Body Shop Naples specializes in both full collision and minor collision repairs; we offer Full Collision repairs as you would expect from any auto body shop, but in addition we offer an express lane service for minor collision repairs. In our unique Express Repair Program we primarily repair and replace front and rear bumpers, headlight and tail light assemblies, and grilles. In these cases our customers' vehicles are still considered drivable so you will be able to come in for an estimate and get your vehicle booked in for repairs within two weeks or less.
Our mission is to get your car repaired and back on the road safely and quickly with minimal interruption to you. Whether you are going through your insurance company or not, Body Shop Naples can assist you in getting your vehicle looking good again and back on the road. Our focus is on customer satisfaction and as such, we have created a 'family friendly environment' at our locations. Our facility is equipped with a customer friendly lounge, equipped with clean, comfortable furniture, a flat panel television, and complimentary wireless Internet and the coffee is always on. Alternatively, you can drop off your vehicle in the morning and pick it up at the end of the day. For Full Collision Repairs we can help arrange for your rental car needs as we have relationships with major rental car companies.
Body Shop Naples prides itself on our qualified appraisers and technicians. They are always available on site to walk you through the repair process to ensure you are apprised of the status of your vehicle from beginning to end regardless of the severity of the damage.


Women often feel cramps before their period begins. You may have cramps a week or two weeks before your period, or just a few days in advance.
Menstrual back pain can be an occasional or regular monthly occurrence for many women. Learn why back ache may accompany your period.
04.02.2013 · How to get rid of cramps, stop cramps, bad menstrual cramps when on your period, relieving cramps, tips on how to relieve cramps, dealing with PMS.
Back pain creates a great deal of hassle as well as hindrance to the normal way of living of an individual. There are a variety of back pain triggers, but the 2 most typical causes associated with discs are disc injury and also degenerative disc. Disc deterioration leads to water material loss that tightens the gap between 2 vertebrae. This can trigger pinching of a nerve and succeeding pain. Protruding discs are usually puzzled with fractured discs. While the former problem is normal, the later problem could be major. Discs may bulge throughout the day as they lug the body weight, as well as return to normal at evening when we rest. Burst discs are ruined discs brought on by leakage of jelly like material called center pulposus.
Cramps Back Pain Period 2019 5 out of 5 based on 209 ratings.


In this article, I'm un-packing a new way to do new-year's resolutions. I became quickly frustrated with having a resolution that lasted at most through March, and I decided there had to be a better way. In Part 1, I talked about the importance of knowing your own playbook and how that provides the insight and awareness that we need to take control over our behaviors. The reflection will provide the insight to fuel the practical steps in this article.
What helps me most is to start with an end-goal. This is the second question I asked in the previous article – where do you want to be. For me, I've found patterns between the 7 areas, so where I wanted to be was actually only two or three things. And that's what I'd like to ask you to do – choose 1 to 3 goals of where you want to be.
I'd like to encourage you to be as specific as you can be. The more specific you can be, the easier it is to figure out how to get there. So instead of saying you want to eat better, your goal might be to eat 3 vegetables per day.
Once you have your specific end-goal, write it down. I have a daily journal that I use to keep me on track. At the beginning of each year, I have a place in the front of the journal where I write down my new year's resolutions. This way, every time I consult my calendar, I'm reminded of my specific goals.
Then, identify some milestones that you can celebrate. Change is hard, and I've found it's a lot easier (and sustainable) when I can see my own progress. I also celebrate the milestones – I give myself a reward for each milestone I reach. So for example, if my goal is to eat 3 vegetables per day, Milestone 1 would be eating 1 vegetable per day for 30 days, Milestone 2 would be eating 2 vegetables for 30 days, etc. If it's an especially tough goal, I try to make more milestones.
Finally, I come up with a game plan. I take all those milestones and map them out over a year. I pay special attention to times that would make accomplishing a milestone difficult. For example, if I'm going to be traveling or spending time away from my kitchen, I'll know not to aim for eating too many vegetables.
I also pay special attention to ways that can help me accomplish my milestones. For example, joining a CSA (community supported agriculture – it's partnering with a local farm and getting weekly produce) would help meet the vegetable goal. I also add these to my calendar.
Over the years, I have found that starting with a specific goal helps me stay focused. Peppering my journey through the year with rewardable milestones keeps me encouraged and I see myself making measurable progress. Finally, seasoning the year with ways to help me accomplish my milestones gives me the extra boost I need when I'm in the throes of the year.
So, how do you accomplish your new year's resolutions? I'd love to hear what methods work for you! Leave me a comment below – I'm looking forward to hearing from you.


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How To Pronounce Saoirse Ronan, Which Is Not As Difficult As It Looks
By Katherine Cusumano
Tristan Fewings/Getty Images Entertainment/Getty Images
Irish actress Saoirse Ronan started earning attention with her role as Keira Knightley's younger sister in Atonement, steadily racking up credits including The Lovely Bones, The Grand Budapest Hotel, and now Brooklyn over the past 10 years. She's an obvious and worthy choice for the Golden Globe nomination for Best Actress, an award that has gone to the likes of Ingrid Bergman, Meryl Streep, Jessica Lange, and Charlize Theron over the course of its history. Yet despite her acclaim, somehow those three consecutive vowels in Saoirse trip up everyone from fans to fellow stars. Here's how you pronounce Saoirse Ronan's name, for everyone out there (ahem, Dennis Quaid) who seems to have a tough time with it.
Just as the name "Siobhan" is pronounced "Shuh-von," different letter combinations in Saoirse's name make syllables that might sound difficult to the anglo-centric ear. And, contrary to how Dennis Quaid pronounced it when he announced her nomination for the Best Actress Golden Globe, it is not "Shee-sha." No, Saoirse is more like "SEER-sheh," emphasis on the first syllable and a slight accent on the second. This silly YouTube video ("Saoirse Ronan, I believe you have stolen my heart," the narrator says) does a far better job of breaking down the pronunciation.
nationalpost on YouTube
Ronan explained the pronunciation to Us Weekly back in May: "I pronounce it Sir-sha like inertia," she said. And when Quaid mispronounced the name on the Golden Globes nomination announcement Thursday morning, Twitter leapt up in Ronan's defense with some incredulous responses. The mishap was likened, of course, to John Travolta's infamous botching of Idina Menzel's name at the 2014 Oscars, when he referred to her as "Adele Dazeem." Vanity Fair critic Richard Lawson picked up on another parallel — Elizabeth Moss's (seemingly very straightforward!) name being mispronounced as "Elizabeth Moths."
Correct pronunciation of the name of a famous and talented actress is important. It matters enough to take the five minutes out before presenting a nomination to learn how to say it properly. And just as Menzel sought her revenge the following year at the 2015 Oscars — she welcomed Travolta to the stage as "Glom Gazingo," Travolta admitting that he might have deserved that — Ronan may have her moment, too. We're watching you, Dennis Kay-Vood.
Image: Fox Searchlight

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: How to write a custom Transformer in MLlib? I want to write a custom Transformer for a pipeline in spark 2.0 in scala. So far it is not really clear for me what the copy or transformSchema methods should return. Is it correct that they return a null? https://github.com/SupunS/play-ground/blob/master/test.spark.client_2/src/main/java/CustomTransformer.java for copy?
As the Transformer extends PipelineStage I conclude, that a fit calls the transformSchema method. Do I understand correctly that transformSchema is similar to sk-learns fit?
As my Transformer should join the dataset with a (very small) second dataset I want to store that one in the serialized pipeline as well. How should I store this in the transformer to properly work with the pipelines serialization mechanism?
How would a simple transformer look like which computes the mean for a single column and fills the nan values + persists this value?
@SerialVersionUID(serialVersionUID) // TODO store ibanList in copy + persist
    class Preprocessor2(someValue: Dataset[SomeOtherValues]) extends Transformer {

      def transform(df: Dataset[MyClass]): DataFrame = {

      }

      override def copy(extra: ParamMap): Transformer = {
      }

      override def transformSchema(schema: StructType): StructType = {
        schema
      }
    }

A: transformSchema should return the schema which is expected after applying Transformer. Example:

*

*If transfomer adds column of IntegerType, and output column name is foo:
import org.apache.spark.sql.types._

override def transformSchema(schema: StructType): StructType = {
   schema.add(StructField("foo", IntegerType))
}

So if the schema is not changed for the dataset as only a name value is filled for mean imputation I should return the original case class as the schema?

It is not possible in Spark SQL (and MLlib, too) since a Dataset is immutable once created. You can only add or "replace" (which is add followed by drop operations) columns.

A: First of all, I'm not sure you want a Transformer per se (or UnaryTransformer as @LostInOverflow suggested in the answer) as you said:

How would a simple transformer look like which computes the mean for a single column and fills the nan values + persists this value?

For me, it's as if you wanted to apply a aggregate function (aka aggregation) and "join" it with all the columns to produce the final value or NaN.
It looks like you want a groupBy to do aggregation for mean and then join which could be a window aggregation, too.
Anyway, I'd start with a UnaryTransformer which would solve the first issue in your question:

So far it is not really clear for me what the copy or transformSchema methods should return. Is it correct that they return a null?

See the complete project spark-mllib-custom-transformer at GitHub in which I implemented the UnaryTransformer to toUpperCase a string column which for the UnaryTransformer looks as follows:
import org.apache.spark.ml.UnaryTransformer
import org.apache.spark.ml.util.Identifiable
import org.apache.spark.sql.types.{DataType, StringType}

class UpperTransformer(override val uid: String)
  extends UnaryTransformer[String, String, UpperTransformer] {

  def this() = this(Identifiable.randomUID("upp"))

  override protected def createTransformFunc: String => String = {
    _.toUpperCase
  }

  override protected def outputDataType: DataType = StringType
}

redpajama_set_name: RedPajamaStackExchange


text:
CHRIS BOURNEA
Lady Wrestler Doc
'Lady Wrestler' At WrestleCon Convention
I'm excited to attend my first WrestleCon Convention, which will be held in Orlando, Fla., March 30-April 1. This is an opportunity to meet people, network and get the word out about my soon-to-be-released documentary, "Lady Wrestler: The Amazing, Untold Story of African-American Women in the Ring."
WrestleCon is like the pro wrestling version of Comic-Con: an event that brings together fans from around the world with the "characters" they know and love. This year's WrestleCon will feature a variety of events, from photo ops and autograph sessions with celebrity wrestlers to actual wrestling matches.
I'll be attending the WrestleCon Women's Wrestle SuperShow on Saturday, April 2. I thought it made sense to sit ringside at this event, since the "Lady Wrestler" documentary is all about the history of women in this sport.
Before embarking on making "Lady Wrestler," I knew next to nothing about professional wrestling, other than watching it on cable TV when I was a kid. I'm looking forward to immersing myself in this fascinating world while attending WrestleCon. I'll post updates about the experience and as many photos as possible.
More information about the "Lady Wrestler" documentary is available at Ladywrestlermovie.com.
This Is Why Black Women Wrestlers Are Missing From History Books
'Lady Wrestler' Is About Succeeding Against the Odds
Film Festivals Pay Unexpected Dividends
My Cannes Film Festival Experience
© 2023 The Journalist. All rights reserved.


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Q: Compiling CUPS: undefined reference to `dnssdDeregisterAllPrinters' I'm trying to build CUPS 1.7.3 on Ubuntu Server 14.04. configure didn't produce any errors, but make dies with:
Making all in ppdc...
Making all in scheduler...
Linking cupsd...
dirsvc.o: In function `cupsdStopBrowsing':
/root/cups-source/cups-1.7.3/scheduler/dirsvc.c:262: undefined reference to `dnssdDeregisterAllPrinters'
dirsvc.o: In function `cupsdStartBrowsing':
/root/cups-source/cups-1.7.3/scheduler/dirsvc.c:244: undefined reference to `dnssdRegisterAllPrinters'
collect2: error: ld returned 1 exit status
make[1]: *** [cupsd] Error 1
make: *** [all] Error 1

I couldn't find anything useful on Google, other than some refrences to zeroconf and avahi. I tried installing avahi-daemon and avahi-autoipd, but same error.

A: apt-get install libavahi-cil-dev libavahi-client-dev libavahi-common-dev

seems to solve the problem. Not sure if all are required, but make completed without errors, so hopefully this helps someone else.


I've been friends with Carol for at least 20 years now. I have few.......well...... no other friends for that length of time.
Her most recent gardening efforts start with her front garden of which I could show many pictures but I'll restrict myself to a very pretty basket of petunias and her newest addition, a leaking birdbath she turned into a lovely hardscape.
Carol and her husband Martin have a garden that I enjoy though it is very different from ours. For one thing their garden is nicely viewed from a large picture window within the house. It's like having a huge painting on the wall. Walking into their house, this is the view.
The garden includes a dry creek bed accented along the way; simple and clean.
I wish my delphiniums looked this good.
And I love her red hollyhocks.
One of her latest additions, and doing well, is this clematis. Isn't this a great looking fence Martin built?
You can view more of his artwork here.
Carol has some shady garden areas including two rhododendrons.
It was from the plant on the right that I received my hellebore starts.
This is not Carol's first garden. She's had a few. For the first time in this garden though, she's growing a few veggies.
I have to mention one other thing about my friend Carol besides her lovely garden. She is an animal lover extraordinaire. She adopted two, TWO, abandoned cats not long ago and a deaf (don't get any ideas, this dog is VERY alert) border collie, Angel.
Carol and Martin enjoy wildlife, have multiple bird feeders in their garden and are knowledgeable about wildlife in general. Actually they are knowledgeable on a multitude of topics and if they don't have the answer to a question they probably own a book that does.
I guess my best wish for you would be to have a friend like my friend Carol.
Great post Victoria - loved the garden full of flowers and the artwork too. Everything! Those red Hollyhocks are a beautiful shade and I've tried and wanted Delphiniums for years now. Ask her what the secret is.
Thanks for sharing your friends place with us.
Your friend has a beautiful garden. Love the birdbath with the sedum in it. Lots of interesting things to look at in her yard.
They have a beautiful garden. I love when artists incorporate their art into the garden. It makes it so personal. Thanks for sharing.
They seem like really cool people! I love all of his artwork! Oneday I want really big windows so I can look out into my garden....sigh...oneday, oneday!
Your friend's yard and garden is beautiful indeed.
Another lovely garden. They are all so unique, like the people that create them.
I really like the what she did with the birdbath, very peaceful looking.
Carol does have a wonderful garden. How very special to have a friend for 20 years.
What a wonderful tribute to your friendship Victoria. She sounds like a gem. We'd all be lucky to have such a friend. What a beautiful garden she has too. It's great you could share it with us. I'm envious of her delphiniums as well ~ they are incredible. I think it gets too hot here for their liking? I had better luck growing them in WY. That bumblebee is almost red like the hollyhocks ~ or maybe that's the lighting??
Can you imagine having such a view of your garden from inside the house at all times? I bet it's a bit of a blessing and a curse, since you get to keep an eye on it, but also can't let garden chores slide. Beautiful garden and a nice story about a long friendship. Cheers to fellow animal lovers.


text:
Bar Management
Scott Suchman
The 8 O'Clock Light Show contains cacao, kola nut, astragalus, ginseng, guarana seed, and cinnamon to treat fatigue.
How Medicinal Cocktails Built a Restaurant's Buzz
Tiger Fork in Washington, D.C., helped build its restaurant's buzz with its Traditional Chinese Medicine-inspired cocktail menu.
March 2019 Laura D'Alessandro
The concept of a medicinal cocktail is nothing new, but the Traditional Chinese Medicine cocktail menu at Tiger Fork in Washington, D.C., goes way beyond the hot toddy. In fact, there's not a hot toddy in sight. Instead guests find beverages that mix liquor and traditional medicinal herbs.
Owners Greg Algie and Nathan Beauchamp opened Tiger Fork in 2017 after a trip to Hong Kong alerted Algie to the need. Originally the concept was Chinese takeout and delivery, which D.C. sorely lacks. But after visiting Chinatowns in other U.S. cities, the idea expanded to a full Hong Kong kitchen.
"We knew we wanted to incorporate Chinese medicine in the concept from the very beginning," says Ian Fletcher, Tiger Fork's beverage director. "We were at a bar during a research trip that had stylized itself as sort of an apothecary. It was then that we had a sort of eureka moment."
The cocktail menu is an homage to Hong Kong's world-renowned cocktail scene, celebrated with a nod to traditional Chinese culture—Traditional Chinese Medicine, or TCM, is practiced around the world.
"For me, it is very important that we recognize that we have a lot to learn and that we respect the traditions," Algie says. "Balancing the medicinal attributes and creating a tasty cocktail takes a lot of collaboration with Nathan, Ian, traditional Chinese medicinal advisors, chefs and bartenders to make sure we create an enjoyable drink."
The drinks are not necessarily geared toward pairing with Tiger Fork's cuisine. Fletcher says the medicinal ingredients themselves are "unsavory," and the team spent a long time working to make them palatable.
"We use a lot of acids and citrus to disguise the flavors of herbs and roots, which just sort of naturally works with Asian cuisine," he says. "Not to say that the TCM cocktails do not pair with our food. ... We have other drinks on menu that are designed to complement our food. The TCM concept is the base of our bar concept and has definitely been a draw for the restaurant as a whole."
While a menu like this takes education, the results have been rewarding, and the restaurant's buzz has helped.
"We've been open now for a while, and there have been several articles about our concept. This has helped a lot, as people kind of know what to expect when they show up now," he says. "We also have a lot of great regulars that bring in friends and pretty much do all the explaining for staff."
Tableware/Tabletop
Hollowick, Inc.
100 Fairgrounds Drive
Quality table lighting and cooking fuel products that enhance the dining (more)
Haynes Lubricants
24142 Detroit Road
Manufacturers of sanitary food-grade lubricants for food service equipment.


UT Dallas retains and disposes all official records in accordance with records and information management policies and procedures. If you have any questions about UT Dallas Records Management, please contact the Records Retention Officer (RecordsManagement@utdallas.edu / 972.883.4111).
Submit a Request for Disposal of State Records (PDF [Portable Document Format File] ) form to the Records Retention Officer. Refer to the Records Retention Schedule to complete the form.
The Records Retention Officer will notify you once your request is approved.
Dispose of your records (see Secured Shredding Service).
Submit a Request for Records Storage (PDF [Portable Document Format File] ) form to the Records Retention Officer. Refer to the Records Retention Schedule to complete the form.
Schedule a time to meet with Records Retention Officer to have your records properly inventoried before being moved into the Records Management storage space.
Arrange to have your records moved into the Records Management storage space.
UT Dallas utilizes a Secured Shredding Service to dispose of large quantities of University records that have reached retention and have been approved by the Records Retention Officer for disposal. The Secured Shredding Service offers departments a choice between three different sized shred bins, which are placed in a secured location at the request of the department. Bins are emptied on-site monthly by a third party vendor. Contact Records Management (RecordsManagement@utdallas.edu) for more information on our Secured Shredding Service.


text:
Home / News / NIGERIA WILL COMPETE WITH THE WORLD, IF THEY START TO COOPERATE WITH IGBO — MURRAY BRUCE
NIGERIA WILL COMPETE WITH THE WORLD, IF THEY START TO COOPERATE WITH IGBO — MURRAY BRUCE
by Giftedfavour.com on Sunday, May 16, 2021 in News
The founder of Sliverbird group, Ben Murray Bruce said that during Nigerian Civil War, Igbos produced all the weapons they used to fight the war, but Nigeria did not manufacture even a gun.
After the civil war, Nigeria still could not produce even toothpick as a country, but Igbos are still producing cars, clothes, shoes etc.
An average Igbo man believes that Nigeria is suppressing his talents, and that is why they want a separate nation where they can reach their potentials.
He added that the day Nigeria starts to cooperate with Igbo man will be the day Nigeria will compete with the rest of the world.
By Giftedfavour.com - Sunday, May 16, 2021


When buying scrap metals they are different factors that should be considered including the type of allow the metals are made of. This is because there are numerous types of alloys of aluminium and brass. If such metals are valued the same way, then it means that the buyer may not get the best deal. Thus by considering the type of alloy the scrap metals are made of, the buyer can ensure that they get them at the best price that matches their worth. This consideration is also useful in ensuring that the alloy in the scrap metals does not produce unpleasant qualities such as fragility in a finished product.
Another important thing to consider before the purchase of scrap metals is the actual market price. The actual market prices for scrap metals can be found on commodities markets where they are published. On the other hand, a good number of scrap metals traders expect their customers to take their price for the reason that they assume customers don't have enough knowledge concerning their prices. Thus, the knowledge of these prices is important in enabling the buyer to estimate how much the metals are to cost them, and also in helping them get utmost valuable from the transaction.
Another important factor to be considered is the fee that is associated with buying the scrap metals before ordering is made. This majorly because sales of scrap metals can sometimes come with hidden fee like standard handling, transportation and other container rentals too. As a result, when given quotation for prices of scrap metals, buyers are required to ask about hidden and associated fee to gauge viability for the deal.
It is also extremely important for one to consider the company or the scrap metal dealer from whom to make the purchase, before actually doing it. Considerations about the dealer or company include their personality, their record, reputation, and whether they offer credit. The record of a scrap dealer could be useful in ensuring that the buyer gets high quality metals, which result in the manufacture of equally quality finished goods. You can get all such information from https://scrapmetalprices-usa.com/copper.
Finally, it is important for a scrap metal buyer to consider how the metals are to be weighed, and also if their dealer uses certified scales to weigh them. Scrap buyers are required to insist on pricing basing on weight measured in pounds to ascertain that the scrap metals weight is accurate and precise. Furthermore, if the buyer finds out that the dealer intends to use uncertified scales to weigh the scrap metals, they should avoid buying the metals from them. This is mostly because of the vulnerability in programming and alteration so as to read whatever the dealer wishes. Learn more about scrap copper here: https://www.reuters.com/article/us-usa-copper/china-scrap-buying-low-demand-may-spur-u-s-copper-stockpiles-above-13-year-high-idUSKBN1A20L1.


text:
Filter Wines (14 results)
France Alsace Burgundy Corsica Loire
Catherine & Pierre Breton Clos Canarelli Domaine Comte Abbatucci Domaine Giudicelli Domaine Robert-Denogent Kuentz-Bas Thierry Germain
Cabernet Franc Chardonnay Chenin Blanc Corsican White Blend Muscat Niellucciu Vermentino Blend
$100+ $51-$100 $41-$50
Biodynamic (certified)
2018 Vin de France Blanc "Faustine"
Domaine Comte Abbatucci France | Corsica | Vin de France
In the granite hills above the capital city of Ajaccio, white wines are among the island's most delicate.
2018 Vin de France Blanc "Tarra di Sognu"
Clos Canarelli France | Corsica | Vin de France
Experience Bonifacio, one of Corsica's historic wine regions, through Canarelli's epic, age-worthy biancu.
Select Quantity 1 2 3 4 5 6
2018 Vin de France Blanc "Général de la Révolution"
A nod to the island's rich history of viticulture, the Général is simply a stunning bottle of white wine.
Select Quantity 1 2 3 4 5 6 7 8 9
2018 Vin de France Blanc "Diplomate d'Empire"
Rich, exotic, and appealing—a monument to the grandeur of the forgotten Corsican varietals.
Select Quantity 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
2018 Saumur-Champigny "Terres Chaudes"
Thierry Germain France | Loire | Saumur-Champigny
April Club Rouge Selection
Select Quantity 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
2018 Saumur Blanc "L'Échelier"
Thierry Germain France | Loire | Saumur
This chiseled Chenin Blanc comes from 70-year-old vines planted on an ancient limestone slope. Burgundian-like in character from its time spent in barrel, the laser-like acidity will become even more enticing with some age.
Select Quantity 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
2018 Saumur Blanc "Le Clos du Moulin"
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2018 Saumur Blanc "Clos Romans"
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2018 Pouilly-Fuissé "La Croix Vieilles Vignes"
Domaine Robert-Denogent France | Burgundy | Pouilly-Fuissé
Farming incredibly old vines in the region's top terroirs, brothers Antoine and Nico at Robert-Denogent are stars of the Maconnais.
2018 Pouilly-Fuissé "Cuvée Claude Denogent Vieilles Vignes" Les Cras
Select Quantity 1 2 3 4 5 6 7 8 9 10 11 12
2018 Patrimonio Rouge
Domaine Giudicelli France | Corsica | Patrimonio
Muriel Giudicelli's Patrimonio rouge is elegant, deep, bursting with ripe black fruits, silky smooth, and offering great length.
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2018 Muscat Grand Cru "Pfersigberg Trois Châteaux"
Kuentz-Bas France | Alsace | Alsace Grand Cru
Kuentz-Bas vinifies a glorious dry Muscat from grand cru Pfersigberg, an ample and fleshy white scented of ripe citrus, tropical flowers, and exotic fruits.
Select Quantity 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2018 Corse Figari Blanc
Clos Canarelli France | Corsica | Corse Figari
What about real-deal vanilla aromatics? I'm talking cured Madagascar bourbon seed, lightly crushed, delicate and discreet.
Select Quantity 1 2 3 4 5 6 7 8 9 10
2018 Bourgueil "Les Perrières"
Catherine & Pierre Breton France | Loire | Bourgueil
There isn't a spot in the world better suited for Cabernet Franc, and their old vines produce the raw material for one of the best reds in the Loire valley.


text:
George Woodbridge
Gustav von Wangenheim
Douglas Walton
Douglas Walton was born John Douglas Duder in Toronto, Canada on the 16th of October, 1910.
Percy Bysshe Shelley (Douglas Walton) and Lord Byron (Gavin Gordon) encourage Mary Shelley (Elsa Lanchester) to continue her tale in Bride of Frankenstein (Universal 1935)
His acting career began on the stage and frequently saw him portray urbane English gentlemen. Making the leap into movie work at the dawn of the sound era, he took uncredited roles in movies such as Always Goodbye (1931), Dr Jekyll and Mr Hyde (1931, as a student) and Scarface (1932).
More substantial fare followed with the likes of The Count of Monte Cristo and Charlie Chan in London (both 1934), but it was the following year's Bride of Frankenstein that would make the biggest impression on horror movie fans. As Percy Bysshe Shelley in the prologue sequence, he helped to ramp up the tension as Mary Shelley (Elsa Lanchester) prepared to reveal the next part of her terrifying tale. The same year, he appeared in the Charles Laughton / Clark Gable retelling of Mutiny on the Bounty.
Douglas Walton as the young blond student in Dr Jekyll and Mr Hyde (Paramount 1931)
His later work included a small part in Bette Davis film noir The Letter (1940), Murder, My Sweet (1944) and The Picture of Dorian Gray (1945). He passed away on the 15th of November, 1961.


text:
Games and Empathy
People put themselves at a distance from whatever stories we hear, unless extraordinary measures are taken by the storyteller. Our inabilities to conjure the emotional and physical enormities within a news story are ingrained as a defense mechanism, and it's one we sorely need.
Empathy Engines
Elizabeth Sampat
In the previous post, I wrote about why journalism needs to find new ways — beyond personal relevance and the utility of information — to make people care about the news. To do so, I argued, we need to encourage curiosity and empathy through the stories we tell.
But as Elizabeth Sampat noted, doing so requires "extraordinary measures" because people instinctively shield themselves from emotional transference. Reading the news with dispassion and seeking out stories that confirm, rather than challenge, our worldview are not signs of our moral failure; they're acts of self-preservation.
How can we invite people to close the distance they put between themselves and others' stories? I believe games are one way to do so.
Games shrink the complexity of our world, creating a safer arena to put our selves into. They give permission for us to reconnect with our sense of curiosity. They engage our imagination.
Games lend themselves to being a dialogue between the designer and the player. "Players speak to you in the breaths and pauses between the constraints you've created. This collaboration is precisely how something incredibly personal can become resonant and universal," Ms Sampat says.
They can also fulfill the journalistic mission of helping people understand the world. Games may not be the best medium to record facts and events as they happen, but by making their rules visible, they teach us to critically examine the constraints and biases of real-world systems. They equip us to ask the right questions, instead of feeding us the answers.
Even Bret Victor, who argued strongly against the use of interactivity in information software design, saw games as an exception to his argument:
It must be mentioned that there is a radically alternative approach for information software—games. Playing is essentially learning through structured manipulation—exploration and practice instead of pedagogic presentation.
Magic Ink
Bret Victor
Until recently, there have been many barriers to using games for journalism. The historical development of games have given it a "stigma of immaturity [that] is tough to overcome," says Mr Victor.
Compared to traditional news articles, games were expensive and difficult to produce because newsrooms lacked the relevant skills and technology. It was also simply outside of the boundaries of what newsrooms thought they should be doing, given the belief that journalism consists primarily of objectively recording facts and events.
But all this is starting to change. Games sit squarely within mainstream culture and directly compete with news for people's attention. Newsrooms have hired developers and designers, and therefore now have many of the skills needed to create digital games. Journalism's crisis is prompting a re-examination of what newsrooms should and shouldn't be doing and opening up possibilities for innovation.
There are people already doing this work. One example is developer Nicky Case, who has created emotionally powerful and personal games, as well as explanatory games that expose the working of systems. He has also made a tool to help others construct interactive simulations. Here's a model of the ad-supported news industry, made using the tool.
Games as a medium for journalism is becoming more important precisely because some of the language and techniques of game design are increasingly being used in other fields under the guise of behavioural science and 'gamification'. For example, when Uber 'nudges' its drivers' behaviour through the design of its app:
When asked about the badges he earns while driving for Uber, Mr. Weber practically gushed. "I've got currently 12 excellent-service and nine great-conversation badges," he said in an interview in early March. "It tells me where I'm at."
How Uber Uses Psychological Tricks to Push Its Drivers' Buttons
Noam Scheiber
As more of our lives are spent within such deliberately designed systems, I believe there is an increasing need for journalism that exposes system constraints and enables cultural understanding. In other words, games.
I am also interested in exploring the role that journalists can play in giving voice to others through games. Many emotionally resonant games (Depression Quest, That Dragon, Cancer, Coming Out Simulator 2014) are personal and autobiographical, but I believe they don't have to be. One of the pillars of journalism, after all, is the journalist's ability to truthfully and fairly tell other people's stories.
Games have a unique power. It has so far mainly been used for entertainment. Some game designers have used it to tell personal stories. But I believe the conditions are ripe for using games to explain what is happening in the world, to author biographies instead of autobiographies, and to help close the emotional distance between people and the stories they hear.
Games changes how we see topics, it changes our perceptions about those people in topics, and it changes ourselves. We change as people through games, because we're involved, and we're playing, and we're learning as we do so.
Gaming for Understanding
Brenda Romero
This is important if journalism is to help foster greater emotional, rather than rational, understanding. The goal is not to paralyse readers through affective empathy. But, in rupturing their shields and showing a different view of the world, to create room for growth and the possibility of creative breakthrough. As Nick Sousanis put it so elegantly in Unflattening:
Unflattening, Nick Sousanis. Harvard University Press
Return to the Fellowship section
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© Robin Kwong 2018


Fish House Burned Down Reward - - - 5 messages. Showing 1 through 5.
Enough money has been raised to replace the items lost in the fire thanks to private donations. A new house has been donated by Ice Castle.
LSF would like the help raise the reward the Sheriff's department is offering. We are only about $380 away from our goal of $500. Please click on the link and donate as little as $5. Lets get this young man some justice!
We are at $250... We are half way to our goal!
$295 is the total right now.
I am sure there are many who appreciate your efforts!


It is open since 1994 in the customs building complex of Ermoupoli, in the harbor. The gallery hosts temporary exhibitions and part of the collection of the Gallery with works of modern Greek artists like Alekos Fasianos. Telephone 22810 80918.
Welcome to the Art Gallery of Cyclades page of Greece Vacation Search! Here you will find all the information you will need for your summer vacations on Art Gallery of Cyclades of Syros.


If you're looking for a cold beer any day or any time, then this bar will do it as they currently provide over 50 brands of beers! Why not just go wild and try a new one perhaps? They also serve up great meals such as Beer-Braised Lamb Philly, Rube Waddell Burger and the Big Dog Burger.


Since its launch, we've had bittersweet feelings about the Amazon Mobile app for Tablets. The app shows promise as a tablet-friendly shopping solution, but until now has suffered an extremely limited compatibility, only working with tablets running 4.1 and up and carrying a 1280x800 resolution.
An update to the app today, however, has changed all that. Along with a few bug fixes, the update (to version 5.50.1010 for those keeping count at home) brings support for devices in 7" or 10" form factors, with a variety of resolutions, and loosened OS requirements.


text:
AEROSMITH – ROCKS ON
Legends. Icons. Idols. These are the words used to describe those rare bands that have been adored for a lifetime and immortalized as distinct creators of rock and roll. But what these reverent words are missing is the notion of now. How do you reconcile a generation-spanning word like icon with the quick beat of the present? Aerosmith does it. The band members are legends, icons and idols, dynamic in the present; as cool and innovative now as they were thirty years ago. They are a phenomenon, a force of nature, trail-blazing, unstoppable, showing no signs of slowing down.Unique even among the select handful of rock bands who are still active after their Rock and Roll Hall of Fame induction, Aerosmith has sold over 100 million albums.
Think for a second about how big a number that is and how many people have heard their music. Huge! Steven Tyler on vocals, Joe Perry and Brad Whitford on guitars, Tom Hamilton on bass, and Joey Kramer on drums. They've outdone the trends and fads of rock and roll to become one of the most powerful and electrifying forces in popular music.
Rewind for a minute to the early '70s, when the phrase "sex, drugs and rock & roll" was a rebellious teenager. Enter Aerosmith with a sexy swagger and thrusts ofmetal, glam and boogie woogie. Tyler's lyrics laced with double entendres and witty humor perfectly complimented by the entire group cool urban charisma. Beyond driving rock and roll tunes, Aerosmith created quintessential power ballads such as Dream On. This dual skill set gave the band a string of gold and platinum albums, including Get Your Wings, Toys in the Attic and Rocks.
The early '80s were rockier times, with Perry and Whitford temporarily leaving the Aero fold to pursue solo projects. The guitarists returned in 1984 and soon after, Aerosmith was back in the saddle again. And they have been on top of the charts ever since. Albums like Permanent Vacation, Pump, Get a Grip and Nine Lives, Just Push Play, and their latest release, the blues-inspired 'Honkin' on Bobo', have all been huge successes. And the killer videos – a driving force of the video medium, these Boston rockers led the look, style and attitude of the '80s MTV generation. Videos for Dude Looks Like a Lady, Livin' On the Edge and Crazy (starring Liv) are solid MTV classics. And later, with videos like Pink and Jaded, Aerosmith continued to cut the edge.
Always a step ahead of the pack, Aerosmith's Just Push Play is the first album to be produced by band members Steven Tyler and Joe Perry (along with Mark Hudson and Marti Frederiksen). The unforgettable pop melodies and bone-shaking rock riffs that are Just Push Play sent Aerosmith even further on their path to musical immortality.
'Honkin' on Bobo' was released in March 2004, and as one Rolling Stone review put it: "Aerosmith don't have much time for pain on Honkin' on Bobo. The songs are mostly about gettin' some, then gettin' outta there -- Dixon's "I'm Ready," Bo Diddley's "Road Runner" -- and the attack is heavy Sixties shindig: snarling guitars, thunderclap drumming, Steven Tyler's 3-D snake hiss and widescreen yowl. Bobo is really a combined tribute: to the originators of the blues' core repertoire and the explosive, electric inventions of 1960s British bands such as the Yardbirds, Mayall's Bluesbreakers and the Peter Green-era Fleetwood Mac." (David Fricke, Rolling Stone)
With such an unstoppable passion for creating great music, a unique creative vision and an unyielding appreciation for their fans, there are no limits to what the future holds for Aerosmith.
Band Sites:
Steven Tyler - http://StevenTyler.com
Joe Perry - http://JoePerry.com
Joey Kramer - http://JoeyKramer.com
Co-Founder Ray Tabano - http://CrazyRaymond.net
Property Of Mug
Wings Logo Keychain


text:
Maria Ho (born March 6, 1983 in Taipei, Taiwan) is a Taiwanese-American poker player and television host/commentator. One of the top ranked female poker players in the world, and a Women in Poker Hall of Fame inductee, she has over $5,000,000 in live tournament winnings.

Ho's live tournament poker record includes 80 WSOP cashes, 8 World Series of Poker final tables (including WSOPC and WSOPE final tables), 14 World Poker Tour cashes, 4 WPT final tables and 1 WPT title), and numerous additional final tables on the professional poker circuit.

Outside of poker, she has been seen on many primetime television shows; making it to "Hollywood Week" on season 3 of American Idol, competing  on the fifteenth season of The Amazing Race and appearing as a celebrity guest on Deal or No Deal in January 2019.

Early life
Fluent in Mandarin and born into a traditional Taiwanese family, Maria grew up just outside Los Angeles in Arcadia, California, after her family moved from Taiwan to the United States when she was four-years-old. Maria's older sister is a media personality and psychologist Judy Ho, who is known for hosting the CBS syndicated talk show Face The Truth.

Ho started playing poker in college. She was drawn to the psychology and competitive spirit of the game and soon went from playing games with college friends to playing limit cash games at nearby Indian casinos. When Maria graduated from UCSD in 2005, with a major in communications and a minor in law, she had gone from playing low limits to high-stakes cash games and had grown her poker bankroll to the point that she felt confident to embark on a career as a professional poker player.

Career

World Series of Poker

Ho's first major tournament success came at the 2007 World Series of Poker where she was the last woman remaining in the Championship Event, placing 38th out of 6,358 players and earning a $237,865 payday. She repeated this accomplishment in 2014, when she came in 77th place out of 6,683 players. Her 27th place "Last Woman Standing" finish at the 2011 World Series of Poker Europe Main Event along with a 2017 6th place final table finish makes Maria the only player to ever hold the title Last Woman Standing four times over and at both the WSOP and WSOPE Main Events.

At the 2012 World Series of Poker, Ho was the Most-Cashing Female of the series, with six individual tournament cashes. She repeated this feat at the 2014 WSOP with a total of eight cashes.

World Poker Tour
In March 2019, for a second year in a row, she final tabled the LA Poker Classic $25,000 High Roller tournament and earned 1st place, earning her second highest live tournament score of $276,690. The following month she made the 6-handed TV final table of the WPT Seminole Hard Rock Poker Showdown Main Event and placed 3rd for $344,960, which was the second highest cash of her tournament career.

Host and Commentator
In 2013, Ho joined the Heartland Poker Tour season 9 broadcast team as a co-host and strategic commentator. She was the first female in history to be hired to a poker television broadcast as the resident strategic commentator, and remained with the production for two years.

Ho has compiled an impressive body of work as a television presenter, hosting and commentating on CBS Sports The Final Table, ESPN's official coverage of the World Series of Poker, Amazon eSports Mobile Masters Invitational series, and she regularly contributes to the PokerGO streaming platform as a strategic commentator many PokerGO broadcasts including the High Roller Triple Crown, US Poker Open, Super High Roller Bowl, and the newly acquired World Series of Poker Main Event.

In 2019, Ho won the Global Poker Award for Broadcaster of the Year. She has also contributed her expertise to several print publications, and authored a chapter in the book Winning Women of Poker: Secret Strategies Revealed.

Awards and accolades
Notable accolades include a 2019 Global Poker Award for Broadcaster of the Year (and a 2020 Global Poker Award nomination for the same category), being inducted into the Women In Poker Hall of Fame the very first year she was eligible and nominated (in 2018), three consecutive nominations as Favorite Female Poker Player by the Bluff Reader's Choice Awards, and on seasons 9 and 10 of the World Poker Tour she was named as one of WPT's "Ones to Watch".

Invitationals
Ho has received invitations to play in various types of games all over the world. In 2008, she traveled to Hong Kong to play in the World Mahjong Tour, going head to head with various Chinese and Taiwanese celebrities and professional Mahjong players.

For two consecutive years, she participated in the Inaugural World Team Poker Invitational, as a member of Team China, helping her team secure a 1st Place victory in 2010.

In 2016, Ho was named one of 12 Team Managers (for Team LA Sunsets) in the inaugural season of the Global Poker League, notably drafting Emmy winning actor Aaron Paul as one of her Wild Card picks, as well as coaching her team to the championship match.

YouTube
On February 22, a video featuring Maria Ho was published on the YouTube Channel "The Try Guys", quickly getting recognition with over 5 million views.

References

External links
 Maria Ho's Official site
 Maria Ho Interview

1983 births
American poker players
Female poker players
Living people
American sportspeople of Taiwanese descent
Sportspeople from Taipei
The Amazing Race (American TV series) contestants
People from Arcadia, California
Taiwanese emigrants to the United States

redpajama_set_name: RedPajamaWikipedia


text:
Taxation in Namibia
Title: Taxation in Namibia
Subject: Namibia, Cost of living in Namibia, Economy of Namibia, LGBT history in Namibia, Community policing in Namibia
Collection: Economy of Namibia
This is an overview of taxes charged to individuals and companies in Namibia.
Value Added Tax 2
Personal income tax is applicable to total taxable income of an Individual and all individuals are taxed at progressive marginal rates over a series of income brackets. The tax year runs from 1 March to 28 February.
Tax rates for the 2010/2011 to 2012/2013 tax years were as follows:[1]
Taxable amount
Rates of tax
Where the taxable amount does not exceed N$ 40 000 0%
between N$ 40 001 and N$ 80 000 27% of the amount by which the taxable amount exceeds N$ 40 000
between N$ 80 001 and N$ 200 000 N$ 10 800 + 32% of the amount by which the taxable amount exceeds N$ 80 000
between N$ 200 001 and N$ 750 000 N$ 49200 + 34% of the amount by which the taxable amount exceeds N$ 200 000
over N$ 750 000 N$ 236 200 + 37% of the amount by which the taxable amount exceeds N$ 750 000
Tax rates proposed for the 2013/2014 tax year are as follows:[2]
between N$ 50 001 and N$ 100 000 18% of the amount by which the taxable amount exceeds N$ 50 000
between N$ 100 001 and N$ 300 000 N$ 9 000 + 25% of the amount by which the taxable amount exceeds N$ 100 000
between N$ 300 001 and N$ 500 000 N$ 59 000 + 28% of the amount by which the taxable amount exceeds N$ 200 000
between N$ 500 001 and N$ 800 000 N$ 115 000 + 30% of the amount by which the taxable amount exceeds N$ 200 000
between N$ 800 001 and N$ 1 500 000 N$ 205 000 + 32% of the amount by which the taxable amount exceeds N$ 200 000
over N$ 1 500 000 N$ 429 000 + 37% of the amount by which the taxable amount exceeds N$ 750 000
Income tax is typically withheld by the employer.
Individuals are responsible for submitting a tax return form to the Receiver of Revenue once a year. Individual taxpayers are categorised into three groups each submitting a different colour tax return. There are brown, blue and yellow forms. [3]
Since 2014 taxpayers can use an online wizard to help prepare the blue tax form[4]
A 15% Value added tax (VAT) is applicable to almost every commodity. Basic commodities like sugar, bread etc. are exempted from VAT.[5]
Cost of Living in Namibia
Economy of Namibia
^ PAYE12 Volume 18 published by The Ministry of Finance in Namibia
^ PWC Namibia 2013 Tax Reference and Rate Card
^ http://www.namtax.com/what-colour-tax-reform-do-i-need-blue-brown-or-yellow
^ http://www.namtax.com
Taxation in Africa
Mayotte / Réunion (France)
Saint Helena / Ascension Island / Tristan da Cunha (United Kingdom)
South Africa, Zambia, Botswana, Zimbabwe, Angola
Uranium, Economy of South Africa, Tin, Diamond, Namibia
Taxation in South Africa
South Africa, Religion, Economy of South Africa, Politics, Export
Taxation in Tanzania
Religion, Export, Tanzania, Tax resistance, Import
United States, United Kingdom, Real estate, Bible, Inheritance tax
Namibia, Bank, Economy of Namibia, Bank Windhoek, First National Bank (South Africa)
LGBT history in Namibia
Namibia, History of Namibia, Apartheid, Regions of Namibia, Politics of Namibia
Community policing in Namibia
Namibia, United States Department of Justice, History of Namibia, Apartheid, Regions of Namibia


text:
Q: Browser Session testing with Selenium WebDriver I have following scenario to automate :

*

*User Logs in to a website. Navigates to a certain page on website

*Save the url for that page.

*Close browser

*Open the browser again and navigate to the saved url.

*User should be able to see the page without logging in.

I can automate first 3 steps. But when I open browser again in step 4, a new session is started and my user sees log in page.
I believe the web driver browser is in incognito mode. So session cookie is not stored.
Is there any way to automate this scenario using selenium web driver?

A: It's because every time when you invoke browser, selenium opens a new browser profile..so your cookies will be lost..
You can inject cookies for the second time..
Cookie ck = new Cookie("name", "value");
driver.manage().addCookie(ck);

Or you can use same browser profile for driver..
FirefoxBinary binary = new FirefoxBinary();
File firefoxProfileFolder = new File("/Users/xxx/work/xxx/selenium/src/test/resources/firefoxprofile");
FirefoxProfile profile = new FirefoxProfile(firefoxProfileFolder);
webDriver driver= new FirefoxDriver(binary, profile);

A: You have to quit the webdriver before launching the saved url.
At 3rd step write driver.quit(); and at 4th step write:
driver.get("<saved_url>");


Yet another class act by Mr. Beau Jangles and Harkaway Daisy and this time a gorgeous filly, Brightwater Thistle. I would love to keep this gal as she reminds me of Treasure whom I lost years ago, with her predominantly black markings and slightly askew blaze. She will be as tall as her dam with those long legs and looks to be homozygous for tobiano judging by the ink spots on her side. However this is never a guarantee and she could still only have of copy of tobiano. She has that sweet head of her dam, Daisy the feather like her sire, Beau and the great back end like both her parents have. She will make a head stopping mare when mature and sure to make you smile from ear to ear. If you want to be noticed then this gal will certainly draw the crowds!
the two are a pair.
15 weeks and a very nice filly that will make someone proud to own her!


This entry was posted in Amazon, Best Selling Author, Bestselling Series, Books, Contemporary Romance, Free ebook, Historical Romance, Medieval, Mystery, New York Times Bestselling Author, Paranormal Romance, Romance Books, Romantic Picks, USA Today Bestselling Author, Women's Fiction and tagged books, contemporary romance, cozy mystery, D.G. Swank, ebook, entertainment, Kathleen Brooks, Lindsay Townsend, Paranormal Romance, R P Dahlke, Romance, romance novels, romance readers, Romantic Suspense. Bookmark the permalink.


This tutorial is related to my DIY remote operated switch kit. If you have come to this page from a search engine, please visit this page first.
Before trying this experiment, I strongly recommend you to learn about relays. It can be dangerous and lead to serious accident if you don't know how to connect a device operating at 220V on to this remote operated switch.
Visit this page to learn about relays.
The following picture depicts how an appliance operating at 220V is connected to relay.
In this tutorial, I am going to show you how a 60W bulb operating at 220V can be connected to the remote operated DIY kit.
Step 1: Break one of the wires that connects to the bulb and the 220V line.
Step 2: Connect extra wires to the broken points.
Step 3: Wound the connected joints with black tape(insulate the connection) so that you don't touch on that point and get a shock. You should do this!
Step 4: Now connect the two wires to pin P and pin NO of 3-pin screw terminal. You know that the screw terminal is connected to the relay.
Step 5: Connect a 9V power supply to the kit and use a general remote control to operate your appliance.
Video 1– Operating with IR transmitter. You can make your own infrared transmitter using NE555. Get project details from buildcircuit.com. Check out this tutorial also.
Video 2– Operating the kit with a TV remote control.
Video 3– Operating the kit with remote control.


text:
\section{Introduction}

Inflationary spacetimes are known to be past-incomplete \cite{Borde:2001nh}.  This indicates that such spacetimes must have a past boundary and raises the question of what determined the initial conditions at that boundary.  Even though it may not be essential for observational predictions of inflationary models, this is an important question of principle, and without resolving it the inflationary cosmology remains incomplete.  Perhaps the most promising approach to this problem is based on quantum cosmology, which suggests that a spatially compact universe can spontaneously nucleate out of `nothing', where `nothing' refers to a state with no classical space, time and matter \cite{Vilenkin:1982de,Hartle:1983ai,Linde:1983mx,Rubakov:1984bh,Vilenkin:1984wp,Zeldovich:1984vk}.

In quantum cosmology the universe is described by a wave function $\Psi(g,\phi)$, which is defined on the space of all possible 3-geometries $(g)$ and all matter field configurations $(\phi)$, called superspace.  The role of the Schr\"{o}dinger equation for $\Psi$ is played by the Wheeler-DeWitt equation \cite{DeWitt:1967yk}
\beq
{\cal H}\Psi = 0,
\label{WDW1}
\end{eqnarray}
where ${\cal H}$ is the Hamiltonian operator.  This is a functional differential equation in superspace.

In ordinary quantum mechanics, the wave function of a system is found by solving the Schr\"{o}dinger equation with boundary conditions determined by the physical setup external to the system.  But since there is nothing external to the universe, it appears that the boundary conditions for the Wheeler-DeWitt equation should be postulated as an independent physical law.  Several possible forms of this law have been discussed in the literature; the most developed proposals are the Hartle-Hawking and the tunneling boundary conditions.\footnote{Alternative boundary conditions have been introduced by DeWitt's \cite{DeWitt:1967yk} and Linde \cite{Linde:1983mx}.  These proposals, however, have been discussed only in the context of one-dimensional minisuperspace models, and no attempt has been made so far to extend them to full superspace.}

The tunneling boundary condition has been discussed in detail in Refs.~\cite{Vilenkin:1986cy,Vilenkin:1987kf,Vilenkin:1994rn}.  Roughly, it requires that $\psi$ should include only outgoing waves at the boundary of superspace, except for the part of the boundary corresponding to vanishing 3-geometries.  This is supplemented by the regularity condition, requiring that $\psi$ remains finite everywhere, including the boundaries of superspace,
\beq
\abs{\Psi(g,\phi)}<\infty.
\label{regularity}
\end{eqnarray}
Thus, the probability flux enters superspace through 3-geometries of vanishing size and leaves it through the rest of the boundary, corresponding to singular or infinitely large universes.  The resulting wave function can be interpreted as describing a universe originating at zero size, that is, from `nothing'.  It was conjectured in \cite{Vilenkin:1984wp} that the same wave function can be expressed as a path integral over Lorentzian histories interpolating between a vanishing 3-geometry and a given configuration in superspace,
\begin{equation}
\Psi_T=\int_\emptyset^{(g,\phi)} {\cal D} g {\cal D} \phi \, e^{iS},
\label{psiT}
\end{equation}
where $S$ is the action.  However, the equivalence of the two definitions has not yet been generally demonstrated.

The Hartle-Hawking (HH) wave function \cite{Hartle:1983ai} is defined as a path integral over compact Euclidean `histories' bounded by given 3-geometry and matter field configuration,
\begin{equation}
\Psi_{HH}=\int^{(g,\phi)} {\cal D} g {\cal D} \phi \, e^{-S_E},
\label{psiHH}
\end{equation}
where $S_E$ is the Euclidean action obtained by the standard Wick rotation $t\to -i\tau$.  This wave function has also been interpreted as describing quantum nucleation from nothing.  The gravitational part of the Euclidean action $S_E$ is unbounded from below, and as it stands the integral (\ref{psiHH}) is divergent.  One can attempt to fix the problem by additional contour rotations, extending the path integral to complex metrics \cite{Halliwell:1988ik, Halliwell:1989dy}.  However, the space of complex metrics is very large, and no obvious choice of integration contour suggests itself as the preferred one.

This is where things stood until the last year, when Feldbrugge, Lehners and Turok (FLT) reinvigorated the field with a new approach to Lorentzian quantum cosmology \cite{Feldbrugge:2017kzv}.  Working in minisuperspace framework, they showed that the path integrals (\ref{psiT}), (\ref{psiHH}) can be rigorously defined with the aid of the Picard-Lefschetz theory.  They first applied this method to de Sitter minisuperspace model and found that in this case the Euclidean path integral cannot be made convergent by any deformation of the lapse integration contour, while the Lorentzian path integral is well defined and gives the tunneling wave function, as it was claimed in \cite{Vilenkin:1984wp,Vilenkin:1994rn}.  (See Refs.~\cite{Halliwell:1988ik, Halliwell:1989dy, Brown:1990iv} for related earlier work.)  In the following papers \cite{Feldbrugge:2017fcc,Feldbrugge:2018gin} FLT considered perturbative minisuperspace, with the gravitational wave field $\phi$ added as a small perturbation.  Here, their results for the tunneling wave function were far less reassuring.  They found that this wave function predicts a runaway instability, where the probability of quantum fluctuations of the field $\phi$ grows with their amplitude.  Similar claims about instability of the tunneling proposal have also been made in the earlier literature \cite{Halliwell:1989dy}.

FLT work has led Diaz Dorronsoro {\it et al.} \cite{DiazDorronsoro:2017hti,DiazDorronsoro:2018wro} to further develop the HH proposal.  They studied de Sitter plus scalar field and Bianchi-IX models and showed that for specific choices of the lapse integration contour in the complex plane the wave function is well defined and exhibits the qualitative behavior expected of $\Psi_{HH}$.%
\footnote{
Dispute about the behavior of these wave functions beyond perturbation theory is still ongoing~\cite{Feldbrugge:2017mbc,Feldbrugge:2018gin,DiazDorronsoro:2018wro}, but here we focus exclusively on perturbative superspace.
}
In our view, however, the basic criticism against this approach still remains: the HH proposal is incomplete without a choice of a complex integration contour in the path integral (\ref{psiHH}).  Some general requirements to this contour have been given in Ref.~\cite{Halliwell:1989dy}, but it is not clear that they can always be satisfied or what contour should be used in models admitting a number of choices that satisfy the requirements.%

In the present paper we focus mostly on the path integral formulation of the tunneling proposal.  We show that the field fluctuations in the wave function (\ref{psiT}) are well behaved if the action $S$ is supplemented with a suitable boundary term.  In the next section we review the calculation of $\Psi_T$ using the tunneling boundary conditions in perturbative superspace and give an alternative formulation of the boundary conditions, which is more suitable for our purposes here.
In Section 3 we introduce into the action a boundary term, which is appropriate for these boundary conditions, and show that the resulting path integral coincides with the wave function obtained using the tunneling boundary conditions.  We also propose a physical interpretation of the boundary term in terms of the initial scalar field wave function in a tunneling universe.  Our conclusions are summarized in Section 4.

In the main text of the paper we consider a massive conformally coupled scalar field.  The case of a minimally coupled field, which in the massless case is equivalent to that of gravitational waves, is discussed in the Appendix.  Throughout this paper, we use the reduced Planck units: $8 \pi G = 1$.

\section{Tunneling boundary conditions}
\label{sec:wavefunction}

\subsection{The model}

We consider a de Sitter minisuperspace model with a conformally coupled massive scalar field,
where the metric is assumed to be homogeneous, isotropic and closed:
\beq
 d s^2 = a(\eta)^2 ( -N^2 d \eta^2 + d \Omega^2_3).
 \label{metric}
\end{eqnarray}
Here, $N$ is the lapse function, $a$ is the scale factor, $\eta$ is the conformal time, and $d\Omega_3^2$ is the metric on a unit 3-sphere.
In this section the lapse function is irrelevant and is set to be unity.

The action for this model is given by
\beq
S=\int \sqrt{-{g^{(4)}}} \, d^4 x \left( \frac{R}{2}- 3 H^2 \right) + S_m
+S_B ,
\label{action}
\\
S_m = \int \sqrt{-g^{(4)}} \, d^4 x \left[ - \frac{1}{2}(\nabla\phi)^2-\frac{1}{2}m^2\phi^2 -\frac{\xi}{2}R\phi^2\right],
\end{eqnarray}
where $g^{(4)}$ is the determinant of the metric, $H={\rm const}$ is the de Sitter expansion rate, $\xi = 1/6$ is the conformal coupling, $S_m$ is the matter part of the action, and $S_B$ is the boundary term.
The boundary term is not relevant in this section and will be specified in Sec.~\ref{sec:PI}.
The case of a minimally coupled field (i.e., $\xi = 0$) is discussed in the Appendix.

We expand the field $\phi$ as
\beq
\phi(x,t)=\frac{1}{a(t)} \sum \chi_n(t)Q_n(x),
\end{eqnarray}
\beq
\int Q_n Q_{n'} d\Omega_3 = \delta_{n n'},
\end{eqnarray}
where $Q_{nlm}(x)$ are suitably normalized spherical harmonics and we have suppressed the indices $l,m$ for brevity.
The superspace of this model is an infinite-dimensional space $\{a,\chi_n\}$.
The wave function of the Universe obeys the Wheeler-DeWitt (WDW) equation:
\beq
 \left[ \frac{\hbar^2}{24 \pi^2} \frac{\partial^2}{\partial a^2} - 6\pi^2 V(a) - \sum_n {\cal H}_n \right] \Psi (a, \chi_n) = 0,
 \label{WDW}
\end{eqnarray}
where
\beq
 V(a) = a^2 - H^2 a^4
 \label{Va}
 \\
 {\cal H}_n \equiv \frac{\hbar^2}{2} \frac{\partial^2}{\partial \chi_n^2} - \frac12 \omega_n^2 (a) \chi_n^2
 \label{H_n}
 \\
 \omega_n^2(a)=n^2 + m^2 a^2
 \label{omega_n}
\end{eqnarray}
with $n=1,2,...$.  In this paper we disregard the ambiguity of factor ordering.

With the modes $\chi_n$ treated as small perturbations, a solution of Eq.~(\ref{WDW}) can be expressed as a superposition of terms of the form \cite{Halliwell:1984eu,Wada:1986uy, Vachaspati:1988as}
\beq
 \Psi (a, \chi_n) = A \exp \left[ - \frac{12\pi^2}{\hbar} S(a) - \frac{1}{2\hbar} \sum_n R_n (a) \chi_n^2 \right],
 \label{wavefunction}
\end{eqnarray}
where $A$ is a normalization constant.  Substituting this in (\ref{WDW}), we neglect terms ${\cal O}(\chi_n^4)$.  We also
use the WKB approximation for $S(a)$ and neglect terms ${\cal O}(\hbar)$.
Then the WDW equation is rewritten as
\beq
 \left( \frac{dS}{da}\right)^2 - V(a) = 0,
 \label{EoM:Sa}
 \\
 \left( \frac{dS}{da} \right) \left( \frac{dR_n}{da} \right) - R_n^2 + \omega_n^2 (a) = 0.
 \label{EoMSn}
\end{eqnarray}

\subsection{Tunneling boundary conditions}

The wave function has different behavior in the classically allowed $(V(a)<0)$ and classically forbidden $(V(a)>0)$ regions.
For the tunneling wave function, we require that $\Psi$ includes only an outgoing wave in $a$ at large $a$.
Thus, for $V (a) < 0$ the wave function should be given by Eq.~(\ref{wavefunction}) with
\beq
 S(a) = i  \int_{a_*}^{a} \sqrt{-V(a')} d a' + C ,
 \label{Sa}
\end{eqnarray}
where $a_*=H^{-1}$ is the classical turning point defined by $V(a_*) = 0$ and $C={\rm const}$.

In the under-barrier region $V(a)>0$, the wave function can be expressed as
\beq
\Psi(a,\chi_n)
&=&A_+ \exp\left[-12\pi^2 S^+(a)-\frac{1}{2} \sum_n R_n^+(a)\chi_n^2\right]
\nonumber \\
&&+A_- \exp\left[- 12\pi^2 S^-(a)-\frac{1}{2} \sum_n R_n^-(a)\chi_n^2\right],
\label{psi}
\end{eqnarray}
where
\beq
 S^\pm(a) = \mp \int_{a}^{a_*} \sqrt{V(a')} d a' + C .
 \label{Spm}
\end{eqnarray}
The $A_+$ and $A_-$ terms correspond respectively to decreasing and growing wave functions.
We have chosen the integration constant $C$ in Eqs.~(\ref{Sa}),(\ref{Spm}) to be the same, so that $S(a_*)=S^\pm(a_*)$.   With this choice the coefficients $A$ and $A_\pm$, which can be determined by the WKB connection formulas, have comparable magnitude, $A_+\sim A_- \sim A$.  Their precise form, which was found in Ref.~\cite{Vilenkin:1984wp}, will not be important for our discussion here.

For $a<a_*$ it will be convenient to introduce a Euclidean conformal time variable $\tau$ via
\beq
 \frac{da}{d \tau} \equiv
 \left\{
 \bea{ll}
  \sqrt{V(a)} ~~~~{\rm for}~~ \tau < \tau_*
 \vspace{0.3cm}\\
 - \sqrt{V(a)}  ~~~~{\rm for}~~ \tau_* < \tau
 \end{array}
 \right.,
 \label{dadeta}
\end{eqnarray}
where the threshold $\tau_*$ is defined by $a (\tau_*) = a_*$.
This can be solved as
\beq
a(\tau)= (H\cosh \tau)^{-1},
\label{atau}
\end{eqnarray}
where the turning point $a_*$ corresponds to $\tau_*=0$, and $a=0$ corresponds to ${\tau} \to \pm\infty$.
This scale factor describes a Euclidean 4-sphere, which is an analytic continuation of de Sitter spacetime.
$a(\tau)$ in Eq.~(\ref{atau}) is an even function of $\tau$, so each value of $a<a_*$ corresponds to two values $\tau_\pm$ with $\tau_+(a)=-\tau_-(a)$.  We shall set $\tau_+(a)<0$.

It follows from Eqs.~(\ref{Spm}) and (\ref{dadeta}) that
\beq
 \frac{d S^\pm}{d \tau} = V(\tau) .
\end{eqnarray}
Then we can set
\beq
S^\pm = \int_{-\infty}^{\tau_\pm} V(\tau)d\tau.
\label{Spmtau}
\end{eqnarray}
This corresponds to setting the integration constant $C$ in (\ref{Spm}) to
\beq
C=\int_{-\infty}^{\tau_*} V(\tau)d\tau =  \int_{0}^{a_*} \sqrt{V(a')} d a' .
\label{C}
\end{eqnarray}
The actions $S_-$ $(S_+)$ then correspond to histories that do (do not) traverse the mid-section $a_*$ of the Euclidean 4-sphere as they go from $a=0$ to a given value $a$.

We now turn to Eq.~(\ref{EoMSn}) for the functions $R_n^\pm(a)$:
\beq
 \left( \frac{dS^\pm}{da} \right) \left( \frac{dR_n^\pm}{da} \right) =\left(R_n^\pm\right)^2-\omega_n^2,
\label{Riccati}
\end{eqnarray}
or
\beq
 \frac{dR_n^\pm}{d \tau}=\left(R_n^\pm\right)^2-\omega_n^2 (\tau).
\label{Riccati2}
\end{eqnarray}
The matching conditions at $a=a_*$ require that $R_n^+(\tau_*)=R_n^-(\tau_*)$ \cite{Vachaspati:1988as,Hong:2003pe}.
Since the functions $R_n^\pm$ satisfy a first-order differential equation of the same form and have the same value at $\tau=\tau_*$, they can be represented by a single function $R_n(\tau)$ with $\tau$ taken to be $\tau^+(a)$ $(\tau^-(a))$ for $R^+_n$ $(R^-_n)$.

Eq.~(\ref{Riccati2}) is a Riccati equation.  It can be reduced to a linear equation by the substitution
\beq
 R_n(\tau) = - \frac{1}{\nu_n} \frac{d \nu_n}{d \tau},
\label{R_npm}
\end{eqnarray}
where the mode functions $\nu_n(\tau)$ satisfy
\beq
 \frac{d^2 \nu_n}{d \tau^2} - \omega_n^2 \nu_n =0.
\label{nueq}
\end{eqnarray}

To impose the regularity condition (\ref{regularity}), we require that
\beq
{\rm Re} R_n^\pm (a)>0.
\label{regularity2}
\end{eqnarray}
This ensures that $|\Psi|$ decreases as the amplitudes $\chi_n$ are increased, so that scalar field fluctuations are suppressed.
Strictly speaking, (\ref{regularity}) does not follow from (\ref{regularity2}), since our approximation breaks down at large values of $\chi_n$, but this seems the best one can do in a perturbative superspace model.  The condition (\ref{regularity2}) is non-local, in the sense that the functions $R_n^\pm(a)$ depend on the form of the potential $V(a)$ everywhere under the barrier.  We will now show that it can be replaced by equivalent local boundary conditions for $\nu_n$ at $\tau\to -\infty$.

It has been shown in \cite{Hong:2003pe} that the condition (\ref{regularity2}) is satisfied for $R_n^+(a)$ at $a<a_*$ and for $R_n(a)$ in the classically allowed range $a>a_*$, provided that it is satisfied at the turning point $a=a_*$. However, this is not automatic for $R_n^-(a)$ under the barrier, and the regularity condition gets violated at small $a$, unless we adopt a special choice of boundary conditions at $a\to 0$.  Specifically, it was shown in \cite{Hong:2003pe} that the regularity condition is satisfied by $R_n^-$ everywhere under the barrier if it is satisfied at $a\to 0$, or $\tau\to \infty$.  (Here we choose the branch $\tau^-(a)>0$ appropriate for the functions $R_n^-(\tau)$.)

To explore the behavior of the mode functions $\nu_n(\tau)$ at $a \to 0$ (or $\tau\to \pm\infty$), we can replace $\omega_n^2 \approx n^2$ in Eq.~(\ref{nueq}).  Then the solution is
\beq
\nu_n (\tau)\approx A_n e^{- n \tau}+B_n e^{n \tau},
\label{nusolution}
\end{eqnarray}
and
\beq
 R_n(\tau) \approx n \frac{A_n-B_n e^{ 2 n \tau}}{A_n+B_n e^{ 2 n \tau}}.
\end{eqnarray}
It is now easy to see that $R_n (\tau \to \infty) = -n <0$, unless we set $B_n=0$, or $\nu_n (\tau \to \infty)\propto \exp(-n \tau)$.
This corresponds to the boundary condition
\beq
 \frac{d\nu_n}{d \tau} = - n \nu_n ~~~ (\tau \to  \infty).
\label{bc-}
\end{eqnarray}
Note that for a massless field the solutions (\ref{nusolution}) are exact in the entire range $-\infty<\tau<\infty$. In this case $R_n^\pm(a)=R_n(a)=n$ and the $\chi_n$- and $a$-dependent parts of the wave function factorize -- as they should for a conformally invariant field.

To find the boundary conditions for $\nu_n$ at $\tau\to -\infty$, we note that since Eq.~(\ref{nueq}) is symmetric with respect to the replacement $\tau\to -\tau$, the mode function $\nu_n(\tau)$ can be expressed in terms of a symmetric function $g_{sn}(\tau)$ and an antisymmetric function $g_{an}(\tau)$ as
\beq
\nu_n(\tau)=A_n \left[g_{sn}(\tau)-g_{an}(\tau)\right] +B_n\left[g_{sn}(\tau)+g_{an}(\tau)\right],
\label{nu_n sym}
\end{eqnarray}
where $g_{sn}(-\tau)=g_{sn}(\tau)$, $g_{an}(-\tau)=-g_{an}(\tau)$, and $g_{sn}(\tau\to\infty)\approx \cosh(n\tau)$, $g_{an}(\tau\to\infty)\approx \sinh (n\tau)$.  It then follows from (\ref{nu_n sym}) that for $\tau\to -\infty$
\beq
 \nu_n (\tau) &\approx& A_n \left( g_{sn} (-\tau) + g_{an} (-\tau) \right)
 \\
 &\approx& A_n e^{-n\tau},
\end{eqnarray}
and the boundary condition is the same as (\ref{bc-}),
\beq
 \frac{d\nu_n}{d \tau} = -n \nu_n ~~~ (\tau \to - \infty).
\label{bc+}
\end{eqnarray}
After imposing the matching conditions at $a = a_*$ to determine the mode function in the classically allowed range,
one finds that this choice of the mode functions corresponds to the Bunch-Davies vacuum state~\cite{Hong:2003pe}.

If the boundary condition (\ref{bc+}) is enforced at $\tau\to -\infty$, then, according to the results of \cite{Hong:2003pe}, $R_n^-(a)$ satisfy the regularity condition in the range $0<a\leq a_*$.  On the other hand, the matching conditions at $a=a_*$ require that \cite{Vachaspati:1988as} $R_n(a_*)=R_n^+(a_*)=R_n^-(a_*)$, and it follows from the analysis in \cite{Hong:2003pe} that the regularity condition is satisfied by $R_n^+(a)$ and $R_n(a)$ as well.  Thus we conclude that the boundary conditions (\ref{bc+}) are sufficient to ensure that the regularity condition is satisfied in the entire range $0<a<\infty$.  Combined with the outgoing wave condition, these boundary conditions uniquely determine the tunneling wave function in our model.  We show in the Appendix that the same conclusions apply to the de Sitter model with a minimally coupled scalar field.

The mode functions $\nu_n (\tau)$ selected by the boundary condition (\ref{bc+}) diverge at $\tau \to - \infty$.  This may look worrisome, but we note that $R_n^\pm$ and the wave function (\ref{psi}) are well behaved at $a\to 0$.  We therefore see no reason to require finiteness of $\nu_n(\tau\to -\infty)$ in the tunneling approach.  We shall return to this issue in Sec.~3.

\section{Path-integral formulation}
\label{sec:PI}

\subsection{de Sitter minisuperspace}

In the path integral formalism, the transition amplitude from an initial state $(g_0, \phi_0)$ to a final state $(g_1, \phi_1)$
can be symbolically written as
\beq
G(g_0,\phi_0;g_1,\phi_1)=\int_{(g_0,\phi_0)}^{(g_1,\phi_1)} {\cal D} g {\cal D} \phi \, e^{iS}.
\label{G}
\end{eqnarray}
We will be interested in the limit where the initial geometry shrinks to a point.

We first consider the leading-order homogeneous de Sitter minisuperspace model.
In the gauge where the lapse function is $N={\rm const}$, the path integral in (\ref{G}) reduces to
\beq
G^{(0)}(0; a_1)=\int_0^\infty dN \int {\cal D}a ~ e^{iS^{(0)}[a,N]},
\label{PsiG}
\end{eqnarray}
where
\beq
 S^{(0)}[a,N] = 6 \pi^2 \int_{-\infty}^{\eta_1} \left[ - \frac{\dot{a}^2}{N} + N V(a) \right] d \eta
\label{SdS}
\end{eqnarray}
is the action for the de Sitter model with metric (\ref{metric}).
Note that our starting point is a purely Lorentzian path integral and the lapse integration is performed over a semi-infinite range $N>0$.  The latter condition ensures that we include only histories where $\eta_1$ occurs later than $\eta=-\infty$ and not the geometrically identical histories related to them by $\eta\to -\eta$.  This is the choice adopted in Refs.~\cite{Teitelboim:1983fk, Feldbrugge:2017kzv, Vilenkin:1994rn}.  With this choice, $G(a_0,a_1)$ is a Green's function of the Wheeler-DeWitt operator satisfying
\beq
{\cal H} G(a_0;a_1)=-i\delta (a_1-a_0).
\end{eqnarray}
However, in the limit of $a_0\to 0$, $G(0;a_1)$ is a solution of the WDW equation in the entire range $0<a_1<\infty$.

The path integral over $a$ in (\ref{PsiG}) was first evaluated by Halliwell and Louko \cite{Halliwell:1988ik}.  They noticed that the analysis can be greatly simplified by introducing a new time coordinate $t$, which is related to $\eta$ by $d\eta=a^{-2}(t)dt$ and which can be chosen to vary between 0 and 1.  Then the metric takes the form
\beq
ds^2=-\frac{N^2}{q(t)}dt^2+q (t) d\Omega_3^2,
\end{eqnarray}
where $q=a^2$, and the action (\ref{SdS}) becomes
\beq
S^{(0)}[q,N]=6\pi^2\int_0^1 \left[-\frac{{\dot q}^2}{4N} +N(1-H^2 q)\right] dt .
\label{S0q}
\end{eqnarray}
This action is quadratic in $q$, so the path integral can be evaluated exactly.

The classical equation of motion for $q(t)$ obtained by minimizing the action (\ref{S0q}) is
\beq
{\ddot q}=2N^2 H^2,
\end{eqnarray}
its solution satisfying the boundary conditions $q(0)=0$ and $q(1)=a_1^2$ is
\beq
 q (t) = H^2 N^2 t^2 + \left( a_1^2 - H^2 N^2 \right) t,
 \label{qt}
\end{eqnarray}
and the action (\ref{S0q}) for this solution is given by
\beq
S^{(0)}(a_1,N)=6\pi^2\left(N^3\frac{H^4}{12}+N\left(1-\frac{1}{2}H^2 a_1^2\right) -\frac{a_1^4}{4N}\right).
\label{S0q2}
\end{eqnarray}
The propagator (\ref{PsiG}) can now be expressed as \cite{Halliwell:1988ik}
\beq
G^{(0)}(0; a_1)=\int_{0^+}^\infty \frac{dN}{N^{1/2}} e^{iS^{(0)}(a_1,N)},
\label{Nintegral}
\end{eqnarray}
where we have omitted an overall numerical factor.

The remaining integration over $N$ can be performed using the saddle point approximation.  The relevant saddle points and the steepest descent contours in the complex $N$-plane can be found using Picard-Lefschetz theory.
The action (\ref{S0q2}) generally has four saddle points, which can be found from $\partial S^{(0)}/\partial N =0$.  In the under-barrier region $a_1<a_*$, the corresponding values of $N$ are purely imaginary and the relevant saddle points are located at \cite{Halliwell:1988ik,Feldbrugge:2017kzv}
\beq
 N^\pm = \frac{i}{H^2} \left( 1 \mp \sqrt{1-H^2 a_1^2} \right).
 \label{Npm}
\end{eqnarray}
The corresponding actions are
\beq
S^{(0)}(a_1,N^\pm)=12\pi^2 i S^\pm(a_1),
\label{S0pm}
\end{eqnarray}
where $S^+(a)$ and $S^-(a)$ are given by Eqs.~(\ref{Spm}),(\ref{C}) and correspond respectively to Euclidean paths that do and do not traverse the mid-section of the 4-sphere.  The pre-factors of the $\exp(iS^{(0)}(a_1,N^\pm))$ terms have comparable magnitudes at $a\sim a_*$.  In fact, it can be verified~\cite{Brown:1990iv} that they differ by a factor $i/2$, as they should for the tunneling wave function.

At this point it will be convenient to switch back to the time variable $\eta$, which is related to $t$ as
\beq
t=\frac{2i}{H^2 N} \frac{1}{e^{2iN\eta}+1}.
\end{eqnarray}
It can be verified that the classical solution (\ref{qt}) is then given by $a(\eta)=1/H\cosh(-iN\eta)$, which is the same as (\ref{atau}), up to the normalization of $\eta$.  (Note that the Euclidean time $\tau$ that we used in the Section 2 is related to $\eta$ via $i \tau = N \eta$.)  The values $t=0$ (where $a=0$) and $t=1$ (where $a=a_1$) correspond respectively to $\eta\to -\infty$ and
\beq
 \eta_1^\pm =
 \frac{i}{2N^\pm} \ln \left( \frac{-H^2 (N^\pm)^2}{a_1^2} \right) .
\end{eqnarray}
One can check that $\eta_1^+ < 0$ and $\eta_1^- > 0$.  The actions (\ref{S0pm}) can now be expressed as
\beq
 S^{(0), N^\pm} = 12 \pi^2 \int_{-\infty}^{\eta_1^\pm} V(a) N^\pm d \eta,
\end{eqnarray}
which is equivalent to (\ref{Spmtau}).

In the classically allowed range $V(a_1) < 0$ one finds that only one saddle point contributes \cite{Halliwell:1988ik,Feldbrugge:2017kzv},
\beq
 N = \frac{1}{H^2} \left( i + \sqrt{H^2 a_1^2 -1} \right) ,
 \end{eqnarray}
and the transition amplitude (\ref{Nintegral}) is
\beq
G^{(0)}(0,a_1)\propto \exp\left(-12\pi^2 S(a_1)\right)
\end{eqnarray}
with $S(a)$ given by Eqs.~(\ref{Sa}),(\ref{C}).  This describes a wave traveling in the positive $a_1$-direction, as expected for the tunneling wave function.  Thus, we can identify
\beq
G^{(0)}(0;a)=\Psi_T(a).
\end{eqnarray}

\subsection{The problem with perturbations}
\label{sec:PI1}

We now consider the wave function for scalar field fluctuations $\chi_n$.  Assuming that the backreaction of fluctuations on the metric is negligible, the scale factor and the lapse parameter can be treated as background variables.  For definiteness we shall consider the under-barrier wave function with $a_1<a_*$.  Then the path integral in Eq.(\ref{psiT}) reduces to
\beq
\Psi_T(a_1,\phi_{n1})=\sum_{r=\pm} A_r e^{iS^{(0)}(a_1,N^r)} \prod_n \int {\cal D}\phi_n e^{iS_n [\phi_n; N^r]}
\label{Psiaphi}
\end{eqnarray}
where
\beq
 S_n[\phi_n; N] = \frac12 \int_{\eta_0}^{\eta_1} d \eta \left(\frac{a^2}{N}{\dot\phi}_n^2 -Na^2(n^2-1)\phi_n^2 -Na^4 \left(m^2+\frac{1}{6}R\right)\phi_n^2\right) + S_{Bn}
 \label{Sn2}
\end{eqnarray}
with $\eta_0\to -\infty$.
The integration is taken over histories where $\phi_n(\eta) \equiv \chi_n(\eta)/a(\eta)$ have specified values $\phi_{n1}$ at $\eta=\eta_1$, with suitable boundary conditions for $\phi_n$ at $\eta\to -\infty$.  The boundary term in (\ref{Sn2}) is usually not included; we shall discuss it in the next subsection.  From now on we omit the superscript $r=\pm$ for notational simplicity.

The path integral in (\ref{Psiaphi}) is again determined by the history $\phi_n(\eta)$ satisfying the classical equation of motion:
\beq
\frac{1}{N^2}\left({\ddot\phi}_n+2\frac{\dot a}{a} {\dot\phi}_n\right) + (n^2-1)\phi_n + (m^2+2H^2)a^2\phi_n=0
 \label{EoM2}
\end{eqnarray}
Disregarding the boundary term for the moment, the action is then given by
\beq
 S_n = \frac{a_1^2}{2 N} \phi_n (\eta_1) \dot{\phi}_n (\eta_1) - \frac{a_0^2}{2 N} \phi_n (\eta_0) \dot{\phi}_n (\eta_0).
 \label{solution2}
\end{eqnarray}

In the limit of $\eta \to - \infty$, $a(\eta)\approx 2H^{-1}e^{-i N\eta}$ and the solution to the equation of motion is approximated to be
\beq
 \phi_n (\eta) \approx A_n e^{i (n+1) N \eta} + B_ne^{-i (n-1) N \eta} .
 \label{phi_n}
\end{eqnarray}
Since ${\rm Im} N > 0$ for both saddle points in Eq.~(\ref{Npm}),
the second term of $S_n$ diverges in the limit of $\eta_0 \to - \infty$ unless we take $A_n = 0$.
This seems to suggest that we should set $A_n=0$ in order to make the action finite.
With this choice, the $\phi_n$-dependent part of the wave function becomes (in the regime where the approximation (\ref{phi_n}) is applicable)
\beq
\psi_n(\phi_{n1})\propto e^{iS_n}=\exp\left(ia_1^2 \frac{\phi_{n1}{\dot\phi}_{n1}}{2N}\right)=\exp\left(\frac{n-1}{2} a_1^2 \phi_{n1}^2\right),
\end{eqnarray}
which has the obvious problem that the wave function grows with increasing amplitude of the fluctuations.  One can check that the problem persists in the classically allowed range $a>a_*$.
This is the basis for numerous claims made in the literature that the tunneling wave function predicts an unstable runaway behavior of the fluctuation modes \cite{Halliwell:1989dy,Feldbrugge:2017fcc,DiazDorronsoro:2018wro}.  We shall see, however, that the problem can be resolved by inclusion of a suitable boundary term.

\subsection{Boundary terms}
\label{sec:PI2-1}

The boundary term $S_B$ in the action (\ref{action}) should be selected in such a way that boundary contributions obtained after varying the action and integrating by parts vanish, once the boundary conditions are imposed.  The form of the boundary term, of course, depends on the choice of boundary conditions.  The choice adopted in most of the literature on quantum cosmology is Dirichlet boundary conditions, with the 3-metric and the scalar field specified at the boundary.
The corresponding boundary action is
\beq
S_B=S_{GH} + \xi \int_{\cal B} \sqrt{-g^{(3)}} \, d^3 y K \phi^2 ,
\label{SB1}
\end{eqnarray}
where $S_{GH}$ is the Gibbons-Hawking term,
$\xi$ is the scalar field coupling to the curvature,
$g^{(3)}$ is the determinant of the induced metric on the boundary ${\cal B}$,
$y^a$ are the coordinates on the boundary,
and $K$ is the extrinsic curvature of the boundary.  The second term in (\ref{SB1}) is absent for a minimally coupled field, but in our case $\xi=1/6$ and it has to be included in order for the variation of the action with respect to the metric not to give any uncompensated boundary terms \cite{Barvinsky:1995dp}.

The Dirichlet boundary conditions are appropriate for the Hartle-Hawking wave function,\footnote{This is because the mode functions $\chi_n(\eta)$ in the Hartle-Hawking approach are required to have specified values at $\eta=\eta_1$ and to satisfy $\chi_n(\eta\to -\infty)=0$.  This is sometimes justified by the requirement that the scalar field action should be finite.  We note, however, that the logic here is somewhat circular: the finiteness of the action depends on the choice of the boundary term, which in turn depends on boundary conditions.} but for the tunneling wave function one needs to take a different approach.  The spacetimes included in the path integral for $\Psi_T$ have two boundaries: the upper boundary ${\cal B}_1$ $(\eta=\eta_1)$ with specified values of $a_1$ and $\chi_{n1}$ and a lower boundary ${\cal B}_0$ where $a\to 0$ $(\eta_0\to -\infty)$.
According to Eq.~(\ref{bc+}), the histories $\chi_n(\eta)=a(\eta)\phi_n(\eta)$ for the tunneling wave function should satisfy the Robin boundary condition
\beq
\frac{1}{N}\frac{d\chi_n}{d\eta}=in\chi_n ~~~ (\eta\to -\infty),
 \label{bcchi}
\end{eqnarray}
where we have used the relation $i\tau=N\eta$.  We will now show that a suitable choice of the boundary terms in this case is
\beq
S_B=S_{GH} +\frac{1}{2\pi^2} \sum_n \int_{{\cal B}_0} \sqrt{-g^{(3)}} \, d^3 y \left( \xi K -\frac{1}{2}h_n \right) \phi_n^2
+\frac{1}{2\pi^2} \sum_n \int_{{\cal B}_1} \sqrt{-g^{(3)}} \, d^3 y \xi K \phi_n^2 ,
\nonumber \\\label{SB}
\end{eqnarray}
where $h_n$ are parameters to be determined.

Variation of the action with respect to $\phi_n$ gives
\beq
&& 2\pi^2 \delta S= -\int \sqrt{-g^{(4)}} \, d^4 x\, \delta\phi_n \left(-\nabla^2+ \xi R+m^2\right)\phi_n
\nonumber \\
&& +\int_{{\cal B}_0} \sqrt{-g^{(3)}} \, d^3 y \delta\phi_n \left(\partial_\perp \phi_n +2\xi K\phi_n -h_n\phi_n\right)
+\int_{{\cal B}_1} \sqrt{-g^{(3)}} \, d^3 y \delta\phi_n \left(\partial_\perp \phi_n + 2\xi K\phi_n \right).\nonumber \\
\label{variation}
\end{eqnarray}
Here, $\partial_\perp$ is the derivative in the direction of outer normal to the boundary.  For our metric (\ref{metric}) it is given by
\beq
 \partial_\perp = \pm \frac{1}{N a} \frac{d}{ d \eta} ,
\label{dperp}
\end{eqnarray}
where the upper and lower signs correspond to upper and lower boundaries, respectively.
The boundary term in (\ref{variation}) vanishes on the upper boundary ${\cal B}_1$, where $\phi_n$ are fixed, while on the lower boundary ${\cal B}_0$ we will impose the boundary conditions
\beq
\partial_\perp \phi_n + 2\xi K\phi_n -h_n\phi_n=0.
\label{bc}
\end{eqnarray}
Noticing that
\beq
K = \frac{\partial_\perp V_B}{V_B}=3\frac{\partial_\perp a}{a},
\end{eqnarray}
where $V_B = 2\pi^2 a^3$ is the boundary volume, we can express (\ref{bc}) as
\beq
\partial_\perp \chi_n-h_n\chi_n =0 ,
\label{chibc}
\end{eqnarray}
where we have used $\xi=1/6$.
This coincides with (\ref{bcchi}) if we set
\beq
h_n = -i n a^{-1}.
\label{BC}
\end{eqnarray}

Let us now consider the part of the action that depends on $\phi_n$, Eq.~(\ref{Sn2}).  Integrating by parts and
using the boundary conditions, we find that the contribution of the lower boundary cancels out and we obtain
\beq
 S_n = \frac{1}{2\pi^2} \int_{{\cal B}_1} \sqrt{-g^{(3)}} \, d^3 y \left( \frac12 \phi_n \partial_\perp \phi_n + \xi K \phi_n^2 \right) = \frac{a_1}{2} \chi_n (\eta_1) \partial_\perp \chi_n (\eta_1).
 \label{S_m}
\end{eqnarray}
Then the wave function for $\chi_n$ becomes
\beq
\psi_n(\chi_{n1})\propto\exp\left(-\frac{1}{2}R_n\chi_{n1}^2\right),
\label{psinR}
\end{eqnarray}
where
\beq
R_n=-\frac{i}{N}\frac{{\dot\chi}_{n1}}{\chi_{n1}}.
\label{Rnchi}
\end{eqnarray}
With $N\eta=i\tau$, this is the same as Eq.~(\ref{R_npm}) that we obtained using the WDW formalism.  Since the condition $R_n >0$ is satisfied at $\eta_1 \to-\infty$, it is guaranteed to be satisfied for all $\eta_1$.  Thus we conclude that the path integral formalism with appropriate boundary terms in the action gives the same wave function as the WDW equation with
tunneling boundary conditions.  In both approaches the scalar field fluctuations are suppressed.

\subsection{Boundary term as the initial wave function}
\label{sec:PI2}

The new boundary term that we introduced in Eq.~(\ref{SB}) can be written as
\beq
{\tilde S}_{Bn}\equiv -\frac{1}{4\pi^2}\int_{{\cal B}_0} \sqrt{-g^{(3)}} \, d^3 y h_n\phi_n^2 =\frac{i}{2} n \chi_{n0}^2,
\end{eqnarray}
where $\chi_{n0}=\chi_n(\eta_0)$.  This term allows an interesting interpretation, which we shall now discuss.

Let us first show that the scalar field path integral in Eq.~(\ref{Psiaphi}) can be expressed as
\beq
\psi_n(\chi_{n1})\propto  \int {\cal D} \chi_n e^{i {\tilde S}_n [\chi_n]} \psi_{n0} (\chi_{n0}),
\label{intchi}
\end{eqnarray}
where
\beq
 \psi_{n0} (\chi_{n0}) \equiv  e^{i{\tilde S}_{Bn}} =  e^{- n \chi_{n0}^2/2}
 \label{initialPsi}
\end{eqnarray}
and ${\tilde S}_n [\chi_n]$ is the action (\ref{Sn2}) with only $\xi K$ boundary terms included.  The integration in Eq.~(\ref{intchi}) is to be taken over paths $\chi_n(\eta)$ starting at $\chi_n(\eta_0)=\chi_{n0}$ and ending at $\chi_n(\eta_1)=\chi_{n1}$; in other words this path integral assumes Dirichlet boundary conditions.  We assume also that the functional measure includes an integral over $\chi_{n0}$.

Substituting $\phi_n=\chi_n/a$ and
\beq
R=\frac{6}{a^2}\left(1+\frac{\ddot a}{N^2 a}\right)
\label{R}
\end{eqnarray}
in the action (\ref{Sn2}) we obtain
\beq
{\tilde S}_n = \frac{1}{2} \int_{\eta_0}^{\eta_1} d\eta \left[\frac{1}{N}{\dot\chi}_n^2-N n^2\chi_n^2-N m^2 a^2 \chi_n^2 -\frac{1}{N} \frac{d}{d\eta}\left(\frac{{\dot a}}{a} \chi_n^2\right)\right] +\frac{1}{12\pi^2} \int_{\cal B} \sqrt{-g^{(3)}} \, d^3 y \frac{K}{a^2} \chi_n^2.\nonumber \\
\label{SnK}
\end{eqnarray}
With $\int_{\cal B} \sqrt{-g^{(3)}} \, d^3 y = 2\pi^2 a^3$ and $K = \pm 3{\dot a}/(Na^2)$, we find that the result of integration of the total derivative in (\ref{SnK}) cancels out with the boundary term, so the result is
\beq
{\tilde S}_n = \frac{1}{2} \int_{\eta_0}^{\eta_1} d\eta \left(\frac{1}{N}{\dot\chi}_n^2-N n^2\chi_n^2-N m^2 a^2 \chi_n^2 \right).
\label{SnK2}
\end{eqnarray}

The functional integral in Eq.~(\ref{intchi}) is Gaussian, so the saddle point approximation is exact.  Integrating by parts   and using the classical equation of motion for $\chi_n$, we can express the action (\ref{SnK2}) as
\beq
 {\tilde S}_n = \frac{1}{2 N} \chi_{n1} \dot{\chi}_{n1} - \frac{1}{2 N} \chi_{n0} \dot{\chi}_{n0}.
 \label{tildeS}
\end{eqnarray}
Extremizing $i {\tilde S}_n [\chi] + \ln[\psi_{n0} (\chi_{n0})]$ with respect to $\chi_{n0}$, we find
\beq
 \dot{\chi}_{n0}= i n N \chi_{n0},
 \label{init1}
\end{eqnarray}
which is precisely the Robin boundary condition (\ref{bcchi}).  Also, from Eqs.~(\ref{tildeS}), (\ref{initialPsi}), and (\ref{init1}),
the amplitude (\ref{intchi}) is given by
\beq
 \psi_n (\chi_{n1}) \propto e^{i \chi_{n1} \dot{\chi}_{n1}/ 2N},
\label{psichi1}
\end{eqnarray}
where the second term in \eq{intchi} has cancelled out with $\Psi_0 (\chi_{n0})$.
The combination $i {\tilde S} + \ln ( \Psi_0)$ is now finite in the limit $\eta_0 \to -\infty$, because of the cancellation.
Eq.(\ref{psichi1}) is equivalent to Eqs.~(\ref{psinR}),~(\ref{Rnchi}) that we derived in Sec.~\ref{sec:PI2-1}.  Thus we conclude that Eq.~(\ref{intchi}) is equivalent to the path integral with Robin boundary conditions.

Now, the form of Eq.~(\ref{intchi}) is very suggestive.  We can interpret $\Psi_0 (\chi_{n0})$ as the initial wave function for the scalar field at $\eta_0 \to -\infty$.  As suggested in Ref.~\cite{Hong:2003pe}, we can think of the tunneling wave function as describing a small initial universe that tunnels to $a\approx a_*$ after reaching the bounce point at $a_0 \ll a_*$, in the limit of $a_0 \to 0$.%
\footnote{
More precisely, the background cosmology assumed in Ref.~\cite{Hong:2003pe} included a small amount of radiation with density $\rho_r = \epsilon_r / a^4$. The bounce point $a_0$ then depends on $\epsilon_r$, and the limit $a_0 \to 0$ is obtained at $\epsilon_r \to 0$.
}
The wave function (\ref{initialPsi}) is that for a massless scalar field in the state of
Euclidean vacuum, which is defined by requiring that the mode functions are regular at $\tau \to \infty$.
It was shown in Ref.~\cite{Hong:2003pe} that the same quantum state is obtained if one considers a small initial universe that tunnels through a barrier in the limit when the size of the initial universe goes to zero.
In this limit the mass of the field $\chi$ can be neglected in the wave function (\ref{psichi1}).

\section{Conclusions}

We discussed three different approaches to defining the tunneling wave function of the universe $\Psi_T$.   The first approach is to impose the outgoing wave and regularity conditions in superspace.  This has been previously studied in Refs.~\cite{Vilenkin:1987kf,Vachaspati:1988as,Hong:2003pe}, with the conclusion that the resulting wave function is uniquely defined and describes a universe nucleating with the scalar field in a de Sitter invariant Bunch-Davies state.  The regularity condition, requiring that the absolute value of the wave function decreases with growing amplitude of scalar field fluctuations, is a non-local condition on $\Psi_T$.  Here we showed that it is equivalent to the requirement that the scalar field modes $\phi_n$ satisfy a (local) Robin boundary condition at $a\to 0$.

Our main focus in this paper was to explore the conjecture made in Refs.~\cite{Vilenkin:1984wp} that $\Psi_T$ can also be expressed as a Lorentzian path integral taken over histories interpolating between a vanishing 3-geometry $(a=0)$ and a given configuration $\{a,\phi_n\}$.  We showed that the Robin boundary conditions for $\phi_n$ require an addition of a new boundary term to the scalar field action and that the path integral is then identical to the wave function specified by the tunneling boundary conditions.

We showed also that the path integral with the new boundary term can be expressed as a transition amplitude from a universe of vanishing size with a scalar field in the state of Euclidean vacuum.  All three approaches give identical wave functions with well behaved scalar field fluctuations, contrary to earlier claims in the literature.

Our discussion in this paper was limited to a de Sitter minisuperspace model with a scalar field included as a perturbation.
A natural extension of this model would be to consider non-perturbative minisuperspaces, including a few degrees of freedom, but allowing large variations of the scalar field and large deviations from de Sitter geometry.  Such models with a homogeneous scalar field \cite{Vilenkin:1987kf} and with a Bianchi-IX metric \cite{delCampo:1989hy} have been studied in the framework of boundary conditions in superspace, with the conclusion that the tunneling and regularity conditions determine a unique wave function with well-behaved fluctuations.  Extension of the path integral approach to non-perturbative models remains an open problem for future research.

\begin{acknowledgments}
We are grateful to Juan Diaz Dorronsoro, Jonathan J. Halliwell, James B. Hartle, Thomas Hertog, Oliver Janssen, Jean-Luc Lehners, and Yannick Vreys for their useful and stimulating comments on the manuscript.  This work was supported in part by the National Science Foundation.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


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Notes: Two varieties are both widespread in Zimbabwe: var. gardeniifolia has the leaves, flowering branchlets and stalks hairless; var. subtomentosa K. Schum. has rough hairs on the leaves, stalks and branchlets.
Hyde, M.A., Wursten, B.T., Ballings, P. & Coates Palgrave, M. (2019). Flora of Botswana: Species information: Pavetta gardeniifolia.


ABUJA—The First Lady, Dame Patience Jonathan, Monday, called on the feuding parties in Rivers State to consider the social, political and economic costs of the crisis to the state and its people and urgently find a way of resolving their political differences amicably.
Meanwhile, the Rivers State Government, yesterday, set up a commission of inquiry to investigate last week's crisis in the state House of Assembly.
The panel is headed by Justice Biobele Georgewill. Inaugurating the Commission, the deputy governor, Mr. Tele Ikiru, who represented the governor, charged the commission to investigate the remote and immediate causes of the crisis, adding that it should submit its report to the state government on or before October 15, this year.
However, Dame Jonathan in a statement in Abuja, by her Senior Special Assistant, Ayo Osinlu, said if the crisis was not resolved, "the greater consequence of the impasse is, as usual, reserved for the poor, the weak and the vulnerable, especially women and children, who are usually innocent bystanders in all these.
"This derives naturally from the saying that when two elephants fight, it is the grass that suffers. On a larger scale, we subscribe to the fact that conflicts and violence are the most lethal threats to peace, which itself is the irreducible minimum condition for development.
"The situation must, therefore, not be allowed to degenerate to a level that can be hijacked by miscreants and hoodlums, thus exposing everyone to insecurity from which there may be no easy escape.
The Rivers Commission of Inquiry is to ascertain how many persons were injured, threatened and property destroyed. The Commission is also to determine if the incidents were caused by external factors or by members of the House.
Chairman of the Commission, Justice Georgewill, assured that they would discharge their duties without sentiments.
He appealed to the state government to ensure that the recommendations of the panel were implemented when submitted.