{eq:b2}\\
\sigma \eta_{\rm A}(\infty) - \kappa {c}_{\rm A}'(\infty)  &= 0
&&\textrm{(normal force)}
\label{eq:b3}\\
{c}_{\rm A}(\infty) &= 0, \label{eq:b4}
&&\textrm{(torque)}
\end{align}
where $c(r)$ is the curvature:
\begin{equation}
  c = \left\{
    \begin{array}{c@{\qquad}l}
      \eta'&(\hbox{stripes})\\
      \noalign{\vskip6truept}
      {\displaystyle\frac{1}{\rho}\frac{\partial}
        {\partial\rho}\left(\rho\eta\right)}&(\hbox{caplets}).
    \end{array}\right.
\end{equation}
Eqs.~(\ref{eq:b2}) and~(\ref{eq:b4}) are torque balances at the ${\rm
  A}-{\rm B}$ interface \cite{KozlHelf95} and at the system boundary,
and Eqs.~(\ref{eq:b3}) are the consequence of zero vertical force at
the ${\rm A}-{\rm B}$ interface. For the concentrated limit, the last
two equations should be replaced by the equivalent result for periodic
boundary conditions:
\begin{equation}
\left.\eta_{\rm A}\right|_{\partial_{S_B}} =
\left.c'\right|_{\partial_{S_B}}=0\qquad\hbox{(concentrated regime)}.
\end{equation}

\section{Monge Limit: Results}\label{sec:regimes}
The general solutions to the Euler-Lagrange equations are given in
Appendix~\ref{app:b}. Before discussing the phase behavior in the
general (concentrated) case, we discuss the dilute limit for large
frame tensions, where several approximations simplify the results.
\subsection{Dilute Limit ($\hat{\sigma}\gg\hat{\mu}\simeq 0$)}

Since the height profiles decay in the ${\rm A}$ phase with a
characteristic length $\sqrt{\kappa/\sigma}$, the dilute limit is
valid provided that the domains are separated by more than this
length. The general solutions in the Monge gauge,
Eqs. ~(\ref{eq:sol1d}, \ref{eq:sol2d}), have inverse penetration depths
$\zeta_{\rm A}=\sqrt{\hat\sigma}$ and $\zeta_{\rm B}=\sqrt{\hat\sigma+\hat\mu}$. In the
dilute limit and for large frame tension we may ignore $\hat\mu$ relative
to $\hat{\sigma}$ in the penetration depths.
Taking the limits
$R_0\rightarrow\infty$ and $X_0\rightarrow\infty$, the solutions (given in Appendix~\ref{app:b})
reduce to
\begin{equation}
  \frac{\eta (\xi)}{\eta_0}=
    \begin{cases}
      \dfrac{\sinh[\sqrt{\hat{\sigma}}\xi]}{\sinh[\sqrt{\hat{\sigma}}\xi_0]}
      &  (\xi \leq \xi_0) \\[15truept]
      \exp[\sqrt{\hat{\sigma}}(\xi_0-\xi)] & (\xi \geq \xi_0),
    \end{cases}\qquad\hbox{(stripes)}\label{etaofxi}
\end{equation}
and
\begin{equation}
  \frac{\eta (\rho)}{\eta_0}=
    \begin{cases}
      \displaystyle \frac{I_1[\sqrt{\hat{\sigma}}\rho]}
      {I_1[\sqrt{\hat{\sigma}}\rho_0]}
      &  (\rho \leq \rho_0) \\
      \noalign{\vskip8truept}
      \displaystyle \frac{K_1[\sqrt{\hat{\sigma}}\rho]}
      {K_1[\sqrt{\hat{\sigma}}\rho_0]}
      &  (\rho \geq \rho_0),
    \end{cases}\qquad\hbox{(caplets)}\label{etaofrho}
\end{equation}
where
\begin{equation}
  \eta_0=
  \begin{cases}
  \left[\sqrt{\hat\sigma}\left(1+\coth\sqrt{\hat{\sigma}}\xi_0\right)
  \right]^{-1}& \textrm{(stripes)} \\[10truept]
  \rho_0 I_1[\sqrt{\hat{\sigma}}\rho_0]
  K_1[\sqrt{\hat{\sigma}}\rho_0]& \textrm{(caplets)}.
  \end{cases}
\end{equation}

Substituting these profiles into Eq.\ (\ref{Eq1}), the free energy per
impurity of a single domain is (recall that we set $\hat\mu=0$ in the
dilute limit)
\begin{equation}
  \frac{G_0}{{A^{\perp}_{\rm B}}}=
  \begin{cases}
    \displaystyle\frac{1}{\xi_0}\left[\hat{\lambda} -
      \tfrac{1}{2}\eta_0\right]&\textrm{(stripes)}\\[12truept]
    \displaystyle\frac{1}{\rho_0}\left[2\hat{\lambda} -
      \eta_0\right] & \textrm{(caplets)},
  \end{cases}
\end{equation}
where the impurity area ${A^{\perp}_{\rm B}}$ is $2Lx_0$ (stripes) or $\pi r_0^2$ (caplets).  The free energies can be rewritten as
\begin{equation}
  \frac{G_0}{{A^{\perp}_{\rm B}}}=
  \begin{cases}
    \displaystyle
    \frac{\left[\tau- \frac{1}{2}\left(1+\coth\sqrt{\hat\sigma}{\xi}_0\right)^{-2}\right]}
{\sqrt{\hat\sigma}{\xi}_0}
&\textrm{(stripes)}\\ \\%[12truept]
    \displaystyle\frac{\left[2\tau -
      \sqrt{\hat\sigma}\rho_0 I_1\left(\sqrt{\hat\sigma}\rho_0\right) \,
      K_1\left(\sqrt{\hat\sigma}\rho_0\right) \right]}
{\sqrt{\hat\sigma}\rho_0} &  \textrm{(caplets)},
  \end{cases}
\end{equation}
so that the phase diagram in the dilute limit only depends on the
control parameter $\tau\equiv\hat{\sigma}^{1/2}\hat{\lambda}$
\footnote{An analogous stability limit was derived for the model in
  Ref.~ \protect{\cite{Kawa+93}} for stripes in the strong segregation
  limit.}.  Minimizing the free energies over the periods yield the
equilibrium domain sizes, shown in Fig.~\ref{dilutestripesize}. The
caplet phase is stable with respect to stripes for
$\tau\lesssim0.2115$, while stripes are unstable with respect to a flat
phase for $\tau>0.25$.

\begin{figure}[t]
\includegraphics[scale=0.4]{./figures/dilutelengths.eps}
\caption{
  Reduced domain size as a function of $\tau$ in the dilute limit
  ($\phi\rightarrow0, \hat\mu\rightarrow0$). The solid lines denote the
  stable phase. Caplets are stable for $\tau\lesssim0.2115$, and
  stripes are stable for $0.2115\lesssim\tau<0.25$. For $\tau>0.25$
  the stable state is a macroscopically phase separated flat phase.}
\label{dilutestripesize}
\end{figure}

The stripe domain size diverges as the limit $\tau=0.25$ is
approached, as
\begin{equation}
  \label{eq:20}
  \lim_{\tau\rightarrow0.25}\xi\hat{\sigma}^{1/2} =
  \frac12\ln\left(\frac{2}{4\tau-1}\right),
\end{equation}
while the caplet radius grows from zero for small $\tau$ as
\begin{equation}
  \label{eq:23}
  \lim_{\tau\rightarrow 0}\rho\hat{\sigma}^{1/2} =
  \left[\frac{4\tau}{3}\ln\left(\frac{1}{4\tau} \right)\right]^{1/3}.
\end{equation}
Thus, the domain size diverges as either the line tension or the
surface tension becomes large.  The latter case simply corresponds to
the fact that for large surface tensions there will be complete phase
separation in a nearly flat two-dimensional system.  The former case
is somewhat more subtle, although, as we shall see, this limit
corresponds to budding, since the resulting slope $\eta_0$ above
becomes large.
\subsection{Finite Concentration of the ${\rm B}$ Phase}

For finite impurity concentration of the two phases, the the effective
surface tensions of the two phases differ by the chemical potential
(Lagrange multiplier) $\mu$, which cannot strictly speaking be
ignored. In this case the phase diagram does not depend solely on the
dimensionless quantity $\tau=\hat{\lambda}\hat\sigma^{1/2}$. This was
also noted by  G\'o\'zd\'z and Gompper, in the case of systems with two
different spontaneous curvatures \cite{gozdz01}. However, we will see
that the reduction to a phase diagram that depends only on $\tau$ is
an excellent approximation in many cases.

For finite area fraction $\phi$ of the ${\rm B}$ phase, we assume a
regular array of monodisperse (stable) domains, each within cell
dimensions determined by the concentration.  We approximate the
hexagonal Wigner-Seitz cell (see Fig.~\ref{domains}) by a set of
circular domains of equal area \cite{ziman72}.  The solutions are
given by Eqs.~(\ref{eq:sol1d}) (stripes) and~(\ref{eq:sol2d})
(caplets), with corresponding free energies $\hat{g}$ given by
Eqs.~(\ref{eq:fstripe}) and~(\ref{eq:fcap}).  To calculate the phase
diagram we minimize the free energies over both domain dimensions
($x_0$ and $X_0$ for stripes, $r_0$ and $R_0$ for caplets) for a given
set of control parameters (line tension $\hat{\lambda}$, frame tension
$\hat{\sigma}$, chemical potential $\hat{\mu}$), and determine the phase
boundaries by that chemical potential $\hat{\mu}$ for which the free
energies of the caplet and stripe phases are the same.

Our procedure differs slightly from that of Ref.~\cite{HardMack94} in
that, here, the effective overall ``tension'' is different in the two
phases. In the impurity phase $B$ the quantity $\hat{\sigma}+\hat{\mu}$ acts
like a mechanical tension penalizing area changes, while (because we
have chosen a reference chemical potential $\hat{\mu}_A=0$) only
$\hat{\sigma}$ penalizes area changes in the $A$ phase. Hence the inverse penetration
lengths ${\zeta}_A$ and ${\zeta}_B$ differ.  In the strong tension
limit $\hat{\sigma}\gg\hat{\mu}$, which is exact for vanishing $\phi$ where
$\hat{\mu}$ becomes quite small (see Fig.~\ref{fig:mu}), this approach
recovers the results of Ref.~\cite{HardMack94}, while for smaller
$\hat{\sigma}$ the height profile of the impurity phase contains a
contribution from the chemical potential as well as the frame tension.
In the limit $\hat{\sigma}\gg\hat{\mu}$ where the penetration depths are the
same, the phase diagram depends on only the generalized reduced
tension ${\tau}$.

\begin{figure}[t]
\includegraphics[width=3.0truein]{./figures/mu.eps}
\caption{Chemical potential as a function of generalized tension for
  different frame tensions $\hat{\sigma}$. Note the extrapolation to small
  $\hat{\mu}$ with increasing $\tau$.}
\label{fig:mu}
\end{figure}
\begin{figure}[ht]
  \includegraphics[scale=0.43]{./figures/phasediag_all2.eps}
\caption{Phase diagram as a function of
  $B$-phase area fraction $\phi$ and generalized reduced tension
  ${\tau}$, for different constant frame tensions $\hat{\sigma}$
  ($\hat{\lambda}$ was varied to scan $\tau$).  The region between
  upper and lower pairs of lines are two-phase regions of coexisting
  stripes and caplets. The inset shows convergence for large
  $\hat{\sigma}$ near the small $\tau$ phase boundary. An equilibrium
  flat phase is predicted for ${\tau}>0.25$.  Scans for different
  $\hat{\sigma}$ converge to the results of Ref.~\cite{HardMack94},
  which corresponds to the limit $\hat{\sigma}\rightarrow\infty$.}
\label{fig:diag}
\end{figure}

With increasing $\phi$, the domains grow monotonically with
$r_0(\phi)\simeq2\xi_0(\phi)$, which corresponds to nearly equal mean
curvature $c\sim c_0$.  Note that a finite preferred domain size
implies the existence of an equilibrium mesophase.  With increasing
$\phi$ there is a first order transition from circular caplets to
stripes for small $\tau$ (Fig.~\ref{fig:diag}).  For small $\tau$ the
transition depends very weakly on $\tau$ and coexistence occurs over a
range of concentrations near $\phi =0.35$.  This range moves to
smaller concentration with increasing $\tau$, while for $0.2115 <
{\tau} < 0.25 $, however, the stripe phase becomes stable at all
concentrations.

Figs.~\ref{fig:mu}, \ref{fig:diag}, and \ref{fig:slopes} show that for
large $\hat{\sigma}$ the phase diagrams converge to a scaling form
that depends only on $\tau$, recovering the phase diagram calculated
in Ref.~\cite{HardMack94}. For larger $\hat{\sigma}$ the concentration
range of the stable caplet phase widens at small $\tau$, moving to
larger $\phi$.  Recall, Eq.~(\ref{eq:24}), that the characteristic
inverse decay length in the impurity phase is
$\zeta_B=\sqrt{\hat{\sigma} + \hat{\mu}}$, where we find $\hat{\mu}<0$
along the phase boundary.  Hence, for a smaller tension $\hat{\sigma}$
the negative potential decreases the energetic cost of buckling
against tension, which destabilizes the stripe phase.  The deviation
of the phase boundary near $\tau\simeq0.2115$ is due to departures
from the Monge limit.

\begin{figure}[ht]
\includegraphics[width=3.0truein]{./figures/taubw.eps}
\caption{Phase boundaries $\phi_{\rm caplet}$ and $\phi_{\rm stripe}$,
  and stripe and caplet slopes $dh/dx$ for fixed $\tau=0.001$ and varying
  $\hat{\sigma}$.}
\label{fig:slopes}
\end{figure}

The length scales in the concentrated limit are larger than in the
dilute limit, for the same $\tau$, and converge to the dilute limit
result when the caplet phase loses stability at $\tau\simeq0.2115$, as
expected (Figure \ref{fig:sizes}).

\begin{figure}[ht]
\includegraphics[width=3.0truein]{./figures/lengthsall.eps}
\caption{Scaled domain sizes for caplet and stripe phases along the
  phase coexistence line, for both the concentrated and dilute limit
  calculations. For each geometry the two dimensions (stripe
  half-period $\xi_0$ and minority domain half width $\Xi_0$, and caplet
  inner radius $\rho_0$ and Wigner-Seitz radius $\bar{R}$, all scaled by
  $\hat{\sigma}$) are shown. The variation in domain sizes with
  tension $\hat{\sigma}$ can be seen to be very small.}
\label{fig:sizes}
\end{figure}

\section{Numerical solutions in the budding regime}\label{sec:num}
The calculations presented above and in Ref.~\cite{HardMack94} are
based on a small-slope approximation, and are only valid for small
tensions $\sigma$. In order to both test the validity of this
approximation as well as to study the possible transition from the
caplet state above to a budded states, we have performed direct
numerical minimization of the model free energy in Eq.~(\ref{Eq1}),
beyond the small-slope approximation. We present here the equilibrium
shapes and phase diagram for the stripe phase, the (azimuthally
symmetric) caplet phase, and for buds.

We focus on the dilute limit, i.e., for small area fraction $\phi$. It
is expected that phase separation may, under appropriate conditions,
lead to the formation of buds (nearly spherical domains of one phase
connected with a narrow neck to another phase that is flat). It has
previously been shown theoretically that the line tension between two
phases alone may result in budding \cite{Lipo92b,JuliSeif94}. The role
of phase separation in budding and fission has also been studied in
recent experiments \cite{Miao+94}. As described above, our small-slope
approximation used in the previous sections is expected to fail for
large line tension $\lambda$.

In order to address both the validity of the preceding analysis, as
well as to treat possible budding transitions, we describe the
membrane shape by a local tangent angle $\theta$ relative to a
horizontal, flat conformation. For a stripe domain, the shape can be
completely characterized by the tangent angle as a function of only
one contour length coordinate $s$, which is defined along a line
perpendicular to the stripe. For a caplet or bud domain, a single
tangent angle as a function of a single coordinate $s$ can also be
used to completely describe the membrane shape, even in the presence
of overhangs.  This can be done provided that the domain is symmetric
about an axis perpendicular to a horizontal plane. In this case, the
contour length coordinate is defined along a radial direction. A
similar approach was used in \cite{gozdz01}.

\begin{widetext}
  \begin{center}
\begin{figure}[h]
    \includegraphics[width=6.0truein,bb=65 30 740 520]{./figures/freddy2003.eps}
\caption{Data collapse of the free energy per unit area (in units of
  $\kappa c_0^2$), domain size (units of $c_0$) and boundary slope as
  a function of $\tau$ for both stripes and caplets, for various values
  of the line tension $\hat\lambda$.}
\label{scaling}
\end{figure}
  \end{center}
\end{widetext}
If the center of the domain is taken as the origin, then the membrane
shape in three dimensions is given by
\begin{equation}
\left(x(s),y(s),z(s)\right)
=\left(r(s)\cos(\phi),r(s)\sin(\phi),z(s)\right),
\end{equation}
where $r(s)=\int\cos(\theta)\;ds$ is a radial coordinate,
$z(s)=\int\sin(\theta)\;ds$, and $\phi$ is the azimuthal angle.
In this coordinate system, the mean curvature is given by
\begin{equation}
H=\frac{d\theta}{ds}+\frac{\sin\theta}{r}
\end{equation}
for caplet and bud domains. For stripes, only the first term above is
necessary.

The resulting free energy is evaluated numerically for a domain shape
defined by a discrete set of 50 to 200 angles
$\{\theta_i\}_{i=0,\ldots,N}$, which are defined at equally-spaced
points $s_i$ along the contour from the origin to the Wigner-Seitz
boundary described previously. These values, together with an overall
scale factor $\Delta s=s_{i+1}-s_i$ determine the membrane shape.

A discrete approximation to the free energy $f$ per unit area of
domain is minimized to determine equilibrium shape and free energy.
Here, we quote results for an area fraction of 10\%. As shown above
within the small-slope approximation, the phase boundary between
stripes and caplets is very narrow and relatively insensitive to area
fraction in this range. In Fig.\ \ref{scaling}, we show the normalized
stripe domain size ($\xi_0$), boundary slope
($\eta_0$), and free energy $f$ vs $\tau$ for several
different combinations of $\hat\sigma$ and $\hat\lambda$.  The
apparent collapse of the data demonstrates one of the conclusions of
the previous analysis, namely that the results can be well-represented
in terms of a single combination of parameters,
$\tau=\hat\lambda\sqrt{\hat\sigma}$, of surface tension and line
tension. Similar results for caplet domains are shown in Fig.\
\ref{scaling}.  Here, too, the results show the dependence on the
single parameter $\tau$.

These numerical results can also be used to determine the phase
boundary between the caplet and stripe phases. For simplicity, we do this
only in the dilute limit, in which the phase boundary is rather
insensitive to concentration. Specifically, we find the crossing of
the free energies of the caplet and stripe phases ($f_c$ and $f_s$) for
10\% area fraction.  The results are shown in Fig.~\ref{regimes}. We
note the excellent agreement of this phase boundary with that shown in
Fig.~\ref{fig:diag}, at least for $\hat\lambda\alt 0.2$. For larger
$\hat\lambda$ the former approximations fail. One consequence of this
is that the stripe phase vanishes with increasing $\hat\lambda$:
specifically, there is a narrow range of values of the line tension
for which the only stable domains are caplets. This can be seen in Fig.\
\ref{regimes}. The simple physical reason for the enhanced stability
of the caplet phase (compared with the small-slope results above) in this
limit is that the line tension cost is lowered in the caplet geometry for
large slopes, given a fixed domain area: for caplets, the circumference
to area ratio is reduced with increasing slope.

Also shown in Fig.~\ref{regimes} is the transition between caplet and
bud states, as well as a spinodal line beyond which no stable caplet
structures are possible. No spinodal representing the limit of
metastability of buds is found. This is an artifact of the use of a
bending free energy using only leading order terms. Such a spinodal
depends on the details, and especially the radius $a$ of the neck in
the budded state. Without further assumptions, this length shrinks to
of order $\Delta s$. The surface tension required to pull-out such a
bud is of order the two dimensional Laplace ``pressure''
${\sigma}\sim{\lambda/a}$, which diverges for small necks. Thus, this
spinodal cannot be reliably determined, if at all, by our numerical
scheme. Within the approximation that the neck of the budded state
shrinks to a size much smaller than the domain size, we find that buds
are, in fact, metastable throughout the phase diagram. This is
because, for small necks, there is a linear increase in the free
energy due to the line tension when the neck expands, while both
bending and surface tension contributions are quadratic.

The remaining phase boundary shown in
Fig.~\ref{regimes} is that of the transition from
the flat phase (macro phase separation) to the budded state. This
phase boundary is simple to estimate. The free energy per unit
area of the bud is simply $-\tfrac12\kappa c_0^2$, while the bud
accounts for an excess area of $4\pi\left(2/c_0\right)^2$,
assuming an optimal mean curvature of $c_0$. As noted above, the
radius of the neck tends to zero. This results in a phase
boundary given by $\hat\sigma=1/2$ in reduced units. This simple
phase boundary estimate is well borne out by the numerical
minimization, as shown in the figure.
\begin{figure}
\includegraphics[width=2.8truein,angle=0]{./figures/PD04combined.eps}
\caption{The calculated phase diagram, indicating bud, caplet, and stripe
  phases, as well as the flat phase corresponding to macroscopic phase
  separation. This has been obtained by the numerical procedure
  outlined in Sec.\ \ref{sec:num}. The solid lines indicate
  thermodynamic phase boundaries, while the dashed line indicates the
  limit of metastability of caplets. As discussed in the text, we
  expect that buds are metastable throughout the phase diagram, within
  the approximations used here.  The thin region shown is that of the
  stripe phase. This vanishes at a triple point near $(\hat{\sigma},
  \hat\lambda)=(1,0.2)$. The bud, caplet, and flat phases meet at the
  other triple point along $\hat{\sigma}=0.5$.  Upper and right hand
  axes are dimensionless, while lower and left hand axes are in
  physical units for typical values of the bending energy and
  spontaneous curvature, $\kappa=100\,\textrm{pN nm},
  c_0^{-1}=100\,\textrm{nm}$.}
\label{regimes}
\end{figure}

\section{Discussion}\label{sec:yadayada}
The transition from caplets to stripes with increasing $\phi$ and
$\tau$ can be understood in simple physical terms.  On the one hand,
with increasing $\phi$ the unit cells in the stripe and caplet
morphologies are of size $\sim 1/\phi$ and $\sim 1/\sqrt{\phi}$,
respectively.  Thus, with increasing $\phi$, the constraints on the
membrane profiles due to the unit cell boundaries become more costly
in the caplet phase than the stripe phase.  On the other hand, with
increasing tension $\tau$, the regions of largest slope (i.e., largest
difference between projected area and membrane area), which occur near
the domain boundaries, become energetically more costly because of the
work required against tension.  For caplets, this represents a larger
fraction of the domain area than for stripes.  Thus, stripes are
preferred for sufficiently large $\tau$.

From the numerical approach of the previous section, we see, perhaps
surprisingly, that the Monge approximation works rather well to
describe the various phases and transitions. Specifically, we see from
Fig.\ \ref{scaling} that for $\hat\lambda\alt 0.2$ there is little
disagreement between the Monge approximation and the numerical
solutions that can account for finite slopes. This is particularly
true of the caplet phase.

In general, we expect the Monge approximation to be best for large
$\hat\sigma$, which tends to flatten the membrane. Since the phase
boundaries between caplets, stripes, and the flat phase tend to occur for
a fixed $\tau=\hat\sigma^{1/2}\hat\lambda$ (specifically
$\tau\simeq0.21$ and $\tau=0.25$ for the caplet-stripe and stripe-flat
boundaries, respectively, in the dilute limit), we expect the Monge
approximation to be valid near both transitions, except for large
$\lambda$, which is what we find. Here, of course, $\sigma$ tends to be
smaller.

As noted above, however, the discrepancy is smaller for the caplet
phase.  The deviation that we find for stripes suggests an instability
toward larger domains and, ultimately, the flat phase. This tends to
be compensated in the case of caplets by the line tension $\lambda$,
which prevents domains from growing. This enhanced stability of
caplets is also consistent with the observation from the phase diagram
in Fig.~\ref{regimes} that the caplet-stripe phase boundary shifts in
favor of caplets as $\lambda$ increases. We find, in fact, a triple
point, where caplet, stripe and flat phases meet, although this is
hard to see in the figure.  For larger $\lambda$, no stripe phase
is observed.

Away from these transitions, however, we begin to see significant
deviation from the Monge results for the largest $\lambda$ as sigma
decreases. Thus, the Monge approximation tends to fail to the left in
Fig.\ \ref{regimes}. In particular, the Monge approximation is
insufficient to characterize the transition between buds and caplets.

This work shares some common features with several previous
theoretical studies.  Undulating stripe and hexagonal phases were
predicted in the limit of weakly segregated two-component films
\cite{leibler87} based on a phenomenological coupling of local
membrane composition and shape.  These phases are analogous to the
stripe and caplet phases discussed in this letter for well-segregated
mixtures.  The approach of Ref.\ \cite{leibler87} has recently been
utilized to study one-dimensional shape profiles of two-component
membranes and vesicles in the strong segregation regime as well
\cite{AKK92,Kawa+93}.  The stripe phases of planar membranes in the
limit of small domains or large bending energies reported in
Ref.\cite{Kawa+93} are qualitatively similar to our stripe mesophases.
The stable stripe and caplet mesophases reported in this letter should
occur in phase-separated two-component films under tension, provided
that one phase has finite spontaneous curvature and that the line and
surface tensions are sufficiently small.  In particular, one must have
$\tau<1/4$ and $\hat\lambda <\hat\sigma$ to observe these mesophases.
The calculation presented above assumes an asymptotically flat matrix
phase, as in the case of a globally flat monolayer or bilayer
membrane.  However, our results should be qualitatively valid for
two-component bilayer vesicles, provided that the vesicle diameter $D$
is sufficiently large compared with the characteristic domain
dimension, \emph{i.e.}, if $c_0D\gg 1$.

G\'o\'zd\'z and Gompper performed a similar calculation to ours in a
different ``slice'' of parameter space. They considered phases with
\textit{different} signs of spontaneous curvature, and predicted a
variety of different budding, stripe, and circular domains. It is
difficult to compare the results directly, since they chose only one
parameter set, $\hat{\lambda}=0.5, \hat{\sigma}=0.4$. For our model,
with just one spontaneous curvature, this leads to a budded state.
They show that this set of parameters can lead to a variety of phases
that can be stabilized by the different spontaneous curvatures.

We estimate the region of domain stability for the following values of
the parameters in our model:
\begin{align}
  \kappa&= 25 k_BT\simeq 100 \textrm{pN nm},& c_0^{-1}&=100 {\rm
    nm}.\label{eq:numbers}
\end{align}
The results are shown schematically in Fig.~\ref{regimes}.  Thus,
caplet domains of order $100\,\textrm{nm}$ in size (as in Ref.\
\cite{Baek+95}) are stable for line tensions
$\lambda\alt0.3\,\textrm{pN}$ and surface tensions
$\sigma\sim10^{-2}\,\textrm{mN/m}$.  For comparison, membrane rupture
occurs for surface tensions of order $10 \textrm{mN/m}$
\cite{biomembranes}.

Finally, we wish to note a couple of important general observation
relevant to phase separating membrane systems.  First, given the
coupling between membrane composition and shape, it is possible to
have both composition-induced changes in shape or curvature
\cite{leibler86,JuliLipo93,MackSafr93}, as well as curvature-induced
changes in composition \cite{Seif93}. However, unless the curvature is
of a molecular scale (\emph{i.e.}, if curvature radii are comparable
to the size $a$ of a single lipid), it is generally expected that
composition will drive shape, or, in other words, that chemistry
determines geometry. This is because, on a per molecule basis, the
curvature energy $\kappa a^2c_0^2$ is very small compared with $kT$.
Thus, unless one happens to be very close to a critical point
\cite{Seif93}, the shift in chemical potential due to the local
curvature of the membrane is expected to be insufficient to cause a
significant composition change.  Second, the Gaussian curvature and
associated modulus $\bar\kappa$, which we have so far neglected, is
expected to affect the stability of the caplet and budded phases
described above. In fact, this can have an order one effect on both
phases, since the corresponding shift on the curvature energy is of
order $\Delta\bar\kappa c_0^2$ per unit area, where $\Delta\bar\kappa$
represents the difference in moduli between the two phases. This is
comparable to the (mean) curvature energy contribution in both phases.
There will be no effect, however on the stripe phase free energy.
Thus, the main qualitative effect of taking into account the Gaussian
curvature effects will be on the stability of the bud and caplet
phases relative to the stripe phase. For instance, the expected
increase or decrease in the energy of bud and caplet phases may result
in a more pronounced or even absent stripe. Finally, we have imposed
the strong segregation limit, in which the compositions of the two
phases are unaffected by the local bending.  This is likely to break
down near critical points, at which point the compositions will vary
in concert with the degree of bending
\cite{leibler87,safranpinc90,safranpinc91,AKK92,Kawa+93,Tani+94}. In
this case the local line tension can be expected to be lower and
depend on the degree of local membrane deformation. Moreover, elastic
constants and the spontaneous curvature will be inhomogeneous in the
more highly deformed regions. Possible effects of this could be to
stabilize the caplet phase in favor of the stripe phase (since line
tension may be reduced), as well as shifting other phase boundaries.
However, as we have emphasized above, the strong segregation limit is
expected to apply more generally, because of the wide separation of
scales between the molecular and curvature lengths.

\section*{Acknowledgements}
We thank A.~Ajdari, F.~J\"ulicher, D.~Morse, J.~Prost, R.~Ross, and
E.~Sackmann for useful discussions and comments.  FCM acknowledges
support from the NSF (Grant No. DMR-9257544), the Donors of the
Petroleum Research Fund, and the Exxon Education Foundation. PDO and
FCM acknowledge NATO CRG 960678.  All three authors thank the (K)ITP
UCSB and the Isaac Newton Institute for Mathematical Sciences, where
portions of this work were also performed. The authors wish to thank
the ICTPC for a stimulating environment.

redpajama_set_name: RedPajamaArXiv


text:
Home invasion suspect allegedly tells police "Just take me in so I can sleep"
When police interviewed Francis Jerome Taisacan, he said another man was responsible for the Ordot incident, documents state.
Home invasion suspect allegedly tells police "Just take me in so I can sleep" When police interviewed Francis Jerome Taisacan, he said another man was responsible for the Ordot incident, documents state. Check out this story on guampdn.com: https://www.guampdn.com/story/news/2019/05/17/home-invasion-suspect-allegedly-tells-police-just-take-me-so-can-sleep-guam-news-crime/3690538002/
Jasmine Stole Weiss, Pacific Daily News Published 5:36 p.m. ChT May 17, 2019
Call, text or send an online, anonymous tip to Guam Crime Stoppers. Pacific Daily News
A jar that contained coins stolen from an Ordot woman on Tuesday led police to Francis Jerome Taisacan, who was charged with multiple felonies Friday.
According to a magistrate's complaint filed in the Superior Court of Guam, Taisacan at one point in his interview with police told them, "Never mind, you're just getting frustrated. I'll do the time. Just take me in so I can sleep."
More: Woman recounts being robbed at gunpoint at Ordot home
More: Detectives arrest Francis Jerome Taisacan in Ordot home invasion
He refused to write a statement for authorities, documents state.
Deanna Quitugua, 68, was robbed early Tuesday morning at her house. Two men, one armed with a handgun and another armed with a bat, threatened her before taking things from her home, she said.
A purse, her keys, $30 cash, a checkbook, a credit card and a glass jar with about $100 worth of coins were stolen, documents state.
Francis Jerome Taisacan (Photo: Courtesy of Department of Corrections)
Police tracked the vehicle used in the robbery to an unnamed suspect and Taisacan, documents state.
Also found in the car was the jar the woman had used to store coins, the charging documents state.
When officers spoke with Taisacan, he told them he saw police looking for him along Aguero Road and he ran "because that's what he always does," court documents state.
Officers asked what happened in Ordot and Taisacan responded the other suspect had done that. When pressed as to how he knew what the other man did, Taisacan said he was asked to help, documents state.
Officers asked what Taisacan meant and he replied, "The one on the PDN about the old lady," documents state.
'Never mind, you're just getting frustrated'
Taisacan said he was never in the car, then said he always rides in that car, then he said GPD wouldn't find his fingerprints on the jar in the car, documents state. The person interviewing Taisacan hadn't mentioned the car or its location and Taisacan said he learned of the jar from the PDN, court papers state.
But that information wasn't released in the media, the interviewer said. To which Taisacan replied, "Never mind, you're just getting frustrated. I'll do the time. Just take me in so I can sleep," court documents state.
Taisacan was charged with home invasion as a first-degree felony, second-degree robbery as a second-degree felony, burglary as a second-degree felony and theft as a misdemeanor. He also faces special allegations for guilt established by complicity and a special allegation for a crime committed against a vulnerable victim.
Past robbery convictions
Court records show Taisacan was convicted of other robberies from 2011 and 2013.
Pacific Daily News files state Taisacan pleaded guilty to three counts of second-degree robbery in exchange for 10 years in prison, of which he'd only have to serve five.
In 2011 he robbed a Mermaid Tavern employee, with a gun pressed to her head and fled with her purse, files state. He robbed Ebenezer Store of cash, phone cards and cigarettes, estimated to be worth $787, according to news files. And at Club High 57, he took a woman's purse after holding two sisters at gunpoint, files state.
While he was released in that case, so he could go to Southern High School and finish his education, he was charged in a robbery of a woman at M.U. Lujan Elementary School, files state. Court documents state Taisacan approached the woman when she was in her car, sprayed her with pepper spray and ran away with her purse. The woman picked him out of a photo lineup. Three months after he was charged in that case, he pleaded guilty to third-degree robbery and was sentenced to three years in prison, court records show.
Andes Nauta Quenga, 26, accused of molesting 12-year-old girl
Interior: Closer look at EITC as factor in Guam's costs for hosting regional migrants
Read or Share this story: https://www.guampdn.com/story/news/2019/05/17/home-invasion-suspect-allegedly-tells-police-just-take-me-so-can-sleep-guam-news-crime/3690538002/
Drug smuggler attacked, killed while in custody
New rape charges filed in murder of 15-year-old
Man on pretrial release allegedly hit truck with machete
Man charged in case of car reported stolen 7 months ago
Supervisor gets 30 months for meth mailed to office
Man charged in car theft, family violence


I want to play more than 2 player with multitap emulation but with 4 USB gamepads connected when I press a button FPSE only show me only two possible pads to assign. I tried with Crash Team Racing, Crash Bash, micromachines but no success with any.
It´s already enabled, but still showing only 2 gamepads.
I just bought your amazing working emulator running on a brand new RockPi4 (clone of the Raspberry Pi 3 but way more powerful). It seems to work smoothly . I have a wireless receiver for 4 Xbox 360 Controllers which are running very well; but I can't find a way to have the multitap working with my 4 controllers.


text:
#ifndef VIEWBUTTONMOVE_H
#define VIEWBUTTONMOVE_H

#ifdef printMessages
#warning "Inside ViewButtonMove"
#endif

#pragma once
#include "ViewButton.h"

#ifdef printMessages
#warning "    Compiling ViewButtonMove"
#endif

namespace edk{
class ViewButtonMove : public edk::ViewButton{
public:
    ViewButtonMove();
    ~ViewButtonMove();

    virtual void updateView(edk::WindowEvents* events);
    //Function to set button position
    virtual void setPosition(edk::vec2f32 position);
protected:
    //save mouse position
    edk::vec2f32 saveMousePos;
    //save the button position
    edk::vec2f32 savePosition;
    //set holded
    bool holdedMouse;
    //set if save the first position
    bool saveFirst;
private:
    //mouse events
    void eventMousePressed(edk::vec2f32 point,edk::uint32 button);
    void eventMouseMoved(edk::vec2f32 point,edk::uint32 button);
    void eventMouseReleased(edk::vec2f32 point,edk::uint32 button);
};
}//end namespace edk

#endif // VIEWBUTTONMOVE_H

redpajama_set_name: RedPajamaGithub


How time flies! It was a year ago when Rae, Rae's parents, JP, and I travelled to China to start production on Autumn Gem. Earlier last month, we've completed the final cut of the film. Tomorrow afternoon, we'll be showing it to the first time at our cast and crew screening party!
An so begins the next phase — marketing and business development — for Autumn Gem. It's something we're both excited and scared about at the same time. On the one hand, we're happy that we're able to show a finished product that we're proud of. On the other hand, there's the chance that people who see it will not like it! We've already experienced a tiny bit of rejection with some of the film festivals to whom we submitted earlier in the year. I like to focus on the positive, however, and that's the task of showing this film to as many people as possible who are interested in learning about this important heroine from China's history.
We'll have photos and a recap from the event after tomorrow!
Despite my best efforts and hours of render time, the credits never scrolled properly on our MXO-powered 23-inch ADC broadcast monitor or when output to a progressive QuickTime movie. They might start out fine, but every few seconds, the screen would suddenly jerk up a few extra pixels, creating an uncomfortable stutter effect.
At this point, I've about given up, and that's a good thing, because I came up with a simpler solution that looks just as good. Instead of scrolling a 10800-pixel tall Photoshop graphic over seventy-two seconds, we're cross-dissolving eleven credit screens over that same time. This comes out to about 6 seconds per screen, which is more than enough time for our cast and crew to find themselves.
One day, I'll figure out the magical formula to getting silky smooth scrolling credits. I'll leave that task, however, for the next film!
We've completed our ADR recording yesterday at Matt's house. Preston was the final actor to come in and record his lines. Now, Rae and I are off to make the final picture lock on the film while Matt continues his audio mixing magic. Here are some photos from the past three weeks of ADR work with our actors and actresses from Autumn Gem.
Here are some photos from our ADR recording sessions.
Lately, the numbers 0.82, 0.84, 0.88, 1.0, 1.24, 1.3, and 1.4 have been foremost on my mind. These are the gamma correction values that I find myself frequently applying to video clips coming into and out of Apple's Final Cut Pro, Color, Compressor and DVD Studio Pro software. Although I've read numerous articles on the handling of gamma on Mac OS X, I don't find myself anywhere closer to understanding the whole picture.
Exports from Final Cut using QuickTime Conversion and the ProRes 422 codec look great on my Mac in QuickTime Player. The same sequence exported using QuickTime Movie looks washed out in QuickTime Player unless I have the Enable Final Cut Studio Color Compatibility preference enabled. When I export the film using Compressor, I have to enter at least 1.24 in the Gamma Correction filter. This is done so the colors on the DVD, burned using DVD Studio Pro, don't look washed out.
This has got to be a common problem for filmmakers using Apple's professional products. Trial and error seems to be what most people do to get something acceptable across all broadcast medium.
When the final cut of Autumn Gem is complete next month, I'm sure I'm going to revisit this problem again when we transfer the movie to HDCAM and other festival screening formats.


Business Lobby | Bellevue Hotel and Spa , Addis Ababa, Ethiopia. Enjoy the Beautiful View!
Glass walled, ambiently lit up, with the view of the city, the Bellevue business lobby is great choice for business meetings, meet and greet or just having coffee..
At the Business Lobby grants you can access to local news papers to have an insight of the latestdevelopments in Addis Ababa and Ethiopia., Have coffee and snack bites, even a drink You can use the lobby to conduct meetings too.


I already love this beautiful little face so much. The perfect little girl of my best friends Kristy and Jarrod. She has already brought so much joy into so many lives. She loves to have her hands by her head, she WILL marry my boy when she is older, is a total mummies girl, has perfect petite little features and I think she is going to give her parents a run for their money when she gets older.


text:
Olivia Newton-John says she has breast cancer; cancels tour
by: Cody Nickel
Posted: May 30, 2017 / 08:22 PM EDT / Updated: Aug 7, 2019 / 04:42 PM EDT
Olivia Newton John performs during the Viña del Mar International Song Festival at the Quinta Vergara in Viña del Mar, Chile, Thursday, Feb. 23, 2017. Believed to be one of the largest musical events in Latin America, the annual five-day festival was inaugurated in 1960. (AP Photo/Esteban Felix)
NEW YORK (AP) — Olivia Newton-John says she has a breast cancer and is canceling her June tour.
The 68-year-old singer said Tuesday she initially thought she was suffering from back pain, but learned it was "breast cancer that has metastasized to the sacrum."
Newton-John said she will complete "a short course of photon radiation therapy" and hopes to perform later this year. She said she will be treated by the medical team at the Olivia Newton-John Cancer Wellness and Research Centre in Melbourne, Australia.
Says Newton-John: "I decided on my direction of therapies after consultation with my doctors and natural therapists."
Ticket buyers will be refunded for the canceled shows.
A cold start to the weekend but we have the sun to share through Sunday AM
by Karyssa D'Agostino / Jan 21, 2021
COLUMBUS, Ga. (WRBL) - As of Jan. 20th Piedmont Columbus Regional hospital updated their visitation restrictions to no visitors allowed except for a few exceptions. Strict visitation restrictions have been a tough new challenge for patients, their families and even hospital staff.
Piedmont Columbus Regional has implemented the "Meet My Loved One" Project, which began at the University of Alabama at Birmingham, in order to help ease the impact of visitor restrictions caused by the ongoing pandemic.
Auburn man facing federal charges in U.S. Capitol Riot, new details revealed


How Do Taxes Work With Money Borrowed From My 401(k)?
HomeBlog LoansHow Do Taxes Work With Money Borrowed From My 401(k)?
If you have a 401(k) retirement account with your employer, you may be able to withdraw funds from it to use as a personal loan. In fact, nearly 20 percent of people with 401(k) retirement accounts have outstanding loans on them. People use these low-interest loans for a myriad of reasons, from dealing with overwhelming financial emergencies to covering the cost of college. However, while these loans are increasingly popular, some tax implications are associated with them. Here's how taxes work with money borrowed from your 401(k). Before you dive in, however, it's important to remember that we are not tax professionals and that you should consult with one before making any major financial decisions.
How Much Can You Borrow from a 401(k)?
You can have more than one loan from a 401(k) plan, too. However, the combined total of all the loans has to be within accordance of the rules listed above Finally, it's important to note that 401(k) loans aren't an individual right; some plans don't allow loans to be taken out against them. If you're considering a 401(k) loan for something, you should definitely verify that your plan allows loans first. If your 401(k) plan does allow loans, they're generally tax-exempt. However, under some circumstances, you could become liable for taxes on an outstanding 401(k) loan.
If you do decide to take a loan from your 401(k) plan, it's generally considered tax-exempt if you meet certain requirements. The 401(k) must be paid back within a payback period that's no longer than five years, and payments must be structured to occur regularly. At a minimum, you should expect to make loan payments every quarter. Additionally, the loan repayments will go back into your 401(k) account, but they won't be considered contributions. Any outstanding loan balance after the five-year payback period will be considered an early withdrawal, and it'll be taxed accordingly. However, there's an exception to the five-year deadline: a 401(k) loan that's taken out to purchase a primary residence isn't subject to the mandatory five-year repayment timeline.
If you take a loan against your company's 401(k) plan and then your employment status ends abruptly, due to quitting or being fired, that loan could lead to tax implications. In most cases, you'll have 60 days or so to pay back the 401(k) loan in its entirety. In many instances, any remaining balance on the loan that isn't repaid within the designated period will be considered a retirement distribution and subjected to taxes and potentially other fees.
The tax code allows other exemptions to 401(k) loan repayments that help to minimize the tax liabilities of account holders. For example, a 401(k) plan can allow leaves of absence of up to one year for activities such as advanced education or sabbaticals. If it does, then that time isn't included in the calculation of the loan repayment period. Additionally, plans may allow for the suspension of loan payments for account holders who are mobilized for military service in the reserves or national guard. However, while some 401(k) plans can allow these types of exceptions, not all do. Therefore, if you're considering one of these loans, be sure to determine what types of repayment exceptions are in place.
Prior to taking out a 401(k) loan, be sure to consider all your options. While there are tax advantages to these loans, alternatives may allow you to accomplish your financial objectives without impacting your retirement plans. For example, if you intended to use a 401(k) to repay high levels of outstanding debt, take note that the debt settlement services offered at National Debt Relief may be a great fit for your personal situation. In other cases, a debt consolidation loan or home equity line of credit (HELOC) may suffice. Before you decide to borrow against your 401(k) account, talk to a trusted advisor about all your loan options. A good advisor can help you determine the loan plan that'll work best for you.


text:
Reebok's High-Concept Collab Inspires New Footwear Launch
Walmart Copycat Lawsuit
Subscription Commerce Takes Another Hit as Trunk Club Closes Chicago Facility
By Lyndsay McGregor
Lyndsay McGregor
More Stories by Lyndsay
ILRF Files Complaint to Halt Imports of Cotton Goods from Turkmenistan
Most Stores Miss the Mark When Marketing Ethical Fashion
Photo: screenshot of Trunk Club website
Earlier this week beauty products e-tailer Birchbox, known for its subscription service, cut staff for the second time in six months. On Tuesday, Trunk Club announced that 250 jobs would be eliminated by the closure of its distribution center in Goose Island, Chicago, adding to the growing belief that subscription commerce is on the way out.
Acquired by Nordstrom for $350 million in 2014, Trunk Club offers online and in-person concierge services for men and women. Customers can try on items at home or at the company's "clubhouses" and pay for what they want to keep, with no commitment or minimum purchase requirements.
Goose Island will transition to its close by August 2017, impacting about 250 full- and part-time employees. Trunk Club said it will integrate its operations into its parent company's network of fulfillment and distribution centers. Nordstrom said it will work to help employees interested in staying with the company find roles at the Trunk Club Chicago clubhouse or at nearby Nordstrom or Nordstrom Rack locations.
"As Trunk Club has grown significantly over the past several years, we're continuing to find opportunities to support that growth while also giving our customers the best experience possible," Brian Spaly, chief executive officer of Trunk Club, said. "While our space at Goose Island has served us well, we realize we're going to outgrow it soon. We decided this was the right time to integrate Trunk Club orders into the Nordstrom fulfillment network, which will allow us to share more of their inventory and better serve our customers with a wider mix of merchandise."
Is another dot-com bust on the way?
Nordstrom has three fulfillment centers, located in Elizabethtown, Pennsylvania, San Bernardino, California, and Cedar Rapids, Iowa. The Cedar Rapids facility currently fulfills all orders for Trunk Club for Women. Integrating the rest of the Trunk Club business into the Nordstrom network will begin at the end of 2016.
Once Valued at $11B, Bolt Lays Off 10% of Staff in Third Job Cuts
Skechers: Who Needs Hypebeasts When You've Got the High Earners?
"It will take us some time to transition our operations and ensure we're taking care of impacted employees, so we wanted to let our people know as soon as we could," Spaly continued. "We still have a lot of customers to serve here, and we'll be working with each of our employees over the coming months to share more details about our staffing changes and to discuss their individual opportunities."
Nordstrom recently decided to delay any decision to build a fourth distribution center until 2020 in the hopes that market conditions will have improved. The Seattle-based retailer's profits fell from $128 million to $46 million in the most recent quarter.
Trunk Club
Manifest 2023: Automation and Electrification Key to a More Sustainable Future for Logistics


text:
Q: C: Throw error on parameter check or let it hit the fan? I have a simple design(?) question.
I'm writing a simple program, that has a couple of functions that look like these.
float foo (float* m,size_t n){

   float result;
   //do some calculations, for example a sum

   return result / n;
}

I have a couple of questions on this, with no intention of re opening some holy war.
Should I add a sanity check on the n ? If so, how should I let the caller know?
Returning -1 looks weird on floats;
float foo(float *m,size_t n){
     if (n == 0) return -1f

     ...
  }

My other option is an out parameter
float foo(float *m,size_t n, int *error){

        if (n==0){
           *error = 1;
            return 0f;
        }
       ...
}

update
This is kind of a toy program, just trying to practice some stuff. The question excedes that fact. Maybe I should rephrase to "how to handle errors without (OOP) exceptions".
Also considering testing n before doing the call, but don't like it as much.
Any thoughts?
Thanks in advance.

A: I guess your out parameter option is a good one. But I guess it would be better the other way. Use the out parameter to get the result and the return value to denote the status of the call. Like this
int foo(float *m, size_t n, float* result)
{
  if(someFailureCondition)
    return ERROR; // ERROR being an error integer
  // else
  // do some calculation
  // set your result
  return NO_ERROR; // NO_ERROR being an integer
}

Edit:
The return value can be more verbose to denote the current state of the out parameter. See Jamesdlin's comment!

A: If -1 would not be returned by the function anyway, by all means return -1. But if passing n=0 won't break the function, then it isn't really needed. I assume that n is the size of the array m.
Handling errors is a matter of preference. OpenGL handles errors by returning an error code (-1 or otherwise) when a function fails. The error code is returned througha call to GetLastError() (or something like that). This seems like an ideal error handling solution.

A: There are special floating point values you can use if you want - for example, if your floating-point implementation supports quiet NaNs (Not-a-Number) then you can use the NAN macro from math.h:
#include <math.h>
float foo(float *m,size_t n)
{
     if (n == 0) return NAN;

     ...
}

A: You should let callers know what your function's semantics are by clearly documenting your code.
What is the contract to your function?  If callers are required to not pass 0 for n, then that needs to be explained, and the function should use assert to verify that those requirements are met.  Logical errors should be detected early, and those failures should be as spectacular as possible.
Now, if you're writing code for a library that will be consumed by other developers and are concerned that people will compile with assert disabled, then it's reasonable to combine that with a softer failure mode that's always enabled:
if (n == 0)
{
    assert(0);
    return NAN; /* Or return some error code */
}


CARTOON VALENTINE HOTTIE – Cody Shore!
Super buff Sydney based beach Lifeguard, Fitness First Personal Trainer and popular underwear & swimwear model sensationally photographed for DNA magazine by HOT Australian photographers Simon Le and Pedro Virgil … CODY SHORE!
FUN FACTS: A big fan of brands AussieBum & C-in2, Cody started working out at 19! Cody's training tip: Eat to grow!


text:
NCIS season 17: Will anyone else catch on to Bishop, Torres?
NCIS	 July 18, 2019
Mrs. Carter: The future of Bishop and Torres on NCIS season 17 is a little more complicated than it has been in the past now that people are noticing that spark!
Think back to the end of season 16 and the small, but very important line thrown in there by Kasie in relation to how Nick feels about Bishop. It's clear to Kasie that he has feelings for her. As for how much he's willing to express it, well that's a different story. Maybe he isn't even willing to recognize them in himself, but it's something that could manifest itself more now that it's been said out loud by Kasie. Someone like Nick may have been burying how he feels about her, but with Kasie bringing it into the light he may find himself having to deal with it.
Also, it's possible that someone else could start to mention this to Nick and cause him to think about his feelings even more. There are SO many interesting stories that could come from this, especially when you start to think about McGee. Why him? He works alongside Bishop and Torres on a regular basis and we could see him being a great conduit of conversation. If nothing else, he could be someone for Torres to talk about this stuff too if Nick was the sort to open up. Tim's seen people develop feelings for each other on the job before — one of them (Cote de Pablo's Ziva) is back for the premiere!
Want to get some other NCIS video insight? Then take a look at our latest video below. Remember to subscribe to CarterMatt on YouTube so you don't miss out on our weekly NCIS videos throughout season 17 and also visit our NCIS playlist.
If Tim recognizes something in Torres' feelings for Bishop, this is a conversation I'd like to see explored — and the same goes for someone like Jimmy Palmer, who is someone that has a bit of a bond with Torres after their crazy night out that landed them covered in paint and in a holding cell. Jimmy also had a relationship with Ziva where the two had plenty of conversations separate from just the case and maybe he is someone who could see something in Ellie/Nick and if he does, he's definitely someone who would vocalize it.
At this point, it feels like NCIS is moving in a particular direction when it comes to Bishop and Torres as characters. The question becomes just how fast they want to pursue it — beyond that, there's also the question of how they want to pursue it. Kasie referencing it to Nick was a foundation; if a couple more people start to bring it up, then I imagine there could be some more action where Torres is going to have to deal with it. It's not something that will happen right away in season 17, but it could blossom more as the story goes along.
Related News – Check out some more news when it comes to filming kicking off!
What do you want to see coming up on NCIS season 17?
Let me know in the comments below and don't go anymore — more news will be coming out shortly. (Photo: CBS.)
This article was written by Jessica Carter. Be sure to follow her on Twitter.
Love TV? Be sure to like CarterMatt on Facebook for more updates!


text:
About the Solihull MRC
OO A Scottish Branch
OO Cherwell Junction
OO Tidbury Green
Avonbridge O Gauge
Moxley O Gauge
Les & his loft layout
Why do we model?
Why Model in OO Gauge?
Digital Command Control
Loco Building and Detailing by John t
Loco Detailing and Weathering by Robert Reynolds
OO Loco Maintenance by John Ross
OO Loco Maintenance by John t
Modelling Coaches GWR V5
Hints on buying second hand locomotives
Tools required for successful modelling
Transfer and Decal Application
How to build plastic wagon kits
Club Premises
Early Club History
The Stratford & Moreton Railway
Henley and Lapworth Railway
Alcester Railway
Head and Headlamp Codes
Wheel Arrangements
Coach TOPS codes
Wagon TOPS codes
Train Videos
For enquiries email here
HOME | OUR EXHIBITION | RAILWAY LINKS
What would you like to see on this site?
The Bad News - Track Gauge
I describe 'OO' as a gauge rather than a scale for a very good reason. You cannot call it a scale when one of the fundamental components is by definition not to scale. This component is the track. The 'gauge', or distance between the inside edges of the rails, is 16.5mm in 'OO', which equates to 4 feet and 1.5 inches at the nominal 'scale' applied to 'OO' of 1:76 or 4mm:1 foot. The correct British standard gauge for railways since Victorian times is 4 feet 8.5 inches, or about 18.83mm in 'OO'. This is represented by the niche scale known as 'P4' which has this correct gauge and closer to scale wheel standards and track. Another problem with 'OO' is that it is usually 'coarse scale' in that the rails are deeper and wider than they should be to allow for correspondingly deeper than scale flanges on rolling stock wheels that give better running on less than perfect track with very tight curves.
Having said that, 'OO' is a lot finer than it used to be before about the 1970s and some modellers use much finer rails and wheels with closer-to-scale flanges, similar to 'P4' standards, but still with the wrong gauge. Some people say that the difference in gauge is not very noticeable, but if you look at a 'P4' layout, the 2.33mm difference is surprisingly noticeable. A compromise is 'EM' which has an 18.2mm gauge.
The gauge was a kind of accident where someone decided to model rolling stock at 1:76 scale and the closest to scale track available was continental 'HO' (or half 'O'), at 1:87. A useful side-effect of this is that there is more clearance for outside motion on steam locomotives, but at the same time there is less clearance for motors and transmissions between the chassis frames.
The Good News - Size
'OO' is large enough so that modellers do not need to be watchmakers to build rolling stock kits or detail stock, but it is small enough that you can have a layout where you can run full length mainline trains in one room or the loft of a small British house.
More Good News - Availability
'OO' is effectively the standard ready-to-run gauge in Britain, probably largely due to Hornby's many years of production, despite their occasional financial scares, making them a household name synonymous with model railways. Indeed, when I have occasionally worked in Bob's Models in Solihull, some customers describe themselves as owning 'a Hornby' if they have a trainset, even if Hornby was not the manufacturer. Over the years other manufacturers have come and gone, but Bachmann and Hornby are probably the two largest suppliers of British ready-to-run model railway items today and between them and with the addition of smaller suppliers such as Dapol and Heljan, a very wide range of model railway rolling stock dating mainly from about the 1920s to the present day is now available.
This long term production, wide range, the many manufacturers and the fact that the hobby has been from time to time one of the most popular in Britain means that there is a vast amount of second hand rolling stock available at shops, toy fairs and on e-bay in addition to all the new items. Since the 1970s and 1980s, many of the offerings that have been produced are very close to scale and only require some detailing work to make them accurate models. Recently introduced models are supplied so well detailed and sometimes ready-weathered that, if you wanted to, you wouldn't have to change them at all to own an excellent model.
In addition to this large amount of ready-to-run rolling stock there is also a vast range of rolling stock kits from many manufacturers for the more adventurous modeller.
Still More Good News - Interchangeability
Within reason, all the British ready-to-run manufacturers' products produced over the last 30 years will run on the same track using the same controllers and will couple together completely without modification. Having said that, it is always wise to aim to have similar widths and heights of couplings on all vehicles and similar length hooks to minimise derailments. An alternative would be to fit 3-link or screw couplings to all your rolling stock which gives standardisation and removes the need for the ugly tension-lock couplings all current ready-to-run models are supplied with. All available ready-to-run rolling stock has wheels of similar widths with similar sized flanges and runs on a nominal 12 to 18 Volts Direct Current supply.
Kit built products often come with their own wheels and couplings and these will also run on the same track and couple to ready-to-run rolling stock, but they are better fitted with easily-available Jackson metal wheels if these are not supplied, and suitable standardised couplings.
Yet More Good News - Price
Ready-to-run rolling stock has become more expensive in recent years, partly due to the fact that it is often better detailed and runs better than items from just five or ten years ago. Excellent models of large steam locomotives can be bought for under 100 pounds and diesels for under 60. Second hand locos which are still good models can be bought from around 25 pounds. New Items cost about the same as they do in 'N' gauge, despite 'OO' being nearly twice as large in terms of the scale. There are few 'O' gauge ready-to-run items and what is available is usually built from a kit and as such costs hundreds of pounds per locomotive.
This low cost means that you can gradually build up a large collection if you want to without it costing a fortune.
'OO' model railways can be anything you want it to be. You can commission someone to build expensive etched brass rolling stock kits and finescale kit-built track if you want to or you can buy cheap second hand ready-to-run items from a toy fair and run them un-modified. You can mix kits and modified ready-to-run, perhaps with a little scratch-building as I do to produce (hopefully) reasonably accurate models at low cost and run them on the same track as a brand new 70 pound Bachmann or Hornby steam locomotive and all the items you run can be good models and perhaps weathered also. Friends can bring models round to run on your layout with no modifications required.
If you are new to the model railway hobby, there is little question that it would be a wise move to start with an 'N' or 'OO' gauge train set. The same is not currently available in 'O' gauge and if it was, it would be a lot more expensive. The added size of 'OO' models means they are intrinsically more robust than 'N' gauge ones, which is a major issue if small children are in the house.
SMRC Events:Diary
Our Next Exhibition:
2022 SMRC Exhibition
Future Exhibitions:
Outings:
The Great Central Model Railway Event
Dean Forest Railway
- 1960's Mixed Traction Weekend
Chernet Valley Railway, Model Railway and Classic Car Event
The Great Gathering (A4's)
- National Railway Museum, York
Chinner & Risborough Open Day
& Buckinghamshire Railway Centre
1940s Weekend
Didcot Railway Centre
& Pendon Museum
Barrow Hill Roundhouse
& Peak Rail
York Railway Museum
Warley MRC Exhibition
Didcot & Pendon Railway Trip
Llangollen Railway Trip
Five set of to the
Toddington Railway Trip
Didcot Railway Trip
Archive Section:
2019 Exhibition Photos
2013 Alan Bell Exhibition	Photos
2013 David Tidman Exhibition Photos
2012 Alan Bell Exhibition Photos
2012 Mike Pointer Exhibition Photos
2002 SMRC Exhibtion
1973-1998 SMRC Exhibitions
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© Solihull Model Railway Circle 2000-2022. Whilst every care has been taken in the preparation of this website the publisher, Solihull Model Railway Circle, cannot be held responsible for the accuracy of the information contained in the website, nor for any consequence arising from such information. The articles included and the views expressed on this website are those of the writers and do not necessarily reflect the views of Solihull Model Railway Circle or its members or advisors. This website is intended to be a resource, but initially it is for promoting the Solihull Model Railway Circle.


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