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Allergies in Children
What are allergies in children?
Allergies are problems of the immune system. Most allergic reactions happen when the immune system reacts to a "false alarm." Normally, the human body defends itself against harmful things such as viruses or bacteria. But sometimes the defenses violently attack mostly mild things, such as dust, mold, or pollen.
Normally, allergens are harmless. But when a person has allergies, the body thinks these allergens are harmful. The body then attacks allergens with antibodies called immunoglobulin E (IgE). These antibodies are attached to special cells called mast cells. Allergens stick to the antibodies. This makes the mast cells release histamine and other chemicals causing an allergic reaction. When the chemicals irritate nearby nasal tissue, this causes nasal allergy symptoms. When this happens in the lungs' breathing tubes, it can cause asthma symptoms such as cough and wheeze. When the reaction involves the whole body, this can be a severe allergic reaction.
What are the symptoms of allergies in a child?
An allergic reaction can happen anywhere in the body. This includes the skin, eyes, lining of the stomach, nose, sinuses, throat, and lungs. These are the places where immune system cells are found to fight off germs that are breathed in, swallowed, or come in contact with the skin. Allergic reactions can cause:
Stuffy nose, sneezing, itching, or runny nose, and itching in ears or roof of mouth
Red, itchy, watery eyes
Red, itchy, dry skin
Hives or itchy welts
Itchy rash
Asthma symptoms, such as shortness of breath, coughing, wheezing
A severe, life-threatening allergic reaction (anaphylaxis). This can cause trouble breathing, vomiting, diarrhea, low blood pressure, fainting, or death.
What causes allergies in a child?
Many things can trigger allergic reactions. But the most common triggers or allergens are:
Tree, grass, and weed pollens
Animal dander, urine, and oil from skin
Pests such as cockroaches and mice
Which children are at risk for allergies?
Allergies can affect anyone. It doesn't matter regardless of age, gender, race, or socioeconomic status. Generally, allergies are more common in children. But allergies can happen at any age. And they can come back after being in remission for many years.
Allergies tend to happen in families. But the exact reason isn't yet understood. Allergy symptoms often happen slowly over time.
How are allergies diagnosed in a child?
To diagnose an allergy, the healthcare provider will take a complete health history and examine your child. The provider may also do these tests:
Skin test. This is the most common allergy test. Skin tests measure if there are IgE antibodies to certain allergens (like foods, pollens, or animal dander). A small amount of diluted allergen is placed on the skin. The area is pricked or scratched. If a person is allergic to the allergen, a small raised bump (like a mosquito bite) appears after about 15 minutes. Testing for many allergens may be done at the same time. An allergist may also do an intradermal test. In this test, a small amount of allergen is injected just under the skin. This type of skin testing is more sensitive than prick or scratch testing. Skin test results are available right after the testing is done.
Blood test. Blood tests for allergies measure IgE antibodies to certain allergens in the blood. The testing that is most often used is called RAST (radioallergosorbent test). Blood tests may be used when skin tests can't be done. For example, in people with certain skin conditions. Or people with a very recent severe allergic reaction. A positive blood test does not always mean that you have a certain allergy. Any positive blood test needs to be interpreted by a healthcare provider who is familiar with the tests and knows your child's health history. These tests take longer to get results. They may cost more than other allergy tests.
Challenge test. This test is supervised by an allergist. A very small amount of the allergen is given to the child by mouth. Or it is breathed in. Only a challenge test can figure out how severe an allergy is. Skin or blood test reactions only tell the likelihood of having any type of reaction, not what that reaction will be.
Any positive test needs to be explained by a healthcare provider who is familiar with the test and your child's health history.
How are allergies treated in a child?
Treatment will depend on your child's symptoms, age, and general health. It will also depend on how severe the condition is.
The symptoms of allergies sometimes look like other conditions or health problems. Always see your child's healthcare provider for a diagnosis.
The 3 most effective ways to treat allergies are avoidance, allergy shots (immunotherapy), and medicine. Avoidance means staying away from something that gives you an allergic reaction.
Suggestions for staying away from allergens are:
Stay indoors when the pollen count is high and on windy days.
Control dust in the home, particularly your child's bedroom.
Use air conditioning instead of opening the windows.
Put a dehumidifier in damp areas of the home. But remember to clean it often.
After playing outside when the pollen counts are high, have your child take a bath or shower, wash his or her hair, and change clothes.
Take vacations in areas where pollen is not as common, such as near the ocean.
Your child's healthcare provider will also have suggestions for staying away from the allergens that cause reactions.
Treatments for hay fever (rhinitis) may include:
Medicines for asthma symptoms
Allergy shots (allergy immunotherapy)
Allergy tablets (sublingual immunotherapy)
Decongestants are not recommended for children younger than age 4. Talk with your child's healthcare provider for more information about allergy medicine.
Key points about allergies in children
Allergies are problems of the immune system. Most allergic reactions happen when the immune system reacts to a "false alarm."
Allergic reactions are often caused by tree, grass, and weed pollens, latex, molds, dust mites, foods, and medicines.
Tests used to diagnosed allergies include skin tests, blood tests, or challenge tests.
The 3 most effective ways to treat allergies are avoidance, allergy shots (immunotherapy), and medicine.
Working with your child's healthcare provider or allergist can help reduce or get rid of allergies.
Tips to help you get the most from a visit to your child's healthcare provider:
Know the reason for the visit and what you want to happen.
Before your visit, write down questions you want answered.
At the visit, write down the name of a new diagnosis, and any new medicines, treatments, or tests. Also write down any new instructions your provider gives you for your child.
Know why a new medicine or treatment is prescribed and how it will help your child. Also know what the side effects are.
Ask if your child's condition can be treated in other ways.
Know why a test or procedure is recommended and what the results could mean.
Know what to expect if your child does not take the medicine or have the test or procedure.
If your child has a follow-up appointment, write down the date, time, and purpose for that visit.
Know how you can contact your child's provider after office hours. This is important if your child becomes ill and you have questions or need advice.
Online Medical Reviewer: Daphne Pierce-Smith RN MSN CCRC
Online Medical Reviewer: Deborah Pedersen MD
Date Last Reviewed: 10/1/2018
© 2000-2019 The StayWell Company, LLC. 800 Township Line Road, Yardley, PA 19067. All rights reserved. This information is not intended as a substitute for professional medical care. Always follow your healthcare professional's instructions.
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A big thank you to Rounded Edge Studio for building MTData's stand at the PHTM Expo. I organised the stand from Australia, and right from my initial enquiry through to completion, they were delightful to work with – very responsive, helpful and professional. Special thanks to Collette who helped me achieve the best stand within my budget. The quality of the stand and graphics were superb. I look forward to working with them again.
Linda Foschini, Marketing Manager, MTData.
Bespoke modular exhibition products and services.


Subsoil is the property of the Republic of Uzbekistan, subject to rational use and protected by state.
Minerals produced in the order established by legislation may be in state property, property of legal and physical entities. Right of property for anthropogenic mineral formation received during production of minerals and processing of mineral raw is preserved by user for the period of subsoil area use.
Subsoil use on community areas, suburban zones, areas of industry facilities, transportation and communication may be limited in cases if such use may pose threat to life and health of population and damage to environment.
State inspection on supervision over safe carrying out of operations in industry, mining business and utility sector.
The mineral fields may be transferred for commercial development only after approval of their reserves and state expertise of geological materials by State commission on mineral reserves under the State Committee of the Republic of Uzbekistan on geology and mineral recourses.
Recently the Uzbekistan Government has established criteria for selection of promising mineral deposits; and publicly listed all the perspective mineral deposits offered to foreign investors for exploration or for development. Such information shall be updated every 5 years.
The part of the activity in petrochemical, energy and mining sectors is subject to licensing. Currently, the Uzbekistan Law on Licensing of Certain Types of Activity" bans transfers of licenses and any rights under the licenses to third parties. This may raise questions regarding permissibility of any transfers of right from the original licensee to the successor.
consulting on various legal issues related to international merger and acquisition of the legal entities, involved in petrochemical, energy and mining activity in Uzbekistan.


"Forget it; why even talk about it anymore," my husband shouted and slammed the door behind him.
I stood rooted to the bedroom floor, reeling against the tidal wave of questions sweeping my imagination. How could our marriage survive? My husband and I had been fighting more and more about issues that seemed to defy resolution, and this last argument was off the Richter Scale. I knew we were teetering on the brink of divorce. How could I start a new life with two little boys to support? I couldn't bear to think of them shuttled between parents. All this turmoil made my throat and chest hurt so much I could scarcely breathe.
To combat my paralyzing fear, it seemed I needed to repeat this verse every five minutes the first few days. So I composed a simple melody to help me remember the words. Singing pried my thoughts away from circumstances and lifted me into the presence of the Lord. In this way I clung to hope and controlled my panic.
Other passages in Isaiah also encouraged me. "I have engraved you on the palms of my hands," God says. Jesus literally fulfilled these words. His great love for me compelled him to lie down on the cross and offer his hands to the executioner's nails. How could I and my family not be kept safe in such hands? Surely he would not abandon me in this dark place.
Eventually my marriage recovered, but I learned an important lesson—regardless of the outcome of circumstances, I have a God who holds me safely in the palm of his hands.
©2007 Ruth Wood. All rights reserved. Used by permission.
Lord, thank you that I may rest in the palm of your hands. I need not struggle with my fears alone for you are with me. In you I have peace, comfort and hope. In Jesus name, Amen.
Putting it into action: Memorize Isaiah 41:10, 49:15-16; and Phil. 4:6, then meditate on these passages throughout the day. For a deeper understanding of these truths, try rewriting the verses in your own words. Then express your response to the Lord by composing a poem, painting a picture, or writing your own song based on these verses.


text:
Q: Object Error in Outlook Function I am writing a function that prints out the folder name in the debug window. For some reason when I call this function I get an object required error. I have set the object so I am unsure what is wrong. Any help will be greatly appreciated. Thanks!
    function email_function(fldr as outlook.folder)
         debug.print fldr
    end function

    Sub email()

    Set objOutlook = CreateObject("Outlook.Application")
    Set objNspace = objOutlook.GetNamespace("MAPI")
    Set start_fldr = objNspace.GetDefaultFolder(olFolderInbox)

    Debug.Print start_fldr

    If Not start_fldr Is Nothing Then
       email_function (start_fldr)
    End If

    End Sub

A: Wrong syntax.
Call email_function(fldr)

'or

email_function fldr

Original code in Question:
Sub email()
    Dim objOutlook As Application
    Dim objnSpace As Namespace
    Dim start_fldr As folder
    Dim fldr As folder

    Set objOutlook = Application
    Set objnSpace = objOutlook.GetNamespace("MAPI")
    Set start_fldr = objnSpace.GetDefaultFolder(olFolderInbox)

    Set fldr = start_fldr.Folders.GetFirst

    Call email_function(fldr)

    email_function fldr

End Sub

redpajama_set_name: RedPajamaStackExchange


text:
HOTEL SEARCH IN Prague
Hotel in Prague
Book cheap hotel rates in Prague, enjoy great discounts. Prague is the capital and the largest city in Czech Republic. The city boasts a wonderful architecture of their buildings, many of which survived the violence and destruction of 20th century Europe. There is Charles Bridge, or Prague Castle, that featuring beautiful carvings on the wall. The name of the city is derived from an old Slavic root, praga, which means "ford". Besides their buildings, prague is also famous for their classical music. The city voted as one of the most visited city in Europe.
250 Hotels Found in Prague
Ibis Praha Old Town
The city hotel is located in the historical district of Prague, 5 minutes from Wenceslas Square and Staromestske Namesti (Old Town Square). Guests will find restaurants, bars, nightlife, shops and links to the public transport network on the hotel's doorstep and nearby places of interest include Prague Castle (3 km), Charles Bridge (2 km) and the National Theatre (2.5 km). The hotel is approximately 15 km from Prague - Ruzyne International airport, around 250 km from Schwechat International Airport and only 2 minutes on foot from the central railway station.
BOTEL RACEK
This hotel is docked on the Vltava River, opposite the National Swimming Pool. The tram stop is a few metres away and it is only 10 minutes to the centre of Prague. 3 kms to city centre 14 kms to the nearest airport (ruzyne) 5 km to the nearest station (wilson main station)
This pleasant hotel is located just outside Prague's city centre in the peaceful neighbourhood of Vysocany. A range of bars and pubs are found right by the hotel. Shopping venues are found slightly further away and the nearest bus stop is 200 metres from the hotel.
The hotel is located within walking distance from Wenceslas Square (about 20 minutes) or only four stops by tram. The hotel is situated in a quiet residential area of Prague called Zizkov. 5 kms to city centre 20 kms to the nearest airport (ruzyne) 20 minute walk to the nearest metro station (hlavni nadrazi) 1 km to the nearest station (central railway station) 2 minute walk to the nearest bus stop 3 km to the nearest fair site (vystaviste)
This city hotel lies on the edges of the large Prague park, approximately 4 km from the city outskirts. The international airport is just a short 24 km drive away; the nearest métro station (Roztyly) lies some 12 minutes from the city centre.
Vitkov
Set in the Zizkov district, this hotel is 200 metres away from Vitkov Park. Prague's Old Town Square can be reached within a 20-minute tram ride and The Praga Airport is just about 15 km away.
Dalimil
This city hotel is located on the edge of Prague's city centre. The city and tourist centre is easily reached in 15 minutes walk away, it is approximately 50 m to some bars and a mere 100 m to an array of shops and superb public transport connections. Prague Ruzyne airport is approximately 15 km away.
This hotel is located a couple of minutes' walk from the Nadrazi Branik tram and bus stations. It lies 15 minutes from the city centre in a quiet area, some 7 km from Wenceslas Square and around 8 km from Charles Bridge. Guests have easy and rapid access to the main attractions of Prague as well as to the main points of interest, including sport stadiums, the offices of local and international companies and Czech dignitaries.
This hotel is situated at the heart of the city, only 5 min by foot to the famous Wenceslas Square and within a few minutes walk of countless bars, nightclubs and entertainment venues. Public transport departs from stops just 100 m from the hotel.
Prague Centre Plaza
This hotel is centrally located within a few minutes walk of the Czech metropolis' most famous sights where European history was written. Links to the public transport network may be reached on foot in minutes and the airport may be access by making use of the hotel taxi or by taking the number 119 bus.
A&O Prague Metro Strizkov
The hotel is located 2 km from Prague city centre, right next to PVA Letnany and Holesovice Exhibition Centre. It is easily accessible from all main access routes to Prague and just minutes from the centre by subway or bus.
Sophieâ´S Hostel
This attractive city hotel is situated in a quiet location in a park in the SK Slavia sports arena. The nearest underground station lies just 200 m from the hotel and a tram stop is a mere 100 m away, putting all of the city's major tourist sights within easy reach, as well as countless bars and nightclubs. The city centre is just around 15 minutes away by taxi. The main train station is approximately 6 km from the hotel.
The hotel Astra is set in a quiet residential part of Prague - Skalka. It is 300 metres from the metro station Skalka (green line). Metro reaches the City Centre (Wenceslas Square) in 10 minutes.
Le Petit Hotel Prague
Hotel Golf is located in a quiet area of Prague 5, surrounded by a beautiful park with a golf course. Thanks to its easy transport accessibility to the city center/ 15 minutes by tram/ as well as to the airport, it is an excellent choice for accommodation in Prague. 6 kms to city centre 10 kms to the nearest airport (ruzyne) 40 minute walk to the nearest metro station (andel) 5 km to the nearest station (prague-smichovske nadrazi) 3 minute walk to the nearest bus stop 5 km to the nearest fair site (zlicin)
U Ceske Koruny Hotel
The hotel is located in the district of Reporyje in the western part of Prague. Reporyje train station, as well as a leisure centre with billiards, bowling and a solarium, is just 200 m away. There are plenty of shops about 10 minutes away. The Astronomical Clock and Petrin Tower are both about 20 minutes away on public transport.
This hotel is situated close to the city centre in a quiet area of Prague. It enjoys easy and quick connections to the historical centre of the city, where guests will find restaurants, bars, nightspots and links to the public transport network. Prague Airport is only 15 km away.
Fortuna West
The hotel is located near Prague Castle and is ideally situated in a quiet and tranquil part of the city, around 25 minutes from the city centre by public transport. The hotel offers good connections to the Prague-Plzen - Rozvadov expressway, providing easy access to many of the area's attractions. Nearby points of interest include the Saint Vitus Cathedral, the Petrin Viewing Tower (Petrínská Rozhledna) and Strahov Monastery (Strahovsky klaster). The Prague Castle (Prazský Hrad) - the largest castle in Europe featuring more than 700 rooms - are both just minutes away. The surrounding area offers many things to see, including historical landmarks, museums, theatres, cafés and speciality shops. Prague Airport is only 9 km away.
Hotel Krystal
This hotel is located is located conveniently on the shortest route from Prague airport to the centre of the city. The subway station Veleslavin (line A) is just around the corner and will comfortably get you to the centre of the city in 15 minutes. For those who perefer tram, the tram stop is a 2 minute walk. The area is peaceful with residential builidings, schools and offices. 8 kms to city centre 5 kms to the nearest airport (václav havel airport prague) 60 minute walk to the nearest metro station (dejvicka-line a) 1 km to the nearest station (tram)
Prague Airport | Prague Ruzyně International Airport hotels
Need a Flight to Prague?
Cheap flight tickets to Prague Fly to Ruzyne Airport

redpajama_set_name: RedPajamaCommonCrawl


Complete, great condition. English second edition.
Good condition, minor wear, rules are a print-out replacement. Sweetener: "Of Dungeons Deep! (2013) rating=6.81 (Of Dungeons Deep!)" Complete, minor box wear, looks great.
First edition items, many never opened. All the following are included: Two base sets (one red, pictured, opened but in great condition; one "Star Wars: X-Wing Miniatures Game – The Force Awakens Core Set (2015) rank=254 rating=8.03 (Force Awakens blue)", new in shrink) "Star Wars: X-Wing Miniatures Game – Millennium Falcon Expansion Pack (2013) rating=8.2 (Millennium Falcon)" and "Star Wars: X-Wing Miniatures Game – Slave I Expansion Pack (2013) rating=8.02 (Slave I)" expansion packs -- opened but complete, in excellent condition. No boxes. "Star Wars: X-Wing Miniatures Game – A-Wing Expansion Pack (2013) rating=7.84 (A-Wing)", "Star Wars: X-Wing Miniatures Game – B-Wing Expansion Pack (2013) rating=8 (B-Wing)", "Star Wars: X-Wing Miniatures Game – X-Wing Expansion Pack (2012) rating=7.96 (X-Wing)", "Star Wars: X-Wing Miniatures Game – TIE Bomber Expansion Pack (2013) rating=7.71 (TIE Bomber)" expansion packs -- all new, unopened.
Kickstarter edition with bonus gems and cards. New in shrink! Sweetener: "Batik (1997) rank=5361 rating=5.94 (Batik)" Box shows wear, but pieces/tower look great.
In great condition, comes with small printed player aids. Sold, removed from math trade.
New in shrink. 'Queen Bee' Kickstarter edition with extra dice/tokens. Sweetener: "Maya Madness (2003) rank=12962 rating=5.52 (Maya Madness)" Complete, good condition.
New in shrink. Sweetener: "Sequence (1982) rank=3094 rating=5.95 (Sequence)" Box opened but never played, cards/components in shrink/bags.
New in shrink! Sweetener: "Spectral Rails (2011) rank=4943 rating=6.34 (Spectral Rails)" Minor box wear. Complete, never played.
Complete, looks great. Sweetener: "Boomtown (2004) rank=1466 rating=6.55 (Boomtown)" Complete, in fine condition.
Complete, good condition. Sweetener: "Dragonlance (1988) rank=15125 rating=5.33 (Dragonlance)" This is a well-played copy, great if you just want to play around with this old game. Box shows wear but corners are intact. Both sets of rules are included, thought they also show some wear. The base of the tower has one panel that is not connected. One of the bases for the dragon gates is missing. One red dragon is missing. One bronze dragon stand is missing. One silver dragon stand is missing. One of the two d20s is missing. Cards and hex tiles are complete, though worn. Lots of altitude markers.
Sold, removed from math trade This is for 15 Skylanders hero figures, including 3 giants. Also, 4 items for use in the game, and 2 adventure figures that give you more levels to play. Spyro's Adventure and Giants for Xbox 360 are both included, as are cards, stickers, and a portal that works with both games. All in good condition and fine working order. This is a terrific, all-ages video games series if you haven't tried it.
From Kickstarter. Good condition, non-smoking home. kickstarter.com/projects/... Bonus game included: "***Missing Data*** "
Won at a gaming event, played ONCE. Good condition.
Never played, box shows minor wear.
Very good condition, only played a few times. From Kickstarter, comes with DRAGON: One of everything! You'll receive one (1) copy each of Villages, Distant Lands, Ghost Town, and the Holiday Pack, as well as a pair of Power Dice.
Minor play, good condition. Comes with 5-6 player expansion, never used.
Game is used. 100% Complete. Box and components are in very good condition.
Game has been opened, but game has not been played. Box has some minor wear on corners. Inset has some damage on corners.
Game is used but complete. Components are in good condition. Box has some small peeling on the sides where there was some tape. Also has some wear on the corners.
Game is new in shrink.
Opened and played once. In very good condition.
Excellent condition. Only played once.
Excellent condition. Box has minor shelfwear.
Excellent condition. Includes several booster packs.
Excellent condition. Sweetener: "Race to Adventure! Expansion Pack: Dinocalypse Now and the Hollow Earth (2013) rating=6.82 "
Box cover has a water stain on it, insert has suffered some small damage. All cards and components in excellent condition.
Excellent condition. German language edition, includes printout of English rules. Game is language independent.
Excellent condition, only played once. "Standard" second edition.
Box has some slight shelfwear on the corners, otherwise excellent condition.
Excellent condition, only played once.
Box has some slight shelfwear, other wise excellent condition. Travel Blokus, Educational Insight edition.
All five decks, cards are in good condition, boxes have some shelfwear.
Excellent condition. Gigamic 2003 edition.
Box has some shelfwear, other wise great condition.
Excellent condition. All wood. Brightways Products edition.
Excellent condition. Third edition with Dark City expansion.
One corner of the box was crushed. Components are in great shape.
Box cover has some dings, purple pawn has been replaced. Otherwise in good condition.
Box has some minor shelfwear. Components in great condition.
Box has some shelfwear. Missing 1 tower piece (91/92) One player reference card (2/3) and one Master card (7/8). All components in excellent condition.
Box has some slight dishing. Good condition.
Slight crease on front cover, other excellent condition.
Box is gone, in a Ultra Pro deck box. Cards in good condition.
Some wear on the box corners. Second Edition Sweeteners: "The Resistance: Hidden Agenda (2014) rating=7.82 " and "The Resistance: Hostile Intent (2014) rating=7.28 "
Great condition. English First Edition.
Excellent condition. Opened, never played.
corners are slightly dinged, overall great condition.
some shelfwear, price-tag on the cover. Overall good condition.
One creased corner, otherwise great condition.
Good condition, back cover has a creased corner. Sweetener: "Dark Champions: The Animated Series rating=8.5 " Large crease on front cover.
Good condition Sweeteners: "The Apokolips Sourcebook rating=7.5 " good condition and "The Belle Reve Sourcebook rating=8 " good condition.
New in shrink. KS promos and 5&6 player expansion included.
Opened and plated. In very good condition. Includes "Core Worlds: Galactic Orders (2012) rating=7.96 (Core Worlds: Galactic Orders )"
Box has minor shelf wear, Components are new in shrink. Sweetener: "The Great Dalmuti (1995) rank=1182 rating=6.55 (The Great Dalmuti)" Box has wear, but components are new in shrink.
Game is in good condition. Box has some minor wear. Also includes "Infernal Contraption 2: Sabotage! (2007) rating=6.31 " Infernal Contraption 2: Sabotage! does not have a box, mixed with the main game.
Game is new in shrink, but a couple corners of the box has some damage. Shrink on the back started to peel off some.
Multilingual including English. Mayfair Games. Lupus in Tabula. Just for fun, will select all Board Games with an Average Rating of 6.00 or higher! (not for expansions without base) Edit: Removed when I'm at Carnage (doesn't matter as I'll make the trade time and location). Modified above to ensure Board Games only and not an expansion.
Comment (added Sat, 20 Oct 2018 20:01:31 +0000): C u there!
Multilingual including English. Unique card game. Played once. Just for fun, will select all Board Games with an Average Rating of 6.00 or higher! (not for expansions without base) Edit: Removed when I'm at Carnage (doesn't matter as I'll make the trade time and location). Modified above to ensure Board Games only and not an expansion.
English. Very good. Played a couple times. Just for fun, will select all Board Games with an Average Rating of 6.16 or higher! (not for expansions without base) With a current average rating of 6.15, I will have "bought" low to "sell" high! Get it?!? Haha Edit: Removed when I'm at Carnage (doesn't matter as I'll make the trade time and location). Modified above to ensure Board Games only and not an expansion.
Includes both of the following: "Rook (1906) rank=2000 rating=6.38 " English. Cards in Shrink but box is beat up. Edition in picture below. "Phase 10 Dice (1993) rank=15736 rating=5.27 " English. Tin. Never played. Low expectations here, will select all games!! (Matt did that a few years ago). Post a loser game... I'll select it gladly! Will be at Carnage from early Friday to mid-Sunday.
Open played a few times. In very good condition.
Opened never played. In very good condition.
Opened played a few times. In very good condition.
Opened played once. In very good condition.
Great condition. Played once. Includes "Empire Engine (2013) rank=4996 rating=5.89 ", also great condition and played once, as a sweetener.
Includes Kickstarter add-ons. Opened, but never played. Great condition.
I believe this is a prototype version. Great condition. Played once.
NIS. Includes a stuffed voodoo doll.
Opened played once. Some slight wear on box, otherwise in very good condition.
Box wear from moving, but otherwise in Very Good condition.
Very Good condition. Sweetener: "Martian Dice (2011) rank=1904 rating=6.33 "
Very Good condition. Sweetener: "Lagoon: Land of Druids (2014) rank=2381 rating=6.41 "
Like new. Sweetener: "Cold War: CIA vs KGB (2007) rank=1130 rating=6.65 "
Very Good condition. Sweetener: "Crappy Birthday (2011) rank=8532 rating=5.67 "
Good Condition (box wear). Sweetener: "Pandemic: Contagion (2014) rank=1635 rating=6.47 "
Very Good condition. Z-Man Games English edition.
Very Good condition. Sweetener: "50 Fathoms rank=837 rating=7.7 "
Box is open, components still in shrink. Box has sticker remnant on it.
Very good condition, played a handful of times. Minor shelf wear on the box.
Very good condition, played a handful of times IELLO, English edition No insert, all components are bagged Sweetener: "King of New York: Power Up! (2016) rating=7.8 (King of New York: Power Up!)" No original expansion box, included in the base game.
Played three times Minor shelf wear. Very good condition. English 2014. Also includes (original packaging thrown away): "Munchkin 2: Unnatural Axe (2002) rating=6.44 (Munchkin 2: Unnatural Axe)" "Munchkin Naughty & Nice (2012) rating=7.01 (Munchkin: Naughty and Nice)" "Munchkin The Guild (2012) rating=6.87 (Munchkin: The Guild)"
Game is used. Box and components are in good condition.
Game is used. Box has minor wear on corners and components are in good condition. This edition has the small cards.
Opened and played a few times. In very good condition.
Game is used. Box has small puncture on top, also has wear on the corners and edges. Components are in good condition. There is no insert.
Played a handful of times. Box corners show slight shelf wear, otherwise excellent condition.
In very good shape. Only played a handful of times.
Box lid is a little loose, but all the components are in great shape. Played once.
Includes "Yardmaster Express: Caboose Expansion (2014) rating=6.26 ", a drawstring bag, and a train-shaped first player token. All components in great shape.
Very good condition. Includes King of the Keg expansion.
Includes "Dungeon Roll: Winter Heroes Pack (2014) rating=6.02 ". Box is the Mimic Version and has some minor wear at the corners. Components are all in great shape.
Great condition. Comes with 2 bullet-shaped dice.
Game Condition: Very Good. Cards Sleeved. Box Condition: Good. Some whitening at corners. Comes from a smoke-free home. I often toss useless inserts, so my games may or may not have the original insert. If this matters to you, let me know and I can check.
Game Condition: Good. Box Condition: Good. Some whitening on box. Comes from a smoke-free home. I often toss useless inserts, so my games may or may not have the original insert. If this matters to you, let me know and I can check.
Game Condition: Very good. Played once or twice. Box Condition: Very good. Comes from a smoke-free home. I often toss useless inserts, so my games may or may not have the original insert. If this matters to you, let me know and I can check.
Game Condition: Good. Box Condition: Good. Some whitening on edges. Comes from a smoke-free home. I often toss useless inserts, so my games may or may not have the original insert. If this matters to you, let me know and I can check.
Includes expansion cards: "Captain's Wager: The Maelstrom (2015) rating=6.35 "
2009 Asmodee Version. Includes the expansion "Dice Town: Wild West (2011) rating=7.35 " (the 2011 version called "Dice Town: Expansion"), stored in the base game box. Game Condition: Good. Box Condition: Fair to good. Whitening on box. Comes from a smoke-free home. I often toss useless inserts, so my games may or may not have the original insert. If this matters to you, let me know and I can check.
Third edition from FFG. Game Condition: Very good. Box Condition: Very good. Comes from a smoke-free home. I often toss useless inserts, so my games may or may not have the original insert. If this matters to you, let me know and I can check.
Z-Man English version. Game Condition: Good. Box Condition: Good. Whitening on edges. Comes from a smoke-free home. I often toss useless inserts, so my games may or may not have the original insert. If this matters to you, let me know and I can check.
Includes "Core Worlds: Galactic Orders (2012) rating=7.96 ". All is stored in the expansion box. Game Condition: Very good. Box Condition: Good. Some whitening on box edges. Comes from a smoke-free home. I often toss useless inserts, so my games may or may not have the original insert. If this matters to you, let me know and I can check.
Box is a little dinged up, but components are in good shape.
Box shows some light wear. Components are in excellent condition.


Are you all ready for some more free food? I've recently been on this kick of downloading the apps for restaurants just to see how they work and (yes, I'll admit) get free food. Last month I wrote about the McDonald's and the Burger King apps but now let's talk chicken.
This month, if you download the Chick-fil-A app and sign in (either through Facebook, Google, or create a restaurant specific account) you'll get a free 8 piece nugget order! The Chick-fil-A app is different than the other restaurant apps I've tried because it makes you sign in and then keeps track of your orders and earns you points. Those points can be used later to purchase free food. I have yet to earn any points so I don't know how well that works but I will be getting some free chicken nug nugs soon.
Don't forget, we are still waiting for those Chick-fil-A home meal kits to become a reality too.


text:
namespace NadekoBot.Classes._DataModels {
    class CurrencyState : IDataModel {
        public long Value { get; set; }
        [SQLite.Unique]
        public long UserId { get; set; }
    }
}

redpajama_set_name: RedPajamaGithub


text:
\section{Introduction}
The proliferation of smart mobile devices, coupled with new types of wireless applications, has led to an exponential growth of wireless and mobile data traffic.  In order to meet the data explosion, many advanced network architectures with dense deployment and coordination among the access points (APs) have been proposed for 5G cellular networks.  For instance, in network MIMO systems  \cite{Andrews_TIT2013}, all the APs are connected
through the backhaul links such that the channel state information (CSI) and user data can be shared among
the APs. By deploying a large number of APs, a large-scale full cooperative
network will be created.  In the recently proposed Cloud-RAN \cite{Yuanming_TWC2013,Yuanming_arXivOpt13}, all the
baseband signal processing is shifted to a single baseband unit (BBU)
pool with very powerful computational
capability.  The centralized signal processing is
performed at the BBU pool, to support large-scale cooperative transmission/reception among APs.

With the increasing demand of high capacity, it is critical to design efficient coordinated beamforming to take advantage of the full cooperation in dense networks. Considering the computational complexity, zero-forcing (ZF), regularized zero-forcing (RZF), and maximum ratio transmission (MRT) precoding are often adopted. However, such low-complexity strategies might significantly degrade system performance. The existing works on designing optimal coordinated beamforming
either apply the advanced off-the-shelf interior-point solvers like SeDuMi \cite{SeDuMi_1999using} or exploit the problem structures to design the custom solver, e.g., using the uplink-downlink duality theory \cite{WeiYu_WC10}. Although these algorithms have polynomial time complexity, such second-order methods
still are not efficient for the coordinated beamforming problems with a large
dimension. For practical implementation, the first-order method ADMM \cite{boyd2011distributed} has recently been widely used to solve large-scale optimization problems to modest accuracy within reasonable time. However, most existing works (e.g., \cite{shen2012distributed}) on applying the ADMM algorithms still need to solve convex problems (e.g., semidefinite programming (SDP) problem) for the subproblems at each iteration, though they enjoy the distributed implementation property. Therefore, in order to improve the efficiency of the ADMM algorithm, we need to reduce the computational complexity for solving the subproblems in the ADMM algorithm.

In this paper, we propose a framework to design a scalable optimization algorithm based on the ADMM method to solve the coordinated beamforming problems in dense networks, with the number of cooperating APs as high as 100. By introducing a new variable for each subexpression in the original coordinated beamforming problem based on the \emph{Smith form} reformulation \cite{boyd_code2013}, we transform the original problem into the equivalent ADMM-compliant problem. For any fixed size networks (i.e., given the number of APs and MUs), the structure of the ADMM-compliant problem is fixed. Therefore, we can first generate and store the structure of the ADMM-compliant problem for any network  with a  fixed size, which can be done offline. For any particular network realization, we only need to copy the parameters of the original problem to the ADMM-compliant problem. A similar idea was presented in \cite{boyd_code2013} for embedded systems, called the \emph{matrix stuffing} technique. Compared to the modeling framework CVX \cite{cvx}, this method only needs to copy the memory and can be much more efficient. We shall propose to use the ADMM method to solve the transformed ADMM-compliant problem. With the special structure of the transformed ADMM-compliant problem, we can solve the subproblems of the corresponding ADMM algorithm at each iteration with closed-forms and in parallel. Simulation results will demonstrate  speedups of
several orders of magnitude of the proposed techniques
for large-scale coordinated beamforming over the state-of-the-art interior-point solvers. Furthermore, simulation
results will show that the optimal coordinated beamforming outperforms zero forcing beamforming significantly.

\section{Coordinated Beamforming for Maximizing the minimum network-wide achievable rate}
Consider a cellular network with $L$ access points (APs), where the $l$-th AP is equipped with $N_{l}$ antennas, and with $K$ single-antenna mobile users (MUs). We mainly consider the full cooperative networks, though the algorithms proposed in this paper can be easily extended to other kinds of cooperation strategies. The critical question is how to take full advantage of the cooperation with scalable and efficient coordinated beamforming algorithms instead of simply adopting the suboptimal strategies such as zero-forcing beamforming. In this paper, we mainly focus on maximizing the minimum network-wide achievable rate. This problem is formulated as the following max-min fairness
optimization problem with per-AP transmit power constraints:
\begin{eqnarray}
\label{mm}
\mathop {\rm{maximize~}}_{{\bf{v}}}&&\left(\min_{1\le k\le K}\omega_{k}\log_2(1+{{\Gamma}}_{k}({\bf{v}};
{\bf{h}}_k))\right)\nonumber\\
{\rm{subject~to~}}&&  \sum_{k=1}^K\|{\bf{v}}_{lk}\|_2^2\le P_l, \forall l,
\end{eqnarray}
where $\omega_k>0$ is the weight for MU $k$ and $\Gamma_{k}({\bf{v}}; {\bf{h}}_k)$ is the achievable SINR at MU $k$ using the single user detection
\setlength\arraycolsep{1pt}
\begin{eqnarray}
{{\Gamma}}_{k}({\bf{v}}; {\bf{h}}_k)={{|{\bf{h}}_k^{\sf{H}}{\bf{v}}_k|^2}\over{\sum_{i\ne
k}|{\bf{h}}_{k}^{\sf{H}}{\bf{v}}_i|^2}+\sigma_k^2}, \forall k,
\end{eqnarray}
where ${\bf{h}}_{k}= [{\bf{h}}_{k1}^{T},{\bf{h}}_{k2}^{T},\dots,{\bf{h}}_{kL}^{T}]^{T}\in\mathbb{C}^{N}$
with ${\bf{h}}_{kl}\in\mathbb{C}^{N_l}$ as the channel coefficient vector between AP $l$ and MU $k$ and $N=\sum_{l=1}^{L}N_{l}$, and ${\bf{v}}_{k}=[{\bf{v}}_{1k}^{T},
{\bf{v}}_{2k}^{T},\dots, {\bf{v}}_{Lk}^{T}]^{T}\in\mathbb{C}^{N}$ with ${\bf{v}}_{lk}\in\mathbb{C}^{N_l}$ as the beamforming vector at AP $l$ for MU $k$, and $P_l$ is the maximum transmit power at AP $l$.

Problem (\ref{mm}) can be solved by
a bi-section method \cite{boyd2004convex}. Specifically, given a threshold $\gamma$, we need to
solve the following optimization
problem
\begin{eqnarray}
\label{feasible}
\mathscr{P}:
\mathop {\rm{minimize~}} && \|{{\bf{v}}}\|_2\nonumber\\
{\rm{subject~to~}}&&  \omega_{k}\log_2(1+{{\Gamma}}_{k}({\bf{v}};
{\bf{h}}_k))\ge\gamma, \forall
k\nonumber\\
&&\sum_{k=1}^K\|{\bf{v}}_{lk}\|_2^2\le P_l, \forall l,
\end{eqnarray}
which can be reformulated as an SOCP problem \cite{Yuanming_TWC2013,WeiYu_WC10}.  Therefore, the max-min fairness optimization algorithm is presented as Algorithm 1.
\begin{algorithm}
\caption{Max-min Fairness Optimization Algorithm }
\begin{itemize}
\item Initialize the $\gamma_{\textrm{low}}=0$ and $\gamma_{\textrm{up}}=\gamma_{\textrm{max}}$;\\
\item Repeat
\begin{enumerate}
\item Set $\gamma\leftarrow (\gamma_{\textrm{low}}+\gamma_{\textrm{up}})/2$;
\item Solve problem $\mathscr{P}$ with the given $\gamma$; if it is feasible,\\
set $\gamma_{\textrm{low}}\leftarrow\gamma$; otherwise, set $\gamma_{\textrm{up}}\leftarrow\gamma$;
\end{enumerate}
\item Until $r_{\textrm{up}}-r_{\textrm{low}}<\epsilon$, where
$\epsilon$ represents the accuracy requirement.
\end{itemize}
\end{algorithm}

\subsection{Problem Analysis}
The main computational complexity of the optimal coordinated beamforming  is solving the convex optimization problem $\mathscr{P}$ with different SINR thresholds. In order to solve the problem $\mathscr{P}$, one might use the advanced off-the-shelf interior-point solvers like SeDuMi \cite{SeDuMi_1999using}. But such second-order method is unable to handle problems with a large dimension, as it has the computational complexity $\mathcal{O}(N^{3.5}K^{3.5})$. Moreover, in order to use the standard interior-point solvers, one needs to transform the problem $\mathscr{P}$ into a standard form. The modeling framework CVX \cite{cvx} can carry out a sequence of equivalence transformations to yield a problem that can be handled by a standard interior-point solver. But this procedure is not efficient, as for each problem instance (i.e., given the problem parameters), CVX will check the convexity of the problem $\mathscr{P}$ and then transform it to a standard form using the graph implementation \cite{boyd2008graph} to represent the convex functions. In order to solve the large-scale optimization problem $\mathscr{P}$, in this paper, we propose a framework based on the ADMM method.

\subsubsection{ADMM Algorithm}
For practical implementation of the coordinated beamforming, we propose to use the first-order method, i.e., the ADMM algorithm, to solve the large-scale optimization problem $\mathscr{P}$. Consider the following convex optimization problem of the form
\begin{eqnarray}
\label{admmo}
\mathop {\rm{maximize~}}_{{\bf{x}}, {\bf{y}}}&&f({\bf{x}})+g({\bf{y}})\nonumber\\
{\rm{subject~to~}}&&  {\bf{x}}-{\bf{y}}={\bf{0}},
\end{eqnarray}
where $f({\bf{x}})$ and $g({\bf{y}})$ are convex functions. The ADMM algorithm solves problem (\ref{admmo}) iteratively by the following three steps at each iteration $k$:
\begin{eqnarray}
\label{admm1}
{\bf{x}}^{[k+1]}&=&\arg\min_{\bf{x}} (f({\bf{x}})+(\rho/2)\|{\bf{x}}-{\bf{y}}^{[k]}+{\boldsymbol{\lambda}}^{[k]}\|_2^2),\\
\label{admm2}
{\bf{y}}^{[k+1]}&=&\arg\min_{\bf{y}} (g({\bf{y}})+(\rho/2)\|{\bf{x}}^{[k+1]}-{\bf{y}}+{\boldsymbol{\lambda}}^{[k]}\|_2^2),\\
{\boldsymbol{\lambda}}^{[k+1]}&=&{\boldsymbol{\lambda}}^{[k]}+{\bf{x}}^{[k+1]}-{\bf{y}}^{[k+1]},
\end{eqnarray}
where $\rho>0$ is a step size parameter and $\boldsymbol{\lambda}$ is the dual variable associated with the constraint ${\bf{x}}-{\bf{y}}={\bf{0}}$. Under some very mild conditions \cite[Section 3.2]{boyd2011distributed} (e.g., the functions $f$ and $g$ are closed, proper, and convex),  the solutions obtained from the ADMM algorithm converge to a global optimal solution, i.e., $f({\bf{x}}^{[k]})+g({\bf{y}}^{[k]})$ converges to the optimal value, ${\boldsymbol{\boldsymbol{\lambda}}}^{[k]}$ converges to an optimal dual variable, and ${\bf{x}}^{[k]}-{\bf{y}}^{[k]}$ converges to zero.

The main advantage of the ADMM algorithm is that the subproblems (\ref{admm1}) and (\ref{admm2}) can be solved with closed-form and in parallel
in many applications, e.g., in machine learning and high dimensional statistics. However, for the coordinated beamforming problem $\mathscr{P}$,  it is not clear how to reformulate the problem $\mathscr{P}$ such that the subproblems of the corresponding ADMM algorithm can be solved with closed-forms and in parallel. Although there are some works applying the ADMM algorithm to solve the coordinated beamforming problems \cite{shen2012distributed} with distributed implementation, they still need to solve SDP problems for the subproblems of the ADMM algorithm at each iteration. This is not efficient in terms of computational complexity.

To apply the ADMM algorithm to solve the large-scale optimization problem $\mathscr{P}$ efficiently, in this paper, we propose a framework as shown in Fig. {\ref{dcp}}. It will first transform the original problem $\mathscr{P}$ to the equivalent ADMM-compliant form $\mathscr{P}_{\textrm{ADMM}}$ as follows based  the Smith form reformulation \cite{boyd_code2013}:
\begin{eqnarray}
\mathscr{P}_{\textrm{ADMM}}:
\mathop {\rm{minimize~}}_{{\bs{\nu}}, {\bs{\mu}}}&&{\bf{c}}^{T}{\bs{\nu}}\nonumber\\
{\rm{subject~to~}}&& {\bf{A}}{\bs{\nu}}+{\bs{\mu}}={\bf{b}}\nonumber\\
&& ({\bs{\nu}}, {\bs{\mu}})\in\mathbb{R}^{n}\times\mathcal{V}.
\end{eqnarray}
where ${\bs{\nu}}\in\mathbb{R}^n$ and ${\bs{\mu}}\in\mathbb{R}^{m}$ are the
optimization variables, $\mathcal{V}=\{0\}^{r}\times\mathcal{Q}^{m_1}\times\cdots\times\mathcal{Q}^{m_q}$
with ${\mathcal{Q}}^{p}=\{(t, {\bf{x}})\in\mathbb{R}\times\mathbb{R}^{p-1}|
\|{\bf{x}}\|\le t\}$ as the second-order cone of dimension $p$, and $\mathcal{Q}^{1}$ is defined as the cone of nonnegative reals, i.e., $\mathbb{R}_{+}$.
Here, each $\mathcal{Q}^i$
has dimension $m_i$ such that $(r+\sum_{i=1}^q m_i)=m$, ${\bf{A}}\in\mathbb{R}^{m\times
n}$, ${\bf{b}}\in\mathbb{R}^{m}$, ${\bf{c}}\in\mathbb{R}^{n}$. The idea of Smith form reformulation is simple and we only need to introduce a new variable for each subexpression in the original problem $\mathscr{P}$. We then propose to use the ADMM algorithm to solve the homogeneous self-dual embedding \cite{ye1994nl} of the problem$\mathscr{P}_{\textrm{ADMM}}$. As a result, each subproblem in the corresponding ADMM algorithm can be solved with closed-forms and in parallel. This will be much more efficient than the previous works on applying the ADMM algorithms to design the coordinated beamformers \cite{shen2012distributed}.
\begin{figure}[!t]
\centering
\tikzstyle{int}=[draw, fill=blue!20, minimum size=2em]
\tikzstyle{init} = [pin edge={to-,thin,black}]
\begin{tikzpicture}
    [node distance=4cm,auto,>=latex']
    \node [int, ] (a) {Transformation};
    \node (b) [left of=a,node distance=2cm, coordinate] {a};
    \node [int, ] (c) [right of=a] {ADMM Solver};
    \node [coordinate] (end) [right of=c, node distance=2.0cm]{};
    \path[->] (b) edge node {$\mathscr{P}$} (a);
    \path[->] (a) edge node {$\mathscr{P}_{\textrm{ADMM}}$} (c);
    \draw[->] (c) edge node {$\bf{x}$} (end) ;
\end{tikzpicture}
\caption{The framework of the large-scale optimization algorithm}
\label{dcp}
\end{figure}

\section{Matrix stuffing for Fast Transformation}
\label{mats}
In this section, we propose a framework to transform the original
problem $\mathscr{P}$ to the equivalent ADMM-compliant problem $\mathscr{P}_{\textrm{ADMM}}$, i.e., for the first stage of Fig. 1. Although CVX can perform this procedure automatically, it needs to carry out a sequence of equivalence transformations. This is not efficient, especially with a large number of constraints in a dense network.

Instead, in this paper, we propose to transform the original problem
$\mathscr{P}$ using the {Smith form} reformulation, which involves introducing a new variable for each subexpression in the functions of problem $\mathscr{P}$. This transformation has two advantages: first, the parameters in the original problem $\mathscr{P}$ only appear in the affine functions of the transformed ADMM-compliant problem $\mathscr{P}_{\textrm{ADMM}}$, which is suitable for matrix stuffing as will be shown in Section {\ref{ms}}; second, the cone in $\mathscr{P}_{\textrm{ADMM}}$ is a Cartesian product of the standard cones, thus the subproblems (\ref{admm1}) and (\ref{admm2}) of the corresponding ADMM algorithm can be solved with closed-forms and in parallel. We first deal with the real-field case,  the extension to the complex-field case will be discussed in Section \ref{complex}.

\subsection{ADMM-Compliant Form Reformulation for Problem $\mathscr{P}$}
In this subsection, we reformulate the real-field problem $\mathscr{P}$ by introducing a new variable for each subexpression in $\mathscr{P}$, resulting in the equivalent ADMM-compliant form $\mathscr{P}_{\textrm{ADMM}}$.

Specifically, for the objective function $f({\bf{v}})=\|{\bf{v}}\|_2$, by introducing the new variables $x_0$ and ${\bf{x}}_1$, minimizing $f({\bf{v}})$ is equivalent to minimizing $x_0$ with the following constraints
\begin{eqnarray}
\mathcal{G}_1:\left\{\begin{array}{l}
(x_0, {\bf{x}}_1)\in\mathcal{Q}^{M+1}\\
{\bf{x}}_1={\bf{v}}\in\mathbb{R}^{M},
\end{array}\right.
\end{eqnarray}
where $M=KN$. With variable $[x_0; {\bf{v}}]$ and the same order of equations as in $\mathcal{G}_1$, $\mathcal{G}_1$ can be rewritten as
\begin{eqnarray}
{\bf{M}}[{{x}}_0; {\bf{v}}]+{\bs{\mu}}_1={\bf{m}},
\end{eqnarray}
with ${\bf{M}}={\rm{blkdiag}}\{-1,-{\bf{I}}_M\}\in\mathbb{R}^{(M+1)\times(M+1)}$
and ${\bf{m}}=[0,{\bf{0}}_M^T]^{T}$ and ${\bs{\mu}}_1\in\mathcal{Q}^{M+1}$.

For the per-AP transmit power constraint $\|\tilde{\bf{v}}_l\|_2\le \sqrt{P_l}$
with $\tilde{\bf{v}}_l=[{\bf{v}}_{l1}^{T},\dots, {\bf{v}}_{lK}^{T}]^{T}\in\mathbb{R}^{KN_l}$,
we first have the following
equivalent expressions
\begin{eqnarray}
\|\tilde{\bf{v}}_l\|_2\le\sqrt{P_l}\Longrightarrow\|{\bf{D}}_l{\bf{v}}\|_2\le
\sqrt{P_l},
\end{eqnarray}
where ${\bf{D}}_{l}={\rm{blkdiag}}\{{\bf{D}}_l^1,\dots,{\bf{D}}_l^K\}\in\mathbb{R}^{KN_l\times
M}$ with ${\bf{D}}_{l}^k=\left[{\bf{0}}_{N_{l}\times\sum_{i=1}^{l-1}N_i},{\bf{I}}_{N_l\times
N_l}, {\bf{0}}_{{N_l}\times
\sum_{i=l+1}^{L}N_i}\right]\in\mathbb{R}^{N_{l}\times N}$ such that ${\bf{D}}_l{\bf{v}}\triangleq\tilde{\bf{v}}_l$. By introducing the new variables $y_{0}^l$ and ${\bf{y}}_1^l$, we have the following equivalent formulation for the constraint $\|{\bf{D}}_l{\bf{v}}\|_2\le
\sqrt{P_l}$, i.e.,
\begin{eqnarray}
\mathcal{G}_2(l):\left\{\begin{array}{l}
 (y_0^l, {\bf{y}}_1^{l})\in\mathcal{Q}^{KN_l+1}\\
y_0^l=\sqrt{P_l}\in\mathbb{R}\\
{\bf{y}}_1^l={\bf{D}}_l{\bf{v}}\in\mathbb{R}^{KN_l}.
\end{array}\right.
\end{eqnarray}
With variable $[y_0^l; {\bf{v}}]$ and the same order
of equations as in $\mathcal{G}_2(l)$, $\mathcal{G}_2(l)$ can be rewritten as
\begin{eqnarray}
{\bf{P}}^l[{{y}}_0^{l}; {\bf{v}}]+{\bs{\mu}}_2^l={\bf{p}}^l,
\end{eqnarray}
where
\begin{eqnarray}
\!\!\!\!\!{\mathbf{P}}^l =
\left[ \begin{array}{rc}
1&  \\
\hline
-1&   \\
&   -{\bf{D}}_l

\end{array} \right]\in\mathbb{R}^{(KN_l+2)\times(M+1)},
{{\bf{p}}}^l=\left[ \begin{array}{c}
\sqrt{P_l} \\
\hline
0\\
{\bf{0}}_{KN_l}
\end{array} \right],
\end{eqnarray}
and ${\bs{\mu}}_2^l\in\mathcal{Q}^{1}\times\mathcal{Q}^{KN_l+1}$.

For the QoS constraint of MU $k$, let $\theta_k=2^{\gamma/\omega_k}-1$,
we have the following equivalent expressions
\begin{eqnarray}
\label{qs1}
\!\!\!\!\!\!{{|{\bf{h}}_k^{{T}}{\bf{v}}_{k}|^2}\over{{\sum\nolimits_{i\ne
k}|{\bf{h}}_k^{{T}}{\bf{v}}_{i}|^2}}+\sigma_{k}^2}\ge \theta_{k}\Longrightarrow\|{\bf{C}}_k{\bf{v}}+{\bf{g}}_k\|_2\le
\beta_{k}{\bf{r}}_k^{T}{\bf{v}},
\end{eqnarray}
where $\beta_k=\sqrt{1+1/\theta_k}\in\mathbb{R}$, ${\bf{g}}_k=[{\bf{0}}_K^T,
\sigma_k]^T\in\mathbb{R}^{K+1}$, ${\bf{C}}_k\in\mathbb{R}^{(K+1)\times
M}$ is
given by
\begin{eqnarray}
\mathbf{C}_k =
\left[ \begin{array}{ccc}
{\bf{h}}_k^{T} & & \\
&\ddots &\\
& & {\bf{h}}_k^{T} \\
 \hline\\[-3.7mm]
&{\bf{0}}_{M}^{T} &
\end{array} \right]\in\mathbb{R}^{(K+1)\times M},
\end{eqnarray}
and ${\bf{r}}_k=\left[{\bf{0}}_{(k-1)\sum_{l=1}^LN_l}^{T},{\bf{h}}_k^{T},
{\bf{0}}_{(K-k)\sum_{l=1}^LN_l}^{T}\right]^{T}\in\mathbb{R}^M$. By introducing the new variables $t_0^k$ and ${\bf{t}}_1^k$, we have the following equivalent formulation for $\|{\bf{C}}_k{\bf{v}}+{\bf{g}}_k\|_2\le
\beta_{k}{\bf{r}}_k^{T}{\bf{v}}$, i.e.,
\begin{eqnarray}
\mathcal{G}_3(k):\left\{\begin{array}{l}
(t_0^k, {\bf{t}}_1^k)\in\mathcal{Q}^{K+1}\\
t_0^k=\beta_{k}{\bf{r}}_k^{T}{\bf{v}}\in\mathbb{R}\\
{\bf{t}}_1^k={\bf{t}}_2^k+{\bf{t}}_3^k\in\mathbb{R}^{K+1}\\
{\bf{t}}_2^k={\bf{C}}_k{\bf{v}}\in\mathbb{R}^{K+1}\\
{\bf{t}}_3^k={\bf{g}}_k\in\mathbb{R}^{K+1}.
\end{array}\right.
\end{eqnarray}
As a result, with variable $[t_0^k; {\bf{v}}]$ and the same order
of equations as in $\mathcal{G}_3(k)$, $\mathcal{G}_3(k)$ can be rewritten as
 \begin{eqnarray}
{\bf{Q}}^k[t_{0}^k;{\bf{v}}]+{\bs{\mu}}_3^k={\bf{q}}^k,
\end{eqnarray}
where
\begin{eqnarray}
{\mathbf{Q}}^k =
\left[ \begin{array}{rc}
1& -\beta_{k}{\bf{r}}_k^{T} \\
\hline
-1&   \\
&   -{\bf{C}}_k

\end{array} \right]\in\mathbb{R}^{(K+3)\times(M+1)},
{{\bf{q}}}^k=\left[ \begin{array}{c}
0 \\
\hline
0\\
{\bf{g}}_k
\end{array} \right],
\end{eqnarray}
and ${\bs{\mu}}_3^k\in\mathcal{Q}^{1}\times \mathcal{Q}^{K+2}$.

Now we arrive at the following ADMM-compliant problem $\mathscr{P}_{\textrm{ADMM}}$
with the
optimization variables given by ${\bs{\nu}}=[x_0; y_0^{1};\dots; y_0^{L};
t_0^1; \dots, t_0^K; {\bf{v}}]\in\mathbb{R}^{n}$
and ${\bf{c}}=[1; {\bf{0}}_{n-1}]$. The ADMM-compliant problem $\mathscr{P}_{\textrm{ADMM}}$
structure is characterized by the following data
\begin{eqnarray}
\label{ds1}
n&=&1+L+K+M,\\
m&=&(L+K)\!+\!(M+1)\!+\!\sum_{l=1}^{L}(KN_l+1)\!+\!K(K+2),\\
\mathcal{V}&=& \underbrace{\mathcal{Q}^{1}\times\cdots\times\mathcal{Q}^1}_{L+K}\times\mathcal{Q}^{M+1}\times
\underbrace{\mathcal{Q}^{KN_1+1}\times\dots\times\mathcal{Q}^{KN_L+1}}_{L}\nonumber\\
&&\times\underbrace{\mathcal{Q}^{K+2}\times\dots\times\mathcal{Q}^{K+2}}_{K},
\end{eqnarray}
where $\mathcal{V}$ is the Cartesian product of $2(L+K)+1$ closed convex ones, and
 ${\bf{A}}$ and $\bf{b}$ are given as
follows:
\begin{eqnarray}
\label{ds2}
\!\!\!\!\!\!\!\!\!\!{\mathbf{A}} =
\left[ \begin{array}{ccccccc|c}
&1&&&&&\\
&&\ddots&&&&\\
&&&1&&&\\
\hline
&&&&1&&&-\beta_{1}{\bf{r}}_1^{T}\\
&&&&&\ddots&&\vdots\\
&&&&&&1&-\beta_{K}{\bf{r}}_K^{T}\\
\hline
-1&&&&&&&\\
&&&&&&&-{\bf{I}}_B\\
\hline
&-1&&&&&&\\
&&&&&&&-{\bf{D}}_1\\
\hline
&&&\vdots&&&&\vdots\\
\hline
&&&-1&&&&\\
&&&&&&&-{\bf{D}}_L\\
\hline
&&&&-1&&&\\
&&&&&&&-{\bf{C}}_1\\
\hline
&&&\vdots&&&&\vdots\\
\hline
&&&&&&-1&\\
&&&&&&&-{\bf{C}}_K\\
\end{array} \right],
{\bf{b}}=\left[ \begin{array}{c}
\sqrt{P_1}\\
\vdots\\
\sqrt{P_L}\\
\hline
0\\
\vdots\\
0\\
\hline
{\bf{0}}_{B}\\
\hline
0\\
{\bf{0}}_{KN_1}\\
\hline
\vdots\\
\hline
0\\
{\bf{0}}_{KN_1}\\
\hline
0\\
{\bf{g}}_1\\
\hline
\vdots\\
\hline
0\\
{\bf{g}}_K
\end{array}\right],
\end{eqnarray}

\subsection{Matrix Stuffing for Transformation}
\label{ms}
Given the network size, i.e., the number of APs and MUs, the structure of the ADMM-compliant problem $\mathscr{P}_{\textrm{ADMM}}$ is fixed. Therefore, we can first generate and store the problem structure of $\mathscr{P}_{\textrm{ADMM}}$ for a fixed-size network, i.e., the structure of ${\bf{A}}$, $\bf{b}$, $\bf{c}$, and the descriptions of $\mathcal{V}$. This procedure can be done offline as the number of APs and MUs will keep constant  for a long period. Then for any specific network realization, we only need to
copy the parameters of the original problem  to the corresponding data in $\mathscr{P}_{\textrm{ADMM}}$. Specifically, we only need to copy the parameters of the maximum transmit power $P_{l}$'s to the data of the ADMM-compliant problem, i.e.,  $\sqrt{P_l}$'s in $\bf{b}$, copy the parameters of the SINR thresholds $\gamma$ to the data of the ADMM-compliant problem, i.e., $\beta_k$'s in ${\bf{A}}$, and copy the parameters of the channel realizations ${\bf{h}}_k$'s to the data of the ADMM-compliant problem, i.e., ${\bf{r}}_k$'s and ${\bf{C}}_k$'s in $\bf{A}$. As we only need to perform copying the memory for the transformation, this procedure can be very efficient compared to the state-of-the-art modeling framework CVX.

\subsection{Extension to the Complex Case}
\label{complex}
In this subsection, we present how to extend the real-field problem to the complex-field problem. For ${\bf{h}}_k\in\mathbb{C}^{N},
{\bf{v}}_{i}\in\mathbb{C}^{N}$, we have
\begin{eqnarray}
{\bf{h}}_k^{\sf{H}}{\bf{v}}_i\Longrightarrow
{\underbrace{\left[ \begin{array}{cc}
\mathfrak{R}({\bf{h}}_k)\ & -\mathfrak{J}({\bf{h}}_k) \\
\mathfrak{J}({\bf{h}}_k)\ & \mathfrak{R}({\bf{h}}_k)
\end{array} \right]}_{\tilde{\bf{h}}_k}}^{T}\underbrace{\left[ \begin{array}{c}
\mathfrak{R}({\bf{v}}_i)\ \\
\mathfrak{J}({\bf{v}}_i)
\end{array} \right]}_{\tilde{\bf{v}}_i},
\end{eqnarray}
where $\tilde{\bf{h}}_k\in\mathbb{R}^{2N\times
2N}$ and $\tilde{\bf{v}}_i\in\mathbb{R}^{2N}$. Therefore, the complex-field problem can be changed into the real-field problem by
the transformations: ${\bf{h}}_k\Rightarrow\tilde{\bf{h}}_k~{\textrm{and}}~{\bf{v}}_i\Rightarrow\tilde{\bf{v}}_i$.

\section{The ADMM Algorithm For Large-Scale Coordinated Beamforming}
\label{os}
In this section, we propose
to use the ADMM algorithm \cite{boyd2011distributed}, a.k.a. the operator splitting method \cite{Boyd_arXiv2013}, to solve the ADMM-compliant problem $\mathscr{P}_{\textrm{ADMM}}$. Specifically,
we first introduce the homogeneous self-dual embedding \cite{ye1994nl} for the ADMM-compliant problem $\mathscr{P}_{\textrm{ADMM}}$. Then we use the ADMM algorithm \cite{boyd2011distributed,Boyd_arXiv2013} instead of the interior-point method to solve the embeddings with a large dimension. This approach can solve large-scale optimization problems to modest accuracy very efficiently and can also be parallelizable  across multiple processors.

\subsection{Homogeneous Self-Dual Embedding}
The dual problem of $\mathscr{P}_{\textrm{ADMM}}$ is given by
\begin{eqnarray}
\mathscr{D}_{\textrm{ADMM}}:
\mathop {\rm{minimize}}_{{\boldsymbol{\eta}}, {\boldsymbol{\lambda}}}&&-{\bf{b}}^{T}{\boldsymbol{\eta}}\nonumber\\
{\rm{subject~to}}&& -{\bf{A}}^{T}{\boldsymbol{\eta}}+{\boldsymbol{\lambda}}={\bf{c}}\nonumber\\
&& ({\boldsymbol{\lambda}}, {\boldsymbol{\eta}})\in\{0\}^{n}\times\mathcal{V}^{*},
\end{eqnarray}
where $\boldsymbol{\lambda}\in\mathbb{C}^{n}$ and $\boldsymbol{\eta}\in\mathbb{C}^m$
are the dual variables, $\mathcal{V}^*$ is the dual cone of the non-empty
closed convex cone $\mathcal{V}$ and $\{0\}^n$ is the dual cone of $\mathbb{R}^n$. The Karush-Kuhn-Tucker (KKT) conditions are necessary and sufficient for optimality when strong duality holds. Specifically, when\begin{eqnarray}
{\bf{A}}{\bs{\nu}}^{\star}+{\bs{\mu}}^{\star}&=&{\bf{b}}, {\bs{\mu}}^{\star}\in\mathcal{V}, {\bf{c}}^{T}{\bs{\nu}}^{\star}+{\bf{b}}^{T}{\boldsymbol{\eta}}^{\star}={\bf{0}}, \nonumber\\ {\bf{A}}^{T}{\boldsymbol{\eta}}^{\star}+{\bf{c}}&=& {\boldsymbol{\lambda}}^{\star}, {\boldsymbol{\lambda}}^{\star}={\bf{0}}, {\boldsymbol{\eta}}^{\star}\in\mathcal{V}^{*},
\end{eqnarray}
$({\boldsymbol{\nu}}^{\star},
{\boldsymbol{\mu}}^{\star}, {\boldsymbol{\lambda}}^{\star}, {\boldsymbol{\eta}}^{\star})$
satisfies the KKT conditions and is primal-dual optimal. By introducing two new nonnegative variables ${{\tau}}$ and ${{\kappa}}$, the original primal-dual problems $\mathscr{P}_{\textrm{ADMM}}$ and $\mathscr{D}_{\textrm{ADMM}}$ can be converted into a single feasibility
problem by embedding the Karush-Kuhn-Tucker (KKT) conditions into the following
single system of equations, i.e., the homogeneous self-dual embedding \cite{ye1994nl}:
\begin{eqnarray}
\label{emb}
\underbrace{\left[ \begin{array}{c}
{\bs{\lambda}} \\
{\boldsymbol{\mu}} \\
{{\kappa}}
\end{array} \right]}_{\bf{y}}=\underbrace{\left[ \begin{array}{ccc}
{\bf{0}} & {\bf{A}}^{T} & {\bf{c}} \\
-{\bf{A}} & {\bf{0}} & {\bf{b}} \\
-{\bf{c}}^{T} & -{\bf{b}}^{T} & {\bf{0}}
\end{array} \right]}_{\bf{Q}}
\underbrace{\left[ \begin{array}{c}
{\bs{\nu}} \\
{\boldsymbol{\eta}} \\
{{\tau}}
\end{array} \right]}_{\bf{x}},
\end{eqnarray}
where $({\bf{x}}, {\bf{y}})\in \mathcal{C}\times \mathcal{C}^{*}$ with $\mathcal{C}=\mathbb{R}^n\times \mathcal{V}^*\times
\mathbb{R}_+$ and $\mathcal{C}^{*}=\{0\}^n\times\mathcal{V}\times\mathbb{R}_{+}$.

\subsection{ADMM Algorithm for the Homogeneous Self-Dual Embedding}
To apply the
 ADMM algorithm, we first transform the embedding system (\ref{emb}) to the following ADMM form
\begin{eqnarray}
\label{admm}
\mathscr{P}_{\textrm{Emb}}:
\mathop {\rm{minimize}}_{{\bf{x}}, \tilde {\bf{x}},{\bf{y}},  \tilde{\bf{y}}}&& I_{\mathcal{C}\times\mathcal{C}^{*}}({\bf{x}}, {\bf{y}})+I_{{\bf{Q}}\tilde{\bf{x}}=\tilde{\bf{y}}}(\tilde{\bf{x}}, \tilde{\bf{y}})\nonumber\\
{\rm{subject~to}}&& ({\bf{x}}, {\bf{y}})=(\tilde{\bf{x}}, \tilde{\bf{y}}),
\end{eqnarray}
where $I_{\mathcal{S}}$ is the indicator function of the set $\mathcal{S}$. Applying the ADMM algorithm to the problem $\mathscr{P}_{\textrm{Emb}}$, the final algorithm is shown as follows \cite{Boyd_arXiv2013}:
\begin{eqnarray}
\tilde{\bf{x}}^{[i+1]}&=&({\bf{I}}+{\bf{Q}})^{-1}({\bf{x}}^{[i]}+{\bf{y}}^{[i]})\\
\label{prox}
{\bf{x}}^{[i+1]}&=&\Pi_{\mathcal{C}}(\tilde{\bf{x}}^{[i+1]}-{\bf{y}}^{[i]})\\
{\bf{y}}^{[i+1]}&=&{\bf{y}}^{[i]}-\tilde{\bf{x}}^{[i+1]}+{\bf{x}}^{[i+1]},
\end{eqnarray}
where $\Pi_{\mathcal{S}}({\bf{x}})$ denotes the Euclidean projection of $\bf{x}$ onto the set $\mathcal{S}$. The first step is performing projection onto a subspace, i.e., solving a linear system with the coefficient matrix ${\bf{I}}+{\bf{Q}}$. Some efficient algorithms can be found in \cite{Boyd_arXiv2013}. The last step is computationally trivial. The second step is performing projection onto the cone $\mathcal{C}$. As $\mathcal{C}$ is the Cartesian produce of the cones $\mathcal{C}_i$, we can project onto $\mathcal{C}$ by projecting onto $\mathcal{C}_i$ separately and in parallel. Furthermore, the projection onto  cones can be done with closed-forms and can be very efficient. For instance, for $\mathcal{C}_i=\mathbb{R}_{+}$, we have that \cite[Section 6.3]{Boyd_2013proximal}
\begin{eqnarray}
\Pi_{\mathcal{C}_i}({\boldsymbol{\omega}})={\boldsymbol{\omega}}_+,
\end{eqnarray}
where the nonnegative part operator $(\cdot)_+$ is taken elementwise. For the second-order cone ${\mathcal{C}}_i=\{(t, {\bf{x}})\in\mathbb{R}\times\mathbb{R}^{p-1}|
\|{\bf{x}}\|\le t\}$, we have that \cite[Section 6.3]{Boyd_2013proximal}
\begin{eqnarray}
\Pi_{\mathcal{C}_i}({\boldsymbol{\omega}},\tau)=\left\{\begin{array}{l}
0, \|{\boldsymbol{\omega}}\|_2\le -\tau\\
({\boldsymbol{\omega}},\tau), \|{\boldsymbol{\omega}}\|_2\le \tau\\
(1/2)(1+\tau/\|{\boldsymbol{\omega}}\|_2)({\boldsymbol{\omega}},\|{\boldsymbol{\omega}}\|_2), \|{\boldsymbol{\omega}}\|_2\ge \tau.
\end{array}\right.
\end{eqnarray}
The details on the convergence and termination criteria of this ADMM algorithm can be found in \cite{Boyd_arXiv2013}.

\section{Simulation Results}
\label{simu}
In this section, we simulate the large-scale optimization framework consists of matrix stuffing and the ADMM solver for the large-scale coordinated beamforming problems. We consider
the following channel model for the link between the $k$-th MU and the
$l$-th AP:
\begin{eqnarray}
{\bf{h}}_{kl}=\underbrace{10^{-L(d_{kl})/20}\sqrt{\varphi_{kl}s_{kl}}}_{D_{kl}}{\bf{f}}_{kl},
\forall k,l,
\end{eqnarray}
where $L(d_{kl})$ is the path-loss at distance $d_{kl}$, as given in \cite[Table
I]{Yuanming_TWC2013}, $s_{kl}$ is the shadowing coefficient, $\varphi_{kl}$ is
the antenna gain and ${\bf{f}}_{kl}$ is the small-scale fading coefficient.
We use the standard cellular network parameters as showed in \cite[Table I]{Yuanming_TWC2013}. All the simulations are carried out on a personal computer with 2.3 GHz Intel Core i7 processor and 8 GB of RAM running  OS X 10.9.2.

\subsection{Comparison with CVX and SeDuMi}
In this section, we compare the proposed matrix stuffing and ADMM algorithm (implemented in the software package SCS\footnote{https://github.com/cvxgrp/scs.}) with the modeling framework CVX and the interior-point solver SeDuMi.  Consider a network with $L = 100$ $2$-antenna RRHs and
$K = 50$ single-antenna MUs uniformly and independently
distributed in the square region $[-1000, 1000] \times [-1000, 1000]$
meters. We consider a particular network realization for the optimization problem $\mathscr{P}$\footnote{The channel coefficients can be found at http://ihome.ust.hk/$\sim$yshiac/.}.

\begin{table}[!t]
\renewcommand{\arraystretch}{1.3}
\caption{Time in [s] Comparison with CVX and Proposed Matrix Stuffing}
\label{mats_table}
\centering
\begin{tabular}{c|c|c|c|c|c}
{{SINR [dB]}} & {{0}} & 2 & 4 & 6 & 8\\
\hline
CVX & 18.87 & 17.86 & 17.53 & 17.36 & 17.17\\
\hline
Matrix Stuffing & 0.26 & 0.24 & 0.24 & 0.24 & 0.27
\end{tabular}
\end{table}

\begin{table}[!t]
\renewcommand{\arraystretch}{1.3}
\caption{Time in [s] Comparison with Different Solvers}
\label{algorithm}
\centering
\begin{tabular}{c|c|c|c|c|c}
{{SINR [dB]}} & {{0}} & 2 & 4 & 6 & 8 \\
\hline
SeDuMi& 2668.43 &  2255.29 & 1879.07 & 1518.83 & 1569.06 \\
\hline
SCS & 1.17 & 2.29 & 3.99 & 6.29 & 10.06
\end{tabular}
\label{solver_table}
\end{table}

\begin{table}[!t]
\renewcommand{\arraystretch}{1.3}
\caption{Comparison with the Optimal Values IN [dBm] of Different Algorithms}
\label{algorithm}
\centering
\begin{tabular}{c|c|c|c|c|c}
{{SINR [dB]}} & {{0}} & 2 & 4 & 6 & 8 \\
\hline
CVX+SeDuMi& 33.29 & 35.49 & 37.69 & 39.86 &41.99\\
\hline
Matrix Stuffing+ SCS & 33.28 & 35.49 & 37.69 & 39.86 & 41.99
\end{tabular}
\label{algorithm_table}
\end{table}

Table {\ref{mats_table}} compares the time consumption of the proposed matrix stuffing and CVX for transforming the original problem $\mathscr{P}$ to the equivalent ADMM-compliant problem $\mathscr{P}_{\textrm{ADMM}}$. This table demonstrates that the time for transformation of proposed matrix stuffing technique is less than one second and can speedup about 200 times compared to the modeling framework CVX.

 Table {\ref{solver_table}} compares the ADMM method with the interior-point method. With closed-form solutions for the subproblems in the ADMM algorithm and parallelized projection on the cones (\ref{prox}), the ADMM algorithm can speedup in several orders of magnitude over the interior-point method (i.e., about 1000 times from this table).

Table {\ref{algorithm_table}} presents the optimal values obtained from the modeling framework CVX with the interior-point solver SeDuMi and the proposed large-scale optimization framework. We can see that the proposed framework can provide a solution to modest accuracy with much less time.

\subsection{Minimum Network-Wide Achievable Rate Versus SNR}
Consider a network with $L = 100$ single-antenna RRHs and
$K = 50$ single-antenna MUs uniformly and independently
distributed in the square region $[-5000, 5000] \times [-5000, 5000]$
meters. Fig. {\ref{snr}} demonstrates the minimum network-wide achievable rate versus different SNRs. Each point of the simulation results is averaged over 1000 randomly generated network realizations. From this figure, we can see that the optimal coordinated beamforming can improve the per-user rate by 2.0 {bps/Hz} compared to the zero-forcing beamforming, which is quite an improvement at low to medium SNRs. This motives us to develop the large-scale optimization algorithm to find the optimal coordinated beamformers to improve the spectral efficiency.
\begin{figure}[h]
\centering
\includegraphics[width=1\columnwidth, height=2.5in]{snr}
\caption{The minimum network-wide achievable versus transmit SNR.}
\label{snr}
\end{figure}

\subsection{Capacity Scaling Law of Large-Scale Networks}
Consider a network with $L$ 2-antenna RRHs and $K$ single-antenna MUs uniformly and independently distributed in the square region $[-5000, 5000] \times [-5000, 5000]$ meters. The SNR is set as 10 dB. We keep the ratio of $\beta={K/L}=1$ and investigate the rate scaling law of large-scale cooperative networks. Fig. {\ref{scaling}} demonstrates the minimum network-wide achievable
rate versus the user density. Each point of the simulation results is averaged
over 400 randomly generated network realizations. From this figure, we can see that the performance gap between the optimal
coordinated beamforming and the zero-forcing beamforming becomes larger when the network density is higher.
Thus optimal beamforming is required for dense networks.
\begin{figure}[!t]
\centering
\includegraphics[width=1\columnwidth, height=2.5in]{scaling}
\caption{The minimum network-wide achievable rate versus user density.}
\label{scaling}
\end{figure}

\section{Conclusions}
In this paper, we proposed a framework for large-scale optimization for coordinated beamforming  in dense wireless cooperative networks. We first proposed to use the matrix stuffing method to transform the original problem to the equivalent ADMM-compliant problem. The ADMM algorithm was then applied to solve the transformed ADMM-compliant problem. Simulation results have demonstrated the advantage and thus the necessity of the proposed large-scale optimal beamforming algorithm.

\bibliographystyle{ieeetr}

redpajama_set_name: RedPajamaArXiv


text:
Wärtsilä Collaborating On Rotor Sail Solutions
By Jack Burke29 October 2020
Wärtsilä has signed an agreement with UK-based Anemoi Marine Technologies for the future sales and servicing of Rotor Sail solutions to the shipping industry.
Rotor Sails, also referred to as Flettner Rotors, are comprised of vertical cylinders which, when driven to rotate, harness the renewable power of the wind to propel ships. These mechanical sails capitalize on the aerodynamic phenomenon known as the Magnus Effect to provide additional thrust to vessels and deliver significant fuel and emission savings, the company said.
"Our patented designs overcome operational constraints such as air draft and cargo handling, making the technology suitable for the majority of shipping sectors. As the industry focuses on emission reduction targets and energy saving, we are collaborating with Wärtsilä to strengthen our offering and facilitate the global uptake of our Rotor Sails by offering clients a full end-to-end solution including sales, supply and lifecycle support," said Kim Diederichsen, CEO of Anemoi Marine Technologies.
Wärtsilä will fully integrate Anemoi Marine Technologies' Rotor Sails within its Propulsion Business. By offering wind propulsion solutions as an integral part of Wärtsilä's propulsion offering, compliance with the IMO's Energy Efficiency Design Index (EEDI) will be further facilitated. Furthermore, it will add to Wärtsilä's efforts to increase fuel efficiency and reduce emissions. The collaboration will enable the adoption of wind-assisted solutions for most marine vessel types, with the immediate focus likely to be on dry and wet bulk vessels, the company said. Wärtsilä will promote the solution for both newbuild projects and for retrofitting to existing ships.
"Wärtsilä is committed to fully supporting its customers by reducing their operating costs and reducing the environmental impact of their operations. This agreement further enhances our ability to meet this commitment, and we look forward to working closely with Anemoi Marine Technologies to realize the potential of this technology," said Bernd Bertram, vice president, Propulsion, Wärtsiä Marine Power.
Products Engines, Hydraulics & Powertrains Marine Emissions Green Technology
TotalEnergies, Veolia agree to biomethane production
Plan to produce up to 1.5 TWh per year
Twin Disc sales rose 23% in second quarter
Company remains optimistic recovery is underway as order rates and demand improve


With its umpteen natural wonders and a beautiful landscape, it's no wonder Oman has become one of the most amazing destinations in the world. Oman is not just a desert. Rich with a unique cultural heritage to spectacular canyons, fjords, and pristine beaches, it has something unusual to offer everyone. Whatever travel adventures you dream about, here's your chance to turn them into an experience of your lifetime.


text:
Horizons (Orizzonti) è un partito politico francese di centro-destra fondato nell'ottobre del 2021 dal sindaco di Le Havre ed ex primo ministro Édouard Philippe. Fa parte della maggioranza presidenziale di Emmanuel Macron.

Risultati elettorali

Altri progetti

Collegamenti esterni

Partiti politici francesi

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text:
the media room of
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ZetrOZ Systems is an FDA cGMP and ISO 13585 medical technology company headquartered in the southern coastal region of Connecticut. The organization also has manufacturing facilities across the United States.
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Insurance Companies Benefit From Reduced Healthcare Reimbursements, Lowering Costs by Approving the Sustained Acoustic Medicine (sam®) Device
Press Release - updated: Jun 23, 2020
TRUMBULL, Conn., June 23, 2020 (Newswire.com) - Insurance companies benefit from the reduced healthcare reimbursements they enjoy when they approve the long duration continuous ultrasound device (sam®). In fact, approving the device saves insurers well over $30,000 while treating musculoskeletal injuries of the back, shoulder and knee.
At just the fraction of the cost of a surgical procedure, sam® eliminates the risk of infection and injury that can occur as a result of surgery. This helps insurers avoid reimbursing even more costs. sam® is so effective, it can improve surgical outcomes, thereby decreasing the chances that patients will need a follow-up surgery. Furthermore, the solution reduces the need to provide in-office physical therapy and provides pain relief while accelerating healing.
sam® is a non-invasive prescription medical device that patients apply at home to the location of their injury or at the site of their pain. The solution administers a localized treatment. The device is ideal for delaying surgery, as well as improving postoperative healing and surgical outcomes. sam® goes a long way in aiding patients whose healing capability is compromised. Avoiding or delaying surgery to resolve conditions such as disk herniation and tendonitis is much easier with sam®, as the solution also treats pain very effectively. The device provides more than four hours of treatment at 18,720 joules and is backed by over 20 clinical research studies funded by the United States Government.
sam® is the only multi-hour, home-use, ultrasound-based mechanobiological device available and approved by the FDA. The durable device administers treatment similar to sophisticated targeted pharmacotherapy agents, but it delivers a mechanobiological therapy localized to the injury site in order to stimulate biological repair. sam® appears similar to a bone-growth stimulator, but the dosing and treatment regimen is more aggressive. This facilitates the body's healing process and delays the need for surgery or medication to treat soft tissue injuries, chronic conditions and the pain that can result from both. The solution is priced similarly to a bone-growth stimulator and comes with a one-year warranty.
sam® 2.0 is new technology approved in 2020 by the FDA for use at home. The device is completely unique and based on seven years of development and clinical validation. The generation-one device costs $4,400 and the generation-two device costs $6,800. These prices are modestly expensive considering the significant improvements they give patients. Since the generation-two version of sam® is for the individual patient, the patient owns the device.
sam® is covered for most government employees, and over 90 percent of workers compensation insurance carriers to help employees get back to work and reduce medication requirements after injury; this includes professional and college athletes who get injured on the job.
"Insurance companies can significantly decrease their reimbursement costs when they approve sam® and provide better care for their policy holders. The solution has been proven an effective treatment for musculoskeletal injuries and pain relief. By approving sam®, insurers help delay expensive surgeries, as well as the pre-and-post surgical costs associated with them," said George Lewis, chief executive officer of ZetrOZ Systems.
ZetrOZ Systems is an FDA cGMP and ISO 13585 medical technology company headquartered in the southern coastal region of Connecticut. The organization also has manufacturing facilities across the United States. ZetrOZ Systems produced UltrOZ®, sam®Sport and sam®Pro 2.0 to provide safe and effective treatment options for prevalent conditions such as arthritis. Learn more at zetroz.com and samrecover.com.
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On Monday, January 7, Kalamazoo County Health & Community Services Environmental Health Unit sent a letter to all residents who have received a PFAS filter to date. The letter states that free replacement filter cartridges can be obtained at the Environmental Health office located at 311 East Alcott Street, 8:00 am to 5:00 pm, Monday through Friday. The filter replacement cartridges are designed to be simply and easily replaced, without the need of a plumber. For the convenience of the residents there are instructions attached with the letter and this press release that detail and depict how to replace the cartridge. If any questions arise in this process, please contact the Environmental Health Office at 269-373-5210.


text:
The Secret Life of Lyft Drivers
Life lessons in creating instant intimacy
Photo by Haut Risque on Unsplash
It was THAT kind of phone call.
The one you see in movies, the one you probably only get once in your lifetime — the one that changes your life.
"We'd like to offer you an all-expense paid secondment to Los Angeles for 12 months. Can you be there in a month?"
"Hell, yes!" was what I was thinking as I heard myself respond with a very professional, "Yes, that works."
A month later, I left my life in Australia and arrived in LA on a beautiful Sunday morning with no clue what to do with myself. I decided to do what I do best — wander aimlessly. My first foray into downtown LA involved accidentally walking the length of skid row and feeling extremely confused while sticking out like a sore thumb in my workout gear. The locals were not pleased and I spent the remainder of that afternoon googling the unique cultural phenomenon that is Skid Row. To this day, I still find the history of Skid Row remarkably fascinating but decided against venturing through it on foot again.
Fortunately for me, my contract included a travel allowance — a rather generous one at that considering I lived four blocks from my office. I had also serendipitously received a Lyft coupon. So, off I went at my second attempt at exploring the city.
My first Lyft driver ever was Etienne and I will never forget him. He had beautifully chiseled features and a genteel personality. Etienne was an immigrant from Algeria who had lovely mocha skin and spoke with an even lovelier French accent. He had come to LA to study computer science. I excitedly revealed that I had just arrived in LA and that this was my first ever ride sharing experience!
"Tell me everything about LA!"
I say, in what must have been the human imitation of an excited golden retriever.
He pauses and considers his response.
"It's nice….it's just…it's hard to make friends here."
There is something so beautiful about this moment, when a stranger chooses to be vulnerable, even if only for an instant.
He quickly caught himself.
"I mean, I HAVE friends, of course. It's hard making new ones though. It's easy to meet people but it's hard to make friends, you know?"
Etienne proceeds to teach me something about LA. People don't like to go very far and distance is not measured in miles, it's measured in the time it takes to reach a destination and that changes depending on the time of day. He had friends in LA but they didn't live close and so they never saw each other.
I could sense he had wanted to say this out loud for a while. I'm lonely, I want to connect. Maybe it is easier to say that to a stranger, there is less judgment.
I listened and asked questions about his life. What motivated you to come here? What do you love about what you are doing? What do you hope to do with your degree?
They were such basic questions but they seem to change Etienne's mood immediately. It felt like it had been a while since someone had bothered asking Eitienne about what truly mattered to him. When the ride ended, he turned around, looked me in the eye and said "Thank you" like he meant it. As I closed the door, I felt a warmth cascade over me. I had experienced a sense of intimacy in that exchange. I felt that it had mattered to him that I was in his car. The ride lasted 21 minutes and for the second time that month, my life was changed.
I decided that in a city where I knew nobody and apparently could not walk anywhere, I was going to set a challenge for myself. I would make it my goal to take Lyft rides everywhere and try to create an intimate connection within each of those rides. I wouldn't just be sharing a ride, I would be sharing care.
After Etienne, there was Paul. He was only 22-years old but his family had sacrificed a lot for him to pursue his dreams as a singer in LA. He was plagued with a lot of self-doubts but his family was unwavering in their belief. He sang to me for 20 minutes and I took his autograph, because one day, that boy will be famous. He showed me that having people who believe in you has power, especially when pursuing a dream millions of other people also want.
Then there was James, we hit it off instantly. He was a charismatic African American man who was a self-published author. He had eyes that seem to pierce right through you and the banter rolled off our tongues the whole ride and continued for many weeks after. It was flirty and just great fun. I loved that he had strayed so far off the path that life had dealt him and was intent on creating his own destiny.
There was Zhao, who had me glued to my seat with his totally crazy, Shantaram-like life story as an immigrant who had hitchhiked across Asia after being kicked out of his rich family in China for being a total lout. He had then built a successful business only to lose it all because of love and proceeded to end up being homeless for years. His family had eventually found him and forgave him right before his mother died but she did not want him to have any share of her wealth. He then managed to pick himself up and somehow make his way to LA but was going through another rough patch because well….he didn't really like to work. I can't verify any of his claims but boy, was it an entertaining ride. He taught me that LA traffic is a thing to be reckoned with because, even after everything he endured, he still complained about LA traffic.
There were so many great stories in between. Riding in a Lyft is like being invited into someone's couch for a while. The drivers had me rolling with laughter, taught me Californian slang ("The" 110, po-po, K-town, hella, baller), introduced me to great music, told me about the best hole-in-the-wall restaurants and gave me the rundown on celebrities (who was nice, who was always broke,etc.), and more importantly, bared their souls.
Of the hundreds of rides that I took (more than 400 according to my receipts), one ride stands out in my mind. It was only 3-minutes long. I was tired and definitely not in the mood to stick to my challenge. My driver made a valiant effort.
"How was your night?"
"You have an accent. Where are you from?"
"I used to live in Australia."
"Wow, how did you end up in LA?"
I ended up telling him about my career and how my company had brought me out to the United States.
"Wow, you should be a life coach or something."
I stopped. Somehow this was like a sign that I had spent too long talking about myself. I pivoted.
"Tell me about you."
His name was Gabriel. He had grown up in a poor neighborhood and nobody he knew had gone to college. He had gotten a job recently and he was doing well, but…..
"I have all these ideas. I think I can do more and start my own business but I don't know how. My dad hasn't really been around."
He was 20-years old and asking some incredibly profound questions. How do I break out of my social norm? How do I break out of the expectations and the limitations that everyone in my world has conditioned me to believe?
"I know I can be something more, do something different. I just need a guide. Even just to know that someone like me can do it."
The ride ended in 3-minutes but we talked for almost two hours outside my apartment afterwards. I will never forget Gabriel either. That encounter taught me so much about myself — about the impact I can have on anyone I encounter in a day if only I would snap out of my own needs and pay attention.
After a while, I could tell almost immediately if it was going to be a challenge to create intimacy with someone. Not because they looked vastly different but because they would project almost an apologetic air for existing. These were people who didn't have dreams or any hopes for something greater. You don't have to want to be a movie star to be hopeful. I certainly sat in the passenger seat of many housewives who had big dreams for themselves or their children. They were not embarrassed about being a Lyft driver, they enjoyed it. This was different, these were people who didn't believe in themselves. To them, they were "just" a Lyft driver and that must be what the passenger is thinking too. They were often extremely reluctant to talk about themselves, believing that they had little of interest to contribute. I often wondered if they knew they were projecting such a strong message to the world. They taught me that hope and self-love are important and that dreams are the fuel for our soul. People can sense when someone lacks it right away. If I cajoled one of these people into a smile and made them talk about something they were passionate about, I would always be pretty proud of myself.
This experiment taught me a lot about myself. It taught me that I wanted to be the person who could show up unexpectedly and make someone feel good. The pleasant surprise you weren't expecting that had the ability to change your mood. The person who could instantly make you feel like you were seen and that you mattered. I wanted that to be my superpower.
I've since extended my Random Intimacy challenge beyond Lyft rides to new venues — buses, planes, and coffee shops. It's also progressed beyond conversations in a car to other activities such as dinners, hikes, and even a spontaneous search for temporary tattoos.
This concept of creating random intimacy is so strange to most of us. You might be one of those people asking — why would you want to create intimacy with a random stranger you might never meet again?
It's because there is something uniquely meaningful about connecting with someone when you don't need something from them or when neither of you have an agenda. You're not trying to be someone else and neither are they. You are just two people, showing up. It's more honest, more raw, and more pure. I see you, you see me. I feel you, you feel me.
It's because, in a world where everyone is so wrapped up in themselves, there is something meaningful about being that person who surprises someone and totally changes their day — to being that person they will never forget.
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text:
San Jose Sharks heavy on road games in early…
San Jose Sharks heavy on road games in early season
By David Pollak |
PUBLISHED: November 8, 2014 at 12:00 a.m. | UPDATED: September 14, 2018 at 12:00 a.m.
SAN JOSE — Even in the first draft of the 2014-15 NHL schedule, the Sharks were going to start this season with more games on the road than at home.
From the business side, that wasn"t necessarily a bad thing.
"Including the Canadian clubs, including the clubs that sell out, nobody wants to play at home in October," Steve Hatze Petros, the NHL senior vice-president in charge of scheduling, said Friday in reference to that month"s overcrowded sports calendar.
Yet things were not going to be as dramatically imbalanced as they ended up. When San Jose completes its seven-game trek that begins Saturday night in Dallas and ends Nov. 18 in Buffalo, 16 of its first 21 contests will have been played away from the SAP Center.
Initially, Hatze Petros said, there were going to be three fewer road games and one more home game over that same period of time.
Then stuff happened. And how all the changes occurred provides a peek into the complicated world of the NHL schedule-maker.
For one thing, the season opener against the Los Angeles Kings was originally a Sharks home game. After the Kings won the Stanley Cup, the site was switched to Staples Center for the banner-raising ceremony.
For another, the eventual green light for a Feb. 21 outdoor game at Levi"s Stadium brought the Sharks back to the Bay Area at a time when they were scheduled to be on the road because the SAP Center was booked for Disney on Ice.
New dates then had to be found for two of the mid-February road games, and the early season provided the most logical alternative for trips to face the Boston Bruins and Buffalo Sabres.
But adding those games to existing road trips also took away any chance for the Sharks to decompress from all that travel before playing at home.
"Let"s say you didn"t have to go to Buffalo at the end of this trip," Hatze Petros said. "That"s a six-game road trip. You finish off the trip in Carolina on Nov. 16 and you have three days to come home to play Florida on Nov. 20. Would that be a better trip?"
Another factor — and Hatze Petros labeled it the "greatest challenge" in general — came into play when a team, either the Sharks or an opponent, told the NHL that an available arena date was off the table. Teams are fined for doing that, but are willing to pay when an added event is more lucrative.
"Dominos start to fall," Hatze Petros said, "and that"s how things wind up where they wind up."
Sharks assistant general manager Wayne Thomas works closely with the league on scheduling matters. He pointed out the situation was also complicated by the fact SAP Center is booked for a special event — not yet on its online calendar — for the final week of the regular season in April.
Thomas doesn"t fault the NHL for the way things had to play out, noting "they did everything they could to correct it."
At this point, the Sharks seem resigned to playing the hand they were dealt.
"We talk about it a little bit, but nobody"s complaining or whining about it," coach Todd McLellan said this week. "We know we have to do it."
The fact that San Jose finished 2-3 in its five home games and is 5-2-2 elsewhere may make it easier to head out on the current 7,593-mile journey that will have it zig-zag around the Southwest, Great Lakes and Southeast for two weeks.
"You"ve got to look at it as if we get through it in good shape," forward Tommy Wingels said, "it sets us up for the rest of the season."
Along those lines, maybe the Sharks can take some comfort in this: When this trip ends, 11 of the next 13 games are at home. And starting in mid-January, 10 of 12 will be at SAP Center, too.
For a team coming off a summer of uncertainty and talk of a divided locker room, all those games away from home can have a side benefit.
"With a few new guys, spending time on the road isn"t the worst thing," Wingels said Thursday night. "Guys have families and other obligations here. When you"re on the road, it"s team only. You spend time with each other on the planes, on the buses, going out for dinners as a group. We enjoy it."
For more on the Sharks, see David Pollak"s Working the Corners blog at blogs.mercurynews.com/sharks.
SATURDAY"S GAME
Sharks (7-5-2) at Dallas (4-5-4), 5 p.m. CSNCA
COMING HOME LATE
A look at the Sharks" monthly split of home and road games:
Month Hm Rd Total
October 3 9 12
November 6 7 13
December 8 5 13
January 8 4 12
February 8 5 13
March 5 8 13
April 3 3 6
David Pollak
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DNR is a San Antonio based funky rock band playing originals throughout Texas. Their songs feature tongue-in-cheek lyrics about subtle sexual themes (no profanity). Tight and pounding rhythms from a truly natural bass and drum tandem lay a foundation for upbeat songs with dual guitar. This is a really fun band that always leaves the crowd with a warm fuzzy. When in San Antonio, Remember the Alamo but don't forget DNR!
After having carpal tunnel surgery in early november drummer, John, played two shows in December with one hand! (Please, no Def Leppard jokes) Since then he has been playing two handed, but taking it easy. We expect for John to be playing with all appendages fully functional in January.
After a plethora of guest and fill in bassists DNR has their first full time bass player. Chuck Marshall joined the band in early December and played both shows in December with the band.