text:
Ziegler Advises CareSignal on its Acquisition by Lightbeam Health Solutions
Ziegler is pleased to announce it served as the exclusive financial advisor to CareSignal (St. Louis, MO), the pioneer of Deviceless Remote Patient Monitoring technology, on its acquisition by Lightbeam Health Solutions (Irving, TX), a leading pop...
Ziegler Advises ESAC on its Acquisition by ICF
Ziegler is pleased to announce it served as the exclusive financial advisor to Enterprise Science and Computing (ESAC) on its acquisition by ICF (NASDAQ: ICFI), a global consulting and digital services provider.
Ziegler Advises Avera Health on Sale of Telemedicine Unit, eCare, to Aquiline Capital Partners
Ziegler is pleased to announce its role as financial advisor to Avera Health, an integrated health care system in the Midwest, in the selling of Avera eCare, its telemedicine services unit, to Aquiline Capital Partners. As part of the acquisition,...
Ziegler Advises Versant Diagnostics on its Formation Investment from Iron Path Capital
Ziegler is pleased to announce its role as the exclusive financial advisor to Versant Diagnostics on a formation and growth investment from Iron Path Capital.
Ziegler Advises Diagnostic Centers of America on its Acquisition by Rayus Radiology
Ziegler is pleased to announce it served as the exclusive financial advisor to Diagnostic Centers of America on its acquisition by RAYUS Radiology, backed by private equity firm Wellspring Capital.
Ziegler Supporting Telehealth Awareness Week 2021 as a Founding Partner
Ziegler is pleased to announce that it is an official Founding Partner of the inaugural Telehealth Awareness Week, presented by the American Telemedicine Association, taking place September 19-25, 2021.
Ziegler Advises Center for Language and Autism Support Services in the Acquisition by ACES
Ziegler is pleased to announce it served as the exclusive financial advisor to Center for Language and Autism Support Services in its acquisition by ACES 2020, LLC. The acquisition will enable ACES to continue scaling its evidence-based clinical m...
Ziegler Advises Bluegrass Orthopaedics on the Creation of a New Platform with Trivest Partners
Ziegler is pleased to announce it served as the exclusive financial advisor to Bluegrass Orthopaedics on its partnership with Trivest Partners, L.P, together forming a new national orthopedic management services organization.
Ziegler Advises Windsong Radiology on its Partnership With US Radiology Specialists
Ziegler is pleased to announce it served as the exclusive financial advisor to Windsong Radiology on its partnership with US Radiology Specialists, backed by private equity firm Welsh, Carson, Anderson & Stowe.
Ziegler Advises CareFirst BlueCross BlueShield on its Acquisition of Trusted Health Plan
Ziegler is pleased to announce its role in advising CareFirst BlueCross BlueShield in the acquisition of Trusted Health Plan (District of Columbia), Inc.
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text:
Steamship Authority's website is back in business following ransomware attack
FALMOUTH - The Steamship Authority's website is up and running again and customers can book reservations for vehicle travel and fast-ferry travel online, the agency announced Saturday.
The Authority was the target of a ransomware attack on the morning of June 2. The attack caused delays and affected operations. The extent and origin of the attack is still under investigation.
The FBI is leading the investigation, and is working in conjunction with the Coast Guard and the Massachusetts State Police Cyber Security Unit, according to an email received from Coast Guard First District Petty Officer Amanda Wyrick.
The safety of vessels was never threatened since the cyberattack did not affect radar or GPS functions, according to Steamship Authority spokesman Sean Driscoll.
Previously:FBI investigating ransomware attack on Steamship Authority
Booking travel
Customers can call the Mashpee Reservation Office at 508-477-8600 to book travel, or do so in person at one of five terminals in Hyannis, Woods Hole, Oak Bluffs, Vineyard Haven and Nantucket.
All restrictions on the time frame in which customers can book reservations have been lifted. Customers can book for any point through Oct. 18, which is the end of the late summer schedule. Reservation confirmation emails may be intermittent.
The Reservation Office has extended its hours to 7 a.m. to 6 p.m. through Sunday.
All reservations that were made prior to the incident are being honored. Customers who had booked prior to that date do not need to rebook their reservations.
Colonial Pipeline:Reportedly pays $5M in cryptocurrency to hackers to end ransomware cyberattack
Waitlist requests for travel from July 1are now being processed. Waitlist requests for travel before July 1 will be processed in the near future. All waitlist requests remain intact and customers do not need to re-create them. If their request is honored, they will be notified by email or text.
Customers can use credit cards at terminals and parking lots.
Fall reservations delayed
Multiride cards (the Lifeline and Ferry Pass cards) cannot be reloaded at this time.
The opening date for fall reservations, which covers travel between Oct. 19 and Jan. 4 has been delayed for two weeks until Monday, June 28.
'Nothing is safe':Five times ransomware attackers have impacted our lives
The Steamship Authority is continuing to work with local, state, and federal officials to address the incident. The investigation is ongoing, and with the assistance of third-party cybersecurity and forensic investigators the company is working to determine the full nature and scope of the event.
Driscoll said he would provide updates when appropriate. He thanked customers for their patience.
The Authority typically makes about $7.3 million in profits annually and carries millions of passengers and supplies upon which Martha's Vineyard and Nantucket depend.
-- Denise Coffey

redpajama_set_name: RedPajamaCommonCrawl


Black Bull is a brand of blended Scotch whisky that's been around since 1864. However, there's none of this 40% abv nonsense found here. Like it's namesake, the strength is in the proof. All of their whiskies are bottled at 50% abv. When the brand was founded, it was made up of 50% malt whiskies and 50% grain whiskies bottled at 50% abv. That still holds true. Current owner Duncan Taylor has kept the tradition going.
The core lineup is comprised of a non-age statement Kyloe, a 12-year-old and 21-year-old. The prices range from $30-$35 for Kyloe, $50-$55 for the 12 year, and $170-$180 for the 21 year.
Three whiskies that seem to get better with age. Where else can you drink 21-year-old whisky at 100 proof for that price? I was so impressed after tasting Black Bull's core range that I went out and purchased their limited edition 40-year-old whisky. Once I get around to that, you can bet I'll share my experience with that expression! As for the subject of this post, the 12- and 21-year-old come with a very high recommendation, especially for the price. Black Bull Kyloe is fine, but I think I'd rather pay the extra $20 and upgrade to the 12-year.
Thanks to Shand Imports and Duncan Taylor for the samples. As always, all thoughts and opinions are my own.


text:
nBuildKit provides the following MsBuild packages:

## Requirements

The `nBuildKit` package makes the following assumptions:

* There is an installation of the command line version of NuGet available for use during the build process. This may be either be found via the PATH environment variable or may be found via the path value provided in the `settings.props` file.
* Certain tasks cannot be skipped
 * Workspace preparation - Cleans out the `build` directory
 * Gather version information - Collects information about the current version and stores it in a temporary file to be used by the rest of the build. Current options are to use a MsBuild version file or to use the GitHubFlowVersion application.
* Certain tasks require certain applications / packages to be available. These are:
 * Release notes are gathered via [GitReleaseNotes](https://github.com/GitTools/GitReleaseNotes)
 * Version numbers are either gathered via a `version.xml` msbuild file, via [GitVersion](https://github.com/ParticularLabs/GitVersion), or via [GitHubFlowVersion](https://github.com/JakeGinnivan/GitHubFlowVersion)
 * [CCM](http://www.blunck.se/ccm.html)
 * [SourceMonitor](http://www.campwoodsw.com/sourcemonitor.html)
 * Binaries --> should be able to build with MsBuild, hence all tasks need to be available
 * [Moma](http://www.mono-project.com/docs/tools+libraries/tools/moma/)
 * FxCop
 * [Sandcastle](https://github.com/EWSoftware/SHFB) for documentation
* All binaries are dropped in a specific directory (`workspace/build/bin`) at the end of the compilation process.

## Workspace layout

The `nBuildKit.MsBuild` package makes the following assumptions about the layout of the build environment:

* There is a `packages.config` file in the same directory as the `nbuildkit.msbuild` main build script. The `packages.config` file is used to find the installed version of nBuildKit.
* There is either a `packages` directory, which contains the installed NuGet packages for the project, or a `nuget.config` file in the same directory as the `nsbuildkit.msbuild`  main build script. If the `packages` directory is found then it will be assumed that the installed version of nBuildKit will be in that directory, otherwise the `nuget.config` file will be searched for a `repositorypath` which will be used to determine the location of the packages directory.

In other words `nBuildKit` expects at least either one of the following directory (`[D]`) and file structures:

    [D] workspace
        |
        |- myproject.msbuild
        |- nuget.config
        |- packages.config
        |- settings.props

where the `nuget.config` file points to a `repositorypath`, or the following situation

    [D] workspace
        |
        |- [D] packages
        |- myproject.msbuild
        |- packages.config
        |- settings.props

By default the `settings.props` file describes a workspace with the following layout:

    [D] workspace
        |
        |- [D] build
        |      |
        |      |- [D] bin
        |      |- [D] deploy
        |      |- [D] logs
        |      |- [D] temp
        |- [D] packages
        |- [D] src
        |- [D] templates
        |- nbuildkit.msbuild
        |- packages.config
        |- settings.props

Where:

* __build__ - The directory that will contain all files generated during the build process, including binaries, artifacts, log files etc. etc.
 * __bin__ - The directory that will contain the binary files generated during the build process.
 * __deploy__ - The directory that will contain the artifacts (e.g. NuGet packages, ZIP archives etc.) generated during the build process.
 * __logs__ - The directory that will contain all the log files that were generated during the build process including the reports from the unit tests and the static analysis.
 * __temp__ - The directory that will contain all the temporary files that were generated during the build process.
* __packages__ - The directory that contains the NuGet packages for the build process. This directory may also contain the NuGet packages for the Visual Studio solution but that is not required.
* __src__ - The directory that contains the source files and Visual Studio solution and projects.
* __templates__ - The directory that contains the template files which are used as a basis for generated files.

Note that all these locations, other than the location of the `settings.props` file, which has to be in the 'root' of the workspace, may be changed by specifying where they are located in the `settings.props` file.

## Updating the settings file
Once a basic version of the `settings.props` file is available in the workspace directory you may want to configure it so that it fits your specific case better. All sections, properties and collections are fully documented in the `settings.props` file. The documentation should provide enough information to determine the goal of each item. The `settings.props` file contains the following sections:

* __Global settings__ - Contains the properties and collections that apply to all parts of the build, test and deploy process. These are items such as product information, directory and file locations and the selected processes for getting version numbers and release notes.
* __Build settings__ - Contains the properties and collections that apply to the build part of the process. These are items such as source code analysis with tools like CCM, compilation of source code, execution of unit tests, execution of static analysis through tools like FxCop, generation of API documentation through tools like Sandcastle and finally creating NuGet packages or ZIP archives. Note that any type of tests done in this part of the process should be assumed to be running in the same workspace and process environment as the compilation part of the build.
* __Test settings__ - Contains the properties and collections that apply to the test part of the process. These are items such as automated regression or performance tests. Any tests executed during this stage of the process can be assumed to be executed in a different workspace and process space from the build steps, making this section more suitable for longer running tests.
* __Deploy settings__ - Contains the properties and collections that apply to the deploy part of the process. These are items such as tagging the current VCS revision, pushing NuGet packages to a NuGet feed and copying files to a local or remote location.

### Build settings specifics
There are several build specific settings defined in the `settings.props` file.

#### Available build steps
The build part of `nBuildKit` has defined the following default steps:

* __Build / workspace preparation__
 * __Workspace cleaning__ - Removes the `build` directory and all the files generated during the build.
 * __Restore NuGet packages__ - Restores the NuGet packages for all of the build.
 * __Gather version numbers__ - Gathers the version number information for the build.
 * __Gather release notes__ - Gathers the release notes for the build.
 * __Gather VCS information__ - Gathers information about the current revision number and branch. Currently only supported for GIT.
 * __Generate license file__ - Generates an XML file containing the license information for each of the NuGet packages used in the build.
 * __Generate files__ - Generate one or more files based on a set of templates.
* __Analysis of source code__
 * __CCM__ - Analyzes the source code with [CCM](http://www.blunck.se/ccm.html).
 * __SourceMonitor__ - Analyzes the source code with [SourceMonitor](http://www.campwoodsw.com/sourcemonitor.html).
* __Compilation__ - Invokes MsBuild on one or more Visual Studio solutions.
* __Unit testing__
 * __MsTest__ - Executes the unit tests with [MsTest]()
 * __NUnit__ - Executes the unit tests with [NUnit](http://nunit.org)
 * __VsTest__ - Executes the unit tests with [VsTest]()
* __Analysis of binaries__
 * __MoMA__ - Analyzes the binaries with the [Mono Migration Analyzer](http://www.mono-project.com/MoMA).
 * __FxCop__ - Analyzes the binaries with FxCop.
* __API documentation__ - Builds the API documentation with [Sandcastle](http://sandcastle.codeplex.com/) and [Sandcastle helpfile builder](http://shfb.codeplex.com/).
* __Packing__
 * __NuGet__ - Creates the [NuGet](http://nuget.org/) packages.
 * __ZIP archives__ - Creates one or more ZIP archives.

Note that the build steps described above may have its own set of properties that need to be configured. These properties can also be found in the `settings.props` file below the build steps `ItemGroup`.

### Test settings

#### Available test steps
The test part of `nBuildKit` can execute the following steps:

* __Build / workspace preparation__
 * __Workspace cleaning__ - Removes the `build` directory and all the files generated during the build.
 * __Restore NuGet packages__ - Restores the NuGet packages for all of the build.
 * __Gather version numbers__ - Gathers the version number information for the build.
 * __Gather release notes__ - Gathers the release notes for the build.
 * __Gather VCS information__ - Gathers information about the current branch. Currently only supported for GIT.
 * __Generate files__ - Generate one or more files based on a set of templates.

### Deploy settings

#### Available deploy steps
The deploy part of `nBuildKit` can execute the following steps:

* Tag current revision with the version number
 * GIT
 * TFS
* Push artifacts to local / remote directory
* Push NuGet packages to NuGet feed
* Push NuGet symbol packages to local symbol server (copy to directory) (nAnicitus approach)
* Create release on GitHub (based on earlier tag) and push artifacts to release

### Custom build steps

All sections allow custom build steps to be executed before and after the section. Custom build step must be a MsBuild script. Custom build steps can be inserted in the sequence by adding them in the desired location in the `BuildStepsToExecute`, `TestStepsToExecute` or `DeployStepsToExecute` item groups.

## Versions

* Build scripts require a version. Using the [semantic version](semver.org) at all times. Normally provide `major.minor.patch`. Note that binaries are versioned according to the way they are set up. The build scripts do not change that.
* Version can be gotten from a custom MsBuild script that defines the major, minor, patch and build numbers, e.g.

        <Project xmlns='http://schemas.microsoft.com/developer/msbuild/2003'
                 ToolsVersion="4.0">
            <UsingTask TaskName="CalculateCustomVersion"
                       TaskFactory="CodeTaskFactory"
                       AssemblyFile="$(MSBuildToolsPath)\Microsoft.Build.Tasks.v4.0.dll">
                <ParameterGroup>
                    <VersionMajor ParameterType="System.String" Output="true" />
                    <VersionMinor ParameterType="System.String" Output="true" />
                    <VersionPatch ParameterType="System.String" Output="true" />
                    <VersionBuild ParameterType="System.String" Output="true" />
                    <VersionPreRelease ParameterType="System.String" Output="true" />
                    <VersionSemantic ParameterType="System.String" Output="true" />
                    <VersionSemanticFull ParameterType="System.String" Output="true" />
                    <VersionSemanticNuGet ParameterType="System.String" Output="true" />
                </ParameterGroup>
                <Task>
                    <Code Type="Method" Language="cs">
                        <![CDATA[
                            public override bool Execute()
                            {
                                try
                                {
                                    VersionMajor = "4";
                                    VersionMinor = "3";
                                    VersionPatch = "2";
                                    VersionBuild = "1";
                                    VersionPreRelease = "MyPreRelease";
                                    VersionSemantic = string.Format(
                                        "{0}.{1}.{2}",
                                        VersionMajor,
                                        VersionMinor,
                                        VersionPatch);
                                    VersionSemanticFull = string.Format(
                                        "{0}.{1}.{2}-{3}+{4}",
                                        VersionMajor,
                                        VersionMinor,
                                        VersionPatch,
                                        VersionPreRelease,
                                        VersionBuild);
                                    VersionSemanticNuGet = string.Format(
                                        "{0}.{1}.{2}-{3}{4}",
                                        VersionMajor,
                                        VersionMinor,
                                        VersionPatch,
                                        VersionPreRelease,
                                        VersionBuild);
                                }
                                catch(Exception e)
                                {
                                    Log.LogError(e.ToString());
                                }

                                // Log.HasLoggedErrors is true if the task logged any errors -- even if they were logged
                                // from a task's constructor or property setter. As long as this task is written to always log an error
                                // when it fails, we can reliably return HasLoggedErrors.
                                return !Log.HasLoggedErrors;
                            }
                        ]]>
                    </Code>
                </Task>
            </UsingTask>
        </Project>

* Getting the version from a XML file.

        <?xml version="1.0" encoding="utf-8"?>
        <Project ToolsVersion="3.5"
                 DefaultTargets="Build"
                 xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
            <!-- Define the values for the version number -->
            <PropertyGroup>
                <!-- Get the build number from a CI server (e.g. Jenkins) -->
                <BuildNumber>$(BUILD_NUMBER)</BuildNumber>

                <!-- If the build number doesn't exist then just set it to zero so that it has some kind of value -->
                <BuildNumber Condition=" '$(BuildNumber)' == '' ">0</BuildNumber>

                <!-- The version numbers -->
                <VersionMajor>1</VersionMajor>
                <VersionMinor>2</VersionMinor>
                <VersionPatch>3</VersionPatch>
                <VersionBuild>$(BuildNumber)</VersionBuild>
                <VersionPreRelease></VersionPreRelease>
            </PropertyGroup>
        </Project>

* Using the [GitVersion](https://github.com/ParticularLabs/GitVersion) application to get the version.
* Using the [GitHubFlowVersion](https://github.com/JakeGinnivan/GitHubFlowVersion) application to get the version.

## Commonly asked questions

* How to add a custom build step
* Minimal edits to `settings.props` for working build
* How to control what build steps are taken
* How to control what test steps are taken
* How to control what deploy steps are taken
* Multi stage build - test - deploy process
* Deploying through promoting

redpajama_set_name: RedPajamaGithub


On behalf of the American Civil Liberties Union and its over 400,000 members, dedicated to defending the Bill of Rights and its promise of due process under law for all persons, I welcome this opportunity to present the ACLU's views at this hearing on the impact of federal anti-terrorism efforts on civil liberties since September 11, 2001.
I commend Chairman Hatch and Senator Leahy for coming together to look at whether, in our efforts to preserve freedom by fighting terrorism, we have given up too much of it. This country needs exactly this public discussion, and I feel privileged to play a role, as a leader of the ACLU, in challenging the government to see its role as preserving our rights and our system of checks and balances while it ensures our safety.
America faces a crucial test. That test is whether we - the political descendents of Jefferson and Madison, and citizens of the world's oldest democracy - have the confidence, ingenuity and commitment to secure our safety without sacrificing our liberty.
For here we are at the beginning of the 21st century, in a battle with global terror. Terrorism is a new and different enemy. As a nation, we learned this on September 11, 2001 when a group of terrorists attacked us here at home, and within the space of minutes murdered nearly 3,000 of our fellow Americans and citizens of other nations, innocent civilians going about their everyday lives.
ACLU lawyers and activists can never forget that day. Our national offices in New York and near the Capitol in Washington were evacuated. John William Perry, a New York Police Department officer and Board Member of the New York Civil Liberties Union, volunteered to assist employees escaping the World Trade Center on September 11, 2001, and himself became a victim. We pledged on that day to support President Bush in the battle against terror, while standing strong against any efforts to use the attacks to abridge civil liberties or our system of checks and balances.
We must be ready to defend liberty, for liberty cannot defend itself. We as a nation have no trouble understanding the necessity of a military defense. But there is another equally powerful defense that is required, and that is the defense of our Constitution - the defense of our most cherished freedoms.
Put aside our popular culture which changes by the day, and our material success which is now vulnerable to the vicissitudes of the global economy - strip away all that is truly superficial. What is left that distinguishes us if not our constitutional values? These values -freedom, liberty, equality and tolerance - are the very source of our strength as a nation and the bulwark of our democracy. They are what have permitted us to grow abundantly, and to absorb wave after wave of immigrants to our shores, reaping the benefits of their industrious energy.
Now, we are in danger of allowing ourselves to be governed by our fears, rather than our values. How else can we explain the actions of our government over the last two years to invade the privacy of our personal lives and to curtail immigrants' rights, all in the name of increasing our security?
Congress must step in - now - to preserve the freedoms that have been eroded since September 11, 2001.
Mr. Chairman, when Attorney General Ashcroft appeared before this Committee shortly after September 11, he accused the ACLU and other defenders of civil liberties of aiding the terrorists and weakening America's resolve with our criticism of some government policies. It was a statement profoundly unworthy of the Office of Attorney General.
Mr. Chairman, by holding this hearing, and by extending the ACLU an invitation to testify, you have acted in the best traditions of the Senate. Mr. Chairman, I know we disagree about some aspects of the USA PATRIOT Act and some other important civil liberties issues. I hope to convince you and other Senators that some revisions are in order.
Before I describe the freedoms lost since September 11, 2001, and the clear abuses of civil liberties that have taken place, I would like to set the record straight on a few things that have been said about the ACLU and its supporters.
Since September 11, 2001, the ACLU has been privileged to be an important part of a remarkable grassroots movement to defend the Bill of Rights. Resolutions have been passed in 210 communities in 35 states, including three state-wide resolutions.
The resolutions have passed in towns from Maine to Alaska, from New York to Texas. They have attracted support in liberal strongholds, like Berkeley, California, and in small towns in Utah, Idaho, and Alaska - three of the most conservative states in the Union. The resolutions are the most visible symbol of a growing movement that is perhaps most notable for uniting allies across the political spectrum - from the ACLU and its liberal allies like People for the American Way and MoveOn.org, to some of the nation's most important member-based conservative organizations: the Free Congress Foundation, Americans for Tax Reform, and the Gun Owners of America. Our campaign has included closely working with former Congressman Bob Barr (R-GA), a Board Member of the National Rifle Association. I am pleased to share the witness table with Congressman Barr today.
The resolutions take issue with portions of the PATRIOT Act and many other government actions, including Executive Orders and regulations undermining the right to counsel, the right to a jury trial, and the rights of immigrants. Hundreds of thousands of Americans have written their elected representatives to express their views about these issues, and to urge Congress to take corrective actions.
Some have accused these engaged citizens, who are acting in the best tradition of Thomas Jefferson, of being naïve, misinformed, even ignorant. On the contrary, while the arcane details of these issues can flummox the finest legal minds, I have found our supporters to be remarkably well informed.
This is a movement based on knowledge, not ignorance.
Many have read the PATRIOT Act closely and have studied what its defenders have to say. They have also followed the debate around other government powers, including attorney-client monitoring, immigrant registration and detention, and FBI guidelines governing investigations of religious and political groups.
There is no doubt that both PATRIOT Act detractors and defenders alike have sometimes had difficulty wading through the arcane details of the Foreign Intelligence Surveillance Act and other complex federal laws amended by the Act. It does not help matters when spokespersons for the Department of Justice (DOJ) make misleading and inaccurate statements about the PATRIOT Act - such as that ""U.S. citizens cannot be investigated under this act"" or that ""the standard of proof before the [Foreign Intelligence Surveillance Court] is the same as it's always been.""
Ordinary Americans are profoundly troubled by the government's policies. They do not believe America's system of checks and balances, including meaningful judicial review of surveillance and detention, represent ""unreasonable obstacles"" to law enforcement, as President Bush and Attorney General Ashcroft have argued.
Rather, they see judicial review, and meaningful standards for government surveillance and detention, as essential bulwarks against abuse. They view judges as partners - not obstacles - in the war on terrorism.
The online satirical publication, the ""Onion,"" recently had this headline: ""Revised Patriot Act Will Make It Illegal to Read Patriot Act."" The serious point is that the more Americans learn about the government's actions since September 11, the more they say the government went too far, too fast. Thankfully, we do live in a country where people can go to the source, read the law and make up their own minds.
Many members of Congress, from right to left and in between, have heeded their constituents' calls to look at the PATRIOT Act, and other post-9/11 government actions, evaluated arguments for and against, and have decided to bring some of these powers back in line with constitutional freedoms. Congressman Butch Otter (R-ID) and Bernie Sanders (I-VT), and Senators Larry Craig (R-ID), Richard Durbin (D-IL) and Russ Feingold (D-WI) have joined forces to revise the PATRIOT Act.
Americans are concerned because the PATRIOT Act put in place statutory authority for the government to get a court order to come into your home without your knowledge and even take property without notifying you until weeks or months later. Americans are concerned because the PATRIOT Act allows the government to obtain many detailed, personal records - including library and bookstore records, financial and medical records, and Internet communications - without probable cause and without meaningful judicial review. For those records that may be obtained using ""national security letters,"" there is no judicial review at all. Americans are concerned because the PATRIOT Act - as well as changes to immigration regulations since 9/11 and the President's claimed authority to detain ""enemy combatants"" - all sanction indefinite detention without criminal charge and without meaningful judicial review.
Some have dismissed these concerns, saying the government has not used some of these anti-terrorism powers, or has used them appropriately. In fact, as we informed members of this Committee prior to its last hearing, there has already been evidence of widespread and systematic civil liberties abuses of non-PATRIOT powers in the area of detention, both of citizens and non-citizens. There is anecdotal evidence of excessive government surveillance and other overreaching under the PATRIOT Act. Unfortunately, the Administration's excessive secrecy prevents the American people from getting an adequate picture about its use of PATRIOT Act surveillance powers.
What the ACLU can say for certain is that these and other powers make abuses far more likely because they remove the checks and balances that prevent abuse. Excessive power has, throughout our history, inevitably been used excessively.
Some have dismissed concern about an expanded PATRIOT Act - dubbed PATRIOT II - as misinformed, saying that the draft legislation that provoked a firestorm earlier this year was never introduced. In fact, many provisions of this draft legislation have been introduced separately, including bills to sweep aside the last vestiges of prior judicial review from FBI records demands (H.R. 3037), to require automatic pretrial detention for certain crimes (H.R. 3040 and S. 1606), and to expand the death penalty to include any crime that fits the PATRIOT Act's overbroad definition of terrorism (H.R. 2934 and S. 1604).
As reported in the New York Times just last week, a major expansion of the FBI's powers to obtain records without any judicial review was attached to this year's Intelligence Authorization Act. Constituents are right to be concerned about an expanded PATRIOT Act. Part of it will - unless removed by the conference committee - become law this year.
Some have dismissed concerns about immigrants' rights, including the selective fingerprinting and registration of visitors from the Arab and Muslim world under the National Security Entry-Exit Registration System (NSEERS), also known as special registration. This program is seriously damaging the image of the United States abroad and, as a result, hindering international cooperation against terrorism.
Special registration is again creating havoc in Arab and Muslim communities as the deadlines for re-registration approach. The ACLU has discovered that immigration authorities gave many who registered confusing and woefully inadequate notice of their obligations - including the requirement that they register their departure and that they re-register annually. Those who were given inadequate or no notice are at risk of falling afoul of their status through no fault of their own.
The specific freedoms that have been abridged - by the PATRIOT Act and by other government actions - often involve technical and complex changes to surveillance laws, detention regulations, and government guidelines. However, they share common themes. The government's new surveillance and detention powers have undermined important checks and balances, diminished personal privacy, increased government secrecy, and exacerbated inequality.
Checks and Balances. At bottom, the issue with respect to all these powers - PATRIOT Act and non-PATRIOT Act alike - is the removal of basic checks and balances on government power. The genius of our founding fathers was to design a system in which no one branch of government possessed all power, but instead the powers were divided among legislative, executive and judicial branches.
The government's actions since September 11 have undermined this system. Prior to September 11, the government had ample power to investigate, detain, convict and punish terrorists, with meaningful judicial review. The changes have made that review less meaningful.
It is a myth to say that prior to September 11, the government could wiretap organized crime suspects but not terrorist suspects. In fact, the government has always had far greater powers to wiretap foreign terrorist suspects, because it could use either its criminal or its intelligence powers to do so. The PATRIOT Act simply enlarged further the already loose standards for both kinds of wiretapping.
It is a myth to say that prior to September 11, the government was prevented by the Foreign Intelligence Surveillance Act from sharing information acquired in intelligence investigations with criminal prosecutors. In fact, it could do so, under procedures designed to ensure the intelligence powers were not being abused as a prosecutorial end-run around the Fourth Amendment. The PATRIOT Act did not authorize such information sharing - it was already legal. Rather, the Act reduced the judicial oversight designed to prevent abuses of information sharing.
It is a myth that the government lacked adequate power to detain terrorist suspects. In fact, the government could, and did, detain many terrorist suspects prior to September 11 using both immigration and criminal powers. Indeed, President Bush joined the ACLU in criticizing the use of secret evidence against some Arab and Muslim immigration detainees under the Clinton Administration. The PATRIOT Act, and government changes to detention regulations, did not authorize detention of terrorism suspects. Rather, it made immigration hearings and judicial review of those detentions far less meaningful.
It is a myth that the government could not effectively prosecute foreign terrorists without revealing classified information. The Classified Information Procedures Act has long been on the books to protect the government's secrets while ensuring a fair trial, and prosecutors of prior Al Qaeda plots have said the Act worked well to protect both the rights of the accused and the national security interests of the government. The President's military tribunals order was not needed to safeguard classified information. Rather, its effect was to substitute a commission subject to Defense Department control for an independent judge in running terrorism trials.
It is a myth that the government could not listen to the conversations of attorneys who betrayed their profession by abusing the attorney-client privilege to implicate themselves in their clients' ongoing criminal acts. The government could always obtain a court order, based on probable cause, to listen in to conversations that lacked the protection of the attorney-client privilege. The monitoring regulation was drafted to evade that requirement of judicial oversight.
Understanding how these actions undermine checks and balances illustrates the sophistry of one of the government's main defenses of its post 9-11 actions. Government officials point out that courts have not struck down many of their actions - but their actions are a threat to liberty precisely because they are calculated to undermine the role of the courts, diminishing their oversight of government action.
The defense that courts have not struck down these court-stripping measures reminds me of the old cliche of the man who murdered his parents and pleaded for mercy on the grounds he was an orphan.
Personal Privacy. The right of privacy, Justice Brandeis said, is that most simple and most important of freedoms - the right to be left alone. The PATRIOT Act and other legislation, coupled with new investigative guidelines, have eroded this right alarmingly. I will discuss just two - new records powers under sections 215 and 505 of the Act, and ""sneak and peek"" searches under section 213 of the Act.
Under section 215 of the PATRIOT Act, the government may now obtain any and all records, no matter how sensitive or personal, with a ""business records"" order from the Foreign Intelligence Surveillance Court, which sits in secret and has denied or modified a grand total of six out of more than 15,000 surveillance orders sought in a quarter century. Under section 505 of the PATRIOT Act, the FBI has now has broader power to use what are called ""national security letters"" to obtain some records - including records of financial institutions, credit reports, and billing records of telephone and Internet service providers - on its own authority, without any court order at all.
National security letters and records demands under section 215 are not made in the course of ordinary criminal investigations, which involve grand jury subpoenas, search warrants, and other longstanding government powers; rather, they are intelligence powers that do not require any criminal wrongdoing on the part of those being investigated.
Before the PATRIOT Act, the government was required to show ""specific and articulable facts"" that the records it sought in intelligence investigations (whether through a ""business records"" order or a national security letter) pertained to a spy, terrorist, or other agent of a foreign power. As a result of sections 215 and 505, that is no longer the case - now anyone's records may be obtained, regardless of whether he or she is a suspected foreign agent, as long as the government says the records are sought for an intelligence or terrorism investigation. The effect is to put the privacy of many more Americans at risk. The record holder must comply with these records demands, and is prohibited from informing anyone - the person whose records were obtained, the press, or an advocacy group like the ACLU - that they have turned over these records.
Section 213 of the PATRIOT Act substantially lowered the standard for government agents to come into your house, look around, and even take property. These ""sneak and peek"" warrants no longer require, as they did in some circuits, that notice be given within seven days - an indefinite ""reasonable time"" is the new standard. Nor do they require the government to show specific harms from notice, instead also permitting the government to get a delay under a catch-all provision that applies whenever harm to the prosecution may result.
As a result of this provision, the government has acknowledged using these warrants to invade dozens of homes and businesses without providing notice for as long as three months. The government has sought to delay notice in these cases over 200 times.
While sold as a terrorism power, this provision has little to do with terrorism. In answering questions from Congress on how this provision was being used, the Justice Department cited ordinary criminal cases - from drugs to crime - to justify these searches.
Government Secrecy. The American tradition of open government has suffered a severe blow as a result of the government's post 9-11 actions.
The Justice Department's guidance to federal agencies on implementation of the Freedom of Information Act (FOIA) prior to September 11 included a basic affirmation of the policy of open government the Act embodies, urging agencies to comply with FOIA requests absent a good reason. Shortly after September 11, the Attorney General issued a memorandum to all federal agencies reversing that presumption of openness and pledging the Justice Department's support for denial of FOIA requests.
Reform policies governing classification and declassification of government secrets have suffered a similar blow. On March 25, 2003, President Bush issued Executive Order 12958, which continued classification of many historical documents and reverses a presumption against excessive classification for new documents in President Clinton's prior Executive Order. The new Order flies in the face of findings of the Senate and House intelligence committees that excessive classification may have contributed to the intelligence breakdowns that contributed to the September 11 attacks. Former chairman of the Senate Select Committee on Intelligence, Senator Bob Graham (D-FL), criticized the move, saying ""this administration is being excessively cautious in keeping information from the American people.""
Perhaps the most dramatic example of unwarranted secrecy has been the government's secret arrest and deportation of hundreds of Muslim and Arab immigrants after September 11. The Justice Department refused to identify the detainees, arguing that to do so might jeopardize national security and tip its hand to terrorists. The secrecy was alarming and, after our repeated requests for basic information about the detainees were denied, the ACLU filed a federal lawsuit seeking names under the Freedom of Information Act.
Then, in a further effort to deny information to the public and press, the Justice Department closed all immigration hearings involving the September 11 detainees. Twice more, the ACLU went to court - with lawsuits arguing that transparency and accountability are essential to the workings of democracy. In an eloquent decision, a three-judge panel of the United States Court of Appeals in Cincinnati unanimously declared that secret deportation hearings were unlawful. ""A government operating in the shadow of secrecy stands in complete opposition to the society envisioned by the framers of our Constitution,"" Judge Damon Keith wrote. He further noted that ""democracy dies behind closed doors.""
That was a clear victory for civil liberties and stands today, as the government chose not to seek Supreme Court review in that case. However, in the second lawsuit, the federal appeals court in Philadelphia sided with the government's position in a 2-1 ruling. The Supreme Court has declined to hear that case.
The ACLU's actions, however, have not been limited to the legal arena. Concerned that the secret hearings were a cover for civil liberties abuses, we initiated an ambitious effort to identify the people affected. We sent letters to the U.S.-based consulates and embassies of ten countries offering legal assistance to innocent people caught up in the government's crackdown on terrorism.
Then in the spring of 2002, the ACLU extended its investigations abroad. Working with the Human Rights Commission of Pakistan (HRCP), we located 21 detainees who had been forcibly removed to Pakistan, or who had left the U.S. voluntarily to avoid indefinite detentions. The interviews were heart-breaking. Before their detentions, these people were indistinguishable from previous generations of immigrants who had come to our shores. They had been salesmen, housewives, and cab drivers with children and homes in America, grateful to be in a country where they could achieve a better life and live in freedom.
Their detention put an end to all that. They described the anxiety-ridden days, which turned into weeks, and then into months - culminating in deportation. Few had been charged with crimes, and many had been deprived of access to counsel. In some cases, the U.S. government ignored the citizenship rights of spouses or even children born in this country. Back in Pakistan, these American children, unable to speak the local language, were miserable and failing at school. The plight of these families was featured on CNN, National Public Radio and on the front page of The New York Times.
The ACLU's concerns about the treatment of September 11 detainees were vindicated by a highly critical report released this year by the Office of Inspector General of the Department of Justice, finding that detainees were effectively denied access to counsel and languished in jail for months without legal justification. Excessive secrecy clearly contributed to the abuse of the rights of hundreds of Arab and Muslim immigrants and visitors. More sunlight could have prevented many of those abuses from taking place.
Increasing Inequality. ""Equal Justice Under Law"" is the motto inscribed above the Supreme Court building, but the legal system's treatment of the Arab and Muslim community in this country since September 11 has been separate, unequal and wrong.
Military detention of both citizen and non-citizen Arab and Muslim terrorism suspects stands in stark contrast to the treatment of homegrown terrorists like Timothy McVeigh. Arab and Muslim non-citizens - who enjoy the protection of the Bill of Rights no less than citizens - are facing what amounts to an entirely new legal system, with basic due process suspended. Not only do they face potential trial before special military tribunals - with access to counsel and information limited severely, unlike ordinary military courts - they can be whisked away without a hearing to face injustice in the legal netherworld of Guantanamo Bay, Cuba, or to detention and interrogation by governments with some of the worst human rights records in the world.
Recent reports indicate profoundly disturbing, and possibly criminal, United States collusion with regimes that practice torture, including Syria and Saudi Arabia. Maher Arar, a Canadian citizen, was detained by United States authorities in a New York airport while en route to his home in Canada, then sent to Syria, where he was held and, he alleges, tortured by the Syrian secret police. These allegations of torture, with the consent and possible encouragement of the United States, must be thoroughly investigated.


Babymoov is a 15 year old French company which designs innovative products for mums with mums.
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Davies, PE ORCID: 0000-0003-2651-4061 2001 , Blackman River: Woodbury Dam proposal Aquatic environmental assessment.
to some 10-12 farmers between Woodbury and the Macquarie river junction.
valved pipes, as well as via a raceway channel from the dam wall.


Mega sits down with Matt Conn, CEO of MidBoss, creators of the Gaymer X Convention and producer of Read Only Memories, a new cyberpunk adventure game. Ran and Matt talk Clash of Champions 2016, and grade each match, talk about why we feel new times are coming for The New Day, and learn about the Deluxe version of "Read Only Memories," coming soon!
Music selection: "Cruisin USA" (T.J. Perkins) by Mega Ran feat. KadeshFlow and 1UP.


text:
\section{Introduction}

According to inflationary cosmology, the temperature anisotropies in the
cosmic microwave background (CMB) were seeded by primordial quantum
fluctuations \cite{LL00,Muk05,PU09}. Precision measurements of the CMB may
therefore provide us with tests of the quantum Born probability rule at very
early times \cite{AV07,AV08,AV10,CV13,CV15,AV15}.

The de Broglie-Bohm pilot-wave formulation of quantum theory
\cite{deB28,BV09,B52a,B52b,Holl93} provides a natural extension of the usual
quantum formalism, in which corrections to the Born rule are possible. In
pilot-wave theory, the Born rule is not fundamental but only describes a state
of statistical equilibrium
\cite{AV91a,AV91b,AV92,AV96,AV01,AV02,AV07,AV08,AV09,AV10,AVPwtMw,PV06}.

One may consider a universe that begins in a state of `quantum
nonequilibrium', with non-Born rule probabilities
\cite{AV92,AV96,AV01,AV07,AV08,AV10}. The dynamics of pilot-wave theory allows
us to evolve such a state forward in time. Extensive numerical simulations
have been performed for a free scalar field evolving on a radiation-dominated
background \cite{CV13,CV15}, with a view to applying the results to a
cosmology with a radiation-dominated pre-inflationary phase \cite{PK2007,WN08
. The simulations yield efficient relaxation to the equilibrium Born rule at
short (sub-Hubble) wavelengths, with a suppression or retardation of
relaxation at long (super-Hubble) wavelengths. If we assume that the initial
distribution at the beginning of pre-inflation has a width smaller than the
width of the initial Born-rule distribution, then for such initial conditions
we may expect that at the beginning of inflation there will be an anomalous
deficit in the primordial spectrum at sufficiently long wavelengths
\cite{AV07,AV08,AV10,CV13,CV15}.

Data from the \textit{Planck} satellite appear to show a large-scale power
deficit in the CMB \cite{PlanckXV-2013,Planck15-XI-PowerSpec}. The CMB
two-point angular correlation function at large scales is also smaller than
expected \cite{CHSS13}. These effects could be mere statistical fluctuations
or they could amount to genuine anomalies in the primordial spectrum --
possibly arising from new physics. Theoretical models that predict a power
deficit at large scales will help to assess the nature and significance of the
apparent anomalies in the data.

It is conceivable that the large-scale power deficit in the CMB arises from
incomplete relaxation to quantum equilibrium during a pre-inflationary era
\cite{AV07,AV08,AV10,CV13,CV15}. The lengthscale at which the deficit sets in
cannot be predicted by our model as it depends on the unknown number of
inflationary e-folds. However, we are able to predict the `shape' of the
deficit as a function of wavenumber $k$. This arises by performing simulations
of quantum relaxation on an expanding radiation-dominated background for
scalar field modes of varying wavelength -- where the extent of relaxation
broadly increases with decreasing wavelength. As a result, the primordial
spectrum is diminished by a factor $\xi(k)$ which is considerably less than
$1$ for small $k$ and which approaches $1$ (approximately) for large $k$.
Specifically, we find that $\xi(k)$ varies with $k$ approximately as an
inverse-tangent \cite{CV15}.

It would be an advantage to make predictions that are broadly independent of
the details of the putative pre-inflationary era. In this paper, we show that
our prediction of an inverse-tangent power deficit function $\xi(k)$ is robust
under: (i) changes in the initial nonequilibrium distribution, and (ii) the
addition of an inflationary period at the end of the radiation-dominated phase
(adding to the time interval over which the relaxation process is simulated).
In both cases the final result for $\xi(k)$ remains an inverse-tangent
function of $k$. With the inflationary phase, the dependence of the fitting
parameters on the number of superposed pre-inflationary energy states is also
comparable to that found previously. We then have a fairly robust prediction
for the wavelength-dependence of the power deficit, which may be compared with
data \cite{PVV15}.

\section{Quantum relaxation on expanding space}

In de Broglie-Bohm pilot-wave theory \cite{deB28,BV09,B52a,B52b,Holl93}, a
system with wave function $\psi(q,t)$ has a configuration $q(t)$ with velocit
\begin{equation}
\frac{dq}{dt}=\frac{j}{|\psi|^{2}}\ , \label{deB
\end{equation}
where $j=j\left[  \psi\right]  =j(q,t)$ is the Schr\"{o}dinger current
\cite{SV08}. An ensemble of systems with the same $\psi$ can have an arbitrary
distribution $\rho(q,t)$ of configurations, where $\rho(q,t)$ necessarily
obeys the continuity equatio
\begin{equation}
\frac{\partial\rho}{\partial t}+\partial_{q}\cdot\left(  \rho\dot{q}\right)
=0\ . \label{cont
\end{equation}
An initial distribution $\rho(q,t_{i})=\left\vert \psi(q,t_{i})\right\vert
^{2}$ evolves into a final distribution $\rho(q,t)=\left\vert \psi
(q,t)\right\vert ^{2}$ -- the state of quantum equilibrium, for which we
obtain the Born rule and the usual quantum predictions \cite{B52a,B52b}. For a
nonequilibrium ensemble we have $\rho(q,t)\neq\left\vert \psi(q,t)\right\vert
^{2}$ and the statistical predictions generally disagree with quantum theory
\cite{AV91a,AV91b,AV92,AV07,PV06}.

In pilot-wave theory, the state of quantum equilibrium may be understood to
arise dynamically by a process of relaxation or equilibration
\cite{AV91a,AV92,AV01,VW05,EC06,TRV12,SC12,ACV14}, which may have taken place
in the early universe \cite{AV91a,AV91b,AV92,AV96,AV01,AV07,AV08,AV10}.

For our purposes, it suffices to consider a free, minimally-coupled, real
massless scalar field $\phi$ on an expanding background with line element
$d\tau^{2}=dt^{2}-a^{2}d\mathbf{x}^{2}$ where $a=a(t)$ is the scale factor
(with $c=1$). Working with Fourier component
\begin{equation}
\phi_{\mathbf{k}}=\frac{\sqrt{V}}{(2\pi)^{3/2}}\left(  q_{\mathbf{k
1}+iq_{\mathbf{k}2}\right)  \ ,
\end{equation}
where $V$ is a normalisation volume and the $q_{\mathbf{k}r}$'s ($r=1,2$) are
real, the field Hamiltonian is a sum $H=\sum_{\mathbf{k}r}H_{\mathbf{k}r}$
wher
\begin{equation}
H_{\mathbf{k}r}=\frac{1}{2a^{3}}\pi_{\mathbf{k}r}^{2}+\frac{1}{2
ak^{2}q_{\mathbf{k}r}^{2}\ . \label{Ham
\end{equation}
For an unentangled mode $\mathbf{k}$ with wave function $\psi_{\mathbf{k
}(q_{\mathbf{k}1},q_{\mathbf{k}2},t)$, we have the Schr\"{o}dinger equation
(dropping the index $\mathbf{k}$) \cite{AV07,AV08,AV10
\begin{equation}
i\frac{\partial\psi}{\partial t}=\sum_{r=1,\ 2}\left(  -\frac{1}{2a^{3
}\partial_{r}^{2}+\frac{1}{2}ak^{2}q_{r}^{2}\right)  \psi
\end{equation}
for $\psi=\psi(q_{1},q_{2},t)$ (where $q_{1},q_{2}$ are proportional to the
real and imaginary parts of the field mode) and the de Broglie-Bohm velocitie
\begin{equation}
\dot{q}_{r}=\frac{1}{a^{3}}\operatorname{Im}\frac{\partial_{r}\psi}{\psi}
\label{deB3
\end{equation}
for the configuration $(q_{1},q_{2})$ (with $\partial_{r}\equiv\partial
/\partial q_{r}$). The marginal distribution $\rho=\rho(q_{1},q_{2},t)$
obeys\footnote{The marginal $\rho(q_{1},q_{2},t)$ is the probability
distribution for the field mode, which may be obtained from the complete field
probability distribution by integrating over the degrees of freedom of the
other field modes -- though such an operation is redundant if for simplicity
we assume a product distribution over modes.
\begin{equation}
\frac{\partial\rho}{\partial t}+\sum_{r=1,\ 2}\partial_{r}\left(  \rho\frac
{1}{a^{3}}\operatorname{Im}\frac{\partial_{r}\psi}{\psi}\right)  =0\ .
\label{CE2D
\end{equation}

Mathematically, a single field mode is equivalent to a two-dimensional
oscillator with time-dependent mass $m=a^{3}$ and time-dependent angular
frequency $\omega=k/a$ \cite{AV07,AV08}. This is in turn equivalent to a
standard oscillator -- with constant mass and constant angular frequency --
but with appropriately rescaled variables for each system and with standard
time $t$ replaced by a `retarded time' $t_{\mathrm{ret}}(t,k)$, where the
function $t_{\mathrm{ret}}=t_{\mathrm{ret}}(t,k)$ may be determined
\cite{CV13}.

Cosmological relaxation over a time $t$ for a field mode of wavenumber $k$ may
then be conveniently studied in terms of a standard oscillator evolving over a
retarded time $t_{\mathrm{ret}}(t,k)$. Specifically, the time evolution from
initial conditions at $t_{i}$ to final conditions at $t_{f}$ may be obtained
by evolving a standard oscillator -- with the same initial conditions -- from
the same initial time $t_{i}$ up to the retarded final time $t_{\mathrm{ret
}(t_{f},k)$. Note, however, that this is merely a convenient means of evolving
the continuity equation (\ref{CE2D}), which could be integrated directly
(though less efficiently) yielding the same results.

Extensive results have been obtained for a radiation-dominated expansion
($a\propto t^{1/2}$) \cite{CV13,CV15}. In the short-wavelength (sub-Hubble)
limit, $t_{\mathrm{ret}}(t,k)\rightarrow t$ and we recover the usual rapid
relaxation for a superposition of energy states (as on Minkowski spacetime).
At long (super-Hubble) wavelengths, $t_{\mathrm{ret}}(t,k)<<t$ and relaxation
is suppressed or retarded.

The suppression of relaxation at long wavelengths may be quantified in terms
of a deficit in the width of the nonequilibrium distribution. Each degree of
freedom $q_{r}$ has an equilibrium variance $\Delta_{r}^{2}=\left\langle
q_{r}^{2}\right\rangle _{\mathrm{QT}}-\left\langle q_{r}\right\rangle
_{\mathrm{QT}}^{2}$ and a nonequilibrium variance $D_{r}^{2}=\left\langle
q_{r}^{2}\right\rangle -\left\langle q_{r}\right\rangle ^{2}$, where
$\left\langle ...\right\rangle _{\mathrm{QT}}$ and $\left\langle
...\right\rangle $ are respective averages with respect to $\left\vert
\psi(q_{1},q_{2},t)\right\vert ^{2}$ and $\rho(q_{1},q_{2},t)$. The functio
\[
\xi(k)\equiv\frac{D_{1}^{2}+D_{2}^{2}}{\Delta_{1}^{2}+\Delta_{2}^{2}
\]
then measures the width deficit of nonequilibrium relative to equilibrium.

We have argued elsewhere \cite{AV07,AV10,CV13,CV15} that if there was a
radiation-dominated pre-inflationary era then we may expect the spectrum of
primordial perturbations generated during inflation to take the for
\begin{equation}
\mathcal{P}_{\mathcal{R}}(k)=\mathcal{P}_{\mathcal{R}}^{\mathrm{QT}
(k)\xi(k)\ ,
\end{equation}
where $\mathcal{P}_{\mathcal{R}}^{\mathrm{QT}}(k)$ is the standard
quantum-theoretical spectrum. It is of particular interest to make predictions
for $\xi(k)$ with a view to comparing with CMB data.

In previous work \cite{CV13,CV15} we considered initial wave functions for a
single mode (in a putative pre-inflationary era) that are superposition
\begin{equation}
\psi(q_{1},q_{2},t_{i})=\frac{1}{\sqrt{M}}\sum_{n_{1}=0}^{\sqrt{M}-1
\sum_{n_{2}=0}^{\sqrt{M}-1}e^{i\theta_{n_{1}n_{2}}}\Phi_{n_{1}}(q_{1
)\Phi_{n_{2}}(q_{2}) \label{psi_i
\end{equation}
of $M$ energy eigenstates $\Phi_{n_{1}}\Phi_{n_{2}}$ of the initial
Hamiltonian, with coefficients $c_{n_{1}n_{2}}(t_{i})=(1/\sqrt{M
)e^{i\theta_{n_{1}n_{2}}}$ of equal amplitude and with randomly-chosen phases
$\theta_{n_{1}n_{2}}$. The wave function at time $t$ i
\begin{equation}
\psi(q_{1},q_{2},t)=\frac{1}{\sqrt{M}}\sum_{n_{1}=0}^{\sqrt{M}-1}\sum
_{n_{2}=0}^{\sqrt{M}-1}e^{i\theta_{n_{1}n_{2}}}\psi_{n_{1}}(q_{1
,t)\psi_{n_{2}}(q_{2},t)\ , \label{psi_t
\end{equation}
where $\psi_{n_{r}}(q_{r},t)$ is the time evolution of $\psi_{n_{r}
(q_{r},t_{i})=\Phi_{n_{r}}(q_{r})$ under a formal one-dimensional
Schr\"{o}dinger equation with Hamiltonian $\hat{H}_{r}(t)$ (given by equation
(\ref{Ham})) and where the exact solution for $\psi_{n}(q,t)$ with $a\propto
t^{1/2}$ was obtained in ref. \cite{CV13}. For simplicity we assumed an
initial nonequilibrium distributio
\begin{equation}
\rho(q_{1},q_{2},t_{i})=|\Phi_{0}(q_{1})\Phi_{0}(q_{2})|^{2}=\frac{\omega
_{i}m_{i}}{\pi}e^{-m_{i}\omega_{i}q_{1}^{2}}e^{-m_{i}\omega_{i}q_{2}^{2}}
\label{rho_i
\end{equation}
(equal to the equilibrium distribution for the ground state $\Phi_{0
(q_{1})\Phi_{0}(q_{2})$). We then performed a numerical simulation of the time
evolution $\rho(q_{1},q_{2},t)$ up to a final time $t_{f}$.

Such simulations were carried out for varying values of $k$, as well as for
varying values of $M$ and $t_{f}$. For each case we could compare the final
nonequilibrium variance with the final equilibrium variance and hence
calculate the ratio $\xi$ for varying values of $k$, $M$ and $t_{f}$. In fact,
before taking their ratio the nonequilibrium and equilibrium variances were
averaged over mixtures of initial wave functions (\ref{psi_i}) with
randomly-chosen phases. Our calculated function $\xi(k)$ -- for given $M$ and
$t_{f}$ -- is then in fact given b
\begin{equation}
\xi(k)=\frac{\left\langle D_{1}^{2}+D_{2}^{2}\right\rangle _{\mathrm{mixed}
}{\left\langle \Delta_{1}^{2}+\Delta_{2}^{2}\right\rangle _{\mathrm{mixed}
}\ , \label{xi_mixed
\end{equation}
where $\left\langle ...\right\rangle _{\mathrm{mixed}}$ is an average over the
mixed ensemble of quantum states (see ref. \cite{CV15} for details).

Our numerical simulations yielded functions $\xi(k)$ that approximately take
the form \cite{CV15
\begin{equation}
\xi(k)=\tan^{-1}(c_{1}\frac{k}{\pi}+c_{2})-\frac{\pi}{2}+c_{3} \label{numksi
\end{equation}
(neglecting oscillations of amplitude $\lesssim10\%$ around the fitted curve),
where the best-fit parameters $c_{1}$, $c_{2}$, $c_{3}$ depend on $M$ and
$t_{f}$. Our results for $c_{1}$, $c_{2}$, $c_{3}$ are listed in tables I and
II of ref. \cite{CV15}.

Note that $\xi\rightarrow c_{3}$ for large $k$, where $c_{3}$ is generally
found to differ slightly from $1$. There is a nonequilibrium `residue' at
short wavelengths. For a discussion of the significance of this, see ref.
\cite{CV15}.

Our aim is to find a general signature of quantum relaxation in the early
universe that is as far as possible independent of details of the
pre-inflationary era. The `quantum relaxation spectrum' (\ref{numksi}) appears
to be a good candidate for such a signature. Here we extend the generality of
this spectrum in two ways. First, we study initial nonequilibrium
distributions that are more complicated than (\ref{rho_i}). Second, as a first
step towards a more realistic cosmological model, we include a period of
exponential expansion after the radiation-dominated phase. In both cases we
still obtain a spectral deficit $\xi(k)$ of the form (\ref{numksi}).

\section{Quantum relaxation for different initial nonequilibria}

In this section we consider cosmological quantum relaxation for three
different initial nonequilibrium distributions
\begin{align}
\rho_{1}(q_{1},q_{2},t_{i})  &  =|\Phi_{0}(q_{1})\Phi_{0}(q_{2})|^{2
\ ,\label{rho1i}\\
\rho_{2}(q_{1},q_{2},t_{i})  &  =\frac{1}{2}|\Phi_{0}(q_{1})\Phi_{0
(q_{2})+\Phi_{1}(q_{1})\Phi_{1}(q_{2})|^{2}\ ,\label{rho2i}\\
\rho_{3}(q_{1},q_{2},t_{i})  &  =\frac{2}{3}
|\Phi_{0}(q_{1})\Phi_{0}(q_{2})+\frac{1}{2}\Phi_{1}(q_{1})\Phi_{1}(q_{2})+\frac{1}{2}\Phi_{2}(q_{1})\Phi_{2}(q_{2})|^{2}\ ,
\label{rho3i
\end{align}
where as above $\Phi_{n_{1}}(q_{1})\Phi_{n_{2}}(q_{2})$ are energy eigenstates
of the initial two-dimensional harmonic oscillator Hamiltonian.

As before we take the initial wave function $\psi(q_{1},q_{2},t_{i})$ to be a
superposition (\ref{psi_i}) of $M$ energy eigenstates $\Phi_{n_{1}}(q_{1
)\Phi_{n_{2}}(q_{2})$ with coefficients of equal amplitude and with
randomly-chosen phases. We shall consider in particular the cases $M=9$ and
$M=25$. For these initial wave functions, the initial distributions
(\ref{rho1i})--(\ref{rho3i}) are all nonequilibrium states. The first
(\ref{rho1i}) is that used in previous simulations (equation (\ref{rho_i})):
it is equal to what would be the equilibrium distribution if the wave function
were simply the ground state. The second (\ref{rho2i}) contains an admixture
of terms from the excited state $\Phi_{1}(q_{1})\Phi_{1}(q_{2})$, while the
third (\ref{rho3i}) is equal to what would be the equilibrium distribution if
the wave function were simply $\Phi_{1}(q_{1})\Phi_{1}(q_{2})$.

Note that in pilot-wave theory the initial distribution can in principle be
any arbitrary probability function $\rho(q_{1},q_{2},t_{i})\neq|\psi
(q_{1},q_{2},t_{i})|^{2}$. The above three probability functions related to
$\Phi_{0}(q_{1})\Phi_{0}(q_{2})$ and $\Phi_{1}(q_{1})\Phi_{1}(q_{2})$ are
chosen for convenience only.

We shall consider these different initial nonequilibria in order to study two questions.

First, we study relaxation (illustrated with density plots) for the case of
$M=25$ modes. In particular, we compare results obtained with and without
spatial expansion for each of the three initial nonequilibria, thereby
extending the analysis of ref. \cite{CV13}.

Second, for the case of $M=9$ modes we perform simulations of the deficit
function $\xi(k)$ for the three different initial nonequilibria, thereby
extending the analysis of ref. \cite{CV15}.

The three initial nonequilibria (\ref{rho1i})--(\ref{rho3i}) differ
considerably (see the plots below). And yet, as we shall see, relaxation
proceeds similarly for each in the absence of spatial expansion, while in the
presence of spatial expansion there is a similar relaxation suppression for
the three cases. Crucially, the final results for the deficit function
$\xi(k)$ remain of the inverse-tangent form (\ref{numksi}), though with
coefficients $c_{1}$, $c_{2}$, $c_{3}$ that vary with the initial
nonequilibrium distribution.

\subsection{Relaxation and relaxation suppression}

In ref. \cite{CV13} we simulated relaxation on expanding space for the
illustrative case of $M=25$ modes. We compared results obtained in the absence
of spatial expansion (equivalent to the short-wavelength limit) with results
obtained in the presence of spatial expansion and in particular at long
(super-Hubble) wavelengths. For the former, we found efficient and close
relaxation to quantum equilibrium. For the latter, we found a retardation or
suppression of relaxation. These studies were carried out with the fixed
initial nonequilibrium distribution (\ref{rho1i}). Here we present comparable
simulations for all three initial densities (\ref{rho1i})--(\ref{rho3i}), with
similar results (again for $M=25$).

As in ref. \cite{CV13}, we begin at an initial time $t_{i}=10^{-4}$ and we
evolve to a final time $t_{f}=10^{-2}$ (units $\hslash=c=1$), with a scale
factor $a(t)=a_{0}(t/t_{0})^{1/2}$ where for convenience we take $a_{0}=1$ at
$t_{0}=1$. We consider a mode of wavenumber $k=10\pi$. With these values, the
initial physical wavelength $\lambda_{\mathrm{phys}}(t_{i})=a_{i}(2\pi/k)$ is
ten times the initial Hubble radius $H_{i}^{-1}=2t_{i}$ while the final
physical wavelength $\lambda_{\mathrm{phys}}(t_{f})=a_{f}(2\pi/k)$ is equal to
the final Hubble radius $H_{f}^{-1}=2t_{f}$. In other words,\ we study a field
mode that begins an order of magnitude outside the Hubble radius and we evolve
it to the time $t_{f}=t_{\mathrm{enter}}$ of Hubble entry.

We plot the evolving nonequilibrium and equilibrium distributions at the
initial and final times $t_{i}$ and $t_{f}=t_{\mathrm{enter}}$ as well as at
the intermediate time $0.5t_{\mathrm{enter}}$. As explained in ref.
\cite{CV13}, because the support of $|\psi(q_{1},q_{2},t)|^{2}$ in the
$q_{1}-q_{2}$ plane shrinks with time it is convenient to plot the
distributions in terms of appropriately rescaled variables $q_{1}^{\prime
},q_{2}^{\prime}$ with an actual density $\rho^{\prime}(q_{1}^{\prime
,q_{2}^{\prime},t)$ and an equilibrium density $\rho_{\mathrm{QT}}^{\prime
}(q_{1}^{\prime},q_{2}^{\prime},t)$. Furthermore, it is convenient to plot
smoothed densities $\tilde{\rho}^{\prime}(q_{1}^{\prime},q_{2}^{\prime},t)$
and $\tilde{\rho}_{\mathrm{QT}}^{\prime}(q_{1}^{\prime},q_{2}^{\prime},t)$
obtained by coarse-graining with overlapping coarse-graining cells \cite{CV13}.

The results in the absence of spatial expansion are shown in Figure 1. The
first, second and third columns show the time evolution of the initial
nonequilibrium densities (\ref{rho1i}), (\ref{rho2i}) and (\ref{rho3i})
respectively. The fourth column shows the time evolution of the quantum
equilibrium density (for a wave function with a superposition of $M=25$ energy
states). The relaxation is seen to be excellent for all three initial
nonequilibria. This answers a query that is sometimes raised: relaxation on a
fixed background occurs efficiently not only for the initial `ground-state'
nonequilibrium distribution (\ref{rho1i}) but also for other initial
nonequilibria. In the three cases studied here, the results are in fact comparable

\begin{figure}
[ptb]
\begin{center}
\includegraphics[width=\textwidth]
{Figs_Robust_v1/Fig1_M25_relaxation.jpg
\caption{Relaxation in the absence of spatial expansion for different initial
nonequilibria.
\end{center}
\end{figure}

The results in the presence of spatial expansion are shown in Figure 2. Again,
the first, second and third columns show the time evolution of the initial
nonequilibrium densities (\ref{rho1i}), (\ref{rho2i}) and (\ref{rho3i})
respectively while the fourth column shows the time evolution of the quantum
equilibrium density (for $M=25$). As is plain from the plots, at super-Hubble
wavelengths on expanding space we find a comparable retardation or suppression
of relaxation in all three cases

\begin{figure}
[ptb]
\begin{center}
\includegraphics[width=\textwidth]
{Figs_Robust_v1/Fig2_M25_suppression.jpg
\caption{Relaxation suppression at super-Hubble wavelengths on expanding space
for different initial nonequilibria.
\end{center}
\end{figure}

\subsection{Robustness of the inverse-tangent{} deficit $\xi(k)$}

In ref. \cite{CV15} we studied the deficit function $\xi(k)$ for varying
numbers $M$ of modes, evolved over a fixed time interval $[t_{i
,t_{f}]=[10^{-4},10^{-2}]$ and with the fixed initial nonequilibrium density
(\ref{rho1i}). We found a good fit to the inverse-tangent function
(\ref{numksi}) -- with small ($\lesssim10\%$) oscillations around the curve --
in all the cases $M=4,6,9,12,16,25$ that were studied. Here we consider
varying the initial nonequilibrium density with fixed $M$ and evolving over
the same fixed time interval $[10^{-4},10^{-2}]$. We choose the intermediate
value $M=9$.

The simulation is carried out as described in detail in ref. \cite{CV15}. In
particular, we plot mixed-ensemble curves $\xi=\xi(k)$ obtained by averaging
the variances of the densities over six sets of randomly-chosen phases in the
initial wave function (\ref{psi_i}). However, in contrast to ref. \cite{CV15},
here we consider three different initial nonequilibrium distributions.

As shown in Figure 3, we find good fits to the inverse-tangent function
(\ref{numksi}) for all three of the initial densities (\ref{rho1i
)--(\ref{rho3i}) studied

\begin{figure}
[ptb]
\begin{center}
\includegraphics[width=\textwidth]
{Figs_Robust_v1/Fig3_ksis_M9.jpg
\caption{Mixed-ensemble curves $\xi(k)$ for the three initial nonequilibrium
densities (\ref{rho1i})--(\ref{rho3i}) ($\rho_{1}$ in blue, $\rho_{2}$ in red
and $\rho_{3}$ in black), with best fits to the inverse-tangent function
(\ref{numksi}).
\end{center}
\end{figure}

As shown in Table 1, the fitting coefficients $c_{1}$, $c_{2}$, $c_{3}$ depend
on the initial density. The first coefficient $c_{1}$ is almost the same for
the three initial densities but $c_{2}$ and $c_{3}$ vary considerably. Note
that for $\rho_{2}$ and $\rho_{3}$ we find $c_{3}>1$.

\begin{table}
\begin{center
\begin{tabular}
[c]{|c|c|c|c|}\hline
$\rho$ & $c_{1}$ & $c_{2}$ & $c_{3}$\\\hline
$\rho_{1}$ & 0.14 & 1.44 & 0.92\\
$\rho_{2}$ & 0.11 & 2.86 & 1.06\\
$\rho_{3}$ & 0.12 & 2.30 & 1.13\\\hline
\end{tabular}

\end{center}
\caption{Fitting coefficients $c_{1}$, $c_{2}$, $c_{3}$ for the initial
nonequilibrium densities $\rho_{1}$, $\rho_{2}$, $\rho_{3}$.}
\label{Table1}
\end{table}

\section{Radiation-dominated phase with a subsequent inflationary phase}

We now consider how the deficit function $\xi(k)$ will be affected by a period
of exponential (inflationary) expansion added to the end of a
radiation-dominated phase. We assume the fixed initial nonequilibrium density
(\ref{rho1i}) (with initial wavefunctions of the form (\ref{psi_i})) at time
$t_{i}$ at the beginning of the radiation-dominated period, which as before
lasts until a time $t_{f}$; we then add an inflationary period beginning at
$t_{f}$ and lasting until a time $t_{f}^{\prime}$. We shall calculate $\xi(k)$
for varying numbers $M$ of superposed energy states in the initial wavefunction.

To proceed, we must first find the retarded time function $t_{\mathrm{ret
}=t_{\mathrm{ret}}(t,k)$ for an exponential expansion. We may then add
appropriate retarded time intervals (corresponding to $[t_{f},t_{f}^{\prime
]$) to the evolution of the equivalent standard oscillator for modes of
wavenumber $k$, thereby obtaining the time evolution over the combined
radiation-dominated and inflationary eras. From the final densities -- again
simulated for a mixed ensemble with six sets of randomly-chosen initial phases
-- we are then able to calculate the mixed-ensemble deficit function $\xi(k)$.

\subsection{Retarded time for an inflationary phase}

The expression for the retarded time $t_{\mathrm{ret}}=t_{\mathrm{ret}}(t,k)$
arises \cite{CV13} by finding the solution for the time evolution $\psi
_{n_{r}}(q_{r},t)$ of the initial wave function $\psi_{n_{r}}(q_{r
,t_{i})=\Phi_{n_{r}}(q_{r})$ under a formal one-dimensional Schr\"{o}dinger
equation
\begin{equation}
i\frac{\partial\psi_{n_{r}}(q_{r},t)}{\partial t}=\left(  -\frac{1
{2m}\partial_{r}^{2}+\frac{1}{2}m\omega^{2}q_{r}^{2}\right)  \psi_{n_{r
}(q_{r},t)
\end{equation}
with Hamiltonian $\hat{H}_{r}(t)$ (equation (\ref{Ham})), wher
\begin{equation}
m\equiv a^{3}\ ,\ \ \ \omega\equiv k/a\ .
\end{equation}
The exact solution with $a\propto t^{1/2}$ was found in ref. \cite{CV13}. Here
we wish to find the solution with an inflating scale facto
\begin{equation}
a(t)=a_{f}e^{H(t-t_{f})}\ , \label{a_inf
\end{equation}
where $t_{f}$ is the time at which the inflationary phase begins (while ending
at $t_{f}^{\prime}$) and $H$ is assumed to be constant.

As we saw in ref. \cite{CV13}, we first need to find two solutions $f_{1}$ and
$f_{2}$ of the classical equatio
\begin{equation}
\ddot{f}+\frac{\dot{m}}{m}\dot{f}+\omega^{2}f=0~. \label{osc_cl
\end{equation}
Then we define a functio
\begin{equation}
g_{-}=\gamma_{1}f_{1}^{2}+\gamma_{2}f_{1}f_{2}+\gamma_{3}f_{2}^{2}~,
\label{g-
\end{equation}
where $\gamma_{1}$, $\gamma_{2}$, $\gamma_{3}$ are constants (denoted $c_{1}$,
$c_{2}$, $c_{3}$ in ref. \cite{CV13}), and two other derived functions
\begin{equation}
g_{0}=-\frac{m}{2}\dot{g}_{-}\ ,\ \ \ \ g_{+}=m^{2}\omega^{2}g_{-}-m\dot
{g}_{0}\ . \label{g0+
\end{equation}
These functions must satisfy the initial conditions
\begin{equation}
g_{-}(t_{f})=\frac{1}{m_{f}}\ ,\ \ \ \ g_{0}(t_{f})=0\ ,\ \ \ \ g_{+
(t_{f})=m_{f}\omega_{f}^{2}\ . \label{ics
\end{equation}

The retarded time interval $\Delta t_{\mathrm{ret}}(k)$ corresponding to the
standard time interval $t_{f}^{\prime}-t_{f}$ is then given by the integral
\begin{equation}
\Delta t_{\mathrm{ret}}(k)=\int_{t_{f}}^{t_{f}^{\prime}}\frac{dt
{m(t)g_{-}(t)}~. \label{tret
\end{equation}
(See ref. \cite{CV13} for a detailed derivation.)

For the scale factor (\ref{a_inf}) we have $\dot{m}/m=3H$ and $\omega
=ke^{-H(t-t_{f})}/a_{f}$. Equation (\ref{osc_cl}) then become
\begin{equation}
\ddot{f}+3H\dot{f}+\kappa^{2}e^{-2H(t-t_{f})}f=0~,
\end{equation}
where $\kappa=k/a_{f}$. We find the two solutions
\begin{align}
f_{1}  &  =\cos\left(  (\kappa/H)e^{-H(t-t_{f})}\right)  +(\kappa
/H)e^{-H(t-t_{f})}\sin\left(  (\kappa/H)e^{-H(t-t_{f})}\right)  \ ,\\
f_{2}  &  =\sin((\kappa/H)e^{-H(t-t_{f})})-(\kappa/H)e^{-H(t-t_{f})
\cos((\kappa/H)e^{-H(t-t_{f})})\ .
\end{align}

From (\ref{g-}) and (\ref{g0+}), together with the initial conditions
(\ref{ics}), we obtain the constants $\gamma_{1}$, $\gamma_{2}$, $\gamma_{3
$:
\begin{align}
\gamma_{1}  &  =\frac{1}{2k^{4}a_{f}}\left(  -H^{4}a_{f}^{2}\cos
(2k/Ha_{f})-2H^{3}ka_{f}\sin(2k/Ha_{f})+H^{2}(H^{2}a_{f}^{2}+2k^{2})\right)
\ ,\\
\gamma_{2}  &  =\frac{1}{k^{4}}\left(  2H^{3}k\cos(2k/Ha_{f})-Ha_{f
\sin(2k/Ha_{f})\right)  \ ,\\
\gamma_{3}  &  =\frac{1}{2k^{4}a_{f}}\left(  H^{4}a_{f}^{2}\cos(2k/Ha_{f
)+2H^{3}ka_{f}\sin(2k/Ha_{f})+H^{2}(H^{2}a_{f}^{2}+2k^{2})\right)  \ .
\end{align}
The expression (\ref{g-}) for $g_{-}$ is now fully determined.

For the purpose of obtaining the retarded time interval, the important
function is $mg_{-}$. Evaluating it explicitly, we find
\begin{align}
mg_{-}  &  =\left(  -\frac{1}{2\phi_{f}\phi^{3}}-\frac{2}{\phi^{2}}+\frac
{1}{2\phi_{f}\phi}\right)  \cos(2\phi-2\phi_{f})+\nonumber\\
&  \left(  \frac{1}{\phi^{3}}-\frac{1}{\phi_{f}\phi^{2}}-\frac{1}{\phi
}\right)  \sin(2\phi-2\phi_{f})+\nonumber\\
&  \left(  \frac{1}{2\phi_{f}\phi^{3}}+\frac{\phi_{f}}{\phi^{3}}+\frac
{1}{2\phi_{f}\phi}+\frac{\phi_{f}}{\phi}\right)  \ ,
\end{align}
wher
\begin{equation}
\phi\equiv(k/Ha_{f})e^{-H(t-t_{f})}\ .
\end{equation}

To evaluate the integral (\ref{tret}), we first change variables to $\phi$
where $d\phi=-H\phi dt$. The integrand become
\begin{equation}
-\frac{2\phi_{f}}{H}\frac{\phi^{2}}{(-1-4\phi_{f}\phi+\phi^{2})\cos
(2\phi-2\phi_{f})+(2\phi_{f}-2\phi-2\phi_{f}\phi^{2})\sin(2\phi-2\phi
_{f})+(1+2\phi_{f}^{2}+\phi^{2}+2\phi_{f}^{2}\phi^{2})}\ .
\end{equation}
We then use $\cos2x=\cos^{2}x-\sin^{2}x$, $\sin2x=2\sin x\cos x$ and we
introduce two new functions
\begin{align}
u  &  =-\sin(\phi-\phi_{f})+\phi\cos(\phi-\phi_{f})\ ,\\
v  &  =-\frac{1}{\phi_{f}}\sin(\phi-\phi_{f})+\frac{\phi}{\phi_{f}}\cos
(\phi-\phi_{f})-\phi\sin(\phi-\phi_{f})-\cos(\phi-\phi_{f})~.
\end{align}
The integrand can then be written as
\begin{equation}
-\frac{1}{\phi_{f}H}\frac{(du/d\phi)v-u(dv/d\phi)}{u^{2}+v^{2}}\ .
\end{equation}
An indefinite integral with respect to $\phi$ is given b
\begin{equation}
-\frac{1}{\phi_{f}H}\tan^{-1}(\frac{u}{v})\ .
\end{equation}
However, this is discontinuous at zeros of $v$. To proceed, the domain of
integration must be divided into subdomains and each time we cross a zero of
$v$ we must add $\pi a_{f}/k$ to the retarded time interval. (This requires
that we find the zeros of the function $v$, which is straightforward.)

\subsection{Robustness of the inverse-tangent{} deficit $\xi(k)$}

We now consider the effect of adding an inflationary phase. We take the
preceding radiation-dominated period to begin at $t_{i}=10^{-4}$ and end at
$t_{f}=10^{-2}$ just as before. We then take the inflationary phase to begin
at $t_{f}=10^{-2}$ and end at $t_{f}^{\prime}=t_{f}+0.05=0.06$, with an
inflationary Hubble constant $H=25$. The parameters have been chosen so as to
yield an interesting physical range and also to enable us to carry out the
numerical simulation in a reasonable amount of computer time. The chosen
values are not intended to have any particular cosmological
significance.\footnote{We use natural units with $\hslash=c=1$, so that time
has dimensions of an inverse mass. An initial time of $10^{-4}$ in our units
corresponds to $10^{-4}\hbar\sim10^{-37}\ \mathrm{s}$ in standard units.}

As shown in Figure 4, for these parameters the range of physical wavelengths
that we consider are mostly sub-Hubble at the beginning of inflation
($t=t_{f}$) and essentially all super-Hubble at the end of inflation
($t=t_{f}^{\prime}$). The simulation will then probe what happens when modes
exit the Hubble radius during inflation -- a key component of the standard
inflationary scenario

\begin{figure}
[ptb]
\begin{center}
\includegraphics[width=\textwidth]
{Figs_Robust_v1/Fig4.jpg
\caption{The top figure shows physical wavelengths as a function of $k$ at the
beginning of inflation ($t=t_{f}=10^{-2}$), in units of the Hubble radius. For
the range we consider, most of the modes are initially sub-Hubble. The bottom
figure shows physical wavelengths as a function of $k$ at the end of inflation
($t=t_{f}^{\prime}=0.06$), again in units of the Hubble radius. For the range
we consider, the final modes are essentially all super-Hubble.
\end{center}
\end{figure}

Furthermore, for this set of parameters the values of the retarded time
(plotted in Figure 5) are not so large as to prevent a numerical simulation in
an acceptable amount of computer time. It is noteworthy that as $k$ increases
the value of $\Delta t_{\mathrm{ret}}(k)$ quickly saturates

\begin{figure}
[ptb]
\begin{center}
\includegraphics[width=\textwidth]
{Figs_Robust_v1/Fig5.jpg
\caption{Retarded time interval $\Delta t_{\mathrm{ret}}(k)$ corresponding to
the lapse $t_{f}^{\prime}-t_{f}$ of standard cosmological time during the
inflationary phase, plotted as a function of wavenumber $k$.
\end{center}
\end{figure}

For this set of parameters, then, we numerically simulate the function
$\xi(k)$ for the combined radiation and inflationary eras, taking initial
wavefunctions (\ref{psi_i}) that are superpositions of $M$ energy states and
with the fixed initial nonequilibrium density (\ref{rho1i}). The simulation is
again carried out as described in ref. \cite{CV15}, plotting mixed-ensemble
curves $\xi=\xi(k)$ obtained by averaging the variances over six sets of
randomly-chosen initial phases, except that now the retarded time interval
(for the evolution of the equivalent oscillator) is increased by the value
$\Delta t_{\mathrm{ret}}(k)$ corresponding to the additional lapse
$t_{f}^{\prime}-t_{f}$ of standard cosmological time during the inflationary
phase. Our results for $M=4,6,9,12,16$ are shown in Figure 6. For each curve
in the figure we include a fit to the inverse-tangent function (\ref{numksi})

\begin{figure}
[ptb]
\begin{center}
\includegraphics[width=\textwidth]
{Figs_Robust_v1/Fig6_ksi_atanfit_july8.jpg
\caption{Mixed-ensemble curves $\xi(k)$ for the combined radiation-dominated
and inflationary eras, for $M=4,6,9,12,16$ modes and with the fixed initial
nonequilibrium density (\ref{rho1i}), with fits to the inverse-tangent
function (\ref{numksi}).
\end{center}
\end{figure}

For smaller $M$ we are able to integrate further in $k$-space since the
velocity field is less erratic for smaller $M$. In Figure 6 we show all of the
data that we were able to obtain to good accuracy in an acceptable amount of
computer time.

Despite the limited extent of our results in $k$-space for larger $M$, the
goodness of fit to the inverse-tangent function (\ref{numksi}) is clear
enough. Thus we may conclude that the inverse-tangent deficit (\ref{numksi})
is robustly valid under the addition of an inflationary phase.

\subsection{Dependence of the fitting coefficients on $M$}

Given the fits to the function (\ref{numksi}) for $M=4,6,9,12,16$, we may
study how the fitting coefficients $c_{1}$, $c_{2}$, $c_{3}$ vary with $M$.

Since we have generated data for all of the considered values of $M$ only up
to about $k=10\pi$, in order to compare like with like we consider it better
to omit the extra data at $k>10\pi$ for the case $M=4$. Thus, for $M=4$ we
truncate the curve at $k=10\pi$ before finding the fitting coefficients for
the inverse-tangent function (\ref{numksi}). With this understanding, the
resulting coefficients $c_{1}$, $c_{2}$, $c_{3}$ are shown in Table 2.

\begin{table}
\begin{center
\begin{tabular}
[c]{|c|c|c|c|}\hline
$M$ & $c_{1}$ & $c_{2}$ & $c_{3}$\\\hline
$4$ & $2.39$ & $4.01$ & $0.87$\\
$6$ & $1.72$ & $1.96$ & $0.91$\\
$9$ & $1.70$ & $0.96$ & $0.92$\\
$12$ & $1.58$ & $0.32$ & $0.99$\\
$16$ & $1.37$ & $0.25$ & $1.00$\\\hline
\end{tabular}
\end{center}
\caption{Fitting coefficients $c_{1}$, $c_{2}$, $c_{3}$ for varying
$M=4,6,9,12,16$.}
\label{Table2}
\end{table}

In Figure 7 we show how $c_{1}$ varies with $M$, together with a fitted curv
\begin{equation}
c_{1}=1.51+8.55e^{-{0.57M}}{\ .} \label{c1vM
\end{equation}
This has the same functional form (with different coefficients) as the fit
found in our previous simulations for the radiation-dominated phase only
\cite{CV15}. While the fit is not quite as good as before, our results are
consistent with the previous (approximately exponential) decay of $c_{1}$ with
$M$

\begin{figure}
[ptb]
\begin{center}
\includegraphics[width=0.9\textwidth]
{Figs_Robust_v1/Fig7_c1_expfit_july17.jpg
\caption{Plot of $c_{1}$ as a function of $M$, with a best-fit curve
(\ref{c1vM}).
\end{center}
\end{figure}

In Figure 8 we show how $c_{2}$ varies with $M$, together with a fitted curv
\begin{equation}
c_{2}=0.20+16.11e^{{-0.36M}}\ . \label{c2vM
\end{equation}
Again, this has the same functional form as the fit found in our previous
simulations \cite{CV15} and now the goodness of fit is comparable to that
found previously

\begin{figure}
[ptb]
\begin{center}
\includegraphics[width=0.9\textwidth]
{Figs_Robust_v1/Fig8_c2_expfit_july17.jpg
\caption{Plot of $c_{2}$ as a function of $M$, with a best-fit curve
(\ref{c2vM}).
\end{center}
\end{figure}

Finally, in Figure 9 we show how $c_{3}$ varies with $M$, together with a
fitted curv
\begin{equation}
c_{3}=\tan^{-1}{(0.15M+2.11)}-\pi/2+1.22\ . \label{c3vM
\end{equation}
Once again this has the same functional form as the fit found previously
\cite{CV15} and with a fit that is not quite as good as before

\begin{figure}
[ptb]
\begin{center}
\includegraphics[width=0.9\textwidth]
{Figs_Robust_v1/Fig9_c3_revised.jpg
\caption{Plot of $c_{3}$ as a function of $M$, with a best-fit curve
(\ref{c3vM}).
\end{center}
\end{figure}

To a first approximation, our results for $c_{1}$, $c_{2}$, $c_{3}$ as
functions of $M$ are consistent with the results found in ref. \cite{CV15} for
the radiation-dominated phase only. Thus, not only is the inverse-tangent fit
(\ref{numksi}) robustly valid under the addition of an inflationary phase, the
functional dependence of the fitting coefficients on $M$ is also approximately maintained.

\section{Conclusion}

We have shown that our prediction of an inverse-tangent power deficit function
$\xi(k)$ -- arising from quantum relaxation on expanding space -- is robust
under changes in the initial nonequilibrium distribution as well as under the
addition of an inflationary period to the end of the radiation-dominated
phase. In both cases the simulated deficit $\xi(k)$ remains an inverse-tangent
function of $k$. Furthermore, with the inflationary phase the dependence of
the fitting parameters $c_{1}$, $c_{2}$, $c_{3}$ on the number $M$ of
superposed pre-inflationary energy states is found to be comparable to the
dependence found previously. These results suggest that, for the assumed broad
class of initial conditions, the inverse-tangent function (\ref{numksi}) is
likely to be a rather general signature of quantum relaxation in the early
universe. It remains to be seen how well this prediction compares with the
data \cite{PVV15}.

There is clearly a limit, however, to the robustness of our results against
changes in the initial nonequilibrium distribution. As an extreme example, if
a field mode had an initial delta-function distribution $\rho(q_{1
,q_{2},t_{i})=\delta(q_{1}-q_{1}(t_{i}))\delta(q_{2}-q_{2}(t_{i}))$ the
corresponding theoretical ensemble would contain just one trajectory beginning
at $q_{1}(t_{i})$, $q_{2}(t_{i})$ and ending at $q_{1}(t_{f})$, $q_{2}(t_{f
)$. The nonequilibrium distribution at later times would still be a
delta-function, $\rho(q_{1},q_{2},t_{f})=\delta(q_{1}-q_{1}(t_{f
))\delta(q_{2}-q_{2}(t_{f}))$. The final variance would vanish and we would
have $\xi=0$ for that mode. This could in principle happen for a range of
modes or even for all modes, resulting in no primordial power at all. Clearly,
for relaxation considered over a given time interval, if the initial
distribution is sufficiently narrow the final function $\xi(k)$ could differ
considerably from our inverse-tangent result (\ref{numksi}). In our
simulations we have taken initial states that depart fairly mildly from
quantum equilibrium, and for these we have found a final inverse-tangent
deficit over a range of initial conditions. In this sense our results are
robust. But if the changes in the initial state are too extreme, then with a
fixed time interval our inverse-tangent prediction will necessarily fail. On
the other hand, if the considered time interval is not fixed, then even for
very narrow initial nonequilibria one might obtain results resembling ours if
only the modes are evolved over a sufficiently long cosmological time. We
leave a study of this last point for future work.

Some assumptions certainly need to made about initial conditions, otherwise it
is impossible to make predictions. In our simulations we have always
considered initial distributions $\rho(q_{1},q_{2},t_{i})$ of width smaller
than the width of $|\psi(q_{1},q_{2},t_{i})|^{2}$. This may be justified
partly on heuristic grounds: if we regard quantum noise as having a dynamical
origin, it is natural to assume initial conditions such that the initial state
has less noise (or a smaller statistical spread) than a conventional quantum
state. We also assume that $\rho(q_{1},q_{2},t_{i})$ is appropriately smooth,
in the sense of not possessing any significant fine-grained microstructure --
an assumption that is required to obtain relaxation in any time-reversal
invariant theory \cite{AV92,AV96,AV01,VW05}. Our assumed initial conditions
have been guided by simplicity and heuristic arguments. Their ultimate
justification rests on how well our predictions compare with data.

We should also mention a further caveat. We have restricted ourselves to
initial quantum states (at the beginning of pre-inflation) of the form
(\ref{psi_i}). These are equally-weighted superpositions of energy eigenstates
with randomly-chosen phases. One might ask if our results are also robust
under changes to more general initial quantum states. In fact, all previous
studies of relaxation have assumed such equally-weighted superpositions. We
leave the study of more general superpositions for future work.

There is a remaining gap in our scenario. We do not have a proper treatment of
the transition from pre-inflation to inflation. In our simulations, we regard
the behaviour of the free scalar field $\phi$ as representative of the
behaviour of whatever fields may have been present during pre-inflation. We
have not specified the relation between $\phi$ and the inflaton field. Our
simulations yield a correction $\xi(k)$ to the power spectrum of $\phi$ and we
simply assume that the same correction appears in the inflationary spectrum
\cite{AV10,CV13,CV15}. Adding an inflationary period to our simulations of
relaxation for $\phi$ is a step towards filling the gap in our model. However,
a proper understanding requires a full field-theoretical model of the
transition from pre-inflation to inflation, which may involve symmetry
breaking and associated field redefinitions. We hope to develop such a model
in future work, and to run the appropriate numerical simulations required to
obtain the exact predicted deficit function $\xi(k)$.

\textbf{Acknowledgements}. We are grateful to Murray Daw for kindly providing
us with extra computational resources on the Clemson University Palmetto
Cluster. This research was supported in part by the John Templeton Foundation
and by Clemson University.

redpajama_set_name: RedPajamaArXiv


Rendering of the New Community Center at 120 Jackson St.
A night in the middle of March marked the reboot of School Settlement Association's Capital Campaign to raise money for the New School Settlement Community Center. Support for this center is vital as surrounding elementary schools built in the mid-1900s lack indoor gymnasiums and auditoriums for children to play, engage, perform, and practice safely. The new center will feature: a state of the art auditorium-gymnasium, modern classrooms, a computer lab, and elder services.
As the Italian-American community was an intrinsic part of establishing the School Settlement in 1901, this reboot took the form of a dinner and discussion on how to create a permanent legacy exhibit celebrating the Italian American community's immigrant roots and the generational support for the School Settlement Association's past and future.
Dinner was held at the Brooklyn Kitchen (100 Frost Street) and curated from traditional recipes in the new SSA Cookbook. Brooklyn Kitchen owner Taylor Erkkinen collected the recipes and edited this cookbook fundraiser. Current representatives of the Italian-American community: Bamonte's Restaurant, Da Francesco, and Carmine & Sons Pizzeria, Restaurant and Sports Bar generously provided hors d'oeuvres that whet the appetite for the night's presentation and future fundraising that will broaden opportunity via a new community center.


text:
New European Region Update
by AGS — Published on Feb 14, 2022
Heroes of Arkesia,
We're blown away by the number of players that have joined us in Lost Ark since our launch on Friday. Arkesia is filled to the brim with eager players, so we're working as quickly as possible to set up an entirely new region of servers in Europe. Due to the game's architecture this is the only way to accommodate more players in Europe so it's a joint effort between Amazon Games and Smilegate RPG. Rest assured we are working 24/7 until it's live.
While we understand lengthy queue times may persist, we will need time to ensure everything is set up to be in top shape to help accommodate all players to get in game. We'll share an update on exact timings as soon as possible.
Please note that this will be a distinct new region (separated from Central Europe) without cross-region play availability. This also means that region-wide features, such as your Royal Crystal and Silver balances from Central Europe will not be accessible in the new European region. The new region will be ideal for players who have not yet created their character or haven't otherwise committed to stay on their existing server. If you plan to restart in the new region, you may wish to hold off on claiming any "per Account" items, such as the additional Founder's Pack Redemption, until you have created a character and are able to redeem in the new region.
To thank everyone, we also want to announce a launch celebration gift that Smilegate RPG and Amazon Games are granting to all players. The gift includes these items (all non-tradeable):
Vehicle Selection Chest (choice of either mount)
Terpeion
Terpeion of the Shadow
Midsummer Night's Dream Instrument Skin Selection Chest
Healing Battle Item Chest x10
Offensive Battle Item Chest x10
Legendary Rapport Selection Chest x3
Weekly Trade potions Pack x3
Phoenix Plume x20
We will make the gift available after the new region is up and running. Anyone who enters Arkesia from the time the gift is available through March 1st at 11:59pm PT (March 2nd at 8.59am CET) is eligible to receive it.
Thank you for your support and patience as we work to get everyone to their new home in Arkesia.
AGS ---