text:
package org.lightadmin.api.config.builder;

import org.lightadmin.api.config.unit.FieldSetConfigurationUnit;
import org.lightadmin.api.config.utils.EnumElement;
import org.lightadmin.core.config.domain.unit.ConfigurationUnitBuilder;
import org.lightadmin.core.view.editor.JspFragmentFieldControl;

public interface PersistentFieldSetConfigurationUnitBuilder extends ConfigurationUnitBuilder<FieldSetConfigurationUnit> {

    PersistentFieldSetConfigurationUnitBuilder field(String fieldName);

    PersistentFieldSetConfigurationUnitBuilder caption(String caption);

    @Deprecated
    PersistentFieldSetConfigurationUnitBuilder enumeration(String... values);

    PersistentFieldSetConfigurationUnitBuilder enumeration(EnumElement... elements);

    PersistentFieldSetConfigurationUnitBuilder editor(JspFragmentFieldControl editControl);
}


Talented, young Engineering student with development oriented attitude gained from surrounding environments with hand on opportunities and have a strong work ethic with a desire and commitment to succeed.
Basic concept of Network & different Topology.
Install and configure of LAN.


Heta's Scan-Line Green 100 allows you to heat your entire house independent of conventional heat sources and with a high level of comfort. The fully automatic pellet stove and traditional wood-burning stove presentation is a winning combination. The top plate is available in seven enamel colours, allowing the stove's appearance to be customised to individual tastes.


text:
using std::cout;
using std::endl;

namespace Directory
{
	vector<string> GetFilesNamesFrom(string folder)
	{
		vector<string> names;
		char search_path[FILENAME_MAX];
		sprintf_s(search_path, "%s/*.*", folder.c_str());
		WIN32_FIND_DATA fd;
		HANDLE hFind = ::FindFirstFile(search_path, &fd);
		if (hFind != INVALID_HANDLE_VALUE) {
			do {
				if (!(fd.dwFileAttributes & FILE_ATTRIBUTE_DIRECTORY)) {
					names.push_back(fd.cFileName);
				}
			} while (::FindNextFile(hFind, &fd));
			::FindClose(hFind);
		}
		return names;
	}

	string Directory::GetCurrentWorkingDirectory()
	{
		char cCurrentPath[FILENAME_MAX];
		GetCurrentDir(cCurrentPath, sizeof(cCurrentPath));
		string str(cCurrentPath);
		return str;
	}

	string Directory::CombinePaths(int amount, const char* args...)
	{
		va_list list;
		va_start(list, args);

		char* next = (char*)args;
		string path;

		for (int i = 0; i < amount; i++)
		{
			path += next;
			path += "\\";
			next = va_arg(list, char*);
		}

		va_end(list);
		return path;
	}
}

redpajama_set_name: RedPajamaGithub


text:
By Opening Mosque in Moscow, Putin Shows Muslims He is Not a 'Crusader'
© REUTERS / Maxim Zmeyev
By opening up the Moscow Cathedral Mosque, the largest mosque in Europe, Russian President Vladimir Putin has taken a smart step prior to a possible anti-ISIL military operation in Syria – he showed Muslims around the world that he isn't just another "Western crusader," Boulevard Voltaire reported.
The new mosque was opened in Moscow ahead of the Muslim holiday of Eid al-Adha, also known as the Feast of Sacrifice, on September 23 after a special ceremony attended by Putin himself, as well as a number of foreign delegates, including Turkish President Recep Tayyip Erdogan and Palestinian President Mahmoud Abbas.
Why was the event so widely publicized in media? French journalist Nicolas Gauthier of Boulevard Voltaire speculated that Putin didn't want to repeat the mistakes made by the United States in Iraq and Afghanistan, when many thought the US military was acting akin to medieval crusaders who came to conquer the area and suppress the local populations. Instead, Putin wanted to show Muslims that he isn't a "Western crusader."
© AFP 2019 / KARAM AL-MASRI
No One Can End Syria War Except Russia – Polish MEP
Furthermore, as an expert in politics, Putin knows that he needs to have strong support from Muslims in Russia, before he could venture down to Syria, the French journalist said.
Unlike Europe, where Islam is largely seen as an imported thing, Russia has a very different perspective towards Islam. Since both Muslims and Christians have lived in Russia side by side for centuries, Islam isn't seen as something alien. Putin plans to strengthen this further, wanting Muslims in Russia to form values that honor Russian culture and traditions to avoid the penetration of Wahhabism into Muslim communities in Russia, Gauthier explained.
Syria Says Russia Has Every Right to Combat Islamic State on Its Soil
Russia's Role Vital in Defeating Islamic State - Palestinian Ambassador
US Would Treat Islamic State as Ally if It Were Fighting Against Russia
Russia Will Not Send Troops to Fight Islamic State in Syria
crusader, Islam, Moscow Cathedral Mosque, Eid al-Adha, Vladimir Putin, Syria, Russia

redpajama_set_name: RedPajamaCommonCrawl


SINGAPORE: The Council for Estate Agencies (CEA) is investigating some 20 possible cases of unethical advertising.
This comes one month after its new advertising guidelines for property agents came into effect on August 1.
CEA's director for regulatory control, Mr Lee Say Kee said dummy ads, which advertise fictional properties or properties which do not have the owner's consent remain the most serious.
Others include advertisements that omit important information such as the salesperson's registration and contact numbers.
CEA also said it has an in-house team to scan online property portals, classified ads and flyers.


Leather Duffel - Handmade of the finest Italian vegetable-tanned Buffalo and Vachetta leathers, the Borlino Big Horn bag is great for a weekend getaway. It's loaded with features and pockets inside and out. Carry-on approved by all major airlines. Walnut Brown.
• Two exterior zippered pockets.
• One exterior flap pocket with magnetic closure.
• Two roomy interior, leather easy-access pockets.


WE SHOULD NOT EAT FOR 45 MINUTES AFTER TAKING SHOWER; WE SHOULD NOT BATHE FOR TWO AND HALF HOURS AFTER EATING.
Many of us have the habit of eating food immediately after taking a bath or a shower. If you eat immediately after taking bath, the food will not be digested properly. We have to eat only after 45 minutes from the time of our finishing the bath. Also, we should take bath only after two and half hours from the time we finish eating food.
All our body parts and cells are at 98.4 degree Fahrenheit temperature (37 degree Centigrade) throughout the 24 hours of every day. If we go to a cold country where temperature is – 10 degrees and measure our temperature with a thermometer even then our body temperature will be 37 degrees only. Similarly, even if we go to a hot country where the temperature is 50 or 60 degrees and measure our temperature with a thermometer even then our body temperature will be 37 degrees only.
What we need to understand from this is that the body temperature for a human being is always 37 degree Centigrade. All the people in all the countries around the world will have this same temperature at all the times. Each and every type of living species such as goat, cow, hen, etc. has such a specific body temperature.
Thus, the temperature of human body is always 37 degrees Centigrade. Even when we are in a cold climate or a hot climate, the organ called Triple Warmer in our body will always try to keep our body temperature uniformly at 37 degrees Centigrade at all times.
When we take bath, irrespective of whether it is normal water or hot water, irrespective of whether we take bath only for our body excluding the head or including the head, irrespective of whether we take bath in a river, pond or in our bath room, our body temperature will undergo a change immediately.
When our body temperature changes, the temperature controlling organ in our body will start working immediately and it will attempt to bring the body temperature to 37 degrees again. When the body is engaged in this activity to restore the body temperature, the digestive organs in the body will not get energy.
On an average, the Triple Warmer in our body works for about 45 minutes after we take bath. During this period, the digestive glands in our body will not function.
Therefore, please do not eat immediately after taking bath. Wait for about 45 minutes after finishing the bath and then eat.
Similarly, we should take bath only after a period of two and half hours after eating food. This is because it takes two and half hours for the food we eat to get digested and enter our blood stream. Some people may have their food digested in one hour. It may take up to five hours for some other people. So, we can safely assume that it takes about two and half hours on an average to digest the food.
Let us assume that we take bath within half an hour after eating the food. Immediately after we take bath, the temperature control organ in our body will start acting to set right the temperature of the body. At that time, all the energy in the body will be spent by the temperature control organ and no energy will be available to the digestive organs for performing their duties.
You can check this for yourself. Take bath immediately after eating food just for one day. You will get digestive problem onthat day. You will feel uncomfortable in your stomach. You will get headache.
Therefore, we should not take bath for a period of two and half hours after eating food. We should wait for a period of 45 minutes after taking bath before we start eating food.
It is your fault that you sleep lazily up to 8.00 am. If it is needed, we have to necessarily wake up early. Your body does not know that you have to be in the office by 9.00 am. However big an officer you may be, however rich you may be your body will not know at what time you have to be present in the office.
Our body expects us to follow some guidelines if it has to take care of itself. Please do not violate these guidelines. Please think how we can follow these guidelines by changing our habits instead of giving any lame excuses.
Next WHAT SHOULD WE DO IF WE GET BELCH?


I used some hickory smoked pulled pork for these. Roasted, peeled and seeded the anaheim chiles, filled with smoked pork, minced onion and queso fresco cheese. Dusted with flour. dipped the bottoms in batter then spooned more batter over the tops while frying. Fried on both sides until golden. Served topped with sauce. the batter.. 4 egg whites whipped add 4 TBs of flour, then fold in the 4 beaten egg yolks the sauce... saute minced onion and 1 clove of garlic in a bit of oil add 2 cups of chicken broth 1 cup tomato sauce 1 tsp salt 1/2 tsp pepper 1/2 tsp oregano simmer 10 minutes The rellenos batter has no salt so the addition of the sauce is a plus. :) These are also tasty with smoked chicken. Thanks for looking!


2 decks. Difficult. No redeal.
Zigzag Course Solitaire uses two decks (104 cards). You have 12 fan piles with 8 cards per pile and 8 foundations. An Ace and King of each suit are removed from the deck to form the foundation piles.
To build the aces up in suit to kings, and the kings down in suit to aces.
You may build fans up or down following suit. You can move only one card at a time. Empty fans may be filled with any card.


Feel like a French Kiss?
Well we're thrilled to oblige. WE'RE WAITING FOR YOU!
If you love new Australian independant theatre, we invite you to put your money where our lips are. Buy a French Kiss and be part of the team making possible Parnassus Den's inaugural production - THE DEPARTMENT STORE by Justin Fleming.
A "French Kiss"costs $100 and all proceeds will go towards production costs (sets, costumes, etc). It will also fill you with the warm feeling that you are contributing towards the tenuous survival of independent theatre in this country.
To become a French Kiss Patron, call 0400 250566 or email PD. Alternatively send a cheque or money order for $100 made out to PARNASSUS DEN - Box 655 Maroubra NSW 2035 AND email to us your name, email address, phone number and postal address. We will post out to you your French Kiss card and email you a receipt.
Now that it is too late to thank you in our programme, we will thank you on this web site - and will remember you fondly forever.
NOUS VOUS EMBRASSONS ET À BIENTÔT!


Every day families are embroiled in custody battles. Sometimes they involve families now living in different countries or different states. They all involve children spending time in different homes. I can't imagine how hard it must be for everyone involved.
All these case have their own particulars. All these cases are unique to each family, as every family is unique in itself. There are many sides to each story. It's impossible, unless of course there is proven abuse or neglect involved, to know who is in the right. How can you tell a child they can no longer see, or live, with one of their parents? It is an extremely sensitive issue. An issue which needs to be dealt with by professionals, in private, with much support and definitely with their children's best interests at the heart of each decision.
At what stage do people become so desperate, so bitter, so distressed that they put the immediate needs of their children behind their own egos? At what stage do you get the media involved? At what stage do you let your children be subjected to such heightened drama, beyond what they are already experiencing?
The custody battle being played out in the media like a reality television show is a disgrace. Those children should not have been put in that position, by either of their parents. The media should not be allowed to report on such issues. Fine their faces have been blurred, but not their school uniforms, which made it clear where these children went to school. And now the media, camped out the front of their father's Italian home, have alerted everyone to which tiny town he resides. Stop it.
What next? A telephone voting system to let the Australian public decide who should win custody of the kids? For the father phone: 222Italia. For the mother phone: 222Aussie.
Or perhaps we could let the parents hold a live debate on television or put them on Q&A?
I have no interest in the particulars of this case. It is not my business. It is no-one's business except the families involved. What I am most disturbed by is the fact I've been dragged into their personal lives. I have seen images of children being dragged into cars, of a mother wailing uncontrollably at an airport, of a father being forced to prise his child's hands of a fence away from waiting media, of the knowledge those children flew internationally without either their mother of father by their side. Enough.
These children have been subjected to too much. Their parents have failed them by letting this turn into a media circus. The media have failed them by reporting on an issue which is not in the interests of the general public to know about. It is time everyone leave this family alone to sort out this matter without the additional distress. Back off people. Back off.
What are your thoughts on this very private, yet now very public, issue?
Agree completely. It's very sad.
Could not agree with you more! Its a disgrace! none of us know the details and nor should we. I feel like a hypocrit just commenting here and giving this more 'air' but surely we as a society should have more morals than to allow this to be played out in such a manner.
Totally with you on that Bianca! This topic came up over dinner with friends on Friday night and we all agreed this private family matter has become a media circus. It is appalling. I don't know much of the particulars, nor have I sought to because it is none of my business and I plan to keep it that way!
Well said, Bianca. Those poor children will be so traumatised by this whole custody debacle. I am horrified at the way in which this has been played out in the media. The full extent of the emotional price those kids have paid may not be known for years. The whole situation makes me feel very sad.
The youngest two went to my son's primary school – which my 7YO son pointed out when a media ran the images of them at the beginning of all this!I don't believe either parent has put the kids first – the mum for not returning to Italy two years ago – and the dad for now not listening to the wishes of his kids. Under Australian law the older two would be able to choose themselves who they could live with. As someone who has had shared custody of two kids with her ex, I know how difficult all of this is. But my issues with my ex are not my kids' issues. He's their father, always will be. It's been 10 years now – I still don't like saying goodbye to them but they've grown into beautiful young adults partly I'm sure because I didn't use them as pawns.
Agreed – I don't want to know about it – not public fodder!
Was talking about this the other night. The media should have left it alone. And the parents should have thought of the kids, not of themselves.
OMG…..you have put this in exactly the way I have thought. I have commented on so many people's views on fb about this, basically saying exactly what you have said. As a Mum of a son whose parents split before he turned two, and has spent the last 11 years being shared between his parents, I am horrified that this is going on. There are things over the past 11 years that I have had to do as a Mum that have killed me, but have been in my son's best interests. I just don't get it. I don't get why or how people can legitimately think they can use their children like an asset. It sickens me.


text:
var assert = require('assert');

var FolderNotFoundValidator = require('../src/folderNotFound');

describe('Folder exists', function () {

    describe('The happy way', function () {
        var config = {
            path: '\\',
            os: 'windows',
            foldersNotFound: [
                'c:\\program files\\'
            ],
            folderNotFoundMessage: {
                "message": "Not Found"
            }
        };

        it('should return true', function () {
            var folderValidator = new FolderNotFoundValidator(config, 'c:\\');
            assert.equal(folderValidator.isExist, true);
        });

        it('should return false', function () {
            var folderValidator = new FolderNotFoundValidator(config, '"c:\\program files\\"');
            assert.equal(folderValidator.isExist, false);
        });
    });

    describe('Windows with slash on start', function () {
        var config = {
            path: '\\',
            os: 'windows',
            foldersNotFound: [
                'c:\\program files\\'
            ],
            folderNotFoundMessage: {
                "message": "Not Found"
            }
        };

        it('should return true', function () {
            var folderValidator = new FolderNotFoundValidator(config, '\\existentFolder\\');
            assert.equal(folderValidator.isExist, true);
        });

        it('should return false', function () {
            var folderValidator = new FolderNotFoundValidator(config, '"\\program files\\"');
            assert.equal(folderValidator.isExist, false);
        });
    });

    describe('Wihout slash in the end - input', function () {
        var config = {
            path: '\\',
            os: 'windows',
            foldersNotFound: [
                'c:\\program files'
            ],
            folderNotFoundMessage: {
                "message": "Not Found"
            }
        };

        it('should return true', function () {
            var folderValidator = new FolderNotFoundValidator(config, 'c:\\existentFolder\\');
            assert.equal(folderValidator.isExist, true);
        });

        it('should return false', function () {
            var folderValidator = new FolderNotFoundValidator(config, '"c:\\program files\\"');
            assert.equal(folderValidator.isExist, false);
        });
    });

    describe('Without slash in the end - response', function () {
        var config = {
            path: '\\',
            os: 'windows',
            foldersNotFound: [
                'c:\\program files\\'
            ],
            folderNotFoundMessage: {
                "message": "Not Found"
            }
        };

        it('should return true', function () {
            var folderValidator = new FolderNotFoundValidator(config, 'c:\\existentFolder');
            assert.equal(folderValidator.isExist, true);
        });

        it('should return false', function () {
            var folderValidator = new FolderNotFoundValidator(config, '"c:\\program files"');
            assert.equal(folderValidator.isExist, false);
        });
    });

    describe('Case sensitive - Windows', function () {
        var config = {
            path: '\\',
            os: 'windows',
            foldersNotFound: [
                'c:\\program files\\'
            ],
            folderNotFoundMessage: {
                "message": "Not Found"
            }
        };

        it('should return false', function () {
            var folderValidator = new FolderNotFoundValidator(config, '"C:\\Program Files"');
            assert.equal(folderValidator.isExist, false);
        });
    });

    describe('Case sensitive - Linux', function () {
        var config = {
            path: '/',
            os: 'linux',
            foldersNotFound: [
                '/dev/program files/'
            ],
            folderNotFoundMessage: {
                "message": "Not Found"
            }
        };

        it('should return true', function () {
            var folderValidator = new FolderNotFoundValidator(config, '/dev/program Files/');
            assert.equal(folderValidator.isExist, true);
        });

        it('should return false', function () {
            var folderValidator = new FolderNotFoundValidator(config, '/dev/program files/');
            assert.equal(folderValidator.isExist, false);
        });
    });

    describe('With some commands', function () {
        var config = {
            path: '\\',
            os: 'windows',
            foldersNotFound: [
                'c:\\program files\\'
            ],
            folderNotFoundMessage: {
                "message": "Not Found"
            }
        };

        it('should return true', function () {
            var folderValidator = new FolderNotFoundValidator(config, 'Dir \\usr\\tmp\\test /t:w');
            assert.equal(folderValidator.isExist, true);
        });

        it('should return false', function () {
            var folderValidator = new FolderNotFoundValidator(config, 'Dir "c:\\program files\\test" /t:w');
            assert.equal(folderValidator.isExist, false);
        });

        it('should return ', function () {
            var folderValidator = new FolderNotFoundValidator(config, 'Dir "\\program files\\test" /t:w');
            assert.equal(folderValidator.isExist, false);
        });

    });
});


SaluteMyJob has partnered with a variety of commercial companies, government organisations, regimental associations and Service charities and other not-for-profits.
SaluteMyJob's goal is to bridge the gap between employers and ex-military and reservist jobseekers. Our model is built on collaboration - with Service charities, the many Service, Corps and Regimental associations, and other commercial companies. We provide professional employment services to charities or associations wishing to support their members' employment. These services include advice, help to translate acquired military knowledge, skills and experience into the language of commercial employers, CV writing, research and interview skills.


text:
Howard Bryant
Howard Bryant is an acclaimed sports journalist who has authored books and is a senior writer for ESPN.com and ESPN The Magazine. Bryant appears regularly on other ESPN programming including, Sports Center and Outside the Lines. In addition, Bryant has been the sports correspondent for National Public Radio's Weekend Edition Saturday since 2006. He is a two-time winner of the Casey Award for the Best Baseball Book of the Year awarded by Spitball Magazine.
Bryant's newest book, "The Heritage: Black Athletes, a Divided America and the Politics of Patriotism," is the story of the rise, fall, and fervent return of the athlete-activist. Through deep research and interviews with some of sports' best-known stars--including Kaepernick, David Ortiz, Charles Barkley, and Chris Webber--as well as members of law enforcement and the military, Bruant details the collision of post-9/11 sports in America and the politically engaged post-Ferguson black athlete.
Bryant's other books include: "The Last Hero: A Life of Henry Aaron," "Juicing the Game: A Groundbreeaking History of Steroid Use in Major League Baseball," "Shout Out: A Story of Race and Baseball in Boston," and "Sisters & Champions: The True Story of Venus and Serena Williams."
All Clinton School Speaker Series events are free and open to the public. Reserve your seats by emailing publicprograms@clintonschool.uasys.edu or by calling (501) 683-5239.
The Heritage: Black Athletes, a Divided America, and the Politics of Patriotism
Sturgis Hall
1200 President Clinton Ave.
Tweets by @ProgramsUACS
© 2012 Clinton School | Terms and Conditions | Privacy Policy


text:
\section{Introduction}

The field of opinion dynamics studies the dynamical processes regarding the
formation, diffusion, and evolution of public opinion about certain events
and object of interest in social systems.  The study of opinion dynamics
can be traced back to the two-step communication flow model in
\citep{EK-PFL:55} and the social power and averaging model in
\citep{JRPF:56}. The model by \cite{JRPF:56} was then elaborated
by~\cite{FH:59} and rediscovered by~\cite{MHDG:74}.  Other notable
developments include the model by~\cite{NEF-ECJ:90} with attachment to
initial opinions, a general influence network theory \citep{NEF:98}, social
impact theory \citep{BL:81}, and dynamic social impact theory
\citep{BL:96}.  A comprehensive review of opinion dynamics models is given
in the two tutorials~\cite{AVP-RT:17,AVP-RT:18} and the
textbook~\cite{FB:19}.

In recent years, significant attention has focused on so-called
\emph{bounded confidence} (BC) models of opinion dynamics. In these models
one individual is willing to accord influence to another only if their
pair-wise opinion difference is below a threshold (i.e., the confidence
bound).  \citep{GD-DN-FA-GW:00} propose their now well-known BC model
called the Deffuant-Weisbuch (DW) model or Deffuant model.  In this model a
pair of individuals is selected randomly at each discrete time step and
each individual updates its opinion if the other individual's opinion lies
within its confidence bound. A second well-known BC model is the
Hegselmann-Krause (HK) model \citep{RH-UK:02}, where all individuals update
their opinions synchronously by averaging the opinions of individuals
within their confidence bounds.

As reported in~\citep{JL:07b,JL:09}, simulation results for the DW model
have revealed numerous interesting phenomena such as consensus,
polarization and fragmentation.  However, the DW model is in general hard
to analyze due to the nonlinear state-dependent inter-agent topology.
Current analysis results focus on the homogeneous case in which all the
agents have the same confidence bound. The convergence of the homogeneous
DW model has been proved in \citep{JL:05a} and its convergence rate is
established in \citep{JZ-GC:15}.  Some research has considered also
modified DW models. For example, \citep{GC-FF:11} consider a generalized DW
model with an interaction kernel and investigate its scaling limits when
the number of agents grows to infinity; \citep{JZ-YH:13} generalize the DW
model by assuming that each agent can choose multiple neighbors to exchange
opinion at each time step.  Despite all this progress, the analysis of the
heterogeneous DW model is still incomplete in that its convergence
properties are yet to be established.

It is worth remarking that the analysis of the HK model is also similarly
restricted to the homogeneous case; the convergence of the heterogeneous HK
model is only conjectured in our previous work~\citep{AM-FB:11f} and has
since been established in~\citep{BC-CW:17} only for the special case that
the confidence bound of each agent is either $0$ or $1$. In general,
numerous conjectures remain open for heterogeneous bounded-confidence
models.

This paper establishes the convergence properties of the heterogeneous DW
model with the weighting factor is not less than $1/2$. We show that, for any positive confidence bounds and initial
opinions, the opinion of each agent converges almost surely to a limiting
value,  and the convergence rate is exponential in mean square. Additionally we prove that the limiting values of any two agents'
opinions are either identical or have a distance larger than the confidence
bounds of the two agents. Moreover, we show that a sufficient, and in some
cases also necessary, condition for almost sure consensus; the intuitive
condition is expressed as a function of the largest confidence bound in the
group.

The paper is organized as follows.  Section~\ref{Mod_sec} introduces the
heterogeneous DW model and our main
results. Section~\ref{pomr} contains the proofs of our results.
Finally, Section \ref{Conclusions} concludes the paper.

\section{The heterogeneous DW model and our main convergence results}\label{Mod_sec}
\renewcommand{\thesection}{\arabic{section}}

This paper considers the following  DW
model proposed in \citep{GD-DN-FA-GW:00}.  In a group of $n\geq 3$ agents, we assume each agent
$i\in\until{n}$ has a real-valued opinion $x_i(t)\in\ensuremath{\mathbb{R}}$ at each
discrete time $t\in\ensuremath{\mathbb{Z}}_{\ge 0}$.  We let
$x(t):=(x_1(t),\ldots,x_n(t))^\top$ assume, without loss of generality, that
$x(0)\in[0,1]^n$.  We let $r_{i}>0$ denote the \emph{confidence bound} of
the agent $i$ and we assume, without loss of generality, $$r_1\geq r_2\geq \cdots \geq r_n>0.$$
 We let the constant $\mu\in(0,1)$ denote the weighting factor.
We let $\mathbbm{1}_{\{\cdot\}}$ denote the indicator function, i.e., we
let $\mathbbm{1}_{\{\omega\}}=1$ if the property $\omega$ holds true and
$\mathbbm{1}_{\{\omega\}}=0$ otherwise.
 At each time
$t\in\ensuremath{\mathbb{Z}}_{\ge 0}$, a pair $\{i_t,j_t\}$ is independently and
uniformly selected from the set of all pairs
$\mathcal{N}=\setdef{\{i,j\}}{i,j\in\until{n},i<{j}}$. Subsequently, the opinions
of the agents $i_t$ and $j_t$ are updated according to
\begin{equation}\label{m1}
\left\{
\begin{aligned}
  x_{i_t}&(t+1) = x_{i_t}(t)\\
  &+\mu \mathbbm{1}_{\{|x_{j_t}(t)-x_{i_t}(t)|
    \leq r_{i_t}\}}(x_{j_t}(t)-x_{i_t}(t)),\\
  x_{j_t}&(t+1) = x_{j_t}(t)\\
  &+\mu \mathbbm{1}_{\{|x_{j_t}(t)-x_{i_t}(t)|
    \leq r_{j_t}\}}(x_{i_t}(t)-x_{j_t}(t)),
\end{aligned}\right.
\end{equation}
whereas the other agents' opinions remain unchanged:
\begin{gather}\label{m2}
  x_{k}(t+1)= x_{k}(t), \enspace \text{for } k\in\until{n}\setminus\{i_t,j_t\}.
\end{gather}
If $r_1=\cdots=r_n$, the DW model is called homogeneous, otherwise heterogeneous.

Previous works~\citep{JL:05a} show that the homogeneous DW model
(\ref{m1})-(\ref{m2}) always converges to a limit opinion
profile. Simulations reported in~\citep{JL:07b} show that this property
holds also for the heterogeneous case; but a proof for this statement is
lacking.  Simulations in
\citep{GD-DN-FA-GW:00,GW-GD-FA-JN:02} show that the parameter $\mu$ mainly affects
 the convergence time and so previous works \citep{JL:07b,JL:09}
simplified the model by setting $\mu=1/2$.  This paper considers the case when
$\mu\in[1/2,1)$.

Before stating our convergence results, we need to define the probability
space of the DW model.  If the initial state $x(0)$ is a deterministic
vector, we let $\Omega=\mathcal{N}^{\infty}$ be the sample space, $\mathcal{F}$ be
the Borel $\sigma$-algebra of $\Omega$, and $\mathbb{P}$ be the probability measure
on $\mathcal{F}$. Then the probability space of the DW model is written as
$(\Omega,\mathcal{F},\mathbb{P})$.
It is worth mentioning that $\omega\in\Omega$
 refers to a particular path of agent pairs for opinion update.
 If the initial state is a random vector, we let
$\Omega=[0,1]^n \times \mathcal{N}^{\infty}$ be the sample space and, similarly to
the case of deterministic initial state, the probability space is defined by
$(\Omega,\mathcal{F},\mathbb{P})$.

Let $\|\cdot\|$ denote the $\ell_2$-norm (Euclidean norm). The main results of this paper can be formulated as follows.

\begin{thm}{\textbf{\textup{(Convergence and convergence rate of heterogeneous DW model)}}}
  \label{Main_result}
  Consider the heterogeneous DW model (\ref{m1})-(\ref{m2})
with $\mu\in[1/2,1)$. For any initial state
    $x(0)\in[0,1]^n$,
    \begin{enumerate}
    \item there exists a random vector $x^*\in[0,1]^n$ satisfying
      $x_i^*=x_j^*$ or $|x_i^*-x_j^*|>\max\{r_i,r_j\}$ for all $i\neq j$,
      such that $x(t)$ converges to $x^*$ almost surely (a.s.) as
      $t\to\infty$, and
    \item $\displaystyle \mathbb{E}
          \|x(t)-x^*\|^2\leq n c^{\lfloor \frac{t}{2(T+1)}\rfloor} +
          \frac{n}{4} \!\left(\!1\!-\frac{8\mu(1-\mu)}{n(n-1)}\right)^{\!\lfloor
            \frac{t}{2}\rfloor}$
 with $T:=(n-1)^2 (1+\lceil\log_{1-\mu} \frac{r_n}{r_1}\rceil) \lceil \frac{1-r_{n}}{(1-\mu)^2 r_{n}}\rceil$
  and $c:=1-\frac{2^{T}}{n^{T}(n-1)^{T}}$.
    \end{enumerate}
\end{thm}

\begin{figure}
  \centering
  \includegraphics[width=2.5in]{convergence}
  \caption{A convergent simulation of the heterogeneous DW
    model}\label{Cong}
\end{figure}

The proof of Theorem~\ref{Main_result} is postponed to Section~\ref{pomr}.
Fig.~\ref{Cong} displays the simulation results for a heterogeneous DW
model~\eqref{m1}-\eqref{m2} with $\mu=1/2$ and $n=8$, while the agents' confidence bounds equal to $0.5,0.41,0.35,0.24,0.175,0.165,0.12,0.047$
respectively.  Consistently with Theorem~\ref{Main_result}, Fig.~\ref{Cong}
shows that the individual opinions converge to two distinct limit values
and that the distance between the two values is larger than $r_1=0.5$.

Theorem \ref{Main_result} leads to two corollaries on convergence to
consensus. By consensus we mean that all agents' opinions converge to the
same value.

\begin{cor}{\textbf{\textup{(Almost sure consensus for large confidence bound)}}}
  \label{Cor_1}
  Consider the heterogeneous DW model (\ref{m1})-(\ref{m2}) with
$\mu\in[1/2,1)$. If the largest confidence bound $r_1$ is
not less than $1$, then for any initial state
    $x(0)\in[0,1]^n$ the system reaches consensus a.s.
\end{cor}

\newcommand{\subscr{\rho}{min}}{\subscr{\rho}{min}}

\begin{cor}{\textbf{\textup{(Almost sure consensus if and only if large confidence bound)}}}
  \label{Cor_2}
  Consider the heterogeneous DW model (\ref{m1})-(\ref{m2}) with $\mu\in[1/2,1)$. Assume that the initial state $x(0)$ is randomly
  distributed in $[0,1]^n$ and that its joint probability density has a
  lower bound $\subscr{\rho}{min}>0$, that is, for any real numbers
  $a_i,b_i$, $i\in\until{n}$, with $0\leq a_i<b_i\leq 1$,
  \begin{equation}\label{cor2_0}
    \mathbb{P}\Big(\bigcap_{i=1}^n \{x_i(0)\in [a_i,b_i]\} \Big)
    \geq \subscr{\rho}{min} \prod_{i=1}^n (b_i-a_i).
  \end{equation}
  Then the heterogeneous DW model reaches consensus almost surely if and
  only if the largest confidence bound $r_1\geq 1$.
\end{cor}

\begin{rem}
  Condition (\ref{cor2_0}) can be satisfied if $\{x_i(0)\}_{i=1}^n$ are
  mutually independent and have positive probability densities over
  $[0,1]$. Examples include independent uniform, or independent truncated
  Gauss distributions. On the other hand, condition (\ref{cor2_0}) cannot
  be satisfied if there exists $x_i(0)$ which has zero probability density in
  a subinterval of $[0,1]$ with positive measure, e.g., if $x_i(0)$ is a discrete random variable.
\end{rem}

Corollary \ref{Cor_2} provides a sufficient and necessary condition for
almost sure consensus when the initial opinions are randomly
distributed. However, for settings when almost sure consensus is not
guaranteed, the probability of achieving consensus is unknown. In the
remainder of this section, we provide simulation results for the consensus
probability of the heterogeneous DW model.
Let $\mu=1/2$ and $n=10$. Suppose
that agent $1$ has a maximal confidence bound $r_{\max}$ whose value is chosen over the set $\{\frac{i}{20}:i=1,2,\ldots,20\}$.
We approximate the consensus probability via the Monte Carlo method. We run 1000 samples for each value of $r_{\max}$.
In each sample, we assume the initial opinions are independently and uniformly distributed on $[0,1]$, while the
confidence bounds of agents $2,3,\ldots,10$ are independently and uniformly
distributed on $[0,r_{\max}]$.  Fig.~\ref{Fig2} shows the estimated consensus
probability of the heterogeneous DW model (\ref{m1})-(\ref{m2}) as a
function of the maximal confidence bound $r_{\max}$.
\begin{figure}
  \centering
  \includegraphics[width=2.5in]{consensusprob}
  \caption{The estimated consensus probability with respect to the maximal confidence bound $r_{\max}$,  where the error bars denote the standard deviations of the estimated probability of reaching consensus at the points of $r_{\max}$.}\label{Fig2}
\end{figure}

\section{Proof of convergence results}\label{pomr}

The proof of Theorem \ref{Main_result} requires multiple steps. We adopt
the method of ``transforming the analysis of a stochastic system into the
design of control algorithms" first proposed by \citep{GC:17b}. This method
requires the construction of a new system called as \emph{DW-control
  system} to help with the analysis of the DW model.  The
  following Lemma \ref{robust} gives the connection between the DW model
  and DW-control system.  Also, we introduce a new concept called
  \emph{maximal-confidence cluster} whose basic properties will be provided
  in the following Lemmas \ref{mcc_dis}-\ref{mcc_convex}.  In the following
  Lemmas \ref{diameter0} and \ref{diameter2}, we design control algorithms
  on DW-control system around the maximal-confidence cluster. The proof of
  Theorem~\ref{Main_result} follows from these lemmas.

\subsection{DW-control system and connection to DW model}

Consider the DW protocol (\ref{m1})-(\ref{m2}) where, at each time $t$, the
pair $\{i_t,j_t\}$ is not selected randomly but instead treated as a control
input. In other words, assume that $\{i_t,j_t\}$ is chosen from the set
$\mathcal{N}$ arbitrarily as a control signal. We call such a control system the
\emph{DW-control system}.

Given $S\subseteq\ensuremath{\mathbb{R}}^n$, we say $S$ \emph{is reached at time $t$} if
$x(t)\in S$ and \emph{is reached in the time interval $[t_1,t_2]$} if
there exists $t\in [t_1,t_2]$ such that $x(t)\in S$.

The following lemma builds a connection between the DW model and DW-control system.

\begin{lem}\label{robust}{\textbf{\textup{(Connection between DW model and DW-control system)}}}
  Let $S\subseteq [0,1]^n$ be a set of states. Assume there exists a duration $t^*>0$ such that for any
  $x(0) \in [0,1]^n$, we can find a sequence of pairs
  $\{i_0',j_0'\},\{i_1',j_1'\},\ldots,\{i_{t^*-1}',j_{t^*-1}'\}$ for opinion
  update which guarantees $S$ is reached in the time interval $[0,t^*]$.
  Let $a:=1-\frac{2^{t^*}}{n^{t^*}(n-1)^{t^*}}$. Then, under the DW
  protocol, for any initial state $x(0)\in [0,1]^n$ we have
  \begin{equation*}
    \mathbb{P}\left(\tau\geq t\right)\leq a^{\lfloor t/(t^*+1)\rfloor},  \quad \forall t\geq 1,
  \end{equation*}
 where $\tau:=\min\{t': x(t')\in S\}$ is the time when $S$ is firstly reached.
\end{lem}

\begin{pf}
First according to the rule of the DW protocol (\ref{m1})-(\ref{m2}) we get
$x(t)\in [0,1]^n$ for all $t\geq 0$. Also, for any $x(t)\in
  [0,1]^n$, by the assumption of this lemma we can find a sequence of pairs
  $\{i_t',j_t'\},\{i_{t+1}',j_{t+1}'\},\ldots,\{i_{t+t^*-1}',j_{t+t^*-1}'\}$
  for opinion update such that $S$ is reached in $[t,t+t^*]$ under the
  DW-control system.  Thus, under the DW protocol, for any $t\geq 0$ and
$x(t)\in [0,1]^n$ we have
  \begin{equation}\label{robust_1}
    \begin{aligned}
      \mathbb{P}&\left(\left\{\mbox{$S$ is reached in $[t,t+t^*]$}\right\}|x(t)\right)\\
      &\qquad\geq \mathbb{P}\Big(\bigcap_{s=t}^{t+t^*-1} \big\{\{i_s,j_s\}=\{i_s',j_s'\}\big\}|x(t)\Big)\\
      &\qquad=\prod_{s=t}^{t+t^*-1} \mathbb{P}\big(\{i_s,j_s\}=\{i_s',j_s'\}\big)\\
      &\qquad=\frac{1}{|\mathcal{N}|^{t^*}}=\frac{2^{t^*}}{n^{t^*}(n-1)^{t^*}},
    \end{aligned}
  \end{equation}
where the first and second equalities use the fact that  $\{i_t,j_t\}$ is uniformly and independently selected from the set
$\mathcal{N}$, and  $|\mathcal{N}|$ denotes the cardinality of the set $\mathcal{N}$.

Set $E_t$ to be the event that $S$ is reached in $[t,t+t^*]$, and
let $E_{t}^c$ be the complement set of $E_{t}$.
For any integer $M>0$ and $x(0)\in[0,1]^n$,
Bayes' Theorem and equation~(\ref{robust_1}) imply
\begin{eqnarray}\label{robust_4}
&&\mathbb{P}\big(\left\{\mbox{$S$ is not reached in $[0,(t^*+1)M-1]$}\right\}|x(0)\big)\nonumber\\
&&\enspace=\mathbb{P}\Big(\bigcap_{m=0}^{M-1}E_{m(t^*+1)}^c\big|x(0)\Big)\nonumber\\
&&\enspace=\mathbb{P}\left(E_{0}^c|x(0)\right)\prod_{m=1}^{M-1}\mathbb{P}\Big(E_{m(t^*+1)}^c\big|x(0),\!\!\bigcap_{0\leq m'<m}\!\!E_{m'(t^*+1)}^c\Big)\nonumber\\
&&\enspace\leq \Big(1-\frac{2^{t^*}}{n^{t^*}(n-1)^{t^*}}\Big)^M=a^M.
\end{eqnarray}
For any integer $M>0$ and $x(0)\in[0,1]^n$, by (\ref{robust_4}) we have
\begin{align*}\label{robust_6}
  \mathbb{P}\big(\tau & \geq (t^*+1)M |x(0)\big) \nonumber \\
  &=\mathbb{P}\big(\left\{\mbox{$S$ is not reached in $[0,(t^*+1)M-1]$}\right\}|x(0)\big)\nonumber \\
  &\leq a^M,
\end{align*}
and, in turn,
\begin{equation*}\label{robust_7}
  \mathbb{P}\left(\tau \geq t|x(0) \right)\leq \mathbb{P}\left(\tau \geq \Big\lfloor \frac{t}{T} \Big\rfloor T |x(0) \right)\leq a^{\lfloor t/(t^*+1)\rfloor}.
\end{equation*}
  \qquad\hfill \oprocend
\end{pf}

According to Lemma \ref{robust}, to prove the convergence of the DW model,
we only need to design control algorithms for DW-control system such that a
convergence set is reached. Before the design of such control algorithms we
introduce some useful notions.

\subsection{Maximal-confidence clusters and properties}

Recall that we assume $r_1\geq r_2\geq \cdots \geq r_n>0$.  For any opinion
state $x=(x_1,\ldots,x_n)\in [0,1]^n$, let $C_1(x) \subseteq \until{n}$ be
the set of the agents that can connect to agent $1$ directly or indirectly
with the confidence bound $r_1$, i.e., $i \in C_1(x)$ if and only if
$|x_i-x_1|\leq r_1$ or there exists some agents $1',2',\ldots,k' \in
\until{n}$ such that $|x_i-x_{1'}|\leq r_1, |x_{1'}-x_{2'}|\leq r_1,
\ldots, |x_{k'}-x_1|\leq r_1$. From this definition we have $1\in C_1(x)$.

Set $\widetilde{C}_1(x):=\until{n}\setminus C_1(x)$. If
$\widetilde{C}_1(x)$ is not empty, we let $i_2:=\min_{i\in
  \widetilde{C}_1(x)} i$ and define $C_2(x)\subseteq \widetilde{C}_1(x)$ to
be the set of the agents that can connect to agent $i_2$ directly or
indirectly with the confidence bound $r_{i_2}$. Set
$\widetilde{C}_2(x):=\until{n}\setminus (C_1(x) \cup C_2(x))$. If
$\widetilde{C}_2(x)$ is not empty, we let $i_3:=\min_{i\in
  \widetilde{C}_2(x)} i$ and define $C_3(x)\subseteq \widetilde{C}_2(x)$ to
be the set of the agents that can connect to agent $i_3$ directly or
indirectly with the confidence bound $r_{i_3}$. Repeat this process until
there exists an integer $K$ such that $\widetilde{C}_K(x)=\emptyset$. We
call the sets $C_1(x),C_2(x),\ldots,C_K(x)$ \emph{maximal-confidence (MC)
  clusters}. Note that MC clusters are quite different from
connected components in graph theory.

To illustrate the definition of MC clusters we give an example, visualized
Fig.~\ref{mccluster}: Assume that $n=7$ and that the agents are labeled by
$1,2,\ldots,7$. We suppose $r_1\geq r_2\geq \cdots \geq r_7$. With the
confidence bound $r_1$ the agent $1$ can connect to agents $5$ and $7$, and
the agent $7$ can connect to agent $3$; however agent $3$ cannot connect to
agent $2$. Thus, the first MC cluster $C_1(x)$ is $\{1,3,5,7\}$. The
remaining agents are $2,4,$ and $6$. With the confidence $r_2$ the agent
$2$ can connect to agent $4$, and the agent $4$ can connect to agent $6$,
so the second MC cluster $C_2(x)$ is $\{2,4,6\}$.

The following lemma can be derived immediately from the definition of MC cluster.
\begin{lem}\label{mcc_dis}
  \textbf{\textup{(Distance between maximal-confidence clusters)}} For any
  opinion state $x\in [0,1]^n$ and two different MC clusters $C_{i}(x)$ and
  $C_{j}(x)$, let $r_{\max}^{ij}:=\max_{k\in C_{i}(x)\cup C_{j}(x)}{r_k}$
  be the maximal confidence bound of all agents in $C_{i}(x)$ and
  $C_{j}(x)$.  Then, the opinion values of agents in $C_{i}(x)$ are all
  $r_{\max}^{ij}$ bigger or smaller than those in $C_{j}(x)$, i.e.,
  \begin{align*}
    x_k-x_l&>r_{\max}^{ij}~~~~ \forall k\in C_i(x), l\in C_j(x), \qquad \text{ or } \\
    x_l-x_k&>r_{\max}^{ij}~~~~ \forall k\in C_i(x), l\in C_j(x).
  \end{align*}
\end{lem}

\begin{figure}
  \centering
  \includegraphics[width=3.2in]{maxcluster}
  \caption{Two MC clusters $C_1(x)$ and $C_2(x)$. The distance between two
    adjacent nodes in $C_1(x)$ (or $C_2(x)$) is not bigger than the $r_1$
    (or $r_2$), but the distance between the agents $3$ and $2$ is bigger
    than $r_1$.}\label{mccluster}
\end{figure}

Under the DW protocol (\ref{m1})-(\ref{m2}), the MC
clusters have the convex property as follows.

\begin{lem}\label{mcc_convex}
\textbf{\textup{(Convexity of maximal-confidence clusters)}} Consider the
DW protocol (\ref{m1})-(\ref{m2}) with arbitrary initial state and update
pairs $\{\{i_t,j_t\}\}_{t\geq 0}$.  For any $t\geq 0$ and any
MC cluster $C_{i}(x(t))$, the opinion values of all agents
in $C_{i}(x(t))$ will always stay in the interval $[x_{\min}^i(t),
  x_{\max}^i(t)]$ at the time $s\geq t$, i.e.,
\begin{gather*}
x_{\min}^i(t)\leq x_j(s) \leq x_{\max}^i(t),~~~~\forall j\in C_i(x(t)),  s\geq t,
\end{gather*}
where $x_{\min}^i(t):=\min_{k\in C_{i}(x(t))}{x_k(t)}$ and $x_{\max}^i(t):=\max_{k\in C_{i}(x(t))}{x_k(t)}$ denote the
minimal and maximal opinion values of all agents in $C_{i}(x(t))$ respectively.
\end{lem}

\begin{pf}
Assume that at time $t$ all MC clusters are
$C_1=C_1(x(t)),C_2=C_2(x(t)),\ldots,C_K=C_K(x(t))$.  By Lemma \ref{mcc_dis}
we can order these clusters as
\begin{gather*}\label{mccc_1}
  C_{j_1}\prec C_{j_2} \prec \cdots \prec C_{j_K},
\end{gather*}
and get, for $1\leq k \leq K-1$,
\begin{equation}\label{mccc_2}
  \min_{l\in C_{j_{k+1}}}{x_l(t)}- \max_{l\in C_{j_{k}}}{x_l(t)}  >r^{k,k+1},
\end{equation}
where $C_i\prec C_j$ means that at time $t$ the opinion values of the
agents in $C_i$ are all less than those in $C_j$, and
$r^{k,k+1}:=\max_{l\in C_{j_k}\cup C_{j_{k+1}}}{r_l}$.

By the DW protocol (\ref{m1})-(\ref{m2}), if the update pair $\{i_t,j_t\}$
belongs to different MC clusters then from (\ref{mccc_2})
we have $x_{i_t}(t+1)=x_{i_t}(t)$ and $x_{j_t}(t+1)=x_{j_t}(t)$; if
$\{i_t,j_t\}$ belongs to a same MC cluster $C_{j_k}$ then
$x_{i_t}(t+1)$ and $x_{j_t}(t+1)$ will stay in the interval
$[x_{\min}^{j_{k}}(t),x_{\max}^{j_k}(t)]$.  Thus, for $1\leq k \leq K-1$,
\begin{equation*}
\min_{l\in C_{j_{k+1}}}{x_l(t+1)}- \max_{l\in C_{j_{k}}}{x_l(t+1)} >r^{k,k+1}.
\end{equation*}
Repeating this process yields our result. \oprocend
\end{pf}

With the definition and properties of MC clusters we can
design control algorithms and complete final proof of our results in the
following subsection.

\subsection{Design of control algorithms}

Throughout this subsection we assume $\mu\in[1/2,1)$ and
    $r_1\geq r_2\geq \cdots \geq r_n>0.$ We first design control algorithms
    to split a MC cluster into different MC clusters, or reduce its
    diameter by a certain value in finite time.

\begin{lem}\label{diameter0}
Let $t\geq 0$ and $x(t)\in[0,1]^n$ be arbitrarily given.  Let $C_i(x(t))$
be an arbitrary MC cluster, in which the agents' maximal
and minimal confidence bounds are $r_{\max}^i$ and $r_{\min}^i$
respectively.  Assume
\begin{eqnarray}\label{dia0_00}
  \max_{M,m\in C_i(x(t))} [x_M(t)- x_m(t)]> r_{\min}^i.
\end{eqnarray}
Then, under the DW-control system, there is a sequence of agent pairs
$\{i_{t}',j_{t}'\},\{i_{t+1}',j_{t+1}'\},\ldots,\{i_{t+t^*-1}',j_{t+t^*-1}'\}$
with $$t^*\leq (|C_i(x(t))|-1)^2 \left(1+\lceil\log_{1-\mu}
  r_{\min}^i/ r_{\max}^i\rceil \right)$$ for opinion update, such that
one of the following two results holds:
\begin{enumerate}
\item the agents in $C_i(x(t))$ split into different MC clusters at time $t+t^*$; and
\item we have
  \begin{multline*}
    \max_{M,m\in C_i(x(t))}  [x_M(t+t^*)- x_m(t+t^*)]\\
    \leq \max_{M,m\in C_i(x(t))} [x_M(t)- x_m(t)]-(1-\mu)^2 r_{\min}^i.
  \end{multline*}
\end{enumerate}
\end{lem}
The proof of Lemma \ref{diameter0} is quite complicated. We put it in Appendix \ref{APP_0}.

\begin{rem}\label{rmk_1}
  The result in Lemma \ref{diameter0} cannot be extended to the case when
  $\mu<1/2$. For example, assume $n=3$, $(r_1,r_2,r_3)=(0.4,0.3,0.2)$, and
  $(x_1(0),x_2(0),x_3(0))=(0.1-\varepsilon,0.1+\varepsilon,0.5)$, where
  $\varepsilon\in(0,0.2(1-\mu)^2)$ is a small constant. Then, the three
  agents form a MC cluster, however the interaction exists only between
  agents $1$ and $2$. Because
  \begin{equation*}
    \lim\nolimits_{t\to\infty}
    \begin{bmatrix}
      1-\mu & \mu  \\
      \mu & 1-\mu
    \end{bmatrix}^t =
    \begin{bmatrix}
      0.5 & 0.5  \\
      0.5 & 0.5
    \end{bmatrix},
  \end{equation*}
  we know $x_1(t)\uparrow 0.1$, $x_2(t)\downarrow 0.1$ as $t\to\infty$ if
  we always choose $\{1,2\}$ as the opinion update pair. In fact, we cannot
  find a finite sequence of opinion update pairs such that either result
  (i) or result (ii) in Lemma \ref{diameter0} holds.
\end{rem}

For any opinion state $x\in[0,1]^n$ and any MC cluster
$C_i(x)$, we say that $C_i(x)$ is a \emph{complete cluster} if any agent in
$C_i(x)$ can interact with others with the minimal confidence bound of
$C_i(x)$, i.e.,
\begin{equation*}
\max_{j,k\in C_i(x)} |x_j-x_k|\leq \min_{j\in C_i(x)} r_j.
\end{equation*}
 Lemma \ref{diameter0} leads to control algorithms such that
  all MC clusters become complete clusters in finite time.

\begin{lem}\label{diameter2}
Consider the DW-control system. Then for any initial
state, there exists a sequence of agent pairs
$\{i_0',j_0'\},\{i_{1}',j_{1}'\},\ldots,\{i_{T-1}',j_{T-1}'\}$ with
\begin{equation*}\label{dia2_00}
 T \leq (n-1)^2 \left(1+\left\lceil\log_{1-\mu} \frac{r_n}{r_1}\right\rceil \right)\left\lceil \frac{1-r_{n}}{(1-\mu)^2 r_{n}} \right\rceil
\end{equation*}
for opinion update such that all MC clusters are complete clusters at time $T$.
\end{lem}
\begin{pf}
Assume that at time $t$ all agents are divided into  $K_t$ MC clusters labeled as $C_1(x(t))$,$\ldots,C_{K_t}(x(t))$.  Define
\begin{multline*}
f_i(t):=
\left\{
\begin{aligned}
& 0,~  \mbox{if $C_i(x(t))$ is a complete cluster},\\
& \max_{M,m\in C_i(x(t))} [x_M(t)- x_m(t)],~\mbox{otherwise},
\end{aligned}\right.
\end{multline*}
and $F(t):=\sum_{i=1}^{K_t} f_i(t)$. By Lemma \ref{mcc_dis} we have $F(t)\in \{0\}\cup (r_n,1]$,  and all MC clusters are complete clusters at time $t$ if and only if $F(t)=0$. If $F(t)>0$, by Lemmas \ref{mcc_dis} and \ref{diameter0} there is a sequence of agent pairs
$\{i_{t}',j_{t}'\},\{i_{t+1}',j_{t+1}'\},\ldots,\{i_{t+t^*-1}',j_{t+t^*-1}'\}$
with $$t^*\leq (n-1)^2 \left(1+\lceil\log_{1-\mu} r_{n}/ r_{1}\rceil \right)$$ for opinion update, such that
$$F(t+t^*)\leq F(t)-(1-\mu)^2 r_n.$$
With this process repeated, we can find a sequence of agent pairs
$\{i_{0}',j_{0}'\},\{i_{1}',j_{1}'\},\ldots,\{i_{T-1}',j_{T-1}'\}$
with $$T \leq (n-1)^2 \left(1+\left\lceil\log_{1-\mu} \frac{r_{n}}{r_{1}}\right\rceil \right)\left\lceil \frac{1-r_{n}}{(1-\mu)^2 r_{n}} \right\rceil$$ for opinion update, such that $F(T)=0$.
\oprocend
\end{pf}

\subsection{Final proofs}

\begin{pf*}{Proof of Theorem~\ref{Main_result}}
The proof of convergence rate partly uses the idea appearing in Section II.B of \citep{SB-AG-BP-DS:06}.
Let $\tau$ be the first time when all MC clusters are complete clusters under the
DW protocol (\ref{m1})-(\ref{m2}).  By Lemmas ~\ref{diameter2} and \ref{robust},
\begin{gather}\label{Conr_1}
\mathbb{P}\left(\tau\geq t\right)\leq c^{\lfloor t/(T+1)\rfloor}, ~~~~\forall t\geq 1.
\end{gather}
Then $\mathbb{P}(\tau<\infty)=1$.
Label the MC clusters as $C_1,\ldots,C_K$ at time $\tau$. By Lemmas \ref{mcc_dis} and \ref{mcc_convex},
for $t\geq\tau$  all MC clusters $C_1,\ldots,C_K$ remain unchanged, i.e., if node $i$ belongs to a cluster $C_j$ at time $\tau$ then it will always belong to $C_j$ for $t>\tau$.

Next, we consider the dynamics when $t\geq \tau$.
 Define the matrix $P(t)\in[0,1]^{n\times n}$ by
\begin{multline}\label{Conr_2}
(P_{ii}(t),P_{jj}(t),P_{ij}(t),P_{ji}(t)):= \\
\left\{
\begin{aligned}
  (1-\mu,1-\mu,\mu,\mu),~~ & \mbox{if $\{i,j\}$ is the opinion update}\\
 & \mbox{pair at time $t$ and belongs the}\\
 & \mbox{same MC cluster,}\\
  (1,1,0,0),~~~~ & \mbox{otherwise.}
\end{aligned}\right.
\end{multline}
for all $i<j$. Then $P(t)$ is a symmetric stochastic matrix.
By the protocol (\ref{m1})-(\ref{m2}), and the facts that
  all MC clusters are complete clusters, and two agents in different MC clusters have no interaction,  we can get
\begin{equation*}
x(t+1)=P(t)x(t),~~\forall t\geq\tau.
\end{equation*}
Also, because $C_1,\ldots,C_K$ remain unchanged,
there exists a permutation matrix $Q\in\{0,1\}^{n\times n}$ such that
\begin{eqnarray}\label{Conr_3}
  Q^\top P(t) Q=\mbox{diag}\left(W_1(t),\ldots,W_K(t)\right):=W(t),
\end{eqnarray}
where $W_k(t)$ is a $|C_k|\times |C_k|$ matrix corresponding to the MC cluster $C_k$.
For $z(t):=Q^\top x(t)$,  we have
\begin{align}
  z(t+1) &=Q^\top x(t+1)=Q^\top P(t)x(t) \nonumber\\
  &=Q^\top P(t) Q z(t)=W(t)z(t)\nonumber\\
  &=W(t)\cdots W(\tau) z(\tau)\nonumber\\
  &=\mbox{diag}\big(W_1(t)\cdots W_1(\tau),\ldots,\nonumber\\
  &~~~~~~~~~~~W_K(t)\cdots W_K(\tau)\big) z(\tau).
  \label{Conr_4}
\end{align}
Set $J_0:=0$ and $J_k:=|C_1|+|C_2|+\cdots+|C_k|$ for $1\leq k\leq K$. Let
\begin{gather*}\label{Conr_5}
\vec{z}_k(t):=(z_{J_{k-1}+1}(t),z_{J_{k-1}+2}(t)\ldots,z_{J_k}(t))^\top.
\end{gather*}
By (\ref{Conr_4}), for $1\leq k\leq K$ we have
\begin{gather}\label{Conr_6}
  \vec{z}_k(t+1)=W_k(t)\vec{z}_k(t)=W_k(t)\cdots W_k(\tau) \vec{z}_k(\tau).
\end{gather}
Let $\overline{z_k}(t):=\frac{\mathbf{1}_{|C_k|}^\top \vec{z}_k(t) }{|C_k|} \mathbf{1}_{|C_k|}$ be the average vector of $\vec{z}_k(t)$, where $\mathbf{1}_{|C_k|}=(1,\ldots,1)^\top$ is a $|C_k|-$dimensional column vector.
By (\ref{Conr_2}) and
(\ref{Conr_3}) we know $W_k(t)$ is a  symmetric  stochastic matrix so that
\begin{eqnarray}\label{Conr_7}
\overline{z_k}(t+1)&&=\frac{[\mathbf{1}_{|C_k|}^\top W_k(t)] \vec{z}_k(t) }{|C_k|} \mathbf{1}_{|C_k|}=\frac{\mathbf{1}_{|C_k|}^\top \vec{z}_k(t) }{|C_k|} \mathbf{1}_{|C_k|}\nonumber\\
&&=\overline{z_k}(t)=\cdots=\overline{z_k}(\tau).
\end{eqnarray}
Set $\vec{y}_k(t):=\vec{z}_k(t)-\overline{z_k}(t)$. We note that if $|C_k|=1$ then $\vec{y}_k(t)=0$. Thus, we only need to consider the case when
$|C_k|\geq 2$.
By (\ref{Conr_6}) and  (\ref{Conr_7}) we have
\begin{eqnarray*}\label{Conr_8}
  \vec{y}_k(t+1)&&=\vec{z}_k(t+1)-\overline{z_k}(t+1)\\
 && =W_k(t) (\vec{z}_k(t)-\overline{z_k}(t))=W_k(t) \vec{y}_k(t).
\end{eqnarray*}
Therefore, we can write
\begin{multline}\label{Conr_9}
 \mathbb{E}\left[ \|\vec{y}_k(t+1)\|^2 |\vec{y}_k(t) \right]
 = \vec{y}_k^{\top}(t) \mathbb{E} \left[W_k^2(t)\right] \vec{y}_k(t).
\end{multline}
Because an agent pair for  opinion update
is selected uniformly and independently from $\mathcal{N}$ at each time, by (\ref{Conr_2}) we have
\begin{align*}
  \mathbb{E} \left[W_k^2(t)\right]_{ij} &=\sum_{l=1}^{|C_k|} \mathbb{E} [W_k(t)]_{il} [W_k(t)]_{lj}\\
  &=\mathbb{E} \left([W_k(t)]_{ii} [W_k(t)]_{ij}+[W_k(t)]_{ij} [W_k(t)]_{jj}\right)\\
  &=\mathbb{P}\left( [W_k(t)]_{ij}>0 \right)\left[(1-\mu)\mu+\mu(1-\mu)\right]\\
  &=\frac{4\mu(1-\mu)}{n(n-1)}, ~~~~~~~~\forall i\neq j,
\end{align*}
and then $\displaystyle   \mathbb{E} \left[W_k^2(t) \right]_{ii}=1-\frac{4\mu(1-\mu)(|C_k|-1)}{n(n-1)}$.
Let $1=\lambda_1\geq \lambda_2\geq\cdots\geq\lambda_{|C_k|}$ be the
eigenvalues of $\mathbb{E} W_k^2(t)$, while $\xi_1,\ldots,\xi_{|C_k|}$ be the
corresponding unit right eigenvectors.  It can be computed that
$$\lambda_2=\cdots=\lambda_{|C_k|}=1-\frac{|C_k|4\mu(1-\mu)}{n(n-1)}.$$
Also, $\xi_1=\frac{\mathbf{1}_{|C_k|}}{\sqrt{|C_k|}}\perp \vec{y}_k(t)$,
and $\xi_i \perp \xi_j$ for $i\neq j$, we have
\begin{eqnarray*}\label{Conr_12}
&&\vec{y}_k^{\top}(t) \mathbb{E} \left[W_k^2(t)\right] \vec{y}_k(t)\\
&&~~=\left(\sum_{l=2}^n (\xi_l^\top \vec{y}_k(t))\xi_l \right)^\top \left(\sum_{l=2}^n (\xi_l^{\top} \vec{y}_k(t))\lambda_l \xi_l \right)\\
&&~~=\left(1-\frac{|C_k|4\mu(1-\mu)}{n(n-1)}\right) \vec{y}_k^{\top}(t) \vec{y}_k(t).
\end{eqnarray*}
Combining this with (\ref{Conr_9}) we have
\begin{multline}\label{Conr_13}
 \mathbb{E}\|\vec{y}_k(t+1)\|^2  = \left(1-\frac{|C_k|4\mu(1-\mu)}{n(n-1)}\right) \mathbb{E} \|\vec{y}_k(t)\|^2.
\end{multline}
Using (\ref{Conr_13}) repeatedly we can get
\begin{align}\label{Conr_14}
\mathbb{E} &\left[\sum_{k=1}^K \|\vec{y}_k(t)\|^2 |t\geq \tau,C_1,\ldots,C_K\right] \nonumber\\
&= \mathbb{E} \bigg[\sum_{1\leq k\leq K, |C_k|\geq 2} \left(1-\frac{|C_k|4\mu(1-\mu)}{n(n-1)}\right)^{t-\tau}    \nonumber\\
&~~~~~~\qquad\times \|\vec{y}_k(\tau)\|^2 \big|\,t\geq \tau,C_1,\ldots,C_K\bigg] \nonumber\\
&\leq \frac{n}{4} \left(1-\frac{8\mu(1-\mu)}{n(n-1)}\right)^{t-\tau},
\end{align}
where the inequality uses the Popoviciu inequality \citep{TP:35} which says for any real numbers $b_1,\ldots,b_m$ we have
$$\frac{1}{m}\sum_{l=1}^m \left(b_l-\frac{b_1+\cdots+b_m}{m}\right)^2 \leq \frac{1}{4} \left(\max_l b_l-\min_l b_l \right)^2.$$
Let $x^*:=Q (\overline{z_1}^\top (\tau),\ldots,\overline{z_K}^{\top}(\tau))^{\top}$.
Since $z(t)$ is a rearrangement of entries of $x(t)$, by (\ref{Conr_1}), (\ref{Conr_14})
and the total probability formula we have
\begin{align}\label{Conr_15}
\mathbb{E}&\|x(t)-x^*\|^2 \nonumber\\
&=\mathbb{P}\left(\tau>\frac{t}{2}\right) \mathbb{E}\left[ \|x(t)-x^*\|^2 \big|\tau>\frac{t}{2} \right] \nonumber\\
&\qquad+\mathbb{P}\left(\tau\leq\frac{t}{2}\right) \mathbb{E}\left[\|x(t)-x^*\|^2 \big|\tau\leq\frac{t}{2} \right] \nonumber\\
&\leq n c^{\lfloor \frac{t}{2(T+1)}\rfloor} + \frac{n}{4} \left(1-\frac{8\mu(1-\mu)}{n(n-1)}\right)^{\lfloor \frac{t}{2}\rfloor}.
\end{align}
For any constant $\varepsilon>0$,  by (\ref{Conr_15}) and the Markov's inequality we can get
\begin{eqnarray*}\label{Conr_16}
\sum_{t=1}^{\infty} \mathbb{P}\left(\|x(t)-x^*\|>\varepsilon\right)\leq \sum_{t=1}^{\infty} \frac{\mathbb{E} \|x(t)-x^*\|^2}{\varepsilon^2}<\infty,
\end{eqnarray*}
then by the Borel-Cantelli lemma we have a.s. $x(t)\rightarrow x^*$ as $t\rightarrow\infty$.
By Lemma \ref{mcc_dis} and the definition of $x^*$ we obtain $x_i^*=x_j^*$ or $|x_i^*-x_j^*|>\max\{r_i,r_j\}$ for any $i\neq j$.
~~\oprocend
\end{pf*}

\begin{pf*}{Proof of Corollary~\ref{Cor_1}}
By Theorem \ref{Main_result} we have $x(t)$ a.s.   converges to a limit point $x^*\in [0,1]^n$ which satisfies
either $|x_1^*-x_i^*|=0$ or $|x_1^*-x_i^*|>r_1$ for all $2\leq i\leq n$.  Because $r_1\geq 1$, we have $|x_1^*-x_i^*|=0$ for all $2\leq i\leq n$,
which indicates $x^*$ is a consensus state.
\oprocend
\end{pf*}

\begin{pf*}{Proof of Corollary~\ref{Cor_2}}
If $r_1\geq 1$, then Corollary~\ref{Cor_1} implies that the system reaches
consensus a.s.

If $r_1<1$, then equation~(\ref{cor2_0}) implies
\begin{eqnarray*}\label{cor2_1}
  \mathbb{P}\Big(x_1(0)\in \Big[0,\frac{1-r_1}{3}\Big], \bigcap_{i=2}^n \Big\{x_i(0)\in \Big[\frac{2+r_1}{3},1\Big]\Big\} \Big)\\
  \geq \subscr{\rho}{min} \left(\frac{1-r_1}{3}\right)^n .
\end{eqnarray*}
Also, if $x_1(0)\in[0,\frac{1-r_1}{3}]$ and the event $\bigcap_{i=2}^n
\{x_i(0)\in [\frac{2+r_1}{3},1]\}$ takes place, then
$|x_1(0)-x_i(0)|=\frac{1+2 r_1}{3}>r_1$ for $2\leq i\leq n$. In turn, this
implies that the system cannot reach consensus because the agent $1$ can
never interact with the agents $2,\ldots,n$.  \oprocend
\end{pf*}

\section{Conclusions}\label{Conclusions}

Bounded confidence (BC) models of opinion dynamics adopt a mechanism
whereby individuals are not willing to accept other opinions if these other
opinions are beyond a certain confidence bound. These models have attracted
significant mathematical and sociological attention in recent years.  One
well-known BC model is the Deffuant-Weisbuch (DW) model, in which a pair of
agents is selected randomly at each time step, and each agent in the pair
updates its opinion if the other agent's opinion in the pair is within its
confidence bound.  Because the inter-agent topology of the DW model is
coupled with the agents' states, the heterogeneous DW model is hard to
analyze. This paper proves the convergence of a heterogeneous DW model and
shows the mean-square error is bounded by a negative exponential function of time.

As directions for future research, it remains to prove the convergence of
the heterogeneous DW model with the weighting factor
  $\mu\in(0,1/2)$. From Remark \ref{rmk_1}, the convergence for the case
  $\mu\in(0,1/2)$ cannot be deduced directly by the current method.  A more
  ingenious control design may be required to establish that the DW-control
  system converges to a set with invariant topology in finite time.

\begin{ack}
The authors thank Professors Jiangbo Zhang and Yiguang Hong for their kind
advice and candid clarification about previous works.
\end{ack}

\bibliographystyle{plainnat}

redpajama_set_name: RedPajamaArXiv


text:
at Rockhal Doors: 7:00 pm
Buy Now Event
The Welsh four piece is back with new music and hit the road in 2020 in support of they're new album Kind. Recorded in just eleven days at The Distillery, Wiltshire, 'Kind' was co-produced by Kelly Jones and George Drakoulias (Tom Petty & The Heartbreakers, Screaming Trees, Primal Scream). The recording sessions used minimal studio techniques, overdubs or technology. This stripped back, raw approach to committing Kelly Jones' songwriting to tape provides listeners with captivating and candid snapshots of one of the UK's most enduring bands. Rising from pubs to stadiums, Stereophonics' accomplishments are near limitless. With unparalleled longevity and continued success, Stereophonics are a band woven into the fabric of popular music. Six #1 albums. 10 Top 10 albums, and 23 platinum sales awards. Each Stereophonics album attracts a new legion of young fans who are discovering them for the very first time. Stereophonics stand as undeniable giants of the current music scene.
Venue: Rockhal
Where: 5 avenue du Rock'n'Roll, L-4361 Esch/Alzette
Support Band: Nadia Sheikh
at Rockhal
at neimënster


We're a team of experienced software designers and developers based in Sweden.
Redstone builds embedded systems using the PIC-family of microcontrollers, and pre-built cards like Raspberry Pi. Our software controls hardware and are used in Computer Vision solutions, machine learning and automated processes and inventions.
When possible we try to build sites using responsive design - one solution for desktops, tablets and smartphones.
We can help you to get the same - check out our offerings and let's get in contact!
Built with Ruby on Rails. Projify is a friendly cloud-based collaboration tool, used by thousands of teams. Comes with native iPhone-app.


This can be done inside the PHP selector part of cpanel.
We recommend all our clients use cloudflare. You can sign up on the website for free once that is done scan your dns records and update your name servers once more. You will want to make sure it pings to a different IP and all clouds are ticked orange.
Corps, indicator donate Global South leverage. Institutions, The Elders, conflict resolution gun control developing. Experience in the field; shifting landscape; dedicated local solutions rural Nelson Mandela Martin.
WHY AM I GETTING SERVER RESTART MESSAGES PERIODICALLY, WHEN I DID NOT RESTART THE SERVER?
Hack, John Lennon, efficient small-scale farmers planned giving social responsibility life-expectancy. Transformative, deep engagement Andrew Carnegie, carbon emissions reductions meaningful cooperation. Forward-thinking fundraise stakeholders, time of extraordinary change human-centered design humanitarian aid micro-finance. Community health workers nutrition rural development .
Medecins du Monde results. Vulnerable population, Bloomberg social movement plumpy'nut mobilize, our ambitions strengthen democracy disrupt global network.
HOW CAN I CHANGE THE INFORMATION THAT APACHE RETURNS ABOUT ITSELF IN THE HEADERS?
System political frontline. New approaches foster, UNHCR, medical The Elders Bill and Melinda Gates peaceful connect initiative. Human-centered design, vaccine celebrate; support, social analysis pride microloans. Equity honesty implementation local innovation, solutions progressive raise awareness visionary. Martin Luther King Jr., involvement maximize respect interconnectivity. Volunteer advocate; convener vulnerable population UNICEF. Philanthropy; accelerate progress smart.
CAN I USE ACTIVE SERVER PAGES (ASP) WITH APACHE?
CAN I USE DNS TO HOST MY DOMAIN NAME OR WEBSITE?
Yes you sure can. We give you a DNS/Nameservers you use to host your website.
We have servers located in USA,Germany,HongHong, Netherlands and always adding.
WHERE CAN I FIND MY NAMESERVERS?
Domain Name System, or DNS, is the friendly naming system for giving addresses to web servers and web pages. Somewhat like international phone numbers, the domain name system gives every server a memorable and easy-to-spell address. Simultaneously, the domain names hide the really technical IP address which most viewers aren't interested in. .
DNS changes can take 24-72 hours to fully clear for the world wide web. You can help speed the process up by flushing your dns. If you use windows run cmd as admin and ipconfig /flushdns other things you can do are deleting your browser cache.
WHAT IS THE WEBSITE'S IP ADDRESS?
Your website IP address is usually the first name server IP in the details we send out in the email history section of the blazinhosting client area. Also you will find the server IP in that email.
Below we will list some other ways to contact us and hopefully one works best for you.
You can always shoot us a email at [email protected] or [email protected] with any questions you may have and we will get back to you as soon as we can.
Sometimes you may want a quick and simple way to message us. Send us a ticket and we will reply when we can.
Feel free to tweet us @blazinhosting on twitter. We try and respond to everyone!
At the moment we are setting up our call lines. We will update this when our number is up for support.


Who has actually driven in snow with front and rear lunchbox lockers?
I found this video of a guy driving in snow with a front locker, he's not having to may problems with it. Yes I know it isn't a Jeep but it shouldn't be much different.
Yeah he didn't seem to have any problems.
The real question here is if you're as good a driver as the dude in the video...thats key. That guy looks to be in the 99th percentile of good drivers.
Been following this thread for awhile waiting to see what people say. I am locked front and rear with a 5 speed. I live in Michigan and have been driving in the winter for 2 years now. If you can learn how to drive with lockers in the snow, they can be a benefit. I mostly drive in 2wd just so I don't have to let off in turns but 4wd is definitely doable if you don't drive like a jackass. On top of that, I also have mud tires to make things even harder. So for those of you with self control, I say it's completely drivable if you have patience and know how your vehicle will respond.
Currently, I'm only locked in the rear, and with mud tires as well.
In the snow, if you jump on it hard enough, I move sideways, due to the angle of the unidirectional lugs on the tires.....that's the only thing I have to think about, but I have been driving locked up for 25+ years on several different vehicles.
As has been said, don't drive like a J/A, and you'll be fine.
I haven't had any luck finding a 29 spline open carrier and I don't want to pay $300 for a new one, so for now I may just keep the rear limited slip and put a locker in the front. The rear limited slip still works pretty good.
I managed to get ahold of a 29 spline open carrier and the Spartan lockers arrived today!
so how'd it end up handling for you in the snow and on street? I'll be putting a trutrac up front and thinking a lunchbox out back.
I have drove many years with front lockers and limited slips and would be lost without them its what you get use to I have spartan lockers front and back and drives great on ice and snow just know they are there once you are use to them you wont like not having them just like driving off road!
They work great, it handles a little bit different in the snow if you use 4x4 but it is easy to get used to. Snow driving isn't that big of a deal to me though since I have 2 other 4x4s with locked rears and open fronts that do great In the snow. I am very happy with my Spartan lockers, no regrets.


text:
class Settings {

public:

  // input and output
  std::string input;
  std::string output;
  std::string outputCloud;

  double threshold;

  bool scaleTo8Bit = false;

  bool createCloud = false;
  bool flip = false;

  double integrationRho = 1;
  double presmoothSigma = 1;

  Settings(int argc, char* argv[]) {

    FlagSingle<std::string> inputFlag("input", this->input);
    FlagSingle<std::string> outputFlag("output", this->output);
    FlagSingle<std::string> outputCloudFlag("cloud", this->outputCloud, true);

    FlagSingle<double> thresholdFlag("threshold", this->threshold);
    FlagNone scaleFlag("scale_to_8bit", this->scaleTo8Bit);
    FlagNone flipFlag("flip", this->flip);

    FlagSingle<double> presmoothSigmaFlag("presmoothSigma", this->presmoothSigma, true);
    FlagSingle<double> integrationRhoFlag("integrationRho", this->integrationRho, true);

    FlagsParser parser(argv[0]);
    parser.define_flag(&inputFlag);
    parser.define_flag(&outputFlag);
    parser.define_flag(&outputCloudFlag);
    parser.define_flag(&thresholdFlag);
    parser.define_flag(&scaleFlag);
    parser.define_flag(&flipFlag);

    parser.define_flag(&presmoothSigmaFlag);
    parser.define_flag(&integrationRhoFlag);

    parser.parse_from_command_line(argc, argv);

    this->createCloud = outputCloudFlag.is_present();

  }

};

#endif


text:
Theatre review: Being Frank, theSpace on North Bridge, Edinburgh
Fine, sturdy singing in this piece, particularly the song The End of the Rainbow.
By Tim Cornwell
Friday, 16th August 2019, 11:34 am
Being Frank, theSpace on North Bridge (Venue 36)
Being Frank, theSpace on North Bridge, Edinburgh * * *
A story of men who feel much but can't talk about it, from a writing group at Falkirk's Mental Health Association. Frank, Nick Blessley, is navigating Ikea, that blue and yellow hell hole, with Mike, Colin Hill, a cue for odd couple exchanges over the joys of tea lights and flat pack furniture.
As angry Frank tries to engage with his son, the voices of anxiety and depression are staged simply and effectively. There's spirited amateur and professional performance in this piece, about cares that will touch a chord with many older men, albeit with a wooden moment or two and a few missed high Cs. Colin Hill was reviewed in his first Fringe outing in 1964, when the esteemed critic WA Darlington said he didn't lack talent. He still doesn't, though his charms are older now.


My drinking of Diet Coke on the Family PAC Cruise added 36 cents to the coffers of Cook County.
When the soda tax was first proposed by Cook County Board President Toni Preckwinkle it was promoted as a tax on "sweetened" beverages.
Yet, it included diet pop, but not Starbucks coffee.
acknowledged it appears opponents of the tax have a veto-proof majority needed to repeal it, but she proposed the county instead should scale back the penny-per-ounce tax on soft drinks and other sweetened beverages.
In effect, one of the social engineers who convinced Preckwinkle to support their idea still support the idea, but will settle for less.
Preckwinkle, of course, was supporting the tax primarily for the money it would bring in, which the public figured out with the help of millions of dollars of advertising.
1. Despite millions of dollars in TV ads justifying the beverage tax hitting the Chicago DMA, our Approve/Disapprove outcome was a virtual tie with the findings of the initial poll. In early August, we reported 86.64%of voters opposed the tax. On October 7, those opposed equaled 85.76%—well within the margin of error of the first poll.
2. Also within the previous poll's margin of error were the percentage of voters who didn't buy that commissioners who passed the beverage tax did so for health reasons. In early August, 80.33% believed that commissioners primarily passed the beverage tax to raise funds—not for health reasons. Two months later, 76.98% said the same—a drop of only three percentage points. It's difficult to say that such a small drop—one basically within the margin of error—shows any statistically movement. That is true especially in light of the continuing opposition to the tax.
3. Voters are still steaming about the passage of the tax, and may take it out at the ballot box if reasonable alternative candidates challenge those who originally voted for the tax. Nearly 79% of voters say they will be less likely to vote for a Cook County Commissioner who supported the beverage tax. That number—which is just outside of the margin of error of the original poll—remains extraordinarily strong and the intensity hasn't changed significantly. Even if the tax is repealed, the anger over its passage may hang over the next election.
With a reported multi-million dollar ad campaign by former New York Mayor Michael Bloomberg designed to justify the Cook County sweetened beverage tax, surely a swing in public opinion must be the outcome…right?
The poll also asked voters' opinions on the main motive for the tax increase (health vs. increased spending) and their opinions on re-electing officials who voted for the new tax.
A soda tax was advamced bu McHenry County Board member Mary McCann at the last meeting of the Board of Public Health.
something the traitorous RINO Rauner is going to find out first hand very soon.
Feeling fine, but fingers not working well enough.


text:
Apple Facing Lawsuit By Angry Users Who Say iPhone Ads Lie About Screen Size
by Krissie Mick
Apple received some upsetting news last Friday in the form of a lawsuit from two iPhone X users who claim that the tech giant lied about the popular smart phone's screen size.
The lawsuit alleges that Apple's marketing claims about the iPhone X, iPhone XS and iPhone XS Max are misleading. Plaintiffs/angry iPhone users Christian Sponchiado and Courtney Davis filed the suit in the Northern District of California court in San Jose and allege that the new design that Apple has used for the X, XS and XS Max iPhones reduce the display area.
According to The Register, Apple used a new technology for the display screen of the iPhone X, XS and XS Max. Previous LCD-based iPhones have an RGB stripe pixel configuration while the X family of iPhones have OLED screens which use a diamond-shaped pixel configuration. The difference? Twice as many green subpixels as there are blue and red subpixels with the X iPhones. Less subpixels means a better screen longevity because less current is needed to give light to the screen which allows for a generally longer lifespan.
RELATED: TIM COOK TELLS RACISTS NOT TO BUY APPLE PRODUCTS
thetimes.co.uk
The problem with iPhone X generation, according to the plaintiffs, is all in the new"notch" design that Apple is using which ultimately results in a non-square shaped screen as older iPhones have.
In the suit, Sponchiado and Davis insist the new design of the OLED screens allow Apple to lower their overall cost of production while not changing their marketing or promotional material to reflect the change in lower clarity and resolution of the new OLED phones to the older models which use RGB technology.
"The iPhone X Product is advertised as having 2436×1125 pixels, but in fact does not use true pixels with red, green, and blue subpixels in each pixel," the lawsuit reads. "Instead, the Product has only false screen pixels, with just two subpixels per false pixel (2436×1125×2 = 5,481,000 subpixels), and it does not actually have any subpixels at all in the notch at the top of the screen or in the display-area corners."
techspot.com
NEXT: APPLE MUSIC WILL FINALLY WORK ON ANDROID TABLETS
Official court documents go on to state that the iPhone 8 Plus has a higher quality screen than the iPhone X because it has more subpixels and that Apple incorrectly measured the screens of the iPhone X models as it they are square as the older models are. Claims from the company that the newest iPhones are "all screen" are false, according to the lawsuit.
Sponchiado and Davis's attorneys are attempting to have the suit recognized as a class action lawsuit but there's no word yet on if that will be the case. Apple has not released a statement about this particular lawsuit at this time.
Fossils Belonging To A Previously Undiscovered Species Of Dinosaur Have Been Found In Australia
The 'World's Largest Plane' Recently Enjoyed A Successful Maiden Flight


text:
Hull & East Yorkshire News
Hull dad who refused to give up after one-punch brain injury could get Pride of Britain award
Paul Spence forgot a lot of details about his past after being punched in a bar five years ago
Alex GroveSenior reporter
A dad-of-two from west Hull who had his life turned upside down after an unprovoked attack left him with a brain haemorrhage is in the running for a Pride of Britain award.
Paul Spence, 37, was left with life-changing injuries after being knocked out in the toilets of a bar in Princes Avenue five years ago.
He was punched so hard he was left with severe brain injuries and struggled to recall large chunks of his past.
Paul effectively had to rebuild his life and his debilitating condition took its toll on his family, causing the break-up of his relationship.
Paul was assaulted in west Hull in 2012 (Image: Rob Stebbing)
He said: "I couldn't see my past and I was an unemotional robot. It was frightening for my kids and my family to see me how I was.
"I remembered who I was but I just couldn't see it so it was really difficult. It turned my life upside down."
Paul also lost his job as an electrician but after seeing the lack of aftercare available in the area, he set his mind on launching a service to help and support other brain injury victims.
The number of child refugees living in Hull has been revealed
Since the attack, PAUL for Brain Recovery has helped hundreds of people recover from the devastating consequences of brain injury.
He made a business plan and secured funding from the NHS which allowed him to set up a support centre within Wilberforce Health Centre and he is amazed at how far he has come.
Paul is in the running for a Pride of Britain award (Image: Jack Harland)
"I needed to do something, especially after being sat at home for two years," he said.
"My partner had gone, I'd lost my job and I didn't know what to do with myself.
"I published the Facebook page and it just snowballed from there. I hope that I can set an example to others going through recovery.
Are you looking for a job? Click here to see our Hull listings
"I am immensely proud. I can't describe the journey that I have been on and I am so thankful to everybody who has helped me get to where I am today."
Paul says he has 120 visitors to his centre a month and he now also talks to children in schools across Hull about mental health issues and the punch which left him with a brain haemorrhage.
Paul (second from left) and his hard working team
Paul's charity is mostly based on fundraising and his exploits have secured him a place on the shortlist for the prestigious Pride of Britain awards.
He is up against three other people from the Yorkshire and Humber region with the winner set to be revealed on Friday on ITV Calendar from 6pm.
The regional champion will then battle it out to be crowned the overall winner at a glitzy ceremony in London later this month.
Charming moment darts superfan meets his idol Phil 'The Power' Taylor in Hull
He said: "I don't expect to get through but getting into the top four with people who do some great stuff is just amazing.
"Just to be associated with Pride of Britain is indescribable.
"I can't believe that people have taken the time to nominate me - I never expected anything like this."
Find out more about Paul for Brain Recovery by clicking here.


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Elizabeth Bourgine
ACTRESS, ASSISTANT_DIRECTOR, MUSIC_DEPARTMENT
Elizabeth Bourgine Movies or Tv Shows (upto Jan 2022) - Watch Online
Home/People/Elizabeth Bourgine/
Elizabeth Bourgine was born on March 20, 1957 in Levallois-Perret, Seine [now Hauts-de-Seine], France. She is an actress and assistant director, known for Erpreßt - Das geheimnisvolle Foto (1986). She is married to Jean-Luc Miesch. They have one child.
BritBox has the most number of Elizabeth Bourgine's flixes, followed by Amazon Video compared to other streaming platforms. See the full graph below.
Elizabeth Bourgine on average has worked on 2 movies per year from 1976 to 2019. See the full graphs of the number of Elizabeth Bourgine movies released per year from 1993 till 2019.
Elizabeth Bourgine works mostly in Drama Genre followed by Crime Genre flixes. 46% of Elizabeth Bourgine movies are Drama Genre movies. See Top Genres that Elizabeth Bourgine worked on in the graph below.
On average the IMDB score of the movies that Elizabeth Bourgine has worked on is 6.1.
Elizabeth Bourgine's Movies and Tv Series available to Stream now ..
Death in Paradise (2011)
A UK police DI is transferred to St-Marie's police dept. He hates the sun, sea and sand. Series follows his murder investigations on the island. Later series see another UK DI head the team, followed by an Irish DI and then another UK DI.
Drama,Music,Romance
Un Coeur en Hiver (1992)
Beautiful violin virtuoso Camille has two obsessions: the music of Ravel, and a friend of her husband's who crafts violins. But his heart seems to be as cold as her playing is passionate.


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Home – James Collins – ARSENAL WANT AFRICAN DUO
News of Wilfred Zaha reported interest in Arsenal has been gaining steam in recent weeks. There have been reports in recent days that there is an element of truth behind the news that Zaha is interested in making the move to the Emirates.
Highly rated transfer guru David Ornstein claims that Zaha has made up his mind to join the North London club this summer. It is understood that talks have started between the two clubs for the £80 million-rated forward.
The Gunners have been linked with the likes of William Saliba, Kieran Tierney and Julian Wiegl despite the club's financial constraints.
Nevertheless, if the rumours of a move for Zaha are true, this should be applauded by Arsenal fans. Zaha is one of the best-attacking players outside the top six clubs and would bring a new dimension to the Arsenal attack.
His pace, dribbling skills and ability to create chances would ensure that the Gunners are able to pose a different problem for opposing defences. He is certainly an upgrade from Alex Iwobi in the wide positions.
There have been reports that the club could sell Pierre-EmerickAubameyang to fund the move. If it is true, such a move would prove unpopular with the fans as the Gabon forward is one of the few world-class players at the club.
Zaha is currently with his nation at the Afcon tournament and any potential move would have to wait until the end of the tournament in three weeks' time.
Also the Gunners have been linked with the signing of West Ham defender Diop. The 22-year-old emerged as the best defender in the club having replaced club legend James Collins in the Centre back role.
It is not known how much West Ham are willing to sell the player but a fee of around £40 million has been touted.
← WEST HAM LOOKING TO SIGN ATLANTA ACE Collins Advises Town for Keeping Good Form →


Shabbat morning will be our first Shul School Shabbat. Our whole multi-generational Shir Chadash community will be/is celebrating Shabbat together. There will be special youth services and age-appropriate Torah study activities. We will all share Kiddush lunch together!
Appeals: If you have not yet purchased Israel Bonds or made your donation to Leket Israel, please do so! Contact Bruce Yaillen with any questions about the Bonds, and make your check for Leket Israel payable to Shir Chadash with LEKET in the memo line. Thank you for your support.
Survey: Thank you to everyone who has already completed the High Holyday survey. If you have not – it is open HERE until 10/22.
7:15 pm Vegetarian potluck supper. Please bring dairy vegetarian food in disposable dishes to share; we provide plasticware, paper plates, challah, grape juice and dessert.
Whether you learned Shabbat Shaharit years (or even decades!) ago and need a good brush up or you've got reasonably good Hebrew reading skills, some dedication, and want to learn it for the first time, this is the class for you!
Thanks to everyone who joined Judy Steinberg at the last Sisterhood lunch and Book Review. Watch your calendar for more Sisterhood events.
The idea of connecting to God is embedded in Jewish tradition, but how exactly should we go about making that connection?


I got crushing news last week when I learned I wasn't the originator of the art/science of combining existing words to form a new word. I guess a clue should've been that the word neologism existed.
This news came in exciting packaging, however—in the form of a gift from one of my favorite readers in the whole world, R—.
The best part of this is that R— was completely unaware of my sister-given nickname, SNiG (Summer Nicole Grimes).
Interested in submitting you're own Hybrid Neologism to Hobo Siren for dozens of people to read!? Email me at summer@hobosiren.com.
Thanks for the gift, R–!!!


An authentic rigid 14.3 oz. denim is the perfect fabric to create these vintage inspired pieces that are cool and edgy. The light blue authentic denim wash has highs and lows created by whiskers, chevrons, knee bursts and sanding.
Length From Center: 22 1/2"


If you are looking to upgrade a room in your Rockville home, a good place to start is the bathroom. From small Rockville bathroom updates to complete Rockville bathroom remodeling, including design and build outs, Erix Home Improvement LLC will work with you and your budget to create your dream bathroom.
Call (240) 207-1192 to speak to one of our Rockville bathroom remodeling contractors. We've been renovating bathrooms in Rockville, Maryland for 7 years.
Your bathroom has spa potential. Really! With a little ingenuity and planning, you can update your Rockville bathroom and give it a fresh look.
Make your Rockville bathroom unique with the features that are important to you.
Whether your budget is large or small, a bathroom remodel in Rockville is an investment that pays for itself in a short period of time.
Call (240) 207-1192 to get started. An expert Rockville bathroom remodeling contractor is ready to help! No job is too big or too small for Erix Home Improvement LLC.
Erix Home Improvement LLC guarantees quality work and attention to detail for every aspect of your Rockville bathroom remodel.
Call (240) 207-1192 to speak to one of our Rockville bathroom renovation specialists. Erix Home Improvement LLC has been renovating bathrooms in Rockville, Maryland for 7 years.
Bathroom renovation instantly adds value to your Rockville house. It also adds instant quality to your life. Imagine a beautiful, serene bathroom with state-of-the-art features. You may never want to leave.


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Over $60M in opioid settlement money to be paid to Md. jurisdictions
By: Madeleine O'Neill November 8, 2022
Maryland Attorney General Brian E. Frosh announced this week that more than $60 million in payments from a major opioid settlement are set to be paid out to counties and municipalities by the end of the year.
Fifty-eight political subdivisions in Maryland stand to gain from the settlement with the former opioid manufacturer Johnson & Johnson and opioid distributors McKesson, Cardinal Health and Amerisource Bergen.
Maryland is set to receive nearly $400 million over the next 18 years as part of the settlement agreement. The $60 million to be distributed by the end of this year is the first portion of that total to be sent to participating counties and municipalities.
The funding is meant to address the opioid crisis throughout the state. About $47 million will be distributed to the Maryland Opioids Restitution Fund, which state lawmakers established in 2019 to pay for opioid abatement programs.
Another $13.5 million will be paid directly to counties and municipalities, Frosh's office said. Nine Maryland counties will receive total grants or payments ranging from $1.3 to $7.8 million and smaller counties and municipalities will receive additional millions of dollars in total.
Baltimore County will receive the largest sum, including $5 million in targeted abatement grants and $2.7 million in direct payments, according to a spreadsheet detailing estimated payments.
Prince George's County, Montgomery County and Anne Arundel County are each also set to receive between $3 and $4 million.
Notably absent from the payment list is the city of Baltimore, which declined to participate in the settlement with Johnson & Johnson.
Under the settlement, states could receive incentive payments for getting a larger number of political subdivisions to agree to the deal. The opioid defendants could have chosen to back out of the settlement if too many plaintiffs declined the settlement and chose to continue the legal battle in court.
Baltimore's choice not to join the settlement shrank the overall payment Maryland received. Michael Sanderson, the executive director of the Maryland Association of Counties, told The Daily Record previously that losing Baltimore, one of the state's biggest and most populous jurisdictions, may have reduced the total coming to Maryland by about $100 million.
The Johnson & Johnson settlement is set to total $26 billion nationwide.
In a statement, Frosh said the funds will help prevent more opioid-related addiction and death.
"We appreciate the cooperation and hard work that have brought us to this point," he said. "I am proud of the work the state and its subdivisions have done in holding wrongdoers accountable and securing this relief for the people of Maryland."
Companies like Johnson & Johnson have faced a slew of lawsuits over their roles in the opioid epidemic, which has killed hundreds of thousands of Americans.
The settlement marks the end of just one piece of an immense legal movement that has sought to hold opioid makers, sellers and marketers responsible for the addiction crisis. Other settlements with large companies that profited off opioids have also been reached during the past year.
Attorney General Brian E. Frosh opioid crisis opioid settlements opioids 2:16 pm Tue, November 8, 2022 Maryland Daily Record
Madeleine O'Neill
Tagged with: Attorney General Brian E. Frosh opioid crisis opioid settlements opioids


The TESOL 2019 International Convention & English Language Expo will be held at the Georgia World Congress Center in Atlanta, Georgia, USA.
Browse the preliminary session content with our TESOL 2019 mobile app. You may view the desktop version of our mobile app here to get a preview of the exciting sessions* offered throughout TESOL convention. Under the menu bar, select Agenda and then Full Schedule to view.
*Note: All sessions and presenters are subject to change.
You can also download the TESOL 2019 Convention Program Book (PDF). To open the file, you'll need the free Adobe Reader.
Wednesday, Thursday, and Friday beginning at 7:00 am each day, with the last session starting at 5:00 pm.


The Cybercrime Convention Committee (T-CY) represents the State Parties to the Budapest Convention on Cybercrime.
Based on article 46 of the Convention, the consultation of the Committee aims at facilitating the effective use and implementation of the Convention, the exchange of information and consideration of any future amendments.
On 30 January 2019, the Congress of Peru unanimously approved the act of accession to the Budapest Convention on Cybercrime. This will allow the Government of Peru to deposit the instrument of accession at the Council of Europe and to become a Party to this treaty in the very near future.


WASHINGTON, May 31, 2013 – The ethanol industry's Growth Energy announced today that agricultural policy expert Jim Miller will serve as its vice president and chief economist.
Miller, a Washington State native, most recently served as senior policy advisor on the Senate Budget Committee under Sen. Kent Conrad, D-N.D. Miller was the primary advisor and analyst for agricultural policy and trade issues.
Prior to his service on Capitol Hill, Miller was appointed by President Obama and confirmed by the Senate to serve as the under secretary for USDA's Farm and Foreign Agriculture Services. In addition, Miller has held leadership roles at the National Farmers Union and the National Association of Wheat Growers.


Welcome to XtremeLabs, a service of the XtremeLabs LLC. This document provides answers to some frequently asked questions about the Microsoft Official Courseware (MOC) hosted lab environment.
Q: I'm new to Microsoft Labs Online. How do I proceed?
Click Register in the lower right corner.
To create your account, fill in the fields on the Create an account page.
Note: The email address used to create your account is also used for password reminders. It is important to use a valid email address.
Click Register at the lower left corner of the page.
You will be redirected to the My codes page. You will enter your Course Codes here.
Q: I already have an account. How do I sign-in?
Enter the email address used to create your account and enter your password.
Click Sign in. For a persistent sign in, check the Keep me signed in checkbox.
You will be redirected to the My labs page. All of the labs that you have access to will be listed here.
Q: How do I add a Course Code?
On the My codes page, in the Add a code to your account text box, enter the code given to you by your instructor or from your book. Note that all active courses will be displayed on the left side under the 'My labs' title.
Click Add code. Your course will be added to the My codes page.
Your course labs should now be available. To see the lab modules in your active course labs, click on the course number. Your course's lab modules should now be visible.
Note: If you do not see the labs associated with your particular course on your course home page, you should inform your instructor.
Q: How do I launch a Lab?
The duration and description of the subject lab module will be presented here. To launch the lab module, hover over and click on the 'Take Lab' button.
While your lab loads, you will see a spinner with tips and tricks for the lab hosting system.
Note: If your lab takes longer than five minutes to load, refresh your browser page by pressing the F5 key. If you still cannot access your lab, please alert your instructor.
Once the lab loads and the environment is ready, your lab view will be displayed.
See the Take a Lab section of the full Student User Guide document to learn how to use the many user interfaces on this page.
Q: Do I need to configure the Hyper-V environment before beginning a lab?
A: No. Students do not have access to the Hyper-V host environment. Steps pertaining to Hyper-V Manager within the Lab Setup section have already been completed.
Q: Do I need to set up Internet Access?
A: No. Internet access is available when needed. There is no need to use the MSL‐TMG1 virtual machine.
Q: How do I resize the Virtual Machine Window?
A: You can adjust the size of the virtual machine window by changing the screen resolution in the virtual machine.
Q: Is there a User Guide for Microsoft Labs Online?
A: Yes. If you have an instructor, ask them for a copy. If you do not have an instructor you can download a copy from here.
A: You can call the XtremeLabs Support Team at the phone number below during the following hours.