text:
namespace Microsoft.Azure.Management.Synapse
{
    using Microsoft.Rest;
    using Microsoft.Rest.Azure;
    using Models;
    using System.Collections;
    using System.Collections.Generic;
    using System.Threading;
    using System.Threading.Tasks;

    /// <summary>
    /// KustoPoolAttachedDatabaseConfigurationsOperations operations.
    /// </summary>
    public partial interface IKustoPoolAttachedDatabaseConfigurationsOperations
    {
        /// <summary>
        /// Returns the list of attached database configurations of the given
        /// Kusto Pool.
        /// </summary>
        /// <param name='workspaceName'>
        /// The name of the workspace.
        /// </param>
        /// <param name='kustoPoolName'>
        /// The name of the Kusto pool.
        /// </param>
        /// <param name='resourceGroupName'>
        /// The name of the resource group. The name is case insensitive.
        /// </param>
        /// <param name='customHeaders'>
        /// The headers that will be added to request.
        /// </param>
        /// <param name='cancellationToken'>
        /// The cancellation token.
        /// </param>
        /// <exception cref="ErrorResponseException">
        /// Thrown when the operation returned an invalid status code
        /// </exception>
        /// <exception cref="Microsoft.Rest.SerializationException">
        /// Thrown when unable to deserialize the response
        /// </exception>
        /// <exception cref="Microsoft.Rest.ValidationException">
        /// Thrown when a required parameter is null
        /// </exception>
        Task<AzureOperationResponse<IEnumerable<AttachedDatabaseConfiguration>>> ListByKustoPoolWithHttpMessagesAsync(string workspaceName, string kustoPoolName, string resourceGroupName, Dictionary<string, List<string>> customHeaders = null, CancellationToken cancellationToken = default(CancellationToken));
        /// <summary>
        /// Returns an attached database configuration.
        /// </summary>
        /// <param name='workspaceName'>
        /// The name of the workspace.
        /// </param>
        /// <param name='kustoPoolName'>
        /// The name of the Kusto pool.
        /// </param>
        /// <param name='attachedDatabaseConfigurationName'>
        /// The name of the attached database configuration.
        /// </param>
        /// <param name='resourceGroupName'>
        /// The name of the resource group. The name is case insensitive.
        /// </param>
        /// <param name='customHeaders'>
        /// The headers that will be added to request.
        /// </param>
        /// <param name='cancellationToken'>
        /// The cancellation token.
        /// </param>
        /// <exception cref="ErrorResponseException">
        /// Thrown when the operation returned an invalid status code
        /// </exception>
        /// <exception cref="Microsoft.Rest.SerializationException">
        /// Thrown when unable to deserialize the response
        /// </exception>
        /// <exception cref="Microsoft.Rest.ValidationException">
        /// Thrown when a required parameter is null
        /// </exception>
        Task<AzureOperationResponse<AttachedDatabaseConfiguration>> GetWithHttpMessagesAsync(string workspaceName, string kustoPoolName, string attachedDatabaseConfigurationName, string resourceGroupName, Dictionary<string, List<string>> customHeaders = null, CancellationToken cancellationToken = default(CancellationToken));
        /// <summary>
        /// Creates or updates an attached database configuration.
        /// </summary>
        /// <param name='workspaceName'>
        /// The name of the workspace.
        /// </param>
        /// <param name='kustoPoolName'>
        /// The name of the Kusto pool.
        /// </param>
        /// <param name='attachedDatabaseConfigurationName'>
        /// The name of the attached database configuration.
        /// </param>
        /// <param name='resourceGroupName'>
        /// The name of the resource group. The name is case insensitive.
        /// </param>
        /// <param name='parameters'>
        /// The database parameters supplied to the CreateOrUpdate operation.
        /// </param>
        /// <param name='customHeaders'>
        /// The headers that will be added to request.
        /// </param>
        /// <param name='cancellationToken'>
        /// The cancellation token.
        /// </param>
        /// <exception cref="ErrorResponseException">
        /// Thrown when the operation returned an invalid status code
        /// </exception>
        /// <exception cref="Microsoft.Rest.SerializationException">
        /// Thrown when unable to deserialize the response
        /// </exception>
        /// <exception cref="Microsoft.Rest.ValidationException">
        /// Thrown when a required parameter is null
        /// </exception>
        Task<AzureOperationResponse<AttachedDatabaseConfiguration>> CreateOrUpdateWithHttpMessagesAsync(string workspaceName, string kustoPoolName, string attachedDatabaseConfigurationName, string resourceGroupName, AttachedDatabaseConfiguration parameters, Dictionary<string, List<string>> customHeaders = null, CancellationToken cancellationToken = default(CancellationToken));
        /// <summary>
        /// Deletes the attached database configuration with the given name.
        /// </summary>
        /// <param name='workspaceName'>
        /// The name of the workspace.
        /// </param>
        /// <param name='kustoPoolName'>
        /// The name of the Kusto pool.
        /// </param>
        /// <param name='attachedDatabaseConfigurationName'>
        /// The name of the attached database configuration.
        /// </param>
        /// <param name='resourceGroupName'>
        /// The name of the resource group. The name is case insensitive.
        /// </param>
        /// <param name='customHeaders'>
        /// The headers that will be added to request.
        /// </param>
        /// <param name='cancellationToken'>
        /// The cancellation token.
        /// </param>
        /// <exception cref="ErrorResponseException">
        /// Thrown when the operation returned an invalid status code
        /// </exception>
        /// <exception cref="Microsoft.Rest.ValidationException">
        /// Thrown when a required parameter is null
        /// </exception>
        Task<AzureOperationResponse> DeleteWithHttpMessagesAsync(string workspaceName, string kustoPoolName, string attachedDatabaseConfigurationName, string resourceGroupName, Dictionary<string, List<string>> customHeaders = null, CancellationToken cancellationToken = default(CancellationToken));
        /// <summary>
        /// Creates or updates an attached database configuration.
        /// </summary>
        /// <param name='workspaceName'>
        /// The name of the workspace.
        /// </param>
        /// <param name='kustoPoolName'>
        /// The name of the Kusto pool.
        /// </param>
        /// <param name='attachedDatabaseConfigurationName'>
        /// The name of the attached database configuration.
        /// </param>
        /// <param name='resourceGroupName'>
        /// The name of the resource group. The name is case insensitive.
        /// </param>
        /// <param name='parameters'>
        /// The database parameters supplied to the CreateOrUpdate operation.
        /// </param>
        /// <param name='customHeaders'>
        /// The headers that will be added to request.
        /// </param>
        /// <param name='cancellationToken'>
        /// The cancellation token.
        /// </param>
        /// <exception cref="ErrorResponseException">
        /// Thrown when the operation returned an invalid status code
        /// </exception>
        /// <exception cref="Microsoft.Rest.SerializationException">
        /// Thrown when unable to deserialize the response
        /// </exception>
        /// <exception cref="Microsoft.Rest.ValidationException">
        /// Thrown when a required parameter is null
        /// </exception>
        Task<AzureOperationResponse<AttachedDatabaseConfiguration>> BeginCreateOrUpdateWithHttpMessagesAsync(string workspaceName, string kustoPoolName, string attachedDatabaseConfigurationName, string resourceGroupName, AttachedDatabaseConfiguration parameters, Dictionary<string, List<string>> customHeaders = null, CancellationToken cancellationToken = default(CancellationToken));
        /// <summary>
        /// Deletes the attached database configuration with the given name.
        /// </summary>
        /// <param name='workspaceName'>
        /// The name of the workspace.
        /// </param>
        /// <param name='kustoPoolName'>
        /// The name of the Kusto pool.
        /// </param>
        /// <param name='attachedDatabaseConfigurationName'>
        /// The name of the attached database configuration.
        /// </param>
        /// <param name='resourceGroupName'>
        /// The name of the resource group. The name is case insensitive.
        /// </param>
        /// <param name='customHeaders'>
        /// The headers that will be added to request.
        /// </param>
        /// <param name='cancellationToken'>
        /// The cancellation token.
        /// </param>
        /// <exception cref="ErrorResponseException">
        /// Thrown when the operation returned an invalid status code
        /// </exception>
        /// <exception cref="Microsoft.Rest.ValidationException">
        /// Thrown when a required parameter is null
        /// </exception>
        Task<AzureOperationResponse> BeginDeleteWithHttpMessagesAsync(string workspaceName, string kustoPoolName, string attachedDatabaseConfigurationName, string resourceGroupName, Dictionary<string, List<string>> customHeaders = null, CancellationToken cancellationToken = default(CancellationToken));
    }
}


A clean and organised house gives us a peaceful mind. Thus, have you think about it that everyone hates to do the job but everyone loves a clean house? Well, we understand that everybody has its own priority, and cleaning is on the last list. Although many of us seem to be really short on the time and we need to find our ways to do our job quickly and effectively. The biggest secret to efficient house cleaning is proper organisation. Yes, once you have an organised rotating schedule in your mind, it becomes a part of your routine.
Follow these tips below and see how efficient house cleaning reduce your time as you do your clean-up task.
You need to keep in mind that when you clear up the clutters, always start from the top to the bottom, back to front and right to left. When you start your move, make it more precise and accurate to help you not miss an area to clean. And for an efficient house cleaning, try to clear up one area at a time and work your way completely around before you move to another area.
House cleaning is a chore and no one really enjoys doing it. What we are enjoying is the result we get after the clean-up. Hence, if you're distracted as you do the job, the tendency of spending more time to do the task is high. However, you can put some music on and focus on your job at hand. This will give you comfort as you tidy up and you'll finish the job quickly.
Check your cleaning supplies first before you get started. Remember that there is nothing worse than having started your chore and only to find out that you can't finish your task because of your lack of supplies. So be sure to double check your supplies to make things done properly.
Almost all professional cleaners carry their supplies with them as they clean. This helps them do their work fast and efficient. Yes, doing this won't have to stop you from looking things you will be using. Instead, you'll work faster knowing that everything you need is right at your fingertips.
As you start doing the task, the best part to start is to dust first. Start dusting from top to bottom, so you could vacuum it all the way.
We understand that everyone has its own busy life schedule and we don't have time and energy to allocate to cleaning. However, you need to keep your house clean and safe from any harmful disease caused by bacteria. So, you need to set a schedule and plan your clean-up task whenever you have time. Setting up a plan and schedule will help you prevent burnout because you won't feel like you need to clear up the whole house at once.
As a busy person with so many errands in life, it makes sense to get some help from a professional cleaner. Hence, you should take into consideration the qualities of a good cleaning company before hiring them. Check what services they offer and if they are reliable and trustworthy. A good cleaning company should have the following services; Apartment cleaning, end of lease cleaning, spring cleaning, vacate cleaning, commercial cleaning, and etc.
Give some of the above tips a try and you can guarantee an efficient house cleaning work. And if you're too busy to do all the tips, try to consider hiring a professional cleaner to take good care of your needs. Remember that it is important to keep our abode clean and free from dirt and bacteria which may cause sickness to our family. Be responsible enough for giving your family and yourself a secure and healthy environment.
Looking for house cleaning services company?
Browse our entire website for more services offered that will surely fit your needs. For we, at Maid in Perth, guarantees to leave your abode clean and sparkling.
And if you're planning to move, read this recommended article House Cleaning Tips and learn what is the thing you need to do before moving to your new place.
This entry was posted in House Cleaning and tagged After Party Cleaning Perth, Apartment Cleaning Perth, Carpet Steam Cleaning Perth, Commercial Cleaning Perth, End of Lease Cleaning Perth, Grout Cleaning Perth, Home Cleaning Perth, Maid in Perth, Move In Cleaning, Move Out Cleaning, Spring Cleaning Perth, Vacate Cleaning Perth, Window Cleaning Perth.


text:
The Most Controversial Magic Tricks by David Copperfield
Home The Most Controversial Magic Tricks by David Copperfield
Jeffrey J. McCart, August 14, 2020 August 14, 2020 , David Copperfield, 0
David Seth Kotkin or David Copperfield has always managed to surprise the audience each time he comes in front of them with a magic trick. The American magician was once described by Forbes as the most commercially successful magicians in history. This only goes out to prove as to why he won 21 Emmy Awards and around 38 nominations. But all this does not eliminate the different controversies that the 63-year-old has attracted in his life. While his magic tricks were meant to leave you awestruck, some found things to be a bit controversial. So to get the clear picture without tricks, here are some of the most controversial magic tricks by David Copperfield.
1. Lucky #13
Way back in 2013, Copperfield was set to perform at MGM Grand Resort and Casino in Las Vegas. The trick he was about to do was "Lucky #13". While it may sound to be a bit confusing, you need to know that it was about making 13 people disappear. Yes, that's right. Copperfield would call 13 audience members and make them disappear in front of the whole crowd. While the setting and the magic went through on a triumphant note, things got out of hand when a British tourist, Gavin Cox, who was one among the randomly chosen audience members, went ahead and filed a lawsuit against the illusionist.
According to the lawsuit that he filed, Gavin Cox claimed he had suffered from chronic pain and brain injury and went on to spend more than $400,000 on medical bills. Due to all this, the court even ordered Copperfield to reveal his trick. Although Copperfield's attorney argued that revealing the magic trick would be a wrong move financially, the court did not rule it out.
2. Vanishing the Statue of Liberty
Only a Magician like David Copperfield could live up to the challenge of making a 310-foot statue disappear. Back in 1983, the world wasn't ready for an illusion of this nature, and as a result, they couldn't handle what they saw. While the trick did not end up being as controversial as "Lucky #13", it did manage to leave people confused to their very senses. Moreover, the trick was done to emphasize on how we take our freedom for granted. Due to that, when the moment came to light, people realized that they could expect the unexpected from life.
Although the trick was a successful one, things did not reach the true extent as the world came to know about the trick. The effort and the importance of illusion were lost when people realized all about the tricks that were used by David Copperfield. Due to that, if you haven't read about how he did it, then it is best to leave it that way.
Being successful has always brought forward controversy as things tend to get mixed along the line of work. But for Copperfield, such aspects will not undermine his talent and all that he is capable of doing.
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Copyright © 2020 themagiciansbook.com. All rights reserved.

redpajama_set_name: RedPajamaCommonCrawl


text:
HomeUncategorizedThe onset of illness phobia was related to
The onset of illness phobia was related to
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text:
Philips Point was a promontory on the north east bank of the Colorado River in Sonora, Mexico, that marked the mouth of the tidal estuary of the Colorado River in the later 19th century.

"Philips Point may be regarded as the head of deep-water navigation in the Colorado River. At Philips Point spring tides rise 25 to 30 feet, and neap tides from 16 to 20 feet. At a short distance above Philips Point, the spring tide comes in with a bore or bank of water 4 feet high, extending in one huge breaker clear across the river, while the ebb is still running out. The influence of the tide in the Colorado River is felt for about 40 miles up the river, a few miles above Heintzelman's Point."

History
In the mid-19th century, Philips Point also marked the minor southeastern trending distributary channel of the Colorado River. It was divided from the western main channel of the river and the Gulf of California by Montague Island and Gore Island.

It was the deep waters of this side channel at the mouth of Port Isabel Slough that was the anchorage for the steamships visiting Port Isabel, and where they transferred their passengers and cargoes to steamboats and barges of the Colorado Steam Navigation Company between 1871 and 1877.

References

Colorado River
History of Sonora
Lower Colorado River Valley
Steamboat transport on the Colorado River

redpajama_set_name: RedPajamaWikipedia


text:
Q: Simple HTML contact details form with table These are my first steps in FE so please don't hate me. I want to create a page with user details.
What I have is something below:
First name:      Last name:      User status:      Date joined:    Policies accepted:
John             Doe             active            12.12.2021      true

To do so I used table but below that table I need to display user contact details:
Contact details
Email:                        Phone number:
example@example.com           +681234123412

Is there a better way to display such a thing than table or it is a common approach in such situations ?

A: You should use forms instead of table for the user details and the contact details, it's much more effective, productive, and easier.

A:

        First Name:
        Last Name:
        User Status:
        Date Joined:
        Policies Accepted:

        John
        Doe
        Active
        12.12.2021
        True

        Contact Details

        Email:
        Phone Number:

        example@example.com
        +681234123412

Here's the screen shot example.
https://i.stack.imgur.com/zJSqN.jpg

redpajama_set_name: RedPajamaStackExchange


text:
Football League media talk 10/09/2014
Here are a selection of Wednesday 10th September's stories from the media that cover The Football League:
Shane Duffy ready to fight for Blackburn Rovers place - four years after being left to fight for his life (Lancashire Telegraph): Blackburn Rovers new boy Shane Duffy admits he has a huge challenge on his hands to dislodge two of the three 'great' centre backs Gary Bowyer has at his disposal.
New Carlisle United stadium 'not at Kingmoor Park' (News & Star): Carlisle United's long-awaited new stadium will not be located at Kingmoor Park.
Hyypia happy to have game-changer option with LuaLua (The Argus): Albion boss Sami Hyypia is keeping an open mind about the role of Kazenga LuaLua as the explosive winger creeps towards a half-century of league starts for the club.
Saunders steps up recovery from knee injury (Get West London): Brentford have been handed a big boost after Sam Saunders returned to light training following a long injury lay-off.
David McGoldrick would love to play alongside Jonny Williams at Ipswich Town (Ipswich Star): At one stage it looked as though neither would wear the Ipswich Town shirt again. Now Blues supporters can dream of seeing David McGoldrick and Jonny Williams play alongside each other.
Alex Bray 'devastated' after serious knee injury ends his loan to Argyle (The Herald): Alex Bray admitted he was 'devastated' after receiving confirmation that he had ruptured the anterior cruciate ligament in his left knee.
Wilder wants Cobblers wide boys to keep providing the attacking ammunition (Northampton Chronicle & Echo): Chris Wilder is confident his wingers can maintain their supply lines to the strikers as the Cobblers go in search of a third successive league win this weekend.
These stories have been reproduced from a variety of today's media sources and they do not represent the views of The Football League.
Click here for all the latest news


The Gibson Brothers repeated as the big winners at the International Bluegrass Music Association Awards on Thursday night (Sept. 26) in Raleigh, N.C. The ensemble collected their second consecutive entertainer of the year honor, while Eric Gibson won in the bluegrass songwriter category. In addition, their single "They Called It Music" was named the IBMA's song of the year.
Meanwhile, Junior Sisk and Claire Lynch received the male and female vocalist prizes. Della Mae won in the emerging artist category, and the Boxcars earned instrumental group honors. Balsam Range picked up the album of the year trophy for Papertown.
In addition, guitarist Tony Rice and the late Paul Warren were inducted into the International Bluegrass Music Hall of Fame. Warren is best known for his lengthy tenure in Lester Flatt and Earl Scruggs' band, the Foggy Mountain Boys.
Hosted by Steep Canyon Rangers, the event featured performances from Balsam Range, the Bluegrass Youth All-Stars, Blue Highway, Dailey & Vincent, the Del McCoury Band, the Gibson Brothers, Ricky Skaggs & Kentucky Thunder, Kenny & Amanda Smith, Steep Canyon Rangers, Russell Moore & IIIrd Tyme Out and Rhonda Vincent & the Rage.
Here is a full list of winners from the 2013 IBMA Awards.
Additionally, the following Momentum Awards were presented Wednesday.


text:
Daily Archives: Ekim 30, 2013
By Siva SerkisyanCulture Issues Literature November 2013
Shiva is called the destroyer and transformer at the same time. There are some legends that says Shiva is protected and guarded by a bull. The bull is called Nandi. What is your power as a guru? Transform and destroy. Why are you sitting in a yoga position? Because I'm a symbol of yoga and…
Confession of a Murder
By Zeynep KazmazCulture Issues Literature November 2013
In Crime and Punishment by Dostoyevsky, Raskolnikov's cultural, physical and geographical surroundings shape psychological or moral traits in him. These aspects of the main character's life cause him to commit a murder, affect his life until he confesses, and finally convince him to confess. Raskolnikov lives on the top floor of a building, and this…
Turkey's Road to European Union
By Emirhan DegerAlaturca Issues News November 2013
Turkey is a country that is connected to two continents, Europe and Asia. For decades Turkey has been trying to join European Union. The union showed some reasons and consistently declined our applications, even though Turkey fulfilled European demands and removed the reasons that they showed against us, but it wasn't enough for them. Just recently, a Greek negotiator seemingly…
Blood Minerals
By Burak BocugozCulture Issues November 2013 Poetry
The sweat gliding all the way down from his forehead to his chin, Uniting with the hot stream traveling down the deep mine, The child mangling the rocks with his hammer, Desperately looking for the minerals he seek. In the darkness of underground, Where the whole sense of vision relies on a single bulb, He…
Where Music And Culture Come Together
By ssarhonCulture Issues Music November 2013
Istanbul Foundation for Culture and Arts' (IKSV) oldest and most prized event, theInternational Istanbul Music Festival, was first held in June 15-July 15 1973. Since it's beginning it has held a vast selection of programs such as classical music, classical ballet, contemporary dance, opera, traditional music, jazz, pop, film, theater and visual art forms, performed by both local and foreign artists. The festival has…
Could It Be The Beginning of a New Era?
By Suzan KamhiCulture Featured Issues Music November 2013
Modern Turkey lacks support in the performing arts. In many cultural cities all over the world, people have made a habit of going to theatres and various performances regularly. However, such an attitude has not set itself in our country yet. Theatre companies are in extremely difficult positions. They continuously try to attract as many…


text:
Continuity and Rupture: A Catholic Perspective on Christian Conversion in Nepal
Guillaume Boucher
PhD Candidate, Department of Anthropology, Université de Montréal
The anthropology of Christianity has initiated a debate around conversion, on whether it must be considered in terms of continuity or radical break with the past. This presentation will examine Catholic conversion in a Hindu context and question this continuity/break dichotomy. I will draw on a field study conducted over a one-month period, in a parish of Nepal's Tarai. While living in the Presbytery adjunct to an apostolic school, I conducted formal interviews and informal conversations with the parish priest, his auxiliary, their ecclesiastical visitors, and the neighbouring Indian missionary sisters. I also participated in the local daily Catholic ritual life. The data collected will be used to argue that both continuity and break occur.
As Catholicism acknowledges the local supernatural world and allows the inculturation of some pre-conversion ritual practices (such as Baha parab, in the Santhal community of the parish priest, and Pasni, in the Newar community to which one of the students of the apostolic school belongs), it does not initially look for a radical break with the cultural environment where it seeks to take root. However, Catholicism introduces some breaks in the convert's ethos, and asks a new religious agency from its adherents, as will be shown when we examine the implantation of the religion in the priest's parish and the process leading to baptism. The ideal of being a 'Good Catholic' represents a new personhood: converts are expected to develop an 'awareness' and priorities that should enable them to avoid the 'social evils' afflicting their villages, and thus promote a new self-definition which is no longer defined by an 'interiorized inferiority complex'.
Rather than converting to an exclusive and communal religious community, Catholics are still "[I]ntegrated into social systems of caste and participat[ing] in shared popular religious culture with their Hindu neighbours" (Mosse 2006:108). While selective inculturation may reject certain local cultural practices, the ideal pursued is not a total rupture with the local social environment, but rather a reinvestment in it, through the transformation of character by which a successful Catholic conversion is measured.


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Years of ignoring the growing danger of rightwing radicals has finally caught up with America
Posted by Reggie Jackson | Jan 13, 2021 | Columns, Featured, Reggie Jackson |
An online thread discussed specific calls for violence stating: "Be ready to fight. Congress needs to hear glass breaking, doors being kicked in, and blood from their BLM and Antifa slave soldiers being spilled. Get violent. Stop calling this a march, or rally, or a protest. Go there ready for war. We get our President or we die. NOTHING else will achieve this goal," According to the Norfolk, Virginia FBI office. – The Washington Post on January 12, 2021
As social media and right-wing media has fanned the flames of fear about "left-wing radicals," the country has looked the other way. Now in the days after a group of these radicals attempted a coup at the U.S. Capitol, the rioters have told the world that this is just the beginning.
The FBI has warned that there are credible threats against the chambers of lawmakers around the country. Governor Evers has ordered the Wisconsin National Guard to protect the Capitol and workers were seen boarding up the building less than a week after the debacle in Washington DC.
Just over three months ago, after a group of these radicals were arrested in a plot to kidnap Michigan Governor Gretchen Whitmer, thousands of like minded people stormed the U.S. Capitol. When news came out about the attempted kidnapping plot many people yawned. When Kyle Rittenhouse shot three people in Kenosha, killing two claiming to be defending the city many people yawned. Some sent him money. Bootleg lawyers came out of the woodwork to represent him.
The threat is real America. The type of language heard across the South after Abraham Lincoln's election in 1860 is what you are seeing on social media since Trump started to claim the election was stolen.
Death threats to election workers and officials did not wake Americans up to the threat. A year of armed, angry White men carrying weapons talking about taking their country back was not enough for Americans to wake up.
When the Southern Poverty Law Center warned after the first election of President Barack Obama that hate groups and right-wing radicals were growing in size and popularity Americans did not wake up.
When right-wing media like Fox News spread lies and inflamed anger among Whites who've felt disenchanted for years, Americans did not wake up.
When right-wing radicals led by Cliven Bundy had an armed standoff with police in Nevada in 2014 Americans did not wake up. When Ammond Bundy and his followers threatened violence in a standoff with police for over a month in 2016 Americans did not wake up. Two of the ranchers convicted of sparking the occupation were pardoned by Donald Trump in 2018.
When White supremacists in 2017 marched in Charlottesville, mad that Confederate monuments were being taken down, eventually murdering Heather Heyer, and injuring many others Americans did not wake up.
When armed protesters took control of the Malheur National Wildlife Refuge headquarters in Oregon on January 2, 2019 Americans did not wake up.
As social media platforms like Facebook and Twitter refused to do anything about their platforms being used to spread the views of these radicals Americans did not wake up.
As we face the prospect of widespread violence around the country by these heavily-armed radicals many Americans are still sleeping on the threat.
It is time to wake up America. Your comfort zone is no longer comfortable. Your family members, friends, neighbors, co-workers, and community members are the threat you've ignored for far too long.
"In 1923, Adolf Hitler led a failed coup. He was treated leniently. Germany moved on. A decade later, he was a dictator, and the worst disaster in the history of the civilized world ensued. In 2021, when the president of the United States leads a failed coup, we must not move on." – Mark Jacob
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As an award-winning Senior Columnist for the Milwaukee Independent, Reggie Jackson covers a range of African American issues. He is also a Consultant with Nurturing Diversity Partners, and volunteers as Head Griot for America's Black Holocaust Museum (ABHM) in Bronzeville.
Slavocracy: American's false milestones for solving a 400 year forced immigration policy
"Veterans Light Up the Arts" showcases local creative skill and builds community bonds
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Photo Essay: Bud Selig honored as Witness to History


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You are at:Home»Local News»Consumer Protection Bill To materialize in 2018
Consumer Protection Bill To materialize in 2018
By Admin on	 March 15, 2018 · Local News
During his 1 March Speech from the Throne His Excellency Governor Augustus Jaspert reaffirmed Government's promise that the Consumer Protection Bill will be heading to the House of Assembly soon. Repeated calls for such a Bill were made by this newspaper and by the electorate during the last 30 years with successive governments making unfulfilled promises.
His Excellency announced "Madame Speaker, there is unwavering commitment by our Government to introduce a Consumer Protection Bill during this Session to facilitate an attractive business climate with fair business practices."
Governor Jaspert also mentioned that the proposed consumer protection legislation will provide much needed regulation to business and trade in the Territory: "This Bill will establish the rights of both the consumer and the business and it will encourage a free enterprise market economy," he said.
In January this year Junior Minister for Trade and Investment, Hon. Marlon Penn who has championed the cause for the legislation announced that he is eager to see the legislation before the House and that the Bill is almost ready: "We were able to get that legislation drafted. There is now a Cabinet paper prepared for Cabinet to make a decision for us to finalize that legislation. The next step now is for Cabinet to make the decision, and then for the Attorney General to finalize the draft legislation to go to the House of Assembly."
The Junior Minister told reporters that he even told the Premier that he is open to presenting the Bill as a Private Member section of a sitting of the House: "I have even told the Premier that I would do a private members Bill if I need to, because I think it is very important for us to really protect not just the consumers, but to protect the businesses as well because a lot of times the businesses are being accused of things which in fact they are not actually doing."
Hon. Penn said that Consumer Protection legislation will also protect businesses who are getting blamed for matters beyond their control: "When you look at the cost they have to pay for shipping, and the cost they have to pay for increase in price in a lot of the products since the hurricane… If we have a situation where we can monitor a lot of what is happening within the economy it gives us a better perimeter to see what the shocks are in the community and when persons say to us that businesses are taking advantage we have data to prove that it is so or not so."
Hon. Penn further disclosed that he will ensure that the Premier receives the draft legislation and mentioned that the intent is to work to ensure that the Bill is ready for 2018.


text:
\section{Introduction}

Stable quantum currents of topological origin are of great interest from the points of view of mathematical physics as well as for engineering of topological materials.
Here we are in particular interested in the  two dimensional spin-$1/2$ Quantum Walk proposed in \cite{kitagawa} in order to model topological phases in two dimensions and to be technically feasible; it  was recently experimentally realized in a photonic setup \cite{chenEtAl}. On the other hand oriented quantum network models, originally proposed to quantitatively understand the Quantum Hall localization-delocalization transition \cite{cc,kok} continue to be a formidable mathematical challenge \cite{cardy}. In the present article we concentrate on the delocalization aspect of the Kagome network which leads to the study of the Ruby graph. This was used to describe arrays of coupled optical resonators \cite{pasekchong, dft}.

Mathematically speaking both models are a discrete quantum dynamically system characterized by a unitary operator $U$ on $\ell^2(\cV;\bC^d)$, $\cV$ being the vertices of a graph,  which is parametrized by a countable family of $U(2)$ matrices.  Depending on this family these models may have any dynamical behavior.  Known results  which concern delocalization cover the existence of a current and full absolutely continuous spectrum for the  L-lattice network of Chalker Coddington and   coined  Quantum Walks \cite{ABJ5}.  Further mathematical results assert  that the presence of boundaries and symmetries of the bulk imply occurrence of currents, \cite{rlbl,dft,graftauber,ssb}.

We apply the method of \cite{ABJ5}
concerning the topological properties of the self-adjoint flux operator out of the subspace $\mathop{\rm Ran}\nolimits(P)$ of an orthogonal projection
$$
\flux=U^*PU-P.
$$
In particular the existence of a wandering subspace is guaranteed by a non vanishing index of $\Phi$; the subspace  reduces a perturbation of the  evolution operator to  a shift. This may be considered as a current; its existence implies  gapless absolutely continuous spectrum at all quasienergies under decay assumptions.

 In the next section we discuss the Kagome quantum network, exhibit how it leads to the Ruby graph and show under very general conditions that a non trivial flux  through a curve exists, see Theorem \ref{thm:main} and Remark \ref{rem:cap}.

 Then we present our analysis of the two dimensional spin-$1/2$ Quantum Walk and prove the occurrence of an edge state in Theorem \ref{thm:currentKwalk}, again under very mild conditions,  thus providing a mathematical theory for the experimental findings of \cite{chenEtAl}.

To be self contained we present known results on the flux operator in an Appendix.

\section{Transport on  the Ruby graph}\label{section:cc}

We present  transport results for the Chalker-Coddington model defined on the full  two-dimensional Ruby graph which describes the Kagome quantum network. We employ the methods developed in \cite{ABJ5}, in particular the study of a  flux operator for a projection on a suitably chosen half space.

The original Chalker-Coddington model on the L-network  was designed for a numerical study of  quantum transition  events between microscopic currents,  for background see  \cite{cc,kok, cardyoverview,ABJ1}.
In terms of the physical model  the currents are encoded by the vertices of the Ruby graph $\cR$ while  their microscopic transition events   are encoded by a collection of unitary $2 \times 2$ matrices
\[\left\lbrace S_{z}\right\rbrace_{z\in\cK}\in U(2)\]
indexed by the vertices of the   Kagome graph $\cK$.

The collection $\left\lbrace S_{z}\right\rbrace_{z\in\cK}$, which is a priori arbitrary, represent the parameters of the model. It  defines the unitary operator:
\[U:\ell^2(\cR;\bC)\to\ell^2(\cR;\bC)\]
and we shall study the flux operator $\Phi=U^\ast P U-P$ for $P$ a projection on a half space.

We now present the details of this model.
Let $\lbrace v_1,v_2\rbrace$ be a positively oriented basis of $\bR^2$ and denote
\[\cK_1:=\{z\in\bR^2; z= n_1 v_1+n_2 v_2,\quad n_1,n_1\in\bZ\}; \quad \cK_2:=\cK_1+\frac{1}{2}v_1; \quad \cK_3:=\cK_3+\frac{1}{2}v_2.\]
The set of the  Kagome vertices is \[\cK:=\cK_1\bigcup \cK_2\bigcup\cK_3.\]

\begin{figure}[hbt]
\centerline {
\includegraphics[width=8cm]{./kagomegraph.pdf}
}
\caption{The Kagome scattering network represented as graph with vertices $\cK$;  its edges connect  nearest neighbors, their orientation is anticlockwise around the hexagons and clockwise around the triangles.}
\label{fig:kagomegraph}
\end{figure}

The edges connect each vertex to its next neighbors. The faces adjacent to a vertex are in turn: a triangle, a hexagon, a triangle, a hexagon; the orientation of the edges is such that the orientation of the boundaries of the hexagons is anticlockwise, and clockwise for the triangles, see figure (\ref{fig:kagomegraph}) for the choice $v_1=e\left(\frac{\pi}{3}\right),v_2=e\left(\frac{2\pi}{3}\right)$.

The physical model describes microscopic currents flowing along these edges. The two ingoing currents per vertex are scattered to the two outgoing currents which is encoded by the $2\times2$ unitary at the vertex.
We label an edge (as segment of $\bR^2$) by its center. The set of edge-centers are the vertices $\cR$ of  the Ruby graph, {see figure (\ref{fig:rubygraph})}. For background on Archimedean Lattices see \cite{rsh}.  Explicitly:

\[ \cR=\{z\pm\frac{1}{4}v_j; j\in{1,2}, z\in\cK_1\}\bigcup\{z+\frac{1}{2}v_1\pm\frac{1}{4}(v_1-v_2); z\in\cK_1\}.\]

Then for $w\in\cR$ and  with the canonical base vectors \[\Ket{w}\in\ell^2(\cR;\bC) \hbox{ defined by } \ket{w}:= \left(\cR\ni x\mapsto\delta_{w,x}\in\bC\right),\] the edge with center $w$ is associated to the subspace $span\{\Ket{w}\}$; for a vertex $z$ of the Kagome graph define
\[Q_z : \ell^2(\cR;\bC)\to \ell^2(\cR;\bC) \quad\hbox{ the projection on the  subspace  incoming to $z\in\cK$; }\]
as an example for $z\in\cK_1$: $Q_z=\Ket{z+\frac{1}{4}v_1}\Bra{z+\frac{1}{4}v_1}+\Ket{z-\frac{1}{4}v_1}\Bra{z-\frac{1}{4}v_1}$.
As  exactly two edges are incident to exactly one vertex we have
\[\ell^2(\cR;\bC)\equiv\bigoplus_{z\in\cK}\mathop{\rm Ran}\nolimits Q_z\]
and define the unitary $U$ uniquely by the collection of the $2\times2$-unitaries:
\[U:\ell^2(\cR;\bC)\to\ell^2(\cR;\bC); \qquad U\restriction\mathop{\rm Ran}\nolimits Q_z:=S_z\restriction\mathop{\rm Ran}\nolimits Q_z.\]
The subspace associated to the unique two outgoing edges at $z\in\cK$ is $\mathop{\rm Ran}\nolimits \widehat{Q}_z$ with the projection
\[\widehat{Q}_z:=U Q_zU^\ast,\]
see figure (\ref{fig:scatteringsubspaces}).

\begin{figure}[hbt]
\centerline {
\includegraphics[width=6cm]{./scatteringsubspaces.pdf}
}
\caption{The incoming and outgoing projections $Q_z$ and $\widehat Q_z$ }
\label{fig:scatteringsubspaces}
\end{figure}
\begin{rem} Note that $Q_z,\widehat{Q}_z$ do not depend on the collection of scattering matrices.
\end{rem}

The basic tool for the discussion of the flux operator is the following proposition which we adapt form \cite{ABJ5}, proposition 4.2, including its short intuitive proof.

\begin{prop}\label{prop:indexformula} Let $M$ be a subset of $\cR$ and $P$ the multiplication operator $P=\chi(x\in M)$,
\[\Phi=U^\ast P U -P.\]
Then it holds

\begin{enumerate}
\item $\left\lbrack\Phi,Q_z\right\rbrack=0 \quad \forall z\in\cK$;
\item $\Phi Q_z=U^\ast (P\widehat{Q}_z)U- PQ_z$;
\item $\mbox{ ind}(\Phi)$ is well defined iff for a $c,R>0$ : $\sup_{\vert z\vert> R}\Vert \Phi Q_z\Vert\le c<1$;  then it holds:
\begin{equation}\label{eq:indexformula}
\mbox{ ind}(\Phi)=\sum_{z, \vert z\vert \le R} \dim\mathop{\rm Ran}\nolimits(P\widehat{Q}_z)-\dim\mathop{\rm Ran}\nolimits(PQ_z).
\end{equation}
\end{enumerate}
\end{prop}

\begin{proof} By definition $Q_z,\widehat{Q}_z$ are multiplication operators on $\ell^2(\cR;\bC)$ thus commute with $P$, or
\[\lbrack\Phi,Q_z\rbrack=\lbrack U^\ast P U,Q_z\rbrack=U^\ast\lbrack P, \widehat{Q}_z\rbrack U=0.\]
Also $\ker\left(\Phi^2-\bI\right)=\bigoplus_{z\in\cK}\ker\left((\Phi^2-\bI)Q_z\right)$ and $\sigma\left(\Phi^2\right)=\bigcup_{z\in\cK}\sigma\left(\Phi^2Q_z\right)$. By  assumption $dist\left(\{1\},\bigcup_{\vert z\vert>R}\sigma(\Phi^2Q_z)\right)>0$ thus $1$ is an isolated finite dimensional  eigenvalue and
\[\mbox{ ind}(\Phi)=\sum_{\vert z\vert\le R} \dim\ker\left((\Phi-\bI)Q_z\right)-\sum_{\vert z\vert\le R}\dim\ker\left((\Phi+\bI)Q_z\right)=\]\
\[=\sum_{\vert z\vert\le R}\mbox{ ind}(\Phi Q_z)=\sum_{\vert z\vert\le R}trace(\Phi Q_z)=\sum_{z, \vert z\vert \le R} \dim\mathop{\rm Ran}\nolimits(P\widehat{Q}_z)-\dim\mathop{\rm Ran}\nolimits(PQ_z).\]
\end{proof}
In order to efficiently define the projection and to count the relevant dimensions we associate
 to the family of unitaries $U$  the directed Ruby graph  $G=(\cR,\cE)$ whose set of vertices is $\cR$ and whose directed edges $\cE$
 are defined by, c.f. figure (\ref{fig:rubygraph}),
\[\overrightarrow{xy}\in \cE \hbox{ \it iff } \langle y,U_c\ x\rangle\neq0\]
where $U_c$ is the  model which has all its scattering matrices $S_z=\frac{1}{\sqrt{2}}\left(
\begin{array}{cc}
  1   &-1   \\
  1   &  1
\end{array}
\right)$.

For a given $U$ we attribute
\[\hbox{ the weight }\vert\langle y,U x\rangle\vert \hbox{ to the edge } \overrightarrow{xy}\in \cE.\]
For a given $z\in\cK$ there are four edges, we label the weight by $\vert r_z\vert$ (color: black)  if the corresponding current  is scattered to its left and by $\vert t_z\vert$ if it is scattered to its right (color: red). Explicitly we have for $z\in\cK_1$
\[\left\vert\left\langle z-\frac{1}{4}v_2,U (z+\frac{1}{4}v_1)\right\rangle\right\vert=:\left\vert t_z\right\vert, \qquad \left\vert\left\langle z+\frac{1}{4}v_2,U (z+\frac{1}{4}v_1)\right\rangle\right\vert=:\vert r_z\vert\]
and all other cases analogously, see figure (\ref{fig:weights}).

Remark that for a choice of a basis in each $\mathop{\rm Ran}\nolimits Q_z, \mathop{\rm Ran}\nolimits \widehat Q_z$ which is compatible with this convention, the parameters are
\[S_z\equiv q_z\left(
\begin{array}{cc}
  r_z   &-t_z   \\
  \bar{t_z}   &  \bar{r_z}
\end{array}
\right)\quad \hbox{ with } q_z\in S^1, r_z,t_z\in\bC \hbox{ s.t. } \vert r_z\vert^2+\vert t_z\vert^2=1.\]

\begin{figure}[hbt]
\centerline {
\includegraphics[width=6cm]{./weights.pdf}
}
\caption{The weights of $(\cR,\cE)$.}
\label{fig:weights}
\end{figure}

The projection $P$ will be defined by a path in the dual graph.

The faces of the Ruby graph figure (\ref{fig:rubygraph}) which are  adjacent to a fixed vertex are in turn  a triangle, a rectangle, a hexagon, a rectangle. The dual graph
\[G^\ast=(\cR^\ast,\cE^\ast)\]
has its vertices at the center of the faces of $(\cR,\cE)$
and the dual edges (which we call links to distinguish) are segments which connect to all next neighbors  thus bisecting  edges of $\cE$. Remark that the scattering points are the centers of the rectangles in the Ruby graph:  $\cK\subset\cR^\ast$.

\begin{figure}[hbt]
\centerline {
\includegraphics[width=9cm]{./rubygraph.pdf}
}
\caption{The Ruby graph}
\label{fig:rubygraph}
\end{figure}

\begin{figure}[hbt]
\centerline {
\includegraphics[width=9cm]{./projection.pdf}
}
\caption{An admissible path defining the projection on the states on its left}
\label{fig:projection}
\end{figure}

Now consider a partition of $G$ in two infinite connected subgraphs $G_+$ and $G_-$, consider a path in $G^\ast$ which bisects the edge boundary of $G_+$
and visualize this path as an injective, continuous, and piecewise unit speed curve of straight segments on the dual graph in $\bR^2$
\[\gamma: \bR\to G^\ast\subset\bR^2 \hbox{ such that for integer } t\in\bZ: \gamma(t)\in \cR^\ast \hbox{ and } \overrightarrow{\gamma(t)\gamma(t+1)}\in \cE^\ast\]
oriented such that $G_+$ is to the left of $\gamma$; we call it an admissible\ path, see figure (\ref{fig:projection}).
Let $\cR_+$ be the set of vertices of $G_+$  and consider its projection and flux operator in $\ell^2(\cR; \bC)$ :
\[P_\gamma=\chi(x\in \cR_+), \quad \Phi_\gamma=U^\ast P_\gamma U-P_\gamma.\]

In the following we shall give sufficient conditions for non trivial $\mbox{ ind}(\Phi_\gamma)$. By the general theory of Theorem \ref{thm:general} and Proposition \ref{lem:wandering} we know that all vertices which are not incident to the edge boundary of $G_+$ belong to  $\ker(\Phi_\gamma)$;  in view of the basic formula (\ref{eq:indexformula}) we  label the set of interesting vertices as follows:

\begin{definition}Let $\gamma:\bR \to G^\ast$ be an admissible path. We call $\cE_\gamma\subset \cE$
the set of edges bisected by $\gamma$ and $\cK_\gamma$ the labels of subspaces $\mathop{\rm Ran}\nolimits Q_z$ which contain  vertices incident to $\cE_\gamma$, i.e. :
\[\cK_\gamma:=\left\{z\in\cK; P_\gamma^\perp U_c P_\gamma Q_z\neq0 \hbox{ or } P_\gamma U_c P_\gamma^\perp Q_z\neq0\right\}.\]
\end{definition}

From this graphical representation of $U$ and $P$ we can literally read off how to construct a useful admissible path. The basis observation is:
\begin{rem}\label{rem:dimensions} From equation (\ref{eq:indexformula}) and the fact that $Q_z$ and $\widehat{Q}_z$ are diagonally opposite  vertices of the rectangles of the Ruby graph, we observe:  consecutively bisected  links of type hexagon-rectangle-hexagons as well as  triangle-rectangle-triangle do not contribute to the index because at the common dual vertex $z\in\cK$ it holds $\dim\mathop{\rm Ran}\nolimits PQ_z=\dim\mathop{\rm Ran}\nolimits P\widehat Q_z$. On the other hand consecutively bisected  links of type hexagon-rectangle-triangle as well as  triangle-rectangle-hexagon do  contribute to the index because $\dim\mathop{\rm Ran}\nolimits PQ_z\neq\dim\mathop{\rm Ran}\nolimits P\widehat Q_z$, see figure (\ref{fig:randtpath}).
\end{rem}
We define the non contributing parts :

\begin{definition}Let $I\subset\bR$. An admissible path $\gamma$ is called  a $r$-path in $I\subset\bR$ if its restriction to $I$ bisects only edges of weight $\vert r\vert$ and a $t$-path in $I\subset\bR$ if its restriction to $I$ bisects only edges of weight $\vert t\vert$.
\end{definition}

Concerning the regularity of $\Phi_\gamma$ we have
\begin{figure}
    \centering
    \begin{subfigure}[b]{0.20\textwidth}
        \includegraphics[width=\textwidth]{./r-pathV2.pdf}
 \caption{r and r edge}
       \label{fig:rredge}
    \end{subfigure}\qquad\hspace{1cm}
    \begin{subfigure}[b]{0.25\textwidth}
        \includegraphics[width=\textwidth]{./t-path.pdf}
  \caption{t and t edge}
       \label{fig:ttedge}
        \end{subfigure}\qquad
         \begin{subfigure}[b]{0.20\textwidth}
        \includegraphics[width=\textwidth]{./rt-path.pdf}
        \caption{outgoing r and t edge}
       \label{fig:rtedge}
        \end{subfigure}
    \caption{Parts contributing and non contributing to $\mbox{ ind}(\Phi)$}
     \label{fig:randtpath}
\end{figure}
\begin{lem}\label{lem:estimate}Let $\gamma$ be an admissible  $r$-path in $\bR$; then it holds for the operator and the trace norm:
\[\Vert\Phi_\gamma\Vert\le\sup_{z\in \cK_\gamma}\vert r_z\vert,\quad \Vert\Phi_\gamma\Vert_1\le const. \sum_{z\in \cK_\gamma}\vert r_z\vert.\]

\noindent The analogous statement holds true for a $t$-path
\end{lem}

\begin{proof}  Only states with label in $\cK_\gamma$ contribute,    by Theorem \ref{lem:wandering}.\ref{item:phi2}: $\lbrack \Phi_\gamma^2,Q_z\rbrack=0$
and $\gamma$ crosses  only  edges of weight $\vert r_z\vert$  thus $\Phi_\gamma^2 Q_z=\vert r_z\vert^2 Q_z$, see figure (\ref{fig:phi2}), so we have
\[\Phi_\gamma^2=PU^\ast P_\gamma^\perp U P_\gamma+P_\gamma^\perp U^\ast P_\gamma U P_\gamma^\perp=\sum_{z\in\cK} \Phi_\gamma^2 Q_z=\sum_{z\in \cK_\gamma} \Phi_\gamma^2 Q_z=\sum_{z\in \cK_\gamma} \vert r_z\vert^2 Q_z.\]. It follows that  $\vert \Phi_\gamma\vert=\sum_{z\in \cK_\gamma}\vert r_z\vert Q_z$ which implies the assertion.

\begin{figure}[hbt]
\centerline {
\includegraphics[width=6cm]{./phi2.pdf}
}
\caption{The action of $\Phi^2Q_z$ for an $r$-path}
\label{fig:phi2}
\end{figure}
\end{proof}

We are now able to prove that a Chalker Coddington model on the Ruby graph which admits a suitable admissible path  defines a projection with non-trivial flux. We show that  a path is suitable if it  crosses only hexagons and rectangles in the past and only triangles and rectangles in the future, and such that the associated weights are sufficiently regular. Remark that an analogous result was proved in Theorem 4.7  in \cite{ABJ5} for the L-network which leads to the original Chalker Coddington model on the associated Manhattan graph. We can adapt this  result without essential difficulty to the present situation.

\begin{thm} \label{thm:main} Let $U$ be a Chalker Coddington model on the Ruby graph such that there exists  an admissible path $\gamma$  which is an $r$-path in $(-\infty, -N\rbrack$ and a  $t$-path in $\lbrack N, \infty)$ for an integer $N>1$, and such that  for a $c>0$
\[\vert r_z\vert\le c<1 \quad \forall z\in \cK_{\gamma\restriction (-\infty, -N\rbrack} \hbox{ and } \vert t_z\vert\le c<1 \quad \forall z\in \cK_{\gamma\restriction \lbrack N, \infty)}.\]
Then $\mbox{ ind}(\Phi_\gamma)$ is well defined and it holds
\[\vert\mbox{ ind}(\Phi_\gamma)\vert=1.\]
In addition
\begin{enumerate}
\item $\Phi_\gamma$ is compact iff \quad$\lim_{s\to-\infty}{r_{\gamma(s)}}=0=\lim_{s\to\infty}{t_{\gamma(s)}}$
and then
\[\sigma(U)=S^1.\]
\item $\Phi_\gamma$ is trace class iff  \quad$\sum_{z\in \cK_{\gamma\restriction (-\infty, -N\rbrack} }\vert r_z\vert + \sum_{z\in \cK_{\gamma\restriction \lbrack N, \infty)}} \vert t_z\vert <\infty$
and then
\[\sigma_{ac}(U)=S^1,\]
and a trace class perturbation of $U$ contains a shift operator.
\end{enumerate}

\end{thm}
\begin{proof}If $\gamma$ is a path which switches from $r$ to $t$ on one site, i.e : if $\gamma$ is an $r$-path in $(-\infty, 0)$ and a $t$-path in $[0,\infty)$, then as a corollary of Proposition \ref{prop:indexformula} and Remark \ref{rem:dimensions} we have
\[\mbox{ ind}(\Phi)=\sum_{z\in \cK_{\gamma\restriction_{[-N,N]}}}\dim\mathop{\rm Ran}\nolimits(P\widehat{Q}_z)-\dim\mathop{\rm Ran}\nolimits(PQ_z)=\dim\mathop{\rm Ran}\nolimits(P\widehat{Q}_{z_0})-\dim\mathop{\rm Ran}\nolimits(PQ_{z_0})\]
with  $z_0=\gamma(0)$. By the symmetry of the problem the two edges bisected by the links adjacent to $\gamma(0)$ are either incoming or outgoing to $G_+$ thus  $\dim\mathop{\rm Ran}\nolimits PQ_{z_0}=1$ and $\dim\mathop{\rm Ran}\nolimits P\widehat{Q}_{z_0}=0$ or the other way round, see figure (\ref{fig:rtedge}). Thus $\vert \mbox{ ind}(\Phi_\gamma)\vert=1$.

If $\gamma$ switches several times cutting $r$ and $t$ links then  choose two integers $N_\pm\in\bZ$ such that $ \pm N_\pm>\pm N$ and such that $\gamma(N_-)$ is the center of a hexagon and $\gamma(N_+)$ the center of a triangle. Thus all links incident to $\gamma(N_-)$  bisect edges of weight $\vert r\vert$ and all links incident to $\gamma(N_+)$  bisect edges of weight $\vert t\vert$. Then we can define a new admissible path $\widehat\gamma$  replacing the part $\gamma\restriction_{(-N_-,N_+)}$ by an $r$ path inside $G_+$ connecting $\gamma(N_-)$ to $\gamma(N_+)$, c.f. figure (\ref{fig:joinrt}). The new path switches from $r$ to $t$ only at $\gamma(N_+)$.The difference $P_\gamma-P_{\widehat\gamma}$ is of finite rank thus by the invariance properties of the index
 \[\mbox{ ind}(\Phi_\gamma)=\mbox{ ind}(\Phi_{\widehat\gamma}).\]
 The additional assertions follow from Lemma \ref{lem:estimate} and Theorem \ref{thm:general}.
 \begin{figure}
\centerline {
\includegraphics[width=8cm]{./transformtostandardpath}
}
\caption{Join r path to t path in figure (\ref{fig:projection})}
\label{fig:joinrt}
\end{figure}
\end{proof}

As by unitarity we have $\vert r_z\vert^2+\vert t_z\vert^2=1$ it follows:
\begin{cor}
Any Chalker Coddington model on the Ruby graph defined by a collection of scattering matrices such that  for  $c_1,c_2\in(0,1)$ and all $z$:  $0<c_1<\vert r_z\vert<c_2<1$, admits a projection with non trivial index.
\end{cor}

\begin{rem}\label{rem:cap}A remarkable situation which is covered  by the Corollary  is the translation invariant $0<\vert r_z\vert=const\neq1$ case with all phases equal to unity; here the spectrum is absolutely continuous and exhibits gaps or not.  However, for a $\gamma$ with a $r-t$ transition the flux operator $\Phi_\gamma$ is not trace class or even compact. {The analogous situation is present for perturbations of the translation invariant model, see \cite{ABJ3}}.
\end{rem}

\section{Edge current in two dimensional spin-$1/2$ Quantum Walks}

We analyze transport properties of a class of  two dimensional spin-$1/2$ Quantum Walks proposed in \cite{kitagawa}  for which  transport seems to have been experimentally observed \cite{chenEtAl}. The feature of these walks is that they depend on two $\bC^2$ coins. We use the methods which were developed in \cite{ABJ5} for coined Quantum Walks which depend on one $\bC^4$ coin and analyze the flux out of a subspace defined by a projection which can be interpreted as a quantum lead.

We present the class of models. The Hilbert space is $\bH=\ell^2(\bZ^2;\bC^2)$  its canonical scalar product $\left\langle\cdot, \cdot\right\rangle$.

For a family of $2\times2$ matrices $\{M(z)\}_{z\in\bZ^2}\subset\bM(2;\bC)$ the multiplication operator  $\bbM$ on $\bH$ with symbol $M$ is
\[\bbM\psi(z):=M(z)\psi(z), \quad \psi\in\bH.\]
A coin $\bbC$ is a multiplication operator with unitary symbol $\{C(z)\}_{z\in\bZ^2}\subset U(2)$.

With the canonical basis vectors, $e_x,e_y$ of $\bZ^2$ denote  $S_j\psi(z):=\psi(z-e_j),\quad j\in\{x,y\}$ the shift in the $x$ or $y$ direction. The corresponding conditional shifts are
\[{\bf T}_j:\bH\to\bH, \quad {\bf T}_j\psi(z):=
\left(\begin{array}{cc}S_j&   0  \\0  & S_j^\ast \end{array}\right)\psi(z)=\left(\begin{array}{c}\psi_1(z-e_j) \\\psi_2(z+e_j)\end{array}\right).\]
 We use the expressions ${\bf T}_j=S_j\bbP_+ + S_j^\ast \bbP_-$
with the projections $\bbP_\pm$ whose symbols are $\{P_\pm\}_{z\in\bZ^2}$ the projections on the upper resp. lower component of $\bC^2$. We also use $\bZ^2\ni z=(x, y)$ and denote the canonical basis vectors of $\bH$ by
\[\Ket{z_0;+}:=\left(\bZ^2\ni z\mapsto \delta_{z,z_0}\left(\begin{array}{c} 1 \\ 0\end{array}\right)\in\bC^2\right),\quad \Ket{z_0;-}:=\left(\bZ^2\ni z\mapsto \delta_{z,z_0}\left(\begin{array}{c} 0 \\ 1\end{array}\right)\in\bC^2\right).\]
Note that $S_j\Ket{z;\pm}=\Ket{z+e_j;\pm}$.

The family of unitary operators which we study depends parametrically on two unitary symbols:

Let $\bbC_1,\bbC_2$ two coins. Define
\begin{equation}\label{eq:U}
U:\bH\to\bH, \qquad U:={\bf T}_y C_2 {\bf T}_x C_1.
\end{equation}

In order to fix notations, we parametrize the symbols for $z\in\bZ^2$ by
\[C_j(z)=q_j(z)\left(
\begin{array}{cc}
  r_j(z)   &-t_j(z)   \\
  \overline{t_j}(z)  &  \overline{r_j}(z)
\end{array}
\right)\hbox{ with } q(z)\in S^1, r(z),t(z)\in\bC \hbox{ s.t. } \vert r(z)\vert^2+\vert t(z)\vert^2=1.\]

To illustrate the action of $U$, see figure (\ref{fig:actionofU}), we use  the kernel $U(\cdot,\cdot):\bZ^2\times\bZ^2\to\bM(2;\bC)$ such that $(U\psi)(z)=\sum_{w\in\bZ^2}U(z,w)\psi(w)$ which is
\[U(z,w)=\left\lbrace\begin{array}{ll}
(q_2r_2)(w+e_x)q_1(w)\left(\begin{array}{cc}r_1(w)&-t_1(w)\\0&0\end{array}\right)& \hbox{ if }z=w+e_x+e_y\\
(q_2\overline{r_2})(w-e_x)q_1(w)\left(\begin{array}{cc}0&0\\ \overline{t_1}(w)&\overline{r_1}(w)\end{array}\right)& \hbox{ if }z=w-e_x-e_y\\
(-q_2t_2)(w-e_x)q_1(w)\left(\begin{array}{cc}\overline{t_1}(w)&\overline{r_1}(w)\\0&0\end{array}\right)& \hbox{ if }z=w-e_x+e_y\\
(q_2\overline{t_2})(w+e_x)q_1(w)\left(\begin{array}{cc}0&0\\ {r_1}(w)&-{t_1}(w) \end{array}\right)& \hbox{ if }z=w+e_x-e_y\\
\left(\begin{array}{cc}0&0\\ 0&0 \end{array}\right)& \hbox{ elsewhere }
\end{array}\right.
\]

\begin{figure}[hbt]
\centerline {
\includegraphics[width=5cm]{./actionofu.pdf}
}
\caption{The action of $U$ with the identifications $r_1\leftrightarrow\vert q_1r_1\vert$ \\ and $r_2\leftrightarrow\vert q_2r_2(\cdot\pm e_x)\vert\ldots$ }
\label{fig:actionofU}
\end{figure}

The basic observation is:

\begin{proposition}\label{propo:bo}
Let $\bbC_1. \bbC_2$ be two coins such that
\[\left.\begin{array}{ll}r_2(x,\phantom{-}0)=0=t_1(x,\phantom{-}0)& x\in\bZ\\t_2(x,-1)=0=r_1(x,-1)& x\in\bZ\end{array}\right. .
\]
Then for $U={\bf T}_y\bbC_2{\bf T}_x\bbC_1$ the subspace
\[\bH_0:=\bigoplus_{x\in\bZ} span\left\{\Ket{x,0;+}, \Ket{x,-1;-}\right\}\]
is invariant for $U$. Furthermore  $U\restriction\bH_0$ is a two dimensional shift with wandering subspace $\bL_0:=span \left\{\Ket{-1,0;+},\Ket{-1,-1;-}\right\}$, i.e. $U^n\bL_0\perp\bL_0, \quad\forall n\neq0$ and $\bigoplus_{n\in\bZ}U^n\bL_0=\bH_0$
\end{proposition}
\begin{proof}The proof is by  explicit calculation which we present for
\[C_2(x,0)=\left(\begin{array}{cc}0&1\\1&0\end{array}\right) ,\qquad C_1(x,0)=\left(\begin{array}{cc}1&0\\0&1\end{array}\right),
\]
\[C_2(x,-1)=\left(\begin{array}{cc}1&0\\0&1\end{array}\right),\qquad C_1(x,-1)=\left(\begin{array}{cc}0&1\\1&0\end{array}\right),
\]
because for the general case all  the phases which may appear eventually cancel for the projections below. We have for $x\in\bZ$
\[\Ket{x,0;+}\xrightarrow{\bbC_1}\Ket{x,0;+}\xrightarrow{{\bf T}_x}\Ket{x+1,0;+}\xrightarrow{\bbC_2}\Ket{x+1,0;-}\xrightarrow{{\bf T}_y}\Ket{x+1,-1;-}\hbox{ and }\]
\[\Ket{x,-1;-}\xrightarrow{\bbC_1}\Ket{x,-1;+}\xrightarrow{{\bf T}_x}\Ket{x+1,-1;+}\xrightarrow{\bbC_2}\Ket{x+1,-1;+}\xrightarrow{{\bf T}_y}\Ket{x+1,0;+}\]
and thus it holds for the projections in these directions
\[U\Ket{x,0;+}\bra{x,0;+}U^\ast=\Ket{x+1,-1;-}\Bra{x+1,-1;-}\hbox{ and } \]
\[U\Ket{x,-1;-}\Bra{x,-1;-}U^\ast=\Ket{x+1,0;+}\Bra{x+1,0;+}.\]
By induction and unitarity this implies for $n\in\bZ$
\[U^n\left(\Ket{0,0;+}\bra{0,0;+}+\Ket{0,-1;-}\Bra{0,-1;-}\right){U^\ast}^n=\Ket{n,0;+}\Bra{n,0;+}+\Ket{n,-1;-}\Bra{n,-1;-} \]
which proves the three assertions.
\end{proof}

\begin{remark}Remark that under the conditions of proposition \ref{propo:bo} the absolutely continuous spectrum of $U$ is the full unit circle but other types of spectra of $U$ typically coexist because: $\sigma_{ac}(U\restriction\bH_0)=S^1\subset\sigma_{ac}(U)$ and the coins $\bbC_1,\bbC_2$ are arbitrary  on $\bH_0^\perp$.
\end{remark}

Now making use of the theory of the index of two projections and its topological invariance we can substantially extend this to a precise result on the existence of  a current which was observed in the experiment of \cite{chenEtAl}. We consider the projection on a two state quantum half line, i.e.:
\begin{definition}Let  $\bbP$ be the projection valued multiplication operator with symbol $P$ defined by
\begin{equation}\label{eq:P}
P(x):=\left\lbrace
\begin{array}{ll}
P_+ & x\ge0 \hbox{ and } y=0\\
P_- &  x\ge0 \hbox{ and } y=-1\\
0 & \hbox{elsewhere}
\end{array}
\right. .
\end{equation}
\end{definition}
It is a corollary of Proposition \ref{propo:bo} that $\bL_0$ is the incoming subspace for $\mathop{\rm Ran}\nolimits P$:

\begin{remark}$U$ defined in Proposition \ref{propo:bo} is a forward shift in $\mathop{\rm Ran}\nolimits P$, $U^n\bL_0\perp\bL_0,\forall n\in\bN$ and $\mathop{\rm Ran}\nolimits P=
\bigoplus_{n\in\bN}U^n\bL_0$.
\end{remark}

This existence of a current holds true for a large class of  $U$ in the following precise sense:

\begin{thm}\label{thm:currentKwalk}
Let $\bbC_1. \bbC_2$ be two coins such that
\[\sum_{x\in\bN}\left(
\left\vert r_2(x,0)\right\vert+\left\vert t_1(x,0)\right\vert+\left\vert t_2(x,-1)\right\vert+\left\vert r_1(x,-1)\right\vert
\right)<\infty
\]
then it holds for $U$ defined in (\ref{eq:U}),  $P$ in (\ref{eq:P}) and $\Phi:=U^\ast P U-P$:
\[\Phi \hbox{ is trace class with }  \mbox{ ind}(\Phi)=2,
\]
\[\sigma_{ac}(U)=S^1,\]
and there exist a unitary trace class perturbation $\widehat{U}=S\oplus\widetilde{U}$ of $U$ with $S$ a bilateral shift of multiplicity $2$; further there exists a $2$ dimensional subspace
\[\bL\subset\ker P^\perp UP^\perp\restriction_{\mathop{\rm Ran}\nolimits P^\perp}\] such that
\[S^n\bL\perp\bL, \forall \bZ\ni n\neq0 \quad \hbox{and}\quad S^n\bL=PS^n\bL,\forall n\in\bN.\]
\end{thm}
\begin{proof}Separating the phases we write for the parameters of $\bbC_1,\bbC_2$: $r_j=e^{i\rho_j}\vert r_j\vert=e^{i\rho_j}\sqrt{1-\vert t_j\vert^2}$ and $t_j=e^{i\tau_j}\vert t_j\vert=e^{i\tau_j}\sqrt{1-\vert r_j\vert^2}$.

Define two coins $\bbC_1^0,\bbC_2^0$ by the symbols

\[C_2^0(z):=\left\lbrace
\begin{array}{ll}
q_2\left(\begin{array}{cc}0&-e^{i\tau_2}\\e^{-i\tau_2}&0\end{array}\right)(z)& \hbox{ if }z=(x,0),\forall x\in\bN\\
q_2\left(\begin{array}{cc}e^{i\rho_2}&0\\0&e^{-i\rho_2}\end{array}\right)(z)& \hbox{ if }z=(x,-1),\forall x\in\bN\\
C_2(z)& \hbox{ elsewhere }
\end{array} ,
\right.\]
\[C_1^0(z):=\left\lbrace
\begin{array}{ll}
q_1\left(\begin{array}{cc}e^{i\rho_1}&0\\0&e^{-i\rho_1}\end{array}\right)(z)& \hbox{ if }z=(x,0),\forall x\in\bN\\
q_1\left(\begin{array}{cc}0&-e^{i\tau_1}\\e^{-i\tau_1}&0\end{array}\right)(z)& \hbox{ if }z=(x,-1),\forall x\in\bN\\
C_1(z)& \hbox{ elsewhere }
\end{array} .
\right.\]

For the Hilbert-Schmidt norm $\Vert\cdot\Vert_{HS}$ on $\bM(2;\bC)$ we obtain
\[\left\Vert (C_2-C_2^0)(z)\right\Vert_{HS}^2\le 4
\left\{\begin{array}{ll} \vert r_2(z)\vert^2& z=(x,0),\forall x\in\bN \\ \vert t_2(z)\vert^2& z=(x,-1), \forall x\in\bN\\0& \hbox{elsewhere} \end{array}\right. ,
\]
\[\left\Vert (C_1-C_1^0)(z)\right\Vert_{HS}^2\le 4
\left\{\begin{array}{ll} \vert t_1(z)\vert^2& z=(x,0),\forall x\in\bN \\ \vert r_1(z)\vert^2& z=(x,-1), \forall x\in\bN\\0& \hbox{elsewhere}\end{array}\right. .
\]
It follows for the trace norm
\begin{eqnarray*}
&&\Vert \bbC_2-\bbC_2^0\Vert_1+\Vert \bbC_1-\bbC_1^0\Vert_1 \le const. \sum_{z\in\bZ^2}\sum_j \Vert (C_j-C_j^0)(z)\Vert_{HS}\le
\\
&&\sum_{x\in\bN}\left(
\left\vert r_1(x,-1)\right\vert+\left\vert t_2(x,-1)\right\vert+\left\vert t_1(x,0)\right\vert+\left\vert r_2(x,0)\right\vert
\right)<\infty.
\end{eqnarray*}
For $U^0:={\bf T}_y\bbC_2^0{\bf T}_x\bbC_1^0$, $\Phi^0:={U^0}^\ast P U^0-P$ it follows that the difference
\[U-U^0={\bf T}_y(\bbC_2-\bbC_2^0){\bf T}_x\bbC_1+{\bf T}_y\bbC_2{\bf T}_x(\bbC_1-\bbC_1^0)\hbox{ is trace class }\]
and thus
\[\Phi-\Phi^0\hbox{ is trace class }.\]
$\Phi^0$ equals minus the orthogonal projection on  $\bL_0$. It follows that $\Phi$ is trace class and that $\mbox{ ind}(\Phi)=2$.

Now Theorem \ref{thm:general}.\ref{item:trace} and the construction of $\bL$ in its proof (see \cite{ABJ5} Theorem 2.1, adapted by replacing $P\leftrightarrow P^\perp$) implies the assertion.
\end{proof}

As an illustration of this result of the existence of a  current in the subspace $\mathop{\rm Ran}\nolimits P$ for a trace class perturbation of $U$, we explicit the non-triviality of the incoming subspace $\bL$  for $U$ for a  finite rank perturbation of the paradigmatic situation of Proposition \ref{propo:bo}.

\begin{remark}\label{rem:illustration}
Let $\bbC_1. \bbC_2$ be two coins such that, c.f. figure (\ref{fig:illustration})
\[\left.\begin{array}{ll}r_2(x,\phantom{-}0)=0=t_1(x,\phantom{-}0)& x\in\bN\setminus\{1,2\}\\t_2(x,-1)=0=r_1(x,-1)& x\in\bN\bigcup\{-1,0\}\end{array}\right. .
\]
Then for the incoming state $\bL$ of Theorem \ref{thm:currentKwalk} it holds
 $\bL:=span \left\{\Ket{-1,-1;-},\psi\right\}$ where $\psi$ has generically non zero components on all vectors in $\{\Ket{-1,0;+},\Ket{1,0;+},\Ket{3,0;+}\}$
\end{remark}

\begin{figure}[hbt]
\centerline {
\includegraphics[width=5cm]{./illustrationCurrent.pdf}
}
\caption{Illustration of the incoming space for $U$ in Remark (\ref{rem:illustration}). The gray dots represent the states in $\mathop{\rm Ran}\nolimits P$, green arrows the elements of $P^\perp U P$, red arrows the incoming elements of $PUP^\perp$}
\label{fig:illustration}
\end{figure}

redpajama_set_name: RedPajamaArXiv


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text:
Attorney General Josh Stein Announces $11.2 Million Multistate Medicaid Settlement
Nazneen Ahmed (919) 716-0060
(RALEIGH) Attorney General Josh Stein today announced a settlement with Georgia-based SavaSeniorCare LLC, a company that owns and operates skilled nursing facilities in several states. The settlement with North Carolina and 22 other states resolves allegations that Sava billed Medicaid for medically unnecessary rehabilitation therapy services and offered grossly substandard skilled nursing services. Sava will pay the states and the federal government at least $11.2 million – North Carolina will receive $192,045.19 in restitution and other recoveries.
"Health care providers have a responsibility to provide quality care for their patients and be responsible stewards of taxpayer resources," said Attorney General Josh Stein. "When they fail to do so, I will hold them accountable on behalf of North Carolinians."
From October 2008 to September 2012, Sava allegedly engaged in a scheme to maximize billing that improperly caused some therapists to provide rehabilitation therapy to some Medicare and Medicaid beneficiaries. The therapy was either not reasonable and necessary, not skilled, or not covered by the Medicare Part A and Medicaid coinsurance benefits. In addition, this settlement also resolves allegations that from January 2008 through December 2018, some of the nursing services provided by Sava were grossly and materially substandard and/or worthless, partly because Sava failed to provide care that met federal requirements to some of its residents. Sava also failed to follow appropriate pressure ulcer protocols and appropriate falls protocols, and failed to appropriately administer medications to some of the residents to avoid medication errors in certain skilled nursing facilities. The government alleges that Sava's conduct violated the Federal False Claims Statute and the North Carolina False Claims Statute and resulted in the submission of false claims to the North Carolina Medicaid program.
This settlement results from four whistleblower lawsuits filed in the United States District Court for the Middle District of Tennessee and the Eastern District of Pennsylvania. A team from the National Association of Medicaid Fraud Control Units participated in the settlement negotiations on behalf of the states.
About the Medicaid Investigations Division (MID)
The Attorney General's MID investigates fraud and abuse by health care companies and providers, as well as patient abuse and neglect in facilities that are funded by Medicaid. Medicaid is a joint federal-state program that helps provide medical care for people with limited income. To date, the MID has recovered more than $900 million in restitution and penalties for North Carolina.
The Medicaid Investigations Division receives 75 percent of its funding from the U.S. Department of Health and Human Services under a grant award totaling $6,160,236 for Federal fiscal year (FY) 2022. The remaining 25 percent, totaling $2,053,412 for FY 2022, is funded by the State of North Carolina.
To report Medicaid fraud in North Carolina, call the North Carolina Medicaid Investigations Division at 919-881-2320.
Attorney General Josh Stein Releases Statement on DNA Collection Legislation »
« Attorney General Josh Stein Reacts to Supreme Court's Ruling in West Virginia v. EPA


text:
Female directors in Hollywood are still underrepresented, but the gap is narrowing
Director Kasi Lemmons in 2019 joined a small group of women of color having directed multiple films in the past 13-years
(Carolyn Cole / Los Angeles Times)
By Anousha SakouiStaff Writer
The number of women directing top-grossing movies rose to the highest level since 2007, indicating that Hollywood is making modest progress in diversifying its ranks, according to a new report.
A dozen women directed some of the 100 top-grossing films in 2019, representing 10.6% of all directors, up from 4.5% of directors in the same category in 2018, though women of color are still vastly underrepresented among filmmakers, USC Annenberg's Inclusion Initiative found in a study released Thursday.
One reason for the improvement was that Universal Pictures distributed five films directed by women, including the romantic drama "Queen & Slim." Earlier last year, it became the first major studio to support the "4% Challenge," a plan to commit to work with at least one female director on a feature film over the next 18 months.
Paramount Pictures had the worst track record, distributing only three movies from 2007 to 2019 that were directed by women, according to the study. By comparison, Universal had 15 female directors over the same period, including "Queen & Slim" and "Abominable" released last year.
Representatives of Universal and Paramount could not be immediately reached for comment.
"The industry is still so skewed to white men that any forward motion is noted with success," Melissa Silverstein, an activist for gender equality in Hollywood, said in an interview. "The key is maintaining the forward motion over time."
Despite making on average better reviewed movies, women from underrepresented race or ethnic groups had the least opportunities, according to the study.
Less than 1% of all directing jobs went to women of color in the 1,300 top movies released from 2007 to 2019 covered in the study, while white men accounted for 82.5%.
Until 2019, only two women of color, Ava DuVernay and Jennifer Yuh Nelson, directed more than one movie among the 1,300 films surveyed. Last year, four more women of color were added to that group, including Kasi Lemmons, who directed Focus Features' "Harriet," about the story of famed abolitionist Harriet Tubman
"Reading all of these well laid out stats makes you realize there's no possible excuse that explains this discrepancy," said Lemmons via email. "I wonder about the chilling effect these statistics have on women coming up. You would think an art form of dreams and magic, of empathy and humanism would be the exact opposite of blatantly biased. If the movie industry is not a place where a young underrepresented woman can dare to dream of working and thriving, what are we saying?"
While there was no material difference in Metacritic scores by film director gender, films by women from underrepresented race or ethnic groups scored higher on the review aggregator site.
Studios "are missing out on talent because of their own subjective bias," Stacy L. Smith, who coauthored the report, said in an interview.
In this year's study, the Annenberg group focused on how women, particularly women of color, were represented behind the camera. Unlike last year's study, it did not break out specific racial groups.
Of the 113 directors of top 100 films in 2019, 83.2% were white and 16.8% were from underrepresented race or ethnic groups, down from 21.4% in 2018 and substantially below the U.S. Census of 39.6%, according to Annenberg.
Across the 1,300 films from 2007 to 2019, only 4.8% of directors were women.
The survey also highlights the dim prospects for recognition of female directors at the Oscars. Over the last 13 years across the Golden Globes, Directors Guild, Oscars and Critics' Choice awards, only 5.1% of nominations went to women.
Greta Gerwig, who directed the successful December release "Little Women,'' is the most likely among female directors to get a best director nomination for the Oscars, according to awards tracking site Gold Derby.
"These findings reveal that hiring practices have started to shift behind the camera in important ways for women," Smith wrote in the report. "Where more work is needed, however, is to increase access and opportunity for women of color."
Company TownEntertainment & Arts
Anousha Sakoui
Anousha Sakoui is an entertainment industry writer for the Los Angeles Times, covering Hollywood and labor issues. She moved to Los Angeles in 2014 from London and is graduate of the University of Edinburgh.
Paradigm lays off 30 people as Hollywood agencies face headwinds
Paradigm Talent Agency laid off 30 people on Friday, according to a person familiar with the situation who declined to be named. It was part of the agency's effort to eliminate redundancies caused by its recent acquisitions in the music space, the person said.
Hollywood is again bracing for a writers' strike. Here's what's different
Major studios are once again preparing for WGA strike, but much has changed since the last walkout in 2007-2008.
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Walt Disney Co.
L.A. film shoots dip 5% in the fourth quarter. Blame the space crunch
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WGA reaches deal with Gersh, gaining momentum in battle against talent agencies
The Gersh Agency is the latest talent agency to sign a deal with the Writers Guild of America after a long dispute with the Assn. of Talent Agents.
Comcast's streaming service Peacock will have live sports, news and late-night shows early
Comcast is offering three tiers for the streaming service, including a low-priced ad-supported subscription version for $4.99.
After a rough 2019, Hollywood's talent agencies brace for more uncertainty
Talent agencies are under growing pressure to raise capital to finance growth at time of rapid changes in the media industry. The rise of streaming and expected decline of TV packaging, combined with the effects of a longstanding boycott by Writers Guild of America, have put the squeeze on talent agencies, some of which have laid off workers.
Hollywood assistants are getting a pay raise from CAA
The salary bump comes after assistants have spoken out about their financial struggles and the verbal harassment they have faced working at talent agencies in Hollywood.


THE ROYAL LIVINGSTONE VICTORIA FALLS ZAMBIA HOTEL BY ANANTARA is a gracious and environmentally sensitive sanctuary on the banks of the Zambezi River overlooking the Victoria Falls. Minutes walk to Victoria falls, the thunder can be heard from the riverside garden, the water vapor cloud can be seen from its observation deck. Located within a national park, warm and friendly staff that provide personalised, faultless service. Guests can indulge in countless activities and authentic African experiences to create unforgettable moments and memories.
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text:
Camelobaetidius warreni is a species of small minnow mayfly in the family Baetidae. It is found in Central America, North America. In North America, its range includes southwestern Canada, all of Mexico, the northern, and southwestern United States.

References

Mayflies
Articles created by Qbugbot
Insects described in 1968


text:
Q: infinitely loop for org.apache.hadoop.mapred.TaskTracker I am running one simple hadoop application which collect information from a 64MB file, the map finished quickly, roughly in about 2 -5 minutes, then reduce also runs fast up to 16%, then it just stopped.
This is the program output

11/12/20 17:53:46 INFO input.FileInputFormat: Total input paths to process : 1
11/12/20 17:53:46 INFO mapred.JobClient: Running job: job_201112201749_0001
11/12/20 17:53:47 INFO mapred.JobClient:  map 0% reduce 0%
11/12/20 17:54:06 INFO mapred.JobClient:  map 4% reduce 0%
11/12/20 17:54:09 INFO mapred.JobClient:  map 15% reduce 0%
11/12/20 17:54:12 INFO mapred.JobClient:  map 28% reduce 0%
11/12/20 17:54:15 INFO mapred.JobClient:  map 40% reduce 0%
11/12/20 17:54:18 INFO mapred.JobClient:  map 53% reduce 0%
11/12/20 17:54:21 INFO mapred.JobClient:  map 64% reduce 0%
11/12/20 17:54:24 INFO mapred.JobClient:  map 77% reduce 0%
11/12/20 17:54:27 INFO mapred.JobClient:  map 89% reduce 0%
11/12/20 17:54:30 INFO mapred.JobClient:  map 98% reduce 0%
11/12/20 17:54:33 INFO mapred.JobClient:  map 100% reduce 0%
11/12/20 17:54:54 INFO mapred.JobClient:  map 100% reduce 8%
11/12/20 17:54:57 INFO mapred.JobClient:  map 100% reduce 16%

In the data node log, I see tons of same message again and again, the following is there is starts,

2011-12-20 17:54:51,353 INFO org.apache.hadoop.mapred.TaskTracker: attempt_201112201749_0001_r_000000_0 0.083333336% reduce > copy (1 of 4 at 9.01 MB/s) >
2011-12-20 17:54:51,507 INFO org.apache.hadoop.mapred.TaskTracker.clienttrace: src: 127.0.1.1:50060, dest: 127.0.0.1:44367, bytes: 75623263, op: MAPRED_SHUFFLE, cliID: attempt_201112201749_0001_m_000000_0, duration: 2161793492
2011-12-20 17:54:54,389 INFO org.apache.hadoop.mapred.TaskTracker: attempt_201112201749_0001_r_000000_0 0.16666667% reduce > copy (2 of 4 at 14.42 MB/s) >
2011-12-20 17:54:57,433 INFO org.apache.hadoop.mapred.TaskTracker: attempt_201112201749_0001_r_000000_0 0.16666667% reduce > copy (2 of 4 at 14.42 MB/s) >
2011-12-20 17:55:40,359 INFO org.mortbay.log: org.mortbay.io.nio.SelectorManager$SelectSet@53d3cf JVM BUG(s) - injecting delay3 times
2011-12-20 17:55:40,359 INFO org.mortbay.log: org.mortbay.io.nio.SelectorManager$SelectSet@53d3cf JVM BUG(s) - recreating selector 3 times, canceled keys 72 times
2011-12-20 17:57:51,518 INFO org.apache.hadoop.mapred.TaskTracker: attempt_201112201749_0001_r_000000_0 0.16666667% reduce > copy (2 of 4 at 14.42 MB/s) >
2011-12-20 17:57:57,536 INFO org.apache.hadoop.mapred.TaskTracker: attempt_201112201749_0001_r_000000_0 0.16666667% reduce > copy (2 of 4 at 14.42 MB/s) >
2011-12-20 17:58:03,554 INFO org.apache.hadoop.mapred.TaskTracker: attempt_201112201749_0001_r_000000_0 0.16666667% reduce > copy (2 of 4 at 14.42 MB/s) >

...
up to

2011-12-20 17:54:51,353 INFO org.apache.hadoop.mapred.TaskTracker: attempt_201112201749_0001_r_000000_0 0.083333336% reduce > copy (1 of 4 at 9.01 MB/s) >
2011-12-20 17:54:51,507 INFO org.apache.hadoop.mapred.TaskTracker.clienttrace: src: 127.0.1.1:50060, dest: 127.0.0.1:44367, bytes: 75623263, op: MAPRED_SHUFFLE, cliID: attempt_201112201749_0001_m_000000_0, duration: 2161793492
2011-12-20 17:54:54,389 INFO org.apache.hadoop.mapred.TaskTracker: attempt_201112201749_0001_r_000000_0 0.16666667% reduce > copy (2 of 4 at 14.42 MB/s) >
2011-12-20 17:54:57,433 INFO org.apache.hadoop.mapred.TaskTracker: attempt_201112201749_0001_r_000000_0 0.16666667% reduce > copy (2 of 4 at 14.42 MB/s) >
2011-12-20 17:55:40,359 INFO org.mortbay.log: org.mortbay.io.nio.SelectorManager$SelectSet@53d3cf JVM BUG(s) - injecting delay3 times
2011-12-20 17:55:40,359 INFO org.mortbay.log: org.mortbay.io.nio.SelectorManager$SelectSet@53d3cf JVM BUG(s) - recreating selector 3 times, canceled keys 72 times
2011-12-20 17:57:51,518 INFO org.apache.hadoop.mapred.TaskTracker: attempt_201112201749_0001_r_000000_0 0.16666667% reduce > copy (2 of 4 at 14.42 MB/s) >
2011-12-20 17:57:57,536 INFO org.apache.hadoop.mapred.TaskTracker: attempt_201112201749_0001_r_000000_0 0.16666667% reduce > copy (2 of 4 at 14.42 MB/s) >
2011-12-20 17:58:03,554 INFO org.apache.hadoop.mapred.TaskTracker: attempt_201112201749_0001_r_000000_0 0.16666667% reduce > copy (2 of 4 at 14.42 MB/s) >

Here is the code
package com.bluedolphin;

import java.io.IOException;
import java.util.Iterator;

import org.apache.hadoop.conf.Configuration;
import org.apache.hadoop.fs.Path;
import org.apache.hadoop.io.LongWritable;
import org.apache.hadoop.io.Text;
import org.apache.hadoop.mapreduce.Job;
import org.apache.hadoop.mapreduce.Mapper;
import org.apache.hadoop.mapreduce.Reducer;
import org.apache.hadoop.mapreduce.lib.input.FileInputFormat;
import org.apache.hadoop.mapreduce.lib.output.FileOutputFormat;
import org.apache.hadoop.util.GenericOptionsParser;

public class MyJob {
    private final static LongWritable one = new LongWritable(1);
    private final static Text word = new Text();

    public static class MyMapClass extends Mapper<LongWritable, Text, Text, LongWritable> {
        public void map(LongWritable key,
                    Text value,
                    Context context) throws IOException, InterruptedException {
            String[] citation = value.toString().split(",");
            word.set(citation[0]);

            context.write(word, one);
        }
    }

    public static class MyReducer extends Reducer<Text, LongWritable, Text, LongWritable> {
        private LongWritable result = new LongWritable();
        public void reduce(
                Text key,
                Iterator<LongWritable> values,
                Context context) throws IOException, InterruptedException {
            int sum = 0;

            while (values.hasNext()) {
                sum += values.next().get();
            }
            result.set(sum);
            context.write(key, result);
        }
    }

     public static void main(String[] args) throws Exception {
            Configuration conf = new Configuration();
            String[] otherArgs = new GenericOptionsParser(conf, args).getRemainingArgs();
            if (otherArgs.length != 2) {
              System.err.println("Usage: myjob <in> <out>");
              System.exit(2);
            }
            Job job = new Job(conf, "patent citation");
            job.setJarByClass(MyJob.class);
            job.setMapperClass(MyMapClass.class);
           // job.setCombinerClass(MyReducer.class);
           // job.setReducerClass(MyReducer.class);
            job.setNumReduceTasks(0);
            job.setMapOutputKeyClass(Text.class);
            job.setMapOutputValueClass(LongWritable.class);

            job.setOutputKeyClass(Text.class);
            job.setOutputValueClass(LongWritable.class);

            FileInputFormat.addInputPath(job, new Path(otherArgs[0]));
            FileOutputFormat.setOutputPath(job, new Path(otherArgs[1]));
            System.exit(job.waitForCompletion(true) ? 0 : 1);
          }

}

I don't know how to further troubleshooting.
Thanks in advace.

A: I figured out the solution, in the reduce method signature, I should have been using Iterable, not Iterator. Because of that, the reduce method was actually not called. It runs fine now, but I don't know the internal reason that it hung before.

A: A couple of things i noticed in your code:
Since you are updating the Text object "word" in map and the LongWritable object "result" in reduce for each call to map and reduce respectively, you probably shouldn't declare them final (Although i don't see this as a problem in this case, as the objects are only changing the state).
Your code looks similar to the trivial word count, only difference is as you are just emiting one value per record in map. You could just eliminate reduce (i.e., run a map-only job) and see if you get what you expect from map.

A: I also had this infinity loop during the reduce work. After struggling for a day, the solution turns out to be adjust the /etc/hosts file.
It seems that the existence of the entry "127.0.1.1 your_Machine's_Name" confused the Hadoop. One proof of that would be the disability to access the slave:50060, the taskTracker on the slave machine, from the master machine.
As long as this "127.0.1.1 your_machine's_name" entry is deleted and add "your_machine's_name" at the end of the entry "127.0.0.1 localhost", my problem is gone.
I hope this observation can be helpful.