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package signalr
// Copyright (c) Microsoft and contributors. All rights reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
//
// See the License for the specific language governing permissions and
// limitations under the License.
//
// Code generated by Microsoft (R) AutoRest Code Generator.
// Changes may cause incorrect behavior and will be lost if the code is regenerated.
import (
"context"
"github.com/Azure/go-autorest/autorest"
"github.com/Azure/go-autorest/autorest/azure"
"github.com/Azure/go-autorest/tracing"
"net/http"
)
// OperationsClient is the REST API for Azure SignalR Service
type OperationsClient struct {
BaseClient
}
// NewOperationsClient creates an instance of the OperationsClient client.
func NewOperationsClient(subscriptionID string) OperationsClient {
return NewOperationsClientWithBaseURI(DefaultBaseURI, subscriptionID)
}
// NewOperationsClientWithBaseURI creates an instance of the OperationsClient client using a custom endpoint. Use this
// when interacting with an Azure cloud that uses a non-standard base URI (sovereign clouds, Azure stack).
func NewOperationsClientWithBaseURI(baseURI string, subscriptionID string) OperationsClient {
return OperationsClient{NewWithBaseURI(baseURI, subscriptionID)}
}
// List lists all of the available REST API operations of the Microsoft.SignalRService provider.
func (client OperationsClient) List(ctx context.Context) (result OperationListPage, err error) {
if tracing.IsEnabled() {
ctx = tracing.StartSpan(ctx, fqdn+"/OperationsClient.List")
defer func() {
sc := -1
if result.ol.Response.Response != nil {
sc = result.ol.Response.Response.StatusCode
}
tracing.EndSpan(ctx, sc, err)
}()
}
result.fn = client.listNextResults
req, err := client.ListPreparer(ctx)
if err != nil {
err = autorest.NewErrorWithError(err, "signalr.OperationsClient", "List", nil, "Failure preparing request")
return
}
resp, err := client.ListSender(req)
if err != nil {
result.ol.Response = autorest.Response{Response: resp}
err = autorest.NewErrorWithError(err, "signalr.OperationsClient", "List", resp, "Failure sending request")
return
}
result.ol, err = client.ListResponder(resp)
if err != nil {
err = autorest.NewErrorWithError(err, "signalr.OperationsClient", "List", resp, "Failure responding to request")
}
if result.ol.hasNextLink() && result.ol.IsEmpty() {
err = result.NextWithContext(ctx)
}
return
}
// ListPreparer prepares the List request.
func (client OperationsClient) ListPreparer(ctx context.Context) (*http.Request, error) {
const APIVersion = "2018-03-01-preview"
queryParameters := map[string]interface{}{
"api-version": APIVersion,
}
preparer := autorest.CreatePreparer(
autorest.AsGet(),
autorest.WithBaseURL(client.BaseURI),
autorest.WithPath("/providers/Microsoft.SignalRService/operations"),
autorest.WithQueryParameters(queryParameters))
return preparer.Prepare((&http.Request{}).WithContext(ctx))
}
// ListSender sends the List request. The method will close the
// http.Response Body if it receives an error.
func (client OperationsClient) ListSender(req *http.Request) (*http.Response, error) {
return client.Send(req, autorest.DoRetryForStatusCodes(client.RetryAttempts, client.RetryDuration, autorest.StatusCodesForRetry...))
}
// ListResponder handles the response to the List request. The method always
// closes the http.Response Body.
func (client OperationsClient) ListResponder(resp *http.Response) (result OperationList, err error) {
err = autorest.Respond(
resp,
azure.WithErrorUnlessStatusCode(http.StatusOK),
autorest.ByUnmarshallingJSON(&result),
autorest.ByClosing())
result.Response = autorest.Response{Response: resp}
return
}
// listNextResults retrieves the next set of results, if any.
func (client OperationsClient) listNextResults(ctx context.Context, lastResults OperationList) (result OperationList, err error) {
req, err := lastResults.operationListPreparer(ctx)
if err != nil {
return result, autorest.NewErrorWithError(err, "signalr.OperationsClient", "listNextResults", nil, "Failure preparing next results request")
}
if req == nil {
return
}
resp, err := client.ListSender(req)
if err != nil {
result.Response = autorest.Response{Response: resp}
return result, autorest.NewErrorWithError(err, "signalr.OperationsClient", "listNextResults", resp, "Failure sending next results request")
}
result, err = client.ListResponder(resp)
if err != nil {
err = autorest.NewErrorWithError(err, "signalr.OperationsClient", "listNextResults", resp, "Failure responding to next results request")
}
return
}
// ListComplete enumerates all values, automatically crossing page boundaries as required.
func (client OperationsClient) ListComplete(ctx context.Context) (result OperationListIterator, err error) {
if tracing.IsEnabled() {
ctx = tracing.StartSpan(ctx, fqdn+"/OperationsClient.List")
defer func() {
sc := -1
if result.Response().Response.Response != nil {
sc = result.page.Response().Response.Response.StatusCode
}
tracing.EndSpan(ctx, sc, err)
}()
}
result.page, err = client.List(ctx)
return
}
|
{
"pile_set_name": "Github"
}
|
Minimal Left Bias
This article has minimal left bias with a bias score of -33.3 from our political bias detecting A.I.
Despite the fact that Wednesday was to be a bipartisan day at the White House to craft a major infrastructure initiative, Donald Trump reportedly exploded in rage and ended the get-together early with no real results.
“To watch what happened in the White House would make your jaw drop,” the Senate’s top Democrat, Sen Chuck Schumer of New York, told reporters afterward.
Trump had his own 10-minute talk with reporters in the White House Rose Garden.
“Instead of walking in happily to a meeting, I walk in to look at people who said I was doing a coverup,” Trump said, adding that he can’t work on infrastructure “under these circumstances.”
Despite this mention of a “cover up,” Pelosi actually tamped down impeachment talk for what was to be the second in a series of meetings in which congressional Democrats and Trump were to hammer out a legislative $2 trillion deal to rebuild and renovate the nation’s aging infrastructure.
Work on a plan for improved highways, roads, bridges, rail systems, electrical grids and more seemed the rare occasion where the two sides could have come together for a joint legislative win.
“For some reason, maybe it was lack of confidence on his part . . . he just took a pass, and it just makes me wonder why he did,” Pelosi said. “In any event, I pray for the president of the United States, and I pray for the United States of America.”
People familiar with the abortive Wednesday meeting said Trump entered the meeting angrily, declining to shake hands.
This has not been a good news week for Trump as a federal judge struck down Trump’s lawsuit which means financial information which he has long almost seemed desperate to shield may well begin getting turned over next week to House Democrats.
|
{
"pile_set_name": "OpenWebText2"
}
|
india
Updated: Feb 25, 2019 15:21 IST
A 22-year-old student leader of Uday Pratap College here was shot dead by unidentified assailants in front of his hostel in the campus on Sunday night, police said.
Vivek Singh, a B.Com second year student and native of Jamundeeh village in Azamgarh district, was found lying in a pool of blood by a passer-by who informed other students as well as the police, said SSP Anand Kulkarni.
He was shot eight times with a .32 bore pistol, Kulkarni said.
The student was rushed to a nearby government hospital where he was declared dead. Seven teams of police, including crime branch sleuths, have been formed to trace those involved in the murder.
District Magistrate Surendra Singh also rushed to the spot immediately after the incident and tried to pacify angry students of the college. Police force has been deployed in and around the campus to thwart any untoward incident.
|
{
"pile_set_name": "OpenWebText2"
}
|
Q:
c++ type could not be resolved
I am working on a c++ program in Eclipse CDT. I am using the gcc compiler on Ubuntu 13. The program has two classes, Function, and Trial. In one line of the Trial class, I am trying to allocate an array of Functions using new. However, Eclipse is telling me that "type 'function' could not be resolved". What's weird, is that in the same method, creating an instance of Function with new does work. I've included all of the files in case they will be useful, though probably just the Trial.cpp will. The error is marked in the Trial::run method
Trial.cpp
#include "Trial.h"
#include "Function.h"
#include <string>
using namespace std;
Trial::Trial(long double* xs, long double* ys, int length, int popSize, double mutRate, int seed){
this->xs=xs;
this->ys=ys;
this->length=length;
this->popSize=popSize;
this->mutRate=mutRate;
this->seed=seed;
}
void Trial::run()
{
Function* newArray =
new Function[popSize]; //error here
Function* f=new Function('x',0,0); //no error here
}
Trial::~Trial() {
// TODO Auto-generated destructor stub
}
Trial.h
#ifndef TRIAL_H_
#define TRIAL_H_
#include "Function.h"
class Trial {
public:
Trial(long double* xs, long double* ys, int length, int popSize, double mutRate, int seed);
void run();
virtual ~Trial();
private:
long double* xs;
long double* ys;
int length;
int popSize;
double mutRate;
int seed;
};
#endif /* TRIAL_H_ */
Function.h
#include <string>
#include <sstream>
using namespace std;
#ifndef FUNCTION_H_
#define FUNCTION_H_
class Function {
public:
Function(char op, Function* l, Function* r);
long double getValue(long double x);
virtual ~Function();
virtual string toString();
static Function* makeFunction(int maxDepth);
Function* clone();
Function* breed(Function* other);
void setNode(int i, Function* node);
static double mutateChance;
long double getFitness(long double* xs,long double* ys, int length);
private:
Function* left;
Function* right;
char op;
long double fitness;
int getNumNodes();
Function* getNode(int i);
void mutate();
};
#endif /* FUNCTION_H_ */
Function.cpp //This is a long one, and probably not important
#include "Function.h"
#include <sstream>
#include <iostream>
#include <cmath>
#include <cstdlib>
#define NUMBER_WEIGHT 1
#define OP_WEIGHT 5
#define X_WEIGHT 5
#define NUM_SWAPS 3
#define TOTAL 39
//Total is 5*OP_WEIGHT+X_WEIGHT+9*NUM_WEIGHT
using namespace std;
double Function::mutateChance=.01;
bool isOp(char c)
{
return c=='+'||c=='-'||c=='*'||c=='/'||c=='^';
}
Function::Function(char op, Function* l, Function* r) {
this->left=l;
this->right=r;
this->op=op;
}
Function::~Function() {
// TODO Auto-generated destructor stub
delete left;
delete right;
}
string Function::toString()
{
stringstream stream;
if(isOp(op))
{
stream<<'('<<left->toString()<<op<<right->toString()<<')';
}
else
{
stream<<op;
}
return stream.str();
}
long double Function::getValue(long double x)
{
switch(op)
{
/*case '0'://Zeroes are stupid. adding/subtracting does nothing. Dividing makes an error or zero. Multiplying makes 0. exponentiation makes 1, 0 or an error.
return 0;*/
case '1':
return 1;
case '2':
return 2;
case '3':
return 3;
case '4':
return 4;
case '5':
return 5;
case '6':
return 6;
case '7':
return 7;
case '8':
return 8;
case '9':
return 9;
case 'x':
return x;
case '+':
return left->getValue(x)+right->getValue(x);
case '-':
return left->getValue(x)-right->getValue(x);
case '*':
return left->getValue(x)*right->getValue(x);
case '/':
return left->getValue(x)/right->getValue(x);
case '^':
return pow(left->getValue(x),right->getValue(x));
}
return 0.0;
}
char toOp(int i)
{
char c=(char)i;
bool found=false;
for(int i=1;i<=9;i++)
if(c<i*NUMBER_WEIGHT)
{
c=i+48;
found=true;
break;
}
if(!found)
{
c-=9*NUMBER_WEIGHT;
if(c<X_WEIGHT)
{
c='x';
found=true;
}
}
if(!found)
{
c-=X_WEIGHT;
for(int i=1;i<=5;i++)
if(c<i*OP_WEIGHT)
{
switch(i)
{
case 1:
c='+';
break;
case 2:
c='-';
break;
case 3:
c='*';
break;
case 4:
c='/';
break;
case 5:
c='^';
break;
}
break;
}
}
return c;
}
Function* Function::makeFunction(int maxDepth)
{
char c;//first are numbers, then x, then the operators, +-*/^
if(maxDepth==0)
c=rand()%(10*NUMBER_WEIGHT);
else
c=rand()%(10*NUMBER_WEIGHT+5*OP_WEIGHT);
c=toOp(c);
if(isOp(c))
return new Function(c,makeFunction(maxDepth-1),makeFunction(maxDepth-1));
else
return new Function(c,0,0);
}
Function* Function::clone()
{
if(isOp(op))
return new Function(op,left->clone(),right->clone());
else
return new Function(op,0,0);
}
Function* Function::getNode(int i)
{
if(i==0)
return this;
int l=left->getNumNodes();
if(i<=l)
return left->getNode(i-1);
else
return right->getNode(i-l-i);
}
void Function::setNode(int i, Function* node)
{
node=node->clone();
int l=left->getNumNodes();
if(i==1)
right=node;
else if(i==l+1)
left=node;
else if(i<=l)
left->setNode(i-1,node);
else
right->setNode(i-l-1,node);
}
int Function::getNumNodes()
{
if(isOp(op))
return 1+left->getNumNodes()+right->getNumNodes();
else
return 1;
}
double randDouble()
{
return 1.*rand()/RAND_MAX;
}
void Function::mutate()
{
if(isOp(op))
do
op=toOp(rand()%TOTAL);
while(!isOp(op));
else
do
op=toOp(rand()%TOTAL);
while(isOp(op));
}
Function* Function::breed(Function* other)
{
Function* child;//The mom is copied, then functions form the dad are switched in
Function* dad;
if(rand()%2)
{
child=this->clone();
dad=other;
}
else
{
child=other->clone();
dad=this;
}
int num=dad->getNumNodes();
for(int i=0;i<NUM_SWAPS;i++)
child->setNode(1+rand()%(child->getNumNodes()-1),dad->getNode(rand()%num));
num=child->getNumNodes();
for(int i=0;i<num;i++)
if(randDouble()<mutateChance)
child->getNode(i)->mutate();
return child;
}
long double Function::getFitness(long double* xs, long double* ys, int length)
{
long double total=0;
for(int i=0;i<length;i++)
total+=abs(ys[i]-this->getValue(xs[i]));
total/=length;
this->fitness=total;
return total;
}
A:
The new[] operator requires a public default constructor. Class Function doesn't provide one (since Function has a user-defined constructor, the compiler doesn't autogenerate a default constructor). Change that and it shall work.
Btw, you don't need to #include "Function.h" in Trial.h: it's not needed.
|
{
"pile_set_name": "StackExchange"
}
|
Q:
Yarden's River Name
The Torah refers (e.g. Numbers 33) to a river called ירדן. Why is it called ירדן?
A:
Name origin: Hebrew: ירדן (yardén, descender) < ירד (yarad, to descend)
via:
Klein, Ernest, A Comprehensive Etymological Dictionary of the Hebrew Language for Readers of English, The University of Haifa, Carta, Jerusalem, p.264
While שיורד מדן ("which descends from Dan") is a rather neat derivation and mnemonic, the Dan part would seem to be unnecessary, since the nun ending seems morphological; also, we would be reusing the daled. Also, we would need to grapple with Biblical references to "haYarden hazeh" (said to Yaakov), where it was surely not called Dan at that point, to spark the derivation. In sum, a nice derash, but I would favor Klein's related etymology.
A:
The book Mincha Belulah says, from the Gemara in Bechoros, that it's because יורד מדן, i.e. it flows down from the North part of Israel, that belongs to Dan.
|
{
"pile_set_name": "StackExchange"
}
|
#!/bin/sh
set -e
#
# This script is not called by the CI system! It is supposed to be used for
# package creation debugging and as a blue print for CI configuration.
#
usage() {
echo "Sample script that builds the cvmfs-config-default debian package from source"
echo "Usage: $0 <work dir> <source tree root>"
exit 1
}
if [ $# -ne 2 ]; then
usage
fi
workdir=$1
srctree=$(readlink --canonicalize $2)
if [ "$(ls -A $workdir 2>/dev/null)" != "" ]; then
echo "$workdir must be empty"
exit 2
fi
echo -n "creating workspace in $workdir... "
mkdir ${workdir}/tmp ${workdir}/src ${workdir}/result
echo "done"
echo -n "copying source tree to $workdir/tmp... "
cp -R $srctree/* ${workdir}/tmp
echo "done"
echo -n "initializing build environment... "
mkdir ${workdir}/src/cvmfs
cp -R $srctree/* ${workdir}/src/cvmfs
mkdir ${workdir}/src/cvmfs/debian
cp -R ${workdir}/tmp/packaging/debian/config-default/* ${workdir}/src/cvmfs/debian
cp ${workdir}/tmp/packaging/debian/config-default/Makefile ${workdir}/src/cvmfs
echo "done"
echo -n "figuring out version number from rpm packaging... "
upstream_version="$(cat ${srctree}/packaging/rpm/cvmfs-config-default.spec | grep '^Version:' | awk '{print $2}')-0"
echo "done"
echo "building..."
cd ${workdir}/src/cvmfs
dch -v $upstream_version -M "bumped upstream version number"
cd debian
pdebuild --buildresult ${workdir}/result
|
{
"pile_set_name": "Github"
}
|
Doomsday Book (film)
Doomsday Book (; lit. "Report on the Destruction of Mankind") is a 2012 South Korean science-fiction anthology film directed by Kim Jee-woon and Yim Pil-sung. It tells three unique stories of human self-destruction in the modern high-tech era, while displaying an alternative form of genuine humanity and compassion. A Brave New World is a political satire about a viral zombie outbreak; The Heavenly Creature philosophizes on whether a robot can achieve enlightenment; and in Happy Birthday a dysfunctional family bonds in the midst of an apocalypse.
It won the top prize at the 2012 Fantasia Festival. The jury honored it with the Cheval Noir Award for best film for "its intelligence and originality."
Production
Doomsday Book was originally conceived as a three-part anthology film to be directed by Kim Jee-woon, Yim Pil-sung, and Han Jae-rim. Filming began on May 21, 2006, but shortly after Kim and Yim had shot their segments, financing fell apart and the film was put on hold. Han's third segment titled "The Christmas Gift" (a SF musical retelling of O. Henry's short story, about a woman's primal desires emerging when confronted with her last chance to survive after witnessing the end of the world) was never shot, and the two thirds remained unreleased.
But in 2010 with backing from new investor TimeStory, shooting restarted quietly with Yim and Kim collaborating on a new third installment to the trilogy with Yim as the lead director and Kim in more of a "guest director" role.
It was pre-sold to six countries at the Berlin Film Market and screened at the Cannes Film Festival.
Synopsis
A Brave New World
()
Left alone after his parents go abroad on a holiday with his sister, geeky research scientist Yoon Seok-woo (Ryoo Seung-bum) disposes of the accumulated rubbish in the family flat, which includes a rotten apple. Through the waste disposal system, the apple enters the food chain in the form of recycled feed for cows. Seok-woo and his date, Kim Yoo-min (Go Joon-hee), end up eating the toxic beef during a barbecue one evening, and soon they and the rest of the population become flesh-eating zombies.
Directed by Yim Pil-sung. Written by Yim Pil-sung, Lee Hwan-hee. Also starring Kim Roi-ha (as Seok-woo's father), Lee Kan-hee (as Seok-woo's mother), Hwang Hyo-eun (as Seok-woo's sister), Ma Dong-seok (as a disorderly student), Jung Woo (as Joong-dong), Choi Deok-moon (as cook), Kim Mu-yeol (as Ji-ho), Bong Joon-ho (as Lee Joon-ho), Park Ho-young (as Park Ho-young), and Yoon Je-moon (as Joo Je-moon).
The Heavenly Creature
()
Park Do-won (Kim Kang-woo), a young technician employed by robotics corporation UR International, is called out to check an RU-4 robot named In-myung (voiced by Park Hae-il) employed at a Buddhist monastery. In-myung has become Buddhist and claims to have achieved enlightenment; the monks want to know whether he really is one or is just a robot with a technical glitch. Do-won gives In-myung a clean bill of technical health but says he is unqualified to do any more. Later, UR chairman Kang (Song Young-chang), and his team led by research executive Min (Kim Seo-hyung), arrive at the monastery to decommission In-myung, on the grounds that he is an old series. Do-won and Bodhisattva Hye-joo (Kim Gyu-ri) then try to save the robot from its imminent demise.
Written and directed by Kim Jee-woon. Original story by Park Seong-hwan. Also starring Jo Yoon-hee (as Ji-eun), Lee Bong-gyu (as Monk Joo-ji), and Jung Jae-jin (as Spiritual Leader).
Happy Birthday
()
Young Park Min-seo (Jin Ji-hee) secretly orders a replacement 8 Ball from a strange website so her pool-obsessed father (Lee Seung-joon) and nerdy uncle Hwan (Song Sae-byeok) won't notice she's damaged it. She throws the original ball out of the window and it drops down a hole in the street. Two years later, South Korea is threatened by an asteroid that looks exactly like a giant version of the 8 Ball. In their underground shelter, the family tries to cancel the order via the extraterrestrial website. Ten years later, the adult Min-seo (Bae Doona) and her family emerge from their shelter.
Directed by Yim Pil-sung. Written by Yim Pil-sung, Jang Jong-ah. Original story by Park Su-min. Also starring Yoon Se-ah (as Min-seo's mother), Ryu Seung-soo (as male newscaster), Lee Young-eun (as female newscaster Lee Eun-kyung), John Kim (as former NASA researcher), Kevin Lee (as Ministry of Science and Technology resource person), Oh Jae-min (as male home shopping channel host), Kim Ok-jin (as female home shopping channel host), Jung Chul (as home shopping model 1), Jo Seung-min (as home shopping model 2), Nam Yoon-young (as home shopping model 3), Go Joon-hee (as weather girl), Lee Kyung-ho (as signs scholar), and Lee Sang-joon (as Galaxy courier).
Awards and nominations
2012 Fantasia Festival
Cheval Noir Award
2013 Asian Film Awards
Nomination - Best Visual Effects - Kwak Tae-yong, Hwang Hyo-kyun, Im Jung-hoon
References
External links
Category:2012 films
Category:2010s science fiction films
Category:South Korean science fiction films
Category:South Korean zombie films
Category:Android (robot) films
Category:Impact event films
Category:Films about Buddhism
Category:South Korean anthology films
Category:Films set in the future
Category:Films set in Seoul
Category:Films directed by Yim Pil-sung
Category:Films directed by Kim Jee-woon
Category:Korean-language films
Category:Lotte Entertainment films
|
{
"pile_set_name": "Wikipedia (en)"
}
|
---
abstract: 'We prove a maximum principle for local solutions of quasilinear stochastic PDEs with obstacle (in short OSPDE). The proofs are based on a version of Itô’s formula and estimates for the positive part of a local solution which is non-positive on the lateral boundary.'
address:
- 'Université d’Evry-Val-d’Essonne-FRANCE\'
- ' LUNAM Université, Université du Maine - FRANCE\'
- 'Université d’Evry-Val-d’Essonne -FRANCE\'
author:
-
-
-
title: Maximum Principle for Quasilinear Stochastic PDEs with Obstacle
---
Introduction
============
In this paper, we consider an obstacle problem for the following parabolic Stochastic PDE (SPDE in short) $$\label{SPDEO}\left\{ \begin{split}&du_t(x)=\partial_i \left(a_{i,j}(x)\partial_ju_t(x)+g_i(t,x,u_t(x),\nabla
u_t(x))\right)dt+f(t,x,u_t(x),\nabla u_t(x))dt \\&\quad \quad\ \ \
\ \ \ +\sum_{j=1}^{+\infty}h_j(t,x,u_t(x),\nabla
u_t(x))dB^j_t +\nu (t,dx), \\
&u_t\geq S_t \, , \ \ \\ &u_0=\xi\, .\
\end{split}\right.$$ Here, $S$ is the given obstacle, $a$ is a matrix defining a symmetric operator on an open bounded domain ${\ensuremath{\mathcal O}}$, $f,g,h$ are random coefficients.\
In a recent work [@DMZ12] we have proved existence and uniqueness of the solution of equation (\[SPDEO\]) under standard Lipschitz hypotheses and $L^2$-type integrability conditions on the coefficients. Let us recall that the solution is a couple $(u,\nu )$, where $u$ is a process with values in the first order Sobolev space and $\nu$ is a random regular measure forcing $u$ to stay above $S$ and satisfying a minimal Skohorod condition.\
In order to give a rigorous meaning to the notion of solution, inspired by the works of M. Pierre in the deterministic case (see [@Pierre; @PIERRE]), we introduce the notion of parabolic capacity. The key point is that in [@DMZ12], we construct a solution which admits a quasi continuous version hence defined outside a polar set and that regular measures which in general are not absolutely continuous w.r.t. the Lebesgue measure, do not charge polar sets.\
There is a huge literature on parabolic SPDE’s without obstacle. The study of the $L^p-$norms w.r.t. the randomness of the space-time uniform norm on the trajectories of a stochastic PDE was started by N. V. Krylov in [@Krylov], for a more complete overview of existing works on this subject see [@DMS09; @DM11] and the references therein. Concerning the obstacle problem, there are two approaches, a probabilistic one (see [@MatoussiStoica; @Klimsiak]) based on the Feynmann-Kac’s formula via the backward doubly stochastic differential equations and the analytical one (see [@DonatiPardoux; @NualartPardoux; @XuZhang]) based on the Green function.\
To our knowledge, up to now there is no maximum principle result for quasilinear SPDE with obstacle and even very few results in the deterministic case. The aim of this paper is to obtain, under suitable integrability conditions on the coefficients, $L^p$-estimates for the uniform norm (in time and space) of the solution, a maximum principle for local solutions of equation and comparison theorems similar to those obtained in the without obstacle case in [@DMS05; @DMS09]. This yields for example the following result:
Let $(M_t)_{t\geq 0}$ be an Itô process satisfying some integrability conditions, $p\geq 2$ and $u$ be a local weak solution of the obstacle problem (\[SPDEO\]). Assume that $\partial{\ensuremath{\mathcal O}}$ is Lipschitz and $u\leq M$ on $\partial{\ensuremath{\mathcal O}}$, then for all $t\in [0,T]$: $$E\left\| \left( u-M\right)
^{+}\right\| _{\infty ,\infty ;t}^p\le k\left( p,t\right)
\mathcal{C}(S, f, g, h, M)$$ where $\mathcal{C}(S, f, g, h, M)$ depends only on the barrier $S$, the initial condition $\xi$, coefficients $f,g,h$, the boundary condition $ M$ and $k$ is a function which only depends on $p$ and $t$, $\Vert \cdot \Vert
_{\infty ,\infty ;t}$ is the uniform norm on $[0,t]\times {\cal
O}$.
Let us remark that in order to get such a result, we define the notion of [ local solutions]{} to the obstacle problem and so introduce what we call [*local regular measures*]{}.\
The paper is organized as follows: in section 2 we introduce notations and hypotheses. In section 3, we establish the $L^p-$estimate for uniform norm of the solution with null Dirichlet boundary condition. Section 4 is devoted to the main result: the maximum principle for local solutions whose proof is based on an Itô formula satisfied by the positive part of any local solution with lateral boundary condition, $M$. The last section is an Appendix in which we give the proofs of several lemmas.
Preliminaries
=============
$L^{p,q}-$space
---------------
Let $\mathcal{O}\subset {{\ensuremath{\mathbb R}} }^d$ be an open bounded domain and $L^2(\mathcal{O})$ the set of square integrable functions with respect to the Lebesgue measure on $\mathcal{O}$, it is an Hilbert space equipped with the usual scalar product and norm as follows $$(u,v)=\int_\mathcal{O}u(x)v(x)dx,\qquad\parallel u\parallel=(\int_\mathcal{O}u^2(x)dx)^{1/2}.$$ In general, we shall extend the notation $$(u,v)=\int_\mathcal{O}u(x)v(x)dx,$$ where $u,\ v$ are measurable functions defined on ${\ensuremath{\mathcal O}}$ such that $uv\in L^1({\ensuremath{\mathcal O}})$.\
The first order Sobolev space of functions vanishing at the boundary will be denoted by $H_0^1({\ensuremath{\mathcal O}})$, its natural scalar product and norm are $$\left( u,v\right) _{H_0^1\left( {\cal O}\right) }=\left( u,v\right) +\int_{{\cal O}}\sum_{i=1}^d\left( \partial _iu\left( x\right) \right)
\left(
\partial _iv\left( x\right) \right) dx,\;\left\| u\right\| _{H_0^1\left(
{\cal O}\right) }=\left( \left\| u\right\| _2^2+\left\| \nabla
u\right\| _2^2\right) ^{\frac 12}.$$As usual we shall denote $H^{-1}({\ensuremath{\mathcal O}})$ its dual space.\
We shall denote by $ H_{loc}^1
({\ensuremath{\mathcal O}})$ the space of functions which are locally square integrable in $ \mathcal{O}$ and which admit first order derivatives that are also locally square integrable.
For each $t>0$ and for all real numbers $p,\,q\geq 1$, we denote by $L^{p,q}([0,t]\times {\cal O})$ the space of (classes of) measurable functions $u:[0,t]\times {\cal O}\longrightarrow \mathbb{{R}}$ such that $$\Vert u\Vert _{p,q;\,t}:=\left( \int_0^t\left( \int_{{\cal O}}|u(s,x)|^p\,dx\right) ^{q/p}\,ds\right) ^{1/q}$$ is finite. The limiting cases with $p$ or $q$ taking the value $\infty $ are also considered with the use of the essential sup norm.\
Now we introduce some other spaces of functions and discuss a certain duality between them. Like in [@DMS05] and [@DMS09], for self-containeness, we recall the following definitions:\
Let $(p_1,q_1)$, $(p_2,q_2)$ $\in[1,\infty]^2$ be fixed and set $$I=I\left( p_1,q_1,p_2,q_2\right) :=\left\{ \left( p,q\right)
\in \left[ 1,\infty \right] ^2/\;\exists \;\rho \in \left[
0,1\right] s.t.\right.$$ $$\left. \frac 1p=\rho \frac
1{p_1}+\left( 1-\rho \right) \frac 1{p_2},\frac 1q=\rho \frac
1{q_1}+\left( 1-\rho \right) \frac 1{q_2}\right\} .$$ This means that the set of inverse pairs $\left( \frac 1p,\frac 1q\right) ,$ $(p,q)$ belonging to $I,$ is a segment contained in the square $\left[ 0,1\right] ^2,$ with the extremities $\left( \frac
1{p_1},\frac 1{q_1}\right) $ and $\left( \frac 1{p_2},\frac
1{q_2}\right) .$\
We introduce: $$L_{I;t}=\bigcap_{\left(
p,q\right) \in I}L^{p,q}\left( \left[ 0,t\right] \times {\cal
O}\right) .$$ We know that this space coincides with the intersection of the extreme spaces, $$L_{I;t}=L^{p_1,q_1}\left( \left[ 0,t\right] \times {\cal
O}\right) \cap L^{p_2,q_2}\left( \left[ 0,t\right] \times {\cal
O}\right)$$ and that it is a Banach space with the following norm$$\left\| u\right\| _{I;t}:=\left\| u\right\| _{p_1,q_1;t}\vee \left\|
u\right\| _{p_2,q_2;t}.$$ The other space of interest is the algebraic sum$$L^{I;t}:=\sum_{\left( p,q\right) \in I}L^{p,q}\left( \left[
0,t\right] \times {\cal O}\right) ,$$ which represents the vector space generated by the same family of spaces. This is a normed vector space with the norm$$\left\| u\right\|^{I;t} :=\,\inf \left\{ \sum_{i=1}^n\left\|
u_i\right\| _{p_i,q_i;\,t}\,/\;u=\sum_{i=1}^nu_i,u_i\in
L^{p_i,q_i}\left( \left[ 0,t\right] \times {\cal O}\right) ,\,
\left( p_i,q_i\right) \in I,\,i=1,...n;\,n\in
\mathbb{{N}}^{*}\right\} .$$ Clearly one has $L^{I;t}\subset L^{1,1}\left( \left[ 0,t\right] \times {\cal O}\right) $ and $\left\| u\right\| _{1,1;t}\le c\left\| u\right\|
^{I;t},$ for each $u\in L^{I;t},$ with a certain constant $c>0.$
We also remark that if $\left( p,q\right) \in I,$ then the conjugate pair $\left( p^{\prime },q^{\prime }\right) ,$ with $\frac 1p+\frac
1{p^{\prime }}=\frac 1q+\frac 1{q^{\prime }}=1,$ belongs to another set, $I^{\prime },$ of the same type. This set may be described by$$I^{\prime }=I^{\prime }\left( p_1,q_1,p_2,q_2\right) :=\left\{
\left( p^{\prime },q^{\prime }\right) /\;\exists \left( p,q\right)
\in I\;s.t.\;\frac 1p+\frac 1{p^{\prime }}=\frac 1q+\frac
1{q^{\prime }}=1\right\}$$ and it is not difficult to check that $I^{\prime }\left( p_1,q_1,p_2,q_2\right) =I\left( p_1^{\prime
},q_1^{\prime },p_2^{\prime },q_2^{\prime }\right) ,$ where $p_1^{\prime },q_1^{\prime },p_2^{\prime }$ and $q_2^{\prime }$ are defined by $\frac 1{p_1}+\frac 1{p_1^{\prime }}=\frac 1{q_1}+\frac
1{q_1^{\prime }}=\frac 1{p_2}+\frac 1{p_2^{\prime }}=\frac
1{q_2}+\frac 1{q_2^{\prime }}=1.$
Moreover, by Hölder’s inequality, it follows that one has $$\label{dual}\int_0^t\int_{{\cal O}}u\left( s,x\right) v\left(
s,x\right) dxds\le \left\| u\right\| _{I;t}\left\| v\right\|
^{I^{\prime };t},$$ for any $u\in L_{I;t}$ and $v\in L^{I^{\prime };t}.$ This inequality shows that the scalar product of $L^2\left( \left[ 0,t\right] \times {\cal O}\right) $ extends to a duality relation for the spaces $L_{I;t}$ and $L^{I^{\prime };t}.$
Now let us recall that the Sobolev inequality states that$$\label{Sobolev}
\left\| u\right\| _{2^{*}}\le c_S\left\| \nabla u\right\| _2,$$ for each $u\in H_0^1\left( {\cal O}\right) ,$ where $c_S>0$ is a constant that depends on the dimension and $2^{*}=\frac{2d}{d-2}$ if $d>2,$ while $2^{*}$ may be any number in $]2,\infty [$ if $d=2$ and $2^{*}=\infty $ if $d=1.$ Therefore one has$$\left\| u\right\| _{2^{*},2;t}\le c_S\left\| \nabla u\right\|
_{2,2;t},$$ for each $t\ge 0$ and each $u\in L_{loc}^2\left(
\mathbb{R}_{+};H_0^1\left( {\cal O}\right) \right) .$ If $u\in
L_{loc}^{\infty}\left( \mathbb{R}_{+}; L^2\left( {\cal O}\right) \,
\right) \bigcap L^2_{loc} \left( \mathbb{R}_+; H_0^1\left( {\cal
O}\right) \right),$ one has $$\left\| u\right\| _{2,\infty ;t}\vee \left\| u\right\|
_{2^{*},2;t}\le c_1\left( \left\| u\right\| _{2,\infty ;t}^2+\left\|
\nabla u\right\| _{2,2;t}^2\right) ^{\frac 12},$$with $c_1=c_S\vee
1.$
For $d\ge 3$ and some parameter $\theta \in [0,1[$ we set: $$\Gamma_\theta =\left\{ \left( p,q\right) \in \left[ 1,\infty
\right]^2, \, \frac d{2p}+\frac 1q=\frac d2+\theta \right\} ,$$
$$\Gamma _\theta ^{*}=\left\{ \left( p,q\right) \in \left[
1,\infty \right] ^2/\;\frac d{2p}+\frac 1q=1-\theta \right\} ,$$ $$L_\theta ^{*}=\sum_{\left( p,q\right) \in \Gamma _\theta
^{*}}L^{p,q}\left( \left[ 0,t\right] \times {\cal O}\right)$$ $$\left\| u\right\| _{\theta ;t}^{*}:=\,\inf \left\{
\sum_{i=1}^n\left\| u_i\right\|
_{p_i,q_i;\,t}\,/\;u=\sum_{i=1}^nu_i,u_i\in L^{p_i,q_i}\left( \left[
0,t\right] \times {\cal O}\right) ,\right.$$ $$\left. \left( p_i,q_i\right) \in \Gamma _\theta ^{*},\,i=1,...n;\,n\in {\bf N}^{*}\right\} .$$ If $d=1,2.$ we put $$\Gamma _\theta =\left\{ \left( p,q\right) \in \left[ 1,\infty \right] ^2/\;\frac{2^{*}}{2^{*}-2}\frac 1p+\frac 1q=\frac{2^{*}}{2^{*}-2}+\theta
\right\} ,$$ $$\Gamma _\theta ^{*}=\left\{ \left( p,q\right) \in
\left[ 1,\infty \right] ^2/\;\frac{2^{*}}{2^{*}-2}\frac 1p+\frac
1q=1-\theta \right\}$$ and by using similar calculations with the convention $\frac{2^{*}}{2^{*}-2}=1$ if $d=1.$
We remark that $\Gamma _\theta ^{*}=I\left( \infty ,\frac 1{1-\theta },\frac
d{2\left( 1-\theta \right) },\infty \right) $ and that the norm $\left\| u\right\| _{\theta ;t}^{*}$ coincides with $\left\|
u\right\| ^{\Gamma _\theta ^{*};t}=\left\| u\right\| ^{I\left(
\infty ,\frac 1{1-\theta },\frac d{2\left( 1-\theta \right) },\infty
\right) ;t}.$ Moreover we have the following duality relation: $$\label{dual2}\int_0^t\int_{{\cal O}}u\left( s,x\right) v\left( s,x\right)
dxds\le \left\| u\right\| _{\theta;t}\left\| v\right\|_{\theta;t}^*,$$ for any $u\in L_{\theta;t}$ and $v\in L_{\theta;t}^*$ and the following inequality: $$\label{controltheta}
\left\|u\right\|_{\theta;t}\leq
c_1\left(\left\|u\right\|^2_{2,\infty;t}+\left\|\nabla
u\right\|^2_{2,2;t}\right)^{1/2}.$$
Hypotheses
----------
We consider a sequence $((B^i(t))_{t\geq0})_{i\in\mathbb{N}^*}$ of independent Brownian motions defined on a standard filtered probability space $(\Omega,\mathcal{F},(\mathcal{F}_t)_{t\geq0},P)$ satisfying the usual conditions.
Let $A$ be a symmetric second order differential operator defined on the open bounded subset $ {\ensuremath{\mathcal O}}\subset {\mathbb{R}}^d$, with domain $\mathcal{D}(A)$, given by $$A:=-L=-\sum_{i,j=1}^d\partial_i(a^{i,j}\partial_j).$$ We assume that $a=(a^{i,j})_{i,j}$ is a measurable symmetric matrix defined on $\mathcal{O}$ which satisfies the uniform ellipticity condition$$\lambda|\xi|^2\leq\sum_{i,j=1}^d
a^{i,j}(x)\xi^i\xi^j\leq\Lambda|\xi|^2,\ \forall x\in\mathcal{O},\
\xi\in {\mathbb{R}}^d,$$where $\lambda$ and $\Lambda$ are positive constants. The energy associated with the matrix $a$ will be denoted by $$\label{energy}
\mathcal{E} \left( w,v\right)=\sum_{i,j=1}^d
\int_{{\ensuremath{\mathcal O}}}a^{i,j}(x)\partial_i w(x)\partial_j v(x)\, dx .$$ It’s defined for functions $w,\, v \in H^1_{0}
(\mathcal{O} )$, or for $w \in H^1_{loc} (\mathcal{O} )$ and $v \in
H^1_{0} (\mathcal{O })$ with compact support.
We assume that we have predictable random functions$$\begin{aligned}
&&f:{\mathbb{R}}_+\times\Omega\times\mathcal{O}\times
{\mathbb{R}}\times {\mathbb{R}}^d\rightarrow
{\mathbb{R}},\\&&g=(g_1,...,g_d):{\mathbb{R}}_+\times\Omega\times\mathcal{O}\times
{\mathbb{R}}\times {\mathbb{R}}^d\rightarrow
{\mathbb{R}}^d,\\&&h=(h_1,...,h_i,...):{\mathbb{R}}_+\times\Omega\times\mathcal{O}\times
{\mathbb{R}}\times {\mathbb{R}}^d\rightarrow {\mathbb{R}}^{\mathbb{N}^*}.\end{aligned}$$ We define $$\begin{split}
&f ( \cdot
,\cdot,\cdot, 0,0):=f^0, \ g( \cdot,\cdot,\cdot ,0,0) :=g^0 =
(g_1^0,...,g_d^0) \ \mbox{and}
\ h( \cdot,\cdot,\cdot ,0,0) :=h^0 = (h_1^0,...,h_i^0,...) .\\
\end{split}$$ In the sequel, $|\cdot|$ will always denote the underlying Euclidean or $l^2-$norm. For example$$|h(t,\omega,x,y,z)|^2=\sum_{i=1}^{+\infty}|h_i(t,\omega,x,y,z)|^2.$$
Let us note that this general setting of the SPDE we consider, encompasses the case of an SPDE driven by a space-time noise, colored in space and white in time as in [@SW] for example (see also Example 1 in [@DMZ12]).
**Assumption (H):** There exist non-negative constants $C,\
\alpha,\ \beta$ such that for almost all $\omega$, the following inequalities hold for all $(x,y,z,t)\in\mathcal{O}\times\mathbb{R}\times\mathbb{R}^d\times\mathbb{R}_+$:
1. $|f(t,\omega,x,y,z)-f(t,\omega,x,y',z')|\leq C(|y-y'|+|z-z'|),$
2. $|g(t,\omega,x,y,z)-g(t,\omega,x,y',z')|\leq
C|y-y'|+\alpha|z-z'|,$
3. $|h(t,\omega,x,y,z)-h(t,\omega,x,y',z')|\leq
C|y-y'|+\beta|z-z'|,$
4. the contraction property: $2\alpha+\beta^2<2\lambda.$
Moreover we introduce some integrability conditions on the coefficients $f^0, \;
g^0, \, h^0$ and the initial data $\xi$. Along this article, we fix a terminal time $T>0$.\
**Assumption (HI2)** $$E \left(\|\xi \|_2^2 +\left\| f^0\right\|_{2,2;t}^2+\left\|
\left|g^0\right|\right\| _{2,2;t}^2+\left\|\left| h^0\right|\right\|
_{2,2;t}^2\right) <\infty ,$$ for each $t\in[0,T]$.\
**Assumption (HIL)** $$E \int_K |\xi (x)|^2 dx + E \,
\int_{0}^t \int_K \big( |f_s^0(x)|^2 + |g_s^0 (x)|^2 + |h_s^0(x)|^2
\, \big) dx ds < \infty,$$for any compact set $K \subset \mathcal{O}$ and for any $t\in[0,T]$.
Weak solutions
--------------
We now introduce ${\ensuremath{\mathcal H}}_T$, the space of $H_0^1(\mathcal{O})$-valued predictable processes $(u_t)_{t \in[0,T]}$ such that $$\left( E \sup_{0\leq s\leq T} \left\| u_{s}\right\|_2
^{2}+\int_{0}^{T}E\, \mathcal{E}\left( u_{s}\right) ds\right)
^{1/2}\;< \; \infty \;.$$ We define ${{\cal H}}_{loc}={{\cal H}}_{loc}(\mathcal{O})$ to be the set of $H^1_{loc} ({{\cal O}})$-valued predictable processes defined on $[0,T]$ such that for any compact subset $K$ in ${{\cal O}}$:
$$\left( E \sup_{0\leq s\leq T}\int_K u_{s}(x)^{2}\, dx
+E\int_{0}^{T}\int_K |\nabla u_{s}(x)|^2\, dx ds\right) ^{1/2}\;< \;
\infty .$$
The space of test functions is the algebraic tensor product $\mathcal{D}=\mathcal{C} _{c}^{\infty }({{\ensuremath{\mathbb R}} }^+)\otimes
\mathcal{C}_c^2 ({\ensuremath{\mathcal O}})$, where $\mathcal{C} _{c}^{\infty }({{\ensuremath{\mathbb R}} }^+)$ denotes the space of all real infinite differentiable functions with compact support in $\mathbb{R}^+$ and $\mathcal{C}_c^2 ({\ensuremath{\mathcal O}})$ the set of $C^2$-functions with compact support in ${\ensuremath{\mathcal O}}$.
Now we recall the definition of the regular measure which has been defined in [@DMZ12].\
$\mathcal{K}$ denotes $L^\infty([0,T];L^2(\mathcal{O}))\cap
L^2([0,T];H_0^1(\mathcal{O}))$ equipped with the norm: $$\begin{aligned}
\parallel
v\parallel^2_\mathcal{K}&=&\parallel
v\parallel^2_{L^\infty([0,T];L^2(\mathcal{O}))}+\parallel
v\parallel^2_{L^2([0,T];H_0^1(\mathcal{O}))}\\
&=&\sup_{t\in[0,T[}\parallel v_t\parallel^2 +\int_0^T \left(
\parallel v_t \parallel^2 +\mathcal{E}(v_t)\right)\, dt
.\end{aligned}$$ $\mathcal{C}$ denotes the space of continuous functions with compact support in $[0,T[\times\mathcal{O}$ and finally: $$\mathcal {W}=\{\varphi\in L^2([0,T];H_0^1(\mathcal{O}));\ \frac{\partial\varphi}{\partial t}\in
L^2([0,T];H^{-1}(\mathcal{O}))\},$$ endowed with the norm$\parallel\varphi\parallel^2_{\mathcal {W}}=\parallel
\varphi\parallel^2_{L^2([0,T];H_0^1(\mathcal{O}))}+\parallel\displaystyle\frac{\partial
\varphi}{\partial t}\parallel^2_{L^2([0,T];H^{-1}(\mathcal{O}))}$.\
It is known (see [@LionsMagenes]) that $\mathcal{W}$ is continuously embedded in $C([0,T]; L^2 ({\ensuremath{\mathcal O}}))$, the set of $L^2 ({\ensuremath{\mathcal O}})$-valued continuous functions on $[0,T]$. So without ambiguity, we will also consider $\mathcal{W}_T=\{\varphi\in\mathcal{W};\varphi(T)=0\}$, $\mathcal{W}^+=\{\varphi\in\mathcal{W};\varphi\geq0\}$, $\mathcal{W}_T^+=\mathcal{W}_T\cap\mathcal{W}^+$.
An element $v\in \mathcal{K}$ is said to be a [**parabolic potential**]{} if it satisfies: $$\forall\varphi\in\mathcal{W}_T^+,\
\int_0^T-(\frac{\partial\varphi_t}{\partial
t},v_t)dt+\int_0^T\mathcal{E}(\varphi_t,v_t)dt\geq0.$$ We denote by $\mathcal{P}$ the set of all parabolic potentials.
The next representation property is crucial:
(Proposition 1.1 in [@PIERRE])\[presentation\] Let $v\in\mathcal{P}$, then there exists a unique positive Radon measure on $[0,T[\times\mathcal{O}$, denoted by $\nu^v$, such that: $$\forall\varphi\in\mathcal{W}_T\cap\mathcal{C},\ \int_0^T(-\frac{\partial\varphi_t}{\partial t},v_t)dt+\int_0^T\mathcal{E}(\varphi_t,v_t)dt=\int_0^T\int_\mathcal{O}\varphi(t,x)d\nu^v.$$ Moreover, $v$ admits a right-continuous (resp. left-continuous) version $\hat{v} \ (\makebox{resp. } \bar{v}): [0,T]\mapsto L^2
({\ensuremath{\mathcal O}})$ .\
Such a Radon measure, $\nu^v$ is called [**a regular measure**]{} and we write: $$\nu^v =\frac{\partial v}{\partial t}+Av .$$
Let $K\subset [0,T[\times\mathcal{O}$ be compact, $v\in\mathcal{P}$ is said to be *$\nu-$superior* than 1 on $K$, if there exists a sequence $v_n\in\mathcal{P}$ with $v_n\geq1\ a.e.$ on a neighborhood of $K$ converging to $v$ in $L^2([0,T];H_0^1(\mathcal{O}))$.
We denote:$$\mathscr{S}_K=\{v\in\mathcal{P};\ v\ is\ \nu-superior\
to\ 1\ on\ K\}.$$
(Proposition 2.1 in [@PIERRE]) Let $K\subset [0,T[\times\mathcal{O}$ compact, then $\mathscr{S}_K$ admits a smallest $v_K\in\mathcal{P}$ and the measure $\nu^v_K$ whose support is in $K$ satisfies $$\int_0^T\int_\mathcal{O}d\nu^v_K=\inf_{v\in\mathcal{P}}\{\int_0^T\int_\mathcal{O}d\nu^v;\ v\in\mathscr{S}_K\}.$$
(Parabolic Capacity)
- Let $K\subset [0,T[\times\mathcal{O}$ be compact, we define $cap(K)=\int_0^T\int_\mathcal{O}d\nu^v_K$;
- let $O\subset
[0,T[\times\mathcal{O}$ be open, we define $cap(O)=\sup\{cap(K);\
K\subset O\ compact\}$;
- for any borelian $E\subset [0,T[\times\mathcal{O}$, we define $cap(E)=\inf\{cap(O);\
O\supset E\ open\}$.
A property is said to hold quasi-everywhere (in short q.e.) if it holds outside a set of null capacity.
(Quasi-continuous)
A function $u:[0,T[\times\mathcal{O}\rightarrow\mathbb{R}$ is called quasi-continuous, if there exists a decreasing sequence of open subsets $O_n$ of $[0,T[\times\mathcal{O}$ with:
1. for all $n$, the restriction of $u_n$ to the complement of $O_n$ is continuous;
2. $\lim_{n\rightarrow+\infty}cap\;(O_n)=0$.
We say that $u$ admits a quasi-continuous version, if there exists $\tilde{u}$ quasi-continuous such that $\tilde{u}=u\ a.e.$
The next proposition, whose proof may be found in [@Pierre] or [@PIERRE] shall play an important role in the sequel:
\[Versiont\] Let $K\subset {\ensuremath{\mathcal O}}$ a compact set, then $\forall t\in [0,T[$ $$cap (\{ t\}\times K)=\lambda_d (K),$$ where $\lambda_d$ is the Lebesgue measure on ${\ensuremath{\mathcal O}}$.\
As a consequence, if $u: [0,T[\times {\ensuremath{\mathcal O}}\rightarrow {\mathbb{R}}$ is a map defined quasi-everywhere then it defines uniquely a map from $[0,T[$ into $L^2 ({\ensuremath{\mathcal O}})$. In other words, for any $t\in [0,T[$, $u_t$ is defined without any ambiguity as an element in $L^2 ({\ensuremath{\mathcal O}})$. Moreover, if $u\in \mathcal{P}$, it admits version $\bar{u}$ which is left continuous on $[0,T]$ with values in $L^2 ({\ensuremath{\mathcal O}})$ so that $u_T =\bar{u}_{T^-}$ is also defined without ambiguity.
The previous proposition applies if for example $u$ is quasi-continuous.
To establish a maximum principle for local solutions we need to define the notion of [*local regular measures*]{}:
We say that a Radon measure $\nu$ on $[0,T[\times {\ensuremath{\mathcal O}}$ is a [local regular measure]{} if for any non-negative $\phi$ in $\mathcal{C}_c^\infty({\ensuremath{\mathcal O}})$, $\phi\nu$ is a regular measure.
Local regular measures do not charge polar sets (i.e. sets of capacity 0).
Let $A$ be a polar set and consider a sequence $(\phi_n)$ in $\mathcal{C}_c^\infty({\ensuremath{\mathcal O}})$, $0\leq\phi_n\leq1$, converging to 1 everywhere on ${\ensuremath{\mathcal O}}$. By Fatou’s lemma, $$0\leq\int_{[0,T[\times{\ensuremath{\mathcal O}}}{{1} \hspace{-0.25 em}{\rm I}}_A
d\nu(x,t)\leq\liminf_{n\rightarrow\infty}\int_{[0,T[\times{\ensuremath{\mathcal O}}}{{1} \hspace{-0.25 em}{\rm I}}_A\phi_nd\nu(x,t)=0.$$
We end this part by a convergence lemma which plays an important role in our approach (Lemma 3.8 in [@PIERRE]):
\[convergemeas\] If $v^n\in\mathcal{P}$ is a bounded sequence in $\mathcal{K}$ and converges weakly to $v$ in $L^2([0,T];H_0^1(\mathcal{O}))$; if $u$ is a quasi-continuous function and $|u|$ is bounded by a element in $\mathcal{P}$. Then $$\lim_{n\rightarrow+\infty}\int_0^T\int_\mathcal{O}ud\nu^{v^n}=\int_0^T\int_\mathcal{O}ud\nu^{v}.$$
We now give the assumptions on the obstacle that we shall need in the different cases that we shall consider.\
**Assumption (O):** The obstacle $S: [0,T]\times \Omega\times
{\ensuremath{\mathcal O}}\rightarrow {\mathbb{R}}$ is an adapted random field almost surely quasi-continuous, in the sense that for $P$-almost all $\omega\in\Omega$, the map $(t,x)\rightarrow S_t (\omega,x)$ is quasi-continuous. Moreover, $S_0 \leq \xi$ $P$-almost surely and $S$ is controlled by the solution of an SPDE, i.e. $\forall
t\in[0,T],$ $$S_t\leq S'_t,\quad dP\otimes dt\otimes dx-a.e.$$ where $S'$ is the solution of the linear SPDE $$\left\{\begin{array}{ccl} \label{obstacle}
dS'_t&=&LS'_tdt+f'_tdt+\sum_{i=1}^d \partial_i g'_{i,t}dt+\sum_{j=1}^{+\infty}h'_{j,t}dB^j_t\\
S'(0)&=&S'_0 ,
\end{array}\right.$$ with null boundary Dirichlet conditions.\
**Assumption (OL):** The obstacle $S: [0,T]\times \Omega\times
{\ensuremath{\mathcal O}}\rightarrow {\mathbb{R}}$ is an adapted random field, almost surely quasi-continuous, such that $S_0 \leq \xi$ $P$-almost surely and controlled by a **local** solution of an SPDE, i.e. $\forall
t\in[0,T],$ $$S_t\leq S'_t,\quad dP\otimes dt\otimes dx-a.e.$$ where $S'$ is a **local** solution of the linear SPDE $$\left\{\begin{array}{ccl}
dS'_t&=&LS'_tdt+f'_tdt+\sum_{i=1}^d \partial_i g'_{i,t}dt+\sum_{j=1}^{+\infty}h'_{j,t}dB^j_t\\
S'(0)&=&S'_0 .
\end{array}\right.$$ **Assumption (HO2)** $$E \left(\|\xi \|_2^2 +\left\| f'\right\|_{2,2;T}^2+\left\|
|g'|\right\| _{2,2;T}^2+\left\| |h'|\right\| _{2,2;T}^2\right)
<\infty .$$\
**Assumption (HOL)** $$E \int_K |S'_0|^2 dx + E \, \int_{0}^T
\int_K \big( |f'_t(x)|^2 + |g'_t (x)|^2 + |h'_t (x)|^2 \, \big) dx
dt < \infty$$for any compact set $K \subset \mathcal{O}$.
\[remark3\] It is well-known that under [**(HO2)**]{} $S'$ belongs to ${\ensuremath{\mathcal H}}_T$, is unique and satisfies the following estimate: $$\label{estimobstacle1}
E\sup_{t\in[0,T]}\parallel
S'_t\parallel^2+E\int_0^T\mathcal{E}(S'_t)dt\leq CE\left[\parallel
S'_0\parallel^2+\int_0^T(\parallel f'_t\parallel^2+\parallel
|g'_t|\parallel^2+\parallel |h'_t|\parallel^2)dt\right],$$ see for example Theorem 8 in [@DenisStoica]. Moreover, as a consequence of Theorem 3 in [@DMZ12], we know that $S'$ admits a quasi-continuous version.
A pair $(u,\nu)$ is said to be a solution of the problem (\[SPDEO\]) if
1. $u\in\mathcal{H}_T$, $u(t,x)\geq S(t,x),\ dP\otimes dt\otimes
dx-a.e.$ and $u_0(x)=\xi,\ dP\otimes dx-a.e.$;
2. $\nu$ is a random regular measure defined on $[0,T[\times\mathcal{O}$;
3. the following relation holds almost surely, for all $t\in[0,T]$ and all $\varphi\in\mathcal{D}$, $$\begin{split}\label{solution}(u_t,\varphi_t)=&(\xi,\varphi_0)+\int_0^t(u_s,\partial_s\varphi_s)ds-\int_0^t\mathcal{E}(u_s,\varphi_s)ds\\&-\sum_{i=1}^d\int_0^t(g^i_s(u_s,\nabla u_s),\partial_i\varphi_s)ds
+\int_0^t(f_s(u_s,\nabla u_s),\varphi_s)ds\\&+\sum_{j=1}^{+\infty}\int_0^t(h^j_s(u_s,\nabla u_s),\varphi_s)dB^j_s+\int_0^t\int_{\mathcal{O}}\varphi_s(x)\nu(dx,ds);\end{split}$$
4. $u$ admits a quasi-continuous version, $\tilde{u}$, and we have $$\int_0^T\int_{\ensuremath{\mathcal O}}(\tilde{u}(s,x)-S(s,x))\nu(dx,ds)=0,\ \
P-a.s.$$
We denote by ${\ensuremath{\mathcal R}}(\xi,f,g,h,S)$ the solution of the obstacle problem when it exists and is unique.
A pair $(u,\nu)$ is said to be a local solution of the problem (\[SPDEO\]) if
1. $u\in\mathcal{H}_{loc}$, $u(t,x)\geq S(t,x),\ dP\otimes dt\otimes
dx-a.e.$ and $u_0(x)=\xi,\ dP\otimes dx-a.e.$;
2. $\nu$ is a local random regular measure defined on $[0,T[\times\mathcal{O}$;
3. the following relation holds almost surely, for all $t\in[0,T]$ and all $\varphi\in\mathcal{D}$, $$\begin{split}\label{solutionlocal}(u_t,\varphi_t)=&(\xi,\varphi_0)+\int_0^t(u_s,\partial_s\varphi_s)ds-\int_0^t\mathcal{E}(u_s,\varphi_s)ds\\&-\sum_{i=1}^d\int_0^t(g^i_s(u_s,\nabla u_s),\partial_i\varphi_s)ds
+\int_0^t(f_s(u_s,\nabla u_s),\varphi_s)ds\\&+\sum_{j=1}^{+\infty}\int_0^t(h^j_s(u_s,\nabla u_s),\varphi_s)dB^j_s+\int_0^t\int_{\mathcal{O}}\varphi_s(x)\nu(dx,ds);\end{split}$$
4. $u$ admits a quasi-continuous version, $\tilde{u}$, and we have $$\int_0^T\int_{\ensuremath{\mathcal O}}(\tilde{u}(s,x)-S(s,x))\nu(dx,ds)=0,\ \
P-a.s.$$
We denote by ${\ensuremath{\mathcal R}}_{loc}(\xi,f,g,h,S)$ the set of all the local solutions $(u,\nu)$.\
Finally, in the sequel, we introduce some constants $\epsilon$, $\delta>0$, we shall denote by $C_\epsilon$, $C_\delta$ some constants depending only on $\epsilon$, $\delta$, typically those appearing in the kind of inequality $$\label{young}|ab|\leq \epsilon a^2 + C_\epsilon b^2.$$
$L^p-$estimate for the uniform norm of solutions with null Dirichlet boundary condition {#LPestimate}
=======================================================================================
In this section, we want to study, for some $p\geq2$, the $L^p-$ estimate for the uniform norm of the solution of (\[SPDEO\]). To get such estimate, we need stronger integrability conditions on the coefficients and the initial condition. To this end, we consider the following assumptions: for $\theta\in[0,1[$ and $p\geq2$:\
**Assumption (HI$\mathbf{2
p}$)**$$E\left(\left\|\xi\right\|_\infty^p+\left\|
f^0\right\|^2_{2,2;T}+\left\| |g^0 |\right\|^2_{2,2;T}+\left\| |h^0
|\right\|^2_{2,2;T}\right)<\infty .$$
**Assumption (HO$\mathbf{\infty p}$)** $$S'_0\in L^\infty(\Omega\times{\ensuremath{\mathcal O}})\ and\ E\left((\left\|
f'\right\|_{\infty,\infty;T})^p+(\left\| |g'
|^2\right\|_{\infty,\infty;T})^{p/2}+(\left\| |h'
|^2\right\|_{\infty,\infty;T})^{p/2}\right)<\infty .$$
To get the estimates we need, we apply Itô’s formula to $u-S'$, in order to take advantage of the fact that $S-S'$ is non-positive and that as $u$ is solution of (\[SPDEO\]) and $S'$ satisfies (\[obstacle\]), $u-S'$ satisfies $$\label{uminusS'}\left\{ \begin{split}&d(u_t-S'_t)=\partial_i (a_{i,j}(x)\partial_j(u_t(x)-S'_t(x)))dt+(f(t,x,u_t(x),\nabla
u_t(x))-f'(t,x))dt \\&+\partial_i(g_i(t,x,u_t(x),\nabla
u_t(x))-g'_i(t,x))dt+(h_j(t,x,u_t(x),\nabla
u_t(x))-h'_j(t,x))dB^j_t\\&+\nu(x,dt), \\
&(u-S')_0=\xi-S'_0\, ,\\&u-S'\geq S-S'\, . \end{split}\right.$$ that is why we introduce the following functions: $$\bar{f}(t,\omega,x,y,z)=f(t,\omega,x,y+S'_t,z+\nabla
S'_t)-f'(t,\omega,x)$$ $$\bar{g}(t,\omega,x,y,z)=g(t,\omega,x,y+S'_t,z+\nabla S'_t)-g'(t,\omega,x)$$ $$\bar{h}(t,\omega,x,y,z)=h(t,\omega,x,y+S'_t,z+\nabla S'_t)-h'(t,\omega,x).$$ Let us remark that the Skohorod condition for $u-S'$ is satisfied since $$\int_0^T\int_{{\ensuremath{\mathcal O}}} (u_s (x)-S'_s (x))-(S_s (x)-S'_s (x))\nu (ds ,dx)=\int_0^T\int_{{\ensuremath{\mathcal O}}} (u_s (x)-S_s (x))\nu (ds ,dx)=0.$$ It is obvious that $\bar{f}$, $\bar{g}$ and $\bar{h}$ satisfy the Lipschitz conditions with the same Lipschitz coefficients as $f$, $g$ and $h$ and $\left\|\xi-S'_0\right\|_\infty\in
L^p(\Omega,P)$. Nevertheless, we need a supplementary hypothesis:\
**Assumption (HD$\mathbf{\theta p}$)** $$E((\left\|
\bar{f}^0\right\|^*_{\theta;T})^p+(\left\| |\bar{g}^0
|^2\right\|^*_{\theta;T})^{p/2}+(\left\| |\bar{h}^0
|^2\right\|^*_{\theta;T})^{p/2})<\infty .$$
This assumption is fulfilled in the following case:
If $\left\|\nabla S'\right\|^*_{\theta;T},\
\left\|f^0\right\|^*_{\theta;T},\ \left\|g^0\right\|^*_{\theta;T}\
and\ \left\|h^0\right\|^*_{\theta;T}$ belong to $ L^p(\Omega,P), $ and assumptions [**(H)**]{} and [**(HO$\mathbf{\infty p}$)**]{} hold, then:\
$\bar{f}$ satisfies the Lipschitz condition with the same Lipschitz coefficients: $$\begin{aligned}
\left|\bar{f}(t,\omega,x,y,z)-\bar{f}(t,\omega,x,y',z')\right|&=&\big|f(t,\omega,x,y+S'_t(x),z+\nabla S'_t(x))+f'(t,\omega,x)\\&-&f(t,\omega,x,y'+S'_t(x),z'+\nabla S'_t(x))-f'(t,\omega,x)\big|\\&\leq& C\left|y-y'\right|+C\left|z-z'\right|.\end{aligned}$$
$\bar{f}$ satisfies the integrability condition: $$\begin{aligned}
\left\|\bar{f}^0\right\|^*_{\theta;T}&=&\left\|f(S',\nabla
S')-f'\right\|^*_{\theta;T}\leq \left\|f(S',\nabla
S')\right\|^*_{\theta;T}+\left\|f'\right\|^*_{\theta;T}\\&\leq&\left\|f^0\right\|^*_{\theta;T}+C\left\|S'\right\|^*_{\theta;T}+C\left\|\nabla
S'\right\|^*_{\theta;T}+\left\|f'\right\|_{\infty,\infty;T}.\end{aligned}$$
And the same for $\bar{g}$ and $\bar{h}$, which proves that [**(HD$\mathbf{\theta p}$)**]{} holds.
We now give the main result of this Section, which is a version of the maximum principle in the case of a solution vanishing on the boundary of ${\ensuremath{\mathcal O}}$:
\[LPESTIM\] Suppose that assumptions [**(H)**]{}, [**(O)**]{}, [**(HI$\mathbf{2
p}$)**]{}, [**(HO$\mathbf{\infty p}$)**]{} and [**(HD$\mathbf{\theta
p}$)**]{} hold, for some $\theta\in[0,1[$ and $p\geq2$ and that the constants of Lipschitz conditions satisfy $$\alpha+\frac{\beta^2}{2}+72\beta^2<\lambda.$$ Let $(u,\ \nu)$ be the solution of OSPDE (\[SPDEO\]) with null boundary condition, then for all $t\in [0,T]$, $$\begin{split}E\left\| u\right\|^p_{\infty,\infty;t}&\leq c(p)k(t)E\big(\left\|\xi\right\|_\infty^p+\left\|S'_0\right\|_\infty^p+\left\|f'\right\|_{\theta;t}^{*p}+\left\||g'|^2\right\|_{\theta;t}^{*p/2}+\left\||h'|^2\right\|_{\theta;t}^{*p/2}\\&\quad+\left\|\bar{f}^0\right\|_{\theta;t}^{*p}+\left\||\bar{g}^0|^2\right\|_{\theta;t}^{*p/2}+\left\||\bar{h}^0|^2\right\|_{\theta;t}^{*p/2}\big),\end{split}$$ where $c(p)$ is a constant which depends on $p$ and $k(t)$ is a constant which depends on the structure constants and $t\in[0,T]$.
The relations $\left\|f'\right\|_{\theta;t}^{*p}\leq(\left\|f'\right\|_{\infty,\infty;t})^{p}$, $\left\||g'|^2\right\|_{\theta;t}^{*p/2}\leq(\left\||g'|^2\right\|_{\infty,\infty;t})^{p/2}$ and $\left\||h'|^2\right\|_{\theta;t}^{*p/2}\leq(\left\||h'|^2\right\|_{\infty,\infty;t})^{p/2}$ and assumption [**(HO$\mathbf{\infty p}$))**]{} yield $$E\left(\left\|f'\right\|_{\theta;t}^{*p}+\left\||g'|^2\right\|_{\theta;t}^{*p/2}+\left\||h'|^2\right\|_{\theta;t}^{*p/2}\right)<+\infty.$$
As the proof of this theorem is quite long, we split it into several steps.
The case where $\xi$, $\bar{f}^0$, $\bar{g}^0$ and $\bar{h}^0$ are uniformly bounded {#casborn}
------------------------------------------------------------------------------------
In this subsection, we assume that the hypotheses [**(H)**]{}, [**(O)**]{}, [**(HI$\mathbf{2
p}$)**]{}, [**(HO$\mathbf{\infty p}$)**]{} hold and we add the following stronger ones: $$\label{stronger1}\xi\in
L^\infty(\Omega\times{\ensuremath{\mathcal O}}),$$and $$\bar{f}^0,\ \bar{g}^0,\ \bar{h}^0\in L^\infty(\mathbb{R}_+\times\Omega\times{\ensuremath{\mathcal O}}).$$ Then it is obviously that $\xi-S'_0\in L^\infty(\Omega\times{\ensuremath{\mathcal O}})$.\
Under these hypotheses, we know that the SPDE with obstacle (\[SPDEO\]) admits a unique weak solution $(u,\nu) = \mathcal R
(\xi, f,g,h,S)$ and that $(u-S',\nu)={\ensuremath{\mathcal R}}(\xi-S'_0,\bar{f},\bar{g},\bar{h},S-S')$. We start by proving the following $L^l-$estimate:
\[estimateul\] The solution $u$ of the problem (\[SPDEO\]) belongs to $\cap_{l\geq2}L^l([0,T]\times{\ensuremath{\mathcal O}}\times\Omega)$. Moreover there exist constants $c,\ c'>0$ which only depend on $\ C,\ \alpha,\ \beta$ and on the quantity $$\begin{aligned}
K=\left\|\xi-S'_0\right\|_{L^\infty(\Omega\times{\ensuremath{\mathcal O}})}\vee\left\|\bar{f}^0\right\|_{L^\infty(\mathbb{R}_+\times\Omega\times{\ensuremath{\mathcal O}})}\vee\left\|\bar{g}^0\right\|_{L^\infty(\mathbb{R}_+\times\Omega\times{\ensuremath{\mathcal O}})}\vee\left\|\bar{h}^0\right\|_{L^\infty(\mathbb{R}_+\times\Omega\times{\ensuremath{\mathcal O}})}\end{aligned}$$ such that, for all real $l\geq2$, $$\label{uS'l}E\int_{\ensuremath{\mathcal O}}|u_t(x)-S'_t(x)|^ldx\leq cK^2l(l-1)e^{cl(l-1)t}$$ $$\label{nablauS'l}E\int_0^t\int_{\ensuremath{\mathcal O}}|u_s(x)-S'_s(x)|^{l-2}|\nabla(u_s(x)-S'_s(x))|^2dxds\leq c'K^2l(l-1)e^{cl(l-1)t}$$ and$$\label{nuS'l}E\int_0^t\int_{\ensuremath{\mathcal O}}|u_s(x)-S'_s(x)|^{l-1}\nu(dxds)<+\infty.$$
Notice first that if $(u-S',\nu)={\ensuremath{\mathcal R}}(\xi-S'_0,\bar{f},\bar{g},\bar{h},S-S')$, then $$\bar{f}\left(u-S',\nabla(u-S')\right)
,\bar{g}_i\left(u-S',\nabla(u-S')\right) ,\bar{h}_i\left(
u-S',\nabla(u-S')\right) \in L^2\left([0,T];L^2\left( \Omega \times
{\cal O}\right) \right)$$ and consequently we can apply Itô’s formula to $(u-S',\nu)$ (See Theorem 5 in [@DMZ12]).\
We fix a real $l\geq2$, $T > 0$ and introduce the sequence $({\varphi}_n
)_{n\in{{\mathbb{N}}^{\ast}}}$ of functions such that for all $n\in{{\mathbb{N}}^{\ast}}$: $$\forall x\in{\mathbb{R}},\, {\varphi}_n (x)= \left\{
\begin{array}{ll}
\mid x \mid^l&\makebox{ if }\mid x\mid\leq n\\
n^{l-2} \, \big[ \frac{l (l-1)}{2} (|x|-n)^2+ l \, n (|x|-n) + n^2\,\big] &\makebox{ if }\mid x\mid >n
\end{array}\right.$$ One can easily verify that for fixed $n$, ${\varphi}_n$ is twice differentiable with bounded second derivative, $ \varphi_n^{\prime
\prime} (x) \geq 0$, and as $ n \to \infty $ one has $ \varphi_n (x)\longrightarrow |x|^{l}$, $\varphi_n^{\prime} (x)\longrightarrow lsgn(x)|x|^{l-1}$, $\varphi_n^{\prime \prime} (x)\longrightarrow l (l-1)|x|^{l-2}$. Moreover, the following relations hold, for all $x\in {{\ensuremath{\mathbb R}} }$ and $n\geq l$:
1. $\mid x{\varphi}_n^{\prime}(x)\mid\leq l{\varphi}_n (x). $
2. $\mid {\varphi}_n^{\prime}(x)\mid\leq\mid
x{\varphi}_n^{\prime\prime}(x)\mid$.
3. $\mid x^2{\varphi}_n^{\prime\prime}(x)\mid \leq l(l-1){\varphi}_n (x)$.
4. $|{\varphi}_n^{\prime}(x)|\leq l({\varphi}_n (x)+1 ).$
5. $|{\varphi}_n^{\prime\prime}(x)|\leq l(l-1)({\varphi}_n (x)+1 ).$
Applying Itô’s formula to $\varphi_n(u-S')$, we have $P$-a.s. for all $t\in [0,T]$, $$\label{uS'It\^o's}
\begin{split}
& \int_{\mathcal{O}} \varphi_n (u_t (x)-S'_t(x)) \, dx \; + \;
\int_0^t \mathcal{E} \big(\varphi_n^{\prime} (u_s-S'_s), \, u_s-S'_s
\big) \, ds = \int_{\mathcal{O}} \varphi_n (\xi(x)-S'_0(x) ) \, dx
\\ & + \int_{0}^{t}\int_{\mathcal{O}}
\varphi_n^{\prime}(u_s(x)-S'_s(x)) \bar{f} (s,x, u_s-S'_s,\nabla (u_s-S'_s)) \, dx ds \\
& - \sum_{i=1}^{d} \int_{0}^{t} \int_{\mathcal{O}}
\varphi_n^{\prime \prime } (u_s(x)-S'_s(x) )
\partial_i (u_s(x)-S'_s(x)) \, \bar{g}_{i} (s,x,u_s-S'_s, \nabla (u_s-S'_s)) \, dx \, ds \\& +
\sum_{j=1}^{\infty} \int_{0}^{t} \int_{\mathcal{O}}
\varphi_n^{\prime} (u_s(x)-S'_s(x)) \, \bar{h}_{j}( s,x, u_s-S'_s,\nabla (u_s-S'_s))\, dx dB_{s}^{j}\\
& + \frac{1}{2}\, \sum_{j=1}^{\infty} \int_{0}^{t}\int_{\mathcal{O}}
\varphi_n^{\prime \prime } (u_s(x)-S'_s(x)) \bar{h}_{j}^2(s,x,
u_s-S'_s,\nabla (u_s-S'_s)) \, dx\, ds\\&
+\int_0^t\int_{\ensuremath{\mathcal O}}\varphi_n^{\prime}(u_s(x)-S'_s(x))\nu(dxds) \, .\\
\end{split}$$ Since the support of $\nu$ is $\{u=S\}$, the last term is equal to $$\int_0^t\int_{\ensuremath{\mathcal O}}\varphi_n^{\prime}(S_s(x)-S'_s(x))\nu(dxds)$$and it is negative, because $$\int_0^t\int_{\ensuremath{\mathcal O}}\varphi_n^{\prime}(S_s(x)-S'_s(x)){{1} \hspace{-0.25 em}{\rm I}}_{\{\left|S-S'\right|\leq n\}}\nu(dxds)=l\int_0^t\int_{\ensuremath{\mathcal O}}sgn(S-S')\left|S_s(x)-S'_s(x)\right|^{l-1}\nu(dxds)\leq 0$$ and$$\begin{aligned}
\int_0^t\int_{\ensuremath{\mathcal O}}\varphi_n^{\prime}(S_s(x)&-&S'_s(x))I_{\{\left|S-S'\right|>n\}}\nu(dxds)\\&=&\int_0^t\int_{\ensuremath{\mathcal O}}n^{l-2}[l(l-1)(\left|S-S'\right|-n)sgn(S-S')+sgn(S-S')ln]\nu(dxds)\leq0\end{aligned}$$ By the uniform ellipticity of the operator $A$ we get $$\mathcal{E} \big(\varphi_n^{\prime} (u_s-S'_s), \, u_s-S'_s \big) \,
\geq \, \lambda \, \int_{{\ensuremath{\mathcal O}}} \varphi_n^{\prime \prime} (u_s-S'_s)
|\nabla (u_s-S'_s)|^2 \, dx.$$ Let $\epsilon >0$ be fixed. Using the Lipschitz condition on $\bar{f}$ and the properties of the functions $(\varphi_n)_n$ we get $$\begin{split} & |\varphi_n^{\prime} (u_s-S'_s)| \, |\bar{f}(s,x,u_s-S'_s, \nabla u_s-S'_s)| \\&
\leq \, |\varphi_n^{\prime} (u_s-S'_s)| \, \big( |\bar{f}^0 (s,x)| + C \, (|u_s-S'_s| +
|\nabla (u_s-S'_s)|)\, \big)\\
& \leq \, |\varphi_n^{\prime} (u_s-S'_s)||\bar{f}^0 (s,x)|+ |u_s-S'_s||\varphi_n^{\prime\prime}
(u_s-S'_s)| \, (C |u_s-S'_s| + C
|\nabla (u_s-S'_s)|)\, )\\
&\leq l (\varphi_n (u_s-S'_s) + 1) \, |\bar{f}^0(s,x) | + C|u_s-S'_s|^2|\varphi_n^{\prime\prime}
(u_s-S'_s)| +C|u_s-S'_s| |\nabla (u_s-S'_s)||\varphi_n^{\prime\prime}
(u_s-S'_s)|\\
& \leq l (\varphi_n (u_s-S'_s) + 1) \, |\bar{f}^0(s,x) | + (C +
c_{\epsilon})\, |u_s-S'_s|^2
\varphi_n^{\prime\prime}(u_s-S'_s) + \, \epsilon \varphi_n^{\prime\prime}(u_s-S'_s)|\nabla u_s-S'_s|^2 .\\
\end{split}$$ Now using Cauchy-Schwarz inequality and the Lipschitz condition on $\bar{g}$ we get $$\begin{split}
& \,\sum_{i=1}^d \varphi_n^{\prime\prime}(u_s-S'_s) \partial_i (u_s-S'_s)
\, \bar{g}_i (s,x,u_s-S'_s,\nabla (u_s-S'_s)) \\&\leq \, \varphi_n^{\prime\prime}(u_s-S'_s)
\, |\nabla (u_s-S'_s)|\, \big( |\bar{g}^0 (s,x)| + C|u_s-S'_s| +
\alpha |\nabla (u_s-S'_s)| \, \big) \, \\
& \leq \, \epsilon \, \varphi_n^{\prime\prime} (u_s-S'_s)
|\nabla (u_s-S'_s)|^2 + 2c_{\epsilon} \varphi_n^{\prime\prime} (u_s-S'_s)\, \big( K^2+
C^2|u_s-S'_s|^2\, \big)+ \alpha \, \varphi_n^{\prime\prime} (u_s-S'_s)|\nabla (u_s-S'_s)|^2 \\
& \leq l(l-1)c_{\epsilon}K^2 + 2c_{\epsilon}(K^2 + C^2 ) l (l-1)
|\varphi_n (u_s-S'_s)|+
(\alpha + \epsilon) \, \varphi_n^{\prime\prime} (u_s-S'_s)
|\nabla (u_s-S'_s)|^2. \\
\end{split}$$ In the same way as before $$\begin{split}&
\sum_{j=1}^{\infty} \varphi_n^{\prime \prime } (u_s-S'_s )
\bar{h}_{j}^2(s, u_s-S'_s,\nabla (u_s-S'_s))\\& \leq \,
\varphi_n^{\prime \prime } (u_s-S'_s)
\, \big( \, c'_{\epsilon}(|\bar{h}^0 (s,x)|+ C|u_s-S'_s|)^2 \, + \,
(1 + \epsilon)\beta^2 \, |\nabla (u_s-S'_s)|^2 \, \big) \\
&\leq \varphi_n^{\prime \prime } (u_s-S'_s)
\, \big(2c'_{\epsilon}K^2 \, +\, 2c'_{\epsilon}C^2 |u_s-S'_s |^2 + \,
(1 + \epsilon)\beta^2 \, |\nabla (u_s-S'_s)|^2 \, \big)\\
& \leq \, 2c'_{\epsilon} l (l-1)K^2 + 2c'_{\epsilon}( K^2 +C^2 )l (l-1) \varphi_n(u_s -S'_s)
+ (1 + \epsilon) \, \beta^2\, \varphi_n^{\prime \prime }(u_s-S'_s)|\nabla (u_s-S'_s)|^2.
\end{split}$$ Thus taking the expectation, we deduce $$\label{e6}
\begin{split}
&E \, \int_{\mathcal{O}}\varphi_n (u_t (x)-S'_t(x)) \, dx + (\lambda
- \frac{1}{2}(1+ \epsilon)\beta^2 - (\alpha + 2 \epsilon) \, ) \, E
\, \int_0^t \int_{\mathcal{O}} \varphi_n^{\prime \prime} (u_s -S'_s)
\,
|\nabla( u_s-S'_s) |^2 \, dx \, ds \\
& \, \leq \, l(l-1)c''_{\epsilon} K^2 \, + \, c''_{\epsilon} l
(l-1)\big( K^2 +C^2+C+ c_{\epsilon}\big)
E \, \int_0^t \int_{\mathcal{O}} \varphi_n (u_s(x) -S'_s(x))\, dx \, ds. \\
\end{split}$$ On account of the contraction condition, one can choose $ \epsilon
> 0 $ small enough such that $$\lambda - \frac{1}{2}(1+
\epsilon)\beta^2 - (\alpha + 2 \epsilon)>0$$ and then $$\begin{split}
E\, \int_{\mathcal{O}} \varphi_n (u_t (x)-S'_t(x)) \, dx &
\leq \, c K^2 l (l-1) \, + \, cl (l-1)
E \, \int_0^t \int_{\mathcal{O}} \varphi_n (u_s (x)-S'_s(x))\, dx \, ds \, .\\
\end{split}$$ We obtain by Gronwall’s Lemma, that $$\label{varphi1}
\begin{split}
E\, \int_{\mathcal{O}} \varphi_n (u_t (x)-S'_t(x)) \, dx &
\leq \, c\,K^2 l (l-1) \, \exp{ \big( c \, l (l-1)\,t \big) }\\
\end{split}$$ and so it is now easy from (\[e6\]) to get $$\label{varphi2}
\begin{split}
E \, \int_0^t \int_{\mathcal{O}} \varphi_n^{\prime \prime} (u_s (x)-S'_s(x)) \,
|\nabla (u_s-S'_s) |^2 \, dx \, ds \, \leq \,
c^{\prime}\, K^2 l \, (l-1) \, \exp{ \big( c l (l-1)\,t \big)}.\\
\end{split}$$ Finally, letting $ n \to \infty $ by Fatou’s lemma we deduce (\[uS’l\]) and (\[nablauS’l\]).\
Then with (\[uS’Itô’s\]), we know that $$-\int_0^t\int_{\ensuremath{\mathcal O}}\varphi'_n(u_s-S'_s)\nu(dxds)=-\int_0^t\int_{\ensuremath{\mathcal O}}\varphi'_n(S_s-S'_s)\nu(dxds)\leq C.$$ This yields (\[nuS’l\]) by Fatou’s lemma.
With the help of Lemma \[estimateul\], we are able to prove the following Itô formula:
\[Lp\] Assume the hypotheses of the previous lemma. Let $(u,\nu)$ be the solution of the problem (\[SPDEO\]). Then for $
l\geq2$, we get the following Itô’s formula, $ P$-almost surely, for all $t\in [0,T]$, $$\label{LpIt\^o's}
\begin{split}
& \int_{\mathcal{O}}\left| u_t (x)-S'_t(x) \right|^l \, dx +
\int_0^t {\ensuremath{\mathcal E}}\, \big(l\, (u_s-S'_s)^{l -1}sgn(u_s-S'_s) , \,
u_s-S'_s \big) \, ds =
\int_{\mathcal{O}} \left|\xi (x)-S'_0(x) \right|^l \, dx \\
& +l\int_{0}^{t}\int_{\mathcal{O}}sgn(u_s-S'_s)
\left|u_s (x)-S'_s(x) \right|^{l-1} \bar{f} (s,x, u_s-S'_s,\nabla (u_s-S'_s)) \, dx ds\\
& -l (l-1) \, \sum_{i=1}^{d} \,\int_{0}^{t} \int_{\mathcal{O}} \left|u_s
(x)-S'_s(x) \right|^{l -2}
\partial_i (u_{s}(x)-S'_s(x))\, \bar{g}_{i} (s, x,u_s-S'_s,\nabla (u_s-S'_s)) \, dx \, ds \\
& + l \, \sum_{j=1}^{\infty} \int_{0}^{t}
\int_{\mathcal{O}}sgn(u_s-S'_s)
\, \left|u_s (x)-S'_s(x) \right|^{l-1}\bar{h}_{j}( s,x, u_s-S'_s,\nabla (u_s-S'_s))\, dx dB_{s}^{j}\\
& + \frac{l (l-1)}{2}\, \sum_{j=1}^{\infty}
\int_{0}^{t}\int_{\mathcal{O}}
\left|u_s (x)-S'_s(x) \right|^{l-2} \bar{h}_{j}^2(s,x, u_s-S'_s,\nabla (u_s-S'_s)) \, dx\, ds\\&+l\int_{0}^{t}\int_{\mathcal{O}}sgn(u_s-S'_s)
\left|u_s (x)-S'_s(x) \right|^{l-1} \nu(dx\, ds)\, .\\
\end{split}$$
From Itô’s formula (see Theorem 5 in [@DMZ12]), with the same notations as in the previous lemma, we have $ P$-almost surely, and for all $t\in [0,T]$ and all $ n \in {{\ensuremath{\mathbb N}} }^*$, $$\begin{split}
& \int_{\mathcal{O}} \varphi_n (u_t (x)-S'_t(x)) \, dx \; + \;
\int_0^t \mathcal{E} \big(\varphi_n^{\prime} (u_s-S'_s), \, u_s-S'_s
\big) \, ds = \int_{\mathcal{O}} \varphi_n (\xi(x)-S'_0(x) ) \, dx
\\ & + \int_{0}^{t}\int_{\mathcal{O}}
\varphi_n^{\prime}(u_s(x)-S'_s(x)) \bar{f} (s,x, u_s-S'_s,\nabla (u_s-S'_s)) \, dx ds \\
& - \sum_{i=1}^{d} \int_{0}^{t} \int_{\mathcal{O}}
\varphi_n^{\prime \prime } (u_s(x)-S'_s(x) )
\partial_i (u_s(x)-S'_s(x)) \, \bar{g}_{i} (s,x,u_s-S'_s, \nabla (u_s-S'_s)) \, dx \, ds \\& +
\sum_{j=1}^{\infty} \int_{0}^{t} \int_{\mathcal{O}}
\varphi_n^{\prime} (u_s(x)-S'_s(x)) \, \bar{h}_{j}( s,x, u_s-S'_s,\nabla (u_s-S'_s))\, dx dB_{s}^{j}\\
& + \frac{1}{2}\, \sum_{j=1}^{\infty} \int_{0}^{t}\int_{\mathcal{O}}
\varphi_n^{\prime \prime } (u_s(x)-S'_s(x)) \bar{h}_{j}^2(s,x,
u_s-S'_s,\nabla (u_s-S'_s)) \, dx\, ds\\&
+\int_0^t\int_{\ensuremath{\mathcal O}}\varphi_n^{\prime}(u_s(x)-S'_s(x))\nu(dxds) \, .\\
\end{split}$$ Therefore, passing to the limit as $ n \to \infty $, the convergences come from the Lemma \[estimateul\] and the dominated convergence theorem.
From now on, we assume the following stronger hypothesis:$$\label{alphabet}\alpha+\frac{1}{2}\beta^2+72\beta^2<\lambda.$$ At this stage, the idea is to adapt the Moser iteration technics to our setting. To this end, in order to control uniformly the $L^l$ norms and make $l$ tend to $+\infty$, we introduce for each $l\geq2$, the processes $v$ and $v'$ given by $$\begin{split}
\label{v} v_t :&=\sup _{s\leq t}\left( \int_{{\ensuremath{\mathcal O}}}\left|
u_s-S'_s\right|^l dx +\gamma l\left( l-1\right)
\int_0^s\int_{{\ensuremath{\mathcal O}}}\left| u_r-S'_r\right|
^{l-2}\left| \nabla( u_r-S'_r)\right| ^2\, dx\, dr\right), \\
v_t^{\prime } :&=\int_{{\ensuremath{\mathcal O}}}\left| \xi-S'_0 \right| ^l\, dx+l^2 c_1
\left\| \left| u-S'\right| ^l\right\| _{1,1;t} +l\left\|
\bar{f}^0\right\| _{\theta ,t}^{*}\left\| \left| u-S'\right|
^{l-1}\right\| _{\theta ;t} \\&\quad+ l^2 \left( c_2\left\|
|\bar{g}^0 |^2\right\| _{\theta;t}^{*}
+ c_3\left\| |\bar{h}^0 |^2\right\| _{\theta ;t}^{*}\right) \left\|
\left| u-S'\right|^{l-2}\right\|_{\theta ;t},\\
\end{split}$$ where the constants are given by $$\label{const}
\begin{split}
& \gamma =\lambda -\alpha -\frac{\epsilon l}{l-1}-\frac{1+\epsilon }{2} \beta ^2\\
& c_1=\frac {C}{2} \left( 1+\frac{C}{4\epsilon }\right)
+\frac{3+2\epsilon }{ 2\epsilon}C^2+3\frac{1+\epsilon}{\epsilon^2}C^2\\
& c_2=\frac 1{2\epsilon } \quad \mbox{and} \quad c_3=\frac{\left(
3+\epsilon
\right) \left( 1+\epsilon \right) }{\epsilon} \\
\end{split}$$ The main difficulty in the stochastic case is to control the martingale part. We start by estimating the bracket of the local martingale in $$M_t := l \sum_{j=1}^{\infty}
\int_{0}^{t} \int_{\mathcal{O}}sgn(u_s-S'_s)
\,\left| u_s (x)-S'_s(x)\right|^{l-1}\bar{h}_{j}( s,x, u_s-S'_s,\nabla (u_s-S'_s))\, dx
dB_{s}^{j}$$
\[bracket\] For arbitrary $\varepsilon >0,$ one has
$$\label{e5}
\begin{split}
\left\langle M\right\rangle _t^{\frac 12}& \le \varepsilon
v_t+\frac{l^2}{ 2\varepsilon }\left( \frac{1+\varepsilon}\varepsilon
\left\| |\bar{h}^0 |^2\right\| _{\theta ;t}^{*}\left\| \left|
u-S'\right| ^{l-2}\right\| _{\theta ;t}+\frac{ 1+\varepsilon
}\varepsilon C^2\left\| \left| u-S'\right| ^l\right\|
_{1,1;t}\right) \\
& + \sqrt{1+\varepsilon }\sqrt{\frac l{l-1}}\frac \beta {\sqrt{\gamma }}v_t \, .
\end{split}$$
The proof is the same as Lemma 12 in [@DMS05] replacing $u$ by $u-S'$ and also $h$ by $\bar{h}$.
In what follows we will use the notion of domination, which is essential to handle the martingale part. We recall the definition from Revuz and Yor [@RevuzYor].
A non-negative, adapted right continuous process $X$ is dominated by an increasing process $A$, if $$E \, \big[X_{\rho} \,] \, \leq \, E \, \big[A_{\rho} \,]$$ for any bounded stopping time, $ \rho$.
One important result related to this notion is the following domination inequality (see Proposition IV.4.7 in Revuz-Yor, p. 163), for any $ k\in ]0,\, 1[$, $$\label{domination} E \big[ (X_\infty^*)^k \, \big] \, \leq \, C_k\,
E \big[ (A_\infty )^k \, \big]$$ where $ C_k$ is a positive constant and $ X_t^* := \sup_{ s \leq
t} |X_s|$.\
We will also use the fact that if $A,A^{\prime }$ are increasing processes, then the domination of a process $X$ by $A$ is equivalent to the domination of $X+A^{\prime }$ by $A+A^{\prime }.$
\[tau\] The Process $ \tau v$ is dominated by the process $
v'$ where $$\tau =1-6\epsilon -6\sqrt{1+\epsilon }\sqrt{\frac l{l-1}}\frac{\beta} {\sqrt{ \gamma }}.$$ In other words, we have $$\begin{split}
& \tau \, E \sup _{0 \leq s\leq t}\left( \int_{{\ensuremath{\mathcal O}}}\left|
u_s-S'_s\right|^l\, dx +\gamma l\left( l-1\right)
\int_0^s\int_{{\ensuremath{\mathcal O}}}\left| u_r-S'_r\right| ^{l-2}\left| \nabla
(u_r-S'_r)\right| ^2dx dr\right) \\& \leq E \int_{{\ensuremath{\mathcal O}}}\left|
\xi-S'_0 \right|^l dx \, +\, l^2c_1 E \, \left\| \left| u-S'\right|
^l\right\| _{1,1;t} +l E \left\| \bar{f}^0\right\| _{\theta
,t}^{*}\left\| \left| u-S'\right| ^{l-1}\right\| _{\theta
;t}\\&\quad+ \, l^2 E \, \left( c_2 \left\| |\bar{g}^0 |^2\right\|
_{\theta ;t}^{*}+c_3\left\| |\bar{h}^0 |^2 \right\| _{\theta
;t}^{*}\right) \left\| \left| u-S'\right|^{l-2}\right\|_{\theta ;t},
\end{split}$$ where $ \gamma, \; c_1, \, c_2 $ and $ c_3$ are the constants given above.
Starting from the relation (\[LpItô’s\]): $$\begin{split}
& \int_{\mathcal{O}}\left| u_t (x)-S'_t(x) \right|^l \, dx +
\int_0^t {\ensuremath{\mathcal E}}\, \big(l\, (u_s-S'_s)^{l -1}sgn(u_s-S'_s) , \,
u_s-S'_s \big) \, ds =
\int_{\mathcal{O}} \left|\xi (x)-S'_0(x) \right|^l \, dx \\
& +l\int_{0}^{t}\int_{\mathcal{O}}sgn(u_s-S'_s)
\left|u_s (x)-S'_s(x) \right|^{l-1} \bar{f} (s,x, u_s-S'_s,\nabla (u_s-S'_s)) \, dx ds\\
& -l (l-1) \, \sum_{i=1}^{d} \,\int_{0}^{t} \int_{\mathcal{O}} \left|u_s
(x)-S'_s(x) \right|^{l -2}
\partial_i (u_{s}(x)-S'_s(x))\, \bar{g}_{i} (s, x,u_s-S'_s,\nabla (u_s-S'_s)) \, dx \, ds \\
& + l \, \sum_{j=1}^{\infty} \int_{0}^{t}
\int_{\mathcal{O}}sgn(u_s-S'_s)
\, \left|u_s (x)-S'_s(x) \right|^{l-1}\bar{h}_{j}( s,x, u_s-S'_s,\nabla (u_s-S'_s))\, dx dB_{s}^{j}\\
& + \frac{l (l-1)}{2}\, \sum_{j=1}^{\infty}
\int_{0}^{t}\int_{\mathcal{O}}
\left|u_s (x)-S'_s(x) \right|^{l-2} \bar{h}_{j}^2(s,x, u_s-S'_s,\nabla (u_s-S'_s)) \, dx\, ds\\&+l\int_{0}^{t}\int_{\mathcal{O}}sgn(u_s-S'_s)
\left|u_s (x)-S'_s(x) \right|^{l-1} \nu(dx\, ds)\, ,\ \ \ a.s.\\
\end{split}$$ The last term is negative: from the condition of minimality, we have the following relation, $$\begin{aligned}
&&\int_{0}^{t}\int_{\mathcal{O}}sgn(u_s-S'_s)
\left|u_s (x)-S'_s(x) \right|^{l-1} \nu(dxds)\\&=&\int_{0}^{t}\int_{\mathcal{O}}sgn(S_s-S'_s)
\left|S_s (x)-S'_s(x) \right|^{l-1} \nu(dxds)\leq0.\end{aligned}$$ Then we can do the same calculus as in the proof of Lemma 14 in [@DMS05], replacing $u$ by $u-S'$ and $f$, $g$, $h$ by $\bar{f}$, $\bar{g}$, $\bar{h}$ respectively.
The proofs of the next 3 lemmas are similar to the proofs of Lemmas 15, 16 and 17 in [@DMS05], just replacing $u$ by $u-S'$ and replacing $f$, $g$ and $h$ by $\bar{f}$, $\bar{g}$ and $\bar{h}$ respectively.
\[sob\]
The process $v$ satisfies the estimate$$v_t\ge \delta \left\| \left| u-S'\right| ^l\right\| _{0;t}$$ with $\delta = 1 \wedge \left(2c_S^{-1} \gamma\right) ,$ where $c_S$ is the constant in the Sobolev inequality (\[Sobolev\]).
\[sup\] The process $$w_t :=\left[ \left\| \left| u-S'\right| ^{\sigma l}\right\| _{\theta
;t}^{\frac 1\sigma }\vee \left\| \xi-S'_0\right\| _\infty ^l\vee
\left\| \bar{f}^0\right\| _{\theta ;t}^{l} \vee \left\| |\bar{g}^0
|^2\right\| _{\theta ;t}^{*\frac{l}{2}}\vee \left\| |\bar{h}^0 |^2
\right\| _{\theta ;t}^{*\frac{l}{2}}\right]$$ is dominated by the process $$w_t^{\prime }:=6k\left( t\right) l^2\left[ \left\| \left|
u-S'\right| ^{l}\right\| _{\theta ;t}\vee \left\| \xi -S'_0\right\|
_\infty ^l\vee \left\| \bar{f}^0\right\| _{\theta ;t}^{l}\vee
\left\| |\bar{g}^0 |^2 \right\| _{\theta ;t}^{*\frac{l}{2}}\vee
\left\| |\bar{h}^0 |^2 \right\| _{\theta ;t}^{*\frac{l}{2}}\right] ,$$ where $ \sigma = \frac{d + 2\theta}{d}$ and $k:{{\ensuremath{\mathbb R}} }_{+}\rightarrow
{{\ensuremath{\mathbb R}} }_{+}$ is a function independent of $l$, depending only on the structure constants.
[\[estimev\]]{} There exists a function $k_1:{{\ensuremath{\mathbb R}} }_{+}\times {{\ensuremath{\mathbb R}} }_{+}\rightarrow
{{\ensuremath{\mathbb R}} }_{+}$ which involves only the structure constants of our problem and such that the following estimate holds$$Ev_t\le k_1\left( l,t\right) E\left( \int_{{\ensuremath{\mathcal O}}}\left| \xi-S'_0
\right| ^l dx +\left\| \bar{f}^0\right\| _{\theta ;t}^{*l}+\left\|
|\bar{g}^0 |^2 \right\| _{\theta ;t}^{*\frac{l}{2}}+\left\|
|\bar{h}^0 |^2 \right\| _{\theta ;t}^{*\frac{l}{2}}\right) .$$
We now prove Theorem \[LPESTIM\] in the case where $\xi$, $\bar{f}^0$, $\bar{g}^0$ and $\bar{h}^0$ are uniformly bounded:\
We set $l=p\sigma ^n,$ with some $n\in {{\ensuremath{\mathbb N}} }^*.$ By Lemma \[sup\] and the domination inequality (\[domination\]) we deduce, for $n\ge 1,$$$\begin{split}
& E\left( \left\| \left| u-S'\right| ^{\sigma l}\right\| _{\theta
;t}^{\frac 1\sigma }\vee \left\| \xi-S'_0 \right\| _\infty ^l\vee
\left\| \bar{f}^0\right\| _{\theta ;t}^{*l}\vee \left\| |\bar{g}^0
|^2\right\| _{\theta ;t}^{*\frac{l}{2}}\vee \left\| |\bar{h}^0
|^2\right\| _{\theta
;t}^{*\frac{l}{2}}\right) ^{\frac 1{\sigma ^n}}\\
& \leq \, C_{\sigma ^{-n}}\left( 6k\left( t\right) l^2\right)
^{\frac 1{\sigma ^n}}E\left( \left\| \left| u-S'\right| ^l\right\|
_{\theta ;t}\vee \left\| \xi-S'_0 \right\| _\infty ^l\vee \left\|
\bar{f}^0\right\| _{\theta ;t}^{*l}\vee \left\| |\bar{g}^0
|^2\right\| _{\theta ;t}^{*\frac{l}{2}}\vee \left\| |\bar{h}^0
|^2\right\| _{\theta ;t}^{*\frac{l}{2}}\right) ^{\frac 1{\sigma
^n}},
\end{split}$$ where $C_{\sigma ^{-n}}$ is the constant in the domination inequality. This constant is estimated by $$C_{\sigma ^{-n}}\le \sigma ^{\frac n{\sigma ^n}}\left( 1-\frac
1{\sigma ^n}\right) ^{-1}.$$ (See the exercise IV.4.30 in Revuz -Yor, p. 171). So let us denote by $$a_n :=\left\| \left| u-S'\right| ^{p\sigma ^n}\right\| _{\theta
;t}^{\frac 1{\sigma ^n}}\vee \left\| \xi-S'_0 \right\| _\infty
^p\vee \left\| \bar{f}^0\right\| _{\theta ;t}^{*p}\vee \left\|
|\bar{g}^0|^2\right\| _{\theta ;t}^{*\frac{p}{2}}\vee \left\|
|\bar{h}^0|^2\right\| _{\theta ;t}^{*\frac{p}{2}}$$ and deduce from the above inequality the following one$$Ea_{n+1}\le \sigma ^{\frac n{\sigma ^n}}\left( 1-\frac 1{\sigma
^n}\right) ^{-1}\left( 6k\left( t\right) \left( p\sigma ^n\right)
^2\right) ^{\frac 1{\sigma ^n}}Ea_n.$$ Iterating this relation $n$ times we get$$Ea_{n+1}\le \sigma ^{3\sum_{m=1}^n\frac m{\sigma
^m}}\prod_{m=1}^n\left( 1-\frac 1{\sigma ^m}\right) ^{-1}\left(
6k\left( t\right) p^2\right) ^{\sum_{m=1}^n\frac 1{\sigma ^m}}Ea_1.$$ Now we shall let $n$ tend to infinity in this relation. Since in general one has$$\lim _{q,q^{\prime }\rightarrow \infty }\left\| F\right\|
_{q,q^{\prime };t}=\left\| F\right\| _{\infty ,\infty ;t},$$ for any function $F:{{\ensuremath{\mathbb R}} }_{+}\times {\ensuremath{\mathcal O}}\rightarrow {{\ensuremath{\mathbb R}} },$ it is easy to see that $ \lim _{n \to \infty} \left\| \left| u-S'\right|
^{p\sigma ^n}\right\| _{\theta ;t}^{\frac 1{\sigma ^n}}=\left\|
u-S'\right\| _{\infty ,\infty ;t}^p.\,$\
Therefore we have $$\lim_{n \to \infty} a_n=\left\| u-S'\right\| _{\infty ,\infty
;t}^p\vee \left\| \xi-S'_0\right\| _\infty ^p\vee \left\|
\bar{f}^0\right\| _{\theta ;t}^{*p}\vee \left\| |\bar{g}^0 |^2
\right\| _{\theta ;t}^{*\frac{p}{2}}\vee \left\| |\bar{h}^0
|^2\right\| _{\theta ;t}^{*\frac{p}{2}},$$ which implies $$E\left\| u-S'\right\| _{\infty ,\infty ;t}^p\le \rho \left( t\right)
Ea_1,$$ with $$\rho \left( t\right) =\sigma ^{3\sum_{m=1}^\infty \frac m{\sigma
^m}}\prod_{m=1}^\infty \left( 1-\frac 1{\sigma ^m}\right)
^{-1}\left( 5k\left( t\right) p^2\right) ^{\sum_{m=1}^\infty \frac
1{\sigma ^m}}.$$ Now we estimate $Ea_1$ by using the fact that $\delta \left\| \left|
u-S'\right| ^{p\sigma }\right\| _{\theta ;t}^{\frac 1\sigma }\le
v_t,$ with $p$ replacing $l$ in the expression of $v.$ So we have$$\begin{split} Ea_1& =E\left( \left\| \left| u-S'\right| ^{p\sigma }\right\|
_{\theta ;t}^{\frac 1\sigma }\vee \left\| \xi-S'_0\right\| _\infty
^p\vee \left\| \bar{f}^0\right\| _{\theta ;t}^{*p}\vee \left\|
|\bar{g}^0 |^2 \right\| _{\theta ;t}^{*\frac{p}{2}}\vee \left\|
|\bar{h}^0 |^2\right\|
_{\theta ;t}^{*\frac{p}{2}}\right)\\
&\leq E\left( \delta ^{-1}v_t+\left\| \xi-S'_0 \right\|
_\infty ^p+\left\| \bar{f}^0\right\| _{\theta ;t}^{*p}+\left\|
|\bar{g}^0 |^2 \right\| _{\theta ;t}^{*\frac{p}{2}}\vee \left\|
|\bar{h}^0 |^2\right\| _{\theta ;t}^{*\frac{p}{2}}\right) .
\end{split}$$ Finally one deduces the following estimate by applying Lemma \[estimev\] with $l=p$: $$\label{Maxestimate}
E\left\| u-S'\right\| _{\infty ,\infty ;t}^p\le k_2\left(
t\right) E\left( \left\| \xi-S'_0\right\| _\infty ^p+\left\|
\bar{f}^0\right\| _{\theta ,t}^{*p}+\left\| |\bar{g}^0 |^2 \right\|
_{\theta ;t}^{*p/2}+\left\| |\bar{h}^0 |^2\right\| _{\theta
;t}^{*p/2}\right).$$
Moreover (see Theorem 11 [@DMS05]), we have $$\begin{aligned}
E\left\|S'\right\|_{\infty,\infty;t}^p\leq
k(t)E\left(\left\|S'_0\right\|_\infty^p+\left\|f'\right\|_{\theta;t}^{*p}+\left\||g'|^2\right\|_{\theta;t}^{*p/2}+\left\||h'|^2\right\|_{\theta;t}^{*p/2}\right)\end{aligned}$$
Hence, $$\begin{split}E\left\|
u\right\|^p_{\infty,\infty;t}&\leq
c(p)(E\left\|u-S'\right\|_{\infty,\infty;t}^p+E\left\|S'\right\|_{\infty,\infty;t}^p)\\&\leq
c(p)k(t)E\big(\left\|\xi\right\|_\infty^p+\left\|S'_0\right\|_\infty^p+\left\|f'\right\|_{\theta;t}^{*p}+\left\||g'|^2\right\|_{\theta;t}^{*p/2}+\left\||h'|^2\right\|_{\theta;t}^{*p/2}\\&\quad+\left\|\bar{f}^0\right\|_{\theta;t}^{*p}+\left\||\bar{g}^0|^2\right\|_{\theta;t}^{*p/2}+\left\||\bar{h}^0|^2\right\|_{\theta;t}^{*p/2}\big).\end{split}$$ This ends the proof of Theorem \[LPESTIM\] in this particular case where $\xi$, $\bar{f}^0$, $\bar{g}^0$ and $\bar{h}^0$ are uniformly bounded. We now turn out to the general case.
Proof of Theorem \[LPESTIM\] in the general case {#casgen}
------------------------------------------------
We now assume that [**(H)**]{}, [**(O)**]{}, [**(HI$\mathbf{2p}$)**]{}, [**(HO$\mathbf{\infty p}$)**]{} and [**(HD$\mathbf{\theta p}$)**]{} hold. We are going to prove Theorem \[LPESTIM\] in the general case by using an approximation argument. For this, for all $n\in{{\mathbb{N}}^{\ast}}$, $1\leq i\leq d ,1\leq j\leq\infty$ and all $(t,w,x,y,z)$ in ${\mathbb{R}}^+ \times\Omega\times{\ensuremath{\mathcal O}}\times{\mathbb{R}}\times{\mathbb{R}}^d$, we set $$\begin{aligned}
\label{approximation}
\bar{f}_n (t,w,x,y,z)&=& \bar{f}(t,w,x,y,z) -\bar{f}^0 (t,w,x) +\bar{f}^0 (t,w,x)\cdot{\bf 1}_{\{ |\bar{f}^0 (t,w,x)|\leq n\}}\nonumber\\
\bar{g}_{i,n}(t,w,x,y,z)&=& \bar{g}_i (t,w,x,y,z) -\bar{g}_i^0 (t,w,x) +\bar{g}_i^0 (t,w,x)\cdot{\bf 1}_{\{ |\bar{g}_i^0 (t,w,x)|\leq n\}}\nonumber\\
\bar{h}_{j,n}(t,w,x,y,z)&=& \bar{h}_j (t,w,x,y,z) -\bar{h}_j^0
(t,w,x) +\bar{h}_j^0 (t,w,x)\cdot{\bf 1}_{\{ |\bar{h}_j^0
(t,w,x)|\leq n\}}\nonumber\\\xi_n (w,x)&=& \xi (w,x)\cdot {\bf
1}_{\{ |\xi(\omega, x)|\leq n\}}\end{aligned}$$ One can check that for all $n$, $\bar{f}_n$, $\bar{g}_n$, $\bar{h}_n$ and $\xi^n-S'_0$ satisfy all the assumptions of the Step 1 of the proof, and that Lipschitz constants do not depend on $n$. And the obstacle $S-S'$ is controlled by 0, which obviously satisfies [**(HO2)**]{}. For each $n\in{{\mathbb{N}}^{\ast}}$, we put $(\bar{u}^n,\nu^n)={\ensuremath{\mathcal R}}(\xi^n-S'_0,\bar{f}^n,\bar{g}^n,\bar{h}^n,S-S')$ and we know that $\bar{u}^n$ satisfies the estimate of Step 1. We are now going to prove that $(\bar{u}^n,\, \nu^n)$ converges to $(\bar{u},\nu)={\ensuremath{\mathcal R}}(\xi-S'_0,\bar{f},\bar{g},\bar{h},S-S')$.\
Let us fix $n\leq m$ in ${{\mathbb{N}}^{\ast}}$ and put $\bar{u}^{n,m} :=\bar{u}^n -\bar{u}^m$ and $\nu^{n,m}:=\nu^n-\nu^m$ We first note that $\bar{u}^{n,m}$ satisfies the equation$$\begin{split}
d\bar{u}_t^{n,m}\left( x\right) +A\bar{u}_t^{n,m}\left( x\right)
dt &=\bar{f}_{n,m}\left( t,x,\bar{u}_t^{n,m}\left( x\right) ,\nabla
\bar{u}_t^{n,m}\left( x\right) \right) dt \\
&\quad -\sum_{i=1}^d\partial _i\bar{g}_{i,n,m}\left(
t,x,\bar{u}_t^{n,m}\left( x\right) ,\nabla \bar{u}_t^{n,m}\left(
x\right) \right) dt\\& \quad
+\sum_{j=1}^{\infty}\bar{h}_{j,n,m}\left( t,x,\bar{u}_t^{n,m}\left(
x\right) ,\nabla \bar{u}_t^{n,m}\left( x\right) \right) dB_t^j +
\nu^{n,m}(x,\, dt)
\end{split}$$
where $$\begin{split}
\bar{f}_{n,m}\left( t,w,x,y,z\right) & =\bar{f}\left(
t,w,x,y+\bar{u}_t^m\left( x\right) ,z+\nabla \bar{u}_t^m\left(
x\right) \right) -\bar{f}\left(
t,w,x,\bar{u}_t^m\left( x\right) ,\nabla \bar{u}_t^m\left( x\right) \right) \\
& \quad +\bar{f}_n^0\left( t,w,x\right) -\bar{f}_m^0\left(
t,w,x\right)
\end{split}$$ and $\bar{g}_{i,n,m},\bar{h}_{j,n,m}$ have similar expressions. Clearly one has $$\bar{f}_{n,m}\left( t,w,x,0,0\right) =\bar{f}_n^0\left( t,w,x\right)
-\bar{f}_m^0\left( t,w,x\right) :=\bar{f}_{n,m}^0\left( t,w,x\right)$$ and some similar relations for $\bar{g}_{i,n,m}\left(
t,w,x,0,0\right) $ and $ \bar{h}_{j,n,m}\left( t,w,x,0,0\right) .$ On the other hand, one can easily verify that
$$\begin{split}
& E\left\| \xi _n-\xi \right\| _\infty ^p\longrightarrow 0,\quad
\quad \quad E\left\|
\bar{f}_n^0-\bar{f}^0\right\| _{\theta;T}^{*p}\longrightarrow 0, \\
& E\left\|\bar{g}_n^0-\bar{g}^0\right\| _{\theta ;T}^{*p}
\longrightarrow 0,\qquad E\left\|\bar{h}_n^0-\bar{h}^0\right\|
_{\theta;T}^{*p}\longrightarrow 0.
\end{split}$$
By Lemma \[estimvdiff\] with $l=2$ (see Appendix) we deduce that $$\label{unum}
E\left\| \bar{u}^n-\bar{u}^m\right\| _T^2 \longrightarrow 0,\quad
as\ n,\, m\rightarrow \infty .$$ Therefore, $(\bar{u}^n)$ has a limit $\bar{u}$ in ${\ensuremath{\mathcal H}}_T$.
We now study the convergence of $(\nu^n )$. Denote by $v^n$ the parabolic potential associated to $\nu^n$, and $z^n=\bar{u}^n-v^n$, so $z^n$ satisfies the following SPDE$$\begin{split}
dz_t^n (x) +
Az_t^n (x)dt &=\bar{f}_n (t,x,\bar{u}_t^n (x),\nabla \bar{u}_t^n (x))dt-\sum_{i=1}^d
\partial_i \bar{g}_{i,n}(t,x,\bar{u}_t^n(x),\nabla \bar{u}_t^n (x)
)dt\\
& + \sum_{j=1}^{\infty} \bar{h}_{j,n}(t,x,\bar{u}_t^n(x),\nabla \bar{u}_t^n(x))\, dB_t^j .\\
\end{split}$$ We define $z^{1,n}$ to be the solution of the following SPDE with initial value $\xi^n-S'_0$ and zero boundary condition: $$\begin{split}
dz_t^{1,n}(x) +Az_t^{1,n}(x)dt &=(\bar{f}_t (x,\bar{u}_t^n(x),\nabla
\bar{u}_t^n(x))-\bar{f}_t^0(x))dt-\sum_{i=1}^d \partial_i
(\bar{g}_{i,t}(x,\bar{u}_t^n(x),\nabla \bar{u}_t^n(x))\\&\ \ \ \
-\bar{g}^0_t(x))dt
+ \sum_{j=1}^{\infty} (\bar{h}_{j,t}(x,\bar{u}_t^n(x),\nabla \bar{u}_t^n(x))-\bar{h}_t^0(x))\, dB_t^j .\\
\end{split}$$ This is a linear SPDE in $z^{1,n}$, its solution uniquely exists and belongs to ${\ensuremath{\mathcal H}}_T$. Applying Itô’s formula to $(z^{1,n})^2$ and doing a classical calculation, we get: $$E\left\|z^{1,n}-z^{1,m}\right\|^2_T\leq CE\big(\left\|\xi^n-\xi^m\right\|_2^2+\left\|\bar{u}^n-\bar{u}^m\right\|^2_T\big)\rightarrow0,\quad as\ n,\ m\rightarrow\infty.$$ Then, we define $z^{2,n}$ to be the solution of the following SPDE with initial value $0$ and zero boundary condition: $$dz_t^{2,n}(x) +Az_t^{2,n}(x)dt =\bar{f}_n^0(t,x)dt-\sum_{i=1}^d
\partial_i \bar{g}_{i,n}^0(t,x))dt + \sum_{j=1}^{\infty}
\bar{h}_{j,n}^0(x)\, dB_t^j .$$ This is still a linear SPDE in $z^{2,n}$, its solution uniquely exists and from the proof of Theorem 11 in [@DMS05], we know that $$E\left\|z^{2,n}-z^{2,m}\right\|^2_T\leq CE\left(\left\|\bar{f}_{n,m}^0\right\|_{\theta;T}^{*2}+\left\|\left|\bar{g}_{n,m}^0\right|^2\right\|_{\theta;T}^{*}+\left\|\left|\bar{h}_{n,m}^0\right|^2\right\|_{\theta;T}^{*}\right) \rightarrow0, \quad as\ n,\ m\rightarrow\infty.$$ This yields: $$E\left\| z^n-z^m\right\| _T^2 \longrightarrow
0,\quad as \quad n,\, m\rightarrow \infty .$$ Hence, using (\[unum\]) and the fact that $\bar{u}^n =z^n+v^n$, we get: $$E\left\| v^n-v^m\right\| _T^2 \longrightarrow 0, \quad as\
n,\, m\rightarrow \infty .$$ Therefore, $(v^n)$ has a limit $v$ in ${\ensuremath{\mathcal H}}_T$. So, by extracting a subsequence, we can assume that $( v^n)$ converges to $v$ in $\mathcal K$ almost-surely. Then, it’s clear that $ v \in \mathcal
P$, and we denote by $\nu$ the random regular measure associated to the potential $v$. Moreover, we have $P$-a.s., $\forall\varphi\in{\ensuremath{\mathcal W}}_t^+$: $$\begin{aligned}
\int_0^t\int_{\ensuremath{\mathcal O}}\varphi(x,s)\nu(dxds)&=&\lim_{n\rightarrow\infty}\int_0^t\int_{\ensuremath{\mathcal O}}\varphi(x,s)\nu^n(dxds)\\&=&\lim_{n\rightarrow\infty}\int_0^t-(v^n_s,\frac{\partial\varphi_s}{\partial s})ds+\int_0^t{\ensuremath{\mathcal E}}(v^n_s,\varphi_s)ds\\&=&\int_0^t-(v_s,\frac{\partial\varphi_s}{\partial s})ds+\int_0^t{\ensuremath{\mathcal E}}(v_s,\varphi_s)ds.\end{aligned}$$
As a consequence of Lemma \[Lemme63\] in the Appendix, we know that $$E\left\| \bar{u}^n-\bar{u}^m\right\| _{\infty ,\infty ;T}^p
\longrightarrow 0.$$ Therefore, we can apply Proposition \[Lp\] to $\bar{u}^n$ and pass to the limit and so we obtain that this proposition remains valid in this case. Then, one can end the proof by repeating the first part of Step 1 starting from Proposition \[Lp\].\
We conclude thanks to the uniqueness of the solution of the obstacle problem ensuring that $\bar{u}$ is equal to $u-S'$. [$\hfill \Box$]{}
Maximum Principle for local solutions
=====================================
We now introduce the lateral condition on the boundary that we consider:
If $u$ belongs to ${\ensuremath{\mathcal H}}_{loc}$, we say that $u$ is non-negative on the boundary of ${\ensuremath{\mathcal O}}$ if $u^+$ belongs to ${\ensuremath{\mathcal H}}_T$ and we denote it simply: $u\leq0$ on $\partial{\ensuremath{\mathcal O}}$. More generally, if $M$ is a random field defined on $[0,T]\times {\ensuremath{\mathcal O}}$, we note $u\leq M$ on $\partial {\ensuremath{\mathcal O}}$ if $u-M\leq 0$ on $\partial{\ensuremath{\mathcal O}}$.
Itô’s formula for the positive part of a local solution
-------------------------------------------------------
The following proposition represents a key technical result which leads to a generalization of the estimates of the positive part of a local solution. Let $(u,\nu)\in\mathcal{R}_{loc}(\xi,f,g,h,S)$, denote by $u^+$ its positive part. For this we need the following notation:$$\label{f0+} \begin{split} &f^{u,0}=1_{\left\{ u>0\right\}
}f^0,\;g^{u,0}=1_{\left\{ u>0\right\} }g^0,\;h^{u,0}=1_{\left\{
u>0\right\} }h^0,\\
& f^{u,0+}=1_{\left\{ u>0\right\} }\left( f^0\vee 0\right) ,\;\xi
^{+}=\xi \vee 0.
\end{split}$$
\[Itô’slocalposi\] Assume that $\partial{\ensuremath{\mathcal O}}$ is Lipschitz and that $u^+$ belongs to ${\ensuremath{\mathcal H}}_T$, i.e. $u$ is non-positive on the boundary of ${\ensuremath{\mathcal O}}$ and that the data satisfy the following integrability conditions$$E\left\| \xi ^{+}\right\| _2^2<\infty ,\;E\left( \left\|
f^{u,0}\right\| ^*_{\theta;t}\right) ^2<\infty ,\;E\left\|
g^{u,0}\right\| _{2,2;t}^2<\infty ,\;E\left\| h^{u,0}\right\|
_{2,2;t}^2<\infty ,$$ for each $t\ge 0.$\
Let $\varphi
:{\mathbb{R}}\rightarrow {\mathbb{R}}$ be a function of class ${\cal
C}^2,$ which admits a bounded second order derivative and such that $\varphi ^{\prime }\left( 0\right) =0.$ Then the following relation holds, a.s., for each $t\in [0,T],$ $$\begin{aligned}
\label{It\^o'spositivepart}&&\int_\mathcal{O}\varphi(u_t^+(x))dx+\int_0^t\mathcal{E}(\varphi'(u_s^+),u_s^+)ds=\int_\mathcal{O}\varphi(\xi^+(x))dx+\int_0^t\int_{\ensuremath{\mathcal O}}\varphi'(u_s^+(x))f_s(x)dxds\nonumber\\&&-\sum_{i=1}^d\int_0^t\int_{\ensuremath{\mathcal O}}\varphi''(u_s^+(x))\partial_iu_s^+(x)g_s^i(x)dxds+\frac{1}{2}\int_0^t\int_{\ensuremath{\mathcal O}}\varphi''(u_s^+(x)){{1} \hspace{-0.25 em}{\rm I}}_{\{u_s>0\}}|h_s(x)|^2dxds\nonumber\\&&+\sum_{i=1}^\infty\int_0^t\int_{\ensuremath{\mathcal O}}\varphi'(u_s^+(x))h_s^j(x)dxdB_s^j+\int_0^t\int_\mathcal{O}\varphi'(u_s^+(x))\nu(dxds).\end{aligned}$$
We consider $\phi\in\mathcal{C}_c^\infty({\ensuremath{\mathcal O}}),\ 0\leq\phi\leq1$, and put $$\forall t\in[0,T],\quad w_t=\phi u_t.$$
A direct calculation yields the following relation: $$dw_t=Lw_tdt+\bar{f}_tdt+\sum_{i=1}^d\partial_i\widetilde{g_{i,t}}dt+\sum_{j=1}^\infty\widetilde{h_{j,t}}dB_t^j+\phi\nu(x,dt)$$ where $$\bar{f}_t=\phi f_t-\sum a_{i,j}(\partial_i\phi)(\partial_j
u_t)-\sum(\partial_i\phi)g_{i,t}\, ,$$ $$\widetilde{g_{i,t}}=\phi g_{i,t}-u_t\sum a_{i,j}\partial_j\phi\, ,\quad\widetilde{h_{j,t}}=\phi h_{j,t}\, .$$
Now we prove that $\phi\nu$ is a regular measure:\
We know that: $$\label{regularmeas}\forall\varphi\in\mathcal{W}_T^+,\quad\int(-\frac{\partial\varphi_s}{\partial s},v_s)ds
+\int\mathcal{E}(\varphi_s,v_s)ds=\int\int\varphi(s,x)d\nu.$$ We replace $\varphi$ by $\phi\varphi$ in (\[regularmeas\]), where $\phi$ is the same as before, and we obtain the following relation: $$\int(-\frac{\partial\phi\varphi_s}{\partial s},v_s)ds+\int\mathcal{E}(\phi\varphi_s,v_s)ds=\int\int\phi\varphi(s,x)d\nu$$ note that $\phi$ does not depend on $t$ and by a similar calculation as before, we get $$\int(-\frac{\partial\varphi_s}{\partial s},\phi v_s)ds+\int\mathcal{E}(\varphi_s, \phi v_s)ds+\int(K_s,\varphi_s)ds-\int(k_s,\nabla\varphi_s)ds
=\int\int\varphi(s,x)d\phi\nu$$ where $$K_t=\sum
a_{i,j}(\partial_i\phi)(\partial_j v_t),\quad k_t=v_t\sum
a_{i,j}\partial_j\phi.$$ We denote by $\bar{z}$ the solution of the following PDE with Dirichlet boundary condition and the initial value $0$: $$d\bar{z}_t+A\bar{z}_tdt=K_tdt+div k_tdt.$$ If we set $\bar{v}=\phi v+\bar{z}$, then $\bar{v}$ satisfies the following relation: $$\int_0^t(-\frac{\partial\varphi_s}{\partial s},\bar{v}_s)ds+\int_0^t\mathcal{E}(\varphi_s,\bar{v}_s)ds=\int_0^t\int_{\ensuremath{\mathcal O}}\varphi(x,s)d\phi\nu.$$ It is easy to verify that $\bar{v}\in\mathcal{P}$. Thus $\phi\nu$ is a regular measure associated to $\bar{v}$.\
Hence, we deduce that $(\phi u,\phi\nu)$ satisfies an OSPDE with $\phi\xi$ as initial data and zero Dirichlet boundary conditions.\
Now, we approximate the function $\psi:\ y\in\mathbb{R}\rightarrow\varphi(y^+)$ by a sequence $(\psi_n)$ of regular functions. Let $\zeta$ be a $\mathcal{C}^\infty$ increasing function such that $$\forall y\in]-\infty,1],\ \zeta(y)=0\ and\ \forall y\in[2,+\infty[,\ \zeta(y)=1.$$ We set for all $n$:$$\forall y\in\mathbb{R},\ \
\psi_n(y)=\varphi(y)\zeta(ny).$$ It is easy to verify that $(\psi_n)$ converges uniformly to the function $\psi$, $(\psi'_n)$ converges everywhere to the function $(y\rightarrow\varphi'(y^+))$ and $(\psi_n'')$ converges everywhere to the function $(y\rightarrow
{{1} \hspace{-0.25 em}{\rm I}}_{\{y>0\}}\varphi''(y^+))$. Moreover we have the estimates: $$\label{controlofpsi}
\forall y\in\mathbb{R}^+,\ n\in\mathbb{N}^*,\ \
0\leq\psi_n(y)\leq\psi(y),\ \ 0\leq\psi'_n(y)\leq Cy,\ \
\left|\psi_n''(y)\right|\leq C,$$ where $C$ is a constant. Thanks to Itô’s formula for the solution of OSPDE (\[SPDEO\]) (see Theorem 5 in [@DMZ12]), we have almost surely, for $t\in[0,T]$, $$\begin{aligned}
&&\int_{\ensuremath{\mathcal O}}\psi_n(w_t(x))dx+\int_0^t\mathcal{E}(\psi'_n(w_s),w_s)ds=\int_{\ensuremath{\mathcal O}}\psi_n(\phi(x)\xi(x))dx+\int_0^t\int_{\ensuremath{\mathcal O}}\psi'_n(w_s(x))\bar{f}_s(x)dxds\\&&-\sum\int_0^t\int_{\ensuremath{\mathcal O}}\psi_n''(w_s(x))\partial_iw_s(x)\widetilde{g_{i,s}}(x)dxds+\sum\int_0^t\int_{\ensuremath{\mathcal O}}\psi'_n(w_s(x))\widetilde{h_{j,s}}(x)dxdB_s^j\\&&+\frac{1}{2}\int_0^t\int_{\ensuremath{\mathcal O}}\psi_n''(w_s(x))|\widetilde{h_{j,s}}(x)|^2dxds+\int_0^t\int_{\ensuremath{\mathcal O}}\psi'_n(w_s(x))d\phi\nu(x,s).\end{aligned}$$ Making $n$ tends to $+\infty$ and using the fact that ${{1} \hspace{-0.25 em}{\rm I}}_{\{w_s>0\}}\partial_iw_s=\partial_iw_s^+$, we get by the dominated convergence theorem: $$\begin{aligned}
&&\int_{\ensuremath{\mathcal O}}\varphi(w_t^+(x))dx+\int_0^t\mathcal{E}(\varphi'(w^+_s),w^+_s)ds=\int_{\ensuremath{\mathcal O}}\varphi(\phi(x)\xi^+(x))dx+\int_0^t\int_{\ensuremath{\mathcal O}}\varphi'(w^+_s(x))\bar{f}_s(x)dxds\\&&-\sum\int_0^t\int_{\ensuremath{\mathcal O}}\varphi''(w^+_s(x))\partial_iw^+_s(x)\widetilde{g_{i,s}}(x)dxds+\sum\int_0^t\int_{\ensuremath{\mathcal O}}\varphi'(w^+_s(x))\widetilde{h_{j,s}}(x)dxdB_s^j\\&&+\frac{1}{2}\int_0^t\int_{\ensuremath{\mathcal O}}\varphi''(w^+_s(x)){{1} \hspace{-0.25 em}{\rm I}}_{\{w_s>0\}}|\widetilde{h_{j,s}}(x)|^2dxds+\int_0^t\int_{\ensuremath{\mathcal O}}\phi\varphi'(w^+_s(x))d\nu(x,s), \quad a.s.\end{aligned}$$ Then we consider a sequence $(\phi_n)$ in $\mathcal{C}_c^\infty({\ensuremath{\mathcal O}})$, $0\leq\phi_n\leq1$, converging to 1 everywhere on ${\ensuremath{\mathcal O}}$ and such that for any $y\in H_0^1({\ensuremath{\mathcal O}})$ the sequence $(\phi_ny)$ tends to $y$ in $H_0^1({\ensuremath{\mathcal O}})$ and $$\sup_n\left\|\phi_ny\right\|_{H_0^1({\ensuremath{\mathcal O}})}\leq C\left\|
y\right\|_{H_0^1({\ensuremath{\mathcal O}})},$$ where $C$ is a constant which does not depend on $y$. Such a sequence $(\phi_n )$ exists because $\partial
{\ensuremath{\mathcal O}}$ is assumed to be Lipschitz (see Lemma 19 in [@DM11]).\
One has to remark that if $i\in\{1,...d\}$ and $y\in H_0^1({\ensuremath{\mathcal O}})$, then $(y\partial_i\phi_n)$ tends to 0 in $L^2({\ensuremath{\mathcal O}})$.\
Now, we set $w_n=\phi_n u$ and $$\widetilde{f^n_t}=\phi_n f_t-\sum a_{i,j}(\partial_i\phi_n)(\partial_j u_t)-\sum(\partial_i\phi_n)g_{i,t}$$ $$\widetilde{g^n_{i,t}}=\phi_n g_{i,t}-u_t\sum a_{i,j}\partial_j\phi_n,\quad\widetilde{h^n_{j,t}}=\phi_nh_{j,t}$$ Applying the above Itô formula to $\varphi(w_n^+)$, we get $${\label{It\^o's5}}\begin{split}&\int_{\ensuremath{\mathcal O}}\varphi(w_{n,t}^+(x))dx+\int_0^t\mathcal{E}(\varphi'(w^+_{n,s}),w^+_{n,s})ds=\int_{\ensuremath{\mathcal O}}\varphi(\phi_n(x)\xi^+(x))dx+\int_0^t\int_{\ensuremath{\mathcal O}}\varphi'(w^+_{n,s}(x))\bar{f}_s(x)dxds\\&-\sum\int_0^t\int_{\ensuremath{\mathcal O}}\varphi''(w^+_{n,s}(x))\partial_iw^+_{n,s}(x)\widetilde{g_{i,s}}(x)dxds+\sum\int_0^t\int_{\ensuremath{\mathcal O}}\varphi'(w^+_{n,s}(x))\widetilde{h_{j,s}}(x)dxdB_s^j\\&+\frac{1}{2}\int_0^t\int_{\ensuremath{\mathcal O}}\varphi''(w^+_{n,s}(x)){{1} \hspace{-0.25 em}{\rm I}}_{\{w_{n,s}>0\}}|\widetilde{h_{j,s}}(x)|^2dxds+\int_0^t\int_{\ensuremath{\mathcal O}}\phi_n\varphi'(w_{n,s}^+(x))d\nu(x,s),\quad a.s.\end{split}$$ We have $$\begin{aligned}
\varphi'(w^+_{n,s})\bar{f}^n_s&-&\sum\varphi''(w^+_{s,n})\partial_iw^+_{n,s}\widetilde{g^n_{i,s}}=\varphi'(w^+_{n,s})\phi_nf_s-\sum
a_{i,j}\varphi'(w^+_{n,s})\partial_j\phi_n\partial_iu_s^+\\&+&\sum
a_{i,j}\varphi''(w^+_{n,s})u^+_s\partial_iw^+_{n,s}\partial_j\phi_n-\sum(\varphi'(w^+_{n,s}))g_{i,s}\partial_i\phi_n+\varphi''(w^+_{n,s})\phi_ng_{i,s}\partial_iw^+_{n,s}
.\end{aligned}$$ Remarking that for all $s\in(0,T]$, $(\phi_n\varphi'(w^+_{n,s}))$ (resp. $(\partial_i\phi_n\varphi'(w^+_{n,s}))$) tends to $\varphi'(u^+_s)$ (resp. 0) in $H_0^1({\ensuremath{\mathcal O}})$ (resp. $L^2({\ensuremath{\mathcal O}})$) we get by the dominated convergence theorem the convergence of all the terms in equality excepted the one involving the measure $\nu$. For this last term, we know that $w_n$ is quasi-continuous and from and it is easy to verify $$\sup_{n}\int_0^t\int_{\ensuremath{\mathcal O}}\phi_n\varphi'(w_{n,s}^+(x))d\nu(x,s)\leq C.$$ Then, by Fatou’s lemma, we have $$\int_0^t\int_{\ensuremath{\mathcal O}}\varphi'(u^+_s)\nu(dxds)=\liminf_{n\rightarrow\infty}\int_0^t\int_{\ensuremath{\mathcal O}}\phi_n\varphi'(w_{n,s}^+(x))d\nu(x,s)<+\infty,\ \ a.s.$$ Hence, the convergence of the last term comes from the dominated convergence theorem.
The comparison theorem for local solutions
------------------------------------------
Firstly, we prove an Itô formula for the difference of local solutions of two OSPDE, $(u^1,\nu^1)\in{\ensuremath{\mathcal R}}_{loc}(\xi^1,f^1,g,h,S^1)$ and $(u^2,\nu^2)\in{\ensuremath{\mathcal R}}_{loc}(\xi^2,f^2,g,h,S^2)$, where $(\xi^i,f^i,g,h,S^i)$ satisfy assumptions [**(H)**]{}, [**(HIL)**]{}, [**(OL)**]{} and [**(HOL)**]{}. We denote by $\hat{u}=u^1-u^2$, $\hat{\nu}=\nu^1-\nu^2$, $\hat{\xi }=\xi^1-\xi ^2,$ and $$\hat{f}\left( t,\omega ,x,y,z\right) =f^1\left( t,\omega
,x,y+u_t^2\left( x\right) ,z+\nabla u_t^2\left( x\right) \right)
-f^2\left( t,\omega ,x,u_t^2\left( x\right) ,\nabla u_t^2\left(
x\right) \right) ,$$ $$\hat{g}\left( t,\omega ,x,y,z\right)
=g\left( t,\omega ,x,y+u_t^2\left( x\right) ,z+\nabla u_t^2\left(
x\right) \right) -g\left( t,\omega ,x,u_t^2\left( x\right) ,\nabla
u_t^2\left( x\right) \right) ,$$ $$\hat{h}\left( t,\omega
,x,y,z\right) =h\left( t,\omega ,x,y+u_t^2\left( x\right) ,z+\nabla
u_t^2\left( x\right) \right) -h\left( t,\omega ,x,u_t^2\left(
x\right) ,\nabla u_t^2\left( x\right) \right) .$$
Assume that $\partial{\ensuremath{\mathcal O}}$ is Lipschitz and that $\hat{u}^+$ belongs to ${\ensuremath{\mathcal H}}_T$. Let $\varphi :{\mathbb{R}}\rightarrow {\mathbb{R}}$ be a function of class ${\cal C}^2,$ which admits a bounded second order derivative and such that $\varphi ^{\prime }\left( 0\right) =0.$ Then the following relation holds for each $t\in [0,T],$ $$\begin{aligned}
\label{It\^o'spositivepartdiff}&&\int_\mathcal{O}\varphi(\hat{u}_t^+(x))dx+\int_0^t\mathcal{E}(\varphi'(\hat{u}_s^+),\hat{u}_s^+)ds=\int_\mathcal{O}\varphi(\hat{\xi}^+(x))dx
+\int_0^t\int_{\ensuremath{\mathcal O}}\varphi'(\hat{u}_s^+(x))\hat{f}_s(x)dxds\nonumber\\&&-\sum_{i=1}^d\int_0^t\int_{\ensuremath{\mathcal O}}\varphi''(\hat{u}_s^+(x))\partial_i\hat{u}_s^+(x)\hat{g}_s^i(x)dxds+\frac{1}{2}\int_0^t\int_{\ensuremath{\mathcal O}}\varphi''(\hat{u}_s^+(x)){{1} \hspace{-0.25 em}{\rm I}}_{\{\hat{u}_s>0\}}|\hat{h}_s(x)|^2dxds\nonumber\\&&+\sum_{i=1}^\infty\int_0^t\int_{\ensuremath{\mathcal O}}\varphi'(\hat{u}_s^+(x))\hat{h}_s^j(x)dxdB_s^j+\int_0^t\int_\mathcal{O}\varphi'(\hat{u}_s^+(x))\hat{\nu}(dxds)\qquad
a.s.\end{aligned}$$
We consider $\phi\in\mathcal{C}_c^\infty({\ensuremath{\mathcal O}}),\ 0\leq\phi\leq1$, and put $$\forall t\in[0,T],\quad \hat{w}_t=\phi \hat{u}_t.$$ From the proof of Proposition \[Itô’slocalposi\], we know that $(\phi u^1,\phi\nu^1)$ and $(\phi u^2,\phi\nu^2)$ are the solutions of problem (\[SPDEO\]) with null Dirichlet boundary conditions. We have the Itô formula for $\hat{w}$, see Theorem 6 in [@DMZ12]. Then we do the same approximations as in the proof of Proposition \[Itô’slocalposi\], we can get the desired formula.
We have the following comparison theorem:
[\[comparison\]]{} Assume that $(\xi^i,f^i,g,h,S^i)$, $i=1,2$, satisfy assumptions [**(H)**]{}, [**(HIL)**]{}, [**(OL)**]{} and [**(HOL)**]{}. Let $(u^i,\nu^i)\in {\cal R}_{loc}\left( \xi ^i,f^i,g,h,S^i\right)
,i=1,2$ and suppose that the process $\left( u^1-u^2\right) ^{+}$ belongs to ${{\cal H}}_T
$ and that one has$$E\left( \left\| f^1\left(.,., u^2,\nabla u^2\right) -f^2\left(.,.,
u^2,\nabla u^2\right) \right\| ^*_{\theta;t}\right) ^2<\infty ,\;\;
\mbox{ for all} \quad t\in[0,T].$$ If $\xi ^1\le \xi ^2$ a.s., $f^1\left(t,\omega, u^2,\nabla u^2\right) \le f^2\left(t,\omega,
u^2,\nabla u^2\right) $, $dt\otimes dx \otimes dP$-a.e. and $S^1\leq S^2$, $dt\otimes dx\otimes dP$-a.s., then one has $u^1
(t,x)\le u^2 (t,x)$, $dt \otimes dx\otimes dP$-a.e.
Applying Itô’s formula (\[Itô’spositivepartdiff\]) to $(\hat{u}^+)^2$, we have $\forall t\in[0,T]$, $$\begin{aligned}
\label{itoposipart}&&\int_\mathcal{O}(\hat{u}_t^+(x))^2dx+2\int_0^t\mathcal{E}((\hat{u}_s^+))ds=\int_\mathcal{O}(\hat{\xi}^+(x))^2dx
+2\int_0^t\int_{\ensuremath{\mathcal O}}\hat{u}_s^+(x)\hat{f}_s(x,\hat{u}_s(x),\nabla\hat{u}_s(x))dxds\nonumber\\&&-2\sum_{i=1}^d\int_0^t\int_{\ensuremath{\mathcal O}}\partial_i\hat{u}_s^+(x)\hat{g}_s^i(x,\hat{u}_s(x),\nabla\hat{u}_s(x))dxds+\int_0^t\int_{\ensuremath{\mathcal O}}{{1} \hspace{-0.25 em}{\rm I}}_{\{\hat{u}_s>0\}}|\hat{h}_s(x,\hat{u}_s(x),\nabla\hat{u}_s(x))|^2dxds\nonumber\\&&+2\sum_{i=1}^\infty\int_0^t\int_{\ensuremath{\mathcal O}}\hat{u}_s^+(x)\hat{h}_s^j(x,\hat{u}_s(x),\nabla\hat{u}_s(x))dxdB_s^j+2\int_0^t\int_\mathcal{O}\hat{u}_s^+(x)\hat{\nu}(dxds),\qquad
a.s.\end{aligned}$$ Remarking the following relation $$\begin{aligned}
\int_0^t\int_\mathcal{O}\hat{u}_s^+(x)\hat{\nu}(dxds)=\int_0^t\int_\mathcal{O}(S^1-u^2)^+\nu^1(dxds)-\int_0^t\int_\mathcal{O}(u^1-S^2)^+\nu^2(dxds)\leq0\end{aligned}$$ The Lipschitz conditions in $\hat{g}$ and $\hat{h}$ and Cauchy-Schwarz’s inequality lead the following relations: for $\delta$, $\epsilon>0$, we have $$\begin{aligned}
\int_0^t(\nabla
\hat{u}^+_s,\hat{g}_s(\hat{u}_s,\nabla\hat{u}_s)ds\leq(\alpha+\epsilon)\left\|\nabla
\hat{u}^+\right\|^2_{2,2;t}+c_\epsilon\left\|\hat{u}^+\right\|^2_{2,2;t}+c_\epsilon\left\|\hat{g}^{\hat{u},0}\right\|
_{2,2;t}^2,\end{aligned}$$ and $$\begin{aligned}
\int_0^t\left\|{{1} \hspace{-0.25 em}{\rm I}}_{\{\hat{u}_s>0\}}\hat{h}_s(\hat{u}_s,\nabla\hat{u}_s)\right\|^2ds\leq(\beta^2+\epsilon)\left\|\nabla\hat{u}^+\right\|^2_{2,2;t}+c_\epsilon\left\|\hat{u}^+\right\|^2_{2,2;t}+c_\epsilon\left\|\hat{h}^{\hat{u},0}\right\|^2_{2,2;t}.\end{aligned}$$ Moreover, the Lipschitz condition in $\hat{f}$, the duality relation between elements in $L_{\theta;t}$ and $L_{\theta;t}^*$ and Young’s inequality yield the following relation: $$\begin{aligned}
\int_0^t\left(\hat{u}_s^+,\hat{f}_s\left( \hat{u}_s,\hat{u}_s\right) \right)
ds\leq\epsilon \left\| \nabla \hat{u}^+\right\|
_{2,2;t}^2+c_\epsilon \left\|\hat{u}^+\right\| _{2,2;t}^2+\delta
\left\|\hat{u}^+\right\| _{\theta;t}^2+c_\delta \left( \left\|
\hat{f}^{\hat{u},0+}\right\| ^*_{\theta;t}\right) ^2.\end{aligned}$$ Since ${\ensuremath{\mathcal E}}(\hat{u}^+)\geq\lambda\left\|\nabla\hat{u}^+\right\|^2_2$, we deduce from that for all $t\in[0,T]$, almost surely, $$\begin{aligned}
\label{8}
\left\|\hat{u}^+_t\right\|_2^2&+&2\left( \lambda -\alpha-\frac{\beta
^2}2-\frac 52\epsilon \right) \left\| \nabla\hat{u}^+\right\|
_{2,2;t}^2\le \left\|\hat{\xi}^+\right\|_2^2+\delta
\left\|\hat{u}^+\right\| _{\theta;t}^2+2c_\delta \left(
\left\|\hat{f}^{\hat{u},0+}\right\| ^*_{\theta;t}\right)
^2\nonumber\\&+&2c_\epsilon \left\|\hat{g}^{\hat{u},0}\right\|
_{2,2;t}^2+c_\epsilon \left\|\hat{h}^{\hat{u},0}\right\|
_{2,2;t}^2+5c_\epsilon \left\|\hat{u}^+\right\| _{2,2;t}^2+2M_t,\end{aligned}$$ where $M_t:=\sum_{j=1}^{\infty}\int_0^t\left(\hat{u}^+_s,\hat{h}_s^j\left(
\hat{u}_s,\nabla\hat{u}_s\right) \right) dB_s^j$ represents the martingale part. Further, using a stopping procedure while taking the expectation, the martingale part vanishes, so that $$\begin{aligned}
&&E\left\|\hat{u}^+_t\right\|_2^2+2\left( \lambda -\alpha
-\frac{\beta ^2}2-\frac 52\epsilon \right) E\left\|
\nabla\hat{u}^+\right\| _{2,2;t}^2\le
E\left\|\hat{\xi}^+\right\|_2^2+\delta E\left\|\hat{u}^+\right\|
_{\theta;t}^2\\&&+2c_\delta E\left(
\left\|\hat{f}^{\hat{u},0+}\right\| ^*_{\theta;t}\right)
^2+2c_\epsilon E\left\|\hat{g}^{\hat{u},0}\right\|
_{2,2;t}^2+c_\epsilon E\left\|\hat{h}^{\hat{u},0}\right\|
_{2,2;t}^2+5c_\epsilon \int_0^tE\left\|\hat{u}^+_s\right\|^2_2ds .\end{aligned}$$ Then we choose $\epsilon=\frac{1}{5}\left(\lambda-\alpha-\frac{\beta^2}{2}\right)$, set $\gamma=\lambda-\alpha-\frac{\beta^2}{2}$ and apply Gronwall’s lemma obtaining $$\label{1star}
E\left\|\hat{u}^+_t\right\|^2_2+\gamma
E\left\|\nabla\hat{u}^+\right\|^2_{2,2;t}\leq\left(\delta
E\left\|\hat{u}^+\right\|^2_{\theta;t}+ E\left[F\left(\delta,
\hat{\xi}^+,\hat{f}^{\hat{u},0+},\hat{g}^{\hat{u},0},\hat{h}^{\hat{u},0},t\right)\right]\right)e^{5c_\epsilon t},$$ with $F(\delta,
\hat{\xi}^+,\hat{f}^{\hat{u},0+},\hat{g}^{\hat{u},0},\hat{h}^{\hat{u},0},t)=\big(\|\hat{\xi}^+\|^2+2c_\delta\big(
\|\hat{f}^{\hat{u},0+}\|
^*_{\theta;t}\big)^2+2c_\epsilon\|\hat{g}^{\hat{u},0}\|_{2,2;t}^2+c_\epsilon\|\hat{h}^{\hat{u},0}\|_{2,2;t}^2\big)$. As a consequence one gets $$\label{2star}
E\left\|\hat{u}^+\right\|^2_{2,2;t}\leq\frac{1}{5c_\epsilon}\left(\delta
E\left\|\hat{u}^+\right\|^2_{\theta;t}+E\left[F\left(\delta,
\hat{\xi}^+,\hat{f}^{\hat{u},0+},\hat{g}^{\hat{u},0},\hat{h}^{\hat{u},0},t\right)\right]\right)\left(e^{5c_\epsilon
t}-1\right) .$$ Now we return to the inequality (\[8\]) and take the supremum in time, getting $$\label{supremum}
\left\|\hat{u}^+\right\|^2_{2,\infty;t}\leq\delta\left\|\hat{u}^+\right\|^2_{\theta;t}+F\left(\delta,
\hat{\xi}^+,\hat{f}^{\hat{u},0+},\hat{g}^{\hat{u},0},\hat{h}^{\hat{u},0},t\right)+5c_\epsilon\left\|\hat{u}^+\right\|^2_{2,2;t}+2\sup_{s\leq
t}M_s$$ We would like to take the expectation in this relation and for that reason we need to estimate the bracket of the martingale part, $$\begin{aligned}
\left\langle M\right\rangle _t^{\frac 12}\le \left\|\hat{u}^+\right\|
_{2,\infty ;t}\left\|\hat{h}(\hat{u},\nabla\hat{u})\right\|
_{2,2;t}\le \eta \left\|\hat{u}^+\right\| _{2,\infty ;t}^2+c_\eta
\left( \left\| \hat{u}^+\right\| _{2,2;t}^2+\left\|
\nabla\hat{u}^+\right\|
_{2,2;t}^2+\left\|\hat{h}^{\hat{u},0}\right\|^2_{2,2;t}\right)\end{aligned}$$ with $\eta $ another small parameter to be properly chosen. Using this estimate and the inequality of Burkholder-Davis-Gundy we deduce from the inequality (\[supremum\]): $$\left( 1-2C_{BDG}\eta \right) E\left\|\hat{u}^+\right\| _{2,\infty
;t}^2\le \delta E\left\|\hat{u}^+\right\|
_{\theta;t}^2+E\left[F\left(\delta,
\hat{\xi}^+,\hat{f}^{\hat{u},0+},\hat{g}^{\hat{u},0},\hat{h}^{\hat{u},0},t\right)\right]$$ $$+\left( 5c_\varepsilon +2C_{BDG}c_\eta
\right) E\left\|\hat{u}^+\right\| _{2,2;t}^2+2C_{BDG}c_\eta E\left\|
\nabla \hat{u}^+\right\| _{2,2;t}^2+2C_{BDG}c_\eta
E\left\|\hat{h}^{\hat{u},0}\right\|^2_{2,2;t}$$ where $C_{BDG}$ is the constant corresponding to the Burkholder-Davis-Gundy inequality. Further we choose the parameter $\eta =\frac 1{4C_{BDG}}$ and combine this estimate with and to deduce an estimate of the form: $$\begin{aligned}
E\left( \left\|\hat{u}^+\right\| _{2,\infty ;t}^2+\left\| \nabla
\hat{u}^+\right\| _{2,2;t}^2\right) \le \delta c_2\left( t\right)
E\left\| \hat{u}^+\right\|
_{\theta;t}^2+c_3(\delta,t)E\left[R\left(\delta,
\hat{\xi}^+,\hat{f}^{\hat{u},0+},\hat{g}^{\hat{u},0},\hat{h}^{\hat{u},0},t\right)\right]\end{aligned}$$ where $R\left(\delta,
\hat{\xi}^+,\hat{f}^{\hat{u},0+},\hat{g}^{\hat{u},0},\hat{h}^{\hat{u},0},t\right)=\left(\left\|\hat{\xi}^+\right\|^2+\left(
\left\|\hat{f}^{\hat{u},0+}\right\|
^*_{\theta;t}\right)^2+\left\|\hat{g}^{\hat{u},0}\right\|_{2,2;t}^2+\left\|\hat{h}^{\hat{u},0}\right\|_{2,2;t}^2\right)$ and $c_3(\delta,t)$ is a constant that depends on $\delta $ and $t,$ while $c_2\left( t\right) $ is independent of $ \delta .$ Dominating the term $E\left\|\hat{u}^+\right\| _{\theta;t}^2$ by using the estimate (\[controltheta\]) and then choosing $\delta =\frac
1{2c_1^2c_2\left( t\right) }$, we get the following estimate: $$\begin{aligned}
E\left(\left\|\hat{u}^+\right\|^2_{2,\infty;t}+\left\|\nabla\hat{u}^+\right\|^2_{2,2;t}\right)\leq
k(t)E\left(\left\|\hat{\xi}^+\right\|^2_2+\left(\left\|\hat{f}^{\hat{u},0+}\right\|^*_{\theta;t}\right)^2+\left\|\hat{g}^{\hat{u},0}\right\|^2_{2,2;t}+\left\|\hat{h}^{\hat{u},0}\right\|^2_{2,2;t}\right).\end{aligned}$$
This implies the desired result since $\hat{\xi}\leq0$, $\hat{f}^0\leq0$ and $\hat{g}^0=\hat{h}^0=0$.
Maximum principle {#maxprinciple}
-----------------
We first consider the case of a solution $u$ such that $u\leq0$ on $\partial{\ensuremath{\mathcal O}}$.
\[maxprinc\] Suppose that Assumptions [**(H)**]{}, [**(OL)**]{}, [**(HIL)**]{}, [**(HOL)**]{},[**(HI$\mathbf{2 p}$)**]{}, [**(HO$\mathbf{\infty p}$)**]{} and [**(HD$\mathbf{\theta p}$)**]{} hold for some $\theta \in [0,1[$, $p\geq2$ and that the constants of the Lipschitz conditions satisfy $$\alpha +\frac{\beta ^2}2+72\beta ^2<\lambda.$$ Let $(u,\nu)\in
{\cal R}_{loc}\left( \xi ,f,g,h,S\right) $ be such that $u^{+}\in {{\cal H}}.$ Then one has$$\begin{aligned}
E\left\| u^{+}\right\| _{\infty ,\infty ;t}^p&\le &k(t)c(p)E\big(\left\|\xi^+-S'_0\right\|^p_\infty+(\left\| \bar{f}^{0,+}\right\|^*_{\theta;t})^p+
(\left\||\bar{g}^0|^2\right\|^*_{\theta;t})^{\frac{p}{2}}+(\left\||\bar{h}^0|^2\right\|^*_{\theta;t})^{\frac{p}{2}}\\&+&\left\|(S'_0)^+\right\|^p_\infty+(\left\|f^{',+}\right\|^*_{\theta;t})^p+
(\left\||g'|^2\right\|^*_{\theta;t})^{\frac{p}{2}}+(\left\||h'|^2\right\|^*_{\theta;t})^{\frac{p}{2}}\big)\end{aligned}$$ where $k\left( t\right) $ is constant that depends on the structure constants and $t\in [0,T].$
Set $(y,\nu')=\mathcal{R}(\xi^+,\check{f},g,h,S)$ the solution with zero Dirichlet boundary conditions, where the function $\check{f}$ is defined by $\check{f}=f+f^{0,-}$, with $f^{0,-}=0\vee(-f^0)$. The assumption on the Lipschitz constants ensure the application of the Section \[LPestimate\], which gives the following estimate : $$\begin{aligned}
E\left\| y-S'\right\|^p_{\infty,\infty;t}\leq k(t)E(\left\|\xi^+-S'_0\right\|^p_\infty+(\left\| \bar{f}^{0,+}\right\|^*_{\theta;t})^p+
(\left\||\bar{g}^0|^2\right\|^*_{\theta;t})^{\frac{p}{2}}+(\left\||\bar{h}^0|^2\right\|^*_{\theta;t})^{\frac{p}{2}})\,,\end{aligned}$$ where $\bar{f}^{0,+}=\check{f}^0-f'=f^{0,+}-f'$. On the boundary, $y=0$ and $u\leq0$, hence, $u-y\leq0$ on the boundary, i.e. $(u-y)^+\in\mathcal{H}$. Moreover, the other conditions of Theorem \[comparison\] are satisfied so that we can apply it and deduce that $u-S'\leq y-S'$. This implies that $(u-S')^+\leq (y-S')^+$ and the above estimate of $y-S'$ leads to the following estimate: $$\begin{aligned}
E\left\| (u-S')^+\right\|^p_{\infty,\infty;t}\leq k(t)E(\left\|\xi^+-S'_0\right\|^p_\infty+(\left\| \bar{f}^{0,+}\right\|^*_{\theta;t})^p+
(\left\||\bar{g}^0|^2\right\|^*_{\theta;t})^{\frac{p}{2}}+(\left\||\bar{h}^0|^2\right\|^*_{\theta;t})^{\frac{p}{2}}).\end{aligned}$$ with the estimate of $S'$ $$\begin{aligned}
E\left\|(S')^+\right\|^p_{\infty,\infty;t}\leq k(t)E(\left\|(S'_0)^+\right\|^p_\infty+(\left\|f^{',+}\right\|^*_{\theta;t})^p+
(\left\||g'|^2\right\|^*_{\theta;t})^{\frac{p}{2}}+(\left\||h'|^2\right\|^*_{\theta;t})^{\frac{p}{2}}).\end{aligned}$$ Therefore, $$\begin{aligned}
E\left\| u^{+}\right\| _{\infty ,\infty
;t}^p&\le &k(t)c(p)E\big(\left\|\xi^+-S'_0\right\|^p_\infty+(\left\|
\bar{f}^{0,+}\right\|^*_{\theta;t})^p+
(\left\||\bar{g}^0|^2\right\|^*_{\theta;t})^{\frac{p}{2}}+(\left\||\bar{h}^0|^2\right\|^*_{\theta;t})^{\frac{p}{2}}\\&+&\left\|(S'_0)^+\right\|^p_\infty+(\left\|f^{',+}\right\|^*_{\theta;t})^p+
(\left\||g'|^2\right\|^*_{\theta;t})^{\frac{p}{2}}+(\left\||h'|^2\right\|^*_{\theta;t})^{\frac{p}{2}}\big).\end{aligned}$$
Let us generalize the previous result by onsidering a real Itô process of the form$$M_t=m+\int_0^tb_sds+\sum_{j=1}^{+\infty}\int_0^t\sigma_{j,s}dB_s^j$$ where $m$ is a random variable and $b=(b_t)_{t\geq0}$, $\sigma=(\sigma_{1,t},...,\sigma_{n,t},...)_{t\geq0}$ are adapted processes.
\[maintheo\] Suppose that Assumptions [**(H)**]{}, [**(OL)**]{}, [**(HIL)**]{}, [**(HOL)**]{},[**(HI$\mathbf{2 p}$)**]{}, [**(HO$\mathbf{\infty p}$)**]{} and [**(HD$\mathbf{\theta p}$)**]{} hold for some $\theta \in [0,1[$, $p\geq2$ and that the constants of the Lipschitz conditions satisfy $$\alpha +\frac{\beta ^2}2+72\beta ^2<\lambda.$$ Assume also that $m$ and the processes $b$ and $\sigma $ satisfy the following integrability conditions$$E\left| m\right| ^p<\infty ,\;E\left( \int_0^t\left| b_s\right|
^{\frac 1{1-\theta }}ds\right) ^{p\left( 1-\theta \right) }<\infty
,\;E\left(
\int_0^t\left| \sigma _s\right| ^{\frac 2{1-\theta }}ds\right) ^{\frac{p\left( 1-\theta \right) }2}<\infty ,$$ for each $t\in[0,T].$ Let $(u,\nu)\in {\cal R}_{loc}\left( \xi ,f,g,h,S\right) $ be such that $\left( u-M\right) ^{+}$ belongs to ${{\cal H}}_T$. Then one has $$\begin{aligned}
\label{MaxiPrinc}E\left\|(u-M)^+\right\|^p_{\infty,\infty;t}&\leq& c(p)k(t)E\big[\left\|(\xi-m)^+-(S'_0-m)\right\|_\infty^p+
\left(\left\|\bar{f}^{0,+}\right\|_{\theta;t}^*\right)^p\nonumber\\&+&\left(\left\|\left|\bar{g}^0\right|^2\right\|_{\theta;t}^*\right)^{\frac{p}{2}}
+\left(\left\|\left|\bar{h}^0\right|^2\right\|_{\theta;t}^*\right)^{\frac{p}{2}}+\left\|(S'_0-m)^+\right\|^p_\infty\\&+&\left(\left\|(f'-b)^+\right\|^*_{\theta;t}\right)^p+\left(\left\||g'|^2\right\|^*_{\theta;t}\right)^{\frac{p}{2}}+\left(\left\||h'-\sigma|^2\right\|^*_{\theta;t}\right)^{\frac{p}{2}}\big]\nonumber\end{aligned}$$ where $k\left( t\right) $ is the constant from the preceding corollary. The right hand side of this estimate is dominated by the following quantity which is expressed directly in terms of the characteristics of the process $M$, $$\begin{aligned}
&&c(p)k(t)E\big[\left\|(\xi-m)^+-(S'_0-m)\right\|^p_\infty+\left(\left\|\bar{f}^{0,+}\right\|_{\theta;t}^*\right)^p
+\left(\left\|\left|\bar{g}^0\right|^2\right\|_{\theta;t}^*\right)^{\frac{p}{2}}+\left(\left\|\left|\bar{h}^0\right|^2\right\|_{\theta;t}^*\right)^{\frac{p}{2}}\\&&
\quad\qquad\quad+\left\|(S'_0-m)^+\right\|^p_\infty+\left(\left\|f^{',+}\right\|_{\theta;t}^*\right)^p
+\left(\left\|\left|g'\right|^2\right\|_{\theta;t}^*\right)^{\frac{p}{2}}+\left(\left\|\left|h'\right|^2\right\|_{\theta;t}^*\right)^{\frac{p}{2}}
\\&&\quad\qquad\quad+\left(\int_0^t\left|b_s\right|^{\frac{1}{1-\theta}}ds\right)^{p(1-\theta)}+\left(\int_0^t\left|\sigma_s\right|^{\frac{2}{1-\theta}}ds\right)^{\frac{p(1-\theta)}{2}}
\big].\end{aligned}$$
One immediately observes that $u-M$ belongs to $\mathcal{ R}_{loc}\left( \xi -m,\check{f},\check{g},\check{h}, S-M\right) ,$ where$$\check{f}\left( t,\omega ,x,y,z\right) =f\left( t,\omega
,x,y+M_t\left( \omega \right) ,z+\nabla M_t(\omega)\right)
-b_t\left( \omega \right) ,$$ $$\check{g}\left( t,\omega ,x,y,z\right) =g\left( t,\omega
,x,y+M_t\left( \omega \right) ,z+\nabla M_t(\omega)\right) ,$$ $$\check{h}\left( t,\omega ,x,y,z\right) =h\left( t,\omega
,x,y+M_t\left( \omega \right) ,z+\nabla M_t(\omega)\right) -\sigma
_t\left( \omega \right) .$$ In order to apply the preceding theorem we only have to estimate the zero terms of the following functions: $$\bar{\check{f}}\left( t,\omega ,x,y,z\right) =\check{f}\left( t,\omega
,x,y+S'-M, z+\nabla(S'-M)\right) - f'(t,\omega,x)+b_t(\omega),$$ $$\bar{\check{g}}\left( t,\omega ,x,y,z\right) =\check{g}\left( t,\omega
,x,y+S'-M, z+\nabla(S'-M)\right) - g'(t,\omega,x),$$ $$\bar{\check{h}}\left( t,\omega ,x,y,z\right) =\check{h}\left( t,\omega
,x,y+S'-M, z+\nabla(S'-M)\right) - h'(t,\omega,x)+\sigma_t(\omega).$$ So we have: $$\bar{\check{f}}_t^0=\check{f}_t(S'-M,\nabla
(S'-M))-f'_t+b_t=f_t(S',\nabla S')-f'_t=\bar{f}^0\, ,$$ $$\bar{\check{g}}_t^0=\check{g}_t(S'-M,\nabla (S'-M))-g'_t=g_t(S',\nabla S')-g'_t=\bar{g}^0\, ,$$ $$\bar{\check{h}}_t^0=\check{h}_t(S'-M,\nabla (S'-M))-h'_t+\sigma_t=h_t(S',\nabla S')-h'_t=\bar{h}^0\, .$$ Therefore, applying the preceding theorem to $u-M$, we obtain (\[MaxiPrinc\]).\
On the other hand, one has the following estimates: $$\left\|(f'-b)^+\right\|_{\theta;t}^*\leq c\left[\left\|f^{',+}\right\|_{\theta;t}^*+\left(\int_0^t\left|b_s\right|^{\frac{1}{1-\theta}}ds\right)^{1-\theta}\right],$$ $$\left\||h'-\sigma|^2\right\|^*_{\theta;t})^{\frac{p}{2}}\leq c\left[\left(\left\||h'|^2\right\|^*_{\theta;t}\right)^{\frac{p}{2}}+\left(\int_0^t\left|\sigma_s\right|^{\frac{2}{1-\theta}}ds\right)^{1-\theta}\right].$$ This allows us to conclude the proof.
Appendix {#tecnicLem}
========
In this section, we prove some technical lemmas that we need in the Step 2 of the proof of Theorem \[LPESTIM\]. For simplicity, we put, for fixed $n\leq m$, $\hat{u}:=\bar{u}^n-\bar{u}^m$, $\hat{\xi}:=\xi^n-\xi^m$, $\hat{f}(t,\omega,x,y,z):=\bar{f}_{n,m}(t,\omega,x,y,z)$ and similar for $\hat{g}$ and $\hat{h}$.
We recall that the initial value $\hat{\xi}$ and $\hat{f}^0,\
\hat{g}^0,\ \hat{h}^0$ are uniformly bounded.
Denote $$\begin{aligned}
K=\left\|
\hat{\xi}\right\|_{L^\infty(\Omega\times{\ensuremath{\mathcal O}})}\vee\left\|\hat{f}^0\right\|_{L^\infty(\mathbb{R}_+\times\Omega\times{\ensuremath{\mathcal O}})}\vee\left\|\hat{g}^0\right\|_{L^\infty(\mathbb{R}_+\times\Omega\times{\ensuremath{\mathcal O}})}\vee\left\|\hat{h}^0\right\|_{L^\infty(\mathbb{R}_+\times\Omega\times{\ensuremath{\mathcal O}})
}.\end{aligned}$$ Then there exist constants $c,\ c'>0$ which only depend on $K,\ C,\ \alpha,\ \beta$ such that, for all real $l\geq2$, one has $$\label{diffl}E\int_{\ensuremath{\mathcal O}}|\hat{u}_t(x)|^ldx\leq cK^2l(l-1)e^{cl(l-1)t},$$ $$\label{diffl2}E\int_0^t\int_{\ensuremath{\mathcal O}}|\hat{u}_s(x)|^{l-2}|\nabla\hat{u}_s(x)|^2dxds\leq c'K^2l(l-1)e^{cl(l-1)t},$$ and$$\label{difflm}E\int_0^t\int_{\ensuremath{\mathcal O}}|\hat{u}_s(x)|^{l-1}(\nu^n+\nu^m)(dxds)<+\infty .$$
Beginning from the Itô formula for the difference of solutions of two obstacle problems which has been proved in [@DMZ12]: we take the same $\varphi_n$ as in the proof of Lemma \[estimateul\], $$\label{difflp}
\begin{split}
& \int_{\mathcal{O}} \varphi_n (\hat{u}_t (x)) \, dx \; + \;
\int_0^t \mathcal{E} \big(\varphi_n^{\prime} (\hat{u}_s), \,
\hat{u}_s \big) \, ds=\int_{\ensuremath{\mathcal O}}\varphi_n(\hat{\xi}(x))dx +
\int_{0}^{t}\int_{\mathcal{O}}
\varphi_n^{\prime}(\hat{u}_s(x))\, \hat{f}(s,x)\, dx ds \\
& - \sum_{i=1}^{d} \int_{0}^{t} \int_{\mathcal{O}}
\varphi_n^{\prime \prime } (\hat{u}_s(x))
\partial_i (\hat{u}_s(x)))\,\hat{g}_i(s,x)\, dx \, ds +
\sum_{j=1}^{\infty} \int_{0}^{t} \int_{\mathcal{O}}
\varphi_n^{\prime} (\hat{u}_s(x)) \, \hat{h}_j(s,x)\, dx dB_{s}^{j}\\
& + \frac{1}{2}\, \sum_{j=1}^{\infty} \int_{0}^{t}\int_{\mathcal{O}}
\varphi_n^{\prime \prime } (\hat{u}_s(x))\, \hat{h}_j^2(s,x) \, dx\,
ds
+\int_0^t\int_{\ensuremath{\mathcal O}}\varphi_n^{\prime}(\hat{u}_s(x))\, (\nu^n-\nu^m)(dx\, ds)\, ,\quad a.s.\\
\end{split}$$ The support of $\nu^n$ is $\{\bar{u}^n=S\}$ and the support of $\nu^m$ is $\{\bar{u}^m=S\}$, so the last term is equal to $$\int_0^t\int_{\ensuremath{\mathcal O}}\varphi_n^{\prime}(S_s(x)-\bar{u}^m_s(x))\, \nu^n(dx\,
ds)-\int_0^t\int_{\ensuremath{\mathcal O}}\varphi_n^{\prime}(\bar{u}^n_s(x)-S_s(x))\,
\nu^m(dx\, ds)$$ and the fact that $\varphi'_n(x)\leq0$, when $x\leq0$ and $\varphi'_n(x)\geq0$, when $x\geq0$, ensure that the last term is always negative.\
By the uniform ellipticity of the operator $A$, we get $$\mathcal{E} \big(\varphi_n^{\prime} (\hat{u}_s), \, \hat{u}_s \big)
\, \geq \, \lambda \, \int_{{\ensuremath{\mathcal O}}} \varphi_n^{\prime \prime}
(\hat{u}_s) |\nabla \hat{u}_s|^2 \, dx.$$
Let $\epsilon >0$ be fixed. Using the Lipschitz condition on $\hat{f}$ and the properties of the functions $(\varphi_n)_n$ we get $$\begin{split} & |\varphi_n^{\prime} (\hat{u}_s)| \, |\hat{f}(s,x)|
\leq l (\varphi_n (\hat{u}_s) + 1) \, |\hat{f}^0| + (C +
c_{\epsilon})\, |\hat{u}_s|^2
\varphi_n^{\prime\prime}(\hat{u}_s) + \, \epsilon \varphi_n^{\prime\prime}(\hat{u}_s)|\nabla(\hat{u}_s)|^2 .\\
\end{split}$$ Now using Cauchy-Schwarz inequality and the Lipschitz condition on $\hat{g}$ we get $$\begin{split}
& \,\sum_{i=1}^d \varphi_n^{\prime\prime}(\hat{u}_s) \partial_i (\hat{u}_s)
\, \hat{g}(s,x) \leq l(l-1)c_{\epsilon}K^2 + 2c_{\epsilon}(K^2 + C^2 ) l (l-1)
|\varphi_n (\hat{u}_s)|+
(\alpha + \epsilon) \, \varphi_n^{\prime\prime} (\hat{u}_s)
|\nabla (\hat{u}_s)|^2 . \\
\end{split}$$ In the same way as before $$\begin{split}&
\sum_{j=1}^{\infty} \varphi_n^{\prime \prime } (\hat{u}_s )\,
\hat{h}(s,x) \leq \, 2c'_{\epsilon} l (l-1)K^2 + 2c'_{\epsilon}(
K^2 +C^2 )l (l-1) \varphi_n(\hat{u}_s)
+ (1 + \epsilon) \, \beta^2\, \varphi_n^{\prime \prime }(\hat{u}_s)|\nabla (\hat{u}_s)|^2 .
\end{split}$$ Thus taking the expectation, we deduce $$\begin{split}
&E \, \int_{\mathcal{O}}\varphi_n (\hat{u}_t(x)) \, dx + (\lambda -
\frac{1}{2}(1+ \epsilon)\beta^2 - (\alpha + 2 \epsilon) \, ) \, E \,
\int_0^t \int_{\mathcal{O}} \varphi_n^{\prime \prime} (\hat{u}_s) \,
|\nabla( \hat{u}_s) |^2 \, dx \, ds \\
& \, \leq \, l(l-1)c''_{\epsilon} K^2 \, + \, c''_{\epsilon} l
(l-1)\big( K^2 +C^2+C+ c_{\epsilon}\big)
E \, \int_0^t \int_{\mathcal{O}} \varphi_n (\hat{u}_s(x))\, dx \, ds . \\
\end{split}$$ On account of the contraction condition, one can choose $ \epsilon
> 0 $ small enough such that $$\lambda - \frac{1}{2}(1+
\epsilon)\beta^2 - (\alpha + 2 \epsilon)>0$$ and then $$\begin{split}
E\, \int_{\mathcal{O}} \varphi_n (\hat{u}_t(x)) \, dx &
\leq \, c K^2 l (l-1) \, + \, cl (l-1)
E \, \int_0^t \int_{\mathcal{O}} \varphi_n (\hat{u}_s(x))\, dx \, ds \, .\\
\end{split}$$ We obtain by Gronwall’s Lemma, that $$\begin{split}
E\, \int_{\mathcal{O}} \varphi_n (\hat{u}_t(x)) \, dx &
\leq \, c\,K^2 l (l-1) \, \exp{ \big( c \, l (l-1)\,t \big) }, \\
\end{split}$$ and so it is easy to get $$\begin{split}
E \, \int_0^t \int_{\mathcal{O}} \varphi_n^{\prime \prime} (\hat{u}_s(x)) \,
|\nabla \hat{u}_s |^2 \, dx \, ds \, \leq \,
c^{\prime}\, K^2 l \, (l-1) \, \exp{ \big( c l (l-1)\,t \big)}.\\
\end{split}$$ Then, letting $ n \to \infty $, by Fatou’s lemma we get (\[diffl\]) and (\[diffl2\]).\
From (\[difflp\]), we know that $$-\int_0^t\int_{\ensuremath{\mathcal O}}\varphi'_n(\hat{u}_s(x))(\nu^n-\nu^m)(dxds)\leq C.$$ Moreover, $$\begin{aligned}
&&-\int_0^t\int_{\ensuremath{\mathcal O}}\varphi'_n(\hat{u}_s(x))(\nu^n-\nu^m)(dxds)\\&=&-\int_0^t\int_{\ensuremath{\mathcal O}}\varphi_n^{\prime}(S_s(x)-\bar{u}^m_s(x))\,
\nu^n(dx\,
ds)+\int_0^t\int_{\ensuremath{\mathcal O}}\varphi_n^{\prime}(\bar{u}^n_s(x)-S_s(x))\,
\nu^m(dx\,
ds)\\&=&\int_0^t\int_{\ensuremath{\mathcal O}}\varphi_n^{\prime}(\bar{u}^m_s(x)-S_s(x))\,
\nu^n(dx\,
ds)+\int_0^t\int_{\ensuremath{\mathcal O}}\varphi_n^{\prime}(\bar{u}^n_s(x)-S_s(x))\,
\nu^m(dx\, ds)\end{aligned}$$ By Fatou’s lemma, we obtain $$\begin{aligned}
\int_0^t\int_{\ensuremath{\mathcal O}}|\bar{u}^m_s(x)-S_s(x)|^{l-1}\nu^n(dxds)+\int_0^t\int_{\ensuremath{\mathcal O}}|\bar{u}^n(x)-S_s(x)|^{l-1}\nu^m(dxds)<+\infty,
\ a.s.\end{aligned}$$ which is exactly (\[difflm\]).
One has the following formula for $\hat{u}$: $\forall t\geq0$, almost surely, $$\label{It\^o'sdiff}
\begin{split}
& \int_{\mathcal{O}}\left| \hat{u}_t(x) \right|^l \, dx +
\int_0^t {\ensuremath{\mathcal E}}\, \big(l\, (\hat{u}_s)^{l -1}sgn(\hat{u}_s) , \,
\hat{u}_s \big) \, ds = \int_{\ensuremath{\mathcal O}}\left|\hat{\xi}(x)\right|^ldx\\
& + l\int_{0}^{t}\int_{\mathcal{O}}sgn(\hat{u}_s)
\left| \hat{u}_s(x) \right|^{l-1} \, \hat{f}(s,x) \, dx ds -l (l-1) \, \sum_{i=1}^{d} \,\int_{0}^{t} \int_{\mathcal{O}} \left|\hat{u}_s
(x) \right|^{l -2}
\partial_i (\hat{u}_s(x))\, \hat{g}_i(s,x)\, dx \, ds \\
& + l \, \sum_{j=1}^{\infty} \int_{0}^{t}
\int_{\mathcal{O}}sgn(\hat{u}_s)
\, \left|\hat{u}_s(x) \right|^{l-1}\, \hat{h}_j(s,x)\, dx dB_{s}^{j}+ \frac{l (l-1)}{2}\, \sum_{j=1}^{\infty}
\int_{0}^{t}\int_{\mathcal{O}}
\left|\hat{u}_s(x) \right|^{l-2}\, \hat{h}_j^2(s,x,)\, dx\, ds\\&+l\int_{0}^{t}\int_{\mathcal{O}}sgn(\hat{u}_s)
\left|\hat{u}_s(x) \right|^{l-1} (\nu^1-\nu^2)(dx\, ds)\, .\\
\end{split}$$
From the Itô formula for the difference of two solutions (see Theorem 6 in [@DMZ12]), we have $ P$-almost surely for all $t\in
[0,T]$ and $ n \in {{\ensuremath{\mathbb N}} }^*$ $$\begin{split}
& \int_{\mathcal{O}} \varphi_n (\hat{u}_t(x)) \, dx \; + \; \int_0^t
\mathcal{E} \big(\varphi_n^{\prime} (\hat{u}_s), \, \hat{u}_s \big)
\, ds =\int_{\ensuremath{\mathcal O}}\varphi_n(\hat{\xi}(x))dx\\&+
\int_{0}^{t}\int_{\mathcal{O}} \varphi_n^{\prime}(\hat{u}_s(x))\,
\hat{f}(s,x) \, dx ds - \sum_{i=1}^{d} \int_{0}^{t}
\int_{\mathcal{O}} \varphi_n^{\prime \prime } (\hat{u}_s(x))
\partial_i \hat{u}_s(x) \, \hat{g}_i(s,x) \, dx \, ds \\& +
\sum_{j=1}^{\infty} \int_{0}^{t} \int_{\mathcal{O}}
\varphi_n^{\prime} (\hat{u}_s(x)) \, \hat{h}_j(s,x)\, dx dB_{s}^{j}+
\frac{1}{2}\, \sum_{j=1}^{\infty} \int_{0}^{t}\int_{\mathcal{O}}
\varphi_n^{\prime \prime } (\hat{u}_s(x))\, \hat{h}_j^2(s,x) \, dx\,
ds\\&
+\int_0^t\int_{\ensuremath{\mathcal O}}\varphi_n^{\prime}(\hat{u}_s(x))(\nu^1 -\nu^2)(dxds) \, .\\
\end{split}$$ Then, passing to the limit as $ n \to \infty $, the convergences come from the dominated convergence theorem.
Similar as before, we define the processes $\hat{v}$ and $\hat{v}'$ by $$\begin{split}
\hat{v}_t :&=\sup _{s\leq t}\left( \int_{{\ensuremath{\mathcal O}}}\left|
\hat{u}_s\right|^l dx +\gamma l\left( l-1\right)
\int_0^s\int_{{\ensuremath{\mathcal O}}}\left| \hat{u}_r\right|
^{l-2}\left| \nabla \hat{u}_r\right| ^2\, dx\, dr\right) \\
\hat{v}_t^{\prime } :&=\int_{\ensuremath{\mathcal O}}\left| \hat{\xi}\right|^ldx+l^2 c_1
\left\| \left| \hat{u}\right| ^l\right\| _{1,1;t}
+l\left\|\hat{f}^0\right\| _{\theta ,t}^{*}\left\| \left| \hat{u}
\right| ^{l-1}\right\| _{\theta ;t} \\&+ l^2 \left( c_2\left\|
|\hat{g}^0 |^2\right\| _{\theta;t}^{*}
+ c_3\left\| |\hat{h}^0 |^2\right\| _{\theta ;t}^{*}\right) \left\|
\left| \hat{u}\right|^{l-2}\right\|_{\theta ;t},\\
\end{split}$$ where above and below $\gamma$, $c_1$, $c_2$ and $c_3$ are the constants given by relations .\
We remark first that the last term in (\[Itô’sdiff\]) is non positive, indeed:$$\begin{aligned}
&&\int_{0}^{t}\int_{\mathcal{O}}sgn(\hat{u}_s)
\left| S_s-u^2_s (x) \right|^{l-1} (\nu^1-\nu^2)(dx\, ds)\\&=&\int_{0}^{t}\int_{\mathcal{O}}sgn(S_s-u^2_s)
\left|S_s-u^2_s (x) \right|^{l-1} \nu^1(dx\, ds)\\&&-\int_{0}^{t}\int_{\mathcal{O}}sgn(u^1_s-S_s)
\left|u^1_s (x)-S_s(x) \right|^{l-1} \nu^2(dx\, ds)\leq0.\end{aligned}$$ Then applying the same proof as the one of Lemma \[tau\], we obtain:$$\begin{split}
& \tau E \sup _{0 \leq s\leq t}\left( \int_{{\ensuremath{\mathcal O}}}\left|
\hat{u}_s\right|^l\, dx +\gamma l\left( l-1\right)
\int_0^s\int_{{\ensuremath{\mathcal O}}}\left| \hat{u}_r\right| ^{l-2}\left| \nabla
\hat{u}_r\right| ^2dx dr\right) \\& \leq E\int_{\ensuremath{\mathcal O}}\left|
\hat{\xi}\right|^ldx+ l^2c_1 E \left\| \left| \hat{u}\right|
^l\right\| _{1,1;t} +l E \left\|\hat{f}^0\right\| _{\theta
,t}^{*}\left\| \left| \hat{u}\right| ^{l-1}\right\| _{\theta
;t}\\&\quad+l^2 E\left( c_2 \left\| |\hat{g}^0 |^2\right\| _{\theta
;t}^{*}+c_3\left\| |\hat{h}^0 |^2 \right\| _{\theta ;t}^{*}\right)
\left\| \left| \hat{u}\right|^{l-2}\right\|_{\theta ;t}.
\end{split}$$ and this yields that the process $\tau \hat{v}$ is dominated by $\hat{v}'$.\
Starting from here, we can repeat line by line the proofs of Lemmas 15-17 in [@DMS05] and apply the Moser iteration as at the end of Subsection \[casborn\] to obtain the desired estimations, namely:
[\[Lemme63\]]{} There exists a function $k_2:{{\ensuremath{\mathbb R}} }_{+}\rightarrow {{\ensuremath{\mathbb R}} }_{+}$ which involves only the structure constants of our problem and such that the following estimate holds$$E\|\hat{u}\|^p_{\infty,\infty :t}\le k_2\left( t\right) E\left(
\left\| \hat{\xi}\right\| ^p +\left\|\hat{f}^0\right\| _{\theta
;t}^{*p}+\left\| |\hat{g}^0 |^2 \right\| _{\theta
;t}^{*\frac{p}{2}}+\left\| |\hat{h}^0 |^2 \right\| _{\theta
;t}^{*\frac{p}{2}}\right) .$$
\[estimvdiff\] There exists a function $k_1:{{\ensuremath{\mathbb R}} }_+\times{{\ensuremath{\mathbb R}} }_+\rightarrow{{\ensuremath{\mathbb R}} }_+$ which involves only the structure constants of our problem and such that the following estimate holds $$\begin{aligned}
E\hat{v}_t\leq
k_1(l,t)E\left(\int_{\ensuremath{\mathcal O}}|\hat{\xi}|^ldx+\left\|\hat{f}^0\right\|_{\theta;t}^{*l}+\left\|\left|\hat{g}^0\right|^2\right\|_{\theta;t}^{*\frac{l}{2}}+\left\|\left|\hat{h}^0\right|^2\right\|_{\theta;t}^{*\frac{l}{2}}\right).\end{aligned}$$
[99]{}
Aronson, D.G.: Non-negative solutions of linear parabolic equations. *Annali della Scuola Normale Superiore di Pisa*, Classe di Scienze 3, tome 22 (4), pp. 607-694 (1968).
Aronson D.G. and Serrin J.: Local behavior of solutions of quasi-linear parabolic equations. *Archive for Rational Mechanics and Analysis*, 25, 81-122 (1967).
Bally V., Caballero E., El-Karoui N. and Fernandez, B. : Reflected BSDE’s PDE’s and Variational Inequalities. *preprint INRIA report* (2004).
Denis L. and Stoïca L.: A general analytical result for non-linear s.p.d.e.’s and applications. *Electronic Journal of Probability*, 9, p. 674-709 (2004).
Denis L., Matoussi A. and Stoïca L.: $L^p$ estimates for the uniform norm of solutions of quasilinear SPDE’s. *Probability Theory Related Fields*, 133, 437-463 (2005).
Denis L., Matoussi A. and Stoïca L.: Maximum principle for parabolic SPDE’s: first approach. *Stohcastic Partial Differential Equations and Applications VIII, Levico, Jan.* 6-12 (2008).
Denis L., Matoussi A. and Stoïca L.: Maximum Principle and Comparison Theorem for Quasi-linear Stochastic PDE’s. *Electronic Journal of Probability*, 14, p. 500-530 (2009).
Denis L. and Matoussi A.: Maximum principle for quasilinear SPDE’s on a bounded domain without regularity assumptions. To appear in *Stoch. Proc. and their Applications* (2013).
Denis L., Matoussi A. and Zhang J.: The Obstacle Problem for Quasilinear Stochastic PDEs: Analytical approach. To appear in *Annals of Probability* (2013).
Donati-Martin C. and Pardoux E.: White noise driven SPDEs with reflection. *Probability Theory and Related Fields*, 95, 1-24 (1993).
El Karoui N., Kapoudjian C., Pardoux E., Peng S., and Quenez M.C.: Reflected Solutions of Backward SDE and Related Obstacle Problems for PDEs. *The Annals of Probability*, 25 (2), 702-737 (1997).
Klimsiak T.: Reflected BSDEs and obstacle problem for semilinear PDEs in divergence form. *Stochastic Processes and their Applications*, 122 (1), 134-169 (2012).
Krylov, N. V. : An analytic approach to SPDEs. *Six Perspectives*, *AMS Mathematical surveys an Monographs*, 64, 185-242 (1999).
Lions J.L. and Magenes E.: Problèmes aux limites non homogènes et applications. *Dunod, Paris* (1968). Matoussi A. and Stoïca L.: The Obstacle Problem for Quasilinear Stochastic PDE’s. The *Annals of Probability*, 38, 3, 1143-1179 (2010).
Mignot F. and Puel J.P. : Inéquations d’évolution paraboliques avec convexes dépendant du temps. Applications aux inéquations quasi-variationnelles d’évolution. *Arch. for Rat. Mech. and Ana.*, 64, No.1, 59-91 (1977).
Nualart D. and Pardoux E.: White noise driven quasilinear SPDEs with reflection. *Probability Theory and Related Fields*, 93, 77-89 (1992).
Pierre M.: Problèmes d’Evolution avec Contraintes Unilaterales et Potentiels Parabolique. *Comm. in Partial Differential Equations*, 4(10), 1149-1197 (1979).
Pierre M. : Représentant Précis d’Un Potentiel Parabolique. *Séminaire de Théorie du Potentiel*, Paris, No.5, Lecture Notes in Math. 814, 186-228 (1980).
Revuz, D. and Yor, M. : Continuous Martingales and Brownian Motion. *Springer, third edition*, (1999). Sanz M. , Vuillermot P. : Equivalence and Hölder Sobolev regularity of solutions for a class of non-autonomous stochastic partial differential equations. *Ann. I. H. Poincaré PR* 39, (4) 703-742 (2003).
Xu T.G. and Zhang T.S.: White noise driven SPDEs with reflection: Existence, uniqueness and large deviation principles *Stochatic processes and their applications*, 119, 3453-3470 (2009).
Laurent DENIS\
Laboratoire d’Analyse et Probabilités\
Universit[é]{} d’Evry Val d’Essonne\
23 Boulevard de France\
F-91037 Evry Cedex, FRANCE\
e-mail: ldenis[’100]{}univ-evry.fr
Anis MATOUSSI\
LUNAM Université, Université du Maine\
Fédération de Recherche 2962 du CNRS\
Mathématiques des Pays de Loire\
Laboratoire Manceau de Mathématiques\
Avenue Olivier Messiaen\
F-72085 Le Mans Cedex 9, France\
email : anis.matoussi@univ-lemans.fr\
and\
CMAP, Ecole Polytechnique, Palaiseau
Jing ZHANG\
Laboratoire d’Analyse et Probabilités\
Universit[é]{} d’Evry Val d’Essonne\
23 Boulevard de France\
F-91037 Evry Cedex, FRANCE\
Email: jing.zhang.etu@gmail.com
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State Editions
One held for assault on boxing player
Kolar police have nabbed a 20-year-old youth on the charge of attacking a national boxing player with a sharp edged weapon on Tuesday near Kempfort School.
Police said that the victim Ankit Verma was attacked with a sharp-edged weapon by the accused Jeetu Yadav. The victim was rushed to JP hospital where his condition is reportedly stable. The victim sustained 2-3 injuries in his face.
The police registered a case under section 294, 324, 326 and 506 of the IPC and nabbed the accused.In his complaint the victim stated that on Tuesday during a fight at Baskhedi road he intervened and tried to pacify the youths but one of the youths opposed and the victim punched him in his face. The youth identified as Jeetu Yadav to settle score followed the victim and on Wednesday attacked him.During the investigation police found that the Jeetu Yadav had also sustained injuries and after preliminary investigation a case against Ankit Verma and two others was registered. The police registered a case under section 294,323, 506 and 34 of the IPC and have started further investigation.Meanwhile, Bajaria police have nabbed a 20-year-old youth for abetment to commit suicide of 19-year-old girl at Vijay Nagar in the month of May this year.Police said that the deceased Bharti Shakya committed suicide at her house on June 13, 2017 and after few days her father lodged a complaint against the accused Sanjay Raikwar regarding harassment and molestation of her daughter.During the investigation police found that the accused used to harass the deceased and which forced her to take extreme step. The police registered a case under section 306 of the IPC and started further investigation.
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Volunteer
Are you a patient’s family member? Are you a family member of a current or past employee? Do you just have a passion for helping others? Whoever you are, we would love to have you as a part of our team!!! Our volunteers benefit by:
Opportunity to make a difference!
Lending a helping hand
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Helping in the healing process
We Love Our Volunteers! Our Volunteers receive a free lunch the day of service, gift shop discounts, free flu shots and an annual Christmas Party. Requirements are to have a background check and a tb titre test at the hospital. Come be a part of our Growing volunteer family. Join us today! We would love to have you as part of our team! Get involved and make a real difference. If you are interested, please contact us.
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Preparative Separation of High-Purity Dihydroartemisinic Acid from Artemisinin Production Waste by Combined Chromatography.
In order to make full use of artemisinin production waste and thus to reduce the production cost of artemisinin, we developed an efficient and scalable method to isolate high-purity dihydroartemisinic acid from artemisinin production waste by combining anion-exchange resin with silica-gel column chromatography. The adsorption and desorption characteristics of dihydroartemisinic acid on 10 types of anion-exchange resin were investigated, and the results showed that the 717 anion-exchange resin exhibited the highest capacity of adsorption and desorption to dihydroartemisinic acid. Adsorption isotherms were established for the 717 anion-exchange resin and they fitted well with both Langmuir and Freundlich model. Dynamic adsorption and desorption properties of 717 anion-exchange resin were characterized to optimize the chromatographic conditions. Subsequently, the silica-gel column chromatography was performed and dihydroartemisinic acid with a purity of up to 98% (w/w) was obtained. Finally, the scale-up experiments validated the preparative separation of high-purity dihydroartemisinic acid from industrial waste developed in the present work. This work presented for the first time an isolation of dihydroartemisinic acid with a purity of 98% from Artemisia annua (A. annua) by-product, which adds more value to this crop and has the potential to lower the prices of anti-malarial drugs.
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The Work (band)
The Work were an English post-punk rock group, founded in 1980 by multi-instrumentalist/composer Tim Hodgkinson and guitarist/composer Bill Gilonis, with bass guitarist Mick Hobbs and drummer Rick Wilson. The band toured Europe in 1981 and 1982, and recorded their first album, Slow Crimes in 1982. After a tour of Japan later that year and releasing Live in Japan, the band split up. In 1989, the Work reformed to record Rubber Cage and performed throughout Europe between 1989 and 1994, releasing another album, See in 1992. A live album, The 4th World, recorded in Germany in 1994, was released in 2010.
History
Ex-Henry Cow co-founder Tim Hodgkinson began recording with Bill Gilonis in 1979. They experimented with tape collages which led to the creation of an independent record label, Woof Records and a band. Enlisting the services of Mick Hobbs and Rick Wilson they formed the Work, a post-punk rock group.
In 1981, the Work made their first recording, an EP "I Hate America", released on the Woof label. They then embarked on a tour of Europe, performing in the Netherlands, Belgium, Switzerland, Sweden, Finland, Norway, Germany, France, Italy and Yugoslavia. Extracts from these live performances were later released on a cassette tape album, The Worst of Everywhere (1983). In 1982, the band played at a Rock in Opposition Festival in Bonn with vocalist Catherine Jauniaux, after which they recorded their first album Slow Crimes on the Woof label with Jauniaux as guest musician. Slow Crimes took punk rock to new heights by introducing elements of avant-rock.
The band's next commitment was a tour of Japan in June 1982, but before the tour began, Wilson left to study chenda temple drumming in Kerala, South India, and Hobbs followed soon after over disagreements about the band's musical direction. Committed to the tour, Hodgkinson and Gilonis asked ex-Henry Cow drummer Chris Cutler and bassist Jim "Amos" Welton to join them in Japan. With this altered line-up, the group played three concerts in Tokyo and one in Osaka. The Osaka concert was recorded with a cassette recorder halfway down the hall, which was later cleaned up and released by Recommended Records Japan on an LP Live in Japan. At the end of the tour, the group split up.
In 1989, the Work reformed with its original members and recorded an industrial/noise album Rubber Cage, after which they returned to touring Europe, performing in France, Germany, Austria, Czechoslovakia, Switzerland and Italy over the next two years. In 1992, they made their last album, See, which they played live on their ongoing European tour. In 1993, the band played at the St. Petersburg Open Music Festival in Russia. The Work's last performances were in 1994 in Italy, Switzerland, Germany, Slovenia and the Czech Republic, where they had begun drawing on Hopi Indian mythology for their sets.
The 4th World, a live album recorded in Freiburg im Breisgau, Germany in 1994, was released by Ad Hoc Records in 2010. The original mono recordings were reprocessed into stereo by Udi Koomran.
Personnel
Tim Hodgkinson – saxophones, bass clarinet, keyboards, lap steel guitar, lead vocals
Bill Gilonis – guitar, euphonium, sampling, vocals
Mick Hobbs – guitar, bass guitar, drums, ukulele, recorder, midi-horn, vocals
Rick Wilson – drums, bass guitar, vocals
Discography
Albums
Slow Crimes (1982, LP, Woof Records, UK)
Live in Japan (1982, LP, Recommended Records, Japan)
The Worst of Everywhere (1983, CT, Woof Records, UK)
Rubber Cage (1989, LP, Woof Records, UK)
See (1992, CD, Woof Records, UK)
The 4th World (2010, CD, Ad Hoc Records, US)
Extended plays
"I Hate America" / "Fingers & Toes" / "Duty" (1981, EP, Woof Records, UK)
Singles
"I Hate America" (1982, 7", Eastern Works, UK)
"Slowly Crimes" (1982, 7", Eastern Works, UK)
Compilations
The Work (2018, LP, Jelodanti Records, France)
Appears On
Various artists: Miniatures: A Sequence of Fifty-One Tiny Masterpieces (1980, LP, Pipe, UK) – includes one track, "With Wings Pressed Back" by the Work
Various artists: Recommended Records Sampler (1982, 2xLP, Recommended Records, UK) – includes one track, "Houdini" by the Work
The Lowest Note, The Work, Gilonis / Hodgkinson: WOOF 7 Inches (2004, CD, Ad Hoc Records, US) – includes six tracks by the Work
References
External links
.
Tim Hodgkinson / The Work. Chris Cutler homepage.
Tim Hodgkinson. The Canterbury Website.
Woof Records discography. SquidCo.
Category:English rock music groups
Category:English experimental musical groups
Category:English post-punk music groups
Category:British industrial music groups
Category:Musical groups established in 1980
Category:1980 establishments in England
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6.5in 8.5in -0.25in
2[[cm\^[-2]{}]{}]{} 2[[[cm]{}\^2]{}]{} 3[[[cm]{}\^[-3]{}]{}]{} 3[[[gcm\^[-3]{}]{}]{}]{}
\#1\#2[3.6pt]{}
Michael S. Turner,$^{1,2,3}$ Evalyn I. Gates,$^{2,3}$ and Geza Gyuk$^1$\
\
\
\
**ABSTRACT**
We discuss the implications of the recent upward revision of the LMC microlensing rate by the MACHO Collaboration. We conclude: (i) A good case for the existence of baryonic dark matter in the halo has been made; (ii) The case for the existence of cold dark matter is unaffected and still compelling; and (iii) The Galactic halo is still an excellent place to search for cold dark matter particles (e.g., axions or neutralinos).
Perspective
===========
It is now a little more than two years since the MACHO and EROS Collaborations announced their first microlensing results: one LMC event for MACHO and two LMC events for EROS [@nature]. At about the same time OGLE also reported microlensing events toward the bulge, at a much higher rate than expected rate [@ogle]. Paczynski’s bold idea had become reality.
The initial response to the LMC results was swift and not unexpected: The dark matter problem has been solved – it was baryons after all. A dark cloud of gloom engulfed the particle dark matter searches. After a while, sanity returned: The numbers were small and the uncertainties – both Poisson and galactic modelling – were large [@meaning].
About a year ago MACHO [@machoprl] and EROS [@eroslmc] presented detailed analyses of a big chunk of data (for MACHO the first year’s data with three events toward the LMC; for EROS the same two events). Both groups concluded that the halo MACHO fraction was small, around 20%. Our independent analysis [@prl; @prd] of the LMC and bulge data based upon extensive galactic modelling indicated the same (likelihood function peaked around a halo MACHO fraction of 15%.) WIMP hunters were very happy. However, as we and others (David Bennett especially) emphasized the uncertainties were still large and it was too early to rule out an all-MACHO halo. Moreover, others had suggested radical ideas for an all baryonic halo, e.g., gas clouds [@jetzer].
The OGLE [@ogle] – and later the MACHO [@machobulge] – higher-than-expected bulge results provided further evidence that the bulge is actually a heavy bar, a possibility not considered in the original estimates. This has important consequences for interpreting the LMC events. A heavy bar precludes a light halo, which, for a given LMC microlensing rate, pushes down the halo MACHO fraction [@prl; @prd].
The MACHO Collaboration has now analyzed two years of LMC data and has 8 or 7 or 6 events, depending upon selection criteria. Two year-one events have now been rejected (one turned out to be a repeater). The halo MACHO fraction is now quoted as 50% [@nyt]. The dark cloud threatens WIMP chasers again – 50% is dangerous close to 100%.
What happened? The nearly 100 bulge events seen by the MACHO Collaboration allowed a “tune up” of their event-recognition software, and they have another full year of data. They are able to detect longer duration events – and reject repeaters – and the statistics are better.
Beware! The number of events is still small and galactic uncertainties are still large. More long duration events may be found; some candidates may be rejected, and the software may improve again – leading to higher or lower rates. It is not time for WIMP hunters to panic.
=7.5cm
Based upon the seven MACHO LMC events, the microlensing rate toward the bulge and extensive modelling of the Galaxy, we find a likelihood function for the MACHO halo fraction which is very broad (allowing both 0 and 100%) and which achieves its maximum at around 30% (see Fig. 1). (For reference, the MACHO Collaboration bases its 50% estimate on their standard halo model, which is “light” by industry standards, leading to their higher MACHO halo fraction. In light of the large uncertainties the differences are not important.) Our likelihood function for the local density of “unknown matter” indicates that there is still plenty of room for cold dark matter in our own back yard (see Fig. 2).
=7.5cm
Interpretation
==============
The MACHO Collaboration did not actually measure the MACHO fraction of the halo! They measured the frequency of microlensing toward the LMC, which can be expressed as the optical depth for microlensing – the probability that a given LMC star is being microlensed. Based upon the seven events in the two-year data set $\tau_{\rm LMC} = 2^{+1.0}_{-0.6}\times 10^{-7}$ [@dbatucb].[^1] [*Assuming*]{} that MACHOs are distributed as the halo material (density decreasing as $r^{-2}$) and that the halo MACHO fraction is constant throughout the halo, the optical depth can be used to [*infer*]{} the fraction of the halo mass contributed by MACHOs – about 50% according to the MACHO Collaboration [@nyt; @dbatucb] or 30% according to our analysis.
If, however, MACHOs are distributed differently, the halo MACHO fraction can be much lower. For example, for a spatial density that decreases as $r^{-3}$, like the spheroid component of the Galaxy, the inferred MACHO fraction falls to about 10%.[^2]
Further, since the distance to the LMC is $50\kpc$ microlensing of LMC stars cannot probe the halo beyond this. In fact, most of the optical depth is contributed by MACHOs that are between $10\kpc$ and $30\kpc$ from the center of the Galaxy (see Figure in Ref. [@meaning]). It could be that the inner portion of the Galaxy has a MACHO fraction of 50% and that the MACHO fraction falls off beyond this, so that something else accounts for the bulk of the halo. There is good evidence that the halo of the Galaxy extends to $100\kpc$ or more. (When the density decreases as $r^{-2}$ the mass per interval of radial distance is constant.)
Even more difficult to estimate is the fraction of critical density contributed by MACHOs. As described above, the halo MACHO fraction is difficult to determine, and the fraction of critical density contributed by the dark halos of spiral galaxies is very poorly known. This is because the full extent of dark halos is not known; if halos are small $\Omega_{\rm HALO}$ could be as low as 0.05; on the other hand if halos are as large as they could be, extending to neighboring galaxies, $\Omega_{\rm HALO}$ could be 1.0.
Implications for Particle Dark Matter
=====================================
There are a number of very good reasons to believe that the bulk of matter in the Universe exists in the form of slowly moving elementary particles left over from the earliest moments (cold dark matter), with the most promising cold dark matter candidates being the axion and the neutralino. First, the cold dark matter scenario for structure formation is by a wide margin the most successful, with supporting evidence coming from anisotropy measurements of the CBR, large redshift surveys, and numerous other observations. (By cold dark matter, we mean one of the several variants that have been discussed – cold dark matter plus hot dark matter, a cosmological constant, tilted spectrum of density perturbations, unstable tau neutrino, or very low Hubble constant [@appraise].) While the mean density of the Universe has yet to be determined, the masses of clusters of galaxies [@clusters] and the peculiar velocities of galaxies (including our own) [@peculiar] indicate that $\Omega_0$ is at least 0.2, which is larger than the upper limit to what baryons can contribute that comes from primordial nucleosynthesis, $\Omega_B
\la 0.02h^{-2}$ [@cst]. (Note, this upper limit is only close to 0.2 if the Hubble constant is very small, $h\sim 0.35$. For $h\sim 0.7$, $\Omega_B \la 0.04$ and virtually all cosmologists would agree that $\Omega_0$ is greater than 0.1.) On the theoretical side, inflation predicts a critical density Universe, $\Omega_0 = 1.0$; current measurements of CBR anisotropy are consistent with the inflationary prediction [@mwscience], and measurements made in the next five years or so should decisively test inflation [@kamio].
It should be noted that the dark halos of spiral galaxies like our own never provided evidence for nonbaryonic dark matter for the simple reason that galactic halos need not contribute more mass density than baryons can account for. On the other hand, galactic halos are – and always have been – an excellent place to search for cold dark matter particles since it is virtually impossible to keep cold dark matter out of galactic halos [@gates].
Within the context of the cold dark matter theory the universal fraction of matter in baryons is expected to be between 5% and 20%. The baryonic content of the halo is another matter; galactic halos probably do not provide a fair sample of the cosmos. At least some of the baryons in our galaxy have undergone dissipation – those in the disk – and it is not impossible that the bulk of the baryons have condensed into the disk, in which case the halo MACHO fraction would be smaller than the universal baryon fraction. At the other extreme, it is possible that most of the baryons in our galaxy have undergone only modest dissipation and reside in the inner portion of the halo, in which case the baryon fraction there could be 50% or so. Estimates for the plausible MACHO fraction of the inner halo range from 0% to 50% [@gates].
Finale
======
The MACHO, EROS, and OGLE microlensing experiments have monitored millions of stars over the past few years looking for the proverbial needle in the haystack. And they have found it – making believers of the many nay-sayers who doubted that microlensing could be detected against the background of known variable stars and unknown things that go bump in the night. The detection of microlensing represents a significant scientific achievement as well as an important new probe of the Galaxy.
It is still too early to make definitive statements concerning the composition of the Galactic halo. However, strong evidence has been presented for the existence of massive, dark objects within $30\kpc$ of the center of the Galaxy. The most plausible explanation is dark stars (e.g., white dwarfs or neutron stars of mass $\sim 0.3M_\odot$).
The galactic baryonic dark matter believed to exist on the basis of big-bang nucleosynthesis may well have been identified and one of the two dark matter problems may have been solved! That would be quite an achievement. (Big-bang nucleosynthesis provides a lower limit to the baryon density, $\Omega_B \ga
0.01h^{-2}$, that exceeds the contribution of luminous matter, $\Omega_{\rm LUM} \simeq 0.003h^{-1}$.)
Galactic microlensing has not diminished the case for a Universe comprised primarily of cold dark matter. In fact, the inferred halo MACHO fraction suggests that much of the nearby dark matter in the Galaxy is still of undetermined composition (see Fig. 2), with cold dark matter particles leading the list of possibilities. This, together with the cosmic motivations for cold dark matter, should continue to warm the hearts of WIMP chasers and justify their heroic efforts to detect particle dark matter in our back yard.
#### Acknowledgments.
This work was supported by the DoE (at Chicago and Fermilab) and by the NASA (at Fermilab by grant NAG 5-2788).
[cst]{}
E. Aubourg et al., [*Nature*]{} [**365**]{}, 623 (1993); C. Alcock et al., [*ibid*]{}, 621 (1993).
A. Udalski et al., [*Astrophys. J.*]{} [**426**]{}, L69 (1994); [*Acta Astron.*]{} [**43**]{}, 289 (1993); [*ibid*]{} [**44**]{}, 165 (1994); [*ibid*]{} [**44**]{}, 227 (1994).
M.S. Turner, astro-ph/9310019 (1993).
C. Alcock et al., [*Phys. Rev. Lett.*]{} [**74**]{}, 2867 (1995).
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E. Gates, G. Gyuk, and M.S. Turner, [*Phys. Rev. Lett.*]{} [**74**]{}, 3724 (1995).
E. Gates, G. Gyuk, and M.S. Turner, [*Phys. Rev. D*]{}, in press (1996) (astro-ph/9508071).
F. De Paolis, G. Ingrosso, Ph. Jetzer, and M. Roncadelli, astro-ph/9504080 (1995).
C. Alcock et al., [*Astrophys. J.*]{} [**445**]{}, 133 (1995); astro-ph/9512146 (1995).
D. Bennett, quoted in [*New York Times*]{} (January 17, 1996).
D. Bennett, presented at CfPA seminar at UC Berkeley (January 24, 1996).
S. Dodelson, E. Gates, and M.S. Turner, in preparation; also see, A.R. Liddle et al., astro-ph/9511057.
See e.g., N. Kaiser, astro-ph/9509019.
M. Rowan-Robinson et al., [*Mon. Not. R. astr. Soc.*]{} [**247**]{}, 1 (1990); N. Kaiser et al., [*ibid*]{} [**252**]{}, 1 (1991); M. Strauss et al., [*Astrophys. J.*]{} [**385**]{}, 444 (1992); A. Dekel, [*Ann. Rev. Astron. Astrophys.*]{} [**32**]{}, 319 (1994).
C. Copi, D.N. Schramm, and M.S. Turner, [*Science*]{} [**267**]{}, 192 (1995); [*Phys. Rev. Lett.*]{} [**75**]{}, 3981 (1995).
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[^1]: The optical depth $\tau = {\pi \over 4E}\sum_{i}{t_i \over \varepsilon_i}$, where $t_i$ is the duration of event $i$, $E$ is the exposure (e.g., in star-years), and $\varepsilon_i$ is the efficiency of detecting an event of duration $t_i$.
[^2]: Such a model is only viable if $\tau\la 2\times 10^{-7}$.
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Pineapple whip is a frozen dessert and it's totally vegan and healthy too! This whip is a perfect dessert to cool off the summer heat!
Recipe
Author : Himabindu
Yield : 2 servings
Requirements
Ingredients
2 cups frozen pineapple
1 ripe banana
optional : 1 tbsp honey or maple syrup
: 1 tbsp honey or maple syrup ½ cup coconut water
Directions
Cut a fresh pineapple into cubes and freeze them overnight. Blend all the ingredients in a blender or food processor. Every minute or so, stop and scrape down the sides with a spatula. Blend until evenly creamy consistency is attained. Spoon it into a cup or get fancy with a piping bag and swirl it into a serving cup. Top off with small pineapple cubes and a mint leaf for decoration.
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1720 in piracy
See also 1719 in piracy, 1721 in piracy and Timeline of piracy.
Events
Caribbean Sea
February - Bartholomew Roberts robs four vessels near Barbados.
February 26 - Two pirate ships commanded by Bartholomew Roberts and Montigny la Palisse are attacked near Barbados by local ships and driven away with heavy casualties.
March - Two sloops sent from Martinique to capture Roberts and his men arrive too late to capture the pirates, who have sailed northward. Roberts adopts a new flag threatening death to the inhabitants of Barbados and Martinique.
August - Calico Jack Rackham steals John Haman's sloop from the harbor of Nassau, Bahamas and leads a crew of pirates to sea, including Anne Bonny & Mary Read.
September Rackham and his pirates loot several fishing boats in the Bahamas. They then raid French Hispaniola for cattle and capture two sloops.
Roberts returns to the Caribbean, bombards Saint Kitts and burns two ships in the harbor. Some weeks later, Roberts captures a French ship near Carriacou and commandeers it, renaming it the Royal Fortune.
October - Pirates under Rackham's leadership ransack several vessels off northern Jamaica.
October - Rackham and his crew are captured by a commissioned sloop commanded by Jonathan Barnet. After the main mast is disabled, the surprised pirates make no resistance except for Anne Bonny and Mary Read and one other.
November Rackham & his crew are tried, sentenced & hanged. Rackham & 2 others are gibbetted. Read & Bonny are tried a week later, sentenced (execution delayed due to pregnancy).
Indian Ocean
Undated - Edward England ravages the Malabar Coastal shipping, taking one Dutch vessel and an unknown number of Indian hulls.
October - Captain Condent captures an Arab ship off Bombay, stealing approximately ₤150,000 worth of cash and cargo.
November 20, 1720 - Captain England in the Fancy and Captain Olivier Levasseur alias "la Buse" attack Captain James Macrae in the East Indiaman Cassandra near Anjouan in the Comoros. Macrae is ultimately forced aground after a bloody battle.
November–December - Captain England and some of his friends are marooned by their pirate crew, who elect John Taylor to replace him.
North America
June 21 - Bartholomew Roberts invades the harbor of Trepassey, Newfoundland, plundering 22 vessels and burning all but one.
July - Roberts captures nine or ten French vessels off the Grand Banks and commandeers a new ship, the 26-gun Fortune. Aboard the Fortune, Roberts proceeds to take ten English vessels, then sails back toward the Caribbean.
West Africa
October–November - Roberts in the Royal Fortune tries to reach the Cape Verde Islands, but misses his landfall and is forced back to the West Indies by the trade wind. Shortage of water kills many of his pirates.
Deaths
November 17 - Calico Jack Rackham hanged for piracy at Gallows Point, Port Royal, Jamaica (born December 21, 1682).
Piracy
Category:Piracy by year
Category:1720 in military history
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Image copyright Peter and Jane
When your social media news feeds are filled with images of your friends' smiling, perfectly-groomed children playing contentedly with their siblings in spotlessly clean Pinterest-worthy designer kitchens, it's easy to forget that these are the heavily edited highlights of family life.
Most people don't share the humdrum realities of parenthood and children on Facebook - the endless episodes of Paw Patrol on the "electronic babysitter", the fight over a long-neglected plastic toy from a Christmas cracker pulled in 2012, and the can't-be-bothered Sunday night teas of sugar-coated breakfast cereal.
But Gill Sims is not most people.
Her blog, Peter and Jane, is an honest, sweary, tongue-in-cheek account of a pretty normal, middle-class Scottish family. In less than a year, her daily Facebook posts about Mummy, Daddy, their two "precious moppets", and their pet "Judgy dog" has become a cult hit, attracting more than 250,000 followers.
They enjoy daily updates about mundane events which must happen in homes across the country - but they are recounted in a style which crosses Peppa Pig with Bridget Jones. In one popular recent post, she described a "major catastrophe" when her "busy and important" husband lost his car keys.
She wrote: "Mummy is sick to death of being expected to find things, and has told Daddy to find his own (expletive) keys.
"That's OK though, because Daddy has a special method of looking for things, which involves stamping around the house in a thunderous temper having a massive tantrum and shouting at everybody and blaming them for the missing car keys."
She eventually found the keys in the pocket of his jeans (obviously), along with £40 in cash - which she quietly pocketed as her "finders fee".
"Mummy is going to spend her £40 windfall on posh gin," she wrote. "Mummy is not going to share the posh gin with Daddy, but she may well brain him with the empty bottle when she has drunk it all."
Image copyright Peter and Jane Image caption Gill Sims' blog regularly features her beloved rescue dog, Buddy AKA "Judgy Dog"
Ms Sims, who has a background in engineering and works for a software company, told the BBC Scotland website that the blog was "a bit of light-hearted fun really, about the everyday, really dull bits of parenting - and marriage and family".
She said she started writing the posts after joking with her friend about how much she swears but she has been overwhelmed by the feedback she has received from other parents.
"It was never planned to turn into the something the size of what it's become," she said. "I suppose I do it because it's so nice to see that there are so many people are feeling the same, doing the same things, having the same experiences."
Her page really took off after she described a typical day keeping the family afloat during last year's school summer holidays. It was a post that was shared 67,000 times.
Struck a chord
"It was about the middle of July and it was just a post about a really long day in the school holidays and all the things you end up doing in the school holidays to entertain the children and keep everything going and everything else, and then your husband comes home and says "so what did you do today?"
"For some reason that, I don't know why, that was the one that kind of just took off. I wouldn't even say it was particularly good post or one of the best I've done. But for whatever reason that seemed to be the one the struck a chord."
Another post about post-natal depression, during which she recounts being approached by two police officers as she tearfully pushed the baby in its pram at 02:00 one morning, also provoked a strong reaction.
"It seemed to really make a difference to a lot of people who spoke about their own experiences, for the first time in a lot of cases," she said.
"A lot of people messaged as well to say 'that's how I felt but I've never really been able to put it into words'. So from that perspective, I think that was probably one of the ones that I think was a good one in that it seemed to help a lot of people."
Image copyright Peter and Jane Image caption Ms Sims signs off most of her posts with a picture of two of her favourite things
The camera-shy blogger generally illustrates her writing with two of the recurring elements of her musings - alcohol and her beloved Border Terrier, Buddy, who is known to readers as "Judgy Dog". Indeed, he has built up such a following he now has a Facebook page of his own.
"Some days I have no idea what I'm going to write about, it's just kind of let's see what happens today kind of thing," she said.
"Other days I've got a bit more of an idea. But sometimes it really is what silly thing are they going to do today, my darling children? Or indeed my darling husband?"
She added: "Sometimes I spend quite a lot of time on them and I think that's quite good and it's not that popular.
"Other times, I've got half an hour and I dash something off and everyone really likes it. I'm never able to tell what's going to resonate and what's not.
"I'm still very much winging it, I have to say."
'Mummy bloggers'
She said her school-age children don't really want to feature in the blog - they are only referred to as the Girl Child and the Boy Child - but she has received warm praise at the school gates.
"It seems to have gone down really, really well. People who have never really spoken to me before have come over to me and said 'oh, we really like it'," she said.
"Online feedback is pretty much all positive as well. People find it funny, people feel it reflects their own experiences.
"There's the odd negative bit usually from - and this sounds really bad - but usually from a grumpy man saying you should get a life or whatever else. But that's really the odd comment. It's by and large positive."
Her work has inevitably led to comparisons with other "mummy bloggers", like The Unmumsy Mum and Hurrah for Gin, who have both both been snapped up by publishers since starting blogs.
Ms Sims is coy about any plans for a Peter and Jane book, though she admits there are a few projects in offing. "We'll have to wait and see," she said.
So how would she describe their genre of writing? Are they writing "angry mum blogs"?
"We are sometimes angry, I think just real mums, honest mums, slightly frustrated mums."
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Wild Blackberries
According to the Clean Eating Club, they are “rich in antioxidants, including vitamin c, ellagic acid and anthocyanins”. They also contain “calcium, iron, magnesium, phosphorus, potassium, zinc, copper, manganese, vitamins A and E, selenium and folate”.
Nutrition Data lists blackberries as a low calorie (62) and low fat (6) food – this is based on a 1 cup serving size.
The best way to eat this delicious fruit is to eat them raw, and mix them with other berries :) But, of course, it’s also fun to make a blackberry cobbler and/or blackberry ice cream! (Go ahead…you can indulge once in awhile!)
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Many satellites and other systems have one or more covers or doors to protect internal mechanisms, e.g., optics, sensors and sensitive machinery during transport or other periods of disuse. These types of doors utilize various mechanisms, such as mechanical launch locks to hold them in a closed position and motors to open them. Motors and the control circuitry by which they are operated are expensive to design, procure, manufacture and test. In some applications, such as space-based systems, testing typically includes a life cycle test which could take months to complete. Additional items that drive cost in such space-based systems include the launch lock, the control/telemetry electronics, the drive motor, the gear box, as well as vacuum compatible bearings and grease. Research and development efforts that seek to simplify cover/door mechanisms, and to reduce cost accordingly, are ongoing.
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Q:
ответ Ping в zabbix
Добрый день. Нужно в заббикс выводить график доступности хоста путем его пинга. Комманду предпологаю такую:
ping -s 991 -M do 1.2.3.4
Меня интересует время ответа. Как бы это реализовать в заббикс.
A:
В заббиксе есть стандартный функционал определения задержек и потерь через icmp – https://www.zabbix.com/documentation/2.4/ru/manual/config/items/itemtypes/simple_checks
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Introduction {#s1}
============
Multicellular development relies on the formation of cell-type-specific gene expression programmes that support differentiation. At the most basic level, these expression programmes are defined by cell signaling pathways that control how transcription factors bind DNA sequences in gene regulatory elements and shape RNA polymerase II (RNAPolII)-based transcription from the core gene promoter (reviewed in \[[@bib74]\]). In eukaryotes, the activity of RNAPolII is also regulated by a large multi-subunit complex, Mediator, which can directly interact with transcription factors at gene regulatory elements and with RNAPolII at the gene promoter to modulate transcriptional activation. The Mediator complex functions through regulating pre-initiation complex formation and controlling how RNAPolII initiates, pauses, and elongates. Therefore, Mediator is central to achieving appropriate transcription from gene promoters (reviewed in \[[@bib4]; [@bib56]\]).
In mammalian genomes, CpG dinucleotides are pervasively methylated and this epigenetically maintained DNA modification is generally associated with transcriptional inhibition, playing a central role in silencing of repetitive and parasitic DNA elements ([@bib44]; [@bib70]). Most gene promoters, however, are embedded in short elements with elevated CpG dinucleotide content, called CpG islands, which remain free of DNA methylation ([@bib10]; [@bib38]; [@bib48]). Interestingly, mammalian cells have evolved a DNA-binding domain, called a ZF-CxxC domain, which can recognize CpG dinucleotides when they are non-methylated ([@bib50]; [@bib82]). This endows ZF-CxxC domain-containing proteins with the capacity to recognize and bind CpG islands throughout the genome ([@bib15]; [@bib78]). There are 12 mammalian proteins encoding a ZF-CxxC domain, most of which are found in large chromatin modifying complexes that post-translationally modify histone proteins to regulate gene expression from CpG islands ([@bib53]). This has led to the proposal that CpG islands may function through chromatin modification to affect transcription ([@bib14]).
One of the first characterised ZF-CxxC domain-containing proteins was lysine-specific demethylase 2A (KDM2A) ([@bib15]). KDM2A is a JmjC-domain-containing histone lysine demethylase that removes histone H3 lysine 36 mono- and di- methylation (H3K36me1/2) from CpG islands ([@bib15]; [@bib80]). Like DNA methylation, H3K36me1/me2 is found throughout the genome and is thought to be repressive to gene transcription ([@bib19]; [@bib42]; [@bib63]). Therefore, it was proposed that KDM2A counteracts H3K36me2-dependent transcriptional inhibition at CpG island-associated gene promoters ([@bib15]). Sequence-based homology searches revealed that KDM2A has two paralogues in vertebrates, KDM2B and FBXL19 ([@bib41]). KDM2B, like KDM2A, binds to CpG islands and can function as a histone demethylase for H3K36me1/2 via its JmjC domain ([@bib28]; [@bib33]). However, unlike KDM2A, it physically associates with the polycomb repressive complex 1 (PRC1) to control how transcriptionally repressive polycomb chromatin domains form at a subset of CpG island-associated genes ([@bib12]; [@bib28]; [@bib34]; [@bib85]). These observations have suggested that, despite extensive similarity between KDM2A and KDM2B and some functional redundancy in histone demethylation, individual KDM2 paralogues have evolved unique functions. FBXL19 remains the least well characterized and most divergent of the KDM2 paralogues. Unlike KDM2A and KDM2B, it lacks a JmjC domain and, therefore, does not have demethylase activity ([@bib53]). Previous work on FBXL19 has suggested that it plays a role in a variety of cytoplasmic processes that affect cell proliferation, migration, apoptosis, TGFβ signalling, and regulation of the innate immune response ([@bib24]; [@bib83]; [@bib88]; [@bib89]). More recently, it has also been proposed to have a nuclear function as a CpG island-binding protein ([@bib49]), but its role in the nucleus still remains poorly defined.
Here, we investigate the function of FBXL19 in mouse embryonic stem (ES) cells and show that it is predominantly found in the nucleus where it localizes in a ZF-CxxC-dependent manner to CpG island promoters. Biochemical purification of FBXL19 revealed an association with the CDK-containing Mediator complex and we discover that FBXL19 can target CDK-Mediator to chromatin. Conditional removal of the CpG island-binding domain of FBXL19 in ES cells leads to a reduction in the occupancy of CDK8 at CpG islands associated with inactive developmental genes. FBXL19 and CDK-Mediator appear to play an important role in priming genes for future expression, as these genes are not appropriately activated during ES cell differentiation when the CpG island-binding capacity of FBXL19 is abolished or CDK-Mediator is disrupted. Consistent with an important role for FBXL19 in supporting normal developmental gene expression, removal of the ZF-CxxC domain of FBXL19 leads to perturbed development and embryonic lethality in mice. Together, our findings uncover an interesting new mechanism by which CDK-Mediator is recruited to gene promoters in ES cells and demonstrate a requirement for FBXL19 and CDK-Mediator in priming developmental gene expression during cell lineage commitment.
Results {#s2}
=======
FBXL19 is enriched in the nucleus and binds CpG islands via its ZF-CxxC domain {#s2-1}
------------------------------------------------------------------------------
FBXL19 shares extensive sequence similarity and domain architecture with the other KDM2 paralogues which are predominantly nuclear proteins ([Figure 1A](#fig1){ref-type="fig"}, \[[@bib15]; [@bib28]\]), yet the function of FBXL19 has largely been described in the context of cytoplasmic processes ([@bib24]; [@bib83]; [@bib88]; [@bib89]). Therefore, we first examined the subcellular distribution of FBXL19 to understand whether it was unique amongst KDM2 paralogues in localizing to the cytoplasm. To achieve this, we generated a mouse ES cell line expressing epitope-tagged FBXL19 (FS2-FBXL19) and carried out immuno-fluorescent staining. This revealed that FBXL19 was almost exclusively nuclear ([Figure 1B](#fig1){ref-type="fig"}). When we carried out subcellular biochemical fractionation, FBXL19 was also enriched in the nuclear fractions in agreement with the immuno-fluorescent staining ([Figure 1C](#fig1){ref-type="fig"}). Importantly, FBXL19 was found not only in the soluble nuclear extract but also in the insoluble nuclear pellet, which contains chromatin-bound factors ([Figure 1C](#fig1){ref-type="fig"}). This suggested that FBXL19 may associate with chromatin, like other ZF-CxxC domain-containing proteins.
{#fig1}
Based on the nuclear localization of FBXL19 and the fact that it encodes a highly conserved ZF-CxxC domain ([Figure 1---figure supplement 1A](#fig1s1){ref-type="fig"}), we set out to determine whether FBXL19 is a CpG island-binding protein. To achieve this, we carried out chromatin immunoprecipitation followed by massively parallel sequencing (ChIP-seq) for epitope-tagged FBXL19 and compared its binding profile with those we have previously generated for KDM2A and KDM2B in mouse ES cells ([@bib12]; [@bib28]). A visual examination of FBXL19 ChIP-seq signal revealed that it was highly enriched at both computationally predicted CpG islands and genomic regions that contain BioCAP signal, an experimental measure of non-methylated DNA ([@bib13]) ([Figure 1D](#fig1){ref-type="fig"}). We then identified all non-methylated CpG islands (NMIs) using BioCAP data (n = 27698) ([@bib54]) and extended our analysis across the genome. We observed that FBXL19 ChIP-seq signal at NMIs was highly similar to that of KDM2A and KDM2B ([Figure 1E](#fig1){ref-type="fig"}). Furthermore, FBXL19 ChIP-seq signal correlated well with the density of non-methylated CpG dinucleotides in NMIs, similarly to KDM2A and KDM2B, ([Figure 1F](#fig1){ref-type="fig"} and [Figure 1---figure supplement 1B,C](#fig1s1){ref-type="fig"}), and almost all FBXL19-occupied sites fell within NMIs ([Figure 1---figure supplement 1D](#fig1s1){ref-type="fig"}). Together these findings demonstrate that FBXL19 is a nuclear protein that binds to CpG islands, an observation supported by a recent independent study ([@bib49]).
KDM2A and KDM2B rely on defined residues in their ZF-CxxC domain to recognize non-methylated cytosine and bind CpG islands ([@bib15]; [@bib28]). To determine whether the association of FBXL19 with CpG islands is dependent on this domain, we generated ES cell lines expressing either a mutant version of FBXL19, in which a key lysine residue was substituted to alanine (K49A, [Figure 1---figure supplement 1A](#fig1s1){ref-type="fig"}) to disrupt the recognition of non-methylated CpGs, or a truncated version of FBXL19, where the ZF-CxxC domain was deleted (ΔCXXC) ([Figure 1G](#fig1){ref-type="fig"}). Importantly, the expression levels of wild type (WT) and mutant FBXL19 transgenes were highly similar ([Figure 1---figure supplement 1E](#fig1s1){ref-type="fig"}). We then carried out ChIP-seq for epitope-tagged FBXL19 in these cell lines and compared the binding profiles of the mutant FBXL19 to that of WT FBXL19 ([Figure 1H](#fig1){ref-type="fig"}). This revealed a near complete loss of FBXL19 binding to chromatin when the ZF-CxxC domain was deleted and a slightly less dramatic effect in the K49A mutant ([Figure 1H,I](#fig1){ref-type="fig"}, and [Figure 1---figure supplement 1F,G](#fig1s1){ref-type="fig"}). Together, these observations demonstrate that binding of FBXL19 to CpG islands relies on an intact and functional ZF-CxxC domain.
FBXL19 interacts with the CDK-Mediator complex in ES cells {#s2-2}
----------------------------------------------------------
Our ChIP-seq analyses demonstrated that FBXL19 is targeted to CpG islands in a manner that is highly similar to KDM2A and KDM2B ([Figure 1](#fig1){ref-type="fig"}). Although KDM2A and KDM2B localise to the same genomic regions and show a high degree of sequence conservation, they associate with different proteins ([@bib28]). This raised the interesting possibility that FBXL19 might also have unique interaction partners. To investigate this, we affinity-purified epitope-tagged FBXL19 from ES cell nuclear extract and identified associated proteins by mass spectrometry (AP-MS) ([Figure 2A](#fig2){ref-type="fig"}, [Figure 2---figure supplement 1A](#fig2s1){ref-type="fig"}, and [Figure 2---source data 1](#fig2sdata1){ref-type="supplementary-material"}). This revealed that FBXL19 interacts with SKP1, a known F-box-binding protein that also associates with KDM2A and KDM2B ([@bib6]; [@bib28]), and the nuclear proteasome activator PSME3 ([@bib86]). Interestingly, we also identified multiple subunits of the Mediator complex that appeared to interact with FBXL19 in a sub-stoichiometric manner ([Figure 2A,B](#fig2){ref-type="fig"}). Biochemical purifications of Mediator have identified two distinct assemblies ([@bib52]; [@bib58]; [@bib75]). The first is characterized by the presence of the MED26 subunit which associates with the middle region of Mediator and this form of the complex interacts with RNAPolII ([@bib60]; [@bib61]; [@bib69]; [@bib76]). Alternatively, a kinase module, composed of CDK8/CDK19, MED12/12L, MED13/13L, and CCNC, can bind to Mediator in a manner which is mutually exclusive with MED26 ([@bib75]). Interestingly, our FBXL19 purification identified subunits of the kinase-containing Mediator complex (CDK-Mediator), but not MED26 or RNAPolII ([Figure 2](#fig2){ref-type="fig"}). This suggests that FBXL19 interacts preferentially with CDK-Mediator, however, we cannot exclude the possibly it may also interact with MED26-Mediator. CDK8 and its paralogue CDK19 share 77% amino acid identity (89% similarity) ([@bib5]; [@bib32]; [@bib69]; [@bib81]) and four out of the five peptides identified by mass spectrometry were common between the two proteins (data not shown). Therefore, it is likely that FBXL19 is able to interact with both CDK8- and CDK19-containing Mediator complexes. Importantly, interaction with CDK-Mediator was also evident when we performed affinity-purification of endogenous FBXL19 ([Figure 2---figure supplement 1B--D](#fig2s1){ref-type="fig"}). However, reciprocal immunopurifications of MED12 and CDK8 failed to yield detectable FBXL19 by western blot ([Figure 2---figure supplement 1D](#fig2s1){ref-type="fig"}). This is in agreement with our mass spectrometry analysis, which indicated that the association of FBXL19 with CDK-Mediator is sub-stoichiometric, and suggests that this interaction is likely weak, as opposed to stable, inside cells.
{#fig2}
We next wanted to determine which region of FBXL19 is required for interaction with CDK-Mediator. To do so, we transiently expressed full length FBXL19 or versions of FBXL19 with individual domains removed and performed affinity purification followed by western blot analysis. Intact FBXL19 and a version with the ZF-CxxC domain removed interacted with CDK-Mediator, whereas removing the F-box domain resulted in a loss of this interaction ([Figure 2---figure supplement 1E](#fig2s1){ref-type="fig"}). Therefore, FBXL19 relies on its F-box, and not its capacity to bind non-methylated DNA, for its association with CDK-Mediator.
Based on a candidate approach, it was recently reported that FBXL19 could interact the RNF20/40 E3 ubiquitin ligase in ES cells and regulate histone H2B lysine 120 ubiquitylation (H2BK120ub1) ([@bib49]). In our unbiased biochemical purification of FBXL19, we did not identify an interaction with RNF20/40 by AP-MS or by western blot analysis ([Figure 2A](#fig2){ref-type="fig"} and [Figure 2---figure supplement 1F](#fig2s1){ref-type="fig"}). Furthermore, we failed to observe any relationship between the ability of FBXL19 to associate with CpG islands and the levels of H2BK120ub1 ([Figure 2---figure supplement 1G](#fig2s1){ref-type="fig"}). Therefore, the relevance of this proposed interaction remains unclear.
FBXL19 contains conserved F-box and leucine-rich repeat (LRR) domains. F-box proteins are known to function as scaffolds and substrate recognition modules for the SKP1-Cullin-F-box (SCF) protein complexes that ubiquitylate proteins for degradation by the proteasome ([@bib72]; [@bib73]). Based on the association of FBXL19 with SKP1 and PSME3, we speculated that FBXL19 might function as a SCF substrate-selector for CDK-Mediator, as has previously been observed for the related F-box-containing protein FBW7 ([@bib22]). Interestingly, however, in our FBXL19 purifications, we did not detect the SCF complex components CUL1 and RBX1/2, which are required for ubiquitin E3 ligase activity ([@bib72]) ([Figure 2A](#fig2){ref-type="fig"}). Nevertheless, we investigated in more detail whether FBXL19 might regulate CDK-Mediator protein levels. Treatment of ES cells with the proteasome inhibitor MG132, which sequesters SCF substrates on their substrate selector, did not lead to elevated levels of Mediator subunits in FBXL19 purifications as identified by AP-MS (unpublished observation). In addition, transient overexpression of FBXL19 did not cause an appreciable reduction in CDK-Mediator protein ([Figure 2---figure supplement 1H](#fig2s1){ref-type="fig"}). Based on these observations, we conclude that FBXL19 does not function as a SCF substrate selector for CDK-Mediator. This raised the interesting possibility that FBXL19 may function in a proteasome-independent manner with CDK-Mediator at CpG islands.
FBXL19 recruits CDK-Mediator to chromatin {#s2-3}
-----------------------------------------
It has previously been shown that transcription factors can recruit the Mediator complex to enhancers and gene promoters ([@bib65]), yet the complement of mechanisms by which Mediator is targeted to chromatin remains very poorly defined. Given that FBXL19 does not appear to regulate CDK-Mediator protein levels, we hypothesized that it might instead function to recruit CDK-Mediator to chromatin. To test this possibility, we took advantage of a synthetic system we have developed to nucleate proteins *de novo* on chromatin and test their capacity to recruit additional factors ([@bib12]). Fusion of the Tet repressor DNA-binding domain (TetR) to FBXL19 allowed the recruitment of FBXL19 to a short array of Tet repressor DNA binding sites (TetO), engineered into a single site on mouse chromosome 8 (\[[@bib12]\], [Figure 3A](#fig3){ref-type="fig"}). To determine whether FBXL19 was sufficient to recruit CDK-Mediator to chromatin, we stably expressed TetR or the TetR-FBXL19 fusion protein in the TetO array-containing ES cell line ([Figure 3---figure supplement 1A](#fig3s1){ref-type="fig"}). We then carried out ChIP for CDK-Mediator subunits ([Figure 3B](#fig3){ref-type="fig"}). Consistent with our biochemical observations ([Figure 2](#fig2){ref-type="fig"}), when we examined the binding of CDK8 and MED12 over the TetO array, we observed an enrichment in the TetR-FBXL19 line. Furthermore, binding of MED4, which is part of the core Mediator complex, was also evident at the TetO array ([Figure 3B](#fig3){ref-type="fig"}). This suggests that FBXL19 may be sufficient to recruit a holo-CDK-Mediator complex, in keeping with its biochemical co-purification with multiple components of both the CDK module and core Mediator complex ([Figure 2](#fig2){ref-type="fig"}). Importantly, stable expression of TetR-KDM2A and TetR-KDM2B did not lead to CDK8 recruitment, indicating that this activity is unique to FBXL19 ([Figure 3---figure supplement 1B](#fig3s1){ref-type="fig"}). Further work will be required to determine the dynamics with which individual Mediator components are recruited to chromatin by FBXL19 as well as the precise composition of such complexes. Together these observations demonstrate that FBXL19 interacts specifically with the CDK-Mediator and can recruit this complex *de novo* to chromatin.
{#fig3}
FBXL19 is required for appropriate CDK8 occupancy at a subset of CpG island-associated promoters {#s2-4}
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FBXL19 binds specifically to CpG islands ([Figure 1](#fig1){ref-type="fig"}) and can recruit CDK-Mediator to an artificial binding site on chromatin ([Figure 3](#fig3){ref-type="fig"}). This raised the interesting possibility that FBXL19 may help to recruit CDK-Mediator to CpG islands in ES cells. To examine this, we first performed CDK8 ChIP-seq in ES cells and compared it to FBXL19 ChIP-seq. Unlike FBXL19, CDK8 occupancy was not restricted to CpG islands ([Figure 4---figure supplement 1A](#fig4s1){ref-type="fig"}), with only 67.5% of CDK8 peaks overlapping with NMIs and CDK8 binding showing a limited correlation with BioCAP signal (Spearman correlation -- 0.48, [Figure 4---figure supplement 1B](#fig4s1){ref-type="fig"}). This is in line with previous studies demonstrating that the Mediator complex is recruited to both enhancers and gene promoters ([@bib40]; [@bib56]). Interestingly, however, we observed enrichment of CDK8 at FBXL19 peaks ([Figure 4---figure supplement 1C](#fig4s1){ref-type="fig"}) with 89.4% of FBXL19 peaks overlapping with CDK8 peaks and NMIs ([Figure 4---figure supplement 1D](#fig4s1){ref-type="fig"}) raising the possibility that FBXL19 may contribute to its occupancy at these sites. To directly test this, we developed an ES cell system in which the exon encoding the ZF-CxxC domain of FBXL19 is flanked by loxP sites (*Fbxl19^fl/fl^)* ([Figure 4---figure supplement 1E](#fig4s1){ref-type="fig"}) and which expresses tamoxifen-inducible ERT2-Cre recombinase. Upon addition of tamoxifen (OHT), the ZF-CxxC-encoding exon is excised, yielding a form of FBXL19 that lacks the ZF-CxxC domain (FBXL19^ΔCXXC^) ([Figure 4A,B](#fig4){ref-type="fig"}, and [Figure 4---figure supplement 1F](#fig4s1){ref-type="fig"}) and can, therefore, no longer bind CpG islands ([Figure 1](#fig1){ref-type="fig"}). This model cell system allows us to specifically examine the CpG island-associated functions of FBXL19 without affecting its other proposed roles ([@bib24]; [@bib83]; [@bib88]; [@bib89]). Following removal of the ZF-CxxC domain of FBXL19, we observed some reductions in FBXL19 protein levels ([Figure 4B](#fig4){ref-type="fig"}), but importantly CDK8 levels were unaffected ([Figure 4---figure supplement 1G](#fig4s1){ref-type="fig"}). Using this conditional *Fbxl19^ΔCXXC^* ES cell line, we then examined CDK8 occupancy on chromatin by ChIP-seq before and after OHT treatment. Genome-wide profiling of CDK8 in *Fbxll19^ΔCXXC^* ES cells did not reveal widespread alterations in CDK8 binding ([Figure 4C](#fig4){ref-type="fig"} left and [Figure 4---figure supplement 1H](#fig4s1){ref-type="fig"}), indicating that FBXL19 is not the central determinant driving CDK8 recruitment to most of its binding sites in the genome. Intriguingly, however, a more detailed site-specific analysis revealed a subset of CDK8 target sites that displayed significant alteration in CDK8 occupancy ([Figure 4C,D](#fig4){ref-type="fig"}, and [Figure 4---figure supplement 1H](#fig4s1){ref-type="fig"}). In keeping with a potential role for FBXL19 in CDK8 recruitment, the majority of the affected sites showed reduced CDK8 binding (n = 783) ([Figure 4C](#fig4){ref-type="fig"}).
{ref-type="fig"}) to allow for Western blot detection with an anti-T7 antibody. FBXL19 runs as a doublet that shifts in size following deletion of the CxxC domain. TBP was probed as a loading control. (**C**) Metaplots showing CDK8 enrichment in *Fbxl19^fl/fl^* ES cells (WT) and *Fbxl19^ΔCXXC^* ES cells (OHT) at all CDK8 peaks (left), peaks showing decreased CDK8 occupancy (↑, middle) and peaks showing increased CDK8 occupancy (↓, right). The number of total peaks in each group is indicated. p-values denote statistical significance calculated by Wilcoxon rank sum test comparing ChIP-seq read counts between WT and OHT samples across a 1.5-kbp interval flanking the center of CDK8 peaks. (**D**) Screen shots showing ChIP-seq traces for CDK8 in wild type *Fbxl19^fl/fl^* ES cells (WT) and *Fbxl19^ΔCXXC^* ES cells (OHT). BioCAP and FS2-FBXL19 tracks are given for comparison. Left -- CDK8 peaks showing reduced CDK8 binding in *Fbxl19^ΔCXXC^* ES cells; Right -- CDK8 peaks showing increased CDK8 binding in *Fbxl19^ΔCXXC^* ES cells (indicated with rectangles). (**E**) Boxplots showing log2 fold change (log2FC) of CDK8 ChIP-seq signal (RPKM) at all CDK8 peaks (n = 24273), and those with reduced CDK8 (n = 783, ↓) and increased CDK8 (n = 379, ↑). p-values were calculated using a Wilcoxon rank sum test. (**F**) Boxplots showing the size of CDK8 peaks as in (**E**). p-values were calculated using a Wilcoxon rank sum test. (**G**) Venn diagrams representing the overlap between CDK8 peaks and super enhancers (SE) at CDK8 peaks as in (**E**). Percent overlap of all SEs is indicated. (**H**) A metaplot (left) showing BioCAP enrichment at CDK8 peaks as in (**E**) and boxplot quantification (right) of BioCAP RPKM levels. p-Values calculated using Wilcoxon rank sum test are indicated. (**I**) A metalplot (left) showing FS2-FBXL19 enrichment at CDK8 peaks as in (**E**) and boxplot quantification (right) of FS2-FBXL19 RPKM levels. p-values calculated using Wilcoxon rank sum test are indicated.](elife-37084-fig4){#fig4}
Upon closer examination of sites with reduced CDK8 occupancy in *Fbxll19^ΔCXXC^* ES cells, we discovered that they tended to coincide with broad regions of CDK8 enrichment ([Figure 4E,F](#fig4){ref-type="fig"}), a feature often associated with super-enhancers ([@bib84]). However, a comparison of these sites to the location of super-enhancers in mouse ES cells indicated that these were distinct ([Figure 4G](#fig4){ref-type="fig"}). Instead, sites displaying reduction in CDK8 occupancy coincided with broad regions of non-methylated DNA ([Figure 4D,H](#fig4){ref-type="fig"}, and [Figure 4---figure supplement 1H](#fig4s1){ref-type="fig"}), tended to be associated with gene promoters ([Figure 4---figure supplement 1I](#fig4s1){ref-type="fig"}), and had elevated levels of FBXL19 ([Figure 4I](#fig4){ref-type="fig"} and [Figure 4---figure supplement 1H,I,J](#fig4s1){ref-type="fig"}). Together, these observations suggest that although binding of CDK8 to most of its target sites in the genome is achieved independently of FBXL19, a subset of broad CpG island-associated gene promoters appear to rely on FBXL19 for appropriate CDK8 occupancy.
FBXL19 targets CDK8 to promoters of silent developmental genes in ES cells {#s2-5}
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Despite associating widely with CpG island gene promoters, FBXL19 appears to play a very specific role in maintaining appropriate CDK8 occupancy at a particular subset of broad CpG island-associated promoters ([Figure 4](#fig4){ref-type="fig"}). We were therefore curious to know whether something distinguishes these gene promoters from other FBXL19-bound promoters, where FBXL19 does not contribute appreciably to CDK8 occupancy ([Figure 4---figure supplement 1H](#fig4s1){ref-type="fig"}). To achieve this, we initially performed gene ontology (GO) analysis ([@bib37]) on the genes with reduced CDK8 levels at their promoters in *Fbxl19^ΔCXXC^* ES cells. Interestingly, this revealed that these genes were strongly enriched for developmental processes ([Figure 5A](#fig5){ref-type="fig"}) in agreement with our previous discovery that broad CpG islands are an evolutionary conserved feature of developmentally regulated genes ([@bib54]). In contrast, genes associated with an increased binding of CDK8 did not show any significant GO term enrichment (unpublished observation). GO analysis of the genes associated with unchanged CDK8 levels revealed terms for a broad range of basic molecular processes in line with a general role for Mediator in transcriptional regulation ([Figure 5---figure supplement 1E](#fig5s1){ref-type="fig"}).
{ref-type="fig"}). (**E**) A boxplot showing CDK8 enrichment at all and FBXL19-bound genes separated by expression level as in (**D**). (**F**) A boxplot showing change in CDK8 binding at the TSSs of all and FBXL19-bound genes divided by expression level as in (**D**). p-values were calculated using a Wilcoxon rank sum test.](elife-37084-fig5){#fig5}
In pluripotent mouse ES cells, many developmental genes are inactive and only become expressed as cells commit to more differentiated lineages ([@bib17]). Importantly, the genes that exhibited reductions in CDK8 binding in *Fbxl19^ΔCXXC^* cells were expressed at significantly lower levels than most other genes in ES cells ([Figure 5B](#fig5){ref-type="fig"}). Previous work has identified a subset of poised but inactive developmental genes in ES cells that are proposed to exist in a bivalent chromatin state characterized by the co-occurrence of histone H3 lysine 4 and 27 methylation (H3K4/K27me) ([@bib9]; [@bib57]). Therefore, we examined whether sites that rely on FBXL19 for normal CDK8 binding also corresponded to bivalent regions in ES cells. We found that these regions are enriched for H3K27me3 ([Figure 5---figure supplement 1A](#fig5s1){ref-type="fig"}) and have elevated H3K4me3 compared to other H3K27me3-modified sites that lack CDK8 ([Figure 5---figure supplement 1B](#fig5s1){ref-type="fig"}). Therefore, sites that rely on FBXL19 for normal CDK8 binding and correspond to silent developmental gene promoters are also bivalent. To ask whether these genes are induced during cell lineage commitment, we compared their expression levels in ES cells and following retinoic acid (RA) treatment which induces differentiation ([Figure 6---figure supplement 1B,C](#fig6s1){ref-type="fig"}). This clearly demonstrated that the genes which rely on FBXL19 for appropriate CDK8 binding in the ES cell state can become transcriptionally activated during stem cell lineage commitment ([Figure 5C](#fig5){ref-type="fig"}).
The observation that FBXL19 appears to be important for CDK8 occupancy at largely inactive genes was intriguing given that previous work characterizing Mediator function has usually focussed on its activity at actively transcribed or induced genes (reviewed in \[[@bib65]\]). We therefore set out to examine the relationship between FBXL19, CDK8 and gene expression in more detail. We first separated all promoters based on expression of their associated genes ([Figure 5D](#fig5){ref-type="fig"} and [Figure 5---figure supplement 1D](#fig5s1){ref-type="fig"}). We observed that CDK8 occupancy was in general linked to gene activity ([Figure 5E](#fig5){ref-type="fig"}), in agreement with previous reports ([@bib3]; [@bib7]; [@bib25]; [@bib26]; [@bib31]; [@bib32]). However, at FBXL19-bound gene promoters, CDK8 occupancy was similar in both the lowly and highly expressed subsets of genes ([Figure 5E](#fig5){ref-type="fig"}). Importantly, CDK8 occupancy at promoters of lowly expressed genes was reduced in *Fbxl19^ΔCXXC^* ES cells ([Figure 5F](#fig5){ref-type="fig"}). Therefore, these observations reveal that CDK8 is enriched at promoters of inactive or lowly expressed genes in ES cells and its binding is dependent on recognition of CpG islands by FBXL19.
Removing the CpG island-binding domain of FBXL19 results in a failure to induce developmental genes during ES cell differentiation {#s2-6}
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FBXL19 appears to play a role in recruiting CDK8 to a class of genes that are repressed in the ES cell state and become activated during cell linage commitment ([Figure 5](#fig5){ref-type="fig"}). However, it remained unclear whether FBXL19 is required for the activation of these developmental genes. To address this question, we induced differentiation of *Fbxl19^fl/fl^* and *Fbxl19^ΔCXXC^* ES cells with RA ([Figure 6A](#fig6){ref-type="fig"}) and compared the expression of several genes which showed reduced CDK8 binding in *Fbxl19^ΔCXXC^* ES cells ([Figure 6B](#fig6){ref-type="fig"}). We observed no significant differences in the expression of these genes in wild-type *Fbxl19^fl/fl^* and *Fbxl19^ΔCXXC^* ES cells where these genes are silent. Strikingly, however, following RA treatment, *Fbxl19^ΔCXXC^* cells failed to induce these genes appropriately ([Figure 6B](#fig6){ref-type="fig"}). Similarly, developmental genes were not appropriately induced during embryoid body differentiation of *Fbxl19^ΔCXXC^* ES cells ([Figure 6---figure supplement 1A](#fig6s1){ref-type="fig"}). Importantly, this demonstrates that FBXL19 is required for the appropriate activation of developmental gene expression during cell lineage commitment.
{#fig6}
To understand the extent to which genes are not appropriately induced during differentiation of *Fbxl19^ΔCXXC^* ES cells, we examined ongoing transcription in both the ES cell state and after RA-mediated differentiation using short time-scale 4-thiouridine-based labeling and RNA sequencing (4sU RNA-seq) ([Figure 6A](#fig6){ref-type="fig"}). We observed a significant number of genes that become induced upon RA treatment in wild-type cells (n = 4051) ([Figure 6---figure supplement 1B](#fig6s1){ref-type="fig"} and [Figure 6---source data 1](#fig6sdata1){ref-type="supplementary-material"}). GO term analysis confirmed that these genes are associated with ES cell differentiation and early embryonic development ([Figure 6---figure supplement 1C](#fig6s1){ref-type="fig"}). We then used differential gene expression analysis to compare transcription in *Fbxl19^fl/fl^* and *Fbxl19^ΔCXXC^* cells ([Figure 6C](#fig6){ref-type="fig"} and [Figure 6---source data 1](#fig6sdata1){ref-type="supplementary-material"}). While very few significant changes in gene expression were observed in the ES cell state, following RA-induced differentiation we identified a large number of genes (n = 552) that had significantly lower expression levels in *Fbxl19^ΔCXXC^* cells ([Figure 6C](#fig6){ref-type="fig"}). This is consistent with our results when examining individual genes ([Figure 6B](#fig6){ref-type="fig"} and [Figure 6---figure supplement 1A](#fig6s1){ref-type="fig"}) and with a recent study where the expression of a selection of genes was examined following FBXL19 knock-down ([@bib49]). GO analysis revealed that the set of genes that were not appropriately activated were associated with genes involved in developmental processes ([Figure 6D](#fig6){ref-type="fig"} and [Figure 6---source data 1](#fig6sdata1){ref-type="supplementary-material"}), unlike genes with increased expression (n = 889) which were not associated with these processes ([Figure 6---figure supplement 1D](#fig6s1){ref-type="fig"} and [Figure 6---source data 1](#fig6sdata1){ref-type="supplementary-material"}). It is possible that the observed increases in gene expression in *Fbxl19^ΔCXXC^* cells following RA induction result from secondary effects or as of yet unidentified roles of FBXL19 in inhibiting gene expression. Nevertheless, consistent with our analysis of FBXL19-dependent CDK8 occupancy at promoters of developmental genes ([Figure 5B,C](#fig5){ref-type="fig"}), genes not appropriately induced were lowly expressed in wild-type ES cells ([Figure 6E](#fig6){ref-type="fig"}) and tended to become activated following RA induction ([Figure 6F](#fig6){ref-type="fig"}). Importantly, these genes exhibited a reduction in CDK8 binding in *Fbxl19^ΔCXXC^* ES cells ([Figure 6G](#fig6){ref-type="fig"} and [Figure 6---figure supplement 1E](#fig6s1){ref-type="fig"}), supporting the idea that FBXL19 recruits CDK8 to this subset of CpG island-associated developmental genes and that this may prime these genes for activation during differentiation.
FBXL19 target genes rely on CDK-Mediator for activation during differentiation {#s2-7}
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Given that FBXL19 is required for CDK8 occupancy at the promoters of a series of silent developmental genes and for their activation during differentiation ([Figures 5](#fig5){ref-type="fig"} and [6](#fig6){ref-type="fig"}), we hypothesized that FBXL19 may prime these genes for future activation through the activity of CDK-Mediator. To address this interesting possibility, we developed a system to conditionally remove MED13 and its closely related paralogue MED13L in ES cells (*Med13/13l^fl/fl^* ERT2-Cre ES cells) ([Figure 7A](#fig7){ref-type="fig"} and [Figure 7---figure supplement 1A](#fig7s1){ref-type="fig"}). We chose to inactivate MED13/13L as it has previously been shown to physically link the CDK-kinase module to the core Mediator complex and underpin the formation of a functional CDK-Mediator ([@bib46]; [@bib79]). Treatment of the *Med13/13l^fl/fl^* ES cells with OHT resulted in a loss of MED13 and MED13L protein (MED13/13L KO) and reduced levels of the other subunits of the CDK-kinase module ([Figure 7B](#fig7){ref-type="fig"}). Importantly, removal of MED13/13L also led to a loss of CDK8 binding to chromatin ([Figure 7C](#fig7){ref-type="fig"}) but did not have an appreciable effect on the expression of FBXL19 target genes in the ES cell state ([Figure 7D](#fig7){ref-type="fig"}). We next induced differentiation of the MED13/13L KO cells with RA ([Figure 7A](#fig7){ref-type="fig"}). Importantly, when we then analysed the expression of a series of genes that rely on FBXL19 for activation during differentiation ([Figure 7D](#fig7){ref-type="fig"}), we observed that these genes also failed to appropriately induce in MED13/13L KO cells ([Figure 7D](#fig7){ref-type="fig"}). Together this suggests that FBXL19, via its association with CpG islands, recognises a subset of silent developmental genes in ES cells in order to recruit the CDK-Mediator complex and prime these genes for future activation.
{#fig7}
Ablating the capacity of FBXL19 to bind CpG islands causes embryonic lethality {#s2-8}
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Our results suggest that FBXL19 contributes to gene activation during cell lineage commitment via recognition of CpG islands and recruitment of the CDK-Mediator complex. Given that *Fbxl19^ΔCXXC^* cells display impaired gene activation in our *in vitro* differentiation model, we asked whether the inability of FBXL19 to bind and function at CpG islands could also affect mouse development. In order to address this, we generated *Fbxl19^ΔCXXC^* mutant mice by crossing *Fbxl19^fl/fl^* animals with animals constitutively expressing Cre recombinase. From these crosses, we failed to obtain any viable *Fbxl19^ΔCXXC^* homozygous offspring, indicating that removal of the ZF-CxxC domain of FBXL19 leads to embryonic lethality ([Figure 8A](#fig8){ref-type="fig"}). We then investigated at which stage *Fbxl19^ΔCXXC^* homozygous embryos were affected and found homozygous embryos were observed at normal Mendelian ratios until 10.5 days postcoitum (dpc) ([Figure 8A](#fig8){ref-type="fig"}). At 9.5 dpc, gross embryonic morphology appeared to be intact but at 10.5 dpc ([Figure 8B](#fig8){ref-type="fig"}) the embryos exhibited a clear growth retardation and showed, to varying extents, reduced elongation of the trunk, hypomorphic limb buds and cephalic region. This included undeveloped facial mesenchyme, including defects in maxillary and mandibular components of first branchial arches (indicated by yellow and red arrows in [Figure 8B](#fig8){ref-type="fig"}, respectively), and hypomorphic cardiac mesenchyme. Some living *Fbxl19^ΔCXXC^* homozygous embryos, characterized by a beating heart, were observed at 12.5 dpc but they were of similar size and external appearance to 10.5 dpc mutant embryos suggesting that normal development had ceased by this point. Together our findings demonstrate that FBXL19, and its ability to recognize CpG islands, is essential for normal mouse embryonic development.
{#fig8}
Discussion {#s3}
==========
Here, we discover that FBXL19 recognizes CpG islands throughout the genome in a ZF-CxxC-dependent manner ([Figure 1](#fig1){ref-type="fig"}). Unlike other ZF-CxxC proteins which associate with chromatin-modifying complexes, we show that FBXL19 interacts with the CDK-Mediator complex ([Figure 2](#fig2){ref-type="fig"}). This uncovers an unexpected link between CpG islands and a complex that regulates gene expression through interfacing with the transcriptional machinery. We demonstrate that FBXL19 can recruit CDK-Mediator to chromatin ([Figure 3](#fig3){ref-type="fig"}) and, via recognition of CpG islands, plays an interesting role in supporting CDK8 occupancy at a subset of promoters associated with developmental genes, which are inactive in ES cells ([Figure 4](#fig4){ref-type="fig"} and [Figure 5](#fig5){ref-type="fig"}). At these CpG islands, FBXL19 and CDK-Mediator function to prime the associated genes for activation during ES cell differentiation ([Figure 6](#fig6){ref-type="fig"} and [Figure 7](#fig7){ref-type="fig"}). Consistent with an important role of FBXL19 in supporting normal developmental gene expression, removal of the ZF-CxxC domain of FBXL19 leads to perturbed development and embryonic lethality in mice ([Figure 8](#fig8){ref-type="fig"}). Together these new discoveries reveal that CpG islands and FBXL19 can interface with CDK-Mediator to orchestrate normal gene expression during lineage commitment.
Previously, another F-box protein, FBW7, was shown to function as an E3 ubiquitin ligase substrate selector for the MED13/13L subunit of CDK-Mediator and to regulate its stability through proteasomal degradation ([@bib22]). By controlling CDK-Mediator abundance, one could envisage how this might shape Mediator function in gene expression. FBXL19 also encodes an F-box domain and associates with SKP1, a central component of SCF E3 ubiquitin ligase complexes. However, we do not find evidence that FBXL19 regulates CDK-Mediator stability via the proteasome ([Figure 2---figure supplement 1H](#fig2s1){ref-type="fig"}). Instead, we discover that FBXL19 can recruit CDK-Mediator to chromatin and, more specifically, to CpG islands via its ZF-CxxC domain to support gene activation. Although we currently do not know the defined subunits and surfaces in CDK-Mediator that FBXL19 interacts with, our biochemical experiments indicate that this relies on an intact F-box domain in FBXL19 ([Figure 2---figure supplement 1E](#fig2s1){ref-type="fig"}). It is tempting to speculate that FBXL19 could interact directly with MED13/13L given their recognition by the related F-box protein, Fbw7 ([@bib22]). Nevertheless, a key observation in our work is that FBXL19 appears to have functionally diverged from other F-box proteins during vertebrate evolution by acquiring a DNA-binding domain that allows it to recruit proteins to chromatin, instead of targeting them for ubiquitylation. This general feature is shared with the FBXL19 paralogue, KDM2B, which associates with and recruits the PRC1 complex to CpG islands ([@bib28]; [@bib34]; [@bib85]). In agreement with our observations, a large-scale proteomics screen previously suggested that an interaction between FBXL19 and Mediator may also exist in cancer cells ([@bib77]). Given that CDK8 can function as an oncogene ([@bib1]; [@bib29]; [@bib59]), it will be interesting to understand whether FBXL19 plays a role in targeting CDK-Mediator to CpG islands in non-embryonic tissues, and whether this activity may promote CDK8-driven tumorigenesis.
Individual Mediator subunits have been shown to interact with DNA-binding transcription factors that recruit the Mediator complex to specific DNA sequences in regulatory elements and support gene expression ([@bib11]; [@bib16]; [@bib30]; [@bib56]). In part, Mediator is thought to achieve this by bridging enhancer elements to the core gene promoter and RNAPolII ([@bib4]; [@bib39]; [@bib64]). However, in mammals these proposed mechanisms are extrapolated from studying only a subset of transcription factors and genes. Therefore, the defined mechanisms that shape Mediator occupancy on chromatin remain very poorly understood. Here, we provide evidence for a completely new gene promoter-associated CDK-Mediator targeting mechanism that relies on FBXL19 and CpG island recognition. Surprisingly, although FBXL19 localizes broadly to CpG islands throughout the genome ([Figure 1](#fig1){ref-type="fig"}), we only observed a reliance on FBXL19 for CDK8 binding at a subset of sites ([Figure 4](#fig4){ref-type="fig"}). Similarly, KDM2B binds broadly to CpG islands, yet has a specificity in shaping PRC1 recruitment and polycomb repressive chromatin domain formation at a subset of developmental genes in mouse ES cells ([@bib28]). We have previously suggested that this could result from ZF-CxxC domain-containing proteins broadly sampling CpG islands, with their activity or affinity for certain sites being shaped by local gene activity or chromatin environment ([@bib45]). In keeping with these general ideas, FBXL19 is required for appropriate CDK8 binding at bivalent genes in ES cells ([Figure 5---figure supplement 1A,B](#fig5s1){ref-type="fig"}). In future work, it will be important to understand whether this unique chromatin state and/or the absence of transcriptional activity at these sites define the requirement for FBXL19 in CDK8 recruitment, or whether FBXL19 targeting occurs at most CpG islands sites but is masked through redundancy with transcription factor and gene activity-dependent targeting modalities.
Historically, CDK-Mediator has been associated with gene repression ([@bib2]; [@bib20]; [@bib27]; [@bib35]; [@bib46]; [@bib62]). Therefore, we were not surprised to observe that CDK8 occupied the promoters of repressed developmental genes in ES cells. While abrogating the CpG island-binding activity of FBXL19 or deletion of MED13/13L resulted in reduced CDK8 binding at these sites, it did not lead to an appreciable effect on gene expression in the ES cell state ([Figure 6](#fig6){ref-type="fig"} and [Figure 6---figure supplement 1C,D](#fig6s1){ref-type="fig"}). This suggests that CDK-Mediator is not required for the repression of these genes in ES cells. Instead, these genes fail to properly activate during differentiation ([Figure 6](#fig6){ref-type="fig"}, [Figure 6---figure supplement 1](#fig6s1){ref-type="fig"}, and [Figure 7D](#fig7){ref-type="fig"}). These observations are in line with several reports that support the idea that CDK-Mediator is also involved in gene activation ([@bib3]; [@bib26]; [@bib36]; [@bib25]; [@bib32]). Therefore, in the context of mouse ES cells, we propose that CDK-Mediator may be required to prime silent developmental genes for future gene activation through a mechanism that relies on the recognition of CpG island promoters by FBXL19. This priming could contribute to gene activation during differentiation through one of the several mechanisms by which CDK-Mediator has been proposed to affect gene transcription, including regulating RNAPolII pre-initiation complex assembly, polymerase pausing/elongation, or through mediating long range interactions with distal regulatory elements ([@bib4]; [@bib8]; [@bib25]; [@bib32]; [@bib40]). Clearly, understanding the defined mechanism by which FBXL19-dependent CDK-Mediator recruitment supports normal gene activation during differentiation remains an important question for future work.
Our finding that FBXL19 can target CDK8 to gene promoters and that this is required to prime the expression of developmental genes during ES cell differentiation is conceptually reminiscent of recent work in yeast and human systems which suggested that CDK8 is required for appropriate re-induction of inducible genes following an initial activation stimulus ([@bib21]). In this study, CDK8 was found to associate with the promoters of inducible genes following initial activation, even in the absence of appreciable ongoing gene transcription, thereby acting as a form of transcriptional memory ([@bib21]). Interestingly, this requirement for CDK8 in normal gene activation appears shared in the context of our developmental gene induction paradigm. However, we find that, in the case of developmental genes, previous gene activation may not be required for the recruitment of CDK8. Instead, this could be achieved by FBXL19 directly recognising and targeting CDK8 to CpG islands. Therefore, we prefer to view this as priming as opposed to memory. Nevertheless, collectively these observations point to an important role for CDK-Mediator binding to gene promoters prior to activation and as a way of supporting subsequent gene induction. This provides new evidence that the roles of CDK-Mediator in gene regulation are more complicated than simply conveying activation signals to RNAPolII through recruitment by transcription factors and suggests the complex may have evolved to play a unique role in regulating gene expression in stem cells and during development.
Materials and methods {#s4}
=====================
Cell culture {#s4-1}
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Mouse ES cells were cultured on gelatine-coated dishes in DMEM (Thermo Fisher scientific) supplemented with 15% fetal bovine serum (BioSera), L-Glutamine, beta-mercaptoethanol, non-essential amino acids, penicillin/streptomycin (Thermo Fisher scientific) and 10 ng/mL leukemia-inhibitory factor. *Fbxl19^fl/fl^* ES cells were treated with 800 nM 4-hydroxytamoxifen (Sigma) for 96 hr in order to delete the ZF-CxxC domain. For RA differentiation of ES cells, 2.5 × 10^4^ cells/cm^2^ were allowed to attach to gelatinised dishes (\~12 hr) and treated with 1 µM retinoic acid (Sigma-Aldrich) in EC-10 medium (DMEM supplemented with 10% fetal bovine serum, L-Glutamine, beta-mercaptoethanol, non-essential amino acids and penicillin/streptomycin) for 72 hr. For embryonic body differentiation, 2 × 10^6^ cells were plated on non-adhesive 10 cm dishes in EC-10 medium and cultured for the indicated days. For generation of stable cell lines, E14 ES cells were transfected using Lipofectamine 2000 (Thermo Fisher scientific) following manufacturer's instructions. Stably transfected cells were selected for 10 days using 1 μg/ml puromycin and individual clones were isolated and expanded in the presence of puromycin to maintain the transgene expression. TOT2N E14 cells used for TetR targeting experiments were previously described ([@bib12]). 293 T cells were cultured in EC-10 media. Transient overexpression of FBXL19 was performed by transfecting 293 T cells using Lipofectamine 2000 (Thermo Fisher scientific) followed by selection with 400 ng/μl G418 for 48 hr. Proteasome inhibition was performed for 4 hr using 10 µM MG132 inhibitor (Sigma-Aldrich). All cell lines generated and grown in the Klose and Koseki labs were routinely tested for mycoplasma infection.
Generation of *Fbxl19^ΔCXXC^* conditional knock-out mouse {#s4-2}
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The targeting construct was generated from C57BL6/J mouse genomic sequence spanning mm9 chromosome 7: 134,888,487--134,895,358 containing the exons 1 to 6 of *Fbxl19* genomic region. Recombination was carried out by Gateway system (Life Technologies). One of the loxP sequences was inserted at mm9 chr7:134,891,537, and FRT flanked PGK-neo was inserted at mm9 chr7:134,892,000 together with an additional loxP sequence. The targeting construct was electroporated into M1 ES cells to obtain targeted insertion. Clones of targeted ES cells were aggregated with eight-cell embryos to generate the targeted mouse line. The *Fbxl19^fl/fl^* line was generated by removal of the PGK-neo marker gene by mating the targeted mice with mice expressing FLP recombinase. These *Fbxl19^fl/fl^* mice were further mated with mice harboring the *ROSA26-CreErt2* locus to generate *Fbxl19*^fl/fl^:*ROSA26-CreErt2*^+/-^ mice, from which the *Fbxl19^fl/fl^* ES cells used in this study were derived.
Generation of *Med13/13l^fl/fl^* conditional knock-out ES cells line {#s4-3}
--------------------------------------------------------------------
In order to generate a conditional *Med13*/*13l^fl/fl^* ES cell line, we inserted loxP sites downstream of exons 7 and upstream of exons 8 of the *Med13* and *Med13l* genes. The targeting constructs for the insertion of each loxP site were designed to have 150 bp homology arms flanking the loxP site and to carry a mutated PAM sequence to prevent retargeting by the Cas9 enzyme. The targeting constructs were purchased from GeneArt Gene Synthesis (Thermo Fisher scientific). The pSpCas9(BB)−2A-Puro(PX459)-V2.0 vector was obtained by Addgene (\#62988). sgRNAs were designed to specifically target the desired genomic region for each loxP insertion (<http://crispor.tefor.net/crispor.py>) and were cloned into the Cas9 vector as previously described ([@bib66]). ES cells that express the ERT2-Cre recombinase from the *ROSA26* locus (*ROSA26:ERT2-Cre*) were used. First, the downstream loxP sites for *Med13* and *Med13l* were targeted. *ROSA26:ERT2-Cre* ES cells were transiently co-transfected with 1 μg of each Cas9-sgRNA plasmid and 3.5 μg of each targeting construct using Lipofectamine 3000 (Thermo Fischer Scientific). Successfully transfected ES cells were selected for 48 hr with 1 μg/ml puromycin. Individual clones were screened by genotyping PCR to identify correctly targeted homozygous clones. A clone homozygous for both *Med13* and *Med13l* LoxP1 sites was then used to target the upstream loxP sites using the same transfection protocol and screening strategy. Correct loxP targeting was verified by sequencing of the genomic region surround the loxP sites.
DNA constructs {#s4-4}
--------------
For generation of FBXL19 expression constructs, the full length, ΔCxxC or ΔF-box cDNA of mouse *Fbxl19* (IMAGE ID 6401846, Source Bioscience) was PCR amplified and inserted into a pCAG-IRES-FS2 vector ([@bib28]) via ligation-independent cloning (LIC). Mutation of the ZF-CxxC domain of FBXL19 (K49A) was generated via site-directed mutagenesis using the Quikchange mutagenesis XL kit (Stratagene). To generate TetR-FBXL19 fusion expression plasmid, *Fbxl19* cDNA was cloned into pCAG-FS2-TetR ([@bib12]) via LIC. For transient overexpression in 293 T cells, full length FBXL19 cDNA was cloned into pcDNA3-2xFlag vector by conventional cloning. All plasmids were sequence-verified by sequencing.
Nuclear extract preparation and immunoprecipitation {#s4-5}
---------------------------------------------------
Cells were harvested by scraping in PBS at 4°C, resuspended in 10x pellet volume (PV) of Buffer A (10 mM Hepes pH 7.9, 1.5 mM MgCl~2~, 10 mM KCl, 0.5 mM DTT, 0.5 mM PMSF, cOmplete protease inhibitor cocktail (Roche)) and incubated for 10 min at 4°C with slight agitation. After centrifugation, the cell pellet was resuspended in 3x PV Buffer A containing 0.1% NP-40 and incubated for 10 min at 4°C with slight agitation. Nuclei were recovered by centrifugation and the soluble nuclear fraction was extracted for 1 hr at 4°C with slight agitation using 1x PV Buffer C (10 mM Hepes pH 7.9, 400 mM NaCl, 1.5 mM MgCl~2~, 26% glycerol, 0.2 mM EDTA, cOmplete protease inhibitor cocktail). Protein concentration was measured using Bradford assay.
For small-scale co-immunoprecipitation, 600 µg of nuclear extract was diluted in BC150 buffer (50 mM Hepes pH 7.9, 150 mM KCl, 0.5 mM EDTA, 0.5 mM DTT, cOmplete protease inhibitor cocktail). Samples were incubated with the respective antibodies and 25U benzonase nuclease overnight at 4°C. Protein A agarose beads (RepliGen) were blocked for 1 hr at 4°C in Buffer BC150 containing 1% fish skin gelatine (Sigma) and 0.2 mg/ml BSA (NEB). The blocked beads were added to the samples and incubated for 4 hr at 4°C. Washes were performed using BC150 containing 0.02% NP-40. The beads were resuspended in 2x SDS loading buffer and boiled for 5 min to elute the immunoprecipitated complexes.
Purification of FBXL19-FS2 was performed using StrepTactin resin (IBA) as previously described with the exception of the wash buffer used (20 mM Tris pH 8.0, 150 mM NaCl, 0.2% NP-40, 1 mM DTT, 5% glycerol, cOmplete protease inhibitor cocktail) ([@bib28]). Between 10 and 15 mg of nuclear extract was used for each large scale purification. The samples were treated with 75 U/mL benzonase nuclease (Novagen) in order to disrupt nucleic-acid-mediated interactions.
Mass spectrometry {#s4-6}
-----------------
Samples from FBXL19-FS2 affinity purifications were subjected to in-solution trypsin digestion and mass spectrometry analysis was performed as described previously ([@bib28]). Two biological replicates were performed. A control EV purification was included in each replicate. An interaction with identified proteins was only considered significant if absent from the EV data.
Antibodies {#s4-7}
----------
Antibodies used for IP were rabbit anti-MED12 (A300-774A, Bethyl laboratories), rabbit anti-CDK8 (A302-500A, Bethyl laboratories), rabbit anti-HA (3724, Cell Signaling Technology). A polyclonal antibody against FBXL19 was prepared in-house by rabbit immunisation (PTU/BS Scottish National Blood Transfusion Service) with a recombinant peptide encoding for amino acids 137--336 of mouse FBXL19 protein. The FBXL19 peptide antigen was coupled to Affigel 10 resin (BioRad) and the antibody was affinity-purified and concentrated.
Antibodies used for Western blot analysis were mouse anti-Flag M2 (F1804, Sigma-Aldrich), mouse anti-SKP1 (sc-5281, Santa Cruz), goat anti-CDK8 (sc-1521, Santa Cruz), rabbit anti-MED12 (A300-774A, Bethyl laboratories), rabbit anti-MED13L (A302-420A, Bethyl laboratories), rabbit anti-MED13 (GTX129674, Genetex), rabbit anti-MED1, (A300-793A, Bethyl laboratories), rabbit anti-MED26 (A302-370A, Bethyl laboratories), rabbit anti-T7 (13246, Cell Signaling Technology), rabbit anti-TBP (ab818, Abcam), rabbit anti-RNF20 (11974, Cell Signaling Technology), rabbit anti-ubiquityl-Histone H2B (Lys120) (5546, Cell Signaling Technology), and mouse anti-ubiquityl-Histone H2B (Lys120) (05--1312, Millipore).
Generation of T7-FBXL19 ES cell line {#s4-8}
------------------------------------
As the FBXL19 antibody failed to work reliably for Western blot analysis, we generated an *Fbxl19^fl^*^/*fl*^ ES cell line in which the endogenous *Fbxl19* gene is tagged with a 3xT7-2xStrepII tag by CRISPR/Cas9 knock-in ([Figure 2---figure supplement 1B](#fig2s1){ref-type="fig"}). This allowed us to determine the efficiency of the OHT treatment and endogenous IPs. The tag was synthesised by GeneArt (ThermoFischer Scientific) and the targeting construct was generated by PCR amplification to introduce roughly 150 bp homology arms flanking the 3xT7-2xStrepII tag. The PCR product was cloned into pGEM-T Easy Vector (Promega). The pSpCas9(BB)−2A-Puro vector was obtained by Addgene (\#48139). A sgRNA was designed to overlap with the stop codon of the *Fbxl19* gene (<http://crispr.mit.edu/>) and cloned into the Cas9 vector as previously described ([@bib66]). *Fbxl19^fl/fl^* ES cells were transiently co-transfected with 1 μg of Cas9-sgRNA plasmid and 3.5 μg of targeting construct using Lipofectamine 3000 (ThermoFischer Scientific). Successfully transfected ES cells were selected for 48 hr with 1 μg/ml puromycin. Individual clones were screened by Western blot and genotyping PCR to identify homozygous targeted clones.
Chromatin immunoprecipitation {#s4-9}
-----------------------------
Chromatin immunoprecipitation was performed as described previously ([@bib28]) with slight modifications. Cells were fixed for 45 min with 2 mM DSG (Thermo scientific) in PBS and 12.5 min with 1% formaldehyde (methanol-free, Thermo scientific). Reactions were quenched by the addition of glycine to a final concentration of 125 µM. After cell lysis and chromatin extraction, chromatin was sonicated using a BioRuptor Pico sonicator (Diagenode), followed by centrifugation at 16,000 × *g* for 20 min at 4°C. 200 µg chromatin diluted in ChIP dilution buffer (1% Triton-X100, 1 mM EDTA, 20 mM Tris-HCl (pH 8.0), 150 mM NaCl) was used per IP. Chromatin was precleared with protein A Dynabeads blocked with 0.2 mg/ml BSA and 50 µg/ml yeast tRNA and incubated with the respective antibodies overnight at 4°C. Antibody-bound chromatin was purified using blocked protein A Dynabeads for 3 hr at 4°C. ChIP washes were performed as described previously ([@bib28]). ChIP DNA was eluted in ChIP elution buffer (1% SDS, 100 mM NaHCO~3~) and reversed cross-linked overnight at 65°C with 200 mM NaCl and RNase A (Sigma). The reverse cross-linked samples were treated with 20 μg/ml Proteinase K and purified using ChIP DNA Clean and Concentrator kit (Zymo research).
The antibodies used for ChIP experiments were rabbit anti-FS2 ([@bib28]), rabbit anti-CDK8 (A302-500A, Bethyl laboratories), rabbit anti-MED12 (A300-774A, Bethyl laboratories), mouse anti-MED4 (PRC-MED4-16, DSHB), rabbit anti-SKP1 (12248, Cell Signaling Technology), rabbit anti-KDM2A ([@bib28]), rabbit anti-KDM2B ([@bib28]).
ChIP-sequencing {#s4-10}
---------------
All ChIP-seq experiments were carried out in biological duplicates. ChIP-seq libraries for FS2-FBXL19 ChIP were prepared using the NEBNext Fast DNA fragmentation and library preparation kit for Ion Torrent (NEB, E6285S) following manufacturer's instructions. Briefly, 30--40 ng ChIP or input DNA material was used. Libraries were size-selected for 250 bp fragments using 2% E-gel SizeSelect gel (Thermo scientific) and amplified with 6 PCR cycles or used without PCR amplification. Templates were generated with Ion PI Template OT2 200 kit v3 and Ion PI Sequencing 200 kit v3, or with Ion PI IC 200 kit (Thermo scientrific). Libraries were sequenced on the Ion Proton Sequencer using Ion PI chips v2 (Thermo scientific).
ChIP-seq libraries for CDK8 ChIP were prepared using the NEBNext Ultra DNA Library Prep Kit, and sequenced as 40 bp paired-end reads on Illumina NextSeq500 platform using NextSeq 500/550 (75 cycles).
Reverse transcription and gene expression analysis {#s4-11}
--------------------------------------------------
Total RNA was isolated using TRIzol reagent (Thermo scientific) following manufacturer's instructions and cDNA was synthesized from 400 ng RNA using random primers and ImProm-II Reverse Transcription system kit (Promega). RT-qPCR was performed using SensiMix SYBR mix (Bioline). Idh1 and Atp6IP1 genes were used as house-keeping controls.
4sU-labeling of nascent RNA transcripts {#s4-12}
---------------------------------------
For labeling of nascent RNA transcripts, cells were grown in 15 cm culture dishes. Labeling was performed for 20 min at 37°C by the addition of 50 mM 4-thiouridine (T4509, Sigma) to the culture medium. After the incubation, the medium was removed and RNA was isolated using TRIzol reagent (Thermo scientific) following manufacturer's instructions. The total RNA was treated with TURBO DNA-free kit (Ambion, Thermo scientific) in order to remove contaminating genomic DNA. 300 µg RNA was biotinylated using 600 µg Biotin-HPDP (21341, Pierce, Thermo scientific) in Biotinylation buffer (100 mM Tris-HCl pH 7.4, 10 mM EDTA). The reaction was carried out for one and half hour on a rotor at room temperature. Unincorporated Biotin-HPDP was removed by chloroform/isoamylalcohol (24:1, Sigma) wash followed by isopropanol precipitation of the biotinylated RNA. Labeled biotinylated RNA was isolated using µMacs Streptavidin Kit (130-074-101, Miltenyi) following manufacturer's instructions and purified using RNeasy MinElute Cleanup kit (Qiagen). The quality of the RNA was confirmed using the RNA pico Bioanalyser kit (Agilent).
4sU RNA sequencing {#s4-13}
------------------
Up to 1 µg purified 4sU-labelled RNA was used to prepare libraries for 4sU-RNA-seq. Ribosomal RNA was removed using NEBNext rRNA Depletion Kit and libraries were prepared using NEBNext Ultra Directional RNA Library Prep Kit for Illumina (NEB) following manufacturer's instructions. Library quality was assessed using the High-sensitivity DS DNA Bioanalyser kit (Agilent) and the concentration was measured by quantitative PCR using KAPA Library quantification standards for Illumina (KAPA Biosystems). All 4sU RNA-seq experiments were carried out in biological triplicates. 4sU RNA-seq libraries were sequenced as 80 paired-end reads on Illumina NextSeq500 platform using NextSeq 500/550 High Output Kit v2 (150 cycles).
Analysis of high-throughput sequencing {#s4-14}
--------------------------------------
Sequencing reads were aligned to the mouse genome (mm10) using bowtie2 ([@bib47]) with the '\--no-mixed' and '\--no-discordant' options. Reads that mapped more than once to the genome were discarded. For 4sU RNA-seq analysis, rRNA reads were initially removed by aligning the data to mouse rRNA genomic sequences (GenBank: BK000964.3) using bowtie2. The rRNA-depleted reads were next aligned against mm10 genome using the STAR RNA-seq aligner ([@bib23]). To improve mapping of nascent, intronic sequences, a second alignment step with bowtie2 was included using the reads which failed to map using STAR. PCR duplicates were removed using samtools ([@bib51]). Biological replicates were randomly downsampled to the same number of reads for each individual replicate and merged for visualisation. Bigwig files were generated using MACS2 ([@bib87]) and visualised using the using the UCSC Genome Browser ([@bib67]).
Peak calling was performed using the MACS2 function with the '-broad' option using the biological replicates with matched input ([@bib87]). Peaks mapping to a custom 'blacklist' of artificially high genomic regions were discarded. Only peaks called in both replicates were considered. Differential analysis of CDK8 binding was done using DiffReps ([@bib71]) and the called differential regions were overlapped with CDK8 peaks. Changes in binding of log2FC less than −0.5 or more than 0.5 with adjusted p-value below 0.05 were considered significant.
Differential expression analysis was performed using the DESeq2 package ([@bib55]), version 1.6.3, with R version 3.1.1. Counts were quantified using the summarizeOverlaps() function in R in the mode 'Union' and inter.feature = FALSE. Genes with an adjusted p-value of below 0.1 and a fold change of at least 1.5 were considered differentially expressed. Statistical analysis was performed using two-sample Wilcoxon rank sum test. Gene ontology analysis was done using DAVID 6.8 ([@bib37]). For CDK8 differentially bound peaks, all CDK8 peaks were provided as background. For misregulated genes analysis, all RefSeq genes were provided as background. ATAC peaks were obtained from [@bib43]).
Accession numbers {#s4-15}
-----------------
ChIP-seq and RNA-seq data from the present study are available to download at GSE98756. Previously published studies used for analysis include mouse ES cell BioCAP (GSE43512, \[[@bib54]\]), Kdm2B ChIP-seq (GSE55698, \[[@bib12]\]), Kdm2A ChIP-seq (GSE41267, \[[@bib28]\]), H3K27me3 ChIP-seq (GSE83135, \[[@bib68]\]), H3K4me3 ChIP-seq (GSE93538, \[[@bib18]\]).
Funding Information
===================
This paper was supported by the following grants:
- Sir Henry Wellcome Postdoctoral Fellowship 110286/Z/15/Z to Angelika Feldmann.
- http://dx.doi.org/10.13039/100009619Japan Agency for Medical Research and Development to Haruhiko Koseki.
- http://dx.doi.org/10.13039/100004440Wellcome 098024/Z/11/Z to Robert J Klose.
- http://dx.doi.org/10.13039/501100000781European Research Council 681440 to Robert J Klose.
- http://dx.doi.org/10.13039/501100001255Lister Institute of Preventive Medicine to Robert J Klose.
We thank Anne Turberfield for help with the 4sU-RNAseq protocol and useful discussion, and Hamish King for assistance with computational analysis and critical comments and suggestions. We thank David Brown for initiating the FBXL19 experiments, and Anne Turberfield and Neil Blackledge for critical reading of the manuscript. We thank Ed Hookway and Udo Oppermann for sequencing support on the NextSeq500 at the Botnar sequencing facility in Oxford. Work in the Klose laboratory is supported by the Wellcome Trust, the Lister Institute of Preventive Medicine and the European Research Council. TK and HK are supported by the AMED-CREST programme from the Japan Agency for Medical Research and Development. AF is supported by a Sir Henry Wellcome Postdoctoral Fellowship.
Additional information {#s5}
======================
No competing interests declared.
Conceptualization, Data curation, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing---original draft, Writing---review and editing.
Resources, Data curation, Formal analysis, Methodology.
Resources, Software, Formal analysis.
Resources, Contributed to transgenic mouse generation and embryonic stem cell derivation and characterisation.
Resources, Contributed to transgenic mouse generation and embryonic stem cell derivation and characterisation.
Resources, Contributed to mass spectrometry sample processing and analysis.
Resources, Contributed to mass spectrometry sample processing and analysis.
Supervision, Funding acquisition, Investigation, Project administration.
Conceptualization, Supervision, Funding acquisition, Investigation, Writing---original draft, Project administration, Writing---review and editing.
Additional files {#s6}
================
10.7554/eLife.37084.019
Data availability {#s7}
-----------------
Sequencing data generated in this study have been deposited in GEO under accession code GSE98756.
The following dataset was generated:
Dimitrova E2017FBXL19 recruits CDK8-Mediator to CpG islands and primes developmental genes for activation during lineage commitment<https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE98756>Publicly available at the NCBI Gene Expression Omnibus (accession no. GSE98756)
The following previously published datasets were used:
Blackledge NPFarcas AMKondo TKing HWMcGouran JFHanssen LLIto SCooper SKondo KKoseki YIshikura TLong HKSheahan TWBrockdorff NKessler BMKoseki HKlose RJ2014Variant PRC1 complex dependent H2A ubiquitylation drives PRC2 recruitment and polycomb domain formation<https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE55698>Publicly available at the NCBI Gene Expression Omnibus (accession no. GSE55698)
Farcas AMBlackledge NPSudbery ILong HKMcGouran JFRose NRLee SSims DCerase ASheahan TWKoseki HBrockdorff NPonting CPKessler BMKlose RJ2012KDM2B links the Polycomb Repressive Complex 1 (PRC1) to recognition of CpG islands<https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE41267>Publicly available at the NCBI Gene Expression Omnibus (accession no. GSE41267)
Long HKSims DHeger ABlackledge NPKutter CWright MLGrützner FOdom DTPatient RPonting CPKlose RJ2013Epigenetic conservation at gene regulatory elements revealed by non-methylated DNA profiling in seven vertebrates<https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE43512>Publicly available at the NCBI Gene Expression Omnibus (accession no. GSE43512)
Rose NRKing HWBlackledge NPFursova NAEmber KJFischer RKessler BMKlose RJ2016RBYP stimulates PRC1 to shape chromatin-based communication between polycomb repressive complexes<https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE83135>Publicly available at the NCBI Gene Expression Omnibus (accession no. GSE83135)
Brown DADi Cerbo VFeldmann AAhn JIto SBlackledge NPNakayama MMcClellan MDimitrova ETurberfield AHLong HKKing HWKriaucionis SSchermelleh LKutateladze TGKoseki HKlose RJ2017CFP1 engages in multivalent interactions with CpG island chromatin to recruit the SET1 complex and regulate gene expression.<https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE93538>Publicly available at the NCBI Gene Expression Omnibus (accession no. GSE93538)
10.7554/eLife.37084.036
Decision letter
Espinosa
Joaquín M
Reviewing Editor
University of Colorado School of Medicine
United States
In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.
\[Editors' note: a previous version of this study was rejected after peer review, but the authors submitted for reconsideration. The first decision letter after peer review is shown below.\]
Thank you for submitting your work entitled \"FBXL19 recruits CDK8-Mediator to CpG islands and primes developmental genes for activation during lineage commitment\" for consideration by *eLife*. Your article has been reviewed by four peer reviewers, one of whom is a member of our Board of Reviewing Editor and the evaluation has been overseen by a Senior Editor.
The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this letter to crystallize our concerns going forward. The work presented was deemed important and interesting but key issues reduced enthusiasm for the manuscript considerably. Given that these revisions are substantial and likely to take a significant amount of time, we are currently declining the present version of the paper. That said, if you feel you can successfully address all the concerns raised, we will be open to consider a revised submission, which would be treated as a de novo submission but sent to the same editors and, if possible, referees for re-assessment.
Summary:
The reviewers considered the manuscript to be strong, reporting a thorough characterization of FBXL19, the least-well studied of three proteins that contain a ZF-CxxC domain. The authors demonstrate that over-expressed FBXL19 accumulates in the nucleus, and that a majority of its genome-wide binding is at sites associated with CpG islands. Affinity purification of FS2-tagged FBXL19 indicated a physical association with CDK8-containing Mediator complex, and a TetR-FBXL19 fusion protein was able to recruit CDK8 to a chromosomally-integrated artificial TetO array, suggesting that FBXL19 can recruit CDK8 to chromatin. Conditional deletion of the ZF-CxxC domain of FBXL19 led to reduction of CDK8 binding at CpG islands in ES cells. Many of these sites are associated with silent developmental genes that are no longer activated during ES cell differentiation in the FBXL19 mutants. Finally, deletion of the ZF-CxxC domain was shown to be embryonic lethal in mice. Together, these findings suggest that FBXL19 may prime developmental genes for subsequent activation during differentiation, possibly involving recruitment of CDK8. Overall, this represents an interesting finding and potentially a novel role for CDK8. However, concerns about the degree to which this represents a significant advance over previous FBXL19 studies, some missing controls, and a lack of a direct test of CDK8 requirement for expression of these genes resulted in lessened enthusiasm for this manuscript.
The reviewers discussed these concerns and summarized their critiques into the following points.
Essential revisions:
1\) A key conclusion of the manuscript is that CDK8-Mediator is required for induction of developmental genes regulated by FBXL19, but this is actually not proven in the manuscript. The authors should deplete CDK8 (and/or CDK19, see comment \#2 below) and test for the impact on induction of FBXL19-dependent genes.
2\) Throughout the paper, the authors refer to CDK8-Mediator. Given that there are two paralog kinases associated with the Mediator complex, CDK8 and CDK19, the authors should test for the presence of CDK19 and clarify whether the interaction is exclusive to CDK8-containing complexes or not. In Figure 2A, are the CDK8 peptides identified unique to CDK8 or could they map to CDK19 as well? In Figure 2C, please add western blot for CDK19. As for point \#1 above, is CDK19 required for control of FBXL19-regulated genes? Additionally, the authors should demonstrate that in the \"EV\" control lane, at the similar molecular weight, these candidate hits didn\'t show up in the cut gel, or at least with significantly less numbers of peptides.
3\) If the ZF-CxxC mediates the interaction between FBXL19 and chromatin, then which functional domain(s) on FBXL19 bind to CDK8-Mediator complex? Lee et al., claimed that the F-box is critical for the interaction between FBXL19 and RNF20. Does the same protein structure bind to CDK8?
4\) Most of the findings are based on overexpression of FBXL19 -- what is the level relative to endogenous FBXL19? High-level over-expression could drive nuclear accumulation and other observations (including Figure 3). Authors should provide data demonstrating the degree of overexpression produced in the key experiments.
5\) FBXL19 binding to CpG islands and its requirement in ES differentiation has been described previously: (https://www.ncbi.nlm.nih.gov/pubmed/28453857) \"Our genome-wide target mapping unveils the preferential occupancy of Fbxl19 on CpG island-containing promoters \[...\]\" \"Moreover, we reveal that Fbxl19 is critical for proper differentiation of ES cells \[...\]\" With respect to this, the authors should clarify the novelty of their results presented in the current manuscript.
6\) The conclusion that FBXL19 does not appear to regulate CDK8-Mediator levels is not fully supported by the data. Figure 2---figure supplement 1H needs to be repeated so that CDK8 bands are not over-exposed as there does appear to be a change in amount/mobility when overexpressed -/+ MG132. Furthermore, there seems to be a noticeable increase of MED12 protein upon FBXL19 overexpression, which was even more obvious when cells were treated with MG132.
7\) In Figure 4, CDK8 recruitment has only been tested for the FBXL19 ZF-CxxC deletion -is this recapitulated for depletion of the whole protein? Given that Figure 4B appears to show a decrease in the levels of the deletion protein this is an important point to verify.
8\) The authors need to show that OHT treatment of the delCxxC ES line leads to reduced binding of FBXL19 in conditions used for CDK8 ChIPseq -several genes would be ok -these same genes should be used to validate CDK8 CHIPseq signal.
9\) Supplemental tables with differential gene expression results should be provided -or at least working gene lists used to reach the conclusions in the manuscript. Full GO enrichment results should be included as supplementary tables so that specific gene lists can be examined.
10\) Various figure panels are missing statistical tests: Figure 4C needs statistical tests, e.g. KS/Wilcoxon -See Figure 4E; Figure 4G needs statistical tests; Figure 4H and 4I need boxplots and need statistical tests eg KS/Wilcoxon as for E/F; Figure 4H-J should include FBXL19-bound groups; Figure 6B,E,F need statistical tests.
11\) It is very nice that the authors showed that genome-wide chromatin binding of FBXL19 was completely lost when the ZF-CxxC domain was deleted or mutated. To further confirm that it is indeed this ZF-CxxC domain mediating interaction with the non-methylated CpG islands, some controls are necessary. For example, in Figure 1---figure supplement 1D, the authors showed that almost all of the FBXL19 binding sites are overlapped with NMIs locations, with only 93 exceptions. Then are the signals at these 93 sites also changed in the FBXL19 mutant ChIPSeq data? When the cell DNA methylation levels are modulated, will the binding pattern of FBXL19 changed accordingly?
\[Editors' note: what now follows is the decision letter after the authors submitted for further consideration.\]
Thank you for submitting your article \"FBXL19 recruits CDK-Mediator to CpG islands of developmental genes priming them for activation during lineage commitment\" for consideration by *eLife*. Your article has been reviewed by three peer reviewers, one of whom is a member of our Board of Reviewing Editors and the evaluation has been overseen by James Manley as the Senior Editor. The reviewers have opted to remain anonymous.
The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.
The revised manuscript by Dimitrova et al., is an excellent report describing the characterization of FBXL19, a member of the ZF-CxxC domain-containing family of proteins, and its role in recruiting CDK-Mediator to developmental genes in stem cells.
As for other members of this family, the authors show that FBXL19 recognizes unmethylated CpGs in a ZF-CxxC-dependent manner. Unlike the lysine demethylases KDM2A and KDM2B in this protein family, FBXL19 lacks a JMJ-C domain. Instead, the authors report that FBXL19 interacts with the CDK-Mediator complex. The authors then embark on an experimental tour-de-force to demonstrate that FBXL19 is required for recruitment of CDK-Mediator to a subset of genes containing CpG islands in ES cells, mostly genes involved in lineage commitment. Interestingly, these genes are transcribed at low levels in ES cells when bound by FBXL19 and CDK-Mediator, but their induction is compromised in the absence of FBXL19. This indicates that FBXL19-CDK8-Mediator is required to \'prime\' these genes in ES cells and their subsequent induction upon differentiation stimuli. Finally, the authors demonstrate that FBXL19 depletion is embryonic lethal. Overall, the manuscript is very well written, and the data is of excellent quality.
This is a new submission of a paper that was originally reviewed by the same referees and found to be lacking data to support some of the key conclusions. The Senior Editor opened up the possibility of a new submission without a precise timeline and the authors have taken the opportunity to address the major concerns raised in the original review. The referees are now supportive of publication of a revised manuscript addressing the following issues:
Essential revisions:
1\) In AP-MS (Figure 2A), what is the background value of emPAI? Are there any other FBXL19-interacting proteins that show significantly high levels of emPAI in the list? How significant are the components of CDK-Mediator complex represented in all the hits?
2\) In Figure 3, the authors demonstrated that FBXL19 was able to recruit CDK-Mediator complex, such as CDK8 and MED12, to artificially designed chromatin regions. What about CXXC-domain or F-box deletion mutants in this assay?
3\) In Figure 4B, it is not very clear which band(s) are exactly indicated as full-length FBXL19 and which one(s) are CXXC deletion? Why are there double bands? Did the author use T7 antibody to detect the endogenously introduced protein?
4\) In Figure 4C, what proportions of each group of CDK8 binding sites overlap with FBXL19? In theory, the author expects to see that CDK8 sites showing binding intensity changes upon tamoxifen treatment would tend to overlap more with FBXL19.
5\) In Figure 4---figure supplement 1C, please use a Venn Diagram to show directly the number of peaks of CDK8, FBXI19 and NMI overlapping with each other. This would be more straightforward.
6 In Figure 5, please perform the same GSEA or functional annotation analysis on genes that are associated with unchanged CDK8 binding sites upon FBXL19 CXXC-domain deletion.
7\) In Figure 6B, what is the result for genes that are associated with increased CDK8 binding signals in FBXL19 CXXC-domain deletion mutant upon RA-induced differentiation?
8\) In Figure 6C, even though the authors claimed that those upregulated genes (889) in FBXL19 CXXC-domain deletion mutant upon RA treatment were not involved in developmental processes, it is still interesting to find that significantly more genes were activated upon CXXC-domain deletion. What explanation can the authors provide for this finding?
9\) In Figure 7, the authors claim that FBXL19 relies on CDK-mediator complex to activate the specific set of developmental genes. Is it possible to test this hypothesis in the FBXL19 CXXC-deletion system they established in Figure 6? In wild-type ESC, depletion of MED13 will have similar effects as FBXL19 CXXC deletion, whereas in FBXL19 mutant, the effects would be much alleviated?
10\) In Figure 8, why did heterozygous deletion of FBXL19 CXXC-domain show even better developmental status than the wild type?
11\) The authors demonstrated that the CXXC-domain mediates the binding of FBXL19 at NMIs, where F-Box mediates its interaction with the CDK-Mediator complex. What about CDK8 chromatin binding or gene expression patterns upon F-Box deletion of FBXL19? Will the authors see the same results as what they found in CXXC-domain deletion mutant?
10.7554/eLife.37084.037
Author response
\[Editors' note: the author responses to the first round of peer review follow.\]
> Essential revisions:
>
> 1\) A key conclusion of the manuscript is that CDK8-Mediator is required for induction of developmental genes regulated by FBXL19, but this is actually not proven in the manuscript. The authors should deplete CDK8 (and/or CDK19, see comment \#2 below) and test for the impact on induction of FBXL19-dependent genes.
We agree with the reviewers that testing the impact that removal of CDK-Mediator has on the induction of FBXL19 target genes is an important experiment. To disrupt CDK-Mediator we have developed a new cell system to remove MED13 and its closely related paralogue MED13L (both of which are expressed in mouse ES cells) in an inducible manner. We chose to delete both MED13 and MED13L because they are thought to play an interchangeable role in physically linking the CDK subunits to the core Mediator and to be required to form an intact CDK-Mediator complex (Kuesel et al., 2009; Tsai et al., 2013). To achieve this, we exploited gene targeting to insert loxP sites around essential exons in both MED13 and MED13L. We also engineered these cells to express a tamoxifen inducible form of Cre recombinase allowing inducible deletion of MED13/13L (Figure 7---figure supplement 1). In new Figure 7, we demonstrate that the addition of tamoxifen leads to complete loss of MED13/13L protein. Furthermore, we show by ChIP that CDK8 no longer occupies its target sites. We then examined FBXL19 target genes after loss of CDK-Mediator binding and found that they are no longer appropriately induced during differentiation (Figure 7D), in keeping with a requirement for CDK-Mediator in FBXL19dependent gene activation. We thank the reviewers for suggesting this important experiment as it now robustly supports and strengthens our key argument that FBXL19 recruits the CDK-Mediator complex to the CpG islands of inactive developmental genes to prime them for appropriate activation during differentiation. We have now edited the text throughout the manuscript to reflect these important new observations.
> 2)Throughout the paper, the authors refer to CDK8-Mediator. Given that there are two paralog kinases associated with the Mediator complex, CDK8 and CDK19, the authors should test for the presence of CDK19 and clarify whether the interaction is exclusive to CDK8-containing complexes or not. In Figure 2A, are the CDK8 peptides identified unique to CDK8 or could they map to CDK19 as well? In Figure 2C, please add western blot for CDK19. As for point \#1 above, is CDK19 required for control of FBXL19-regulated genes?
As indicated by the reviewer, CDK8 has a highly similar paralogue, CDK19. As suggested, we have now examined our mass spectrometry results in more detail to determine if we find any peptides that also map to CDK19. From this analysis, we have identified five different peptides covering CDK8/CDK19. Four are common to both CDK8 and CDK19, and one is unique for CDK8 ([Author response image 1](#respfig1){ref-type="fig"}). In our original submission, we had referred to an interaction between FBXL19 and the CDK8-Mediator complex given the identification of a peptide unique to CDK8. However, we agree that this was an oversight as one cannot exclude the possibility that FBXL19 also associates with CDK19-containing Mediator complexes. In fact, given that CDK19 is also expressed in mouse ES cells and is thought to function interchangeably with CDK8, it seems likely that FBXL19 will also interact with CDK19Mediator. Our CKD8 antibody uniquely recognises CDK8, but we have been unable to source an antibody that specifically recognises CDK19, limiting our ability to test whether CDK19 also associates with FBXL19. An antibody with specificity to CDK19 (Atlas antibody HPA007053) has previously been published, but this is currently unavailable, and the company informed us that this is due to a loss of specificity in new batches. Given that we cannot exclude the possibility that FBXL19 also associates with Mediator complexes containing CDK19, we have now added a sentence describing this possibly in the text as follows (subsection "FBXL19 interacts with the CDK-Mediator complex in ES cells"):
*'*CDK8 and its paralogue CDK19 share 77% amino acid identity (89% similarity) (Audetat et al., 2017) and four out of the five peptides identified by mass spectrometry were common between the two proteins (data not shown). Therefore, it is likely that FBXL19 is able to interact with both CDK8- and CDK19- containing Mediator complexes.'
Furthermore, because the FBXL19-associated Mediator complex could contain either CDK8 or CDK19, we have edited the text throughout the manuscript to replace 'CDK8-Mediator' with 'CDK-Mediator'. In future work it will be interesting to understand in more detail if CDK8- and CDK19-containing Mediator complexes have redundant or unique roles in gene activation during differentiation.
{#respfig1}
> Additionally, the authors should demonstrate that in the \"EV\" control lane, at the similar molecular weight, these candidate hits didn\'t show up in the cut gel, or at least with significantly less numbers of peptides.
We carried out mass spectrometry analysis on affinity-purified FBXL19 by in-solution digestion followed by LC-MS. This was to overcome the limitations inherent to cutting bands from SDS-PAGE gels and the isolation of tryptic peptides from gel slices. Importantly, we only considered a protein to be an FBXL19 interactor in our mass spectrometry analysis if it was absent from matched EV control purifications analysed using the same in-solution approach. It would have been beneficial to have described this approach in more detail in the initial submission, so we have now expanded our description of these experiments in the revised Material and Methods. Furthermore, we validated that CDK-Mediator components were not found in the 'EV' control purifications by Western blot analysis (Figure 2C).
> 3\) If the ZF-CxxC mediates the interaction between FBXL19 and chromatin, then which functional domain(s) on FBXL19 bind to CDK8-Mediator complex? Lee et al. claimed that the F-box is critical for the interaction between FBXL19 and RNF20. Does the same protein structure bind to CDK8?
We thank the reviewers for this suggestion and agree this is an important point. To address this, we performed transient overexpression of FBXL19 followed by co-immunoprecipitation comparing wildtype FBXL19 with versions of FBXL19 in which individual domains had been removed. We found that deletion of the F-box largely disrupted the interaction with CDK-Mediator, while removing the ZF-CxxC domain had little effect on this interaction. We have included these new observations in the revised manuscript (subsection "FBXL19 interacts with the CDK-Mediator complex in ES cells", Figure 2---figure supplement 1E). We also attempted to determine whether the LRR domain of FBXL19 was required for this interaction but unfortunately removing this portion of the protein seemed to render it unstable (unpublished observations) limiting our capacity to draw any meaningful interpretation.
> 4\) Most of the findings are based on overexpression of FBXL19 -- what is the level relative to endogenous FBXL19? High-level over-expression could drive nuclear accumulation and other observations (including Figure 3). Authors should provide data demonstrating the degree of overexpression produced in the key experiments.
We have examined FBXL19 transcript levels in the transgene lines and they are roughly eight times that of wild type ([Author response image 2](#respfig2){ref-type="fig"}). Despite exhaustive efforts we have been unable to generate an antibody that recognizes the endogenous protein in cellular extracts by Western blot. Therefore, we have been unable to directly compare endogenous FBXL19 protein levels to the FBXL19 levels in transgene containing lines. Nevertheless, we are confident in the conclusions from our key experiments. We have validated that endogenous FBXL19 is in the nucleus and interacts with CDKMediator. This was demonstrated by immunoprecipitating endogenous FBXL19 protein from nuclear extracts and using Western blot to show that FBXL19 associates with CDK8 and MED12 (Figure 2---figure supplement 1D), consistent with our transgene experiments (Figure 2).
Given that we know FBXL19 is in the nucleus and interacts with CDK-Mediator, tethering experiments in Figure 3 were used to test if de novo targeting of FBLX19 to naïve chromatin would result in recruitment of CDK-Mediator. This showed that FBXL19 binding was sufficient to recruit CDK-Mediator (Figure 3B), in agreement with our observations that when the capacity of FBXL19 to bind CpG island chromatin is disrupted, CDK8 is no longer appropriately recruited to a subset of CpG island-associated target genes (Figure 4).
{#respfig2}
> 5\) FBXL19 binding to CpG islands and its requirement in ES differentiation has been described previously: (https://www.ncbi.nlm.nih.gov/pubmed/28453857) \"Our genome-wide target mapping unveils the preferential occupancy of Fbxl19 on CpG island-containing promoters \[...\]\" \"Moreover, we reveal that Fbxl19 is critical for proper differentiation of ES cells \[...\]\" With respect to this, the authors should clarify the novelty of their results presented in the current manuscript.
During the preparation of our manuscript, the manuscript cited by the reviewer was published in NAR. It reported that FBXL19 occupied CpG islands and appeared to play a role in cellular differentiation. However, we would like to point out that, although our observations were similar with respect to these two points, the main discoveries resulting from our careful and systematic study are completely distinct from that of the published study. In direct contrast to the published work, we find no evidence for any connection between FBXL19 and RNF20 using unbiased biochemistry and mass spectrometry (Figure 2 and Figure 2---figure supplement 1F). Furthermore, using our conditional genetic ablation strategies we do not observe any effect of FBXL19 loss on H2BK120ub1 (Figure 2---figure supplement 1G). Therefore, we are unable to reproduce the central findings of the published study. In our opinion this severely limits and brings into question the validity and, therefore, the novelty of the published work. Our observations likely differ from those of the NAR study because we use unbiased as opposed to candidate-based (guess work) biochemistry and conditional knockout strategies as opposed to stable knockdown cell lines that are prone to indirect and secondary effects due to the long-term culture necessary for their generation. Nevertheless, we agree with the reviewer that the wording of the indicated sentences could have been more inclusive and contrasting of the published work and have clarified this in the revised manuscript (Introduction, Results section, subsection "FBXL19 interacts with the CDK-Mediator complex in ES cells" and subsection "Removing the CpG island-binding domain of FBXL19 results in a failure to induce developmental genes during ES cell differentiation").
We would also like to take this opportunity to clarify the novelty of our study and the importance of its central conclusions. (1) By using unbiased biochemical approaches, we discover a link between FBXL19 and CDK-Mediator in mouse ES cells. (2) Using conditional genetic ablation, de novo targeting strategies, and genomics, we go on to show that FBLX19 can recruit CDK-Mediator to chromatin and the CpG island promoters of silent developmental genes in ES cells. (3) In the absence of FBXL19, these genes are no longer appropriately activated upon differentiation, providing an explanation for why normal differentiation cannot be achieved in the absence of FBXL19. (4) In the revised study, based on the reviewer's suggestions (point 1), we now demonstrate that FBXL19 target genes also rely on CDKMediator for their activation, validating our biochemistry and genomics. (5) Finally, we discover that loss of FBXL19 leads to abnormal development and early embryonic lethality, in agreement with the inability of cells to appropriately regulate gene expression during development.
Therefore, our discoveries are novel in describing a completely new modality by which FBXL19 and CpG islands prime genes for future expression. Furthermore, we provide compelling new evidence that CDKMediator can be recruited to gene promoters independently of classical transcription factors and transcription itself to prime CpG island-associated genes for activation. These new discoveries force us, and the field, to think differently about how CpG islands integrate and regulate gene expression, while also provide new insight into the poorly understood mechanisms by which CDK-Mediator is targeted to genes and functions to control gene expression. We believe these important points are now more clearly framed in the revised manuscript.
> 6\) The conclusion that FBXL19 does not appear to regulate CDK8-Mediator levels is not fully supported by the data. Figure 2---figure supplement 2H needs to be repeated so that CDK8 bands are not over-exposed as there does appear to be a change in amount/mobility when overexpressed -/+ MG132. Furthermore, there seems to be a noticeable increase of MED12 protein upon FBXL19 overexpression, which was even more obvious when cells were treated with MG132.
We have repeated these experiments based on the reviewer's suggestions. We again failed to observe any significant difference in CDK8 protein levels following FBXL19 over-expression at lower exposure levels. We agree it appeared that MED12 levels may have increased slightly when FBXL19 was overexpressed in original Figure 2---figure supplement 1G. However, we believe this is an artefact resulting from inefficient transfer on the left had side of the gel. MED12 is a large protein (250KDa) and we previously have encountered difficulties efficiently transferring MED12 to membrane for Western blot analysis. We have now optimised our transfer of large proteins and fail to see any significant or reproducible alterations in MED12 levels (Figure 2---figure supplement 1H). MED12 is known to be regulated by the proteasome in ES cells (e.g. Buckley et al., 2012). In agreement with this, we observe an increase in MED12 levels after MG132 treatment in both FBXL19 overexpressing cells and in the control cells transfected with an empty vector. This effect is therefore not related to FBXL19. Finally, we have also included in the revised manuscript a Western blot analysis of MED13 (which is also part of the CDK module) and again we observe no change in protein levels following FBLX19 overexpression (Figure 2---figure supplement 1H). We conclude that FBXL19 does not regulate CDK module protein levels.
> 7\) In Figure 4, CDK8 recruitment has only been tested for the FBXL19 ZF-CxxC deletion -is this recapitulated for depletion of the whole protein? Given that Figure 4B appears to show a decrease in the levels of the deletion protein this is an important point to verify.
We reasoned that conditionally removing the ZF-CxxC domain would be the most surgical way of disrupting binding of FBXL19 to CpG islands, without interfering other potential functions of FBXL19. We agree that deletion of the ZF-CxxC domain appears to cause some reduction in FBXL19 protein levels. We speculate that FBXL19 may be more rapidly degraded if not bound to chromatin (something we have observed for other ZF-CxxC domain containing proteins). Importantly, CDK8 proteins levels are unaffected in the ΔCxxC-FBXL19 cells (Figure 4---figure supplement 1F). We have now carried out a biochemical purification of ΔCxxC-FBXL19 and shown that it still interacts with CDK8-Mediator (Figure 2---figure supplement 1E). Given that ΔCxxC-FBXL19 does not bind to CpG islands (Figure 1) yet still interacts with CDK8, we conclude that reductions in CDK8 recruitment at FBXL19 targets genes is most likely explained by the loss of FBXL19 binding to CpG islands. Nevertheless, we now draw attention to the reduced protein levels of the ZF-CxxC deleted protein as follows (subsection "FBXL19 is required for appropriate CDK8 occupancy at a subset of CpG island-associated promoters"):
'Following removal of the ZF-CxxC domain of FBXL19, we observed some reductions in FBXL19 protein levels (Figure 4B), but importantly CDK8 levels were unaffected (Figure 4---figure supplement 1F).'
> 8\) The authors need to show that OHT treatment of the delCxxC ES line leads to reduced binding of FBXL19 in conditions used for CDK8 ChIPseq -several genes would be ok -these same genes should be used to validate CDK8 CHIPseq signal.
All commercially available antibodies for FBXL19 that we have tried fail to ChIP FBXL19 and our exhaustive attempts to generate our own FBXL19-specific antibody that works for ChIP have been unsuccessful (two separate epitopes and 4 rabbits). This has precluded us from carrying out the proposed experiment. However, we do observe a uniform loss of FBXL19 binding when the ZF-CxxC domain is removed in epitope-tagged transgene experiments (Figure 1) suggesting that FBXL19 binding to CpG islands relies on an intact ZF-CxxC domain.
> 9\) Supplemental tables with differential gene expression results should be provided -or at least working gene lists used to reach the conclusions in the manuscript. Full GO enrichment results should be included as supplementary tables so that specific gene lists can be examined.
This information is now included as Supplementary file 1.
> 10\) Various figure panels are missing statistical tests: Figure 4C needs statistical tests, e.g. KS/Wilcoxon -See Figure 4E; Figure 4G needs statistical tests; Figure 4H and 4I need boxplots and need statistical tests eg KS/Wilcoxon as for E/F;
We have now included the necessary statistical tests and plots as requested by the reviewer.
> Figure 4H-J should include FBXL19-bound groups;
As suggested by the reviewer, we divided all CDK8 peaks into those which have FBXL19 (FBXL19+) and those that do not have FBXL19 (Fbxl19-). We then examined FBXL19, BioCAP and CDK8 enrichment in these groups (Figure 4---figure supplement 1I). As observed when we analysed all CDK8 peaks (Figure 4H-J), we found that CDK8 peaks that are bound by FBXL19 have increased levels of FBXL19, CDK8, and BioCAP signal when compared to sites not bound by FBXL19. Furthermore, sites that rely on FBXL19 for CDK8 binding have broader peaks of FBXL19 enrichment. This is consistent with the fact that these are large CpG islands with broad BioCAP signal (Figure 4F, 4H). The majority peaks that show reduction of CDK8 binding in FBXL19^ΔCXXC^ ES cells with FBXL19 peaks (519/783) while there is only a small overlap between FBXL19 binding and sites with increased CDK8 binding (90/379). We have now included this information in Figure 4---figure supplement 1I.
> Figure 6B,E, F need statistical tests.
We have now included the necessary statistical tests.
> 11\) It is very nice that the authors showed that genome-wide chromatin binding of FBXL19 was completely lost when the ZF-CxxC domain was deleted or mutated. To further confirm that it is indeed this ZF-CxxC domain mediating interaction with the non-methylated CpG islands, some controls are necessary. For example, in Figure 1---figure supplement 1D, the authors showed that almost all of the FBXL19 binding sites are overlapped with NMIs locations, with only 93 exceptions. Then are the signals at these 93 sites also changed in the FBXL19 mutant ChIPSeq data? When the cell DNA methylation levels are modulated, will the binding pattern of FBXL19 changed accordingly?
We have now compared the enrichment of WT FBXL19 and ΔCxxC FBXL19 at these 93 sites ([Author response image 3A](#respfig3){ref-type="fig"}), which corresponded to regions that were not associated with NMIs and observed a loss of binding of ΔCxxC FBXL19 ([Author response image 3B](#respfig3){ref-type="fig"}). Importantly, these same 93 sites also show some BioCAP signal, albeit at a level much lower than is observed at NMIs. This suggests that these sites are very weak CpG islands which were not captured in our NMI peak set due to their low Bio-CAP signal.
Furthermore, to illustrate the relationship between FBXL19 binding and CpG-rich non-methylated DNA, we have examined BioCAP and FBXL19 signal across all ATAC-seq peaks in the mouse ES cell genome ([Author response image 3B](#respfig3){ref-type="fig"}). ATAC-seq peaks represent a combination of regulatory elements that are CpGrich (CpG islands) or CpG-poor (usually distal regulatory elements). This provides the necessary contrast to illustrate the correlation of FBXL19 tracks with sites that contain CpG rich non-methylated DNA (BioCAP), consistent with a FBXL19 binding modality that is dependent on its ZF-CxxC domain.
We have not been able to examine FBXL19 binding in cells with altered DNA methylation levels as this would require recreation of a DNMT1 (or DNMT3A/B) null situation in our transgene containing cell line (we don't use 5aza-C for this purpose as it causes extensive DNA damage due to covalent adducts which are formed between DNA and DNMT enzymes). However, when we have previously examined DNA methylation-deficient cells and the behaviour of the closely related KDM2A/B proteins, which have nearly identical CpG island binding patterns to FBXL19 (Figure 1D and 1E), we demonstrated that KDM2A/B occupancy is completely dependent on recognition of CpG-rich non-methylated DNA (Blackledge et al., 2010; Zhou et al., 2012).
{#respfig3}
\[Editors\' note: the author responses to the re-review follow.\]
> Essential revisions:
>
> 1\) In AP-MS (Figure 2A), what is the background value of emPAI? Are there any other FBXL19-interacting proteins that show significantly high levels of emPAI in the list? How significant are the components of CDK-Mediator complex represented in all the hits?
To clarify these points, we have now included a table in the supplementary information (Figure 2---source data 1) detailing the AP-MS results. This includes the biological replicate FS2-FBXL19 purifications and matched empty vector (EV) controls. We limited analysis of our AP-MS data to proteins that were uniquely identified in the FBXL19 purifications (i.e. not the EV control). We have included a column highlighting the proteins that were identified in this screen and their associated emPAI scores in Supplementary file 1. Importantly, Mediator components feature heavily in this table, which is what prompted us to examine CDK-Mediator as a possible interaction of functional relevance. We have yet to validate whether other proteins in this table are bona fide interactors and, therefore, their relationship with FBXL19 and its function is not known.
> 2\) In Figure 3, the authors demonstrated that FBXL19 was able to recruit CDK-Mediator complex, such as CDK8 and MED12, to artificially designed chromatin regions. What about CXXC-domain or F-box deletion mutants in this assay?
In these experiments we purposely used a version of FBXL19 in which the CxxC domain has a single substitution mutation (K49A) that prevents CpG island binding. We designed the experiment in this way to prevent the TetR-fusion protein from binding to CpG islands throughout the genome. This allowed us to focus our analysis on the artificial nucleation site. Although we have not tested a version of FBXL19 with its CxxC domain deleted, we believe that it would function in a very similar way to the K49A mutant as both proteins are deficient in CpG island binding and we have shown that ΔCxxC-FBXL19 retains its interaction with CDK-Mediator (Figure 2---figure supplement 1E).
In all of our artificial tethering experiments we generate clonal stable cell lines expressing the TetR-fusion proteins to ensure uniform expression within lines and comparable expression across test lines. Despite exhaustive efforts, we have been unable to generate stable cell lines expressing FBXL19 lacking the F-box. We are unsure why this is the case but speculate that FBXL19 without the F-box may be unstable or lead to a dominant negative influence that affects cell growth (negative selection). Therefore, we have not been able to examine how the F-box deletion behaves in our tethering experiments. Given that ΔF-box-FBXL19 does not interact with CDK-Mediator in transient overexpression IP experiments (Figure 2---figure supplement 1E), we assume that CDK8 and MED12 would not be recruited to chromatin by TetR-ΔF-box-FBXL19. However, we have been unable to directly test this possibility.
> 3\) In Figure 4B, it is not very clear which band(s) are exactly indicated as full-length FBXL19 and which one(s) are CXXC deletion? Why are there double bands? Did the author use T7 antibody to detect the endogenously introduced protein?
We generated the T7 knock-in FBXL19 ES cell line (Figure 2---figure supplement 1B, C) in order to detect FBXL19 by Western blot. We observe 'double bands' for FBXL19 and speculate that this may be due to post-translational modification. The closely related KDM2A and KDM2B proteins are also extensively post-translationally modified leading to doublets when examined by Western blot. Following tamoxifen treatment of *Fbxl19^CxxCfl/fl^* cells to remove the CxxC domain, we observe a reduction in mobility for these double bands (with the top band shifting to the previous position of the bottom band). We have now clearly indicated which bands represent WT and ΔCxxC FBXL19 in Figure 4B and have described this in the figure legend.
> 4\) In Figure 4C, what proportions of each group of CDK8 binding sites overlap with FBXL19? In theory, the author expects to see that CDK8 sites showing binding intensity changes upon tamoxifen treatment would tend to overlap more with FBXL19.
The overlap of each group of CDK8 peaks with FBXL19 peaks is shown in Figure 4---figure supplement 1H. While roughly 41% of all CDK8 peaks overlap with FBXL19 peaks, the overlap of down-regulated CDK8 peaks is about 66%. This is highlighted in the text in subsection "FBXL19 is required for appropriate CDK8 occupancy at a subset of CpG island-associated promoters". On the other hand, we observed that only 23% of up-regulated CDK8 peaks overlap with FBXL19 peaks.
> 5\) In Figure 4---figure supplement 1C, please use a Venn Diagram to show directly the number of peaks of CDK8, FBXI19 and NMI overlapping with each other. This would be more straightforward.
We chose to represent CDK8 enrichment at FBXL19 peaks as a heatmap in order to circumvent the limitation of peak-calling. However, as suggested by the reviewer, we have now also included a Venn diagram that shows that 89.4% of FBXL19 peaks overlap with CDK8 peaks and NMIs (Figure 4---figure supplement 1D) and mentioned this in the text (subsection "FBXL19 is required for appropriate CDK8 occupancy at a subset of CpG island-associated promoters").
> 6 In Figure 5, please perform the same GSEA or functional annotation analysis on genes that are associated with unchanged CDK8 binding sites upon FBXL19 CXXC-domain deletion.
We have now included the GO analysis for genes associated with unchanged CDK8 binding in Figure 5---figure supplement 1. This revealed a broad range of terms associated with basic molecular processes in line with Mediator being implicated as a key regulator of transcription. We now highlight this observation in the text in subsection "FBXL19 targets CDK8 to promoters of silent developmental genes in ES cells".
> 7\) In Figure 6B, what is the result for genes that are associated with increased CDK8 binding signals in FBXL19 CXXC-domain deletion mutant upon RA-induced differentiation?
We have compared the expression of genes associated with an increase in CDK8 binding in Figure 6---figure supplement 1E. While we observe no overall difference in the expression of these genes in ES cells, there is a slight increase upon RA-induced differentiation (p-value 0.04). This is consistent with Mediator playing a role in gene transcription.
> 8\) In Figure 6C, even though the authors claimed that those upregulated genes (889) in FBXL19 CXXC-domain deletion mutant upon RA treatment were not involved in developmental processes, it is still interesting to find that significantly more genes were activated upon CXXC-domain deletion. What explanation can the authors provide for this finding?
We agree with the reviewer that a significant number of genes were more activated in the *Fbxl19^ΔCxxC^* cells compared to wild type cells upon RA-induced differentiation and that this is potentially interesting. We have yet to find a compelling molecular explanation to link FBXL19 directly to these effects on gene expression. It remains possible that these gene expression changes are due to secondary transcriptional defects that manifest when cells attempt to execute a new expression programme in the absence of normal activation of silent, lineage commitment-associated genes when FBXL19 is not functional, or that FBXL19 plays other, as yet unidentified, roles in inhibiting gene expression. We have now added a sentence drawing attention to these points in the revised manuscript in subsection "Removing the CpG island-binding domain of FBXL19 results in a failure to induce developmental genes during ES cell differentiation".
> 9\) In Figure 7, the authors claim that FBXL19 relies on CDK-mediator complex to activate the specific set of developmental genes. Is it possible to test this hypothesis in the FBXL19 CXXC-deletion system they established in Figure 6? In wild-type ESC, depletion of MED13 will have similar effects as FBXL19 CXXC deletion, whereas in FBXL19 mutant, the effects would be much alleviated?
One could test whether inducible MED13/13L deletion in the *Fbxl19^CxxCfl/fl^* background would not lead to any further effect on gene activation. However, this would require a significant amount of time to generate and characterise a new *Med13^fl/fl^, Med13l^fl/fl^*, and *Fbxl19^CxxCfl/fl^*cell line. While this is an interesting experiment, we believe that the robust and extensive series of observations in Figure 6 and Figure 7 more than adequately support our conclusion that FBXL19 target genes rely on CDK-Mediator for activation during differentiation.
> 10\) In Figure 8, why did heterozygous deletion of FBXL19 CXXC-domain show even better developmental status than the wild type?
We have not observed any significant difference between WT and heterozygous mutant embryos. It is common to have some stage variations until around 12 dpc, even within embryos of the same litter. Therefore, we often find small differences in size and developmental status among embryos regardless of genotypes. Both the WT and heterozygous mutant embryos presented in Figure 8 appear healthy with normal development for this stage. On the other hand, the defects observed in the homozygous *Fbxl19^ΔCxxC^* embryos cannot be explained by such stage variations.
> 11\) The authors demonstrated that the CXXC-domain mediates the binding of FBXL19 at NMIs, where F-Box mediates its interaction with the CDK-Mediator complex. What about CDK8 chromatin binding or gene expression patterns upon F-Box deletion of FBXL19? Will the authors see the same results as what they found in CXXC-domain deletion mutant?
This is an interesting experiment and we hypothesize that disrupting the interaction between CDK-Mediator and FBXL19 via deleting the F-box domain would yield similar results to removing the CxxC domain. However, as described above in response to reviewer point 2, despite exhaustive efforts we have been unable to generate cell lines stably expressing FBXL19 with a deletion of the F-box, precluding us from addressing this point. It will be interesting in future work to see if we can engineer a cell line where we are able to remove the F-box in an inducible manner and examine the effects on CDK8 binding and induction of gene expression.
[^1]: Agilent Technologies, Waldbronn, Germany.
[^2]: These authors contributed equally to this work.
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Q:
Use bash function when executing a command from java
I have written a bash function in my .bashrc which is responsible for updating my java jar file and restarting the application with the new jar, as an auto-updating mechanism.
I am trying to use the following java snippet to execute my function from my java code:
Runtime.getRuntime().exec(new String[] { "/bin/bash", "-c", "update-logbot" });
This returns an exit code of 127, indicating that it cannot find the function.
How would I accomplish executing this bash function from the java application?
A:
If my understanding is right you already have a bash script to close java/jar program and delete it and download new new jar/java program and execute it.
However you would like to achieve the same using Java program.
to achieve this you need a bash script to download the new program into same folder as the old java program with jar name change to next iterative version of the program.
invoke the script using below in the program
proc = Runtime.getRuntime().exec("sh /home/***/Documents/script.sh");
After confirmation of jar/java program copy operation being successful invoke another script to start the new java/app (provide a delayed start of new program in such a way that the new program won't start until older exits)
in the new java program check for existence of older version of program and execute a script to delete or delete it through the java program
you may also require user privilege imitation (user impersonation by the invoked script)to achieve this functionality
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DVD DIGEST | LIVE UPDATE Issue 4
What's new at DVD DIGEST ?
Thursday, November 25th, 1999
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TOP NEWS SUMMARY :
1. Old domains, new domains ...
- some changes abound ...
2. PowerDVD vs WinDVD
- the war heats up ...
3. What's new at Digital Video Downloads ?
- Cinemaster 99, PowerDVD 2.5 and WinDVD 2000 full reviews
- WinDVD 2000 download links
4. A simple thank-you
- a thank-you message for all those that
joined this list
*******************************************************
1. Old domains, new domains ...
As you probably know, our old redirection address : http://getdvd.cjb.net was deleted today =(
So for the next few days, please use the new one : http://softdvd.cjb.net
We've already made the changes on all my pages, so if you bookmarked my other redir addresses, it's okay.
We'll be moving to a new domain soon : http://www.dvd-digest.com
with some suitable sub-domain names like : downloads.dvd-digest.com for our download site ...
We'll keep you informed ...
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2. PowerDVD vs WinDVD
Yes!! The software DVD market is finally heating up, with competing players, PowerDVD and WinDVD going out head to head to out-do each other, in terms of features and quality.
PowerDVD 2.5 and the newly released WinDVD 2000 both are very competent players - software DVD player have finally matured enough to be complete solutions.
DVD Digest has written full reviews for both, as well as for the other main player, Cinemaster 99, on our download site : http://softdvd.cjb.net
You can read them here :
Cinemaster 99 Review - http://dvd.zo8.com/downloads/qirw.html
PowerDVD Review - http://dvd.zo8.com/downloads/pdvdrw.html
WinDVD Review - http://dvd.zo8.com/downloads/wdvdrw.html
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3. What's new at Digital Video Downloads ?
- Cinemaster 99, PowerDVD 2.5 and WinDVD 2000 full reviews
as mentioned above, the reviews are up, with full set of screen-shots and goes over every bit of the players. Links in above section.
- WinDVD 2000 download links
DVD Digest was officially told off by InterVideo for publishing links for their WinDVD player, so we have removed them. But we do still have links to links of WinDVD (hope that's okay), and one of the links is this excellent co-production by DVD Digest and Freeloader :
WinDVD Download Zone - http://windvdzone.cjb.net
They have all your WinDVD download needs, even the new WinDVD 2000 player !! So have a look there to get the best info, and DVD Digest WILL be featuring news about upcoming downloads on our news pages as well as on the news pages of WinDVD Download Zone.
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4. A simple thank-you
Just a note to thank all those people, including you, who joined the DVD Digest LiveUpdate program. We've spent quite a bit of time developing this site, and making it what it is today, and really do appreciate your continued support.
We hoped you enjoyed this LiveUpdate newsletter.
Thankyou
DVDGuy - DVD Digest Owner and Webmaster
======END OF LIVEUPDATE NEWSLETTER======
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Potter Brogan Wade Potter was born July 21, 2010, to Jason and Amanda Potter of Shallowater, Texas, at Covenant Lakeside in Lubbock. He weighed 8 pounds, 7 ounces. Grandparents are Don and Linda Essary of Floyd; and Tom and Claryce Gainer of Levelland.
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Many thousands of words have been written and many more will now be written by the liberal intelligentsia on trying to prove that the 45th President of the United States of America is a fascist. Among the first to leap out of the starting blocks after the triumph of Trump was the hyper-trendy historian Simon Schama who tweeted at dawn on Wednesday to say: 'This calamity for democracy will of course hearten fascists all over the world'.
The trouble is: Trump is not a fascist, let alone a nazi. Even calling him Donald Duck would be more accurate than calling him Donald Duce. The main reason that Trump is, in fact, not a fascist is the most embarrassing of all (at least for the left that is): Trump is not left-wing. For when left-wingers call hate figures 'fascists' nearly always they themselves have much more in common with fascism than their hate figures do. If this were not so scary – similar to branding a woman a 'witch' in 16th Century – it would be hilarious.
To take a conveniently forgotten example: the 1939 alliance between fascism (Germany) and communism (Russia), against capitalism (Britain and France) was far more natural than the subsequent alliance between capitalism (America and Britain) and communism (Russia) against fascism (Germany). But democracy was not the only enemy the fascist and communist dictatorships had in common.
Few people even seem to know this any more, but Benito Mussolini, who invented fascism in 1919 after the First World War, was a revolutionary socialist (what communists used to be called). He was therefore an international socialist who believed in the abolition of nations and world revolution. But the First World War forced him (and many other socialists) to recognise a fundamental point about human nature: people are more loyal to their country than their class. The key event was the decision, in 1914 by the French socialists, to support France against Germany in the war and then by the German socialists to support Germany against France. This convinced Mussolini – who was editor of his party’s daily newspaper Avanti! – that the only path to socialist revolution was by means of national not international socialism. The Italian Socialist Party, which unlike its French and German counterparts supported neutrality, did not agree and expelled him. So he launched his own pro-war socialist newspaper, Il Popolo d’Italia, which was part-financed by the French Socialist party. And then, once the war was over, he founded fascism as an alternative left-wing revolutionary movement.
Fascism replaced the class war between the proletariat and the bourgeoisie with a class war between producers (of whatever class) and parasites (of whatever class). It did not aim to abolish private ownership of the means of production but instead establish the corporate state – the so-called 'Third Way' between communism and capitalism – with each sector of the economy organised in corporations run by the state. Someone like Marine Le Pen in France who is big on the big state and lots of welfare (at least for the French) does have fascism in her DNA. But just what Trump has in common with any of this is beyond me.
After all, it was Hillary Clinton’s husband, Bill, and his soul-mate, Tony Blair, who most recently dusted down the very same phrase – the 'Third Way' - to define their vision of public-private partnerships as the way to economic salvation. Unlike Hillary, the Donald would definitely run a mile from any 'Third Way' economic solution approved by Bill, let alone the corporate state alla Benito. He sells himself as anti-state. He spits out the word 'Washington' as if it is the Devil. Hillary is the one who is pro-state.
Fascism placed the state on a pedestal and believed in government by dictatorship - not by democracy. But not even the Guardian – surely – believes that Trump aims to install a dictatorship, does it? Indeed, right now, it is the liberal intelligentsia who seem much more prone than Trump to the siren calls of dictatorship as they question democracy itself if it gives power to people like him.
Fascism aimed for total control of the citizen, especially of their mind. The closest America (and the rest of us) gets to this today is political correctness which Hillary supports and the Donald despises. Fascism was nationalistic which usually, though not necessarily, goes hand-in-hand with aggressive expansionism abroad. And yes, fascism was aggressively expansionist. But the Donald is much less nationalistic than Hillary. He is the isolationist; she the interventionist.
Ah, they bleat, but he’s a nationalist at home. Come again? What they mean here is that he’s a racist, and that means that he’s a fascist. I shall get lynched for pointing this out but another thing that people seem not to know about fascism (at least Italian fascism) is that it was no more, nor less, racist than any other political creed in the 1920s and 1930s.
The big exception was its German off-spring: National Socialism. The Nazis were most definitely and always anti-Semitic. Italian fascism was not. Mussolini’s main mistress until the early 1930s, Margherita Sarfatti, for example, was Jewish and the majority of Italy’s 50,000 Jews were fascists. Italian fascism became anti-Semitic – and on religious not racial grounds - only after Mussolini’s fatal alliance with Hitler in the late 1930s.
But anyway 'The Donald' has said nasty stuff about Mexicans and Muslims and here he parts company with the Duce for a different reason: Mussolini would have been dead keen on Mexicans on the grounds that they were Latinos. And he did not mind Muslims much either per se - especially when they opposed British and French colonial power.
George Orwell, a socialist who hated communism, drew an important distinction between patriotism and nationalism. A patriot is someone who wants to defends his country, its culture and way of life - wrote Orwell - whereas a nationalist is someone who wants to impose his country, culture and way of life. Patriotism is defensive, nationalism offensive. Trump is a patriot, I reckon, not a nationalist. And the Donald ain’t no Duce.
Nicholas Farrell is the author of 'Mussolini: A New Life'
After the American people have voted, what next for the US and the rest of the world? Join panellists including Sir Christopher Meyer, KCMG, former British ambassador to the US, for a discussion chaired by Andrew Neil on 30 November at RIBA, London. Tickets include a drinks reception. In association with Seven Investment Management. Book now.
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Caustic Comic!
Furious over being killed off as showbiz rivals get the last laugh!
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1907 Marquette Golden Avalanche football team
The 1907 Marquette Golden Avalanche football team was an American football team that represented Marquette University as an independent during the 1907 college football season. In its first and only season under head coach Cody Clark, the team compiled a 6–0 record.
Schedule
References
Marquette
Category:Marquette Golden Avalanche football seasons
Category:College football undefeated seasons
Marquette Golden Avalanche football
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Indie Web
We’re in danger of losing what’s made the Internet the most important medium in history – a decentralized platform where the people at the edges of the networks – that would be you and me – don’t need permission to communicate, create and innovate.
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Interested in learning more about how our
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Cellartis Human Pluripotent Stem Cell Services
Stem cell expertise to assist any stage of research
With Cellartis services, you can focus on your areas of expertise and leave the challenges to us. Since our scientists have over 15 years' experience with human pluripotent stem cell culture and differentiation, you can be confident that we will deliver custom services to expand and enhance the stem cell capabilities and success of your research team. Expect a close, worry-free collaboration with straightforward and prompt communication about timelines and deliverables.
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Manny’s Head is In The Game
For the second day in a row we have articles from all four major pro franchise in New England. The Red Sox win again, the Patriots welcome back Richard Seymour, the Bruins sign another AARP candidate, and the Celtics attempt to figure out what to do next.
The Red Sox extended their winning streak to seven games and their lead in the AL East to 4.5 games with an 8-5 win at Fenway over the Royals. Jeff Horrigan notes that for the last couple nights Manny Ramirez has had his head in the right place. Last night it was in the wrong place as the slugger collided with shortstop Edgar Renteria and had to leave the game. Jeff Goldberg looks at the game, which featured two more Manny moments. Nick Cafardo focuses mostly on starter Wade Miller in his game story, while Steven Krasner notes that the Red Sox got some heads up play on the bases that also helped that attain the win. David Borges calls last night’s game “unsightly”, and in the next sentence uses the word “entertaining” to describe it. Lenny Megliola says that a collision between two of their stars wasn’t enough to stop the Red Sox last night.
This afternoon will mark the return of Matt Clement to the mound for the first time since taking a Carl Crawford line drive off of his head. Jackie MacMullan writes that a scare like that can really put things in proper perspective, as Clement can’t help but think of his three year old son, who saw what happened on TV and was crying for him to get up. Tony Massarotti has Clement saying that he will not be fearful out there on the mound this afternoon. Alex Speier says that no one can doubt Clement’s toughness. Jon Couture notes the Clement is eager to get back out on the mound and get to work, and that the only concerns he has are physical and not mental, as he wonders about his stamina after having the time off. Couture has a couple other items in that article, including a look at the situations of Keith Foulke and Curt Schilling, as well as Manny Ramirez’s production.
Sean McAdam says that just like last year, the Red Sox appear to be using August as the time to turn things on and get down to business. Kelsie Smith looks at aftereffects of last night’s collision for Manny Ramirez. Massarotti reports that Edgar Renteria is a little sore himself after the incident. Horrigan has a brief bit on how Curt Schilling is being prepared slowly to return to the rotation. Jim Donaldson says that the Royals are a team only a cheap owner could love. Smith also has a look at former Sox prospect Chip Ambres, who was able to make his Fenway Part debut after all, only for the Royals.
Borges’ notebook looks at Roberto Petagine getting his Big League chance with Olerud going on the disabled list. That is also the lead topic in Horrigan’s notebook, which also looks at Wade Miller and Keith Foulke. Cafardo’s notebook also leads with Petagrine, and even has a Rich Garces mention. Goldberg’s notebook looks at Matt Clement returning to the hill this afternoon. Krasner’s notebook looks at Manny’s condition after the collision last night and has a couple other injury notes.
Richard Seymour was back on the field yesterday, and glad to be there. Jerome Solomon in the Globe looks at Seymour getting back to where he belongs. Karen Guregian reports that Seymour is ok with his situation after finding “common ground” with the Patriots for this season. Alan Greenberg says that it never crossed Seymour’s mind to extend his holdout merely to sty away from the grind of training camp for a little longer. Chris Kennedy in fact notes that Seymour is happy to be grinding it out with his teammates in camp. Michael Parente and Christopher Price also report on the first day of camp for #93.
Tom E Curran tells us what we have learned to this point in training camp. Mark Blaudschun, who might around the Patriots for more than just a summer vacation assignment this season, reports on the fundamentals that the Patriots are working on, something he says that Bill Belichick feels a little frustrated about. Guregian has a short bit on Tom Brady getting his birthday off, and another on Christian Fauria fighting for his spot on the team, and his thoughts on the retirement of his college teammate, Ted Johnson.
Parente’s notebook reports that Bill Belichick isn’t happy with the fundamentals of many of his players to this point in camp. The Globe notebook reports on Brady’s off day, Guregian’s notebook says Belichick didn’t seem overly pleased with the results of the Tuesday night practice in the stadium. Kennedy’s notebook says that Rosevelt Colvin is preparing for a breakout season with the Patriots. Curran’s notebook reports on the return of Seymour.
Kevin Paul Dupont looks at the Bruins signing 37-year-old defenseman Brian Leetch to a one year contract. Steve Conroy looks at the Bruins signing Leetch while losing out on Mike Modano. Mick Colageo says that the Leetch signing is not another Paul Coffey deal. He says Leetch still has game. Stephen Harris writes that while the Bruins have done well thus far, but that they have plenty of work still to do.
Steve Bulpett looks at the Celtics situation as far as what they have left to spend and what the trade exception is really worth. He says they’re still trying to ship out Mark Blount, and are looking for point guard help. Bill Simmons’ ESPN blog also has a breakout of the trade, with some Celtics information in there, such as why the Celtics got involved in the first place. Gabe Kahn looks at what the Celtics actually got in the Antoine Walker sign-and-trade, and Michael Muldoon takes a look back at the deal as well.
The Yankees continue to scuffle along and the Mets blow a game for Pedro. Those stories, plus a couple articles on Rangers legend Leetch signing with the Bruins are all part of the New York Sports News this morning.
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Earlier today, Ed went over the current state of the pending “nuclear battle” concerning the confirmation of Judge Gorsuch to the Supreme Court. No matter how you look at it, the pickings are slimmer than I’d previously hoped in terms of finding enough Democrats to reach cloture. In Ed’s estimation it looks like we’re going to need Mitch McConnell to pull the trigger on Friday. But that leaves us with one uncomfortable question on the table… is the gun really loaded?
Last week I wrote about some of the back room maneuvering going on, much of it centered on John McCain. While I still think the era of “gang warfare” in the Senate may be pretty much over, I continue to hear rumblings about McCain hoping to strike some sort of a deal. It’s true that he, along with some other veterans of the Gang of 14 and more moderate members, have said they will support the option if they have to, but they wouldn’t have to if they cut some sort of a deal on their own. After all, it only takes three Republicans to scotch the entire thing. The Daily Caller looked at this looming train wreck a week ago and saw some possibilities, including a defection by Susan Collins for starters.
The most likely candidates in this regard are GOP Sens. Susan Collins, John McCain, and Lindsay Graham. All three were members of the “Gang of 14,” a bipartisan group of senators that reached an accord on confirmed Bush-era nominees without invoking the nuclear option in 2005. Other Republicans with something of a moderate streak, like Sens. Lisa Murkowski and Jeff Flake, might also oppose such a dramatic change. Collins is the only Republican senator to express misgivings about the nuclear option thus far. “Senator Collins is not a proponent of changing the rules of the Senate,” a Collins representative told The Daily Caller News Foundation. “She hopes that common sense will prevail and that we will have a normal process for considering Judge Gorsuch’s nomination.”
If you look at the senators on that list it’s not all that crazy to think that you could find three who would kill the nuclear option. But they’d have to get something in return. What do the Democrats have to offer? Well, for one thing there was the previously scoffed at possibility of getting the minority party to find 8 votes to put Gorsuch over the top in exchange for a promise that the nuclear option won’t be invoked in the future and they would retain the right to filibuster the next nominee if they were “too extreme.” In that case, McCain would be looking at causing some serious headaches for Chuck Schumer because he’d effectively need a Gang of Eleven… three Republicans and eight Democrats willing to defy the Minority Leader. Impossible? Definitely unlikely, but after 2016 I’m not sure if I’ll tag anything as totally impossible now.
The worst possibility is that three Republican Senators come forward by Friday and say they can’t bring themselves to pull the trigger but they get nothing in return for it. That basically hands the game, set and match to Chuck Schumer and Trump is left with a split court and no option to fill it unless he wants to go completely insane and let Garland come up for a vote. For what it’s worth, I still think we find the 51 votes and Gorsuch is confirmed this week (unless a few Democrats ride to the rescue quickly and we achieve cloture) but even if a deal is made, this is going to keep coming up every time there’s an opening on the court.
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The invention relates to a device for providing a breathing gas, in particular to a device for conditioning a breathing gas, for managing the weight of a breathing creature, in particular for stimulating weight reduction. The invention further relates to a method and to a use of a device for conditioning a breathing gas and for providing said breathing gas to a breathing creature, for managing the weight of a breathing creature, in particular for stimulating weight reduction of the breathing creature.
In developed countries around the world, there is a tremendous interest in personal fitness, wellness and para medication. At the same time there is a disturbing trend that people, including adults and children are becoming overweight. By overweight, it is meant that the subject has exceeded the acceptable weight range and percent body fat generally considered as healthy determined by factors including, but not necessarily limited to age, height, sex, and body type.
Overweight produces a wide range of health concerns including sleep apnoea, orthopaedic complications, arterial sclerosis, diabetes, heart disease and also social and psychological problems etc. All these undesirable conditions contribute in development of an unsatisfactory quality of life and in some cases premature death.
Therefore, many people want to maintain a specific weight or even lose weight to maintain or enhance their physical condition. To lose weight the body needs to burn more energy than is provided by the food intake. Known diet methods include restriction of amounts and kinds of food, exercises and use of diet drugs to reduce or maintain body weight.
However, managing weight via known diet methods takes a long period of time, even when combined with exercises or diet drugs. Many people are not capable of maintaining a reduced food intake and/or an increased exercise level over a long period of time and therefore do not achieve the amount of weight loss aimed for or even gain weight in spite of there efforts. Also, even when the diet results in a loss of weight, for a variety of reasons, most people find it very difficult to maintain significant weight reduction over time.
Therefore only a few people are able to achieve a significant reduction of weight, and even less are able to maintain this condition.
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I'm quite fond of aerialesque's Sakura's Wish:http://www.animemusicvideos.org/video/129575Not the most original video out there, perhaps, but a very emotional one, and it's hard for Naruto videos to make me feel anything. Only Whipser of the Beast has done that before, so I think Sakura's Wish is definitely worth a look.
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Introduction
============
The choice of the active acylating species used to form a peptide bond is crucial in peptide synthesis.\[[@b1]--[@b4]\] Highly reactive moieties, such as acid halides, are suitable to acylate very poor nucleophilic amines. However, they are often not the best choice for the activation of the *N^α^-*alkoxycarbonyl derivatives of amino acids \[mostly fluorenylmethoxycarbonyl (Fmoc), *tert-*butoxycarbonyl (Boc), and allyloxycarbonyl (Alloc)\] because of their marked electrophilic character, which derives in a considerable loss of configuration.\[[@b5]--[@b9]\] In contrast to acid chlorides, the corresponding active esters offer a more balanced range of reactivity, thus, circumventing most of the side reactions caused by an excessive activation.\[[@b1], [@b2], [@b9], [@b10]\] From the extensive range of these esters, *N-*hydroxylamine esters, preferably prepared in situ by the carbodiimide approach using the corresponding *N*-hydroxylamines as additives, are possibly the most widely used.\[[@b11]--[@b13]\] Among these, 1-hydroxybenzotriazole (HOBt, **1**) and its derivatives, including 1-hydroxy-7-azabenzotriazole (HOAt, **2**), have prevailed over the other carbodiimide additives during recent decades as a result of their great acylation potency (Figure [1](#fig01){ref-type="fig"}).\[[@b12], [@b14], [@b15]\] However, a few years ago, the explosive nature of benzotriazoles prompted the reevaluation of the strongly acidic oxime, ethyl 2-cyano-2-(hydroxyimino)acetate (Oxyma, **3**) as a potential replacement, which represented a hallmark in the field.\[[@b16], [@b17]\]
{#fig01}
In contrast to standard peptide-bond formation, which occurs in common organic solvents, the acylation of peptides or proteins for bioconjugation purposes typically takes place in aqueous pH-buffered environments. Thus, stability rather than reactivity is the main desired feature of active esters generated in such a polar medium. In a similar manner, preformed amino acid active esters need to be stable enough for shelf storage of up to several weeks. Consequently, *N*-hydroxysuccinimide esters (HOSu, **4**) have found broad application in these scenarios as less reactive but more suitable alternatives to benzotriazoles (Figure [1](#fig01){ref-type="fig"}).\[[@b30]--[@b31]\] For example, HOSu derivatives **4** have been used for the preparation of alkoxycarbonyl amino acids, thereby avoiding the undesired formation of oligomers.\[[@b20]\] However, the limited reactivity of HOSu active species continues to be a decisive drawback. In order to pursue an optimal balance of reactivity for stable active esters, we focused our attention on a family of promising *N-*alkyl-cyanoacetamido oximes (**5**--**8**, Figure [2](#fig02){ref-type="fig"}). In a recent publication, Fmoc-carbonates derived from *N*-hydroxy-2-morpholino-2-oxoacetimidoyl cyanide (MorOx, **5**), *N*-hydroxy-2-oxo-2-(piperidin-1-yl) acetimidoyl cyanide (PipOx, **6**), 2-amino-*N*-hydroxy-2-oxoacetimidoyl cyanide (AmOx, **7**), and 2-(ethylamino)-*N*-hydroxy-2-oxoacetimidoyl cyanide *(N*-Oxyma, **8**) presented desirable reactivities with superior performances to Fmoc-OSu (Figure [2](#fig02){ref-type="fig"}).\[[@b21]\]
{#fig02}
Following previous research on Fmoc-oxime carbonates, the present study aimed at performing a screen of *N-*alkyl-cyanoacetamido oximes **5**--**8** as additives to carbodiimides in replacement of HOSu (**4**). In addition to the abovementioned set of cyanoacetamides, 2-(*N,N*-dimethylamino)-*N*-hydroxy-2-oxoacetimidoyl cyanide (DmOx, **9**) was also evaluated. This molecule differs from AmOx (**7**) in its capacity to act as a hydrogen donor and in its nonplanar structure (Figure [2](#fig02){ref-type="fig"}).\[[@b22]\] While oximes **5**--**9** have been broadly applied in organometallic chemistry, biomedicine and agrochemistry, to our knowledge, the only reports of an additive to carbodiimides presenting an *N*-alkyl-cyanoacetamido oxime scaffold were described in the 1970s, excluding the recent reevaluation of Oxyma (**3**).\[[@b17], [@b22]--[@b25]\] At the beginning of that decade, Itoh determined the acidity of Oxyma (**3**, p*K*~a~ 4.6) and AmOx (**7**, p*K*~a~ 5.2), and evaluated the racemization suppression of the former in a dipeptide model.\[[@b22]\] A few years later, Izdebski further examined the capacity of Oxyma (**3**) and AmOx (**7**), together with other less suitable oximes, to decrease epimerization in *N*,*N′*-dicyclohexylcarbodiimide (DCC)-mediated couplings using an optimized protocol.\[[@b24], [@b25]\] Nonetheless, given the preliminary character of these studies, they did not provide a conclusive overview of the performance of these oximes, although a lower reactivity of acetamido analogue **7** was envisaged.\[[@b22], [@b25]\] Here, we revised the capacity of AmOx (**7**) together with *N*-alkyl-cyanoacetamido oximes **5**--**9** to retain the optical configuration of the activated amino acid and their coupling efficiency, while comparing their performance with that of HOSu (**4**).
Results and Discussion
======================
Synthetic approach
------------------
The pool of *N*-alkyl-cyanoacetamido oximes selected for screening as additives (**5**--**9**) included several linear and cyclic *N*-alkyl moieties, which involve diverse bulkiness and the possibility to allow hydrogen-bonding interactions. In comparison with the ester functionality within Oxyma (**3**), the carboxamido group displays restricted conformational rotation around the amide bond, as shown earlier by 1H NMR studies.\[[@b22]\], [@b23b], [@b23f] This limitation could have some impact on the reactivity of the corresponding esters.
Regarding the syntheses of the proposed oximes, **5**--**8** were already reported in the evaluation of the derived Fmoc-carbonates.\[[@b21]\] Following the same methodology, DmOx (**9**) was synthesized in high yield from ethyl cyanoacetate (**10**) in only two steps by means of an amidation/nitrosation sequence (Scheme [1](#sch01){ref-type="scheme"}).\[[@b21]\] In the first step of this synthetic approach, ethyl cyanoacetate (**10**) was readily transformed into *N,N*-dimethylcyanoacetamide (**11**) after reaction with dimethylamine at 70 °C. Next, the subsequent Meyer nitrosation of intermediate **11** in a methanolic solution of sodium nitrite afforded desired oxime **9** in 76 % overall yield.\[[@b26]\] Although this reaction sequence leading to DmOx (**9**) has already been described in the literature, our optimized methodology leads to a significant improvement in yield and purity compared with former strategies, which describe an initial amidation in aqueous medium or do not generate methyl nitrite in situ.\[[@b23]\] Like cyanoacetamido oximes **5**--**8**, the high water solubility of DmOx (**9**) had a positive impact on the final aqueous work-up.\[[@b21]\]
{#sch01}
Control of epimerization
------------------------
Retention of the optical configuration during amino acid coupling is central to peptide synthesis, especially when manufacturing active principle ingredients (APIs).\[[@b9], [@b27]\] The undesired loss of chirality at C~α~ is dramatic in more sensitive building blocks, such as glycopeptides.\[[@b28]\] In order to study the impact of epimerization when using *N*-alkyl-cyanoacetamido oximes **5**--**9** in solution phase, we selected peptides **12**--**14** as test models, which are a reliable platform to study the loss of configuration during stepwise and \[2+1\] fragment couplings (Figure [3](#fig03){ref-type="fig"}).\[[@b29]\] After *N*,*N′*-diisopropylcarbodiimide (DIC)-mediated coupling of equimolar amounts of acid and amine and aqueous work-up, the impact of epimerization on peptides **12**--**14** was determined by reversed-phase HPLC, using optimized conditions that achieve clear separation of the two epimers. Simultaneously, a direct comparison with HOSu (**4**) and Oxyma (**3**), the latter as the most efficient additive, was established in every model.
{#fig03}
The performances of additives **3**--**9** in a stepwise coupling was examined during the coupling of *N*-carboxybenzyl (Cbz)-protected Z-[l]{.smallcaps}-phenylglycine (Z-Phg-OH) onto [l]{.smallcaps}-prolinamide (H-Pro-NH~2~), resulting in dipeptide **12** (Table [1](#tbl1){ref-type="table"}).[@b29] The α-phenyl moiety in Phg ensured a high sensitivity towards epimerization, because of the pronounced stability of the resulting anion. In this model, HOSu (Entry 2, Table [1](#tbl1){ref-type="table"}) rendered the lowest yield of dipeptide and an unacceptable loss of configuration. The percentage of epimerization achieved (32.7 %) was even more detrimental, taking into account that the absence of preactivation in a peptide coupling usually attenuates epimerization. Remarkably, all *N*-alkyl-cyanoacetamido oximes **5**--**9** surpassed HOSu (**4**) in their capacity to maintain the desired chirality of the test dipeptide (cf. Entries 2 and 3--7, Table [1](#tbl1){ref-type="table"}). In particular, PipOx (**6**) was the least efficient in reducing epimerization, but still afforded three times higher purity than HOSu (**4**) (cf. Entry 2 and 4, Table [1](#tbl1){ref-type="table"}). In comparison with MorOx (**5**), the presence of a proton-accepting oxygen in the six-membered ring caused a considerable increase in purity of the desired peptide (cf. Entry 3 and 4, Table [1](#tbl1){ref-type="table"}).\[[@b30]\] Noteworthy, AmOx (**7**) and *N*-Oxyma (**8**) showed similar configuration retentions to Oxyma (**3**), which afforded only 1.0 % of [dl]{.smallcaps} epimer, with a simultaneous improvement in yield (cf. Entry 1 and 5, 6, Table [1](#tbl1){ref-type="table"}).\[[@b17]\]
######
Yield and epimerization during the formation of Z-Phg-Pro-NH~2~ (12) using additives 3--9 (solution phase synthesis)[\[a\]](#tf1-1){ref-type="table-fn"}
Entry Coupling Reagent Yield \[%\] [dl]{.smallcaps} \[%\][\[b\]](#tf1-2){ref-type="table-fn"}
------- ----------------------- ------------------------------------------ ------------------------------------------------------------
1 DIC/Oxyma (**3**) 89.9[\[c\]](#tf1-3){ref-type="table-fn"} 1.0[\[c\]](#tf1-3){ref-type="table-fn"}
2 DIC/HOSu (**4**) 70.3 32.7
3 DIC/MorOx (**5**) 88.4 5.7
4 DIC/PipOx (**6**) 86.8 10.7
5 DIC/AmOx (**7**) 81.4 3.0
6 DIC/*N*-Oxyma (**8**) 92.1 3.8
7 DIC/DmOx (**9**) 93.4 8.3
Couplings were performed without pre-activation in DMF at RT.
The [ll]{.smallcaps} and [dl]{.smallcaps} epimers of this peptide model have been described in the literature.[@b29] Retention times (*t*~R~) for each epimer were identified after co-injection with a pure [ll]{.smallcaps} sample.
Results are extracted from Ref. \[[@b17]\].
Once the stepwise system was evaluated, the next step in the epimerization study of *N*-alkyl-cyanoacetamido oximes **5--9** corresponded to the \[2+1\] assembly of dipeptide Z-Phe-Val-OH onto H-Pro-NH~2~, affording tripeptide **13** (Table [2](#tbl2){ref-type="table"}).[@b29b] The activation of a dipeptide acid is a very interesting scenario to test the performance of an additive, since oxazolone formation is promoted as a result of the electron-donating effect of the *N*-aminoacyl substitution.\[[@b17], [@b30]\] As observed in Table [2](#tbl2){ref-type="table"}, the percentages of unwanted epimer were considerably higher than in the previous stepwise system. Following the trend observed in the synthesis of Z-Phg-Pro-NH~2~ (**12**), most of the cyanoacetamido oximes induced an approximately twofold higher retention of configuration than HOSu (**4**). Nonetheless, this \[2+1\] system produced moderate yields (66--84 %).
######
Yield and epimerization during the \[2+1\] formation of Z-Phe-Val-Pro-NH2 (13) using additives 3--9 (solution phase synthesis).[\[a\]](#tf2-1){ref-type="table-fn"}
Entry Coupling Reagent Yield \[%\] [ldl]{.smallcaps} \[%\][\[b\]](#tf2-2){ref-type="table-fn"}
------- ----------------------- ------------- -------------------------------------------------------------
1 DIC/Oxyma (**3**) 89.8 12.8
2 DIC/HOSu (**4**) 73.1 24.7
3 DIC/MorOx (**5**) 80.5 13.2
4 DIC/PipOx (**6**) 71.5 32.6
5 DIC/AmOx (**7**) 66.7 14.8
6 DIC/*N*-Oxyma (**8**) 83.6 18.4
7 DIC/DmOx (**9**) 79.5 17.0
Couplings were performed without pre-activation in DMF at RT.
The [lll]{.smallcaps} and [ldl]{.smallcaps} epimers of this tripeptide model have been described in the literature.[@b29b] Retention times (*t*~R~) for each epimer were identified after co-injection with a pure sample.
Concerning the relative performance of the *N*-alkyl-cyanoacetamido oxime series (**5**--**9**), PipOx (**6**) again showed the least efficient control of optical purity, providing an even higher percentage of [ldl]{.smallcaps} epimer than HOSu in this system (cf. Entry 2 and 4, Table [2](#tbl2){ref-type="table"}). In sharp contrast, its morpholino analogue **5** showed a similar level of performance to Oxyma (**3**), providing an almost threefold higher retention of chirality than PipOx (**6**) (cf. Entries 1 and 3, 4, Table [2](#tbl2){ref-type="table"}). Moreover, MorOx (**5**) was one of the most efficient oximes in terms of yield of target tripeptide **13**. With regard to AmOx (**7**), a remarkably low content of epimer was detected, although accompanied by one of the lowest yields in the oxime series (Entry 5, Table [2](#tbl2){ref-type="table"}). Finally, *N*-Oxyma (**8**) was again clearly less efficient than its parent Oxyma (**3**) at preventing the loss of chirality (Entry 6, Table [2](#tbl2){ref-type="table"}).
The last epimerization model used to evaluate cyanoacetamido oximes **5--9** also consisted of a \[2+1\] segment coupling, in this case rendering tripeptide Z-Gly-Phe-Pro-NH~2~ (**14**) (Table [3](#tbl3){ref-type="table"}).[@b29b] Although this system is undoubtedly less sensitive than the previous one (**13**), valuable data were gathered. Unlike the synthesis of Z-Phe-Val-Pro-NH~2~ (**13**), PipOx (**6**) was not only more efficient than HOSu in decreasing epimerization (cf. Entry 2 and 4, Table [3](#tbl3){ref-type="table"}), but also superseded the performance of morpholine derivative **5** (cf. Entry 3 and 4, Table [3](#tbl3){ref-type="table"}). Consistent with previous epimerization models, the performance of HOSu (**4**) was poorer than *N*-alkyl-cyanoacetamido oximes **5**--**9**, including the relative yields obtained (cf. Entry 2 and 3--7). Surprisingly, MorOx (**5**) afforded one of the highest obtained contents of [ldl]{.smallcaps} epimer, along with *N*-Oxyma (**8**), which offers threefold less pure crude products than Oxyma (**3**) (cf. Entries 1 and 3, 6, Table [3](#tbl3){ref-type="table"}). Finally, of the cyanoacetamido oximes tested in the stepwise and fragment couplings **12**--**14**, AmOx (**7**) regularly performed at a remarkable level, offering the closest percentages of epimer to those obtained with Oxyma (**3**). Thus, AmOX (**7**) stands out as one of the most promising derivatives to substitute HOSu (**4**) as an epimerization-suppressant additive.
######
Yield and epimerization during the \[2+1\] formation of Z-Gly-Phe-Pro-NH~2~ (14) using additives 3--9 (solution phase synthesis)[\[a\]](#tf3-1){ref-type="table-fn"}
Entry Coupling Reagent Yield \[%\] [ldl]{.smallcaps} \[%\]
------- ----------------------- ------------- -------------------------
1 DIC/Oxyma (**3**) 90.2 2.7
2 DIC/HOSu (**4**) 80.4 9.0
3 DIC/MorOx (**5**) 88.3 8.0
4 DIC/PipOx (**6**) 86.6 7.6
5 DIC/AmOx (**7**) 88.9 4.3
6 DIC/*N*-Oxyma (**8**) 87.6 8.3
7 DIC/DmOx (**9**) 87.9 5.4
Couplings were conducted without pre-activation in DMF at RT.
\[b\] The [lll]{.smallcaps} and [ldl]{.smallcaps} epimers of this tripeptide model have been described in the literature.[@b29b] Retention times (*t*~R~) for each epimer were identified after co-injection with a pure sample.
Coupling potency
----------------
A key step in the assessment of the quality of cyanoacetamido oximes **5**--**9** as additives to carbodiimides was the evaluation of their acylation potency in hindered couplings. To emphasize differences in the reactivity of the various active esters, peptide models containing demanding *N*-methyl or α,α-dialkyl amino acid junctions are often used.\[[@b17], [@b30]\] Among these, those featuring two or more consecutive α-aminoisobutyric acid (Aib) residues are particularly difficult to achieve, not only because of their considerable bulkiness, but also due to the stabilization of helical structures by the Thorpe--Ingold effect.\[[@b31]\] Hence, additives **3**--**9** were used in the solid-phase assembly of the Aib-enkephaline pentapeptide (**15**, Figure [4](#fig04){ref-type="fig"}).\[[@b17], [@b30], [@b32]\]
{#fig04}
The demanding conditions of this efficiency model (using short coupling times) were responsible for the very high percentage of des-Aib deletion tetrapeptide H-(Tyr-Aib-Phe-Leu-NH~2~), obtained with the various additives (**3**--**9**; Table [4](#tbl4){ref-type="table"}). Consistent with the trend observed in the epimerization experiments, the coupling performance of HOSu (**4**) was surpassed by all *N*-alkyl-cyanoacetamido oximes **5**--**9** (cf. Entry 2 and 3--7, Table [4](#tbl4){ref-type="table"}). Thus, most of the crude mixture obtained when using HOSu (**4**) consisted of deletion tripeptides, and no desired pentapeptide **15** was detected (Entry 2, Table [4](#tbl4){ref-type="table"}). In contrast, oximes **5--9** produced 10--30 % of Aib-pentapeptide **15** (Entries **3**--**7**, Table [4](#tbl4){ref-type="table"}). Particularly impressive was the efficiency displayed by the DIC/DmOx (**9**) system, which yielded the highest percentage of pentapeptide **15** in the cyanoacetamido oxime series (Entry 7, Table [4](#tbl4){ref-type="table"}), an efficiency comparable to HOAt (**2**) in similar conditions and similar to that of Oxyma (**3**, Entry 1, Table [4](#tbl4){ref-type="table"}).\[[@b29]\] The Aib-enkephaline model (**15**) also highlighted the enormous difference in acylation potency between DmOx (**9**) and the rest of the cyanoacetamido oximes (Entry 7 and 3--6, Table [4](#tbl4){ref-type="table"}). In a similar fashion to the epimerization assessment, PipOx (**6**) was found to be the least potent additive in amino acid activation (Entry 4, Table [4](#tbl4){ref-type="table"}). With respect to the acetamido analogue of Oxyma (**8**), a threefold decrease in reactivity was observed in comparison with parent ester **3**.
######
Percentage of tetrapeptide des-Aib (H-Tyr-Aib-Phe-Leu-NH~2~) during solid-phase assembly of pentapeptide 15 (H-Tyr-Aib-Aib-Phe-Leu-NH~2~)[\[a\]](#tf4-1){ref-type="table-fn"}
Entry Coupling Reagent **15** \[%\] des-Aib \[%\][\[b\]](#tf4-2){ref-type="table-fn"}
------- ------------------------------------------------------- -------------- ---------------------------------------------------
1 DIC/Oxyma (**3**)[\[c\]](#tf4-3){ref-type="table-fn"} 46.5 53.5
2 DIC/HOSu (**4**) 0 12.2
3 DIC/MorOx (**5**) 13.6 75.8
4 DIC/PipOx (**6**) 10.9 78.0
5 DIC/AmOx (**7**) 18.9 73.1
6 DIC/*N*-Oxyma (**8**) 15.4 79.9
7 DIC/DmOx (**9**) 31.3 68.7
10 min pre-activation and 30 min coupling times were generally applied, except for Aib-Aib (30 min double coupling).
Deletion tetrapeptide des-Aib was identified by peak overlap in reversed-phase HPLC with an authentic sample obtained in solid-phase.
Results are taken from Ref. \[[@b17]\].
Conclusion
==========
Here, we evaluated several *N*-alkyl-cyanoacetamido oximes (**5**--**9**) as additives to carbodiimides in substitution of HOSu (**4**) for the construction of stable amino acid esters. One of the main advantages of the proposed cyanoacetamido oximes, which can be accessed by a shown optimized amidation/nitrosation procedure, is their enhanced water solubility, which was particularly impressive in MorOx (**4**). Consequently, not only was byproduct removal increased, thereby allowing more facile work-up, but the water-soluble nature of cyanoacetamido oximes also allows their use in protein conjugation and labeling in addition to peptide synthesis.
A thorough assessment of the reduction of epimerization in various stepwise and \[2+1\] fragment models and the coupling efficiency in demanding junctions indicated that the cyanoacetamido family of additives showed a much greater capacity of configuration retention and acylation potency than *N*-hydroxysuccinimide (**4**). Among the *N*-alkyl-cyanoacetamido oximes **5--9**, PipOx (**6**) can be considered the least efficient analogue of the series. Nonetheless, the inclusion of an oxygen atom in the six-membered ring (MorOx, **5**) not only resulted in an increase in solubility but also in coupling efficiency. With regard to *N*-Oxyma (**8**), the envisaged decrease in reactivity and control of configuration by abandoning the ester moiety in Oxyma (**3**) was confirmed. Last but not least, carboxamido analogues AmOx (**7**) and DmOx (**9**) are highlighted as the most promising cyanoacetamido oxime derivatives. While the unsubstituted carboxamide (**7**) stands out in the epimerization experiments due to its marked capacity to retain chirality, DmOx (**9**) showed superiority to the rest of the oximes in the reactivity of the corresponding active ester.
Experimental Section
====================
Instruments and materials
-------------------------
All solvents used for recrystallization, extraction, HPLC analyses and TLC were of HPLC-reagent grade. They were distilled before use, and stored under dry conditions. 1 H NMR were recorded on a Mercury 400 MHz spectrometer (Varian) at RT, using tetramethylsilane (TMS) as internal standard. Chemical shifts were reported in *δ* units (parts per million) relative to TMS. Melting points were determined using a Mel-Temp apparatus (B-540, Büchi) and are uncorrected. Reaction monitoring and determination of the purity of the compounds were performed by TLC on silica gel-protected aluminium sheets (Type 60 GF254, Merck), and the spots were detected by exposure to UV light at *λ*=254 nm. Analytical separation and characterization was conducted on a reversed-phase 2695 HPLC separation module (Waters) using a SunFire C~18~ column (3.5 μm, 4.6×100 mm) and a linear gradient of CH~3~CN in H~2~O supplemented with 0.1 % trifluoroacetic acid (TFA) at a flow rate of 1.0 mL min^−1^. Detection at 220 nm was performed using a coupled 2998 PDA UV detector (Waters). Chromatograms were processed with Empower software (Pro version). Peptide mass was detected by means of an HPLC-PDA system as described above, coupled to a Micromass ZQ mass detector (Waters), using the MassLynx 4.1 software. The compounds were named using ChemDraw Ultra version 11 (CambridgeSoft Corporation).
Preparation of N*-*alkyl-cyanoacetamido oximes\[[@b21]\]
--------------------------------------------------------
Oximes **5**--**8** were synthesized in a previous related publication addressing their inclusion in Fmoc-carbonates and were used for the present study.\[[@b21]\] The procedure used is an optimization of earlier amidation/nitrosation protocols and is detailed below for the preparation of DmOx (**9**).\[[@b23]\]
**Preparation of 2-(dimethylamino)-*N*-hydroxy-2-oxoacetimidoyl cyanide (DmOx, 9)**:\[[@b21], [@b23]\] An aq solution of Me~2~NH (40 %, 40 mL, 350 mmol) was added to ethyl cyanoacetate (**10**, 22.6 g, 200 mmol) at −10 °C. The reaction mixture was stirred for 1 h at RT and then refluxed for 6 h at 70 °C. Next, the solvent was evaporated in vacuo, leaving 2-cyano-*N,N*-dimethylacetamide (**11**) as an oil, which was used in the next nitrosation step without further purification. Gaseous methyl nitrite was generated from a suspension of NaNO~2~ (8.3 g) in a mixture of MeOH (10 mL) and H~2~O (10 mL) by dropwise addition of a mixture of concd H~2~SO~4~ (5 mL) and H~2~O (10 mL) and introduced to an ice-cooled solution of intermediate **11** (100 mmol) and NaOH (4 g, 100 mmol) in MeOH (30 mL). The mixture was stirred for 2 h at RT and concentrated to dryness in vacuo. The residue was dissolved in the least amount of H~2~O (5 mL), ice-cooled, and acidified with concd HCl to induce precipitation. The product was obtained as white crystals (21.43 mg, 76 %)\[[@b23]\]: mp 138 °C; ^1^H NMR (C~3~D~6~O): *δ*=3.02, 3.18 (2s, 6 H, C*H*~3~), 13.09 ppm (s, 1 H, O*H*, D~2~O exchangeable).
General method for racemization experiments\[[@b17], [@b30]\]
-------------------------------------------------------------
Acid Z-Phg-OH, Z-Phe-Val-OH, or Z-Gly-Phe-OH (0.125 mmol), DIC (20 μL, 0.125 mmol), and additive (0.125 mmol) were dissolved in dimethylformamide (DMF; 2 mL) at 0 °C. H-Pro-NH~2~ (14.3 mg, 0.125 mmol) was added, and the reaction mixture was stirred for 1 h at 0 °C and overnight at RT. The reaction mixture was diluted with EtOAc (25 mL), extracted with 1 [n]{.smallcaps} HCl (2×5 mL), 1 [n]{.smallcaps} NaHCO~3~ (2×5 mL), and saturated NaCl (2×5 mL), dried over anhyd MgSO~4~ and filtered. The solvent was removed in vacuo, and the crude peptide was directly analyzed by reversed-phase HPLC.
**Z-Phg-Pro-NH~2~**: A linear gradient of 25--50 % CH~3~CN in H~2~O supplemented with 0.1 % TFA over 25 min was applied: *t~R~*([ll)]{.smallcaps}=9.3 min, *t~R~* ([dl)]{.smallcaps}=9.9 min.
**Z-Phe-Val-Pro-NH~2~**: A linear gradient of 20--70 % CH~3~CN in H~2~O supplemented with 0.1 % TFA over 14 min was applied: *t~R~*([lll)]{.smallcaps}=6.7 min, *t~R~*([ldl)]{.smallcaps}=7.1 min.
**Z-Gly-Phe-Pro-NH~2~**: A linear gradient of 20--70 % CH~3~CN in H~2~O supplemented with 0.1 % TFA over 14 min was applied: *t~R~*([lll)]{.smallcaps}=5.5 min, *t~R~*([ldl)]{.smallcaps}=5.8 min.
Solid phase synthesis of H-Tyr-Aib-Aib-Phe-Leu-NH~2~ (15)
---------------------------------------------------------
Pentapeptide **15** was prepared as reported.\[[@b17], [@b30]\] Fmoc-RinkAmide-PS resin (0.7 mmol g^−1^, 100 mg) was deblocked with piperidine in DMF (20 %, 10 mL) for 10 min, and washed with DMF (2×10 mL), CH~2~Cl~2~ (2×10 mL), and DMF (2×10 mL). Fmoc-Leu-OH (3 equiv), DIC (3 equiv) and additive (3 equiv) were mixed in DMF (0.5 mL), preactivated for 10 min and then added to the resin. The resulting slurry was stirred slowly for 1 min and allowed to couple for 30 min (double coupling for Aib-Aib). The ninhydrin test was performed during the introduction of the first residue (negative). The resin was subsequently washed with DMF (2×10 mL) and Fmoc removed with piperidine in DMF (20 %, 10 mL) for 7 min. Next, the peptide resin was washed with DMF (2×10 mL), DCM (2×10 mL), and DMF (2×10 mL), and coupled with the next amino acid. Coupling and deblocking steps were repeated to provide the pentapeptide. The percentage of des-Aib (Tyr-Aib-Phe-Leu-NH~2~) during solid-phase assembly of pentapeptide **15** was confirmed by peak overlap in the presence of an authentic sample. Crude pentapeptide **15** was analyzed by reversed-phase HPLC. A linear gradient of 10--90 % CH~3~CN in H~2~O supplemented with 0.1 % TFA over 20 min was applied: *t~R~* (**15**)=7.30 min, \[*M*+H\]^+^=611.35; *t~R~* (des-Aib)=7.50 min, \[*M*+H\]^+^=526.30.
This work was partially funded by the Secretaría de Estado de Cooperación Internacional (AECI, Spain), the Comisión Interministerial de Ciencia y Tecnologia (CICYT, Spain) (CTQ2009--07758), the Generalitat de Catalunya (Spain) (2009SGR 1024), the Institute for Research in Biomedicine Barcelona (IRB Barcelona), and the Barcelona Science Park. R.S.F. thanks the Ministerio de Educación y Ciencia (Spain) for a FPU PhD fellowship. Yoav Luxembourg (Luxembourg Biotechnologies) is thanked for his support.
|
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|
as v + i*h**3 + d*h + p*h**2 + w*h**4 and give d.
-3
Rearrange -3*y**3 + 4*y**2 + y**3 + 3*y**3 to the form q + z*y**3 + s*y**2 + d*y and give z.
1
Rearrange (-10 - 28 + 65)*(-a + 4*a - a) to the form m + v*a and give v.
54
Express (1 + 0 - 7 + (2 - 2 + 1)*(-1 + 0 - 1) - 1 + 0 + 4)*(-4*v**4 + 3*v**4 + 2*v**4) as d*v**3 + p*v**2 + o*v**4 + j*v + l and give o.
-5
Express -378*x**2 + 1 - 2*x**4 - 2*x**3 + 378*x**2 in the form o + b*x**2 + p*x**4 + l*x**3 + a*x and give p.
-2
Express (2*a + a - a)*(3*a**2 - 4*a**2 + 2*a**2) - a**3 + 2*a**3 + 3*a**3 in the form l*a**3 + h*a**2 + b*a + r and give l.
6
Rearrange (4508 - 4508 + 85*k)*(-4*k**2 + 2*k**2 + 4*k**2) to n*k + p*k**2 + l*k**3 + b and give l.
170
Rearrange -2*c**2 + 7 + 2*c**2 + c**2 to the form l*c + p + y*c**2 and give y.
1
Express u**4 + 26*u**2 - 2*u - 1 - 2*u**4 + 0 - 28*u**2 - 2*u**3 in the form q + h*u**4 + i*u + a*u**2 + g*u**3 and give h.
-1
Express -11*z + 98 - 8*z - 98 as k + n*z and give n.
-19
Rearrange 2 - 3 + 1 + 15*c to the form v*c + y and give y.
0
Rearrange 1 + 11*l - 1 - 32*l to the form h*l + d and give h.
-21
Express -k**3 + k - 3*k + 2*k**2 - 2*k**2 in the form j*k**3 + q*k + a*k**2 + l and give j.
-1
Express -4*l**2 - 2*l**2 - 6*l**2 as z*l**2 + w + k*l and give z.
-12
Rearrange -9*g**4 - 3 + 11*g**4 - 2*g + 0*g + 2*g**2 + 5 to the form z + l*g**3 + o*g + s*g**2 + m*g**4 and give l.
0
Rearrange -h - h - 2*h - 1 - 3*h to the form s + z*h and give z.
-7
Rearrange -3*y**3 + 10 - 10 - 2*y**2 - 2 to the form w + j*y**3 + i*y**2 + z*y and give i.
-2
Express -13*o**3 + 3 - o**2 + o**3 + 2*o**3 as a*o + x + z*o**2 + k*o**3 and give k.
-10
Express 2318*a**4 - a + a**2 + a**2 + 17*a**3 - 2316*a**4 in the form y*a**3 + j + u*a**4 + p*a**2 + o*a and give j.
0
Rearrange 32*b - 3 + 2 + 2 - 2*b to t*b + n and give n.
1
Express -5*g**2 - 14*g + 16*g - g**3 + g**2 - 1 + 8*g**2 in the form p*g**3 + t + q*g + j*g**2 and give j.
4
Rearrange 6*o + 10*o + 18*o to the form g*o + c and give g.
34
Express (-2*h + 2 - 2 - 3)*(2 - 11 + 30) in the form v + b*h and give v.
-63
Express 2*q**3 - 6*q**4 + 2*q**2 - q - 4*q**4 + 0*q as l + i*q**3 + h*q**2 + a*q**4 + u*q and give i.
2
Express (0 + 2 + 0)*(-4 - d + 4)*(2*d - d - 2*d) + 2*d**2 + 0*d**2 + 3*d**2 as l + q*d**2 + f*d and give q.
7
Express 4*v**2 + 0*v**4 + 35 - 36 - 2*v**3 - v**3 - v**4 as l*v**4 + k + t*v + u*v**3 + a*v**2 and give u.
-3
Express 7*z - z + 4*z - 14*z as f + i*z and give i.
-4
Rearrange 8*c**2 - 22*c**2 + c**3 + 16*c**2 + (-c**2 - 2*c**2 + 7*c**2)*(-2 - 2*c + 2) to t + w*c + l*c**3 + p*c**2 and give l.
-7
Rearrange (-7*f - f - 3*f)*(0*f**3 - 4*f**3 + f**3) to the form z*f**3 + m*f**4 + x*f + l + r*f**2 and give m.
33
Rearrange 32*j - 3570 + 3570 to l*j + s and give l.
32
Rearrange -o**2 + 3*o**3 - 37*o + 3 + 2*o**2 + 37*o to a*o**2 + t*o**3 + c + z*o and give a.
1
Rearrange 21 + 14 - 37 - 4*c**2 - c**3 - 4*c**3 to the form d + z*c**2 + q*c + l*c**3 and give z.
-4
Rearrange 1 - p**3 + 85*p + 11*p**2 - 85*p - p**4 to n*p**2 + j*p**4 + w*p + l + h*p**3 and give l.
1
Rearrange (k**2 - k**2 - k**2)*(0 + 3 - 4)*(-22 - 36*k + 22) + k**3 + k**3 - 3*k**3 to v*k**3 + w + u*k + s*k**2 and give v.
-37
Express (4 - 5 - 1)*(-4 - 4 - 32)*(2*w - w - 2*w) as v*w + m and give m.
0
Rearrange ((3 + 0 - 5)*(-2 + 3 - 2) + 0 + 0 - 4)*(-4 + 5 + 6)*(-4*y + 4*y - y) to the form c*y + r and give c.
14
Express 6 - 4*i**4 - 6 + 8*i**4 - 2*i - i**4 - 4*i**4 + (4*i - 4*i - 2*i)*(-2*i**3 + 3*i**3 + 0*i**3) as g + r*i**3 + a*i + c*i**4 + s*i**2 and give a.
-2
Express 3*d - 7*d + 15*d**3 + 3*d - 7*d**3 in the form n*d + x + y*d**2 + t*d**3 and give n.
-1
Rearrange 13*y**3 + 2*y**4 + y + y**2 - 14*y**3 - 11 - 4*y**4 - 9 to the form z*y + c*y**2 + w*y**4 + j*y**3 + v and give v.
-20
Rearrange -26 + 38*a + 3*a + 27 to n*a + d and give d.
1
Express (n + n + n)*(-2*n**2 - 2*n**2 + 3*n**2) + 0*n + 0*n + 16*n**3 in the form p + u*n**2 + s*n + h*n**3 and give h.
13
Rearrange -11*k + 26*k - 1 + 1 - 2 to the form r + n*k and give r.
-2
Express (-113 - 8*g + 113)*(1 + 2 - 4)*(0 + 0 + 2) as k*g + l and give k.
16
Express -69*l + 4*l**2 + 69*l as y + c*l**2 + g*l and give y.
0
Rearrange (q - q - 2*q)*(43 - 49*q - 43) to the form i*q + t*q**2 + g and give g.
0
Rearrange -3 + 4 - 5*j**2 + 14*j**2 - 3 to the form l*j + i + v*j**2 and give i.
-2
Rearrange (12*w**2 - 4*w**2 - 34*w**2 + 1)*(-2 - 1 + 1) to g*w**2 + s*w + y and give y.
-2
Express (6*u + 4*u - 4*u)*(-u - u + 4*u) - u**2 + u**2 - 2*u**2 + u**2 + 0*u - 2*u**2 - 4*u as s*u**2 + r*u + w and give r.
-4
Express -w**4 - 3*w**4 + 2*w**4 + (-10*w**3 + 2*w**3 - 8*w**3)*(-w + w + w) in the form k*w**3 + s*w + m*w**4 + g + r*w**2 and give k.
0
Rearrange (4*g - g - g)*(0*g - g + 3*g) - 1 + g**2 + 1 + (-g + 0*g + 5*g)*(4*g + g - 2*g) to the form n*g + j + x*g**2 and give x.
17
Rearrange (-98 - 5*u + 98)*(-4 + 9 + 2) + (1 - 5 + 2)*(-u + 1 - 1) to d + y*u and give y.
-33
Express -2*m**2 - 6*m**3 - 2*m + 3*m**3 + m**4 + 0*m**2 as s + q*m**4 + h*m**3 + p*m**2 + j*m and give j.
-2
Rearrange (-z - 2*z + 0*z)*(0*z - 3*z - 7*z)*(-3 + 4 - 3) to the form g + v*z + i*z**2 and give i.
-60
Rearrange 9*g - 6*g + 2*g + 8*g to u*g + z and give u.
13
Rearrange ((-4 + 4 + 2)*(-4 - 2*d + 4) - d - d + 4*d)*(-27 + 16 - 75) to the form l + j*d and give l.
0
Express -v + 3*v + v + 0*v in the form l*v + j and give l.
3
Express 15*d**2 - 12*d**2 + 13*d**2 + 24*d**2 in the form s*d**2 + g + q*d and give s.
40
Rearrange (2 - 2 - 4)*(6*g - 9*g - 14*g) to the form b + u*g and give u.
68
Express -2*b**3 + 0*b**3 + 4*b + 3*b**3 - 7*b - b**2 - 3 as m*b**2 + v + a*b + t*b**3 and give a.
-3
Rearrange 4*u**3 - 2*u**4 + 8*u**3 - 10*u**3 - u + 12*u**2 + 2 to the form p*u**2 + i*u**4 + b*u + r + c*u**3 and give p.
12
Express (-7*k - 2*k + 7*k)*(-5*k + 2 + 6*k - 3) as o*k**2 + d*k + r and give r.
0
Rearrange -19*i - 57*i + 8*i to the form u + l*i and give l.
-68
Express 5*f**2 - f**2 + 12*f + 21*f - 2*f**2 as k*f**2 + n*f + m and give k.
2
Rearrange 13*j - 4*j + 2*j**2 - 3*j**2 + 0*j**2 to the form s + p*j + t*j**2 and give p.
9
Express (-4 + 44*y + 51*y - 99*y)*(-3 + 3 + y**3) in the form m + s*y**4 + p*y**3 + i*y + j*y**2 and give p.
-4
Rearrange (0 + 0 - y)*(-12*y + y + 0*y) to j + k*y**2 + l*y and give k.
11
Express (0 + 0 + 1 + 3 - 1 + 0 + (-1 - 1 + 1)*(-2 + 0 + 0))*(n - 4*n - n) + (-4*n + 4*n - n)*(0 + 0 + 2) in the form y*n + g and give g.
0
Rearrange 101*j**2 - 2*j + 0*j + 2*j to the form m + z*j**2 + c*j and give c.
0
Rearrange 4*r**3 - r**3 + 2*r**3 + 1 - 2*r**3 - r**2 - r**4 to the form k*r**2 + g + u*r**3 + p*r + a*r**4 and give g.
1
Rearrange -6*x**2 + x**2 - 1 - 10*x**2 to the form g + h*x**2 + j*x and give h.
-15
Rearrange 0 + 7*p - 10*p - 7 + p to the form f*p + m and give f.
-2
Express -7*v**2 - 35*v**2 + 7*v**2 - 36*v**2 in the form o*v**2 + x + y*v and give o.
-71
Express (2*o + 3*o + 2*o)*(5 - 3 - 3)*(-1 - 2 - 2) in the form i*o + p and give i.
35
Rearrange 4 + r**3 - 3 - 4 + 2 - r**2 to s + x*r**2 + i*r + h*r**3 and give x.
-1
Rearrange (2*o + o - o + o**2)*((2 - 2 - 4*o)*(2 + 1 - 4) + o + 4*o - 3*o) to the form f + m*o**2 + a*o + l*o**3 and give l.
6
Rearrange 4*u - 2*u + 4*u + 41 - 4*u to the form o*u + r and give o.
2
Rearrange -27 + 5*s**2 + 27 - s to o + x*s**2 + z*s and give x.
5
Rearrange (2*h**2 + 4*h - 4*h)*(1173 + 311*h - 1173 - 27*h) to a*h + s*h**2 + n + f*h**3 and give f.
568
Rearrange (2*k + 0*k + 0*k)*(1 - 2*k - 1) + k**2 - 2*k + 2*k + (k**2 - k**2 - k**2)*(-2 + 3 + 1) to p*k + t*k**2 + c and give t.
-5
Express 9*l**3 - 2*l - l + 4*l in the form v + y*l + j*l**3 + w*l**2 and give y.
1
Express (-1 + 5 - 3)*(-1 + 1 + 2*x) + (2*x + 3*x - 3*x)*(2 + 4 - 4) as a*x + m and give m.
0
Rearrange (t + 4*t - 7*t)*(-15*t + 35*t - 70*t + (-3 - 1 + 2)*(t + 0*t + 0*t)) to r + n*t**2 + i*t and give n.
104
Express 3*z + 3*z - 14*z + 5*z - 2*z**4 - 2*z**3 as x + d*z**4 + p*z**2 + f*z**3 + w*z and give x.
0
Express (4*s - 2*s - 3*s)*(1 - 4 + 5) - 44*s + 1 + 68*s - 2 in the form l*s + t and give l.
22
Express -b + 10*b**2 - 2*b**4 - 4*b**3 - 3*b**2 - 1 + 2*b**4 - 2*b**4 as u*b**3 + r + h*b + y*b**2 + w*b**4 and give w.
-2
Rearrange 3 - 3 - 2*l + (4 - 4 - 2*l)*(-2 - 1 + 5) - 3*l - 4*l + 5*l + 6*l - 4*l - l - 9*l - 19 + 19 to the form t + p*l and g
|
{
"pile_set_name": "DM Mathematics"
}
|
NADPH oxidase mediates lipopolysaccharide-induced neurotoxicity and proinflammatory gene expression in activated microglia.
Parkinson's disease is characterized by the progressive degeneration of dopaminergic neurons in the substantia nigra. We have previously reported that lipopolysaccharide (LPS)-induced degeneration of dopaminergic neurons is mediated by the release of proinflammatory factors from activated microglia. Here, we report the pivotal role of NADPH oxidase in inflammation-mediated neurotoxicity, where the LPS-induced loss of nigral dopaminergic neurons in vivo was significantly less pronounced in NADPH oxidase-deficient (PHOX-/-) mice when compared with control (PHOX+/+) mice. Dopaminergic neurons in primary mensencephalic neuron-glia cultures from PHOX+/+ mice were significantly more sensitive to LPS-induced neurotoxicity in vitro when compared with PHOX-/- mice. Further, PHOX+/+ neuron-glia cultures chemically depleted of microglia failed to show dopaminergic neurotoxicity with the addition of LPS. Neuron-enriched cultures from both PHOX+/+ mice and PHOX-/- mice also failed to show any direct LPS-induced dopaminergic neurotoxicity. However, the addition of PHOX+/+ microglia to neuron-enriched cultures from either strain resulted in reinstatement of LPS-induced dopaminergic neurotoxicity, supporting the role of microglia as the primary source of NADPH oxidase-generated insult and neurotoxicity. Immunostaining for F4/80 in mensencephalic neuron-glia cultures revealed that PHOX-/- microglia failed to show activated morphology at 10 h, suggesting an important role of reactive oxygen species (ROS) generated from NADPH oxidase in the early activation of microglia. LPS also failed to elicit extracellular superoxide and produced low levels of intracellular ROS in microglia-enriched cultures from PHOX-/- mice. Gene expression and release of tumor necrosis factor alpha was much lower in PHOX-/- mice than in control PHOX+/+ mice. Together, these results demonstrate the dual neurotoxic functions of microglial NADPH oxidase: 1) the production of extracellular ROS that is toxic to dopamine neurons and 2) the amplification of proinflammatory gene expression and associated neurotoxicity.
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{
"pile_set_name": "PubMed Abstracts"
}
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The Trial is a novel by Franz Kafka about a character named Josef K., who awakens one morning and, for reasons never revealed, is arrested and prosecuted for an unspecified crime.
According to Kafka’s friend Max Brod, the author never finished the novel and wrote in his will that it was to be destroyed. After his death, Brod went against Kafka’s wishes and edited The Trial into what he felt was a coherent novel and had it published in 1925.
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{
"pile_set_name": "Pile-CC"
}
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Posted by A Cozy Kitchen in Step-by-Step Recipes
Is there anything more perfect and pretty for a Sunday brunch than quiche? Probably not. But let’s be honest, if you’re going for easy, making a quiche ain’t it. On most Sunday mornings—when I’m still trying to wake up—pastry dough isn’t something I want to deal with. So when I saw this recipe from Claire, I was definitely intrigued. This quiche’s crust isn’t made with a traditional pastry dough; instead it’s made using roasted spaghetti squash, making it not only a bit more fuss-free, but also healthier.
Let’s get started!
You want to start the quiche process already having roasted the spaghetti squash. Roasting squash is easy enough: Preheat your oven to 400ºF, line a baking sheet with foil or parchment paper, slice the squash in half, place it face down and put it the oven for about 20 minutes.
When it’s done, it’ll be very tender. Start with scooping out the seeds, and then scrape the squash with a fork.
Transfer the spaghetti squash to a bowl and set it aside.
In a medium pan, add a bit of olive oil, the diced onion and sauté for a few minutes. Top the onion with the minced garlic.
Next, trim and cut the asparagus into 1-inch pieces.
Add the asparagus to the pan and cook until slightly tender.
While the asparagus is cooking, crack the eggs in a bowl, add the milk and Swiss cheese.
Next, add some salt and pepper and whisk the ingredients together.
When the asparagus/onion mixture is cooked and you have the egg mixture ready to go, it’s time to get the quiche ready for the oven.
Press the spaghetti squash into the pie dish, lining it evenly all along the bottom and the sides.
Pour the egg mixture into the pie dish.
And then top it all off with the sautéed asparagus and onion mixture.
Transfer it to the oven and bake until it’s golden and delicious.
Spaghetti squash is definitely in season right now, but as we go through fall, I can see it working beautifully with different types of squashes, like acorn or kabocha. Thanks again to Claire for this beautiful and simple recipe. I’m going to enjoy this recipe for many brunches to come! Visit her blog Just Blither Blather for more recipes from this talented and engaging young blogger.
Printable Recipe
Asparagus Quiche with a Spaghetti Squash Crust Print
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Show image Print Description A quiche perfect for supper in spring! Ingredients 13 ounces, weight Asparagus
½ Small Yellow Onion
2 cloves Garlic
1 teaspoon Olive Oil
5 Eggs
1 cup Milk
1 cup Swiss Cheese
½ teaspoons Salt
¼ teaspoons Pepper
3 cups Cooked Spaghetti Squash (1 Small Squash) Preparation Instructions Preheat oven to 400ºF. Cut off the woody ends of the asparagus. Chop the onion, mince the garlic, and cut the asparagus spears into 1-inch pieces. Heat the olive oil in a pan over medium heat, and saute onion and garlic for several minutes, until the onion is soft. Add the asparagus and continue to saute until the asparagus has turned bright green and is soft but not limp. Whisk together the eggs, milk, cheese, salt, and pepper. Grease a pie pan. Press the cooked spaghetti squash to the sides and bottom of the pan, forming an even crust. Pour the egg mixture into the pan. Add the asparagus, onion, and garlic on top of the egg mixture; be sure it sinks in. Bake for 40 minutes until quiche is firm. Enjoy!
_______________________________________
Adrianna is the lovely lady behind the scrumptious blog A Cozy Kitchen. It’s filled with all kinds of mouthwatering recipes and gorgeous photography. Whether you’re in the mood for something vegetarian or meaty, fancy or pure comfort, light or decadent, there’s sure to be something there for everyone.
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{
"pile_set_name": "OpenWebText2"
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Prediction of pain outcomes in Korean older adults: use of a structural equation model.
To construct a structural equation model of pain adjustment outcomes (e.g., depression and fatigue) in Korean older adults based on the cognitive-behavioral model of chronic pain. Nonexperimental research design. Data were collected by questionnaires from 271 Korean older adults. Data analysis was conducted with SPSS 10.1 for descriptive statistics and a PC-LISREL program for covariance structural analysis. In this study, based on the modifications, chi-square statistics were changed, the goodness-of-fit index was 0.97, the adjusted goodness-of-fit index was 0.93, the root mean square residual was 0.04, the normal fit index was 0.98, and the non-normed fit index was 0.98. Path coefficients and their statistical significance for the revised model were as follows: pain adjustment and pain beliefs were found to have a significant direct effect on pain coping. The variable directly related to pain beliefs was pain adjustment, and variables directly influencing fatigue were pain coping and pain beliefs. Lastly, pain adjustment, pain coping, and fatigue were found to have a significant direct effect on depression. Also, pain adjustment, pain coping, and pain beliefs were found to have a significant indirect effect on depression. In conclusion, pain adjustment, pain coping, pain beliefs, and fatigue all contributed to depression. Fifty-four percent of depression could be explained by these variables. This modified model is considered appropriate for explaining and predicting pain adjustment outcomes in Korean older adults. Also, the findings support the development of an intervention strategy to improve pain coping, negative pain beliefs, fatigue, and depression caused by poor pain adjustment.
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{
"pile_set_name": "PubMed Abstracts"
}
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Q:
Inequality of Operators Preserves Hilbert Schmidt Norm
I have been trying to prove the following fact in elementary operator theory without success:
For any two positive operators $0 \leq R \leq S$, we have $\Vert R \Vert_2 \leq \Vert S \Vert_2$, where $\Vert S \Vert_2^2 = Tr(S^* S) = \sum_{i=1}^\infty\Vert S e_i \Vert^2$ for some orthonormal basis of a separable Hilbert Space (if the sum converges). Even more generally, could this be shown for Schattern $p-$norms?
It seems naive, but I couldn't find the right tool to deal with this, any hints are appreciated.
A:
Inside the trace, things commute (cyclically, so in general one needs to be careful, but with only two operators there's no issue).
So (commuting things inside the trace in the first equality in the second line)
\begin{align}
\|S\|_2^2-\|R\|_2^2
&=\operatorname{Tr}(S^2)-\operatorname{Tr}(R^2)
=\operatorname{Tr}(S^2-R^2)\\[0.3cm]
&=\operatorname{Tr}((S-R)(S+R))
=\operatorname{Tr}((S-R)^{1/2}(S+R)(S-R)^{1/2})\geq0.
\end{align}
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{
"pile_set_name": "StackExchange"
}
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Pharmacokinetic variability of routinely administered bisoprolol in middle-aged and elderly Japanese patients.
The nonlinear mixed effects model (NONMEM) was used to analyze the pharmacokinetics of routinely administered bisoprolol in middle-aged and elderly Japanese patients. The subjects consisted of 29 males and 11 females with a mean age of 63.5+/-10.1. Data on the plasma concentration of bisoprolol from 94 blood samples obtained at steady-state following repetitive oral administration were analyzed using the NONMEM program, where a one-compartment model with repetitive bolus dosing was parameterized in terms of oral clearance (CL/F) and apparent volume of distribution (V/F). Individual CL/F values were correlated with body weight (WT) and creatinine clearance (CLcr). The relation between CLcr and the CL/F of bisoprolol was not altered by the CYP2D6 and CYP2C19 genotypes, gender, or age. The mean CL/F value estimated with NONMEM was 0.0612.WT+1.15.CLcr (l/h), and the mean V/F value was 2.61.WT (l). The residual interindividual variability of CL/F and V/F were 22.0% and 12.6%, respectively. The pharmacokinetic variability of bisoprolol is small even in routinely treated Japanese patients, provided that both body weight and renal function are taken into account for the prediction of oral clearance of the drug.
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{
"pile_set_name": "PubMed Abstracts"
}
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MLHS’s Michael Stephens conducted an in-person interview with Steve Spott, head coach of the Toronto Marlies, at the Mastercard Centre earlier this week. Spott touched on a wide variety of Marlies-centric stuff, including the biggest challenges facing the team headed into the new season and the opportunities the Leafs prospects will be embarking on in the 2013-14 campaign.
Here’s a handy list of links to all the other Summer Interviews:
Michael Stephens: As a Toronto boy you must be excited to be back here coaching for the Marlies. What’s the experience been like so far?
Steve Spott: It’s been great. I feel that the people here in the organization have been first class. Just being back in the city, feeling the vibe of the Leaf Nation is exciting. Being a boy from Toronto, being in this building and being around it now is humbling and I’m really excited for it.
MS: They say the Toronto Marlies is the 31st best coaching job in hockey. What are you going to do to make the most of this opportunity? What are you looking forward to?
SS: Making the jump to pro hockey is something I think every coach aspires to do. And to leave the situation that I left, Kitchener was very unique. The way they treat their staff and their players is first class. Coming to Toronto it’s much the same but at the pro level. But ultimately for me it’s about winning and it’s about developing players. I think we’ve done a good job in Kitchener developing our players and here it’s no different. We’re going to be graded not only on winning but on the amount of players Randy Carlyle gets to work with. So, that’s a great challenge.
MS: Speaking of development, you’ve coached Joshua Leivo in Kitchener, who’ll be making the jump to the Marlies this year. Have you talked with him about what it’s going to take to make the leap to the next level of development?
SS: Yeah, we have talked. Coming out of junior hockey it’s about learning to be a pro every day. Josh has to work on little things: shift length; training every day; eating right every day is something he has to develop. But being around good character people is going to make him better. We are going to have to make sure our veteran players are going to be like surrogate coaches for all of our young guys.
MS: Speaking of veteran players, there really aren’t that many on the roster. You’re seeing a lot of guys who are recent grads from the OHL ranks. Was that a big reason why MLSE wanted you to be coach of the Marlies? You’ve seen about a dozen of these guys for 3-4 years.
SS: I think that it was a staple of the interview, where we talked about the familiarity. Not only with players I’ve coached in junior, but being a guy who played in the NCAA and now have coached in the Ontario Hockey League. I will be able to relate to college players as well. Then, through Hockey Canada I’ve dealt with international players. So I like to think that my war chest is where it needs to be to help develop the players and give them the comfort to come in and talk to me when times are tough.
MS: What’s the biggest challenge for you going from Junior to the AHL?
SS: Grinding the players. And I think that’s where Gord [Dineen] and Derek [King] will be important. You grind your guys pretty hard in Junior every day. Here, there’ll be days where you’ll have to lay off and give days off. So I think trusting your staff, and giving the boys a day off so they’re rested for the right time will be the biggest challenge.
MS: You’ve coached Jerry D’Amigo before in Kitchener, and he’ll be fighting for a spot with the Leafs in camp. Where do you see him fitting with the Marlies versus the Leafs?
SS: It’s finding your role and playing it as well you can. For Jerry, he’ll probably find himself getting a lot more power play time this year with me than maybe he’s had in the past. But if he’s going to play for the Leafs, he’ll probably be used as a penalty killer. So he’ll have to choose what skills he wants to focus on. If he wants to play for Randy he’ll need to learn his role.
MS: You mentioned earlier that you wanted to ice a fast team. Do you think you have the personnel to do it?
SS: Our backend is going to be pretty mobile. But (generally) I don’t want our players sitting back. If they are going to be viewed by the Maple Leafs management on a daily basis, I want those people to see what these players can do, and they’re gonna do it with speed.
MS: How often are you speaking with Dave Poulin?
SS: Every day.
MS: What about? Roster decisions? Strategy heading into the season?
SS: Right now it’s about our players, primarily. Obviously that’ll grow once we have our team fully together. And then it will turn to player progress. We’re going to do player evaluation after every game and he’ll be a big part of it.
MS: I just saw Colton Orr walk by, and Nazem Kadri is on the ice. How important is it to have everyday NHLers at the early stages of camp around the prospects?
SS: Hugely important. It’s great for the prospects to see how they train, how they work, how they eat. So that’s a part of it. But now, for a player like Tyler Biggs, having access to video of David Clarkson is going to be great for him. We can show him Clarkson clips and he can say what David’s doing to be the player that he is today. And hopefully Tyler can replicate that.
MS: How often do you guys use video in this way?
SS: A lot.
MS: And do you pick a player as an archetype, break down the video, and say, ‘play like him?’
SS: Yep.
MS: So, would Jay McClement be a guy for D’Amigo to model his game after?
SS: McClement is definitely a guy we want D’Amigo to model his game around. Crescenzi also. For David Broll, Lucic in Boston. It’s about teaching. I was a teacher by trade for five years and it’s about trying to give these players every resource to be successful. And I think a lot of these guys are visual learners now; they need to see. It’s a big part of what I do.
MS: You’ve coached Morgan Rielly internationally a few times now, and you’ll probably get a chance to coach him again next spring. What are your thoughts on him?
SS: Well… his offensive play, his skating ability and passing ability; I think they’re well renowned. I think it’s responsibility. That’s the biggest change in his game. Now you feel safe when he’s out on the ice. He’s been eliminating risk out of his game. [He understands that] One point can mean a playoff spot or home ice, and he’s taking the steps to round out the game.
MS: What do you think is going to be the Marlies biggest chall–
SS: Scoring. Definitely scoring. Our biggest challenge is going to be up front. We’ve lost some players to Toronto who were world class players. So now we’re giving a lot of new guys who haven’t had that opportunity – like the D’Amigo’s of the world – to have that opportunity in an offensive role. Saying that, we also understand that we don’t have Nazem Kadri anymore, a player with things you just can’t teach. So I think it’s going to fall on guys like Greg McKegg and Sam Carrick. These are guys that are going to get a lot more offensive chances, I think, than maybe they have in years past.
MS: How does this affect the defensive make up?
SS: Well, I think the D are going to be a big part of our attack. They’re going to be pretty active from the points.
MS: Who do you think will take over as Captain?
SS: Through team building, that will sort itself out. I can’t say there’s a clear cut Ryan Hamilton in that dressing room yet. So that’ll work itself out in the future.
MS: Are you motivating certain players to fight for a letter? Possibly someone like McKegg needs to take a step forward.
SS: Absolutely, I agree. Yeah, all of the guys that are coming to their third or fourth camps, those are the guys that have to take not only on-ice leadership, but off-ice leadership. Before games, saying the right things, becoming surrogate coaches to the other players in the room. He’s [McKegg] a guy who really comes to mind that’ll have to step up in that area.
MS: The Marlies have won the North Division two seasons in row. Are you excited, or nervous to be stepping into that? Seems like a tough act to follow.
SS: Well, everyone’s telling me it’s going to be a struggle, but the expectation for coaches doesn’t change. We want to make sure that we’re in contention. We’re going to give an opportunity to our young players early, but then it’s going to be up to them to take advantage of that.
MS: Have Derek King and Gord Dineen helped in getting you prepared for the season? What’s the next step?
SS: They have been. We’ll see [Leafs video coach] Chris Dennis tomorrow. We hired a new video coach, Mark Phalon, from Northeastern. So we’ll meet now as a staff and get our technical plan in place.
MS: You also hired a new goalie coach
SS: Piero Greco, yeah.
MS: What can you tell me about him?
SS: Passionate, hard working. He’s very demanding of his goaltenders: he expects perfection. He takes a lot of pride in his work and expects the same of those around him.
MS: What do you think his impact will be on a guy like Garret Sparks?
SS: He knows Garret from junior, we saw him a lot when he was in Guelph. I’m sure they’ll get off on the right foot. I try to give people as much autonomy as possible and I think Piero will be a great mentor for Sparksy.
MS: Have you been able to figure out a roster in your head, or are you waiting till the end of September when you’ll know about Holzer or Brennan.
SS: Well, I’ve got a wish list, yeah, and Smitty’s [Trevor Smith] on it too. Sure, we’ve got depth charts, but ultimately it’s about if they’re able to play for Randy. So, for me it’s wait and see.
MS: How often do you speak with Randy?
SS: Not often. Maybe when he gets into town we’ll have a little bit more of a chance to dialogue. Right now it’s mostly been Chris Dennis from the Leafs and Gord and Derek. My guys.
MS: So you’ve been given a lot of autonomy to do your job?
SS: Dave Poulin said from day one that I’d have full autonomy to make those decisions. And that there’d be no secrets. If there’s going to be a player transaction, or maybe a player is going to be kept out of a certain game, that everybody is kept in the loop. I can tell you, more autonomy than I expected coming in. Having been a general manager and coach, I appreciate that.
MS: Who’s a guy that might be flying under the radar now, but you think could be poised for a breakout season? A lot of people have Petter Granberg penciled in there.
SS: Granberg’s a guy who just came off of the World Championships. I think he might have a hard time flying under the radar here. But I’m more excited in the Leivos and Crescenzis and McKeggs, seeing those kids develop into their own.
|
{
"pile_set_name": "OpenWebText2"
}
|
import React from 'react';
const Api = () => {
return (
<>
<h1>API Overview</h1>
<div className="tableContainer">
<table>
<tbody>
<tr>
<th>Props</th>
<th>Type / Options</th>
<th>Default</th>
<th>Description</th>
</tr>
<tr>
<td>show</td>
<td>boolean: false | true</td>
<td>false</td>
<td>Mount tooltip if true</td>
</tr>
<tr>
<td>fontFamily</td>
<td>string: fontFamily</td>
<td>'inherit'</td>
<td>Font family of text</td>
</tr>
<tr>
<td>fontSize</td>
<td>string: px</td>
<td>'inherit'</td>
<td>Font size of text</td>
</tr>
<tr>
<td>fontWeight</td>
<td>string</td>
<td>'bold'</td>
<td>Font weight of text</td>
</tr>
<tr>
<td>color</td>
<td>string</td>
<td>'inherit'</td>
<td>Font color of text</td>
</tr>
<tr>
<td>animation</td>
<td>string: fade | bounce</td>
<td>'fade'</td>
<td>
Mount/Unmount anmation. For custom animations see examples for more
<a href="#custom-animations" style={{ color: 'purple', fontSize: '15px' }}> info</a>
.
</td>
</tr>
<tr>
<td>hoverBackground</td>
<td>string: hex colors</td>
<td>'#ececec'</td>
<td>Background color on hover</td>
</tr>
<tr>
<td>hoverColor</td>
<td>string: hex colors</td>
<td>'#000000'</td>
<td>Font color on hover</td>
</tr>
<tr>
<td>backgroundColor</td>
<td>string: hex colors</td>
<td>'#ffffff'</td>
<td>Background color</td>
</tr>
<tr>
<td>alert</td>
<td>string: rgb colors</td>
<td>false</td>
<td>Pulse animation</td>
</tr>
<tr>
<td>textBoxWidth</td>
<td>string: px | auto</td>
<td>'150px'</td>
<td>Width of the text box</td>
</tr>
<tr>
<td>padding</td>
<td>string: px</td>
<td>'15px 20px'</td>
<td>Padding of text</td>
</tr>
<tr>
<td>borderRadius</td>
<td>string: px</td>
<td>'5px'</td>
<td>Radius of corners</td>
</tr>
<tr>
<td>zIndex</td>
<td>string: number</td>
<td>'100'</td>
<td>Z-index of tooltip.</td>
</tr>
<tr>
<td>moveDown</td>
<td>string: px</td>
<td>'0px'</td>
<td>Downward position adjustment</td>
</tr>
<tr>
<td>moveRight</td>
<td>string: px</td>
<td>'0px'</td>
<td>Right position adjustment</td>
</tr>
<tr>
<td>static</td>
<td>boolean: false | true</td>
<td>false</td>
<td>Disable hover animations</td>
</tr>
<tr>
<td>flat</td>
<td>boolean: false | true</td>
<td>false</td>
<td>Disable shadows</td>
</tr>
<tr>
<td>lineSeparated</td>
<td>string: css border property</td>
<td>'1px solid #ececec'</td>
<td>Specifies line separation between options (optional).</td>
</tr>
<tr>
<td>arrowAlign</td>
<td>string: 'start' | 'center' | 'end'</td>
<td>'start'</td>
<td>
Vertical or horizontal aligning along the left/right or
top/bottom textbox side respectively. See
<a href="#arrow-align" style={{ color: 'purple', fontSize: '15px' }}> examples </a>
for more information.
</td>
</tr>
<tr>
<td>position</td>
<td>
<p style={{ marginTop: '0' }}>
string: 'position1 position2'
</p>
</td>
<td>'right center'</td>
<td>
Positions tooltip relative to target. See
<a href="#tooltip-positions" style={{ color: 'purple', fontSize: '15px' }}> examples </a>
for more information.
</td>
</tr>
</tbody>
</table>
</div>
</>
);
};
export default Api;
|
{
"pile_set_name": "Github"
}
|
Todays women are whores
Agreed OP. Despite my stupid posts and me generally being an asshole (all in good fun of course), once in a while all of us run into someone that gets it, no matter what "it" may be.
Good luck to all of us men. May we find real women that we can proudly keep and call respectful mother to our children. Our true better half.
Quoting: Anonymous Coward 15756389
Unlikely, for several reasons:
1. Us good women aren't interested in guys who self-style as "studs" but are actually just whores. We want men we can reasonably expect fidelity from, since we have it to offer.
2. You are unlikely to find a good, or decent woman, because you only know where to look for and find 'whores'.
3. Because you only know how to look for and acquire 'whores', you will continue to make yourself more and more jaded and hateful in your mistreatment of women. If you do happen to find a good woman, she will run for the hills because of your loathsome attitudes towards women.
Sigh...cuz a woman cannot possibly enjoy making her man feel good?? You deluded morons are so brainwashed by propaganda it is saddening your pathetic Just cuz you can't get an amazing wife doesn't mean they don't exist
Quoting: Anonymous Coward 9643001
So, you're a whore and admitting it. What's the point of this thread then?
Quoting: Anonymous Coward 2589610
That it is wrong to sleep around before marriage and have kids from a bunch of baby dadies..... now you get it moron??
Quoting: Anonymous Coward 9643001
I am hoping that there is one functioning brain cell in your skull somewhere.
By calling yourself a whore, you are putting yourself in the same category as other so-called whores. If you find whores so very evil, why would you call yourself the very same thing that you claim to hate so much?
Don't you like yourself? I wouldn't call myself ugly, because I am not. I am fucking beautiful. So, using your logic, I actually should call myself ugly...because...why? I don't get it. Maybe because I am such a moron.
Does your husband pay you after sex? Is that why you call yourself a whore? How much do you charge per session?
men expect a woman who:has a full time jobdoes all of the cleaningdoes all of the cookinggives in to any sexual whim, at any timewill listen to him bitch relentlessly about trivial things without saying a wordnever complainshas no friendsgoes no where but the grocery storetells him how sexy and wonderful he is even though he sits on his fat ass watching whatever sport is on HDTV digging in his nasty ass, stenching up the living room with his cesspool gasessays nothing when he gets drunk and pisses, shits or vomits everywheresays nothing when he leaves her alone at home to go hang out with his friends
yes, feminism is fucked up but this modern porn-watching misogynistic masculinism is down right nauseating. just one bullet and one gun will do for me, you low life douche bags that think women are here solely to pleasure you while you use them up, abuse them and throw them out like old dish water.....absolutely disgusting "examples" you are. How about being a model for good behavior instead of expecting women to be better than you are, you sorry sacks of parasitically infested pig shit.
That is what you call love there is nothing wrong with your wife letting you dominate her... It is not a weakness.. A matter of fact it is like her saying to you. "I am yours and I trust you to do whatever you want with me." "Just be gentle"
The true problem in society is that both genders have forgotten what love really means. They have forgotten why women need men and why men need women. the vast majority have been brain washed by social television, cell phones and social networks..
What has really happened is not that everyone has become whores. What has really happened is that it has become 10 times more easy to do it. Also in todays society most people are under an extreme amount of stress from over working and do not have time to be with there spouses.
So they choose to have a good time with someone else that is there with them. Humans are social and all humans need love,sex and a companion in order to be fully satisfied. I dont care what anyone says sex is 100 percent natural. THE PROBLEM IS NOT MEN AND THE PROBLEM IS NOT WOMEN. THE PROBLEM IS THIS SICK SOCIETY WE LIVE IN..
IF ARE ALL MIGHTY POWERFUL OVERLORDS ACTUALLY DID WHAT THEY ARE SUPPOSE TO AND ACTUALLY BALANCED OUT THE SYSTEM SO MEN AND WOMEN DO NOT HAVE TO WORK THERE ASSES OFF LIKE PIGS TO JUST SURVIVE. AND DID NOT BRAIN WASH US WHAT BEAUTIFUL IS AND WHAT LOVE IS AND ALSO GOT RID OF THIS SOCIAL PROPAGATED BULLSHIT AND USED TECHNOLOGY FOR WHAT IS WAS INTENDED TO DO MAKE ARE LIVES MORE EASIER NOT MORE HARDER
IF WE GOT RID OF THIS MATERIALISTIC SOCIETY AND EXCHANGED IT FOR A ECONOMY BASED ONE WHERE WE MAKE MOSTLY WHAT WE NEED NOT WHAT WE WANT IT WOULD THEN EVEN THE ODDS FOR BOTH MEN AND WOMEN. AND MOST LIKELY MEN AND WOMEN WOULD NOT CHEAT BECAUSE THEY HAVE EVERYTHING THEY NEED AND THEY ARE SATISFIED.
LAST THING WHORES IN SOCIETY WILL ONLY INCREASE DUE TO ALL THE OVERWORKING AND STRESS FROM EVERYDAY LIFE. ALSO CELL PHONES, SOCIAL NETWORKING AND SOCIAL MEDIA ACTUALLY MAKE THIS WORST. "WE ALL CAME IN THIS WORLD WITH NOTHING. WE ARE ALL GOING TO LEAVE IT THE SAME WITH NOTHING"
I JUST HOPE THE DAY I DIE I GET TO EXPERIENCE LOVE.
TO ME LEAVING THIS WORLD WITH THAT IS GOOD ENOUGH..
DONT YOU..?
I AM ACTUALLY HOPING FOR A APOCALYPSE TO SOLVE THIS PROBLEM.. I THINK OUR SOCIETY IS UN REPAIRABLE ALL THAT IS LEFT IS THE RESET SWITCH..
SO ON WITH ARE LONG AWAITED DOOM!!!!!!!!
THIS IS WHAT MAKES GLP GREAT THE DOOM... I HAVE NOT FORGOTTEN GLPS ROOTS..
Your sentence structure is lousy. English isn't even my first language and I have a better grasp of if than you do. Is this representative of what the US school system is churning out? Pathetic.
My theory is that border-line retarded people always have to cling on to out-dated and over-valued sexual mores. It's like their brains can't process logic, so they hear something and to them, it in some childish way makes them feel finally superior to SOMETHING. Even thought they themselves were most likely a product of the mythical "whoring" around.
Saving your virginity for your life-partner is like never eating dessert. What's the point? I want to sex up the person I marry before I marry them. What if they suck in bed? Yeah, no thanks. Lucky for me, my husband and I had sex right away, clicked very well, and decided to make it permanent.
Quoting: Anonymous Coward 13019800
So you chose your mate by how well they performed in bed? I can imagine how wore out your ass is! Got any gravy with that roast beef?
Quoting: Anonymous Coward 9643001
Yes, I chose my mate by how good he was in bed. In addition, I also chose him because he is the smartest person I've ever met, is a wonderful human being, has a great job, knows how to fix stuff, is a tall drink of water with a full head of hair, is faithful, very very loving, has a beautiful soul, is giving, forgiving, and we have the same dreams and goals. I would die for him. It is an added bonus that he is the best lover I have ever had.
Chicks dig me because I rarely wear underwear, but when I do, it's usually something unusual.
Also, I don't know what a pc of shit is. Am I a politically correct piece of shit??? Or am I a personal computer piece of shit??? I'm confused.
BTW, all the hot chicks I bang don't find me useless, but I admit I'm a total douchebag. Unlike you, I can at least admit it.
Douchebag.
Quoting: Anonymous Coward 15756389
Which movie is that from?? I can't remember.
And the LORD spake, saying, "First shalt thou take out the Holy Pin, then shalt thou count to three, no more, no less. Three shall be the number thou shalt count, and the number of the counting shall be three. Four shalt thou not count, neither count thou two, excepting that thou then proceed to three. Five is right out. Once the number three, being the third number, be reached, then lobbest thou thy Holy Hand Grenade of Antioch towards thy foe, who being naughty in My sight, shall snuff it.
I am an evil giraffe, and I shall eat more leaves from this tree than perhaps I should, so that other giraffes may die.
All my joking and prodding aside, it is not wise (anonymous on the Internet or not), to tell people to go and kill themselves.
Not only can you be held responsible if something horrible were to happen, it is also a very dangerous thing to put out there. I know I wouldn't want something like that on my soul, and you seem nice enough - I don't think you would either.
So you chose your mate by how well they performed in bed? I can imagine how wore out your ass is! Got any gravy with that roast beef?
Quoting: Anonymous Coward 9643001
Yes, I chose my mate by how good he was in bed. In addition, I also chose him because he is the smartest person I've ever met, is a wonderful human being, has a great job, knows how to fix stuff, is a tall drink of water with a full head of hair, is faithful, very very loving, has a beautiful soul, is giving, forgiving, and we have the same dreams and goals. I would die for him. It is an added bonus that he is the best lover I have ever had.
You could only hope to become the man that he is.
Quoting: Anonymous Coward 2589610
Well good for him. He is very lucky to have found a woman who will love him as much as you do. I wouldnt hope to become the man he is because I am happy to be the man that my father raised me to be. Unfortunately its hard to find a woman who will have respect not only for herself but also for the man who will treat her as an equal as well as his queen. I wish you both many happy years of good health and awesome love.
Honestly they sleep around the first guy they meet and then have a bunch of kids and expect government to support them while they go out and party at a club and sleep around with yet more random men. I think women should only have sex in marriage.
And here is a topic from another forum tell me what you think about it
Women, try this recipe for happy, healthy, well-adjusted kids:
1. Become a person of Character2. Carefully choose and court a man of Character3. Get married4. have intimacy5. Have children6. Stay married for the rest of your lives
As opposed to what normally happens today:
1. Meet an attractive person2. Date3. have intimacy (but not before the 3rd date—that would be slutty)4. Move in together5. Break up and move out6. Repeat steps 1-3 at least 8 times, 1-5 at least twice.7. Finally meet “Mr. Right"8. have intimacy. Lots of intimacy.9. Move in together.10. Get married so you can have kids11. Have a kid, maybe two12. Realize you have married a no-good bum and divorce13. Work lots of hours at Wal-Mart trying to support your children14. Complain openly and often about the plight of single moms, prompting your friends to give you tons of self-indulgent pity.15. have intimacy. Lots of intimacy.16. Visit your grown children Sunday’s at the prison
men expect a woman who:has a full time jobdoes all of the cleaningdoes all of the cookinggives in to any sexual whim, at any timewill listen to him bitch relentlessly about trivial things without saying a wordnever complainshas no friendsgoes no where but the grocery storetells him how sexy and wonderful he is even though he sits on his fat ass watching whatever sport is on HDTV digging in his nasty ass, stenching up the living room with his cesspool gasessays nothing when he gets drunk and pisses, shits or vomits everywheresays nothing when he leaves her alone at home to go hang out with his friends
yes, feminism is fucked up but this modern porn-watching misogynistic masculinism is down right nauseating. just one bullet and one gun will do for me, you low life douche bags that think women are here solely to pleasure you while you use them up, abuse them and throw them out like old dish water.....absolutely disgusting "examples" you are. How about being a model for good behavior instead of expecting women to be better than you are, you sorry sacks of parasitically infested pig shit.
Quoting: Anonymous Coward 9285070
I'm a 43 yr old man and I agree 100%. The MAN is SUPPOSED to be the leader, protector, lover and life giver to his family. Buying the kids an XBOX and modern warfare, the wife a computer and missing the leader, life giver part with an occasional lover part isn't going to get it. What woman with a half a brain would follow the sports obsessed "man" of today? Where is the wisdom and leadership that guides the family through a happy healthy prosperous life? The men are supposed to be the strong ones being less emotional and more equipted to fight the mental temptations and other person attempts to steer things off track that we all deal with.The protector. If it weren't all orchestrated I would blame the average ignorant man more; ignorance is better than foolishness though. I'd rather not know than know and still do the wrong thing. The ostrich in the sand.
|
{
"pile_set_name": "Pile-CC"
}
|
The following disclosure relates generally to integrated circuit (IC) devices, and to methods and apparatus for the design and fabrication of IC devices.
As technology progresses and IC devices include smaller dimensions and increased feature density. As technology nodes shrink, challenges are raised for example, mismatch of device performance becomes more critical. However, for relatively larger devices typically required in system-on-a-chip (SOC), analog, digital signal processing (DSP) and radio frequency (RF) applications, it may be difficult to provide adequate matching of large devices in an IC. These device mismatch issues may arise from the replacement or gate-last methodology employed to provide metal gate technology. The gate-last methodology typically requires additional chemical mechanical processing (CMP) steps. These CMP processes can create differences in gate heights due to loading effects. These loading effects are often exacerbated by the use of large devices (e.g., in concert with smaller features). For example, CMP dishing can result which may result in metal work-function shifts and mismatch degradation of the IC.
Thus, what is needed is an improved manner of circuit design, fabrication and implementation for gate last processes of ICs including differently sized devices.
|
{
"pile_set_name": "USPTO Backgrounds"
}
|
/*
* This file is part of ACADO Toolkit.
*
* ACADO Toolkit -- A Toolkit for Automatic Control and Dynamic Optimization.
* Copyright (C) 2008-2014 by Boris Houska, Hans Joachim Ferreau,
* Milan Vukov, Rien Quirynen, KU Leuven.
* Developed within the Optimization in Engineering Center (OPTEC)
* under supervision of Moritz Diehl. All rights reserved.
*
* ACADO Toolkit is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 3 of the License, or (at your option) any later version.
*
* ACADO Toolkit is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with ACADO Toolkit; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*
*/
/**
* \file include/acado/integrator/radau_IIA3_export.hpp
* \author Rien Quirynen
* \date 2012
*/
#ifndef ACADO_TOOLKIT_RADAU_IIA3_EXPORT_HPP
#define ACADO_TOOLKIT_RADAU_IIA3_EXPORT_HPP
#include <acado/code_generation/integrators/irk_export.hpp>
BEGIN_NAMESPACE_ACADO
/**
* \brief Allows to export a tailored Radau IIA method of order 3 for fast model predictive control.
*
* \ingroup NumericalAlgorithms
*
* The class RadauIIA3Export allows to export a tailored Radau IIA method of order 3
* for fast model predictive control.
*
* \author Rien Quirynen
*/
class RadauIIA3Export : public ImplicitRungeKuttaExport
{
//
// PUBLIC MEMBER FUNCTIONS:
//
private:
/** Default constructor.
*
* @param[in] _userInteraction Pointer to corresponding user interface.
* @param[in] _commonHeaderName Name of common header file to be included.
*/
RadauIIA3Export( UserInteraction* _userInteraction = 0,
const std::string& _commonHeaderName = ""
);
/** Copy constructor (deep copy).
*
* @param[in] arg Right-hand side object.
*/
RadauIIA3Export( const RadauIIA3Export& arg
);
/** Destructor.
*/
virtual ~RadauIIA3Export( );
protected:
};
IntegratorExport* createRadauIIA3Export( UserInteraction* _userInteraction,
const std::string &_commonHeaderName);
CLOSE_NAMESPACE_ACADO
#endif // ACADO_TOOLKIT_RADAU_IIA3_EXPORT_HPP
// end of file.
|
{
"pile_set_name": "Github"
}
|
Trees (comics)
Trees is a science fiction comic book series by Warren Ellis and Jason Howard, published by American company Image Comics. The first issue was published May 28, 2014. The narrative begins ten years after the arrival of massive and silent alien presences who stand on the surface of the earth like the "Trees" of the title, not moving and seeming to take no account of human life and society. While a high concept science fiction story, the series also concerns itself with a cross-section of social and cultural issues as experienced by the characters, including police states, feminism, economic disparity, and transgender identity.
A second series titled Trees: Three Fates was published starting in September 2019. These issues were originally intended to be published as issues 15-19 of volume 1.
Plot
The narrative is divided into several points of view, all centered on the landing site of one of the Trees. Such locations include Rio de Janeiro, Mogadishu, New York City, "The City of Shu", Cefalù, and Spitsbergen. The individual stories, while featuring the Tree sites as settings, having varying degrees of explicit storytelling related to the Trees themselves.
The first volume, In Shadows, divides attention between an Italian woman involved reluctantly with a group of neo-fascists, an African leader hoping to use the Trees as a source of military leverage over neighboring nations, and a young Chinese artist from rural farmland joining an eclectic urban art collective. Finally, as a sort of core narrative, a science team researching a Tree in Norway finds mysterious black flowers growing near the base of the object, culminating in unexpected activity from the seemingly dormant Trees.
The second volume Two Forests, also splits attention between narratives, primarily between a newly christened Mayor of New York City who has a personal subversive plan to take revenge on the city's establishment that nearly cost him his life when the Trees first touched down, and secondly, the sole survivor of the Norway science expedition from the first volume is tasked by the British government to follow up on leads that the mysterious black flowers could be appearing at another Tree landing site.
The third volume Three Fates focuses on Klara Voranova, a police sergeant in the small Russian town of Toska. A murdered body found at the base of a Tree sets off an investigation into the forces and corruption that control the isolated town. At the same time, a ghost from Klara's past gives some clues to the purpose of the Trees.
Reception
The series has been positively reviewed.
TV Adaptation
In 2016, Tom Hardy and NBCUniversal announced a television series adaptation is in early development.
Collected editions
References
Category:Comics by Warren Ellis
Category:Image Comics titles
Category:Science fiction comics
|
{
"pile_set_name": "Wikipedia (en)"
}
|
Story highlights Liu has spent his life fighting for freedom of speech and human rights in China
He was awarded the Nobel Peace Prize but was unable to accept as he was in jail
Beijing (CNN) Despite being one of China's most famous political dissidents, Liu Xiaobo has rarely struck those who know him as a firebrand.
His mild manners and gentle voice belie his conviction for his cause -- improving human rights in China.
"I feel that, in a dictatorship, if you want to be a person with dignity, if you want to be an honest person, you must fight for human rights and fight for freedom of speech," the writer and activist said in an interview in 2007. "Going to prison is part of that, and I have nothing to complain about."
As news spread Monday that Liu had been diagnosed with late-stage liver cancer in prison and granted medical parole, many of his friends and supporters said they feared the 61-year-old dissident was close to death and risked being made into a martyr by the Communist authorities.
"Whether it was negligence or political murder, they have committed an unprecedented crime as no other government of the world has ever seen a Nobel Peace Prize laureate die in its custody," said Hu Jia, a leading Chinese human rights activist who has known Liu's wife for years and has served prison terms for his own advocacy.
Read More
|
{
"pile_set_name": "OpenWebText2"
}
|
Photoset with 1 note
A kitchen buffet converted from an old chest of drawers.
|
{
"pile_set_name": "OpenWebText2"
}
|
Mazraeh-ye Hasanabadu
Mazraeh-ye Hasanabadu (, also Romanized as Mazra‘eh-ye Ḩasanābādū) is a village in Qohab-e Rastaq Rural District, Amirabad District, Damghan County, Semnan Province, Iran. At the 2006 census, its existence was noted, but its population was not reported.
References
Category:Populated places in Damghan County
|
{
"pile_set_name": "Wikipedia (en)"
}
|
e units digit of r?
9
Let u(x) = -x - 8. Let n be u(12). Let y be (-1)/(n/(-7) + -3). Suppose 0 = k - 1 - y. What is the units digit of k?
8
Let s(i) = 2*i + 4. Let h be s(0). Suppose 0 = 2*v - h, v - 1 - 9 = -2*z. Suppose -2*d + 4*r + 2 = 0, 2*d = -z*r + 2*r + 20. What is the units digit of d?
7
Suppose 0 = -4*k - h + 2580, 4*k + 4*h - 2592 = 6*h. What is the units digit of k?
6
Let k(h) = h**2 + 0*h**2 + 13 + 3*h**2 - 6 + 8*h. Let r(p) = -p**2. Let y(l) = -k(l) - 3*r(l). What is the units digit of y(-6)?
5
Let t(q) = -q**2 - 8*q - 7. Let f be t(-7). Suppose f = d + 2*d. Suppose -g - o + 37 = 10, -3*g + 4*o + 109 = d. What is the units digit of g?
1
Suppose -4*i - 2*z + 92 = -3*i, 4*i - 344 = 4*z. Let v = -8 + i. What is the units digit of v?
0
Let u(y) = -8*y**2 + 16*y**2 - 7 + y**3 - 10*y**2. Let a be u(3). What is the units digit of 27*a - (6 - 9)?
7
Let k(c) = 6*c**2 - 3*c + 7. Let f be k(-4). Let g = f - 67. What is the units digit of g?
8
Let y(p) = p**3 - 13*p**2 - 14*p - 1. What is the units digit of y(15)?
9
Let b(c) = -67*c + 73. Let t(x) = 15*x - 18. Let o(a) = -2*b(a) - 9*t(a). Suppose -2*h = 4*v + v - 17, -5*h - 4*v = -51. What is the units digit of o(h)?
5
Suppose -j + 373 = 3*h, -4*j - 5*h + 1322 = -177. Suppose 19*g + j = 23*g. What is the units digit of g?
4
Let a(d) = 2*d**2 + 7*d - 40. What is the tens digit of a(5)?
4
Suppose 3*r - 637 = 5*g, 224 = 5*r + 4*g - 813. What is the units digit of r - ((-1)/(-2)*0 - 2)?
1
Suppose -i = 5, -4*v - 3*i - 339 = -60. Let x = 219 + v. What is the units digit of x?
3
Let g be -5*(1 + -3)/(-2). Let s = g + 14. What is the units digit of (6/s)/((-2)/(-57))?
9
Let g(r) = 3*r**3 + 4*r**2 - 19*r + 8. What is the units digit of g(7)?
0
Let r be (-22)/(-77) - (-38)/14. Let u be 16/4 - (r + 14). Let c(q) = -q**2 - 15*q + 16. What is the units digit of c(u)?
2
Let h(f) = f**2 + 5*f - 9. Let a be h(-8). Let u(x) be the third derivative of x**4/24 + 3*x**3 + 11*x**2. What is the tens digit of u(a)?
3
Let a = -66 + 99. Suppose 138 = -3*c + a. Let w = c + 66. What is the tens digit of w?
3
Let y = -114 - -172. What is the units digit of y?
8
Let c be 0 - -1 - (-1 - 25)/(-2). What is the units digit of (-1593)/c + 2/8?
3
Suppose -4*k = 1272 - 4332. What is the units digit of k?
5
Let l = 103 + -23. Let r = 659 - 423. Suppose -5*s - n + r = 0, 5*s - 4*n = l + 151. What is the tens digit of s?
4
Let q = 428 - 160. What is the tens digit of q?
6
Suppose 0 = -79*l + 59*l + 90420. What is the tens digit of l?
2
Let v(i) be the second derivative of -3*i + 0 - 1/2*i**3 - i**2. What is the tens digit of v(-5)?
1
Suppose 3*q = -2*h + 9086, 3*q = 13*h - 8*h + 9100. What is the hundreds digit of q?
0
Let f(w) = w**3 - 7*w**2 - 9*w + 6. Let a be f(8). What is the hundreds digit of 4/22 + (a - 5670/(-33))?
1
Let b(w) = w**3 + 4*w**2 + w + 1. Let a be b(-4). Let v = 33 - a. What is the tens digit of v?
3
Suppose -s = -5*s + 3*a + 166, 5*s - 4*a = 207. Let l = s - 14. Suppose d - l - 21 = 0. What is the units digit of d?
0
Let r(m) = -m**3 - 10*m**2 - 8*m + 12. Let w be r(-9). Suppose -a = -w*a + 156. What is the tens digit of a?
7
Let a be 27/(-18) + 3/2. Suppose a*y - y - 8 = 0. What is the tens digit of (-342)/12*y/6?
3
Suppose 4*t - 1970 - 990 = 0. What is the units digit of t?
0
Suppose -88*z + 86*z + 154 = 0. Suppose 3*j - 111 = -3*d, -5*j + 4*d + z = -90. What is the tens digit of j?
3
Let r(m) = -17*m**3 - 12*m - 10. What is the hundreds digit of r(-5)?
1
Suppose 0 = 3*l + 4*f + 5, 3 = 5*l - f + 2*f. What is the tens digit of l/((-4)/(-12)*(-6)/(-346))?
7
Let b(v) = v**2 + v + 4. Let l be b(-3). Suppose -3*f + l = -8*f. What is the tens digit of 41 - (0 + f + 1)?
4
Let h = -4214 + 7294. What is the tens digit of h?
8
Let b be (-1)/(-4 + 3)*0. Suppose 126 = 4*o - b*o + q, 2*q = 2*o - 58. What is the tens digit of o?
3
Let x(a) = a**3 + 15*a**2 - 18*a - 10. Let r be x(-16). Let d = 36 + r. What is the units digit of d?
8
Let z = -24 + 28. Suppose -5*y = 2*n - 299, z*y = 8*y + n - 238. What is the units digit of y?
9
Let w = -61 + 279. What is the units digit of w?
8
Let r(s) = -41*s + 115. What is the units digit of r(-10)?
5
Let g(z) = -z**3 + 5*z**2 - 4*z + 1. Suppose -11 = -5*w - 1. Let c be g(w). Suppose 2*b + 4*h + 69 - 197 = 0, -c*h + 15 = 0. What is the units digit of b?
8
Let z(t) be the second derivative of -4*t**3 - 35*t**2/2 - t. What is the units digit of z(-7)?
3
Let g = 420 - 220. What is the units digit of g/6 + 4/6?
4
Let y = -91 + 62. Let n = 21 + y. What is the units digit of (0 - 0) + n + 20?
2
Let m = 22 + -17. Suppose b + 4 = m*j, -j = 3*j - 4*b. What is the units digit of j?
1
Let u(f) = f**2 + 5*f - 3. Let k be u(-6). Suppose 4*d - m = 146, 0 = -k*d - 0*m + 3*m + 114. Let z = 89 - d. What is the units digit of z?
3
Let d(t) = -3*t + 4. Let a be d(-15). Let p = -33 + a. What is the units digit of p?
6
Let a be 34/(-3)*(-6 + 3). Suppose 3*q + 4*m = a, 3*q - 33 = -m - 2*m. What is the tens digit of 2/5 + 96/q?
1
Suppose 0 = -0*q - 5*q + 5. Let x be -33*(3/9 - q). Suppose 0 = 2*g - 0*c + 4*c - 26, g - c - x = 0. What is the tens digit of g?
1
Let q(f) = -564*f - 112. What is the units digit of q(-3)?
0
Let n(j) = 7*j + 5. Suppose g = -3*v + 14, 2*v - 5*g + 18 = 4*v. Let l be n(v). Suppose -5*p - 8 = -l. What is the units digit of p?
5
Let v = -35 + 75. What is the units digit of v?
0
What is the thousands digit of (-11)/77 + (17550/7 - -4)?
2
Let x = 7 + -2. Let r be 2 + x - (-1)/(-1). Let o = 5 + r. What is the units digit of o?
1
What is the units digit of (-1545)/(5 - (3 - (2 + -5)))?
5
Suppose -6 = -2*p + 5*m + 1, 3*m = 9. Suppose p*a = 15*a - 608. What is the tens digit of a?
5
Let t(f) = 4*f**2 - 46*f - 9. What is the tens digit of t(13)?
6
Suppose -4*i = i - 4*z + 18, 4*z = i + 10. What is the units digit of (i + (-2 - -27))/1?
3
Let v = 13 + -11. Suppose 560 = 9*y - 2*y. What is the tens digit of (y/(-30))/(v/(-33))?
4
Suppose 28*y - 22*y - 12 = 0. Let v(a) be the first derivative of 11*a**2/2 + a - 1. What is the units digit of v(y)?
3
Suppose 3*c + 5*c = -72. Let l(w) = -2*w + 11. What is the units digit of l(c)?
9
Let r(u) = -2*u**3 + 77*u - 151*u + u**2 + 70*u + 6. What is the units digit of r(-4)?
6
Suppose 15*d = 2198 + 8932. What is the hundreds digit of d?
7
Suppose 0*j - 5*x - 17 = 2*j, -4*j - 26 = 2*x. Let i = j - 1. Let g(d) = -3*d**2 - 25*d - 5. What is the tens digit of g(i)?
2
Let o = 35 - -278. What is the tens digit of o?
1
Let n = -198 + 101. Let j = -62 - n. What is the tens digit of j + 0/(2/2)?
3
Let u = -1409 - -4002. What is the units digit of u?
3
Let x(b) = 5*b**2 - 18*b - 4. What is the units digit of x(11)?
3
Let v be 8 - 0/(-3) - 2. Let g(w) = 2*w - 1. Let m be g(v). Let t(z) = z**3 - 11*z**2 + 16. What is the units digit of t(m)?
6
Suppose 2*k = 4*q + 4*k - 20, 2*k + 5 = q. Suppose 3*w = 4*b + 190, 10*w - 375 = q*w - 5*b. What is the tens digit of w?
7
Let l(t) = -t**2 - 4*t - 2. Let m be l(-3). Let c be (-10)/((-3)/(-6) - m). Let i = -7 + c. What is the units digit of i?
3
Suppose 4*g + 3920 = 12*b - 10*b, -2*b = -g - 3920. What is the units digit of b?
0
Let g = 826 - 140. What is the units digit of g?
6
Let p(o) = -o**3 + 5*o**2 + 7*o - 3. Let r be p(6). Let j(m) = -2 - 1 - 6 + r*m. What is the tens digit of j(14)?
3
Let c = 12 - 10. Suppose -c*v + 16 = g, 4*v = 5*g - 1 + 5. What is the units digit of v?
6
Suppose f + 24 = 5*f. What is the units digit of 29 + 2/f*0?
9
Let i(r) = 4*r**3 + 3*r**2 + 4*r + 3. Let q be i(-2). Let p(j) = -j. Let d be p(-5). What is the units digit of 97/d - (-10)/q?
9
Let m = 540 - 332. Let a = 297 - m. What is the units digit of a?
9
Suppose -5*k = -c - 3, k + 4*k - 5 = 0. Let u(x) = -2*x + 3. Let f be u(c). Let j(q) = -36*q. What is the units digit of j(f)?
6
Let n = -1300 - -1941. Suppose -t = -4*a + 3*t + 532, -5*a + n = t. What is the hundreds digit of a?
1
Let t = 65 - 35. Let i = 39 + -33. Suppose r = i*r - t. What is the units digit of r?
6
Suppose 0 = r - 3*o + 5, -4*r + 0*o + 5*o = -1. Suppose 8 = -r*n + 6*n. What is the units digit of n?
4
Let c = -12 - -17. Suppose -4*d + 164 = w, -d - c*w = -5*d + 140. What is the units digit of d?
0
Let m(f) = f**2 - 4*f - 4. Let a(c) = -c. Let v(b) = -3*a(b) + m(b). Let r
|
{
"pile_set_name": "DM Mathematics"
}
|
List of Kerala cities by area
The article lists major cities in Kerala based on the total area coming under the jurisdiction of city corporations/municipalities. This list is based on the 2011 Census of India.
**Note:-
The figures mentioned in the article are only based on the area coming under the jurisdiction of corporations & municipalities. It has no relation with the metro areas.
See also
List of cities in India by area
List of states and union territories of India by area
References
Category:Kerala geography-related lists
Category:Cities and towns in Kerala
Category:Lists by area
Category:Indian superlatives
|
{
"pile_set_name": "Wikipedia (en)"
}
|
describe 'less/universalSelector >>', ->
it '1', -> this.shouldBeOk()
it '2', -> this.shouldBeOk()
it '3', -> this.shouldBeOk()
it '4', -> this.shouldBeOk()
|
{
"pile_set_name": "Github"
}
|
tag:blogger.com,1999:blog-424126268865168124.post4325134086759365119..comments2011-03-19T16:56:01.978-07:00Comments on watisdisidontevn: PUT ME DOWN YOU SILLY HUMANwhatisthisidontevenhttp://www.blogger.com/profile/08163029923661348250noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-424126268865168124.post-72556434468258793502010-09-27T04:53:19.446-07:002010-09-27T04:53:19.446-07:00These are so badass! Always wanted to know what th...These are so badass! Always wanted to know what they were calledRatsRunThisTownhttps://www.blogger.com/profile/16985307299170223032noreply@blogger.comtag:blogger.com,1999:blog-424126268865168124.post-35222272058102892782010-09-26T19:06:06.393-07:002010-09-26T19:06:06.393-07:00i used to love catching lizards. brings back memor...i used to love catching lizards. brings back memories.snoobyhttps://www.blogger.com/profile/13911298485008670269noreply@blogger.comtag:blogger.com,1999:blog-424126268865168124.post-41656059506544918622010-09-26T17:21:41.887-07:002010-09-26T17:21:41.887-07:00Those lizards look so bad ass, always wanted one.Those lizards look so bad ass, always wanted one.Beavz0rhttps://www.blogger.com/profile/08608366215258897965noreply@blogger.comtag:blogger.com,1999:blog-424126268865168124.post-2470122898638944322010-09-26T17:09:50.744-07:002010-09-26T17:09:50.744-07:00THIS IS TRUE. HE HAS HORNS REGARDLESS.THIS IS TRUE. HE HAS HORNS REGARDLESS.whatisthisidontevenhttps://www.blogger.com/profile/08163029923661348250noreply@blogger.comtag:blogger.com,1999:blog-424126268865168124.post-48312126310586346452010-09-26T17:05:16.648-07:002010-09-26T17:05:16.648-07:00the thing is that the blood is from the lizard not...the thing is that the blood is from the lizard not the handgabranth17 - http://23f450bc.linkbucks.comhttps://www.blogger.com/profile/15250964611596841126noreply@blogger.com
|
{
"pile_set_name": "Pile-CC"
}
|
RALEIGH, N.C. — Throughout time, the health and wellbeing of humans has been fundamentally altered by dramatic changes in the species we interact with. Much of this change has been brought on by our own destructiveness. Now, it appears, we are beginning a new, better informed phase of our relationship with other species. Learn about… Read More >
During this holiday season, celebrate science with the NC Museum of Natural Sciences. Here are just a few ideas of what you could do … 1 • Dec 18 Naturalist Center, 1–4pm Learn about the natural world using our “magic” tables or peruse an extensive collection of hands-on specimens, including birds, mammals, reptiles, amphibians, fishes,… Read More >
RALEIGH, N.C. — A team of scientists conducting a recent biodiversity survey in the ancient church forests of Ethiopia made an unexpected discovery — a rather infamous ant species (Lepisiota canescens) displaying signs of supercolony formation. According to D. Magdalena Sorger, a post-doctoral researcher with the North Carolina Museum of Natural Sciences and a key… Read More >
New research from North Carolina State University, the Chinese Academy of Sciences and Linyi University has found evidence of original keratin and melanosome preservation in a 130-million-year-old Eoconfuciusornis specimen. The work extends the timeframe in which original molecules may preserve, and demonstrates the ability to distinguish between ancient microstructures in fossils. Eoconfuciusornis, crow-sized primitive birds… Read More >
RALEIGH — Bacteria. We kill them with pills, spray them with bleach, and scrape them off our teeth every morning. But they also help digest our food, keep our crops healthy, and apparently they live in fancy yogurt. So how do you know the good from the bad? Enter the amazing world of germs when… Read More >
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{
"pile_set_name": "Pile-CC"
}
|
Lessons Learned from Responding to Disruptive Breaches
February 16, 2017
9:15AM -10:00AM
Marriott Marquis | Yerba Buena 9
Mandiant has responded to an increasing amount of incidents where attackers destroyed critical business systems, leaked confidential data, held companies for ransom and taunted executives. Some attackers were motivated by money, some claimed to be retaliating for political purposes and others simply wanted to cause embarrassment.
|
{
"pile_set_name": "Pile-CC"
}
|
Let’s Celebrate Math Awareness Month this April
Yes, I know – it’s half way through Math Awareness Month already. I had some technical issues with the website which prevented me from adding any new posts and it took me ages to fix because I didn’t know what I was doing. The good news is that I now know how to migrate a blog to a new host! Woohoo! But I digress…
About Math Awareness Month
Image Source: IQ Internal Quarterly
Math Awareness Month began back in 1986. Its purpose was to bring attention to mathematics as a field of study and to convey the importance of mathematics in furthering discoveries, solving problems, and finding beauty in our world.
April marks a time to increase the understanding and appreciation of mathematics and statistics. Why? Both subjects play a significant role in addressing many real-world problems — internet security, sustainability, disease, climate change, the data deluge, and much more. Research in these and other areas is ongoing, revealing new results and applications every day in fields such as medicine, manufacturing, energy, biotechnology, and business. Mathematics and statistics are important drivers of innovation in our technological world, in which new systems and methodologies continue to become more complex. – Mathematics and Statistics Awareness Month
Despite it’s importance in the world we live in, Math is still a tricky subject for many students. It’s about time we change that.
Image Source: Cengage
Fun Math Puzzles for Math Awareness Month
As one of the essential 3 R’s for success, we need to help our children build a strong foundation in Math beginning as early as possible. For Math Awareness Month, we’d like to highlight some interesting Math resources to help children get into Math.
Puzzle of the Week is an open school challenge that G1’s school is involved in. You don’t have to be a part of it to access the challenges, though. There are a collection of interesting puzzles in the puzzle archive you can try out with full solutions, like these:
“Math exists everywhere across the globe – you can communicate with people all over the world using math as a ‘language’. Your math skills can be your passport to the forefront of almost any field of endeavor.” – Kenichiro Mogi, Japanese brain scientist and senior researcher of Sony Computer Science Laboratories
You have to sign up for this one, too, but it’s free. They also have some sample math puzzles you can try out, like this one:
For a more involved challenge, you can try this one. Entry to 2017 is over but you can still attempt the problem for the fun of it. Just in case you’re interested in the competition, keep a bookmark on this page for the 2018 challenge.
Moody’s Mega Math (M3) Challenge is a mathematical modeling contest for high school juniors and seniors. Through participation, students experience what it’s like to work as a team to tackle a real-world problem under time and resource constraints, akin to those faced by professional mathematicians working in industry. The Challenge is sponsored by The Moody’s Foundation and organized by the Society for Industrial and Applied Mathematics (SIAM) and awards $150,000 in scholarships each year.
The Challenge is entirely Internet-based with no registration or participation fees.
DR SHEN-LI LEE, author of “Brainchild: Secrets to Unlocking Your Child’s Potential”, is best known for her parenting website, figur8.net. Formally trained in dentistry, Lee found her calling when she discovered the challenge in seeking consolidated resources for raising a “wholesome child” in Malaysia. Garnering more than 20,000 visitors every month, figur8.net is a chronicle of Lee’s experience in raising a child who is self-motivated to excellence by nurturing the heart, mind and body. Read More…
|
{
"pile_set_name": "Pile-CC"
}
|
INTRODUCTION
============
*Helicobacter pylori* is regarded as the most important pathogen in the development of gastric cancer ([@B1], [@B2]). According to the hypothesis of Correa, infection with *H. pylori* causes chronic atrophic gastritis, intestinal metaplasia, dysplasia, and gastric cancer in sequence ([@B3]). Based on previous studies, the elimination of *H. pylori* is considered the most promising strategy for the prevention of gastric cancer and is recommended in current guidelines ([@B4], [@B5], [@B6]). However, there have been conflicting results, especially in patients with high-risk lesions. Some studies have indicated that the beneficial effects of *H. pylori* eradication are limited to patients without preneoplastic lesions ([@B7]). However, other studies have suggested that the prophylactic effect is also valid in individuals with neoplastic or preneoplastic lesions ([@B8], [@B9]).
Currently, endoscopic resection, including endoscopic mucosal resection (EMR) or endoscopic submucosal dissection (ESD), is the most widely accepted treatment modality in a specific subset of patients for the treatment of early gastric cancer (EGC) in East Asia ([@B1], [@B2]). This procedure can preserve nearly the entire gastric mucosa. Therefore, metachronous recurrence could develop in the abnormal background mucosa. However, data with regard to the prophylactic effect of *H. pylori* eradication after endoscopic resection of EGC remain unclear. Thus, a meta-analysis was conducted to assess the effect of *H. pylori* eradication on the development of metachronous gastric cancer after endoscopic resection of EGC.
MATERIALS AND METHODS
=====================
Literature search
-----------------
MEDLINE (through PubMed), EMBASE, and the Cochrane Central Register of Controlled Trials (CENTRAL) in the Cochrane Library were searched using common keywords related to *H. pylori* eradication after endoscopic resection of EGC in the development of metachronous gastric cancer (from inception to July 2014). Medical Subject Headings (MeSH) were used because all 3 databases permit searches using MeSH terminology. The keywords included \'*Helicobacter*\' and \'metachronous neoplasms\' using Boolean operators. Only publications on human subjects were sought, and the bibliographies of relevant articles were also reviewed to identify additional studies. The language of the publications was not restricted.
Selection criteria
------------------
We included randomized or non-randomized studies that met the following criteria: 1) the study was designed to evaluate the occurrence of metachronous gastric cancer after endoscopic resection of EGC in the target or control group, or 2) the study included a group that was given medicine for the eradication of *H. pylori* and a comparison group that was given placebo or no antibiotics. The exclusion criteria were as follows: 1) incomplete data, 2) review articles, or 3) abstract-only studies.
Selection of relevant studies
-----------------------------
Two of the authors (C.S.B. and G.H.B.) independently evaluated the eligibility of all studies retrieved from the databases based on the predetermined selection criteria. The abstracts of all identified studies were reviewed to exclude irrelevant articles. Full-text reviews were performed to determine whether the inclusion criteria were satisfied by the remaining studies. Disagreements between the two evaluators were resolved by discussion or by consultation with a third author (D.J.K.).
Assessment of methodological quality
------------------------------------
The methodological quality of the enrolled studies was assessed using the Risk of Bias table (RoB) for randomized studies and the Newcastle-Ottawa Scale (NOS) for non-randomized studies. The RoB was assessed as described in the Cochrane handbook by recording the method used to generate the randomization sequence, allocation concealment, the determination of whether blinding was implemented for participants or staff, and whether there was evidence of selective reporting of the outcomes ([@B10]). Review Manager version 5.3.3 (Revman for Windows 7, the Nordic Cochrane Centre, Copenhagen, Denmark) was used to generate the RoB table. The NOS is categorized into three parameters: the selection of the study population, the comparability of the groups, and the ascertainment of the exposure or outcome. Each parameter consists of subcategorized questions: selection (n=4), comparability (n=1), and exposure or outcome (n=3) (11, 12). Stars awarded for each item serve as a quick visual assessment for the methodological quality of the studies. A study can be awarded a maximum of nine stars, which indicates the highest quality. Two of the authors (C.S.B. and G. H.B.) independently evaluated the methodological quality of all studies, and any disagreements between the two evaluators were resolved by discussion or by consultation with a third author (D.J.K.). Subgroup analyses were performed according to the results of the methodological quality assessment.
Primary and modifier-based analyses
-----------------------------------
We investigated the efficacy of *H. pylori* eradication on the development of metachronous gastric cancer after endoscopic resection of EGC. Efficacy was defined as non-occurrence of metachronous gastric cancer (non-development of new gastric cancer at a previously uninvolved site in the stomach) in the follow-up endoscopic examinations. We also performed subgroup analyses based on the study design (randomized/non-randomized/non-randomized, prospective/non-randomized, retrospective studies), study setting (multicenter vs. single center studies), location of the studies (Korea vs. Japan), the definition of metachronous recurrence, and the methodological quality of the enrolled studies. In randomized studies ([@B9], [@B13]), which enabled both intention-to-treat (ITT) and per-protocol (PP) analysis, a meta-analysis based on the ITT analysis was performed, whenever possible. However, a separate meta-analysis was also performed, and both a cumulative analysis and a one-study-removed analysis were performed.
Statistics
----------
Comprehensive Meta-Analysis (CMA) software (version 2.2.064, Biostat; Borenstein M, Hedges L, Higgins J and Rothstein H. Englewood, NJ, USA) was used for this meta-analysis. We calculated the RRs with 95% confidence intervals (CIs) using 2×2 tables based on ITT analysis, and whenever possible, from the original articles in order to compare the efficacy of *H. pylori* eradication in the prevention of metachronous recurrence after endoscopic resection of EGC. Heterogeneity was determined using the *I^2^* test developed by Higgins, which measures the percentage of total variation across studies ([@B14]). *I^2^* was calculated as follows: *I^2^* (%)=100×(Q-df)/Q, where Q is Cochrane\'s heterogeneity statistic and df signifies the degree of freedom. Negative values for *I^2^* were set to zero, and an *I^2^* value over 50% was considered to be of substantial heterogeneity (range: 0%-100%) ([@B15]). Pooled-effect sizes with 95% confidence intervals (CIs) were calculated using a random effects model and the method of DerSimonian and Laird because of methodological heterogeneity ([@B16]). These results were confirmed by the *I^2^* test. A fixed effects model using the inverse variance-weighted (Woolf\'s) method was used in the subgroup analyses, including cumulative and one-study-removed analyses, based on the assumption of a common effect size shared by the studies within each subgroup ([@B17], [@B18]). Significance was set at *P*=0.05 in both models. Publication bias was evaluated using Begg\'s funnel plot, Egger\'s test of the intercept, Duval and Tweedie\'s trim and fill, and Begg and Mazumdar\'s rank correlation test ([@B19], [@B20], [@B21], [@B22], [@B23]).
Ethics statement
----------------
This study was approved by the institutional review board of Chuncheon Sacred Heart hospital (2015-14). Informed consent was waived by the board.
RESULTS
=======
Identification of relevant studies
----------------------------------
[Fig. 1](#F1){ref-type="fig"} illustrates a flow diagram of how relevant studies were identified. A total of 225 articles were identified by a search of 3 core databases and a manual search of relevant bibliographies. In all, 49 duplicate studies and an additional 128 studies were excluded during the initial screening through a review of the titles and abstracts. The full texts of the remaining 48 studies were then thoroughly reviewed. Among these studies, 38 were excluded from the final analysis. The reasons for study exclusion during the final review were as follows: review article (n=10), incomplete data (n=12), abstract-only article (n=14), letter (n=1), or case study (n=1). The remaining 10 studies (2 randomized and 8 non-randomized studies) were included in the final analysis.
Characteristics of studies
--------------------------
Within the 10 studies ([@B9], [@B13], [@B24], [@B25], [@B26], [@B27], [@B28], [@B29], [@B30], [@B31]), we identified a total of 5,914 patients with EGC or dysplasia. The clinical characteristics of the patients in the included studies are shown in [Tables 1](#T1){ref-type="table"} and [2](#T2){ref-type="table"}. The included studies were published between 1997 and 2014. Two randomized studies ([@B9], [@B13]) and 8 non-randomized studies, 2 prospective ([@B24], [@B26]) and 6 retrospective studies ([@B25], [@B27], [@B28], [@B29], [@B30], [@B31]) were included. All the studies were conducted in Asia, 5 studies ([@B13], [@B28], [@B29], [@B30], [@B31]) in Korea and 5 studies ([@B9], [@B24], [@B25], [@B26], [@B27]) in Japan. Four studies were conducted in a multicenter setting ([@B9], [@B25], [@B26], [@B27]), whereas the other studies were conducted in a single center setting ([@B13], [@B24], [@B28], [@B29], [@B30], [@B31]). All the included studies were written in English.
The age of enrolled patients ranged from 59 to 72 yr (median). Nearly all of the enrolled patients were diagnosed with EGC. However, 2 studies ([@B13], [@B29]) featured patients with EGC or dysplasia, and thus a separate analysis of only patients with EGC was impossible. To minimize the heterogeneity and to confirm the robustness of the main analysis, a subgroup analysis that excluded studies that included patients with dysplasia was performed. The endoscopic treatment method for EGC varied from strip biopsy and ablation to EMR or ESD. The duration of the follow-up ranged from 2 to 5 yr. Five studies ([@B13], [@B27], [@B29], [@B30], [@B31]) reported the definition of metachronous recurrence, whereas the remaining studies did not. Among the studies that reported the definition of metachronous recurrence, 3 studies ([@B27], [@B30], [@B31]) commonly defined the standard occurrence time as at least 1 yr after endoscopic resection of EGC, 1 study ([@B29]) defined the time course as at least 6 months after endoscopic resection of EGC, while the remaining 1 study ([@B13]) did not define the time standards. With respect to the *H. pylori* eradication regimen, the combination, dose, and duration varied. However, a proton-pump inhibitor with clarithromycin and amoxicillin for 1 or 2 weeks was the most frequently prescribed regimen ([Table 2](#T2){ref-type="table"}).
Efficacy of *H. pylori* eradication on the development of metachronous gastric cancer after endoscopic resection of EGC
-----------------------------------------------------------------------------------------------------------------------
The overall efficacy of *H. pylori* eradication on the development of metachronous gastric cancer after endoscopic resection of EGC showed a RR of 0.467 (95% CI: 0.362-0.602, *P*\<0.001) in a random effect model-based meta-analysis of 10 studies ([Fig. 2](#F2){ref-type="fig"}). According to the methodological quality assessment of the randomized studies ([@B9], [@B13]), the risk of random sequence generation and allocation concealment was low in both of the studies. However, blinding was not accomplished (open-label studies) in either of the studies ([Fig. 3](#F3){ref-type="fig"}). In the non-randomized studies, the mean value of the awarded star was 7.375, 6 (2 studies), 7 (2 studies), 8 (3 studies), and 9 (1 study) ([Table 3](#T3){ref-type="table"}).
Subgroup meta-analysis
----------------------
The cumulative meta-analysis of the enrolled studies in the order of the year published showed a consistent result ([Appendix 1](#APP1){ref-type="app"}). A study by Naomi Uemura et al. ([@B24]) demonstrated a relatively low RR compared to other studies. However, the methodological quality of this study was the lowest among the included studies ([Table 3](#T3){ref-type="table"}) and this was the only study which did not prescribe a triple eradication regimen (omeprazole 20 mg/day with clarithromycin 400 mg/day for 2 weeks). Moreover, the definite follow-up duration was unclear (more than 3 yr and not exceeding 4 yr) ([Table 2](#T2){ref-type="table"}). The one-study-removed meta-analysis of the included studies in the order of the year published showed a consistent result and showed no specific outlier ([Appendix 2](#APP2){ref-type="app"}). Among the included studies, 2 studies were randomized trials ([@B9], [@B13]), which enabled both an ITT and a PP analysis. The primary analysis was based on the result of the ITT analysis. Thus, a separate meta-analysis based on the size effects from the PP analysis was performed. The overall efficacy of *H. pylori* eradication on the development of metachronous gastric cancer after endoscopic resection of EGC showed a RR of 0.464 (95% CI: 0.360-0.599, *P*\<0.001) in a random effect model-based meta-analysis of 10 studies ([Appendix 3](#APP3){ref-type="app"}), which was not different from the result based on the ITT analysis ([Fig. 2](#F2){ref-type="fig"}).
The subgroup analysis based on the study design showed consistent results ([Appendix 5](#APP5){ref-type="app"}, [7](#APP7){ref-type="app"}, and [8](#APP8){ref-type="app"}), except for the analysis of the non-randomized prospective studies ([Appendix 6](#APP6){ref-type="app"}). The subgroup analysis of the randomized studies showed a RR of 0.473 (95% CI: 0.277-0.809, *P*=0.006) ([Appendix 5](#APP5){ref-type="app"}), and the subgroup analysis of the non-randomized retrospective studies showed a RR of 0.463 (95% CI: 0.346-0.622, *P*\<0.001) ([Appendix 7](#APP7){ref-type="app"}). The subgroup analysis of all non-randomized studies (prospective and retrospective studies) showed a RR of 0.465 (95% CI: 0.348-0.621, *P*\<0.001) ([Appendix 8](#APP8){ref-type="app"}). However, the analysis of non-randomized prospective studies showed a RR of 0.511 (95% CI: 0.101-2.583, *P*=0.417), which is not statistically significant ([Appendix 6](#APP6){ref-type="app"}). However, non-randomized prospective studies, including the studies by Naomi Uemura et al. ([@B24]) and Akiko Shiotani et al. ([@B26]) showed the lowest methodological quality among the included studies ([Table 3](#T3){ref-type="table"}). In addition, a relatively small number of patients was evaluated in these studies ([Table 1](#T1){ref-type="table"}).
Among all of the included studies, 2 ([@B13], [@B29]) did not feature patients with only EGC but instead had a combined population with EGC or dysplasia (low grade or high grade). However, a subgroup analysis that excluded these studies that featured patients with dysplasia demonstrated a consistent result (RR: 0.422, 95% CI: 0.306-0.582, *P*\<0.001) ([Appendix 9](#APP9){ref-type="app"}).
Among the included studies, 3 studies ([@B13], [@B29], [@B30]) reported metachronous recurrence as not only metachronous cancer but also as metachronous dysplasia. However, a subgroup analysis that excluded these studies gave a consistent result (RR: 0.415, 95% CI: 0.287-0.599, *P*\<0.001) ([Appendix 10](#APP10){ref-type="app"}).
A subgroup analysis based on the study setting (multicenter vs. single center studies) also demonstrated consistent results (multicenter study: RR: 0.481, 95% CI: 0.321-0.721, *P*\<0.001; single center study: RR: 0.457, 95% CI: 0.330-0.634, *P*\<0.001) ([Appendix 11](#APP11){ref-type="app"} and [12](#APP12){ref-type="app"}).
Furthermore, a subgroup analysis based on where the studies were performed (Korea vs. Japan) showed consistent results (Japanese studies: RR: 0.465, 95% CI: 0.311-0.693, *P*\<0.001; Korean studies: RR: 0.468, 95% CI: 0.337-0.651, *P*\<0.001) ([Appendix 13](#APP13){ref-type="app"} and [14](#APP14){ref-type="app"}).
A subgroup analysis based on the definition of metachronous recurrence (studies that gave a definition/studies that did not give a definition/studies that did not define the time standard of at least 1 yr after endoscopic resection of EGC) showed consistent results (RR: 0.503, 95% CI: 0.360-0.702, *P*\<0.001/RR: 0.422, 95% CI: 0.285-0.624, *P*\<0.001/RR: 0.479, 95% CI: 0.304-0.755, *P*=0.002) ([Appendix 15](#APP15){ref-type="app"}, [16](#APP16){ref-type="app"}, and [17](#APP17){ref-type="app"}).
A subgroup analysis based on the methodological quality (among the non-randomized studies, defined as high quality by NOS \>7 vs. low quality for NOS ≤7) showed consistent results (RR: 0.503, 95% CI: 0.360-0.702, *P*\<0.001 / RR: 0.370, 95% CI: 0.209-0.656, *P*=0.001) ([Appendix 18](#APP18){ref-type="app"} and [19](#APP19){ref-type="app"}).
Publication bias
----------------
A funnel plot for the included studies is illustrated in [Fig. 4](#F4){ref-type="fig"} (including studies that comprised the ITT analysis) and in [Appendix 4](#APP4){ref-type="app"} (including studies that comprised the PP analysis). These plots show a symmetrical shape. In the publication bias analysis that consisted of studies included in the ITT analysis, Egger\'s regression test revealed that the intercept was -0.91 (95% CI: -2.37-0.55, *t*-value: 1.43, df: 8, *P*=0.09 (1-tailed) and *P*=0.19 \[2-tailed\]). A trim and fill analysis showed that no study was missed or trimmed. The rank correlation test indicated a Kendall\'s tau of -0.27 with a continuity correction (*P*=0.14 \[1-tailed\] and *P*=0.28 \[2-tailed\]).
In the analysis that consisted of the studies included in the PP analysis, Egger\'s regression test revealed that the intercept was -0.91 (95% CI: -2.37-0.55, t-value: 1.44, df: 8, P=0.09 \[1-tailed\] and P=0.19 \[2-tailed\]). A trim and fill analysis showed that no study was missed or trimmed. The rank correlation test indicated a Kendall\'s tau of -0.27 with a continuity correction (P= 0.14 \[1-tailed\] and P=0.28 \[2-tailed\]).
Overall, there was no evidence of publication bias in this analysis.
DISCUSSION
==========
According to this meta-analysis, *H. pylori* eradication after endoscopic resection of EGC reduced the occurrence of metachronous gastric cancer. This finding was confirmed by the subgroup analyses. This result is not consistent with the findings of some of the included studies ([@B13], [@B26], [@B27]).
In the study by Akiko shiotani et al. ([@B26]), the number of enrolled patients was relatively small, and the incidence of metachronous recurrence after *H. pylori* eradication was higher compared to that in previous Japanese studies (11.2%). Moreover, selection bias was suspected, and the methodological quality among the non-randomized studies was relatively low, although they were prospective in nature ([Table 3](#T3){ref-type="table"}). In the study by Maehata et al. ([@B27]), selection bias was suspected, and the metachronous recurrence after *H. pylori* eradication was also higher (8.5%). In the study by Choi et al. ([@B13]), patients with dysplasia were included in addition to patients with EGC. The time standard definition for metachronous recurrence was not indicated. Thus, metachronous tumors that recurred within 1 yr accounted for about half of all metachronous cancers. It is possible that these tumors were synchronous lesions that were missed at the initial examination. Moreover, after the rapid urease test and histologic examination, positivity by only 1 test indicated *H. pylori* infection, and false positive cases were suspected. These 3 studies commonly indicated that *H. pylori* eradication seemed to reduce the incidence of metachronous recurrence during the early follow-up period. However, the incidence increased after a long-term follow-up period, and there seems to be no prophylactic effect on the late metachronous recurrence of gastric cancer ([@B13], [@B26], [@B27]). However, the study that demonstrated the biggest effect size ([@B29]) showed a decreased incidence of metachronous recurrence in the eradication group. This was consistent with what was observed during the long-term follow-up period (median follow-up: 60 months, range: 24-137 months). The median time to metachronous recurrence was 18 months (range: 7-75 months) in this study.
In the present study, however, substantial methodological heterogeneity was observed among the included studies, which had a potential effect on the risk estimates. This phenomenon was evaluated by subgroup analyses for confirmation of the robustness of this meta-analysis. The most noticeable modifier was the study design. Non-randomized studies tend to exaggerate the effects of an intervention, and this type of study is known to have inherent bias ([@B32]). Our meta-analysis included non-randomized studies due to the lack of randomized studies relevant to this topic. However, we also included randomized studies because of the high-quality evidence typically presented in this type of study. This could be the cause of significant heterogeneity, although subgroup analyses revealed consistent results which were not different from those of the main analysis ([Appendix 5](#APP5){ref-type="app"}, [6](#APP6){ref-type="app"}, [7](#APP7){ref-type="app"}, and [8](#APP8){ref-type="app"}).
Another consideration involves the inclusion of dysplastic lesions. The majority of studies enrolled patients with EGC. However, 2 studies ([@B13], [@B29]) also enrolled patients with dysplasia in addition to the patients with EGC. Moreover, one study ([@B30]) enrolled only EGC patients but reported metachronous dysplasia in addition to metachronous cancer. These points were evaluated by subgroup analyses and showed results consistent with those of the main analysis ([Appendix 9](#APP9){ref-type="app"} and [10](#APP10){ref-type="app"}).
Considering the conflicting results regarding the durability of the effect of *H. pylori* eradication on the prevention of metachronous recurrence as stated above, the various follow-up duration times could result in bias. However, no established time span relevant to this topic exists that would minimize the bias. Therefore, a subgroup analysis was not performed due to the uncertain time standards between the long-term vs. the short-term follow-up times.
Another issue is the unclear definition of metachronous recurrence. Three studies ([@B27], [@B30], [@B31]) set the time standard as 1 yr (new carcinoma that develops in areas other than the site of the primary gastric cancer at least 1 yr after the endoscopic resection). One study set the time standard as 6 months ([@B29]). However, the other studies did not report definite time standards.
Other sources of heterogeneity could be uneven study populations (such as the inclusion of patients with a history of endoscopic resection), different diagnostic methods of *H. pylori* infection, and various eradication regimens among the studies. Although the *I^2^* test showed no heterogeneity, and subgroup analyses demonstrated consistent results, these factors could not be totally controlled for in this analysis.
This study is the meta-analysis of the effect of *H. pylori* eradication on the development of metachronous recurrence after endoscopic resection of EGC. The strength of this study is the rigorous literature search, although there is a lack of data from western countries. When possible, potential modifiers were detected within the articles, and subgroup analyses were performed to confirm the robustness of the results.
Despite the strengths, there are several limitations in the present study. First, a fundamental limitation exists with regard to the interpretation of the results. The risk of development of gastric cancer is known to dependent on the background mucosal inflammation or atrophy, even among patients with *H. pylori* infection ([@B25]). This was progressed to the \'point of no return\' theory, which means that only low-risk lesions without intestinal metaplasia or mucosal atrophy are reversible and that the prevention of gastric cancer is possible with *H. pylori* eradication ([@B7], [@B33]). However, conflicting results regarding this theory still continue to subsist ([@B9], [@B34]). In this meta-analysis, mucosal inflammation and atrophy were not measurable. Genetic or molecular biologic markers including CDX1, CDX2, or spasmolytic polypeptide-expressing metaplasia also was not measurable ([@B35], [@B36]).
The limitations described above could be a cause of heterogeneity and bias. Due to the lack of prospective or randomized studies on this topic, large-scale, well-organized, long-term follow-up studies are needed to confirm these findings. If the development of biomarkers reflects mucosal inflammation or atrophy, longer-term follow-up periods without invasive procedures might be preferred.
In conclusion, *H. pylori* eradication after endoscopic resection of EGC reduces the occurrence of metachronous gastric cancer.
**DISCLOSURE:** The authors have no potential conflicts of interest to disclose.
**AUTHOR CONTRIBUTION:** Conception and design of the study: Bang CS, Baik GH. Data collection, analysis, interpretation: Bang CS, Baik GH, Shin IS, Kim JB, Suk KT, Yoon JH, Kim YS, Kim DJ. Drafting: Bang CS. Revision of manuscript and approval of submission: all authors.
Cumulative meta-analysis of enrolled studies for the efficacy of *H. pylori* eradication for the development of metachronous recurrence after endoscopic resection of EGC. *H. pylori*, *Helicobacter pylori*; EGC, early gastric cancer. Diamond is the summary estimate from the pooled studies (Fixed effect model).
=======================================================================================================================================================================================================================================================================================================================
One study removed meta-analysis of enrolled studies for the efficacy of *H. pylori* eradication for the development of metachronous recurrence after endoscopic resection of EGC. *H. pylori*, *Helicobacter pylori*; EGC, early gastric cancer. Diamond is the summary estimate from the pooled studies (Fixed effect model).
==============================================================================================================================================================================================================================================================================================================================
Total efficacy of *H. pylori* eradication for the development of metachronous recurrence after endoscopic resection of EGC (including studies with PP analysis). *H. pylori*, *Helicobacter pylori*; EGC, early gastric cancer; PP, per-protocol. The size of each square is proportional to the study\'s weight. Diamond is the summary estimate from the pooled studies (random effect model).
================================================================================================================================================================================================================================================================================================================================================================================================
Funnel plot for publication bias (including studies with PP analysis). PP, per-protocol. Funnel plot of studies. The line in center is the natural logarithm of pooled RR, and 2 oblique lines are pseudo 95% confidence limits. RR: risk ratio.
================================================================================================================================================================================================================================================
Subgroup analysis of randomized studies. The size of each square is proportional to the study\'s weight. Diamond is the summary estimate from the pooled studies (fixed effect model).
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Subgroup analysis of non-randomized prospective studies. The size of each square is proportional to the study\'s weight. Diamond is the summary estimate from the pooled studies (fixed effect model).
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Subgroup analysis of non-randomized retrospective studies. The size of each square is proportional to the study\'s weight. Diamond is the summary estimate from the pooled studies (fixed effect model).
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Subgroup analysis of total non-randomized studies. The size of each square is proportional to the study\'s weight. Diamond is the summary estimate from the pooled studies (fixed effect model).
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Subgroup analysis excluding studies having patients with dysplasia. The size of each square is proportional to the study\'s weight. Diamond is the summary estimate from the pooled studies (fixed effect model).
=================================================================================================================================================================================================================
Subgroup analysis excluding studies having patients with metachronous dysplasia other than metachronous cancer. The size of each square is proportional to the study\'s weight. Diamond is the summary estimate from the pooled studies (fixed effect model).
=============================================================================================================================================================================================================================================================
Subgroup analysis of multicenter studies. The size of each square is proportional to the study\'s weight. Diamond is the summary estimate from the pooled studies (fixed effect model).
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Subgroup analysis of single center studies. The size of each square is proportional to the study\'s weight. Diamond is the summary estimate from the pooled studies (fixed effect model).
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Subgroup analysis of Japanese studies. The size of each square is proportional to the study\'s weight. Diamond is the summary estimate from the pooled studies (fixed effect model).
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Subgroup analysis of Korean studies. The size of each square is proportional to the study\'s weight. Diamond is the summary estimate from the pooled studies (fixed effect model).
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Subgroup analysis of studies having definition of metachronous recurrence. The size of each square is proportional to the study\'s weight. Diamond is the summary estimate from the pooled studies (fixed effect model).
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Subgroup analysis of studies having no definition of metachronous recurrence. The size of each square is proportional to the study\'s weight. Diamond is the summary estimate from the pooled studies (fixed effect model).
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Subgroup analysis of studies having definition of metachronous recurrence (new carcinoma developing in areas other than the site of primary gastric cancer at least 1 year after endoscopic resection of EGC). The size of each square is proportional to the study\'s weight. Diamond is the summary estimate from the pooled studies (fixed effect model).
============================================================================================================================================================================================================================================================================================================================================================
Subgroup analysis of high quality studies (among the non-randomized studies). The size of each square is proportional to the study\'s weight. Diamond is the summary estimate from the pooled studies (fixed effect model).
===========================================================================================================================================================================================================================
Subgroup analysis of low quality studies (among the non-randomized studies). The size of each square is proportional to the study\'s weight. Diamond is the summary estimate from the pooled studies (fixed effect model).
==========================================================================================================================================================================================================================
{#F1}
{#F2}
{#F3}
{#F4}
###### Clinical data of included studies
Studies Study design Total No. of patients (M/F) Age (eradication/non-eradication group) Disease Endoscopic treatment Duration of follow up Location, language
-------------------------------- -------------------------- ------------------------------- ----------------------------------------- ------------------ ------------------------------------- ---------------------------------- --------------------
Uemura et al., 1997 ([@B24]) Non-randomized trial (S) 132 (97/35) Mean 69 (44-85 yr ranged) EGC Endoscopic resection (strip biopsy) 3-4 yr (unclear) Japan (English)
Nakagawa et al., 2006 ([@B25]) Retrospective study (M) 2,825 EGC EMR Median 2 yr (0.5-12 yr) Japan (English)
Fukase et al., 2008 ([@B9]) Open-label RCT (M) 544 (ITT), 505 (PP) (386/119) Median 68/69 EGC Endoscopic resection All 3 yr Japan (English)
Shiotani et al., 2008 ([@B26]) Prospective study (M) 91 (82/18)^\*^ 66±8 EGC ESD Median 33 months Japan (English)
Maehata et al., 2012 ([@B27]) Retrospective study (M) 268 (194/74) Median 68/72 EGC Endoscopic resection Median 3 yr (1.1-11.1 yr) Japan (English)
Seo et al., 2013 ([@B28]) Retrospective study (S) 47 (61/13)^†^ Mean 61.92±11.07/62.08±12.55 EGC EMR, ESD Mean 27.2±18.7 months Korea (English)
Choi et al., 2014 ([@B13]) Open-label RCT (S) 901 (596/284)^‡^ Mean 59.8±8.2/61±8.2 EGC or dysplasia EMR, ESD, Ablation Median 3 yr (1.1-11.1 yr) Korea (English)
Bae et al., 2014 ([@B29]) Retrospective study (S) 667 (525/142) Median 62/64 EGC or dysplasia Endoscopic resection Median 60 months (24-137 months) Korea (English)
Kwon et al., 2014 ([@B30]) Retrospective study (S) 283 (190/93) Mean 61.1±9.2/60±7.3 EGC^§^ ESD Median 41 months Korea (English)
Kim et al., 2014 ([@B31]) Retrospective study (S) 156 (112/44) Median 59/64 EGC Endoscopic resection Median 4.3 yr (1.0-11.3 yr) Korea (English)
^\*^Included 9 *H. pylori* negative patients (Total 100 patients); ^†^A total of 74 patients were enrolled, and 47 of them were followed-up for more than 18 months; ^‡^A total of 901 patients were enrolled, but 21 patients were lost to follow-up; ^§^Metachronous recurrence was checked for not only EGC, but also dysplasia. S, single center study; M, multicenter study.
###### Clinical data of included studies (continued)
Studies *H. pylori* eradication group *H. pylori* non-eradication group Definition of metachronous recurrence Eradication regimen
-------------------------------- ------------------------------- ----------------------------------- --------------------------------------- --------------------- -------- ------------------------------------------------------------------------------------------------------
Uemura et al., 1997 ([@B24]) 0 65 6 67 No^\*^ OMP 20 mg 4 weeks, CM 400 mg 2 weeks → 2nd: OMP 20 mg, AMX 1,500 mg, MZ 500 mg 2 weeks
Nakagawa et al., 2006 ([@B25]) 8 356 129 2,469 No Mainly LANS 60 mg, CM 400 mg, AMX 1,500 mg 1 week^\*\*^
Fukase et al., 2008 ([@B9]) 9 272 (ITT), 255 (PP) 24 272 (ITT), 250 (PP) No LANS 60 mg, CM 400 mg, AMX 1,500 mg 1 week.
Shiotani et al., 2008 ([@B26]) 9 80 1 11 No (OMP 40 mg or LANS 60 mg or RABE 20 mg), CM 400 mg, AMX 1,500 mg 1 week → 2nd PPI, AMX, METRO 750 mg
Maehata et al., 2012 ([@B27]) 15 177 13 91 Yes^∥^ (OMP 40 mg or LANS 60 mg or RABE 20 mg), CM 400 mg, AMX 1,500 mg 1 week → 2nd PPI, AMX, METRO 250 mg
Seo et al., 2013 ([@B28]) 4 41 3 6 No (OMP 40 mg or LANS 60 mg or RABE 40 mg, ESOM 80 mg), CM 1,000 mg, AMX 2,000 mg 1 week
Choi et al., 2014 ([@B13]) 10 444 (ITT), 439 (PP) 17 457 (ITT), 441 (PP) Yes^†^ OMP 40 mg, CM 1,000 mg, AMX 2,000 mg 1 week
Bae et al., 2014 ([@B29]) 34 485 24 182 Yes^‡^ (OMP 60 mg or LANS 60 mg or PANTO 80 mg), CM 400 mg, AMX 1,500 mg 1-2 weeks
Kwon et al., 2014 ([@B30]) 18 214 13 69 Yes^§^ (OMP 40 mg or LANS 60 mg or RABE 40 mg), CM 400 mg, AMX 1,500 mg 1 week
Kim et al., 2014 ([@B31]) 2 49 16 107 Yes^¶^ (OMP 40 mg or RABE 20 mg or PANTO 80 mg), CM 1,000 mg, AMX 2,000 mg 1 week
^\*^Not defined. However, all the metachronous recurrence were developed after 12 months of endoscopic resection; ^†^New carcinoma occurring at another site in the stomach; ^‡^New carcinoma occurring after 6 months of endoscopic resection; ^§^New dysplasia or carcinoma (Vienna 3-5) developing in areas other than the site of primary gastric cancers at least 1 yr after the endoscopic resection; ^¶^Development of new gastric cancer at a previously uninvolved site in the stomach at least 1 yr after endoscopic resection; ^∥^New carcinoma developing in areas other than the site of primary gastric cancer at least 1 yr after the endoscopic resection; ^\*\*^Multicenter study. The regimen depended on the choice of each institution. The main regimen is described. ITT, intention-to-treat analysis; PP, per-protocol analysis; week; OMP, omeprazole; LANS, lansoprazole; RABE, rabeprazole; ESOM, esomeprazole; PANTO, pantoprazole; CM, clarithromycin; AMX, amoxicillin; METRO, metronidazole.
###### Methodological quality of included studies measured by Newcastle-Ottawa scale
Studies Selection Comparability Exposure or outcome Total
-------------------------------- ----------- --------------- --------------------- -------
Uemura et al., 1997 ([@B24]) ☆☆☆☆ ☆☆ ☆ 7
Nakagawa et al., 2006 ([@B25]) ☆☆☆☆ ☆ ☆☆ 7
Fukase et al., 2008 ([@B9]) ☆☆☆ ☆ ☆☆ 6
Shiotani et al., 2008 ([@B26]) ☆☆☆ ☆☆ ☆☆☆ 8
Maehata et al., 2012 ([@B27]) ☆☆☆ ☆☆ ☆ 6
Seo et al., 2013 ([@B28]) ☆☆☆☆ ☆ ☆☆☆ 8
Choi et al., 2014 ([@B13]) ☆☆☆☆ ☆☆ ☆☆☆ 9
Bae et al., 2014 ([@B29]) ☆☆☆☆ ☆ ☆☆☆ 8
|
{
"pile_set_name": "PubMed Central"
}
|
French garage mechanic jubilant at Le Vell acquittal
'It's a great day for all French garage mechanics,' said overalled French garage mechanic Jean-Paul Badiou from the forecourt of Dave's Cars, Bolton, clutching an oil-can and a glass of celebratory Cabernet Sauvignon.
'Over the last few weeks people have been looking at me askance when they collected their cars after the MOT,' existentialist Monsieur Badiou said, 'and all because of this Michael Le Vell who is neither French nor a real garage mechanic.'
A spokesman for The British Garage Mechanics Association said he was relieved at the not guilty verdict.
'A guilty verdict would have been a spanner in the works for all of us,' he said, 'and would probably have meant an increase in the cost of an MOT.'
|
{
"pile_set_name": "Pile-CC"
}
|
260 F.3d 1209 (10th Cir. 2001)
UNITED STATES OF AMERICA, Plaintiff - Appellee,v.EFRAIN CARO, Defendant - Appellant.
No. 99-4229
UNITED STATES COURT OF APPEALS TENTH CIRCUIT
August 9, 2001
Richard A. Hostetler, Law Office of Marks and Hostetler, Denver, Colorado, for Defendant-Appellant.
Paul M. Warner, United States Attorney, Barbara Bearnson and Wayne T. Dance, Assistant United States Attorneys, Salt Lake City, Utah, for Plaintiff-Appellee.
Before SEYMOUR, HENRY, and LUCERO, Circuit Judges.
ORDER ON REHEARING
1
On consideration of the petition for rehearing filed by Plaintiff-Appellee the United States of America, the court finds and concludes as follows:
2
The government argues that our opinion erred in concluding that New York v. Class, 475 U.S. 106 (1986), and United States v. Miller, 84 F.3d 1244 (10th Cir. 1996), which relied upon Class, control this case. It contends that the relevant holdings in Class and Miller were dicta, and that those cases were factually inapposite. However, because we accord great weight to the dicta of the Supreme Court, it was not error to rely upon dictum in Class in considering the applicability of Class and Miller to the facts before us. See Gaylor v. United States, 74 F.3d 214, 217 (10th Cir. 1996) ("[T]his court considers itself bound by Supreme Court dicta almost as firmly as by the Court's outright holdings . . . ."). Our opinion reasonably construed those cases.
3
The government also argues that our holding impermissibly considered Trooper Avery's "subjective" intent to examine a doorjamb VIN, because Trooper Avery's actions were objectively justifiable under Pennsylvania v. Mimms, 434 U.S. 106 (1977), Texas v. Brown, 460 U.S. 730 (1982), and Whren v. United States, 517 U.S. 806 (1996). According to the government, Trooper Avery had the authority under Mimms to order Mr. Caro out of his car. When Mr. Caro exited his car, its doorjamb was exposed to view, meaning Trooper Avery could legally view it under Brown. As a consequence, the government argues that under Whren, it is irrelevant that Trooper Avery intended to look for a doorjamb VIN when he asked Mr. Caro to exit his vehicle, as the order to exit was objectively permissible under Mimms.
4
This theory, which was not raised in the government's brief on appeal, is a more serious objection to our holding. In considering whether to grant rehearing on this basis, we have carefully reviewed the evidence presented in the case. Upon revisiting the videotape of the traffic stop, we discovered an obscure but highly relevant error in the sequence of facts that was agreed upon in the appellate briefs of both parties, repeated in the "Background" section of the panel opinion, and reasserted in the petition for rehearing.
5
According to all these statements of facts, Mr. Caro exited his car in response to Trooper Avery's request to view the doorjamb VIN, after Trooper Avery had already inspected the dashboard VIN. But the videotape of the traffic stop clearly shows that this was not the case. In the relevant segment of the tape, Trooper Avery walks to the driver's window and speaks to Mr. Caro, following which Mr. Caro exits the car. As he exits, Mr. Caro leaves the door open, but it swings shut on its own. Trooper Avery then inspects the VIN on the dashboard, comparing it to the registration papers in his hand. While he does this, Mr. Caro stands next to the car, immediately behind the driver's door. After Trooper Avery finishes inspecting the dashboard VIN, he takes several steps towards Mr. Caro and speaks to him briefly. Trooper Avery then opens the car door and bends over to examine the doorjamb. After looking around at the doorjamb, the interior of the vehicle, and the edge of the door, Trooper Avery closes the door and again speaks to Mr. Caro. Mr. Caro then opens the door and releases the trunk of the car, presumably in response to a request by Trooper Avery to search it.
6
If Mr. Caro was already standing outside a closed car door at the time Trooper Avery asked to inspect the doorjamb for a VIN, and if Trooper Avery opened that car door himself in order to effect that inspection, Mimms cannot have "provide[d] the legal justification for the officer's action." Whren, 517 U.S. at 813 (quoting Scott v. United States, 436 U.S. 128, 138 (1978)). This case therefore continues to be controlled by Class and Miller, and there is no need to reach the issue of any possible interplay between Mimms and Class that might pertain to the examination of a vehicle doorjamb in search of a VIN.
7
Accordingly, this panel orders that the petition for rehearing is DENIED.
|
{
"pile_set_name": "FreeLaw"
}
|
Characterization of lymphocyte function-associated antigen 1 (LFA-1)-deficient T cell lines: the alphaL and beta2 subunits are interdependent for cell surface expression.
The leukocyte, or beta2, integrins are heterodimeric cell surface molecules that share a common beta subunit, and have unique alpha subunits. LFA-1 is the predominant beta2 integrin on lymphocytes, and plays an important role in many lymphocyte functions; however, most studies of the cytoplasmic regions of LFA-1 have been performed in transfected epithelial cells, such as COS, in part because no lymphoid cell lines deficient in the LFA-1 alpha subunit have been described. To address structure-function studies of beta2 integrins in relevant cell types, two T lymphoblastoid cell clones that completely lack cell surface LFA-1, J-(beta2).7 and SK-(beta2).7, derived from Jurkat and SKW3, respectively, were prepared by chemical mutagenesis and selection. Biosynthetic labeling and immunoprecipitation showed that the J-(beta2).7 clone did not translate any LFA-1 alpha subunit protein, while the SK-(beta2).7 cells did not synthesize any beta2 subunit protein. Northern blot analysis of poly(A+) RNA from these cells revealed an absence of the corresponding mRNA in each case. By transfection analysis, only the alpha subunit reconstituted LFA-1 expression in the J-(beta2).7 cells, while only the beta subunit restored cell surface LFA-1 expression in the SK-(beta2).7 cells. Functional studies with the parental cell lines, the J-(beta2).7 and SK-(beta2).7 cells, and the transfectants showed that all binding of Jurkat and SKW3 cells to purified ICAM-1 is mediated by LFA-1, and the reconstituted LFA-1 expressed by the J-(beta2).7 and SK-(beta2).7 transfected cells is regulated normally.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
Sources | Medically Reviewed on 02/14/2020 Reviewed by Kathleen M. Zelman, MPH, RD, LD on February 14, 2020
IMAGES PROVIDED BY:
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7) Frank Bean/Uppercut Images
8) Foodcollection
9) Dorling Kinderley/Judd Pilossof/FoodPix
10) Getty
11) Sam Armstrong/Photographer’s Choice/Hans Bjurling
12) DAJ
13) Patrik Giardino/Taxi
14) Jo Sax/Stone+
15) Gentl and Hyers/FoodPix
16) Glowimages
17) Sian Irvine/Image Source/Getty
18) Brayden Knell/WebMD
19) Doring Kindersley/WebMD
20) Sian Kennedy/Photonica
21) Nino Mascardi/Photographer’s Choice
22) Kurtwilson/FoodPix
23) TGStock/Tim Graham Photo Library
24) Somos/Veer
REFERENCES:
Wansink, B. Mindless Eating: Why We Eat More Than We Think, Bantam Books, 2006.
Center for Science in the Public Interest: "New Year's Resolutions."
Framson, C. Journal of the American Dietetic Association, August 2009; vol 109: pp 1439-1444.
Consumer Reports: "6 Secrets of the Slim for Your Diet Plan."
News release, The Endocrine Society.
Kokkinos, A. The Journal of Clinical Endocrinology & Metabolism, published online Oct. 29, 2009.
Michael Breus, Founder of Soundsleep Solutions; author, Good Night: The Sleep Doctor's 4-Week Program to Better Sleep and Better Health.
Sivak, M. Obesity Review, August 2006; vol 7(3): pp 295-6.
Neal Barnard, MD, president, Physicians Committee for Responsible Medicine; adjunct associate professor of medicine, George Washington University School of Medicine.
Judith M. Lukaszuk, PhD, RD, assistant professor, School of Family, Consumer, and Nutrition Sciences, Northern Illinois University.
Elaine Magee,MPH, RD, author Food Synergy, 2008.
Major, G.C. American Journal of Clinical Nutrition, January 2007; vol 85: pp 54-59.
Lukaszuk, J.M. Journal of the American Dietetic Association, October 2007; vol 107: pp 1811-1814.
Ello-Martin, J.A. American Journal of Clinical Nutrition, June 2007; vol 85: pp 1465-1477.
Ledikwe, J.H. American Journal of Clinical Nutrition, May 2007; vol 85: pp 1212-1221.
Katcher, H.I. American Journal of Clinical Nutrition, January 2008; vol 87: pp 79-90.
Public Health – Idaho North Central District: "Make One Change to Lose 10 Pounds in a Year." Women, Infants & Children PDF.
USDA National Nutrient Database.
University of Nebraska, Nutrition Education Program: "Think What You Drink."
Carolyn O'Neil, MS, RD, co-author, The Dish on Eating Healthy and Being Fabulous.
Christine Gerbstadt, MD, MPH, RD, spokeswoman, American Dietetic Association.
Dawn Blatner-Jackson, MS, RD, spokeswoman, American Dietetic Association.
2005 U.S. Dietary Guidelines.
American Heart Association.
UCLA Student Nutrition Awareness Campaign: "Calories Count."
Newby, P.K. The American Journal of Clinical Nutrition, June 2005; vol 81(6): pp 1267-74.
Centers for Disease Control and Prevention. "Physical Activity for a Healthy Weight."
|
{
"pile_set_name": "OpenWebText2"
}
|
Q:
Entries tag search:fieldtype=""
According to the EE doc, within a channel entries tag you can search a grid field as long as the field color is set to "yes" for Include in search.
I have bot he Grid field and the individual column set to yes, but don't get results when I definitely should.
In the example below, there is a Grid titled "product_application" and one of 3 fields with the title "partno".
{exp:channel:entries channel="models" search:partno="={segment_3}"}
<p>{title}-</p>
{/exp:channel:entries}
Has anyone run into difficulties with this?
Russ
A:
To use search parameter in Grid you have to add search parameter in grid fieldtype not in Channel entries tag. You can get more information from below example. https://docs.expressionengine.com/latest/fieldtypes/grid.html#searchcolumn_name
{grid_field search:partno="search_value"}
{grid_field:your_grid_field}
{/grid_field}
I hope this will works for you. Thanks!
|
{
"pile_set_name": "StackExchange"
}
|
FILED
NOT FOR PUBLICATION
JUN 22 2018
UNITED STATES COURT OF APPEALS MOLLY C. DWYER, CLERK
U.S. COURT OF APPEALS
FOR THE NINTH CIRCUIT
CLARK FRATUS; KARLA FRATUS, No. 16-16985
Plaintiffs-Appellants, D.C. No. 3:14-cv-05533-MEJ
v.
MEMORANDUM*
COUNTY OF CONTRA COSTA;
CATHERINE KUTSURIS; JASON
CRAPO, Building Official; MICHAEL
SILVA; GANO THOMAS, Building
Official; ROBERT ERICKSON, Building
Inspector; ARUNA BHAT, Deputy
Director; KEITH DENISON,
Defendants-Appellees.
Appeal from the United States District Court
for the Northern District of California
Maria-Elena James, Magistrate Judge, Presiding
Argued and Submitted December 7, 2017
San Francisco, California
Before: SCHROEDER and BEA, Circuit Judges, and ELLIS,** District Judge.
*
This disposition is not appropriate for publication and is not precedent
except as provided by Ninth Circuit Rule 36-3.
**
The Honorable Sara Lee Ellis, United States District Judge for the
Northern District of Illinois, sitting by designation.
This appeal involves a lengthy history of administrative and legal battles
stemming from Contra Costa County’s enforcement of its zoning and building
code to conclude that the second living units on the properties of Clark and Karla
Fratus (“Plaintiffs”) were unlawful. Plaintiffs were eventually successful in state
court in overturning the administrative decision that found their properties
unlawful, and they then filed an action in federal court claiming violation of federal
and state laws in connection with the original administrative rulings. This court
affirmed the district court’s dismissal of that action at summary judgment. See
Fratus v. Contra Costa Cty. Bd. of Supervisors, 599 F. App’x 707 (9th Cir. 2015)
(Fratus I).
Three days before the district court entered judgment in the first federal
action, the County denied the Plaintiffs’ application for permits for their second
units. The Plaintiffs subsequently brought a second action, alleging federal law
claims of First Amendment retaliation and violations of substantive due process
and equal protection as well as several state law claims. Plaintiffs now appeal the
district court’s dismissal of that action at summary judgment. The district court
granted the County summary judgment with respect to the substantive due process
and equal protection claims on the ground that they were barred by res judicata,
because the Plaintiffs could have brought this action before the judgment was
2
entered in the first case. The district court granted summary judgment to the
County with respect to the retaliation claim for lack of evidence. After granting
summary judgment on all of the federal law claims, the district court declined to
exercise supplemental jurisdiction over the state law claims.
We review de novo the district court’s decision to grant summary judgment.
Clark v. Bear Stearns & Co., 966 F.2d 1318, 1320 (9th Cir. 1992). We also review
de novo matters of res judicata. Id. Finding no error, we affirm.
Plaintiffs argue res judicata does not apply because this complaint is based
on different events, including the denial of a permit and a loan as well as the failure
to reverse penalties on a delinquent tax bill. The County’s actions, however, were
based upon the same interpretation of the relevant code provisions and applied to
the same properties. The nucleus of facts is the same; therefore, the Plaintiffs’
claims based on those facts are barred by res judicata. See ProShipLine Inc. v.
Aspen Infrastructures Ltd., 609 F.3d 960, 968 (9th Cir. 2010) (noting that, among
the factors we examine in determining whether there is an “identity of claims” for
res judicata to apply, “[r]eliance on the transactional nucleus element is especially
appropriate because the element is outcome determinative”) (citations and internal
quotation marks omitted).
3
The Plaintiffs further contend that their challenges to the County’s conduct
could not have been brought in the first action because it came later than the
conduct in the first action. The relevant standard is whether the claims “were
raised or could have been raised in the prior action.” Owens v. Kaiser Found.
Health Plan, Inc., 244 F.3d 708, 713 (9th Cir. 2001) (quoting W. Radio Servs. Co.
v. Glickman, 123 F.3d 1189, 1192 (9th Cir. 1997)). A review of the record shows
that they either were or could have been raised. The Plaintiffs raised their failure-
to-train claim in Fratus I. The Plaintiffs also disputed in Fratus I the County’s
listing of their properties as having only one living space each, which was the basis
for the bank’s loan denial in this case. The Plaintiffs could have raised in Fratus I
the County’s failure to reverse penalties, which occurred as early as June 2012,
several months before judgment was entered in Fratus I. Finally, the district court
did not enter judgment in Fratus I until three days after the challenged permit
denial, and the court actually held a hearing in Fratus I two days after the denial.
The denial could have been raised as well.
Accordingly, the district court correctly ruled that the Plaintiffs’ federal law
claims are barred by res judicata. The court did not abuse its discretion in
declining to exercise supplemental jurisdiction over the state law claims.
4
Plaintiffs unopposed motion for judicial notice is GRANTED. The
judgment of the District Court is AFFIRMED.
5
|
{
"pile_set_name": "FreeLaw"
}
|
Cutaneous angiosarcoma complicating morbid obesity.
Herein, we report a case of cutaneous angiosarcoma in a 35-year-old, morbidly obese woman. The tumor arose in the most dependent portion of the lower abdominal panniculus and showed typical changes of chronic lymphedema. The patient underwent a radical resection of her lower abdominal wall panniculus, which showed a multicentric, high-grade angiosarcoma with bilateral superficial inguinal lymph node metastases. Histologically, conventional vasoformative areas were admixed with poorly differentiated sheets of spindle and epithelioid cells. Factor VIII was focally positive (membranous), whereas CD31 showed robust, diffuse positivity (membranous and cytoplasmic). The initial margins of resection were negative, and no follow-up radiation or chemotherapy was given. Following a recurrence at the previous excision site, the patient died 7 months after the surgery. Postmortem examination revealed a widely metastatic tumor that involved multiple organ systems. We believe this is the second report of cutaneous angiosarcoma occurring in a chronically lymphedematous abdominal panniculus due to morbid obesity.
|
{
"pile_set_name": "PubMed Abstracts"
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|
Q:
how to build a xml response in twiml in ruby with comments
Xml response like below:
<?xml version="1.0" encoding="UTF-8"?>
<Response>
<!--my error message-->
<Reject/>
</Response>
enter code here:
currently i am using ruby to build response
xml.Response do |r|
r.Reject
end.text
I need a comment before reject verb..Any one help?
A:
Twilio Evangelist here.
Twilio's Ruby helper library is built on Builder (see here). Therefore, you can use the standard Builder approach:
xml.Response do |r|
r.comment! "This is a comment!"
r.Reject
end.text
This will generate:
<?xml version="1.0" encoding="UTF-8"?>
<Response>
<!--This is a comment!-->
<Reject/>
</Response>
Hope this helps!
|
{
"pile_set_name": "StackExchange"
}
|
As the school funding wars heat up yet again, it seems the story of Australian education is stuck in an absurd and unresolved plot, uncertain if the climax should be Catholic, independent or state.
Yet for a long time, the history of schooling in Australia was a place to find a national story: a coming of age tale, from illiterate colonies to the great public education covenants of the 1880s, which included the great (Irish) Catholic separation from the educational social contract. A century of fairly stable educational narrative followed. Several generations started and finished in local comprehensive state schools: free, compulsory and non-sectarian. This defined the local community and shaped its networks. In thousands of tiny tales – including mine - it became an epic narrative of Australian progress.
Students at Queanbeyan Public School. Several generations of Australians started and finished in local comprehensive state schools.
Though the majority were fervent in neither demeanor nor Sunday attendance, state schooling was a generally Protestant arrangement for about 80 years. Throughout the 1950s, it became a centrally administered and collectivist model with a persistent Catholic exception. School choice was limited: constrained by geography and – a fact now largely forgotten - tribal sect. It was a progress story, from small to big, from primitive to civilised, from convict to free, from colony to nation.
But now, the story has become crowded by the alternative theme of school choice: bickering about funding is one of its many consequences. School choice is a particularly Australian theme - according to the OECD, Australia has the world’s highest access to school choice.
|
{
"pile_set_name": "OpenWebText2"
}
|
In an effort to get around Apple's ban on rival browsers for its iPhone, Mozilla plans to offer a Firefox application that will give users access to their browser bookmarks and history. The app will also let users open tabs from their most recent Firefox sessions.
The Firefox Home app is a spin-off of the bookmark and tab synchronization technology Mozilla currently offers as an add-on for the Firefox desktop browser. Mozilla will submit the free application to the App Store within the next three weeks. Sadly, Mozilla has no way to know when or if the app will be approved and available to users, so it's hard to say when we'll be able to get our hands on this app.
Firefox Home Coming Soon to the iPhone
We have been working on an application for the iPhone based on the Firefox Sync (formerly Weave Sync) technology. The app is called Firefox Home, and it gives iPhone users instant access to their Firefox browsing history, bookmarks and the set of tabs from their most recent browser session. What’s more, it provides Firefox “Awesome Bar” capability that enables people to get to their favorite web sites with minimal typing.
Firefox Home provides an amazing “get up and go” experience. It’s encrypted end-to-end. It’s your home on the Web, wherever you are. And, of course, it’s free.
Firefox Home for iPhone is part of a broader Mozilla effort to provide a more personal Web experience with more user control. For devices or platforms where we’re unable to provide the “full” Firefox browser (either technically or due to policy), we aim to provide users with “on the go” instant access to their personal Firefox history, bookmarks and open tabs on their iPhones, giving them another reason to keep loving Firefox on their desktops.
Why is this useful?
|
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"pile_set_name": "OpenWebText2"
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|
One Ton Cup Revisited broadens its embrace
by Alan Sefton on 14 Dec 2013
Rainbow 2 goes into action soon after the start of Race 4 in the 1969 One Ton Cup off Heligoland, Germany. The large overlapping genoa and small main were encouraged by the rating rule of the time. . ..
Due to popular demand (as they say in show business), we have decided to open up the proposed 'One Ton Cup Revisited' regatta to include all One Tonners that contested the Cup in the 'modern era' (1965 to 1994*).
On 27 November, Chris Bouzaid and the Royal New Zealand Yacht Squadron announced that they were seeking an indication of potential interest in a proposed 'One Ton Cup Revisited' regatta, in Auckland, New Zealand, in February/March 2015.
The initial thinking was to cater for RORC and IOR One Tonners that were eligible for Cup competition between (and including) the years 1965 to 1983 inclusive. The immediate response was 10 serious intentions, including former winners Rainbow II and Wai-Aniwa.
That response, however, was accompanied by an even larger number of potentials from outside of the original year constraints. We have checked with several of the world’s leading offshore racing designers who have advised that, should we open up the proposed event, the IRC Rule, under normal circumstances, would do a more-than-satisfactory job of rating the performances of what, after all, would be a fairly narrow range of race boats.
We have, therefore, decided to re-launch the initiative and seek expressions of intended entry from the full range of 'modern' One Tonners (1965 to 1994* inclusive).
The time frame and venue for the proposed regatta remain the same – February/March 2015, in Auckland, New Zealand.
'We will do everything possible to ensure everyone has an equitable chance of success on the race course, regardless of the vintage or size of their boat,' Bouzaid said today 'so we will be seeking expert advice on how to divide the potential fleet into divisions to ensure best-possible racing - maybe the Classic Division (1965 to 1972 inclusive), Division Two (1973 to 1983 inclusive) and Division 3 (post 1983).
'The objective will be that everyone will enjoy the experience of racing these boats as a class again. A lot of us will have been lucky enough to have experienced that already, when One Tonners were the hottest offshore racers around.
'We know everyone will have a great time ashore in the City of Sails. It will be our job to ensure a similar experience racing in the Hauraki Gulf'.
In an earlier release the organsiers explained that the regatta would celebrate the (near) 50th anniversary of the One Ton Cup switching from metre class yachts to offshore racers, using an international rule (RORC) to measure and rate contestants. This was when interest in the Cup went global and led to One Tonners being regarded as the Formula One class of ocean racing.
The current thinking is to cater for RORC and IOR One Tonners that were eligible for Cup competition between (and including) the years 1965 to 1983.
The IRC Rating Rule would be used to equitably handicap the fleet which would be raced in two classes – RORC and IOR yachts 1965 to 1971 (inclusive), and IOR yachts 1971 to 1983 (inclusive).
Bouzaid, of course, twice won the One Ton Cup – in the S&S design Rainbow II, in 1969 (off Heligoland), and in the Carter-design Wai-Aniwa, in 1972 (off Sydney).
The RNZYS has had a long involvement in the modern era of the event, first challenging with Rainbow II in 1968. Since then, it has contested the Cup no less than 12 times, in seven different countries. In the process, it has won the Cup on five occasions and hosted the event twice.
The current proposal for the 'Revisited' regatta would be to mirror the One Ton Cup of old - ie there would be three inshore races, a short ocean race and an ocean race-proper. In deference to contestants and boats, however, the inshore races would be of approximately 20 miles length, while the short ocean race would be a 40-miler (approx) and the ocean race a 100-miler (approx).
There would be a Prix d’ Elegance and other innovative awards, with an opening ceremony and prizegiving that would do full justice to New Zealand’s legendary record for celebrating major sailing occasions.
There would also be a New Zealand Millennium Cup super yacht and One Ton Cup Revisited weekend at the beautiful Hauraki Gulf island of Kawau, with its famous Mansion House which, in the mid-to-late 1800s, was the residence of the then Governor of New Zealand, Sir George Grey.
This will be a high-profile sailing period in Auckland.
The Finn Gold Cup will be raced off Takapuna Beach in February, 2015, while the Volvo Ocean Race fleet is scheduled to arrive in Auckland (from China) on or about around 26 February, 2015, and leave for Itajai, in Brazil, on 15 March, 2015.
The proposed 'One Ton Cup Revisited' would be an important and integral part of this major celebration of sail.
Could those interested in the above please communicate, by email, that interest, with brief detail of the One Tonner that might/would be involved, to: Alan Sefton: alansefton@xtra.co.nz
|
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|
Achona
Juliana Ferrie is a junior staffer and second-year journalist in Achona. Ferrie loves spending time reading articles on Buzzfeed, listening to Ed Sheeran, and binge-watching shows on Netflix. Some of her favorites include Grey’s Anatomy and Supernatural. At AHN, she is involved in Key Club, TLC, and Speech & Debate. She loves being a TLC mentor, as it gives her the opportunity to meet and connect with lower school students. In her third year as an Academy Jaguar, Ferrie is looking forward to finally being an upperclassmen. She is excited to feel completely settled in as an older student, without the classic anxiousness that comes with freshman and sophomore year. In her free time, she loves both taking photographs and curling up with a great novel. One of her all time favorite books is The Raven Cycle series by Maggie Stiefvater. Later in life, she hopes to be an accomplished veterinarian after attending a university in the northeast.
Juliana Ferrie, Junior Staff Writer
May 21, 2018
Kilauea Volcano Erupts in Hawaii (Story)
May 15, 2018
Sophomore Megan Hughes Breaks Several Track Records (Story)
May 01, 2018
Toronto Attack Kills 10 People (Story)
Apr 23, 2018
Zuckerberg Testifies in Front of Congress (Story)
Apr 13, 2018
Fake News Spreads About Parkland Survivors (Story)
Mar 23, 2018
Bridge Collapses Near FIU (Story)
Mar 08, 2018
Academy Students Choose Their Favorite Books (Story)
Feb 26, 2018
Junior Class Attends College Planning Retreat Day (Story)
Feb 22, 2018
Academy Changes AP Exam Policy (Story)
Feb 09, 2018
Students and Faculty Choose Lenten Promises (Story)
Jan 30, 2018
Judge Delivers Larry Nassar’s Sentence (Story)
Jan 24, 2018
Mudslides Affect California (Story)
Jan 18, 2018
Academy Students Review Recent Movies (Story)
Dec 08, 2017
High School Students Organize Elementary School Book Drive (Story)
Dec 01, 2017
Ben Platt Departs from Broadway Musical “Dear Evan Hansen” (Story)
Nov 13, 2017
Imagine Dragons Perform at Amway Center (Story)
Nov 08, 2017
Tampa’s Five Most Haunted Places (Story)
Oct 30, 2017
Wildfires Cause Major Destruction in California (Story)
Oct 25, 2017
Digital Media Club Plans to Bring Back Morning Announcements (Story)
Oct 13, 2017
Icekimo Opens Near Academy (Story)
Oct 06, 2017
Advisory Period Sparks Debate (Story)
Sep 28, 2017
Terror Attacks Create Fear Around the World (Story)
Sep 20, 2017
Trump Announces the End of DACA (Story)
May 19, 2017
Disney’s World of Pandora Causes Excitement (Story)
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Live Videos Spark Controversy (Story)
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“Fearless Girl” Statue Sparks Controversy (Story)
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Thoughts the Footloose Cast Has During “Tech Week” (Story)
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London Suffers From a Terror Attack on the Westminster Bridge (Story)
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Academy Students Choose Favorite Songs for Playlist (Story)
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Academy Hosts National Qualifier for Speech and Debate (Story)
Feb 23, 2017
Academy Takes Steps to Encourage STEM (Story)
Feb 14, 2017
Women’s March on Washington Plans General Strike (Story)
Feb 03, 2017
Technical Theatre Class Starts Makeup Unit (Story)
Jan 25, 2017
Jaguarettes Compete in Dance Team Regional Championships (Story)
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Meryl Streep Takes a Political Stand at the Golden Globes (Story)
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Gunman Shoots 39 People in Istanbul Nightclub (Story)
Dec 05, 2016
Jill Stein Files for a Recount in Three States (Story)
Nov 14, 2016
The Perks of Having a Sister (Story)
Nov 04, 2016
FBI Reopens the Investigation Against Hillary Clinton (Story)
Oct 31, 2016
Tackle Academy’s Service Hour Requirement With These Suggested Events and Organizations (Story)
|
{
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|
29th Primetime Emmy Awards
The 29th Primetime Emmy Awards were held on Sunday, September 11, 1977. The ceremony was broadcast on NBC. It was hosted by Angie Dickinson and Robert Blake.
The top shows of the night were Mary Tyler Moore, which, in its final season, won its third consecutive Outstanding Comedy Series Award, it also became the first comedy series to gain eleven major nominations (since broken). Upstairs, Downstairs, also in its final season, won its third Outstanding Drama Series Award in four years (it competed as a miniseries in 1976, and won that category too). But the overwhelming champion of the ceremony was the miniseries Roots.
Roots set several milestones and broke multiple records during the night. It became the first show to receive at least twenty major nominations (21). Adding its nominations in Creative Arts categories, its total expands to 37. Both records still stand for all shows. It was the first show to gain every nomination in an acting category. Its thirteen acting nominations tied the record set the previous year by Rich Man, Poor Man, however all of Roots nominations came in the miniseries category, while Rich Man, Poor Man had nominations cross over into the drama series field. Roots became the first miniseries, and second show overall, along with All in the Family in 1972, to win six of seven major categories. All but one of Roots eight episodes were nominated for major awards (Part VII).
Another distinction of the night was that Mary Kay Place won a Major Acting award for a TV show (Mary Hartman, Mary Hartman) that had no major network, only broadcast in Syndication - the first time this rare feat has occurred.
With this ceremony, the Primetime Emmys began a long residency at the Pasadena Civic Auditorium that would continue until 1997.
Winners and nominees
Programs
Acting
Lead performances
Supporting performances
Single performances
Directing
Writing
Most major nominations
By network
ABC – 59
CBS / NBC – 48
PBS – 14
By program
Roots (ABC) – 21
Mary Tyler Moore (CBS) – 11
M*A*S*H (CBS) – 9
Eleanor and Franklin: The White House Years (ABC) – 8
Family (ABC) / Raid on Entebbe (NBC) – 6
Most major awards
By network
ABC – 13
CBS – 11
NBC – 9
PBS – 2
By program
Roots (ABC) – 6
Sybil (NBC) – 3
Notes
References
External links
Emmys.com list of 1977 Nominees & Winners
029
Category:1977 television awards
Category:1977 in California
Category:September 1977 events in the United States
|
{
"pile_set_name": "Wikipedia (en)"
}
|
Copper Deficiency: Causes, Manifestations, and Treatment.
The metabolism of the essential trace element copper remains incompletely understood and, until recently, nearly ignored in acute medicine. Menkes disease was for long the only known copper deficiency condition, but several case reports and investigations conducted over the last 2 decades have shown that deficiency is more frequent than previously suspected, with devastating individual consequences and potential public health consequences. The copper needs in healthy individuals are 0.9 mg/d, which translates to 0.3 mg/d intravenously in parenteral nutrition; the present review aims at gathering actual knowledge. A review of literature was conducted in PubMed and Cochrane systematic reviews to identify the most recent information about copper deficiency and generate a narrative review. Copper deficiency has hereditary and acquired origins, the latter being the most frequent. Clinical manifestations are nonspecific but affect all organs and systems, particularly the hematologic (anemia) and the neurologic (myeloneuropathy) systems. Deficiency also affects the cardiovascular, cutaneous, and immune systems. Severe copper deficiency due to reduced absorption after bariatric bypass surgery has become frequent. Deficiency is more frequent than previously recognized, probably because of changing nutrition patterns but also because of some treatments that have become very common such as bypass bariatric surgery and, in acute medicine, prolonged continuous renal replacement therapy. The patients may present with severe hematologic and neurologic complications that go untreated because copper deficiency was not considered in the differential diagnosis: These complications often need active intravenous repletion with doses 4-8 times the usual nutrition recommendations.
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{
"pile_set_name": "PubMed Abstracts"
}
|
News
Don’t you hate it when you pay for something and then the next day it goes on sale? Don’t you equally hate it when you’re thinking about buying something but continue to put it off and then the price goes up? That’s why I’m here to give you a friendly heads-up that from October we’re going to be raising our Premium Membership prices in-line with, drum-roll please, inflation. Fact is money isn’t worth as much as it used to be (does that make sense?) and money is exactly what we need right now.
We launched our Premium Membership back in 2006 and since then it’s become an extremely important stream of revenue for the Nexus. Without it this network simply wouldn’t exist. We’ve spent over £120,000 ($187,000) in the past few months on trying to sort out the stability of the network for the future. We’re still not done and we’ll continue to invest in the infrastructure until we’ve got it right. It’s been an expensive year as we’re currently running (and paying for) our new system in parallel with our old one until the new one is ready, which means we’re essentially paying double right now. If you ever wondered what your Premium Membership goes towards, that’s what it goes towards. And the 4 dedicated programmers working on the site. And the 37 servers we have running the network (that number goes up every time I write about this sort of stuff!). And the 3 GBits of bandwidth we use every second. And so on.
From the start of October our prices for Premium Membership will be rising as follows:
Life time of Supporter membership (not the same as Premium). Originally £1. Now £1.29.
1 month of Premium Membership. Originally £2.49. Now £2.99.
3 months of Premium Membership. Originally £6.99. Now £8.49.
6 months of Premium Membership. Originally £11.99. Now £14.49.
12 months of Premium Membership. Originally £19.99. Now £24.49.
Life time of Premium Membership. Originally £39.99. Now £49.99.
Remember Premium Membership at any level gives you an ad free experience on any and all Nexus sites, current or future (yet to be made sites), for life irrespective of whether you buy 1 month or a lifetime. You also get unrestricted download speeds on all the servers and multi-threading enabled file downloads to a maximum of 4 threads per file. For a full list of benefits you can take a look at our Premium Membership info page.
|
{
"pile_set_name": "Pile-CC"
}
|
---
abstract: 'A common bottleneck for materials discovery is synthesis. While recent methodological advances have resulted in major improvements in the ability to predicatively design novel materials, researchers often still rely on trial-and-error approaches for determining synthesis procedures. In this work, we develop a model that predicts the major product of solid-state reactions. The cardinal feature of this approach is the construction of fixed-length, learned representations of reactions. Precursors are represented as nodes on a ‘reaction graph’, and message-passing operations between nodes are used to embody the interactions between precursors in the reaction mixture. Through an ablation study, it is shown that this framework not only outperforms less physically-motivated baseline methods but also more reliably assesses the uncertainty in its predictions.'
author:
- 'Shreshth A. Malik'
- 'Rhys E. A. Goodall'
- 'Alpha A. Lee'
bibliography:
- 'references.bib'
title: Materials Graph Transformer predicts the outcomes of inorganic reactions with reliable uncertainties
---
The discovery of new materials and control of their properties is fundamental to the advancement of technology. Adjusting the structure and composition of crystals allows fine-tuning of properties such as conductivity and band gap [@DInnocenzo:2014aa; @Kalantari2011; @Gong:2014aa]. Advances in first-principles calculations and increased computational power have revolutionised the availability of materials information [@MatProj2013; @OQMD]. Simultaneously, advances in computational materials design [@Jansen:2015aa] have enabled high-throughput prediction and screening in silico [@Ludwig:2019aa].
However, due to the challenges associated with material synthesis, only a small proportion of candidates are produced in the laboratory and experimentally validated. The most common route to the formation of polycrystalline materials is solid-state synthesis [@Kanatzidis:2017aa], which typically involves calcining a mixture of solid reactants. Reactions occur through solid-state diffusion of ions, thus reactants are often milled and mixed to improve the reaction kinetics. However, the interplay between thermodynamically driven energy minimisation and kinetic factors results in products which are often difficult to predict; the field lacks the well-understood reaction mechanisms in organic chemistry. Particular procedures or reactants result in the formation of crystals with unique morphologies and compositions as they form through metastable states. Thus researchers frequently rely on a trial-and-error process of synthesis and evaluation. The development of tools to propose and evaluate the most promising synthetic pathways is, therefore, one of the biggest challenges facing materials discovery [@Aykol:2019aa; @kim2019machinelearned].
A recently released inorganic synthesis dataset has now enabled the possibility of using a data-driven approach to predict the outcomes of inorganic synthesis [@Kononova:2019aa]. To our knowledge, there exists only one study which explores this opportunity [@kim2018inorganic], which addresses the inverse problem of retrosynthesis – predicting precursors that can react to yield a target product – with an architecture that cannot be readily extended to solve the forward problem. However, save for large scale experimental validation, the accuracy of retrosynthesis models cannot be quantitatively benchmarked because there are almost infinitely many ways to synthesize a material, and reactions reported in the literature are not necessarily even the best synthetic route.
Here, we report an accurate forward reaction prediction model with reliable uncertainties. Methodologically, we leverage ideas from graph representation learning to learn the optimal representation of sets of inorganic reactants directly from data. Our work significantly outperforms baselines, and we show that model uncertainty can be robustly estimated using an ensemble. Our work is a building block towards an inorganic retrosynthesis planner that can interface directly with computational tools to close the materials design-make-test cycle.
Data and Model
==============
Solid-State Syntheses Dataset {#sec:data}
-----------------------------
We can define a generalised solid-state synthesis procedure for a target material as a sequence of processes (*actions*) performed on a set of starting materials (*precursors*). A recent study has extracted detailed information for over 19,000 such synthesis procedures from academic literature [@Kononova:2019aa]. Each synthesis procedure has four relevant fields for this problem,
1. **Target:** The stoichiometric formula of the target material for the synthesis.
2. **Precursors:** Defined as starting materials which explicitly share at least one element with the target material, excluding ‘abundant’ materials, i.e. those found in the air.
3. **Processing Actions:** The sequence of synthesis actions performed on the precursors, including the relevant conditions for each action where available.
4. **Balanced Chemical Equation:** Balanced chemical equations for the formation of the target compound provide the relevant molar ratios of precursors in the reaction mixture.
This dataset is the most extensive and highest-fidelity available for inorganic syntheses. Chemical information (precursors, targets and balanced equations) has been extracted with high accuracy (93%).
However, there are some notable limitations that must be considered when utilising it for modelling. Firstly, some procedures have actions and conditions with missing or incorrect data. Over 10% of reactions have no, or only one recorded action. This is primarily because standard procedures are often referenced rather than explicitly stated. The accuracy of the complete procedures (where all actions, conditions, and chemical information are fully correct) is 51%. Further, there is no structural information for the products. This limits physical analysis of the materials and hence a purely stoichiometric approach must be used in this work.
Nevertheless, this dataset provides a wealth of structured information on successful solid-state syntheses. Machine learning (ML) frameworks provide a unique way to assimilate empirical patterns from data. One can thus envisage the target material as being an abstract but learnable function of the precursors and processing procedure.
{width="100.00000%"}
Representation of Inorganic Reactions {#sec:rep-mat}
-------------------------------------
ML models generally operate on fixed-length inputs whilst typically our understanding of inorganic reactions is expressed in terms of variable-sized sets of precursors and sequences of processing steps. Bridging this discrepancy is a key challenge that needs to be addressed in the construction of ML algorithms for inorganic reaction prediction.
Here this process is broken down into 2 stages: 1) obtaining fixed-length representations for the precursors and the processing sequence, and 2) performing set regression on this set of precursors to predict the product given the processing sequence.
### Representation of Precursors
A naïve approach would consider representing materials as sparse vectors with components proportional to the relative amounts of its constituent elements (its stoichiometry). However, such a representation fails to capture critical correlations between different elements. In contrast, *Magpie* embeddings offer powerful general-purpose descriptors for bulk inorganic materials in the absence of structural information [@Ward:2016aa]. These are highly engineered, 145-dimensional vector representations which include as many scientific priors derived from its chemical formula as possible. These features fall into 4 groups: stoichiometric properties, elemental properties, electronic structure, and ionic compound features. We utilise these embeddings as initial precursor feature vectors.
### Representation of Processing Actions {#sec:rep-seq}
Sequence representation is a well studied problem in ML research [@seq2seq; @vaswani2017attention; @devlin2018bert]. Here we utilise single-layer Long Short-Term Memory Units (LSTMs) [@lstm] in an autoencoder architecture to obtain fixed-length representations of the processing sequences.
Reaction Graph Model {#sec:model}
--------------------
In solid-state syntheses, precursors are inherently ‘mixed’ together to form a product. Here we make use of an architecture for set regression based on the *Roost* model introduced in [@goodall2019predicting]. The model treats this process through a series of message-passing stages in which precursors appear as nodes on a dense, weighted graph. A fixed-length representation for the reaction is derived from this graph which allows for generalisation to arbitrary numbers of precursors.
This learned reaction embedding is then used to predict the elements present in the target material. The same embedding is then used to separately predict the product stoichiometry given the elements in the product. If the stoichiometry was directly predicted, an arbitrary threshold stoichiometry would have to be used to select which precursor elements are actually present in the product. The two stage approach used here is therefore necessary to differentiate between products with and without trace elements.
### Reaction Representation Learning {#sec:model-comp}
The crucial first step is to produce a fixed-length representation of the reaction mixture. Figure \[fig:model\]**a.** shows how precursors are represented as nodes on a dense, weighted graph and action sequences are transformed into a fixed-length representation using an LSTM encoder. The initial precursor feature vectors are transformed into a trainable embedding through a learnable affine transformation, $$\label{eq:embedding}
\vec{v}_i = \textbf{W}\vec{v}_{0,i} ,$$ where $\textbf{W}$ is a learnable weight matrix, and $\vec{v}_{0,i}$ is the initial precursor representation.
A series of message-passing operations (Figure \[fig:model\]**b.**) then update the precursor representations $$\vec{v}_{i}^{t+1} = U^{t}(\vec{v}_{i}^{t}, \sum\nolimits_{j\neq i}\vec{v}_{j}^{t}, \vec{u}_{seq}),$$ where $\vec{v}_i^{t}$ is the $i$th precursor feature vector at message-passing layer $t$, $\vec{v}_j^{t}$ are the other precursor features, $\vec{u}_{seq}$ is the fixed-length representations of the action sequences and $U^{t}$ is the update function.
At the heart of the update function is the soft-attention mechanism, which allows the model to capture the importance of the other precursors in the reaction to the precursor in question. *Attention* is in general a method for assigning the importance of certain features in a machine learning task. A *soft-attention* mechanism extends this idea by allowing the model to learn the attention coefficients itself [@vaswani2017attention]. This has been shown to improve graph representation learning [@velikovi2017graph]. Here, unnormalised attention coefficients are first calculated across pairs of precursors $$\epsilon_{ij} = f\left( \vec{v}_{i}^{t} \oplus \vec{v}_{j}^{t} \oplus \vec{u}_{seq}\right),$$ where $f$ is a single hidden-layer neural network, $\oplus$ is the concatenation operation, and $\vec{u}_{seq}$ is the action sequence embedding which is used as a ‘global’ state in all update steps. This gives procedural context to enable differentiation between products formed through different synthesis pathways. $\epsilon_{ij}$ are then normalised by a weighted softmax function,
$$\label{eq:weighted-softmax}
\alpha_{ij} = \frac{\displaystyle w_{ij} \exp(\epsilon_{ij})}{ \displaystyle \sum\nolimits_{k} w_{ik} \exp(\epsilon_{ik})},$$
where the weight $w_{ij}$ is the molar amount of precursor $j$ in the balanced chemical equation. This gives the model context of the quantities of each precursor in the reaction mixture. The node feature is then updated with the pairwise interactions between nodes, weighted by their attention coefficients $$\vec{v}_{i}^{t+1}= \vec{v}_{i}^{t} + \frac{1}{K} \sum_{k=1}^{K} \sum\nolimits_{j\neq i}\alpha_{ij}^{k}g^{k}\left( \vec{v}_{i}^{t} \oplus \vec{v}_{j}^{t} \oplus \vec{u}_{seq}\right).$$ Here $g$ is again a single hidden-layer neural network, and we average over $K$ attention heads, which has been shown to stabilise performance [@velikovi2017graph].
A similar attention-mediated pooling operation is then used to create a fixed-length, learned representation of the reaction $\vec{r}$ from the final graph. The model learns how much attention to pay to each precursor given its final representation and relative quantity.
### Product Prediction
The learned reaction embedding is then fed through a feed-forward neural network trained to perform multi-label element classification for the target product of the reaction. In materials synthesis, the target material cannot contain elements that are not present in the precursors. We add this inductive bias in the form of a binary *‘alchemy mask’* on the output of the network. Oxygen is assumed to be abundant and is additionally included in all masks irrespective of its presence in the precursors. Once the elements in the product have been predicted, the final task is to predict the relative amounts of each element in the product. Here, we use *Matscholar* element embeddings, $\vec{e}_i$, to represent and differentiate between constituent elements [@Tshitoyan:2019aa]. These are concatenated with the reaction representation, $\vec{r}$, to provide a contextualised query and fed through another feed-forward neural network, $h$, to predict the relative amount of element $i$, $$a_i= h\left( \vec{e}_i \oplus \vec{r} \right).$$ These are then normalised using a softmax function to arrive at a fractional stoichiometry $$s_i= \frac{1}{N} \sum_{k=1}^{N} \text{softmax}_{i}(a^k_i),$$ where $s_i$ is the normalised stoichiometry of element $i$ in the product, and we average over $N$ predictions to increase stability and accuracy. In addition, using an ensemble of $N$ models also allow us to estimate the epistemic uncertainty by taking the variance in predictions across the models in the ensemble. We refer to this ensembled model as the reaction graph model.
Results and Discussion {#sec:results}
======================
Product Prediction {#sec:results-main}
------------------
The reaction graph model was tested on solid-state reactions with up to ten precursors. Product elemental composition was predicted with a subset accuracy of 0.940. This can be compared to a null baseline accuracy of 0.338 which would be achieved if all elements in the precursors were assumed to be present in the product. There is evidently a bias towards positive element labelling; 83.9% of elements in the precursors are also present in the product. Thus another metric of interest is the F1 score. The average F1 score achieved was 0.9910, where the score for each element is weighted by the number of true occurrences to account for the elemental imbalance.
The L1 and L2 distances between composition vectors can provide metrics for measuring material similarity. Here, the fractional stoichiometry vector of predicted products was accurate to a mean L1 distance of 0.1259, and L2 distance of 0.0729 to their true stoichiometries. An $R^2$ score of 0.9354 was achieved, which measures the correlation between actual and predicted stoichiometries.
Interpreting Model Predictions {#sec:incorrect-preds}
------------------------------
### Product Elements Prediction
In general, through the inclusion of the *alchemy mask* which prevents chemical inconsistencies, the prediction of which elements are present in the product is very accurate. The small number of erroneous predictions made by the model can typically be attributed to two areas:
\[tab:carbon-false-neg\]
**Carbon False Negatives**
-------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
**Example** 0.19 K~2~CO~3~ + 0.31 Li~2~CO~3~ + 0.5 CO~2~ + 0.25 O~2~ $\Rightarrow$ Li~0.62~K~0.38~CO~3~
**Analysis** Products containing carbon are rare in the dataset and ones that do are mostly carbonates. The model has a structure-agnostic approach and treats each element as a simple ratio of presence in the product. Carbonates are covalently bonded polyatomic ions, and thus do not have the same characteristics as independent elements in a crystal. This could be why a lower accuracy is seen for these reactions.
\[tab:additives\]
**Data Processing of Dopants**
-------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
**Example** 3 MoO~3~ + La~2~O~3~ $\Rightarrow$ La~2~(MoO~4~)~3~; with additives (Eu^3+^) via Eu~2~O~3~
**Analysis** Some products in the dataset have additives/dopants which do not appear in the target stoichiometry. However, the relevant precursors are still present in the data (Eu~2~O~3~ in this case). The model in these cases accurately predicts the presence of these elements in the product, but the additive is not accounted for in the product stoichiometry data.
### Stoichiometry Prediction
The inclusion of precursor amounts as weights is seen to provide vital information in differentiating between product stoichiometries. For example, the model distinguished well between two otherwise equivalent ceramic syntheses:
\[tab:prec-weights\]
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
**Utility of Precursor Weighting**
------------------ ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
**Reaction (A)** $\text{PbO + 0.03 TiO\textsubscript{2} + 0.97 ZrO\textsubscript{2}}
\Rightarrow \text{Pb(Zr\textsubscript{0.97}Ti\textsubscript{0.03})O\textsubscript{3}}$
**Reaction (B)** $\text{PbO + 0.48 TiO\textsubscript{2} + 0.52 ZrO\textsubscript{2}}
\Rightarrow \text{Pb(Zr\textsubscript{0.52}Ti\textsubscript{0.48})O\textsubscript{3}}$
**Analysis** Here, (A) was used to train the model but (B) was in the unseen test set and was predicted with an L1 distance of less than 0.0056 from its true value. The learned reaction representation has thus effectively encoded information about how the relative amounts of precursors affects stoichiometry.
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
However, the model does have some failure modes. As many of these cases can be identified via estimation of the epistemic uncertainty we are primarily interested in explaining the worst predictions – those which have large error but low uncertainty.
Analysis of such erroneous predictions shows that they can generally be grouped into two main areas:
\[tab:over-ox\]
**Oxygen Over-prediction**
---------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
**Example** 1.5 Na~2~CO~3~ + 0.333 Co~3~O~4~ $\Rightarrow$ Na~3~CoO~2~ + 1.5CO~2~ + 0.417O~2~
**Target** Na: 0.5000 Co: 0.1667 O: 0.3333
**Prediction** Na: 0.1985 Co: 0.2692 O: 0.5323
**Analysis** Many errors arise from the over-prediction of oxygen content. This may be due to the over-representation of oxygen in the dataset. A large subset of products are perovskite materials where oxygen typically is present in a fractional amount of 0.6 (e.g. BaTiO~3~).
\[tab:pure-prec\]
**Pure Precursors and Alloys**
---------------- -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
**Example** 8 Ni + 86 Al + 6 La $\Rightarrow$ Al~86~Ni~8~La~6~
**Target** Ni: 0.0800 La: 0.0600 Al: 0.8600
**Prediction** Ni: 0.6859 La: 0.1497 Al: 0.1642
**Analysis** This reaction is for the formation of an amorphous aluminium alloy anode through arc melting. Although it looks as if product prediction should be simple, *Magpie* features are not designed to work with pure elements. This could be the reason for the large errors in these cases.
Overall, many of the incorrect predictions come from either misrepresentation in the dataset or from the lack of structural information. A material is defined not only by its stoichiometry but crucially by its crystal structure. The dataset and therefore this framework is completely structure-agnostic and thus is limited in its predictive abilities. The use of predicted crystal structures from stoichiometry could be an avenue of further investigation [@Zhao:2020aa].
Benchmarking and Ablation Study {#sec:ablation}
-------------------------------
To place the accuracy of our model into context, we benchmark our reaction graph model against a baseline approach and conduct an ablation study on its key features.
The baseline model we use takes the *Magpie* precursor embeddings and concatenates them to be used as the input to a neural network with the same architecture as the output network of the reaction graph model. As with the reaction graph model, we make use of an ensemble of $N$ individual models for this baseline.
While the reaction graph model can handle variable numbers of precursors, this *Magpie* baseline approach is inherently restricted to a certain input size. Thus we limit our model to reactions with up to three precursors only, and zero-pad the input in the *Magpie* baseline model where there are less than three precursors to enable comparison.
The ablation study compares results across reaction graph models with/without the processing actions and the *alchemy mask* to discern which parts of the model design are significant. A summary of the key accuracy metrics is shown in Table \[tab:elempred\] for models in the benchmarking and ablation study. A null baseline result is also given for comparison where we assume all elements in the precursors are present in the product, and are present in their average relative amounts derived from the training data.
-------------------------------- -------------- ---------- ---------- -------- -------- --------
Reaction Representation Alchemy Subset F1 Score Mean Mean $R^2$
Mask Accuracy L1 L2
*Magpie* Baseline 0.625 0.902
Reaction Graph without Actions 0.773 0.950
Complete Reaction Graph 0.770 0.948
Null Baseline $\checkmark$ 0.416 0.988 0.2233 0.1333 0.8406
*Magpie* Baseline $\checkmark$ 0.933 0.990 0.1568 0.0948 0.9050
Reaction Graph without Actions $\checkmark$ 0.960 0.994 0.1298 0.0790 0.9148
Complete Reaction Graph $\checkmark$ 0.960 0.994 0.1326 0.0805 0.9131
-------------------------------- -------------- ---------- ---------- -------- -------- --------
### Reaction Representation Learning {#reaction-representation-learning}
For product element prediction, the reaction graph models are seen to perform significantly better than using *Magpie* features alone. For stoichiometry prediction, Figure \[fig:mae-threshold\] shows the proportion of predictions that are within given L1 error tolerances. A clear improvement is seen through incorporating the graph representation learning framework.
Figure \[fig:stoich\] shows plots of actual against predicted fractional stoichiometry. This figure shows how predictions are distributed about the equivalence line, and their relative confidence as measured through ensemble variance. Similar to the null baseline, the *Magpie* baseline model predictions show a lack of parity about the equivalence line.
![Threshold plot for product stoichiometry prediction. The cumulative proportion of correctly predicted stoichiometries is plotted against an L1 error threshold. A clear improvement is seen through using the learned reaction graph embedding compared to fixed *Magpie* features. No apparent improvement is observed through the inclusion of the action sequences.[]{data-label="fig:mae-threshold"}](figures/threshold_L1.png){width="0.98\linewidth"}
In contrast, the learned reaction graph embeddings show a significant improvement, both in absolute terms and in better prediction of the model uncertainty. In general, the most certain predictions are closest to the equivalence line and there is more parity. This indicates the model has assimilated some chemical knowledge. The improvement in uncertainty prediction can be seen more clearly in the confidence-error plot in Figure \[fig:confidence\]. Including the learned reaction graph embedding shows a clear decrease in the mean error of predicted products as the most uncertain predictions are removed. The almost flat line observed when using fixed *Magpie* embeddings indicates that there is little calibration between error and uncertainty for the baseline model.
{width="1\linewidth"}
![Confidence-error plots for stoichiometry prediction showing the mean L1 error in product stoichiometry prediction as the most uncertain predictions are removed. Uncertainty estimation is greatly improved through using the reaction graph embedding – more erroneous predictions are in general more uncertain. []{data-label="fig:confidence"}](figures/confidence_plot_L1.png){width="0.98\linewidth"}
### Alchemy Mask
The results in the lower half of the table are achieved through the inclusion of the *alchemy mask*, which effectively prevents the model from making predictions which are chemically unfeasible. This inductive bias provides the most notable increase in accuracy across the board for element prediction. This highlights the utility of incorporating physical principles into ML models.
### Processing Action Sequences {#sec:actions}
The synthesis actions are crucial in determining the major product of an inorganic reaction; different procedures on the same precursors can lead to differing products due to the interplay between thermodynamics and kinetics. However, Table \[tab:elempred\] shows the addition of the action sequences in the reaction embedding has a detrimental effect – if any – on model performance.
The level of detail of the action data used in the model can provide an explanation. Different product compositions and morphologies can be formed from even slight changes in temperature or pressure. Thus one cannot expect that using the generic, coarse terms to represent action sequences can lead to significant improvements in performance. The inaccuracies of the processing sequences in the dataset only serve to compound this effect. Thus a model that includes more granular processing procedures is required for practical applications.
Despite this, when the models were extended to the full dataset by including reactions with up to ten precursors, there was a significant improvement in accuracy through incorporating the processing actions sequences. An L1 error of 0.1357 was achieved without the actions, and an L1 error of 0.1259 with the actions. This is likely due to the greater diversity of reactions in the extended dataset, meaning the actions are more important in providing contextual information.
Conclusion
==========
In this work, a data-driven approach to inorganic reaction prediction has been investigated for the first time. A physically-motivated model has been developed which can predict major products of solid-state reactions from precursors and synthesis procedures. The key feature of this work is the generation of a learned reaction embedding which effectively encodes the reaction context for product prediction. Through an ablation study, this framework is shown to predict product stoichiometries more accurately than less physically-motivated models. Importantly, it also more reliably assesses the uncertainty in its predictions.
The reaction representation used here can also be transferred to further problems. One can envisage using it to predict the probability of success of a given synthesis procedure. This would further aid retrosynthesis; precursors and synthesis pathways which have the highest probability of success can be preferentially chosen. This would require supervision in the form of both successful and unsuccessful reactions [@Raccuglia:2016aa].
This work provides a basis for evaluating a future retrosynthesis planner for inorganic materials. For practical use, however, further work is required to differentiate between morphologies of products and more granular synthesis action steps with relevant conditions are needed. Access to greater quality and quantity of synthesis data and a concerted effort between ML practitioners and experimentalists will allow these advances.
Methods {#methods .unnumbered}
=======
Data Processing {#sec:comp-data}
---------------
Reactions with non-stoichiometric or organic precursors and targets, and reactions with pure products or only one precursor were removed from the dataset. This reduced the dataset size to 16,231 reactions with up to ten precursors, and 11,083 reactions for the ablation study with up to three precursors. This was randomly split into training and test sets with an 80:20 ratio.
Processing action sequences ranged from 0 to 16 steps in length, and were represented by 7 unique action types: {Dry Mixing, Mixing in solution, Quenching, Shaping, Heating, Drying, Liquid Grinding}.
Precursor stoichiometries were extracted along with their molar ratios from the balanced chemical equation for each reaction. Where precursors or targets were themselves a mixture of different materials/phases, their stoichiometries were added, weighted by their amounts.
Targets were extracted as 81-dimensional stoichiometric vectors. The set of elements present in the precursors was used to construct the *alchemy mask*.
Implementation Details {#sec:comp-imp}
----------------------
The model was implemented in PyTorch [@NEURIPS2019_9015] and *Matminer* was used for generating *Magpie* features from precursor stoichiometries [@matminer].
An embedding dimension of 8 and a hidden state dimension of 32 were used for the processing actions autoencoder. This lead to a sequence reconstruction accuracy of $\sim87\%$. Reconstruction accuracies of over 95% were achieved using a hidden dimension of 64 but did not significantly improve product prediction accuracy.
The learnable precursor embedding size was set to 128, and 5 message-passing layers were used, each with 3 attention heads. The hidden layer dimension was chosen to be 256 for both $f$ and $g$. The output network of the product element prediction model had hidden layer dimensions of 256, 512, 512 and 256 respectively with ReLU activation. The threshold output probability for elemental presence was chosen through maximising accuracy on a validation set. The stoichiometry prediction model had hidden layer dimensions of 256, 256, 256, 256, 128, 128 and 64 respectively with ReLU activation. These were averaged over 5 iterations. Skip connections were used to reduce the vanishing gradient effect [@resnet].
Learning rates were chosen using a heuristic search where we choose a rate one magnitude lower than that which causes the training loss to diverge. A mini-batch size of 256 and the Adam optimiser was used to train the model [@kingma2014adam]. Early stopping using an 80:20 train:validation split was used in all models to avoid over-fitting.
The ensembles used to estimate the epistemic uncertainty in both the *Magpie* baseline and reaction graph models were constructed using 5 individual models trained on the same data with different initialisation.
Data availability {#data-availability .unnumbered}
-----------------
The exact data used in this work can be found at <https://doi.org/10.6084/m9.figshare.9722159.v3>. More recent versions of the synthesis dataset are released by the original authors at <https://github.com/CederGroupHub/text-mined-synthesis_public>.
Code availability {#code-availability .unnumbered}
-----------------
An open-source repository of the code used in this work is available at <https://github.com/s-a-malik/inorg-synth-graph>.
Acknowledgements {#acknowledgements .unnumbered}
================
R.E.A.G. and A.A.L. acknowledge the support of the Winton Programme for the Physics of Sustainability.
|
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"pile_set_name": "ArXiv"
}
|
A conventional ink jet printer has a carriage which can reciprocate in a predetermined direction (primary scanning direction). A recording head is mounted in or on the carriage and has an ink discharge surface facing downward. A recording sheet can be conveyed intermittently at regular intervals in a direction perpendicular to the primary scanning direction. A platen lies below the discharge surface of the recording head and faces the recording head. Ink droplets are discharged from the nozzles of the recording head onto the surface (upper surface) of the recording medium supported on the platen to form an image on the medium.
The recording head can discharge ink droplets in a zone including an image recording region. The printer may perform marginless image recording on a recording medium by starting the discharge of ink droplets before the leading end of the medium reaches the edge of the recording region disposed in downstream in the conveying direction, and by performing ink discharge until the trailing end of the medium leaves or passes through the edge of the recording region disposed in upstream in the conveying direction. In this case, there is a problem that the discharged droplets dropping outside both ends of the recording medium adhere to the top surface of the platen which lies below. As a result, these ink droplets stain the under side of the succeeding recording medium supported and sliding on the platen.
In order to solve this problem, the printer has been devised as disclosed in U.S. Pat. No. 6,239,817 corresponding to Japanese Patent Application Laid-open No. 2000-118058 (FIGS. 3 and 4A-4C). The recording head of this printer can record an image in an image recording region. The platen of the printer has an upstream wall and a downstream wall, which extend in a primary scanning direction. The upstream and downstream walls stand upright at the edges of the recording region that are upstream and downstream, respectively, in the primary scanning direction. The space between the walls is open upwardly, and an ink absorber is placed in the opened space. The upstream and downstream walls have wavy ribs formed on the top ends thereof, and protrude from the top ends, respectively.
According to the structure of the platen disclosed in U.S. Pat. No. 6,239,817 corresponding to Japanese Patent Application Laid-open No. 2000-118058, however, while a recording medium is passing over the platen, the medium needs to be out of contact with the top side of the ink absorber which is placed in the platen. Therefore, it is necessary to place the ink absorber so that its top side does not protrude over the top ends of the wavy ribs. This makes it necessary to insert, to the platen, an ink absorber which size and shape are strictly controlled. As a result, the incorporation of the ink absorber and other work take time.
If the opening space in the platen is large in area, the capacity of ink absorber can be enhanced. Conceivably, it is possible to make this opening space large in area only by increasing the distance between the upstream and downstream walls of the platen in the conveying direction. If the distance between the walls is long, a front end portion of a soft recording medium is likely to hang down when the leading end of the medium has passed over the wavy ribs of the upstream wall and is positioned in the opening space, namely, when the leading end portion is supported in the form of a cantilever by these ribs. Likewise, if this distance is long, a rear end portion of a soft recording medium is likely to hang down when the trailing end of the medium has passed over the wavy ribs of the upstream wall and is positioned in the space, namely, when the rear end portion is supported in the form of a cantilever by the wavy ribs of the downstream wall. In this case, the end portions of the recording medium are likely to come into contact with the top side of the ink absorber in the opening space, so that the under side of the medium is likely to be stained with ink.
In order to keep a recording medium out of contact with the ink absorber in the platen space, the vertical distance from the top side of the absorber to the top ends of the wavy ribs may be long. In this case, when the recording head discharges ink droplets erroneously without a recording medium lying on the platen during image recording, the droplets float in the form of ink mist over the absorber. When a recording medium enters the recording region, one or both sides of the medium may be stained by the ink mist.
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{
"pile_set_name": "USPTO Backgrounds"
}
|
by Joe Murgia
Happy Anniversary!
One year ago, the subject of UFOs took a quantum leap forward into the mainstream. Thanks to a top notch source, I knew something big was coming but I didn’t know exactly how it would unfold. Then, on a lazy Sunday afternoon, The New York Times published a story about “The Pentagon’s Mysterious U.F.O. Program.” Politico and The Washington Post followed suit with their own stories and eventually, it seemed like everybody was reporting on a type of program our government had repeatedly told us didn’t exist. Surprise!
(If you’re new to this story, you can get caught up by checking out those three links or this massive collection of articles, audio and video put together by the great, Giuliano Marinkovic)
Luis Elizondo, the former head of said UFO program (officially known as the Advanced Aerospace Threat Identification Program) and current Director of Global Security and Special Programs for the Tom DeLonge fronted and UFO-centric, “To The Stars Academy of Arts and Science,” has been very visible over the past year. A few days ago, award-winning, investigative reporter, George Knapp, sat down with him to get a one-year update as they discussed what to expect in 2019.
George Knapp: “Does anybody at the organization – do you or your colleagues there – pay any attention to the chatter?”
Luis Elizondo: “Well, I think as human beings, it’s natural, you know, that you pay attention to some degree, what people are saying. It’s good for many perspectives. It’s also good, you know, frankly, it’s good, common sense if you’re trying to run a business, from a business perspective, right? I think it’s important. You need to know what customers and consumers are saying. But at the same time, you cannot allow yourself to be detracted from your mission, by these voices. So, if there’s a legitimate concern, of course you want to address it. But, in the same respect, there’s a lot of people who are impatient for information. And rightfully so. I get it. We’re human beings. We want our information, we want it now and why are you holding back? But sometimes you have to let the right people, in the right positions, digest information, right? You can’t expect a ten course meal to be digested all in one bite. It just can’t happen. And for some people – this UAP issue – they’re really learning about it for the first time. Despite what they may have seen on popular TV or something like that or maybe on a movie. This is really the first time they’re being told: Hey listen, Jack or Jane. This is a serious topic. This is something that your Department of Defense has been tracking. You probably wanna learn a little bit more about what’s going on and what they’re seeing.”
Knapp: “What can you say about what comes next? You’ve dropped hints that big stuff is coming next year, 2019. Give me some areas where people might hear some news.”
Elizondo: “Sure. So…you know, when you say something big is coming, what does that mean? Well, it can be a whole bunch of things. From my perspective, my goal has always been being able to get the right information to the right people in the right places. That’s really what it is about for me. And informing those individuals so decisions can be made so we can really take a look at this issue from a holistic, a collective perspective. And then have that information get to a point where now the government’s doing its job and informing people, right? So it shouldn’t be the world according to Luis Elizondo. It shouldn’t be Lue informing everybody. It should be those in those positions that have that authority to inform the American people and my job is to facilitate that process. But I think in the course of doing that, we’ve made significant progress in certain key areas. I think we have a much better understanding of the breath and scope that the Department of Defense has played in recent times. Not historical back…[in the] 40s and 50s. I’m talking, very recent, regarding the UFO phenomenon. I think people would be surprised to know just how frequent and the volume in which these things are apparently recorded and observed by active duty, military people on missions. Around the world, by the way. There’s also some very interesting, I think, congruencies. Some interesting relationships that are just now really coming into light for the very first time. New information that I think if people found out, would be very, very surprised. I think some people might be a little bit apprehensive and scratch their heads and say, ‘Wow, what does that mean for the rest of us?’ Other people might say, ‘Ah ha! I told you so!’ Right? So, it depends on who in the audience will be listening. But I think there’s something for everybody. I think, at the end of the day, information is information and you’re gonna do with that information whatever it is you wanna do with it. That’s not up for me to decide. That’s up for you to decide. That’s up for the audience to decide. Ultimately, I think it’s about informing the people. Informing individuals about what we have discovered.”
Knapp: “Is there a form of physical evidence that’s indisputable, that we’re gonna know about?”
Elizondo: “I think there’s a lot of things out there that we’re looking into to include tangibles. Tangibles in a real sense the will hopefully allow us to have a more comprehensive conversation. I don’t want to lead the cart before the horse. There’s a lot of analysis…there’s a lot of homework that needs to be done. And probably the most irresponsible thing that I could do right now is say one thing one way and it turns out to be something else. So we remain, you know, cautiously optimistic, right? And we’re gonna leave no stone unturned. And so far, the stones that we have turned over, some have yielded some really, pretty fantastic results. But we still have a lot more stones to turn over.”
Knapp: “Your first year, you’ve taken a lot of lumps from some crowds, including some of your former colleagues.
Elizondo: “Yeah.”
Knapp: “Has that turned around a little bit? Are there now doors that have opened in terms of interest in this? If you can address that at all without giving something away?”
Elizondo: “Yes. There is definitely…I can say as a matter of fact, there seems to be, finally, a slight turning of the tide. There are now individuals that are more receptive to having the conversation than they were even just a year ago. And data is forthcoming. So, that’s a good thing. I mean, data’s beginning to flow in the direction it’s supposed to flow in and decisions can now finally be made that need to be made! So that’s, in fact, from my perspective, that’s a huge accomplishment. But at the same time, we also have to respect these individuals’ privacy. We have to respect their professional positions and allow them to collect as much data as they can before they really do anything with it. Keep in mind, there’s a lot of data out here, right? It would be almost a dereliction of duty for anybody to make a decision preemptively, without having all the necessary data in front of them.”
~~~~~~~~~~
Joe’s Commentary and Speculation
To The Stars Academy of Arts and Science (TTSA) is a business so it’s nice to see Elizondo not try to hide from that. Here’s their mission, according to their website:
To The Stars Academy strives to be a powerful vehicle for change by creating a consortium among science, aerospace and entertainment that will work collectively to allow gifted researchers the freedom to explore exotic science and technologies with the infrastructure and resources to rapidly transition them to products that can change the world
They want to provide UFO/UAP-related data to the public but we have to remember that while they’re a Public Benefit Corporation (PBC), they’ll have to eventually make a profit or shareholders (such as myself) will be very unhappy and they won’t last very long. More specifically, Jack Markell, former Governor of Delaware, explained that PBCs, “are profitable, but consider profit to be the means — not the exclusive end goal — of their business. They see profits as a means to fuel growth in social impact as well as to generate attractive returns for stockholders.”
On their website, TTSA make that very clear:
“To The Stars Academy is a Public Benefit Corporation (PBC), which means our public benefit purpose is a core founding principle of our corporate charter alongside the traditional goal of maximizing profit for shareholders.”
As far as people being impatient for new information? I see it all the time on social media. Why won’t Elizondo tell us more? Where are all those other UFO videos that Elizondo has referenced? Where are the test results for the anomalous materials from the ADAM research project? Hurry up! Early on, Tom DeLonge said this would play out over a number of years, so I’ve always considered it a long term project. I’ll remain patient, let the next few years roll by and judge things at that point.
So far, I’m very happy with what TTSA has accomplished. DeLonge started a company and provided a landing spot for Luis Elizondo so he could retire from his position as the head of the AATIP program and go public. Without Tom and TTSA, we may never have heard of Elizondo or learned about a UFO program that supposedly didn’t exist. And once that happened, the NYT (and everybody else) had their story.
Now, when I bring up UFOs to random people (I have and continue to do so) and they make that face, I can say, “Have you seen the New York Times article where the former head of the Pentagon’s UFO program went public and a few F-18 pilots spoke about their close-up encounter with a UFO? There’s video.” You have no idea how much I love saying that. It’s very effective. 🙂 Before DeLonge, Elizondo and TTSA, I couldn’t do that. So, I’m willing to give TTSA some time to see if they can take things to the next level.
When Elizondo talks about letting the right people in the right positions digest this information and that some people are learning about the UFO/UAP subject for the first time, I assume he’s referencing our elected officials in Congress who aren’t obsessed with this phenomenon like myself and lots of other people around the globe. For these newbies, the basic fact that something unknown is interacting with our members of the military and humanity in general and has been for a very long time, is going to be paradigm-shattering. Some won’t be able to handle it. So, I agree that taking it slow is the right approach. We already know that Senate staffers are gathering information so hopefully that progresses to the next level in 2019.
Later on in the interview, he mentions people in “positions that have that authority to inform the American people.” Once again, it seems like a reference to more politicians, Who will inform the masses that some UFOs are physical craft that don’t belong to any country and are currently flying around in our skies? Will it be members of Congress? Governors? The President? High ranking members of the military and/or intelligence agencies? The head of NASA? Scientists? All of the above? Or am I thinking too small? Maybe various heads of state will come together to inform the world about our new reality. Hi folks, we’re not alone. Have a great night! All premature, speculation at this point.
Elizondo talks about “new information that I think if people found out, would be very, very surprised.” And suggested that some people would wonder what it means for the rest of us? I can speculate all day long about what that means. Are Reptilian ETs here to feed off of our negative energy? I think people would be surprised by that! Wild speculation aside, I’ll just hope that these revelations actually come about in 2019 and this new information is presented publicly. Anything new within this field is very intriguing to me and anybody who has studied this topic for any length of time.
I think the tangibles, analysis, fantastic results and leaving no stone unturned is in reference to the analysis of various metals or materials that have allegedly come from UFOs. If they get these fantastic results replicated by other, independent labs, it could be a game changer that brings more mainstream scientists into the fold.
Elizondo mentions folks who weren’t receptive to having a conversation about this a year ago and how that’s changing. They’re in professional positions and we have to respect their privacy as they collect data. Is he once again talking about politicians? Or, could he be referencing mainstream scientists? Some of you may vomit as you read this but if I wanted the general population to learn about the reality of UFOs from a science-based, talking head, I’d let bygones be bygones and pull Seth Shostak and Neil deGrasse Tyson (let’s forget about the sexual misconduct allegations against NdT for now) into the Pentagon and show them some data that will knock their socks off. I’d say, “You wanna see the entire Gimbal video, guys? Here ya go! Care to speak with all the pilots involved? We can arrange that. But you have to promise you’ll share what you’ve learned with the general public. It’s time for them to know.”
I’m no fan of either of those guys and their egos but a lot of people listen to what they have to say so I’d be fine with them spilling the beans. Maybe Shostak has already been educated about what’s coming in 2019? That could explain why he’s softened his stance on the possibility that we’re being visited by some sort of artificial intelligence that has an infinite lifespan. And NdT has 13 million followers on Twitter. That’s a powerful audience. Many of whom take every word he says as gospel. He’d have to swallow his pride and walk back his, “Call me when you have a dinner invite from an alien,” response to the UFO videos that were released by the Pentagon. Could he pull it off? I’m willing to give it a shot.
Whatever the plan is for 2019, if it’s as good as what happened on December 16th, 2017 and the weeks and months after, the world is about to be given a shock that may change how we look at ourselves and our place in the Universe. Then again, the masses could hear new data, realize that we’re not alone and give it a giant yawn as they go back to keeping track of celebrities on Instagram. It wouldn’t be the first time and unfortunately, it wouldn’t surprise me.
© Joe Murgia and www.ufojoe.net, 2018. Unauthorized use and/or duplication of this material without express and written permission from this site’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Joe Murgia and www.ufojoe.net with appropriate and specific direction to the original content.
alien, confirmation, Delonge, disclosure, Elizondo. ttsa, et, extraterrestrial, klas, knapp, ufo
By admin
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The invention relates to a brushless electric motor, in particular a miniature motor, comprising a housing, comprising at least one rotor provided with magnetized regions and mounted rotatably about a rotor axis on bearing supports of the housing, and comprising a stator having at least one stator unit, each stator unit including a set of first pole shoes, formed as claw poles, and a set of second pole shoes, formed as claw poles, which are disposed around the rotor axis, as well as a coil positioned following the rotor in the direction of the rotor axis and with its windings arranged to encircle the rotor axis, by means of which the first and second pole shoes can be magnetized.
Such electric motors are known in the prior art, for which the problem is to construct such motors at the lowest possible cost and as simply as possible.
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Around the time that Pokemon exploded in Japan, there was a company called Natsume who decided that they wanted to create a franchise centered around the concept of battling, trading, and two versions for the price of one. Imagineer was hired on to do that very job and an ambitions artist by the name of Rin Homura would lead the charge in designing the concept that would become the foundation of the Medarot, or Medabots as it's known here in the US. The first games were released in November 1997 which was a year after Pokemon Red & Green made their debut in February of 1996. This franchise had a lot of differences compared to Pokemon and we'll detail all of them here.
The world of the first game is similar to ours in a way but in a not so distant future of Japan. You star as Hikaru Agata:
This young man is a normal kid in a normal town who one day while playing with his dog Bonaparte, he finds a medal of the Hercules or Stag Beetle depending on which version you're playing and this triggers him to take up Robattling as a new sport which all the kids in his town are really decent at. His rise isn't easy as he has to juggle school life, Kirara's affection, and even an evil gang called the Rubber Robos who cause mischief throughout the region. Robattling involves a single or team of Medabots shooting, smashing, and all sorts of mayhem until a winner is decided. This is the bread and butter of this game and despite its simplistic nature, it can be insane as RNG is often unfair and can lead to a lot of losses which can result in a game over or a loss of a part. Parts are what makes the bot fight and move and you can't afford to lose those as spares can be sold and traded for money which can go toward buy more parts to build more of these things. Beyond this, the plot is barebones like most battle and trading style RPGs. The soundtrack is very repetitive and grating, but the Robattle song is really good and so much so that later installments would slightly remix and reuse it a lot:
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Momentum against the Iowa first-in-the-nation caucus is sure to explode after Thursday, as many people get their first real close-up look at its undemocratic nature.
First, a look at how the caucuses work:
As in years past, voters must present themselves in person, at a specified hour, and stay for as long as two. And if these caucuses are anything like prior ones, only a tiny percentage of Iowans will participate. In 2000, the last year in which both parties held caucuses, 59,000 Democrats and 87,000 Republicans voted, in a state with 2.9 million people. In 2004, when the Republicans did not caucus, 124,000 people turned out for the Democratic caucuses [...] While the Republican caucuses are fairly simple — voters can leave shortly after they declare their preferences — Democratic caucuses can require more time and multiple candidate preferences from participants. They do not conform to the one-person, one-vote rule, because votes are weighted according to a precinct’s past level of participation. Ties can be settled by coin toss or picking names out of a hat.
So what does this mean, in practical terms?
Jason Huffman has lived in Iowa his whole life. Lately he has been watching presidential debates on the Internet, discussing what he sees with friends and relatives. But when fellow Iowans choose among presidential candidates on Thursday night, he will not be able to vote, because he is serving with the National Guard in western Afghanistan. "Shouldn’t we at least have as much influence in this as any other citizen?" Captain Huffman wrote in an e-mail interview.
Nope, Cpt. Huffman is out of luck. As are these folks:
"It disenfranchises certain voters or makes them make choices between putting food on the table and caucusing," said Tom Lindsey, a high school teacher in Iowa City. Mr. Lindsey plans to attend this year, but his neighbors include a cook who cannot slip away from his restaurant job on Thursday night and a mother who must care for her autistic child [...] But many Iowans have been dutifully watching presidential candidates all summer and fall only to find themselves unable to participate on caucus night. Take Sally Kreamer, a single mother in Johnston, outside Des Moines, who says she cannot escape the pull of her children’s dinner and homework. "I would love to participate," Ms. Kreamer said. Or Carrie Tope, who works at a hospital emergency room in Ames and cannot find anyone to take her shift. She particularly wants to vote this year, she said, because things are so close. Even some campaign volunteers "have bosses who say, ‘We really need you at work that night,’" said Jennifer O’Malley Dillon, state director for John Edwards. "Unfortunately, they just aren’t going to be able to participate," she said.
And the Iowa Democratic Party response to what is a hideous way to conduct an election?
Scott Brennan, chairman of the Iowa Democratic Party, said the party had no responsibility to ensure that voters can caucus. "The campaigns are in charge of generating the turnout," Mr. Brennan said, and the voters who truly care will find their way to their local caucuses. As for Ms. Tope, the emergency room worker, "there’s always the next cycle," Mr. Brennan said.
What an elitist asshole. Yet this ridiculous process he defends will disenfranchises thousands of Iowans as it disenfranchises millions of voters around the country who would like a chance to vote for their favorite primary candidate but will never get the chance.
There's an entire nation out there -- 48 states plus D.C. -- who have tired of this ridiculous calendar and undemocratic way of choosing our nominee. Iowa and New Hampshire will fight like hell to retain their lofty status -- it's worth prestige points and a crapload of money for those states. But no matter what those states may think, they don't have a god-given right to hold our nomination process hostage to their whims (and parochial concerns like ethanol). They should enjoy these next two weeks, because this is likely their swan song.
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69 F.Supp.2d 168 (1999)
ESTADOS UNIDOS MEXICANOS, et al., Plaintiffs,
v.
Austin J. DECOSTER, et al., Defendants.
No. Civ.A. 98-186-P-H.
United States District Court, D. Maine.
May 26, 1999.
Harold J. Friedman, Friedman, Babcock & Gaythwaite, Portland, ME, for Plaintiffs.
Timothy J. O'Brien, Verrill & Dana, Portland, ME, for Defendant Decoster.
Thomas H. Somers, Hoff, Curtis, Pacht, Cassidy & Frame, Portland, ME, Kerin E. Stackpole, Hoff, Curtis, Pacht, Cassidy & Frame, Burlington, VT, for Defendant Maine AG & Quality Egg.
*169 ORDER ON DEFENDANTS' MOTION FOR PARTIAL SUMMARY JUDGMENT
HORNBY, Chief Judge.
The issue here is what statute of limitations applies to a Count seeking relief under the Agricultural Worker Protection Act ("AWPA"), 29 U.S.C. §§ 1801-72, for an employer's provision of unsafe housing, violations of statutory disclosure and posting requirements, and provision of false and misleading information concerning the terms and conditions of employment. See Compl. at. ¶ 52. I conclude that Maine's six-year statute, 14 M.R.S.A. § 752, applies. Therefore, the defendants' motion for summary judgment on Count II is DENIED.
The parties agree that the AWPA contains no express statute of limitations. When a federal statute creates a cause of action but does not expressly provide a statute of limitations, the limitations period depends on the date that the statute was enacted. For causes of action under statutes enacted after December 1, 1990, the limitations period is four years. See 28 U.S.C. § 1658. For other statutory causes of action, the limitations period is determined by borrowing from some analogous statute. The AWPA was enacted in 1983; accordingly, the parties agree that I should "borrow" a statute of limitations for the AWPA, but they disagree over which one I should borrow.
The plaintiffs argue that I should borrow Maine's six-year limitations period, 14 M.R.S.A. § 752. The defendants argue that the proper limitations period should be borrowed from federal law, specifically, the six-month limitation on the Secretary of Labor's issuance of a citation under the Occupational Safety and Health Act ("OSHA"), 29 U.S.C. § 658(c).[1] I conclude that the plaintiffs are correct.
In general, a federal court should borrow a limitations period from state law. See North Star Steel Co. v. Thomas, 515 U.S. 29, 34-35, 115 S.Ct. 1927, 132 L.Ed.2d 27 (1995). Resort to an analogous federal statute is proper only when two conditions are met: (1) the federal statute "clearly provides a closer analogy than available state statutes," and (2) "the federal policies at stake and the practicalities of litigation make that rule a significantly more appropriate vehicle for interstitial lawmaking." DelCostello v. International Broth. of Teamsters, 462 U.S. 151, 172, 103 S.Ct. 2281, 76 L.Ed.2d 476 (1983); accord North Star Steel Co., 515 U.S. at 35, 115 S.Ct. 1927; Reed v. United Transp. Union, 488 U.S. 319, 324, 109 S.Ct. 621, 102 L.Ed.2d 665 (1989). Neither condition applies here.
1. Federal Law Does Not Clearly Provide a Closer Analogy to the AWPA Than State Law Does
The defendants acknowledge that Maine's Housing Standards for Agricultural Labor Act, 26 M.R.S.A. § 586, is closely analogous to the AWPA. See Defs.' Mot. for Summ.J. at 4. They further acknowledge that the Maine statute authorizes a private civil action for people aggrieved by violations of the state statute and regulations promulgated thereunder. See id. The state statute, by its terms, does not apply to employers subject to the AWPA, see 26 M.R.S.A. § 586, but it subjects such employers to regulations that must be identical to federal regulations promulgated under the AWPA. See id. In other words, the state statute clearly is intended to fill any gaps in the AWPA by subjecting employers not regulated under the AWPA to a state regulatory scheme with requirements identical to the AWPA requirements. Thus, the state statute here is not merely closely analogous to the federal statute, it is part of what the State seems *170 to regard as a single federal-state cooperative regulatory program. State law thus provides a closer analogy than any other federal statute.
Nonetheless, the defendants claim I should borrow from federal law on the ground that the state statute contains no limitations period. It is true that the section of the state statute that creates a private right of action makes no reference to a statute of limitations, see 26 M.R.S.A. § 588(2), but Maine's catchall statute of limitations applies to such actions. With exceptions not relevant to this case, "civil actions" in Maine carry a six year statute of limitations, see 14 M.R.S.A. § 752, and the Maine farm worker protection statute creates a right to maintain a "civil action," 26 M.R.S.A. § 588(2). Thus, the six-year statute of limitations applies.
2. Federal Law Is Not Significantly More Appropriate in Light of Relevant Policy and Pragmatic Concerns
The defendants claim that OSHA's six-month period is best suited to AWPA cases for two policy reasons. (They make no similar argument for the FLSA). First, the defendants claim that the short limitations period promotes a rapid resolution of problems with living and working conditions. There is some merit to this argument, but I note that the Supreme Court has stated, with reference to a different federal worker-protection statute (the Worker Adjustment and Retraining Notification Act, 29 U.S.C. §§ 2101-2109, which requires notice to employees prior to a plant closing or major layoff) that a state six-year limitation period is not long enough to frustrate the interest in the rapid disposition of labor disputes, see North Star Steel Co., 515 U.S. at 36, 115 S.Ct. 1927. Second, the defendants claim that the short limitations period is suited to these cases because migrant workers are likely to be important fact witnesses; allowing a plaintiff more time to file may prejudice the defendant, who will be unable to locate the plaintiff's co-workers to obtain testimony. While there is some force to this argument, there are arguments against the short period that are at least equally compelling. First, plaintiffs in such cases are likely to face significant language and cultural barriers that will increase the time that it takes them to find representation. Second, the sums involved in individual suits are likely to be small in the ordinary case, and class actions may be the only practical vehicle for plaintiffs to obtain relief; but a meaningful class in many cases will need to consist of individuals who suffered harm more than six months apart from one another. In order to displace the state-law limitations period, the federal period must be "significantly more appropriate" than the period drawn from state law; whatever the relative merits of the two periods, the balance does not clearly favor the OSHA period.
Nor is the interest in a uniform federal rule sufficient to overcome the presumption in favor of turning to state law. The Supreme Court has refused to turn to federal law in preference to state law merely to avoid a multiplicity of limitations periods. See North Star Steel Co., 515 U.S. at 36, 115 S.Ct. 1927. Moreover, the Court has suggested that where claims are likely to focus on activities at a single workplace, the burden that state-by-state variation in statutes of limitations places on the employer is not sufficient to require a uniform federal rule. See id. at 36-37, 115 S.Ct. 1927. Even in cases where a uniform federal rule is required, the Court does not always draw the uniform rule from federal law. See Wilson v. Garcia, 471 U.S. 261, 280, 105 S.Ct. 1938, 85 L.Ed.2d 254 (1985) (holding that all § 1983 actions should be subject to the relevant state's statute of limitations for personal injury actions). Under the rule reaffirmed in North Star Steel Co., borrowing from federal law would clearly be improper in this case.[2]
*171 For the foregoing reasons, the proper limitations period on the plaintiffs' AWPA claims is six years. Accordingly, the defendants' motion for partial summary judgment on Count II is DENIED.
SO ORDERED.
NOTES
[1] In their reply brief, the defendants for the first time argued that the appropriate limitations period should be borrowed from the Fair Labor Standards Act ("FLSA"), 29 U.S.C. § 255(a), if not from the OSHA. The argument fails for the same reason that the OSHA argument fails: there is no reason to borrow from federal law in this case.
[2] Indeed, the defendants have not pointed to any case in which a court has borrowed a federal limitations period for an AWPA claim. The most helpful case they have been able to provide did not decide that a federal period should apply; the court simply denied summary judgment on the grounds that, even if the federal period applied, the plaintiff's action would not be barred. See Martinez v. Berlekamp Farms, Inc., 635 F.Supp. 1191, 1195-96 (N.D.Ohio 1986).
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In surgical procedures, sutures are commonly used to close incisions and to reunite damaged tissue. Typically, the sutures are maneuvered and passed through the affected tissue and the free ends of the sutures are individually tied together by the surgeon. In some surgical procedures, the surgical site area is sufficiently exposed to permit the surgeon to access and tie the suture manually with a surgical knot. In other surgical procedures, such as endoscopic procedures, laparoscopic procedures, arthroscopic procedures and the like, or when robotic surgical procedures occur, the surgical site is inaccessible to the surgeon's hands. As a result, the surgeon must tie each of the suture ends into a knot at a location remote from the surgical site, and then manipulate suitably configured instruments for sliding the surgical knot to the site of the incision. Further, surgeons may tie surgical knots intracorporeally (inside of the body) using surgical tools to tie the knot down to the tissue. In general, suture knot tying is cumbersome and is one of the more time-consuming steps in the suturing process of the surgical procedure. In the foregoing circumstances, it is desirable to replace knot tying during surgical procedures in order to significantly reduce the duration of surgical operations with a device or method that is simple for the surgeon to utilize. This is especially true with regard to minimally invasive surgical procedures where the tying of surgical knots within confined spaces is extremely difficult and time consuming.
Additionally, it is noted that knots create weak points in a suture. That is to say, when a failure load is applied to a knotted suture, assuming the suture is otherwise free from imperfections, the suture will break at the knot. Therefore, elimination of surgical knots in the suture would also eliminate the weak stress points created in the suture by the surgical knot.
Suture locking and suture anchoring devices such as suture clips, surgical fasteners, hinged clips, suture terminating devices, hemostatic clips, and suture fixation devices of various configurations, designs, structures, and materials of construction are well known in the prior art. For example, U.S. Pat. No. 2,075,508 discloses a suture retainer whereby a suture may be fixed relative to a surgical button. The suture is received and wedged between the button and a clamping plate in order to securely clamp the suture. There are a number of shortcomings to this retainer. First, due to the suture manipulation required to use this retainer, a laparoscopic applicator device would be extremely difficult to produce profitably. Furthermore, the wedging and clamping action will induce stress concentrations in the suture, which likely lead to reduced failure loads.
U.S. Pat. No. 6,066,160 to Colvin, et al. discloses a suture terminator device for use in minimally invasive surgery. The suture terminator device includes a pair of locking apertures with teeth for engaging a portion of a suture at the locking apertures' threaded ends. Not only does this device require laparoscopically guiding two strands of suture between two very small apertures, it also requires that the sutures be squeezed tightly by these teethed apertures, thereby diminishing the integrity of the suture and significantly reducing the maximum tension the suture can withstand.
U.S. Pat. No. 6,106,545 to Egan discloses a suture tensioning and fixation device, which includes a retaining element for frictionally engaging a suture that may subsequently be melted to bond to the suture for a permanent fixation. This melting and bonding action will compromise the integrity of the suture and therefore, because suture strength is of utmost concern in most surgeries, this method of fixation of the retaining element to the suture is not suitable for most surgeries.
U.S. Pat. No. 5,474,572 to Hayhurst and U.S. Pat. No. 5,645,553 to Kolesa et al. disclose the use of a hinged clip that snaps closed after the suture threads are placed within the holding members. The hinge clip is snapped into place such that the suture is held transversely across the holding members, thus locking the suture in place. There is a possibility of improperly actuating or inadvertently releasing the snap, which could lead to an insecure fixation of the suture. In addition, weak stress points are created where the suture is held within the clip.
In view of the deficiencies of the prior art discussed hereinabove, there remains a need for a suture anchoring device that is simple to use, particularly during laparoscopic surgery, in order to eliminate manual knot tying by the surgeon performing the surgical procedure, while not compromising the integrity of the suture.
Another object of the present invention is to provide a suture anchoring device that is at least as strong as conventional surgical knots.
Another object of the present invention is to provide a suture anchoring device that is easy and cost effective to manufacture in bulk.
Another object of the present invention is provide a suture anchoring device that is suitable for a wide variety of sutures (i.e., such as monofilament and braided sutures).
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{
"pile_set_name": "USPTO Backgrounds"
}
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Microdebrider removal of tracheal papilloma via tracheostomy in the child with an obliterated larynx.
In children, recurrent respiratory papillomatosis is the most common benign neoplasm of the airway. The disease frequently involves the larynx and may spread to extralaryngeal sites. Use of a microdebrider has been suggested as a safe and low-cost technique which reduces operating time, compared with laser removal of laryngeal lesions. We describe a technique for using a microdebrider to remove tracheal papillomas when the larynx is obliterated with the disease.
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{
"pile_set_name": "PubMed Abstracts"
}
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According to a report in the Star-Ledger, the state of New Jersey has encountered mismanagement, delays and other difficulties in its effort to spend federal dollars weatherizing the homes of low-income households.
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{
"pile_set_name": "Pile-CC"
}
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Bone histomorphometric reference values in 88 normal Italian subjects.
The study deals with bone histomorphometric results obtained from 88 normal subjects (38 women and 50 men; range: 20-89 years), in order to establish control values in an Italian population. Bone specimens were obtained at autopsy from a standardized area of the iliac crest. The following indicators were measured: bone volume (BV/TV), osteoid volume, osteoid surface, osteoblast surface, eroded surface, osteoclast surface, osteoid thickness. Dependence of histomorphometric indicators on sex and age was evaluated by multiple regression analysis, including sex, age, and also a quadratic term (age2) and two interaction terms (sex x age, sex x age2). BV/TV was mainly affected by age. In fact, a decrease in the amount of bone was found with increasing age in both males and females. The reduction appeared rather regular, with negligible differences between males and females. The other indicators were found to be age- and sex-independent. As a consequence, they did not give information on the possible changes of bone apposition and resorption processes due to aging. On the whole, histomorphometric indicators of trabecular bone of the normal Italian population do not greatly differ from those reported for most other caucasian people.
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{
"pile_set_name": "PubMed Abstracts"
}
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Marchand’s summer in 2 min
Brad Marchand spent most of his summer at home in the Halifax Nova Scotia area. He trained hard during the off season, including some rugby games and attended some charity events as a celebrity.
He admitted he probably would have become a police officer if his hockey career didn’t pan out. Here is a 2 minute video of the Bruins forward who is always among the fittest Bruins to report to training camp.
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{
"pile_set_name": "Pile-CC"
}
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Factor XIII-dependent generation of 5th complement component(C5)-derived monocyte chemotactic factor coinciding with plasma clotting.
Blood coagulation or plasma clotting caused generation of a monocyte chemotactic factor(s) in vitro. The chemotactic factor, of which the apparent molecular mass was 75 kDa, shared antigenicity with complement C5 and possessed the affinity to monocytes, but not to polymorphonuclear leukocytes. The generation of the chemotactic factor was hindered in the presence of a thiol enzyme inhibitor, p-chloromercuriphenyl sulfonic acid, at the concentration of 1 mmol/l, although the gelation of plasma was apparently completed. Furthermore, the generation of chemotactic factor was not observed when a plasma deficient in blood coagulation factor XIII, which is a precursor of a thiol enzyme, plasma transglutaminase, was used; and the activity normally appeared when the deficient plasma was reconstituted with purified factor XIII or with a tissue transglutaminase prior to clotting. When the human sera were injected into guinea pig skin, the serum derived from normal plasma or from the reconstituted factor XIII deficient one caused mononuclear cell infiltration, however, the serum from the deficient plasma without reconstitution infiltrated to a significantly smaller extent. These results indicated that the complement system was initiated somehow during the clotting process resulting in the generation of the C5-derived monocyte chemotactic factor in cooperation with factor XIIIa (activated factor XIII).
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{
"pile_set_name": "PubMed Abstracts"
}
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***Cite this article as:*** Yaghmaei M, Yazdani Sh, Ahmady S. Medical student selection and society: Lessons we learned from sociological theories. Med J Islam Repub Iran 2016 (21 November). Vol. 30:443.
Introduction {#s1}
============
Medical student selection faces many challenges; as there is an imbalance between the number of students who apply and those that can be accommodated, only a limited number of applicants. The first impression is that as this selection process allows the best students to be accepted, it is an acceptable method; however, the real problem lies in determining how the best students are defined. Routinely, medical schools assess applicants in terms of examination results based on individual applicant characteristics. The question that arises is that which should be considered the best selection, the student who had performed best at the entry examination or the one who will perform best in a lifetime of medical practice in the society ([@R1])?
A balancing act for admission to medical school seems to be the fair and appropriate answer: Be fair to the applicants and to the society by choosing those with the potential to be good doctors ([@R2]). There is widespread agreement that applicants should be selected on wider criteria than scores of entry exams ([@R3],[@R4]). Medical schools are to benefit the individual not as a goal but as a means to shape a more progressive and productive society ([@R5]).
Medical schools must encourage participation in higher education by setting clear admissions criteria that if met, offer access to any applicant regardless of socioeconomic background. Universities should actually minimize barriers and seek a student body that reflects in some measure the broad spectrum of the society, including lower income and disadvantaged groups. Universities should also provide academic and professional programs relevant to the individuals and society and to the local, state, and national and international communities ([@R5]).
This notion highlights the importance of developing a close relationship between the applicants, society and medical schools. Understanding and organizing medical student selection in this sense calls for a more profound and basic theoretical approach in sociology. We begin to understand medical student selection through the eyes of sociology, as we believe that medical education has been enriched by perspectives and knowledge developed in sociology ([@R6]). Perspectives on sociology open a new path to determine our choices and policies in selecting students in medical education.
In this study, we aimed to explore how student selection is understood and conceptualized and to offer some promising theoretical considerations and their implications for practice. Sociology, its theories and perspectives on education do not directly focus on student selection, but their extension to this new filed could help us understand and organize it. Thereby, the focus of this article was not on the selection methods per se, but rather, on the relationship between the society, medical schools, and applicants. In other words, our approach examined the policies of the student selection, the relationships between methods and policies and the impact of social factors on them.
Introduction to Sociology of Education {#s1-0-1}
--------------------------------------
The sociology of education is the study of educational structures, processes and practices from a sociological perspective. This means that the theories, methods and the appropriate sociological questions are used to better understand the relationship between educational institutions and society, both at the micro and macro levels ([@R7]). As a source of information and training for future teachers, and as a source of information for policy makers, sociology continues to draw attention to the social context of what goes on in education. In either case, the sociology of education uniquely focuses on the social context of educational structures and processes, and its contribution will continue to be invaluable for understanding and reforming educational systems, particularly as they change to accommodate new social needs and new technologies ([@R8]).
There are two major theories in this field: Functionalist and conflict theories, which reflect underlying beliefs about education and its relationship with the society. Yet, with renewed calls for medical student selection, both conflict and functionalist theoretical perspectives should be reviewed. Within each theoretical framework, the authors begin with a definition of education from that viewpoint and then discuss implications for medical student selection ([@R8]-[@R10]).
The Functional Approach to Education {#s1-0-2}
------------------------------------
In the functionalist theory, education serves many important functions in the society. It transfers moral values, ethics, politics, religious beliefs, habits and norms to the next generation and prepares them for life in the society; this is called socialization. Therefore, education as a social institution develops around central needs or problems of the society. The socialization process is carried out primarily in the family. However, as societies become more complex and the path to becoming a doctor become more twisted, other elements are necessary to continue the process ([@R6]-[@R8]).
The functional approach makes several assumptions about education that requires some attention. Functionalists perceive modern society as a system in which success is achieved; ability and work are more important than being given something or inheriting. The poor should have the same opportunities to enjoy high-status jobs as the rich. Functionalists view society as an expert society, one that needs people who are highly trained and who have developed specialized skills. Modern society is becoming more and more complex, and this implies an ever-increasing need for expertise and technical knowledge. Functionalists also perceive modern society as a democratic society in which an educated citizenry is an informed citizenry composed of people who are more likely to make responsible and informed decisions, are likely to be less prejudiced and more tolerant, and who are more concerned with the quality of life and social justice.
Functionalists view education as providing a number of obvious and important functions: Passing on the culture of the society, facilitating the mixing and merging different classes and ethnic groups, creating the informed citizenry necessary in a complex society, producing cognitive skills, screening, sorting and selecting talents and abilities, developing new knowledge and providing scientific discoveries. Functionalists hope for a sorting mechanism that is truly class and colorblind, in which the sharper and harder-working students are rewarded by being placed in the higher classes. This is basically linked to merit ([@R11],[@R12]).
Governments have asked for medical selection systems to be reviewed, as current systems persistently fail to widen participation for lower socio-economic groups independent of gender and ethnicity. Education is a strong determinant of later-life income and opportunities; and hence, a major contributing factor to patterns of poverty, social immobility and inequality. A review is specifically needed to evaluate the contribution of various initiatives and policies engaged by medical schools to broaden their admission of disadvantaged groups, and review medical school selection processes through the lens of widening access ([@R10],[@R13]).
A rationale for a wider access to medicine is to improve healthcare provision by ensuring that doctors are representative of the society they serve to provide the best possible care to the population ([@R11]). This rationale assumes that increasing the diversity of the medical workforce will improve healthcare based on the assumption that "like would treat like". The data supporting this assumption comes from the U.S. where the approach to WA is a race-conscious affirmative action rather than class-focused meritocratic activities favored in the UK ([@R14]).
Additionally, those students who receive education in more diverse medical schools gain a greater understanding of other people from different socio-cultural backgrounds, and this increases their ability to provide healthcare to those with backgrounds different from their own.
The Conflict Approach to Education {#s1-0-3}
----------------------------------
Conflict theorists view education quite differently than the functionalists. First, conflict theorists see a struggle among the competing groups to control education. The struggle for control represents each group\'s attempts to advance its own set of interests and instill its own values in the education system. Second, the struggle among the groups is unequal, as the privileged class with the superior power and resources always has the upper hand ([@R7]).
Conflict theory looks at the disintegrative and disruptive aspects of education. These theorists argue that education is unequally distributed in the society and is used to separate groups based on class, gender, or race. Therefore, educational level is a mechanism for producing and reproducing inequality in the society. Educational level, according to conflict theorists, can also be used as a tool for discrimination, such as when potential employers require certain educational credentials that may or may not be important for the job. It discriminates against minorities, working-class people, and women -- those who are often less educated and least likely to have credentials because of discriminatory practices within the educational system ([@R7]-[@R9]).
Inequality of access is due to wider societal and economic issues, which are beyond the power of individual universities and medical schools, or ministry of health. Addressing class barriers to attainment is a political mandate, the one that should be targeted during the pre-school and early years of school, and not to be left to secondary school level where social class inequalities are increased even further ([@R15]-[@R17]).
With respect to medical student selection, it seems that some selection processes such as traditional interviews and autobiographical submission, lose their discriminating power and are biased in favor of those from higher socio-economic classes as they become susceptible to coaching. There is a considerable degree of uncertainty around the nature and strength of the relationship between predicted or actual grades at the current level and attainment as a doctor in the UK setting ([@R14]-[@R17]).
Some policies such as deficit model, affirmative action and foundation program have been designed and inserted to neutralize the impact of socio-economic class. The "deficit model" presupposes that young people from disadvantaged backgrounds lack the necessary knowledge, skills and/or qualifications to successfully apply for university admission. Affirmative action is based on defining quotas, percentage plans and targeted recruitment for lower income and disadvantaged groups. Foundation programs (see "Getting ready") address inequalities in attainment. Another approach is the use of contextual data in the admissions process. Contextual data means setting an application in its educational or socio-economic context, such as acknowledging the type of school attended. Supporting Professionalism in Admissions (SPA) has produced an extensive report that outlines the rationale, possible methods and outcomes when the use of contextual data is possible in the university admissions process ([@R14]-[@R17]).
Conclusion {#s2}
==========
The aim of this study was to demonstrate the interaction between the society, applicants and medical schools in terms of medical student selection ([Fig. 1](#F1){ref-type="fig"}). In this study, the trend to implement social factors in the selection process was highlighted. These social factors were explored through functionalism and conflict theories, and it was shown that these theories focus on different categories of social factors. While functionalist theorists pay attention to diversity in the selection process, conflict theorists highlight the importance of socio-economic class. Although both theories believe in sorting, their different views are reflected in their sorting strategies. Both theories emphasize the importance of person-society relationship in the motivation to enter university. Furthermore, the impacts of social goals on the selection policies are derived from both theories.
{#F1}
The perspectives on sociology, both implicitly and explicitly, embody the theories and beliefs we hold about student selection. Medical student selection influences the doctors' life from the day of entry into medical school until the last day of practice. Medical student selection is driven by society concerns and professional needs.
Perspectives on student selection are embedded in the theories. The organization of medical education must define certain assumptions about the relationship between the society, medical institution and medical school.
Theories in the sociology of education offer an approach to student selection that acknowledges and supports complexity, plurality of approaches and innovative means of selection. Medical student selection does not solely focus on the individual assessment and qualification, but it focuses on a social and collective process, which includes all the influences and interactions between the society and medical schools. Sociological perspective of medical student selection proposes a model that both envelops the individual and the society ([Fig. 2](#F2){ref-type="fig"}). In this model, the selection methods should meet the criteria of merit at the individual level, while the selection policies should aim at the society goals at the institutional level.
{#F2}
Our view underlies the theoretical perspectives, which may provide guidance in the future.
It seem to be no financial or reputation incentives for medical schools to widen participation at the current time. Moreover, there are several risks including the possibility of accepting those students who may struggle and bring down the institutional tariff if admitted with lower academic achievement. Therefore, it may be argued that poor progress with WA in medicine is not necessarily a purposeful negative intention of medical schools. Markers that contribute points to national league tables can reward medical school initiatives and admission of students from lower socio-economic backgrounds financially and reputationally.
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{
"pile_set_name": "PubMed Central"
}
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Effects of enamel matrix derivative and transforming growth factor-β1 on connective tissue growth factor in human periodontal ligament fibroblasts.
Enamel matrix derivative (EMD) is suggested to stimulate transforming growth factor-β (TGF-β) production. Connective tissue growth factor (CTGF) is a downstream mediator of TGF-β. This study explores the effects of EMD and TGF-β1 on CTGF in periodontal ligament (PDL) fibroblasts and their interactions in PDL proliferation and development. Human PDL cells were stimulated with EMD. To explore the effects of EMD and TGF-β1 on CTGF expression, cells were treated with and without TGF-β inhibitor, and CTGF protein levels were assayed by Western blot analysis. To study the role of CTGF in PDL development, cells were treated with CTGF inhibitor. DNA synthesis was analyzed by bromodeoxyuridine enzyme-linked immunosorbent assay. Reverse-transcription polymerase chain reaction was performed to examine messenger RNA expression of PDL osteoblastic differentiation markers: type I collagen, alkaline phosphatase, and osteocalcin. EMD induced a concentration-dependent increase of CTGF protein expression in PDL cells. EMD- and TGF-β1-stimulated CTGF expression was significantly reduced in the presence of TGF-β inhibitor. CTGF inhibition downregulated both EMD- and TGF-β1-induced DNA synthesis. The effect of CTGF and EMD on osteoblastic mRNA expression in PDL cells is not obvious. EMD stimulates CTGF expression in human PDL cells, a process modulated by the TGF-β pathway. CTGF can affect EMD- and TGF-β1-induced PDL cell proliferation, but its effects on PDL with regard to osteoblastic differentiation remain inconclusive. The results provide novel insights into EMD-CTGF interaction in PDL cells.
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{
"pile_set_name": "PubMed Abstracts"
}
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Background
==========
The evolutionarily conserved WAVE/SCAR complex has emerged as an important Rac1 small GTPase downstream effector that regulates several aspects of neuronal architecture. The mammalian WAVE/SCAR complex is composed of five proteins: CYFIP (PIR121 or Sra1), Kette (Nap1 or Hem2), Abi (or Abl interactor), SCAR (WAVE) and HSPC300 \[[@B1],[@B2]\]. Whereas in the mouse nervous system WAVE function has so far been analyzed exclusively \[[@B3],[@B4]\], *Drosophila*mutants are available for all but one subunit, HSPC300 \[[@B5]-[@B9]\]. Although our understanding is still far from complete, studies of these mutants and their protein partners have already uncovered that the WAVE/SCAR complex acts as a crucial hub, integrating and regulating various signaling pathways. The SCAR protein, probably the best-studied subunit, is a direct activator of the Arp2/3 actin nucleating complex \[[@B2],[@B10]\], which is required for the formation of a branched actin network \[[@B11]\]. The other complex subunits physically interact to form the WAVE/SCAR complex but also associate with distinct proteins and control specific pathways. CYFIP is a direct Rac1 effector and signals to the Fragile X mental retardation protein (FMRP) \[[@B7],[@B12],[@B13]\], a regulator of local protein translation that controls, among other targets, key players of the actin machinery \[[@B14]-[@B16]\]. CYFIP and Kette both associate with the SH2 SH3 adapter protein Nck/DOCK \[[@B17],[@B18]\].
Despite these diverse protein partners, loss of function phenotypes for *SCAR*, *CYFIP*and *Kette*in the nervous system are remarkably similar, if not even identical \[[@B8],[@B19]\]. These phenotypes include defects in axon growth, branching and pathfinding, as well as abnormal growth and morphology of neuromuscular junctions (NMJs), a fly model system for synaptic plasticity \[[@B6]-[@B9],[@B19],[@B20]\]. Since it was found that mutations in any one of the three fly proteins leads to instability of its partners \[[@B8]\], consistent with data in cellular systems or other organisms \[[@B21]-[@B25]\], these phenotypes are most likely the result of multiple corrupted pathways normally associated with the three proteins.
HSPC300 (haematopoietic stem/progenitor cell protein 300), a small protein of 8 kDa, is the most conserved subunit of the SCAR/WAVE complex and has recently come into focus for its essential role in plant cytoskeleton remodeling \[[@B26],[@B27]\]. Mutations in *Brick1*, one of the *Arabidopsis HSPC300*orthologs, cause morphological defects that are associated with loss of cortical F-actin enrichment and that are in agreement with a role for HSPC300 in promoting Arp2/3 complex activity \[[@B26]-[@B28]\]. While these data support a crucial role of HSPC300 in plant actin remodeling, others have shown that HSPC300 *in vitro*is neither required for assembly of the SCAR/WAVE complex \[[@B29]\] nor impacts on Arp2/3-dependent actin polymerization \[[@B22]\]. Also, RNA interference (RNAi)-mediated knockdown of HSPC300 in cultured *Drosophila*cells results in a reduction of cortical F-actin and alterations in cell morphology that are much weaker than those resulting from RNAi-mediated ablation of all other four subunits \[[@B23]\]. Altogether, these observations make it difficult to predict the importance of HSPC300 in the animal kingdom and its role as a subunit of the WAVE/SCAR complex. This is particularly relevant given the observation that vertebrate HSPC300 interacts with both SCAR and Abi, a subunit of the WAVE/SCAR complex that also interacts with and regulates WASP, another activator of Arp2/3 \[[@B29]-[@B31]\].
We here characterize HSPC300 in an animal model, with particular focus on nervous system development. Loss of HSPC300 recapitulates all aspects of nervous system defects characterizing SCAR, CYFIP and Kette mutants, but notably does not lead to abnormal cell fate choices in sensory organs, an Abi and WASP related function \[[@B5],[@B9]\]. This result, together with genetic and biochemical interaction data, clearly demonstrates the importance of HSPC300 in the nervous system as well as its role in function and integrity of the WAVE/SCAR complex.
Results
=======
HSPC300 accumulates in axons of the central nervous system
----------------------------------------------------------
A putative ortholog of the mammalian HSPC300 subunit of the WAVE/SCAR complex is annotated in FlyBase as *CG30173*. Using the available sequence information, we cloned *Drosophila HSPC300*by RT-PCR and found it to be identical to the predicted gene sequence. In order to assess the expression profile of *HSPC300*, we performed quantitative real time RT-PCR on total RNA extracted from different developmental stages and determined that *HSPC300*transcripts are present throughout the fly life cycle. Normalization against a housekeeping gene coding for ribosomal protein rp49 indicates that the levels of *HSPC300*transcripts progressively increase during development (Figure [1a](#F1){ref-type="fig"}) and are particularly high in adult males and females. Transcript accumulation in ovaries is in line with high levels of *HSPC300*RNA detected by *in situ*hybridization in embryos prior to onset of zygotic gene expression (data not shown).
{#F1}
A polyclonal antibody raised against the HSPC300 protein reveals a single band at the predicted molecular weight (8 kDa) in a western blot on *Drosophila*S2 cell extracts. Signal specificity was demonstrated first, upon transient *HSPC300*overexpression, which induces significant enhancement of the 8 kDa band intensity (Figure [1b](#F1){ref-type="fig"}), and second, by loss of immunoreactivity in HSPC300 mutant extracts (see below). In embryos, HSPC300 primarily accumulates in the central nervous system (CNS), most prominent labeling localizing in axons along longitudinal tracts and commissures (Figure [1c](#F1){ref-type="fig"}). This expression pattern perfectly matches those previously reported for other components of the WAVE/SCAR complex \[[@B7],[@B8]\]. Immunolabeling specificity was further confirmed by loss of immunoreactivity in *HSPC300*mutants (see below).
Generation of HSPC300 mutants
-----------------------------
To address the role of *HSPC300*, we generated loss of function mutants. The *EP(2R)0506*line harbors a P element on the right arm of the second chromosome at position 60B4 and is 100% homozygous viable. The P element lies 75 bases upstream of the HSPC300 start codon (ATG), and in the right orientation to drive *HSPC300*gene expression (Figure [2a](#F2){ref-type="fig"}). *HSPC300*is flanked by two genes for which no mutant strain is reported, *CG3163*, located 263 bases upstream, and *PebIII*, located 497 bases downstream (Figure [2a](#F2){ref-type="fig"}).
{#F2}
We generated *HSPC300*alleles by imprecise excision of the *EP(2R)0506*P element and recovered 116 independent excision events. Among them, four lines are homozygous lethal at late pupal stage and fail to complement each other. These excision alleles were characterized by PCR and sequencing in order to identify the breakpoints. In three of them, the entire HSPC300 coding sequences are deleted, as well as part of the neighboring *PebIII*gene (Figure [2b](#F2){ref-type="fig"} and data not shown). The fourth lethal excision line, *HSPC300*^Δ*54.3*^, shows unaffected *PebIII*and *CG3163*genes as well as the presence of an intact P element. In this line, the P element is unable to drive expression of *HSPC300*as is the case with the original *EP(2R)0506*line. To figure out the molecular lesions associated with this allele, we performed 3\' and 5\' inverse PCR. This confirmed the presence of intact junctions between the P element and surrounding genomic regions and revealed that the 3\' end of the P element is flanked by a stretch of 208 bases of *HSPC300*sequences followed by an insertion of unrelated sequences into the *HSPC300*intron (see Figure [2b](#F2){ref-type="fig"} for schematic representation and Additional file [1](#S1){ref-type="supplementary-material"} for molecular characterization of *HSPC300*^Δ*54.3*^). We characterized this allele further by RT-PCR and detected *PebIII*and *CG3163*, but no *HSPC300*transcripts (Figure [2c](#F2){ref-type="fig"}), indicating that the modified *HSPC300*transcript is either not transcribed or very rapidly degraded. Thus, *HSPC300*^Δ*54.3*^represents a null allele that does not affect neighboring genes. This line was further used to characterize the mutant phenotypes and is referred to as *HSPC300*unless otherwise indicated.
To provide formal evidence that excision line lethality is specifically due to loss of HSPC300, we generated *UAS-HSPC300*transgenic animals and performed rescue experiments. Lethality observed in *HSPC300*^Δ*54.3*^and *HSPC300*^Δ*96.1*^lines is indeed rescued by *HSPC300*re-expression using either *actin-Gal4*or *elav-Gal4*drivers (ubiquitous and pan-neuronal expression, respectively, data not shown). Altogether, these analyses demonstrate that *HSPC300*is an essential gene required in the nervous system, its zygotic depletion inducing lethality prior to eclosion.
HSPC300 is maternally contributed and is required for embryonic CNS axon morphology
-----------------------------------------------------------------------------------
The prominent axonal localization of HSPC300 and phenotypes previously reported for mutations in other components of the WAVE/SCAR complex \[[@B6]-[@B9]\] suggested a role for HSPC300 in axonogenesis. We therefore analyzed the integrity of the embryonic axonal network by immunolabeling with anti-FasII, which specifically recognizes six longitudinal fascicles of the CNS and motor axons, as well as with anti-BP102, which reveals connectives and commissures \[[@B32],[@B33]\] (Figure [3](#F3){ref-type="fig"}). In contrast to the results obtained with *CYFIP*, *SCAR*and *Kette*mutants, complete loss of zygotic *HSPC300*(*HSPC300*^Δ*54.3*^and *HSPC300*^Δ*96.1*^) does not induce any prominent axon defect (Figure [3c,d](#F3){ref-type="fig"}). We speculated that maternal HSPC300 contribution compensates for loss of zygotic gene function, masking an essential requirement during embryogenesis. To test this hypothesis, we generated homozygous *HSPC300*^Δ*54.3*^mutant clones within the germ line of heterozygous females. Deletion of both maternal and zygotic HSPC300 components leads to severe, though variable, nervous system defects ranging from broken and disorganized longitudinal connectives to remnants of axons or depletion of all CNS axon bundles (Figure [3i,j](#F3){ref-type="fig"}). Moreover, upon depletion of both maternal and zygotic HSPC300 components, lethality is shifted to embryonic stages and embryos appear overall disorganized. Identical observations were made using other *HSPC300*alleles, such as *HSPC300*^Δ96.1^(data not shown).
{#F3}
The observed strong and pleiotropic defects did not allow us to score for specific neuronal requirement. We therefore aimed at reducing HSPC300 maternal dose without completely deleting it, using insertion line *EP(2R)0506*, referred to as *HSPC300*^*EP0506*^from now onwards. This line represents a hypomorphic allele since *HSPC300*^*EP0506*^*/HSPC300*^Δ*54.3*^embryos show 30% viability (versus 100% viability for *HSPC300*^*EP0506*^, and 0% viability for *HSPC300*^Δ*54.3*^). *HSPC300*^*EP0506*^*/HSPC300*^Δ*54.3*^females were mated to heterozygous *HSPC300*^Δ*54.3*^males. Amongst the progeny, we indeed noticed embryos with low maternal HSPC300 dose, reflected by reduced axonal HSPC300 immunolabeling in comparison with that observed in wild-type or zygotic null *HSPC300*embryos under the same confocal microscope settings (Figure [3k--m](#F3){ref-type="fig"}). The resulting reduction in maternal HSPC300 dose produces embryos that overall show normal morphology (in contrast to those that are completely devoid of maternal HSPC300), allowing us to examine late CNS development. The embryonic phenotypes observed in this mutant condition, designated as maternal hypomorph, are similar, but of lower penetrance compared to those shown by other members of the WAVE/SCAR complex (midline crossing in 10% of embryos (n = 100) compared to 79% in *CYFIP*embryos (n = 150) \[[@B7]\]) (Figure [3e,g](#F3){ref-type="fig"}). Additional defects shared by mutants affecting the other subunits of the WAVE/SCAR complex \[[@B8]\] are disorganized fascicles, improper separation of commissures and broken longitudinal bundles (Figure [3e--h](#F3){ref-type="fig"}). Taken together, these data clearly implicate HSPC300 in axonogenesis, presumably through regulation of actin cytoskeleton remodeling by SCAR- and Arp2/3-dependent mechanisms. They moreover indicate that the HSPC300 maternal component is sufficient to sustain development in embryos that are devoid of zygotic HSPC300.
HSPC300 regulates synaptic morphology at the NMJ
------------------------------------------------
In addition to the embryonic axonal defects, mutations in other subunits of the WAVE/SCAR complex lead to synaptic defects that are characterized by size reduction of the NMJ and by supernumerary buds on pre-existing boutons \[[@B7],[@B8],[@B19]\]. The fact that *HSPC300*as well as *CYFIP*, *SCAR*and *Kette*mutants show similar embryonic axonal defects prompted us to examine the structures of synaptic terminals in *HSPC300*larvae.
NMJs were labeled using anti-Disc Large antibody, a preferred marker to reveal NMJ morphology \[[@B7],[@B8],[@B34]\]. NMJs of *HSPC300*larvae are severely reduced in length and display supernumerary buds (Figure [4d--h](#F4){ref-type="fig"}) compared to those of wild-type animals, those of rescued animals or those observed in a precise excision line (Figure [4a--c,g,h](#F4){ref-type="fig"}). The latter represents a revertant as it displays the same genetic background as that of imprecise excision lines (Figure [4g,h](#F4){ref-type="fig"}).
{#F4}
To quantitatively assess synaptic *HSPC300*phenotypes, we measured total length of synaptic terminals using a computer-assisted program \[[@B7]\] and counted buds per synaptic terminal. We focused our analysis on muscle 4 in abdominal segments A2-A4, innervated by the inter-segmental nerve (ISN). Since NMJ growth varies in proportion to muscle size \[[@B35]\], we normalized the total length of each synapse with its corresponding muscle surface area. Normalized synapse length of *HSPC300*larvae corresponds to 66% of the wild-type NMJ length, a statistically highly significant difference (1.36 × 10^-3^± 0.11 μm^-1^versus 2.06 × 10^-3^± 0.137 μm^-1^(mean ± standard error of the mean (SEM)); *p*\< 0.001). Likewise, there is 88% increase in the bud number compared to wild type (6.42 ± 0.60 versus 3.51 ± 0.39 (mean ± SEM); *p*\< 0.001) (Figure [4g,h](#F4){ref-type="fig"}). Strong labeling with active zone-specific antibody NC82, which recognizes the Bruchpilot protein \[[@B35],[@B36]\], indicates that *HSPC300*synapses are functional (Figure [4i--n](#F4){ref-type="fig"}). Interestingly, compared to wild-type NMJs, in which NC82 labeling preferentially localizes at boutons, mutant NMJs show uniform labeling. This is in line with the finding that the characteristic bead string structure of NMJs is not preserved in *HSPC300*larvae, in which boutons cannot be easily identified. This phenotype is shared by mutations affecting the other subunits of the WAVE/SCAR complex \[[@B7],[@B8],[@B37]\] and may be related to the supernumerary budding phenotype.
Finally, NMJ phenotypes are rescued by *elav*-*Gal4*-driven *HSPC300*expression but not by postsynaptic *HSPC300*expression induced by the muscle-specific *mhc-Gal4*driver (Figure [4g,h](#F4){ref-type="fig"}, and data not shown). Taken together, these results reveal that HSPC300 is required by motoneurons for synaptic morphogenesis.
HSPC300 in the context of the WAVE/SCAR complex
-----------------------------------------------
The phenotypic similarity of axonal and synaptic architecture of *HSPC300*, *CYFIP*, *Kette*and *SCAR*mutants strongly suggests synergy amongst the wild-type molecules and indicates that HSPC300 represents a functional subunit of the *Drosophila*WAVE/SCAR complex *in vivo*. To provide evidence for the physical association of HSPC300 and the other WAVE/SCAR complex subunits, we performed co-immunoprecipitation experiments in *Drosophila*S2 cells. Both CYFIP and SCAR proteins were found to co-immunoprecipitate with HSPC300 (Figure [5a](#F5){ref-type="fig"}), as revealed by using anti-CYFIP (band at 145 kDa) and anti-SCAR (68 kDa) antibodies \[[@B7],[@B9]\]. Control experiments performed in parallel with unrelated rabbit IgG did not co-immunoprecipitate either of these proteins, thus confirming the specificity of the observed interactions. Thus, *Drosophila*HSPC300 appears to represent, like its mammalian counterpart, a subunit of the WAVE/SCAR complex.
{#F5}
We and others have previously demonstrated that CYFIP, Kette and SCAR are essential for the integrity and the stability of the WAVE/SCAR complex *in vivo*. If any of them is missing, the other subunits fail to be detected \[[@B8],[@B21]-[@B25]\], most likely due to proteasome-mediated degradation \[[@B23]\]. In line with the observation that zygotic *HSPC300*null embryos show neither significant reduction of HSPC300 labeling (Figure [3l](#F3){ref-type="fig"}) nor axonal defects (Figure [3c,d](#F3){ref-type="fig"}), other WAVE/SCAR complex proteins (SCAR and CYFIP) accumulate at wild-type levels in these embryos (Additional file [2](#S2){ref-type="supplementary-material"}). In order to determine the stabilizing potential of HSPC300, we therefore assessed the levels of CYFIP and SCAR later in development, in third instar *HSPC300*mutant larvae, a developmental stage in which maternal contribution has faded. Indeed, we noticed a considerable decrease in CYFIP, Kette, SCAR and Abi protein levels compared to those observed in wild-type larvae. Qualitatively similar results were obtained in zygotic null larvae and in larvae that completely lack the zygotic component and also are maternal hypomorphs, even though the latter genotype shows a stronger defect (Figure [5b](#F5){ref-type="fig"}). Interestingly, there appears to be yet stronger reduction of these proteins in the extracts prepared from *CYFIP*zygotic null animals (Figure [5b](#F5){ref-type="fig"}).
To provide formal evidence that *HSPC300*-induced phenotypes depend on its functional relation with the WAVE/SCAR complex, we performed genetic interaction experiments at the NMJ. We took advantage of our previous observation that single mutations in the subunits of the WAVE/SCAR complex show reduced synapse length in a dose-dependent manner. Heterozygous mutants indeed already show significantly reduced synaptic length \[[@B8]\] (Figure [4g](#F4){ref-type="fig"}). Interestingly, while double heterozygous *HSPC300*, *CYFIP*NMJs are similar to those from larvae that are heterozygous for either gene, imbalance between HSPC and CYFIP content using a sensitized background results in a marked further decrease of synaptic terminal length: the strong *CYFIP*transheterozygous allelic combination *CYFIP*^Δ*85.1*^*/CYFIP*^*EP3267*^(that is, null over hypomorph), in an otherwise heterozygous *HSPC300*background, leads to a significant reduction in the synapse length (Table [1](#T1){ref-type="table"}). This result indicates that *HSPC300*and *CYFIP*synergistically affect synapse growth and provides a first assessment of the molecular pathway requiring HSPC300.
######
Genetic interactions at NMJs
Genotype Mean Synapse length ± SEM (μm) *P*-values
------------------------------------------ -------------------------------- -----------------------------------
Wild type 87.46 ± 2.28
*HSPC300*^Δ*54.3*^/+ 78.48 ± 3.88 *P*^*Wild\ type*^\< 0.05
*CYFIP*^Δ*85.1*^/+ 78.83 ± 2.92 P^Wild\ type^\< 0.05
*CYFIP*^Δ*85.1*^/*CYFIP*^*EP3267*^ 68.18 ± 3.18
*HSPC300*^Δ*54.3*^/+; *CYFIP*^Δ*85.1*^/+ 80.47 ± 2.52
*HSPC300*^Δ*54.3*^/+; 62.00 ± 2.69 *P*^*CYFIP*/*CYFIPEP3267*^\~0.142
*CYFIP*^Δ*85.1*^/*CYFIP*^*EP3267*^
The sample size per genotype in all cases was 25. *P*-values versus indicated genotypes (superscript) were determined by Student\'s *t*-test.
The above data clearly demonstrate that HSPC300 animals share nervous system defects with *SCAR*, *CYFIP*and *Kette*mutants. Flies mutant for subunits of the WAVE/SCAR complex are also characterized by misshaped macrochaetae \[[@B5],[@B19],[@B20]\], a phenotype due to defects in F-actin. The phenotype of bent bristles is also observed in *HSPC300*pharate adults (Figure [6](#F6){ref-type="fig"}, arrows). However, specification of sensory organ precursors (SOPs) is not affected and the number of bristles on the head and thorax are normal (Figure [6](#F6){ref-type="fig"}), as in mutant *SCAR*and *CYFIP*conditions \[[@B9]\] (our unpublished data). This result is particularly interesting in view of the observation that HSPC300 also directly interacts with Abi \[[@B29]\], which in turn interacts with and activates WASP \[[@B5],[@B30]\]. The Abi-WASP biochemical interaction is further sustained by the common phenotype of *WASP*and knockdown *Abi*mutant flies, which lack macrochaete on the thorax, due to SOP cell fate defects \[[@B5],[@B20]\]. On the basis of the phenotypical similarity, we conclude that loss of HSPC300 affects signal transduction through SCAR, not WASP.
{#F6}
Discussion
==========
The evolutionarily conserved WAVE/SCAR complex is known to regulate the actin nucleating Arp2/3 complex in a Rac-dependent manner \[[@B1],[@B2],[@B7],[@B8],[@B23],[@B27],[@B38]\]. While the functions of most components of this complex have been extensively explored, the role of the small protein HSPC300, although one of the complex core subunits, is less understood. Here, we present the first functional analysis of HSPC300 in an animal model and demonstrate the importance of this protein in nervous system development and connectivity.
HSPC300 functions within the Rac1-WAVE/SCAR complex-Arp2/3 pathway
------------------------------------------------------------------
The SCAR, CYFIP, Kette and Abi subunits of the WAVE/SCAR complex have been shown to impact on various processes and structures that depend on actin cytoskeletal remodeling. These include *Dictyostelium*motility \[[@B21]\], development of plant trichomes \[[@B27]\], as well as egg chamber structure and nuclear positioning in the blastoderm of *Drosophila*\[[@B9]\]. Crucial for the versatile functions of the complex is its structural integrity. Loss or mutations in any subunit (CYFIP, Kette or SCAR) leads to proteasome-mediated degradation of the others and, as a consequence, identical mutant phenotypes \[[@B8],[@B21],[@B23]\]. Surprisingly, *HSPC300*knockdown in *Drosophila*S2 cells has been reported to produce much milder cytoskeletal phenotypes than those produced by targeting other components of the WAVE/SCAR complex \[[@B23]\]. In addition, in *in vitro*experiments, lack of HSPC300 affects neither complex assembly \[[@B29]\] nor the complex\'s ability to activate Arp2/3 *in vitro*\[[@B22]\], two features that characterize other complex subunits. These data raise questions as to the real role of *HSPC300*in the context of the WAVE/SCAR complex.
Presented data demonstrate that *Drosophila*HSPC300 constitutes a subunit of the WAVE/SCAR complex *in vitro*and *in vivo*. Like the other subunits of the complex, *HSPC300*is highly expressed in the developing fly nervous system and is crucially required for axonogenesis and neuromuscular synapse morphogenesis. Moreover, *HSPC300*loss of function conditions are marked by a decrease in all members of the WAVE/SCAR complex, a result that is in keeping with a model in which each subunit, including HSPC300, significantly contributes towards the stability of the complex, notably *in vivo*. By using *HSPC300*allele combinations that lead to different amounts of HSPC300 protein, we have revealed that a sharp threshold exists and that the maternal component is sufficient to ensure normal embryonic development and viability. The stringent genetic conditions we generated (loss of zygotic in addition to partial or complete loss of maternal HSPC300) also allowed us to reveal that strong loss of HSPC300 protein is necessary to cause dramatic consequences comparable to those observed in mutants affecting other complex components, thereby suggesting that the previously obtained mild phenotypes (RNAi-mediated knockdown in cells \[[@B23]\]) merely result from the limitation of the utilized technique. Thus, highly similar requirements for HSPC300 and the WAVE/SCAR complex components control cell morphology in CNS neurons and at NMJs.
The genetic interaction observed upon disrupting the balance between CYFIP and HSPC300 levels shows a positive/synergistic role for HSPC300 in the Rac1-WAVE/SCAR complex pathway to control synapse length, thereby providing first genetic evidence for HSPC300 functioning in this pathway. Taken together, the phenotypes and genetic interactions in the fly nervous system, as well as the phenotypes previously described in *Arabidopsis*\[[@B26],[@B27]\], provide strong evidence for HSPC300 being an evolutionarily important integral part of the Rac1-WAVE/SCAR-Arp2/3 pathway.
Interestingly, it has been shown that the control of cotyledon cell size requires *Arabidopsis*Brick1 but not WAVE/SCAR-Arp2/3 \[[@B27]\], suggestive of an additional function that does not depend on the WAVE/SCAR complex. These data are in line with the existence of a significant fraction of free and soluble vertebrate HSPC300 and with our finding that phenotype and genetic interactions can only be revealed upon strong HSPC300 depletion and imbalance, respectively. Whether HSPC300, similar to CYFIP, Kette and Abi, works on additional pathways that are independent of the WAVE/SCAR complex remains to be elucidated. Since HSPC300 is the most conserved subunit of the WAVE/SCAR complex not only in the animal kingdom and *Dictyostelium*, but also in plants, and since no HSPC300 paralogous gene exists in flies, we expect our data to be of predictive value for HSPC300 indispensability with respect to the function of its associated complex in other organisms. We further expect the generated mutant animals to facilitate identification of novel HSPC300-dependent pathways.
Conclusion
==========
We present the first evidence that the small protein HSPC300 is an indispensable component of the WAVE/SCAR complex and plays an important role in nervous system development in *Drosophila*. Moreover, accumulating data suggest that signaling of the small Rho GTPase Rac1 through the WAVE/SCAR complex is implicated not only in structural connectivity in fly \[[@B5]-[@B9]\] (this study) and mouse \[[@B3],[@B4]\] brain, but is also involved in higher cognitive functions and human disease when mutated. Mutations in at least a dozen genes associated with mental retardation in humans directly regulate/mediate Rho GTPase function or may be connected to their associated signaling pathways (reviewed in \[[@B39]-[@B42]\]). This notably includes two genes the products of which directly associate with the WAVE/SCAR complex: FMRP \[[@B7],[@B8],[@B13]\] and a GTPase activating protein termed MEGAP/WRP/srGAP3 \[[@B43],[@B44]\]. These findings emphasize the dominant role of this complex not only in architecture but also in higher functions of the nervous system. Moreover, they place the WAVE/SCAR complex in a central position to genes that are highly relevant to cognitive functions. Based on present data, we propose that *HSPC300*is a new promising candidate gene for genetic causes underlying impaired cognition. Whereas final evidence for the role of *HSPC300*in mammal cognition awaits the characterization of *HSPC300*mouse knockout phenotypes, a *WAVE*knockout mouse does indeed show learning and memory defects \[[@B43],[@B44]\] and altered synaptic plasticity \[[@B4]\].
Materials and methods
=====================
Genetics
--------
The wild-type strain used was *Sevelen*. Line *EP(2R)0506*was provided by the Szeged Stock Center (Szeged, Hungary), and *elav*-*Gal4 (C155)*by the Bloomington Stock Center (Bloomington, Indiana, USA). *HSPC300*excision mutants were obtained upon transposon mobilization in the *EP(2R)0506*line after isogenization. Transgenic lines were obtained using standard protocols. *UAS-HSPC300*(line 4b.1) was recombined onto the *HSPC300*^Δ*54.3*^carrying chromosome. *FRT42B*was recombined separately with *HSPC300*^Δ*54.3*^and *HSPC300*^Δ*96*^. Germ line clones were induced in *hs-FLP; FRT42B Ovo*^*D*^/*FRT42B*, *HSPC300*^Δ*54.3*^flies as described \[[@B45]\]. Other utilized strains were *CYFIP*^Δ*85.1*^, *Kette*^*03335*^and *SCAR*^Δ*37*^\[[@B8]\].
Molecular techniques
--------------------
### DNA constructs
*HSPC300*coding sequence was amplified by RT-PCR on total RNA extract from *Drosophila*S2 cells. Utilized primers were GGG GAA TTC AAA GAT GAG TGG GGC TCA CAG and GGG CTC GAG CGT TTA CGT TAA TGT TTC ACC CTG. After *Eco*RI, *Xho*I digestion, the fragment was cloned into pGEM-T and pUAST vectors.
### Quantitative mRNA analysis
Total RNA was recovered from animals of the indicated developmental stage or tissue and subjected to cDNA synthesis using primers mentioned above. Real time PCR was performed according to standard protocols with a Light Cycler (Roche, Basel, Switzerland) using primers AAA GCA GAT CCA CCA GGA CT and CGC TCC AGG ATC GTT AGT TT. Primers for housekeeping gene *rp49*were GCG CAC CAA GCA CTT CAT C and GAC GCA CTC TGT TGT CGA TAC C. All samples were analyzed in replicates of four.
### 5\' and 3\' Inverse PCR
Total genomic DNA of *HSPC300*^Δ*54.3*^flies was extracted by standard methods, digested with *Msp*I and *Eco*RI, followed by self ligations in separate reactions. *Msp*I severed within the P element and flanking 3\' sequence, resulting in rescue of the 3\' end. *Eco*RI severed within the P element and flanking 5\' sequence, resulting in rescue of the 5\' end. The rescued ends were amplified by standard primer combination of GTA ACG CTA ATC ACT CCG AAC AGG TCA CA and CAA TCA TAT CGC TGT CTC ACT CA. Amplified products were subsequently sequence verified by ACA CAA CCT TTC CTC TCA ACA A for the 5\' end and GAC ACT CAG AAT ACT ATT C for the 3\' end.
### Immunolabeling on embryos and larvae
Immunolabeling on embryos was performed according to standard procedures. Larvae open-book preparations and immunolabeling are described in Bellen and Budnik \[[@B46]\]. Antibodies utilized were: polyclonal HSPC300 antibody (1:1,000), anti-Fas II ID4 (1:50) and anti-Disc large (1:20) (Developmental Studies Hybridoma Bank, Iowa City, USA), anti-GFP (1:50; Santa Cruz Biotechnologies (Santa Cruz, California, USA), anti-SCAR \[[@B9]\] (1:100) and anti-CYFIP \[[@B8]\] (1:100).
### Immunoprecipitations
S2 cells were cultured in Schneider cell medium (Gibco BRL/Invitrogen, Karlsruhe, Germany) + 10% fetal calf serum. Cytoplasmic extracts were prepared by lysing S2 cells in buffer (200 mM NaCl, 20 mM Tris-HCl pH 7.5, 5 mM MgCl~2~, 0.4% Triton X-100, protease inhibitor cocktail (PIC)), kept on ice for 10 minutes. The 2,000 g supernatant was incubated for 6 h with 5 μg of either anti-HSPC300 or rabbit IgG and protein A Sepharose. Beads were extensively washed in lysis buffer, directly boiled in SDS-PAGE loading buffer and subjected to SDS-PAGE analysis.
### Embryonic and larval extracts
Animals of the correct genotype were collected on the basis of labeled balancer chromosomes. Embryonic extracts were prepared from overnight (18 h) cages. Embryos and wandering third instar larvae were mashed using pestles in 150 mM NaCl, 20 mM Tris-HCl pH 7.5, 1 mM EDTA, 0.1 mM MgCl~2~, 1% Triton X-100, PIC, followed by an incubation on ice for 10 minutes. The supernatant of a 12,000 g centrifugation was briefly sonicated, and the amount of total protein was determined by Bradford assay.
### Western blot analysis
Proteins were separated in 7% polyacrylamide gels. For detection of HSPC300, proteins were resolved on precast 4--12% Bis-Tris polyacrylamide gels (Invitrogen, Karlsruhe, Germany) in NuPAGE-MES buffer. SDS-PAGE and blotting were performed according to standard procedures. Primary antibodies used in western blot analysis were anti-HSPC300 (1:3,000), anti-CYFIP \#1719 (1:100), anti-SCAR (1:2,000), anti-Kette \#2081 \[[@B8]\] (1:2,000) and anti-β-tubulin (1:4,000) (Chemicon, Hampshire, UK).
### Microscopy and statistics
The confocal microscope was a Leica TCS-SP1. Confocal images were assembled using in-house developed software. Synapse images for quantification were obtained using a Zeiss Axiophot 2 microscope. Scanning electron microscopy was performed with a Philips -XL20 microscope. Twenty-five NMJs (muscle 4, segments A2-A4) were scored per genotype. All pictures of synapses were taken at 40x and their corresponding muscle area pictures were taken at 10x and subjected to an in-house developed software \[[@B7],[@B8]\]. Statistical significance was calculated using ANOVA and the Newman-Keuls method for *post hoc*pair-wise analyses.
Competing interests
===================
The author(s) declare that they have no competing interests.
Authors\' contributions
=======================
AQ generated HSPC300 mutant flies and drafted a version of the manuscript. AQ and BS carried out the phenotypic analysis. PC and AS participated in coordinating the study, AS also participated in designing it. AQ, BS, AS, and Angela G prepared the figures. Angela G conceived the study and wrote the final version of the manuscript, together with AS. Alexis G produced novel tools required for the study (anti-HSPC300 and anti-SCAR antibodies). All authors have read and approved the final version of the manuscript.
Supplementary Material
======================
###### Additional file 1
Molecular characterization of excision line *HSPC300*^Δ*54.3*^. Sequence obtained upon 5\' and 3\' inverse PCR (compared with original line *EP(2R)0506*) showing the presence of intact junctions between the P element and surrounding genomic sequences. Note that, following 208 bases of the *HSPC300*sequence, an unrelated sequence of at least 74 bases is present.
######
Click here for file
###### Additional file 2
Normal levels and localization of other WAVE/SCAR complex proteins (CYFIP, SCAR) in HSPC300 zygotic null embryos. **(a-f)**Wild-type (WT), HSPC300 zygotic null and, as control, CYFIP zygotic null embryos labeled with anti-CYFIP (a-c) or anti-SCAR (d-f) antibodies. **(g)**Anti-CYFIP and anti-SCAR immunoblot analysis of WT and HSPC300 zygotic null mutant extracts. Note that in contrast to genetic conditions in which maternal and zygotic HSPC300 doses have been depleted, there is no appreciable difference in CYFIP and SCAR levels and distribution in HSPC300 zygotic null embryos. Maternally provided HSPC300 protein is thus sufficient to stabilize other WAVE/SCAR complex proteins during embryonic development. In contrast, despite maternal contribution, loss of zygotic CYFIP destabilizes SCAR. Scale bar: 75 μm.
######
Click here for file
Acknowledgements
================
We are grateful to J Zallen, the Developmental Studies Hybridoma Bank, S Sigrist, the Szeged and Berkeley Stock Centers for providing antibodies and fly strains. We thank C Diebold for excellent technical assistance, N Arbogast for help with fly strains, M Boeglin, D Hentsch and JL Vonesch for help with confocal microscopy and development of software used in this study. This work was supported by: FRAXA foundation, HFSP, ULP, INSERM, CNRS, the Hôpital Universitaire de Strasbourg, Ministère de la Recherche, FRM. AQ was supported by AFM, BS by Bourse Régionale, PC by EMBO, AS by FRM and Lilly foundation.
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Christopher Polk/Getty Images
If you're bitter that your team didn't make the Super Bowl and don't care about the game at this point, consider throwing a couple of bucks on some ridiculous (and fun) prop bets.
Sportsbooks will let paying customers bet on anything Super Bowl-related these days, and the national anthem and halftime performances are no exception.
For this piece, let's play a game.
We're going to take a look at the six national anthem and halftime show prop bets OddsShark lists and give ourselves $100 in Monopoly money to play with.
We'll predict what bet will come through and use our $100 to maximize profits throughout the prop slate.
Read on to find out the picks.
National Anthem Prop Bets
1. How Long Will It Take Luke Bryan to Sing the U.S. National Anthem?
Over 2:15: -120
-120 Under 2:15: -120
I recently went to the video tape and checked out three of Luke Bryan's national anthem performances since 2014. Quoting the article, "Bryan took 2:27 to sing the national anthem at U.S. Bank Stadium in August, 2:12 at Madison Square Garden in 2014 and 2:13 at FarmBorough Festival in 2015."
The oddsmakers did well looking at the tape and putting the mark at 2:15, making this a harder decision.
The guess is that Bryan tries to go for a long, classic anthem performance and surpasses 2:15, as he did most recently in August, but the confidence level here is low given two of those three anthems didn't hit the 2:15 mark.
We're only betting $10 on this one.
2. What Will Luke Bryan Be Wearing When He Starts Singing the U.S. National Anthem?
Blue Jeans: -200
-200 Any Other Pants or Shorts: +150
This man literally sings about blue jeans in one of his bigger hits ("Drunk on You"). Blue jeans is a stone-cold lock.
There's no way he wears shorts while singing the anthem, as Twitter would probably riot.
It's then a battle between blue jeans and other pants, but let the record show that Bryan wore blue jeans for the three aforementioned anthem performances, plus the national anthem at the 2012 MLB All-Star Game.
We're spending a hefty $35 on blue jeans.
3. Will Luke Bryan Be Wearing a Hat When He Appears on Screen Before Singing the U.S National Anthem?
Yes: -120
-120 No: -120
It looks like he didn't have a hat in 2012, 2015 and 2016, but it looks like he did in 2014.
Also, this is just a gut (and uninformed) take because I've never sung or performed in anything in my life, but I can't imagine him holding a hat while he sings the anthem. Wouldn't that be distracting and strange? And he's not just going to throw or drop the hat haphazardly before starting, right? That would be awkward.
Put $25 on no hat.
4. Will Luke Bryan Forget or Omit a Word From the Official U.S National Anthem?
Yes: +400
+400 No: -700
This prop might be in reference to Christina Aguilera's rough anthem performance before Super Bowl XLV, or Bryan infamously reading off lyrics written on his arm in 2012.
Given the backlash Bryan experienced in 2012, it's likely he'll go the extra mile to ensure he'll sing from memory. He did so without a problem in the other three performances linked above.
The call here is "no," but we're not getting great odds. We need to spend $7 just to win $1. It's not worth our time or fake money.
5. Halftime Show: What Color Will Lady Gaga's Hair Be When She Starts Her Halftime Show?
Blonde : -500
-500 Any Other Color: ??
This prop unfortunately does not list a line for "any other color," but we're avoiding it anyway. The guess is her current hair color of blonde, but at -500 (bet $100 to win $20), that's not a great return on investment. No money spent here.
6. Halftime Show: Which Song Will Lady Gaga Sing First?
"Born This Way": +225
+225 "Bad Romance": +250
+250 "Edge of Glory": +600
+600 "Poker Face": +1000
+1000 "Just Dance": +1000
+1000 "Any Other Song": +110
This is a classic Vegas trap line!
At first glance, it seems preposterous that "Just Dance," which is Lady Gaga's top-performing song on the Billboard charts, sits at +1000.
But dig a little deeper, and you'll realize why that's the case. Lady Gaga just had a new studio album drop (Joanne), and she's been promoting it recently through various performances.
Of note, you'll see "Million Reasons" on there quite a bit. Also of note: Lady Gaga sings "Perfect Illusion" in the halftime show commercial that has been shown about 20,000 times during the NFL playoffs.
The sportsbooks could make a killing off this prop, with a bunch of people betting big money on one of her older and more mainstream hits and presumably getting great odds, but the guess based on recent events is that she leads with "Perfect Illusion," so the true play is "any other song" at +110.
We're spending $30 on this bet, exhausting our initial $100.
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$async = it.root.schema.$async === true;
$refCode = 'root.refVal[0]';
}
}}
{{??}}
{{ var $refVal = it.resolveRef(it.baseId, $schema, it.isRoot); }}
{{? $refVal === undefined }}
{{ var $message = it.MissingRefError.message(it.baseId, $schema); }}
{{? it.opts.missingRefs == 'fail' }}
{{ it.logger.error($message); }}
{{# def.error:'$ref' }}
{{? $breakOnError }} if (false) { {{?}}
{{?? it.opts.missingRefs == 'ignore' }}
{{ it.logger.warn($message); }}
{{? $breakOnError }} if (true) { {{?}}
{{??}}
{{ throw new it.MissingRefError(it.baseId, $schema, $message); }}
{{?}}
{{?? $refVal.inline }}
{{# def.setupNextLevel }}
{{
$it.schema = $refVal.schema;
$it.schemaPath = '';
$it.errSchemaPath = $schema;
}}
{{ var $code = it.validate($it).replace(/validate\.schema/g, $refVal.code); }}
{{= $code }}
{{? $breakOnError}}
if ({{=$nextValid}}) {
{{?}}
{{??}}
{{
$async = $refVal.$async === true || (it.async && $refVal.$async !== false);
$refCode = $refVal.code;
}}
{{?}}
{{?}}
{{? $refCode }}
{{# def.beginDefOut}}
{{# def._validateRef:$refCode }}
{{# def.storeDefOut:__callValidate }}
{{? $async }}
{{ if (!it.async) throw new Error('async schema referenced by sync schema'); }}
{{? $breakOnError }} var {{=$valid}}; {{?}}
try {
await {{=__callValidate}};
{{? $breakOnError }} {{=$valid}} = true; {{?}}
} catch (e) {
if (!(e instanceof ValidationError)) throw e;
if (vErrors === null) vErrors = e.errors;
else vErrors = vErrors.concat(e.errors);
errors = vErrors.length;
{{? $breakOnError }} {{=$valid}} = false; {{?}}
}
{{? $breakOnError }} if ({{=$valid}}) { {{?}}
{{??}}
if (!{{=__callValidate}}) {
if (vErrors === null) vErrors = {{=$refCode}}.errors;
else vErrors = vErrors.concat({{=$refCode}}.errors);
errors = vErrors.length;
} {{? $breakOnError }} else { {{?}}
{{?}}
{{?}}
|
{
"pile_set_name": "Github"
}
|
LUXEMBOURG — The eurozone’s finance ministers began making last-ditch efforts on Monday to avoid a clash with France, which must formally submit its budget for scrutiny by the European Union authorities by the middle of the week.
The French government recently announced a “no austerity” budget for 2015, saying it would miss its European Union-mandated deficit target for the second time since 2012 — and by a wide margin. If France makes no modifications before formally submitting the budget on Wednesday, the government could find itself in a standoff with European officials that they assert could threaten the unity of the euro currency bloc.
“The figures we’re hearing from Paris are not very hopeful,” Jeroen Dijsselbloem, the president of the group of eurozone finance ministers, told reporters on Monday as he arrived at the monthly meeting. Recent declarations by the government in Paris were cause for “some worry,” he added.
Ministers agreed on Monday that bloc’s fiscal rule book was “an anchor of confidence in the E.U.” that needed to be preserved, Mr. Dijsselbloem told a news conference after the meeting.
|
{
"pile_set_name": "OpenWebText2"
}
|
Q:
Virtualbox host-only network route is preempted by Pulse Secure VPN client
Virtualbox becomes unavailable for incoming connections from host OS when VPN is on. Accordingly, I cannot use http/ssh/rdp clients to access guest OS from host OS while Pulse Secure VPN stays connected.
Host OS: OSX High Sierra. My understanding is that a VPN client should not preempt routes in private IPv4 address space. Any workarounds to resolve this?
A:
I end up creating a script to launch my virtual machine. Limitation is that you have to launch the VM when VPN is off because Pulse Secure blocks creation of routes required.
I made this script a docked command for convenience -
#!/bin/bash
# visudo as root, add your_username ALL = (ALL) NOPASSWD:ALL
# vboxmanage list vms
guestip="192.168.86.3"
guestmac="8:0:27:22:4c:27"
vmname="WIN_ENT_10_64B"
# if the VM is running, leave it alone in peace:
vboxmanage showvminfo $vmname |grep "running (since"
[ "$?" -eq "0" ] && exit
# hide terminal window:
osascript -e 'tell application "Finder" to set visible of process "Terminal" to false'
# shutdown vbox network:
while [ -n "`netstat -rnf inet |grep $guestip`" ]; do
sudo ifconfig vboxnet0 down
sleep 1
done
# start VM and wait:
vboxmanage startvm $vmname --type separate
while [ -z "`netstat -rnf inet |grep $guestip`" ]; do
sleep 1
done
# delete original route:
sudo route -n delete ${guestip%.*}.0
# create a network singularity in routing table:
sudo route -n add $guestip/32 -interface vboxnet0
# create the host on the network:
sudo arp -s $guestip $guestmac
osascript -e 'tell application "Terminal" to quit' &
The scripts assumes that you can use sudo without a password.
guestip is manually configured in guest OS on the "host only interface" (normally #2). When you create a "host only network adapter" in VirtualBox, it has DHCP enabled by default. I disable DHCP and assign a static IP in the guest OS manually for consistency reasons (here - 192.168.86.3, netmask 255.255.255.0 or CIDR /24, DNS left blank).
guestmac is MAC address of the network interface in the guest OS that has the IP 192.168.86.3. Do not confuse it with MAC address of the "host only network adapter" in VirtualBox configuration. The latter is configured with 192.168.86.1/24 in our case (MAC a:0:27:0:0:0 below).
After the script completes (terminal app disappears from the dock), expected output of netstat -rnf inet shall comprise similar entries:
192.168.86.3 8:0:27:22:4c:27 UHLS 3 4884 vboxnet
192.168.86.3/32 a:0:27:0:0:0 ULSc 0 0 vboxnet
These entries will persist across VPN connects/disconnects and let you access your VM locally regardless of the VPN state.
|
{
"pile_set_name": "StackExchange"
}
|
TALLAHASSEE, Fla. (AP) — Asked this month whether President Donald Trump is doing a good job, Florida Gov. Rick Scott said he was happy with his friend's decisions on offshore drilling and willingness to accelerate repairs to the Lake Okeechobee dike.
Asked the question again, Scott paused and said, "I can tell you, what I want is results, and those are the results I like."
Scott's hesitance to directly answer the question about the Republican president is a small but telling indicator of the balancing act he has performed since deciding to challenge Democratic incumbent U.S. Sen. Bill Nelson.
Trump enjoys strong support among Republicans in the state he won two years ago. But Democrats, who have struggled with turnout in nonpresidential elections, have been energized by Trump's actions and plan to flock to the polls this year.
Scott's current posture is a dramatic shift for the vocal critic of former President Barack Obama who enthusiastically backed Trump during the presidential election. Scott set up a Super PAC to help Trump during the campaign and has visited the president at the White House and Trump's Mar-A-Lago resort in Palm Beach.
Trump publicly urged Scott to run for U.S. Senate, but recently the GOP governor has picked a careful path as he mounts an aggressive push to deny Nelson a fourth term.
He has split with Trump on certain issues, including immigration, but without criticizing the president. At some political events, he has barely mentioned Trump by name.
In April, Scott skipped a Trump round-table discussion of the tax-cut package in South Florida, heading out of state to raise money for his Senate campaign instead.
Brian Ballard, a top GOP lobbyist and fundraiser who knows both Scott and Trump well, said "very few people agree with the president 100 percent of the time." But he added that Scott is already well-liked by Republican voters in Florida and can afford to disagree with the president.
"The governor has his own brand; he doesn't need to grab the president's coattails," Ballard said. "He doesn't have to disparage the president. He has a clean opportunity to be supportive of the president and continue to promote his own brand. If he disagrees, he will disagree in a way that is not disrespectful."
Democratic strategist Steve Schale, however, pointed out that Scott successfully campaigned for governor in 2010 by linking the Democratic nominee to Obama.
"Scott really can't run from Trump," Schale said. "There's too many clips and too much video, and I'm sure it will be making its way to TV screens."
Scott, a former health care executive who is leaving the governor's office because of term limits, is deliberate and tends to stick closely to scripted talking points during public events.
Recently, he has been cautious when it comes to the president:
— During a visit to Puerto Rico, a reporter asked Scott what the federal government should have done differently after Hurricane Maria. Puerto Ricans have complained that the U.S. government responded slowly after the storm battered the American territory. Scott said he didn't know what he would have done differently but said communicating with federal authorities is important.
— Scott split with Trump over the administration's policy of separating families at the border but did not sharply criticize the president. Instead, he sent a letter to federal authorities calling for an immediate end to the policy and demanded that state officials be told about children brought into Florida.
— At the beginning of hurricane season, Scott sidestepped questions about a Trump budget proposal to cut money for hurricane research. At an event in Miami, Scott said several federal agencies had been good partners.
After a meeting in Orlando with Puerto Rican hurricane evacuees, Democratic incumbent Nelson was asked about the governor's relationship to Trump.
"They are great friends," Nelson said. "Scott has been like two peas in a pod with Trump, and that is not going to serve Rick Scott very well when the people of Puerto Rico and other Hispanic cultures find out the closeness between the two of them, as evidenced by the Trump administration over and over again trying to put down Hispanics."
Rick Wilson, a veteran Republican strategist from Tallahassee whose unrelenting criticism of Trump has made him a national celebrity, said Scott is smart to try to distance himself from the president on issues such as the child separation policy. But he was skeptical of how successful it would be for him.
"Scott knows what everyone else knows: This Trump policy polls in the ditch," Wilson said. "It's poison. He's smart to do it now, but there's still a lot of video of Rick Scott and Trump swapping spit."
|
{
"pile_set_name": "Pile-CC"
}
|
Q:
Why a client and not an app?
I searched on the play store for a stack overflow app for my android. I found out there is a client that you can use, but I was wondering why they didn't make an official app? The GUI would be much better and the buttons would look as if they belong on a mobile device. So far it looks like the desktop view squeezed onto a mobile view.
A:
There actually is an app
https://play.google.com/store/apps/details?id=com.stackexchange.marvin&hl=en
It's not specifically or solely for stackoverflow, but stackoverflow is also in there.
|
{
"pile_set_name": "StackExchange"
}
|
Back pain after photodynamic therapy with verteporfin.
To report the incidence of back pain after photodynamic therapy, which suggests methods for prevention that are related to its pathogenesis. Retrospective case series. We retrospectively observed 548 patients who had undergone photodynamic therapy with verteporfin. Of 548 patients at the first treatment, 14 patients (2.6%) experienced pain during the infusion. Eleven patients were being treated for age-related macular degeneration; their mean age was 81 years, which significantly differed from the mean age of the overall age-related macular degeneration group (P = .003). The pain was mild in eight patients, moderate in four patients, and severe in two patients, with dyspnea and precordial pain. Five of the 14 patients had further courses of photodynamic therapy. After being treated prophylactically 60 minutes before photodynamic therapy, only one patient reported further mild pain. The biologic mechanisms of back pain may involve a high level of circulating thromboxanes that are induced by the liposomal composition of verteporfin. Prevention may include hydration, nonsteroidal anti-inflammatory drugs, and halving the infusion rate.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
Hot on the heels of "A Bigger Splash," the filmmaker returns with a film that's worthy of comparisons to "Carol" and "Moonlight."
“Is it better to speak or to die?” That’s the core question of “Call Me By Your Name,” which surfaces in a scene where a character reads the words of Marguerite of Navarre in “The Heptaméron,” but it’s an idea at the heart of all queer narratives. It’s been especially present in queer cinema, where muteness and survival are often the most bittersweet bedfellows. But “Call Me By Your Name” not only quotes Marguerite’s words, it suffuses them into every fiber of its being. It’s a great film because of how lucidly it poses her question, and an essential one because of how courageously it answers it.
Directed by Luca Guadagnino with all of his usual cool (“I Am Love”) and adapted from André Aciman’s beloved 2007 novel of the same name, the rapturous “Call Me By Your Name” nearly rates alongside recent LGBT phenomenons “Carol” and “Moonlight,” matching the artistry and empathy with which those new masterworks untangled the repressive desire of same-sex attraction.
It’s 1983, “somewhere in Northern Italy.” The height of summer, and all of the neighborhood teenagers are in heat. Elio Perlman (Timothée Chalamet, keeping the promise he showed in “Miss Stevens” last September) is still a virgin. A 17-year-old American whose father, a local celebrity, is an eminent professor specializing in Greco-Roman culture (Michael Stuhlbarg), Elio has sprouted from the soil like the apricot trees that surround his family’s villa, and he’s impatiently waiting to bloom. Scrawny enough to be mistaken for a child but sophisticated enough to be mistaken for a man, Elio is a multilingual music prodigy who’s more comfortable with Bach and Berlioz than he is in his own body. He knows everything and nothing. But he’s about to get one hell of an education.
Every summer, Elio’s father flies out a graduate student to stay at the villa and help him with his research — this year’s intern is Oliver (Armie Hammer, as sensational here as he was in “The Social Network,” but similarly a touch too old for the part). Oliver is 24 and his body is an epic unto itself, as big as any one of the ancient statues that have been dredged up from the local seas. Arrogant, eager, and almost suspiciously handsome for an aspiring historian, the mysterious new visitor often seems as though he got lost on his way to a Patricia Highsmith novel. While much of the film feels stretched between the feverish eros of Bertolucci, the budding warmth of Mia Hansen–Løve, and the affected stoicism of James Ivory (who, at 88, has a co-writing credit on this screenplay), a thin shadow of suspense creeps along the outer edges of each frame, priming viewers for a very different kind of pivot than the one Guadagnino deployed during the third act of “A Bigger Splash.”
Elio and Oliver grow closer as the summer sinks toward its dog days — at first they share only a bathroom, the skinny adolescent looking at his unpredictable new friend as though he can’t understand how they could be the same species, let alone be interested in the same thing. But commonalities and semi-secrets soon emerge: For one thing, they’re both Jews in a land of goys. Oliver, no doubt aware that he looks like the winner of Hitler’s master race, wears a Star of David necklace underneath his shirt, a barely visible emblem of his otherness. The Perlmans, on the other hand, are what Elio’s father describes as “Jews of discretion” (one of the funnier lines in a movie that’s laced with a sharp sense of humor), but the strangeness of celebrating Hanukkah within spitting distance of Vatican City eventually makes its mark.
As the film progresses, Elio and Oliver begin to share more tangible things: Bike rides, errant touches, an unknown desire to have sex with one another (that last one is a biggie). Crucially, however, Elio is as conflicted about his own passions as he is those of the boy next door. His tastes are molten and volatile — he performs the same piano piece in a wildly different style every time he plays it, much to Oliver’s amused frustration. When he’s not busy gawking at his brawny infatuation, he’s enthusiastically trying to deflower the French girl down the street (Esther Garrell, of the New Wave Garrells), who wears her wardrobe of summer dresses like she’s trying to shame away the other seasons.
Telling this story with the same characteristically intoxicating capriciousness that has come to define his work, Guadagnino doesn’t dwell on looks of questionably requited longing. He’s not Todd Haynes and — with the possible exception of a long take mid-movie that follows the two leads around a fountain and endows the space between them with a palpably physical sense of attraction and denial — he doesn’t try to be. Instead, he stays attuned to the raw energy of trying to feel someone out without touching them, of what it’s like to live through that one magical summer where the weather is the only part of your world that doesn’t change every day.
Rippling with nervously excited piano compositions and shot with immeasurable sensuality by Thai cinematographer Sayombhu Mukdeeprom (“Uncle Boonmee Who Can Recall His Past Lives” and “Arabian Nights”), “Call Me By Your Name” is a full-bodied film that submits all of its beauties to the service of one simple truth: The more we change, the more we become who we are. Like the Latin prefixes that Oliver and Mr. Perlman trace back to their roots or the antiquated artworks that resonate because of how much the world has changed since their creation, Elio learns that growth — however wild or worrisome it might seem at the time — is the greatest gift that he can give himself.
READ MORE: The 2017 IndieWire Sundance Bible: Every Review, Interview, And News Story From The Fest
Watching him slowly come to that realization is an unforgettable and enormously moving experience because of how the film comes to realize it, too. Guadagnino lives for the climactic portion of this story, when feelings are finally transmuted into action and Oliver’s true nature breaks through the marble bust of his body (Hammer’s warmth in these scenes is extraordinary). The details are best experienced for yourself, but it’s safe to say that movie lives up to the book’s steamy reputation, and Chalamet and Hammer throw themselves at each other with the clumsy abandon of first love. Growingly increasingly divorced from its source material as it goes along, the final beats of Guadagnino’s adaptation galvanize two hours of simmering uncertainty into a gut-wrenchingly wistful portrait of two people trying to find themselves before it’s too late. As Elio’s father puts it in a heart-stopping monologue that every parent might want to memorize for future use: “Don’t make yourself feel nothing so as not to feel anything. What a waste.”
Leaving us with one of the gorgeous new songs that Sufjan Stevens wrote for the film, this achingly powerful story — a brilliant contribution to the queer cinema canon — breathes vibrant new life into the answer that Marguerite of Navarre gave to her own question. “I would counsel all such as are my friends to speak and not die,” she said, ““for ’tis a bad speech that cannot be mended, but a life lost cannot be recalled.”
Grade: A
“Call Me By Your Name” premiered in the Premieres section of the 2017 Sundance Film Festival. Sony Pictures Classics will release it later this year.
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|
{
"pile_set_name": "OpenWebText2"
}
|
Cameronians War Memorial
The Cameronians War Memorial is a war memorial in Kelvingrove Park in the west of Glasgow, Scotland, to the north of Kelvingrove Art Gallery and Museum. It commemorates the service of the Cameronians (Scottish Rifles) regiment in the First and Second World Wars. The memorial includes a bronze sculpture representing a machine gun emplacement, with three human figures. It became a Category B listed building in 1988.
Background
The sculpture was designed by Philip Lindsey Clark. He had enlisted as a private in the Artists' Rifles in 1914, and was commissioned in the 11th (Service) (1st South Down) Battalion of the Royal Sussex Regiment in 1916, ending the war as a captain with a DSO.
Description
The memorial includes a bronze statue with three cast figures of soldiers, slightly larger than life size, cast by the Maneti foundry in London. From right to left, the three figures are: one in a trench firing his Lewis machine gun, while a sergeant to his right advances holding a rifle, and further right an officer lies wounded. The advancing sergeant symbolises victory and may be modelled on Cameronian Pipe Major Jimmy Sanderson, while the wounded officer represents sacrifice. The sculpture now stands on a rectangular grey granite plinth, on a slightly larger base, raised on three steps, enclosed by hedges and a wrought iron fence.
Three plaques on the main west front bear the inscriptions, from the top: "TO THE GLORIOUS MEMORY OF ALL RANKS / THE CAMERONIANS (SCOTTISH RIFLES) WHO, / TO UPHOLD LIBERTY AND JUSTICE IN THE WORLD, / LAID DOWN THEIR LIVES IN THE TWO WORLD WARS 1914 – 1918 AND 1939 – 1945", then: "THE 6/7TH BATTALION, CAMERONIANS (SCOTTISH RIFLES) / WAS DISBANDED ON THE 31ST MARCH 1967 / AND THE 1ST REGULAR BATTALION ON THE 14TH MAY 1968 / THUS ENDING THE REGIMENT'S LONG MILITARY ASSOCIATION / WITH THE CITY OF GLASGOW", and finally: "THIS PLAQUE WAS UNVEILED BY / THE LORD PROVOST OF GLASGOW / THE RT. HON. JOHN JOHNSTON".
A plaque to the south side reads "O VALIANT HEARTS, WHO TO YOUR GLORY CAME / THROUGH DUST OF CONFLICT AND THRO' BATTLE FLAME / TRANQUIL YOU LIE. YOUR KNIGHTLY VIRTUE PROVED / YOUR MEMORY HALLOWED IN THE LAND YOU LOVED", and one on the north side reads "BE THOU FAITHFUL UNTO DEATH AND I / WILL GIVE THEE A CROWN OF LIFE".
A further plaque to the rear of the memorial lists the theatres of war in which the battalions of the regiment served.
The memorial was unveiled by Field Marshal Sir Douglas Haig, who had been the Commander-in-Chief (C-in-C) of the British Expeditionary Force (BEF) on the Western Front, on 9 August 1924, five days after the tenth anniversary of the outbreak of the war.
A plaque for the Second World War was added in 1947. The original sandstone plinth weathered badly and was replaced with a similar style in granite in 1958. Another plaque was added after the regiment was disbanded in 1968. The memorial became a Category B listed building in 1988, and it was restored in 2009.
Other memorials
Another Cameronians memorial in Douglas, South Lanarkshire was built in 1892 to commemorate the bicentenary of the raising of the Cameronian Regiment (26th Regiment of Foot) on 14 May 1689. It depicts the regiment`s first Colonel, James Douglas, Earl of Angus. Another memorial on the Douglas Estate commemorates the disbanding of the 1st Battalion, Cameronians (Scottish Rifles) on 14 May 1968.
Clark created a similar sculpture of an advancing infantryman for his Southwark War Memorial, unveiled in 1922, with the rifle slung over his left shoulder rather than held in his right hand. A similar sculpture of an infantryman with rifle was used by Albert Toft for the Royal Fusiliers War Memorial in Holborn.
References
Kelvingrove Park at Dumbarton Road, Cameronians Monument, Historic Scotland
Cameronians (Scottish Rifles) War Memorial, roll-of-honour.com
Cameronians (Scottish Rifles), Imperial War Museum
Cameronian War Memorial, Kelvingrove, Glasgow,
The Cameronians Regimental Memorials in Douglas, The Scottish Military Research Group
http://www.cameronians.org/
Cameronians (Scottish Rifles) War Memorial, Glasgow – City of Sculpture
Category:Buildings and structures completed in 1924
Category:Category B listed buildings in Glasgow
Category:Monuments and memorials in Glasgow
Category:World War I memorials in the United Kingdom
Category:World War II memorials in Scotland
Category:1924 establishments in Scotland
Category:Listed monuments and memorials in Scotland
|
{
"pile_set_name": "Wikipedia (en)"
}
|
622 F.2d 584
Inmates, Richmond City Jailv.Winston
79-6639
UNITED STATES COURT OF APPEALS Fourth Circuit
5/21/80
1
E.D.Va.
AFFIRMED
|
{
"pile_set_name": "FreeLaw"
}
|
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