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Windy with rain and snow showers this evening transitioning to snow showers overnight. Low 32F. Winds WSW at 20 to 30 mph. Chance of precip 50%. Winds could occasionally gust over 40 mph..
Windy with rain and snow showers this evening transitioning to snow showers overnight. Low 32F. Winds WSW at 20 to 30 mph. Chance of precip 50%. Winds could occasionally gust over 40 mph.
Updated: January 19, 2023 @ 6:10 pm
Bitfarms Provides September 2022 Production and Mining Operations Update
By: Bitfarms Ltd. via Globe NewsWire
October 03, 2022 at 07:00 AM EDT
- 3,733 BTC mined in first nine months of 2022, exceeding full year 2021 production -
- Achieves September 30, 2022 target of 4.2 Exahash/second -
- Initiates production and continues build out at first warehouse in Argentina -
This news release constitutes a "designated news release" for purposes of the Company's prospectus supplement dated August 16, 2021, to its short form base shelf prospectus dated August 12, 2021.
TORONTO, Ontario and BROSSARD, Québec, Oct. 03, 2022 (GLOBE NEWSWIRE) -- Bitfarms Ltd. (NASDAQ: BITF // TSX: BITF), a global Bitcoin self-mining company, provided a Bitcoin (BTC) production and mining operations update for September 2022.
"Accomplishing a significant milestone in early September, we initiated production in Rio Cuarto, Argentina with our first 10-megawatt (MW) module," said Geoff Morphy, President and COO of Bitfarms. "As of September 30, we installed 1,751 miners at this location and have pending 3,000 miners at Argentina Customs slotted to add to production throughout Q4 2022. During the month, we also began construction at our second 50 MW warehouse in Rio Cuarto, which is on target to be completed during Q2 2023."
"Reaching 4.2 exahash/second (EH/s), we achieved our September 30, 2022 target operating hashrate," said Ben Gagnon, Chief Mining Officer of Bitfarms. "During September, we mined 481 BTC, averaging 16 BTC mined per day and exited the month at 17 BTC mined per day. Our increased capacity continues to deliver growth, even while network difficulty increased as much as 13%. A higher network hashrate, due in part to previously idle miners coming back online, and the shorter 30-day month were the primary drivers of lower monthly production compared to August. In the first nine months of 2022, we mined 3,733 BTC, surpassing 2021 full-year production of 3,452 BTC by 8% heading into Q4. With 229 MW planned to be developed by the end of the year, we are well positioned to further grow production in 2023."
Key Performance Indicators Sept. 2022 Aug. 2022 Sept. 2021
Total BTC Mined 481 534 305
Month End Operating Hashrate 4.2 3.9 1.5
BTC/ Avg EH 122 141 211
Operating Capacity (MW) 176 166 69
Hydropower MW 166 166 69
Watts/TH Efficiency 40 40 45
BTC Sold 544 427 12
Select Operating Highlights
4.2 EH/s online as of September 30, 2022, up 180% from September 2021 and 8% from August 31, 2022.
3.95 EH/s average online for month of September.
122 BTC/ average EH/s for the month of September, down 42% from 211 in September 2021 and down 13.5% from 141 in August 2022.
481 new BTC mined during September 2022, up 57% from September 2021 and down 10% from August 2022. The decrease from August 2022 production was primarily due to a 13% increase in network difficulty, a brief farm outage and a shorter month.
16.0 BTC mined daily on average in September, equivalent to about US$310,400 per day and approximately US$9.31 million for the month based on a BTC price of US$19,400 on September 30, 2022.
In Rio Cuarto, Argentina:
Energized first of five 10 MW modules, installed 1,751 miners and initiated production at the first 50-MW warehouse.
Commenced construction on the second 50-MW warehouse. This facility is expected to be completed and ready for mining operations during Q2 2023.
In Sherbrooke, Québec, development continued on schedule:
As the 1,800 square foot expansion at the Garlock farm is nearing completion, 6 MW is expected to be energized in October and the full 18 MW by the end of the year.
Phase 3 of The Bunker is progressing as planned with the remaining 12 MW of this farm expected to be online by the end of 2022.
Sherbrooke, upon the retirement of the de la Pointe farm, will consist of three farms with locations in close proximity to each another that are scheduled to have 96 MW operational by year end.
Bitfarms' BTC Monthly Production
Month BTC Mined 2022 BTC Mined 2021
January 301 199
February 298 178
March 363 221
April 405 232
May 431 262
June 420 265
July 500 391
August 534 354
September 481 305
Total YTD 3,733 2,407
Financial Update
Sold 544 BTC during September 2022, generating proceeds of $10.66 million.
Continued to deleverage the Company's balance sheet by making principal paydowns totaling $3.8 million and $26.8 million during September and the third quarter, respectively, and retiring three higher interest rate equipment loans.
Improved fleet efficiencies and optimized the roll out schedule of miners by selling $3.8 million of surplus miners in Q3 2022 and reducing contractual associated liabilities and capex requirements.
Held 2,065 BTC in custody on September 30, 2022, representing a total value of approximately US$40 million based on a BTC price of US$19,400.
Bitfarms plans to host or attend the following events in the next month:
October 11: Bitfarms 5th Anniversary Celebration in Québec
October 19-20: Canadian Blockchain Summit in Calgary
October 20: Energy Innovator's Roundtable in Toronto
October 25: Bitfarms Open House and Tour at the Washington State Farm
About Bitfarms Ltd.
Founded in 2017, Bitfarms is a global, publicly traded (NASDAQ/TSX: BITF) Bitcoin self-mining company. Bitfarms runs vertically integrated mining operations with in-house management and company-owned electrical engineering, installation service, and onsite technical repair. The Company's proprietary data analytics system delivers best-in-class operational performance and accelerated uptime.
Bitfarms has 10 mining facilities in production around the world, which are housed in four countries: Canada, the United States, Paraguay, and Argentina. Powered by predominantly environmentally friendly hydro-electric and long-term power contracts, Bitfarms is committed to using renewable, locally based, and often underutilized energy infrastructure.
To learn more about Bitfarms' events, developments, and online communities:
Website: www.bitfarms.com
https://www.facebook.com/bitfarms/
https://twitter.com/Bitfarms_io
https://www.instagram.com/bitfarms/
https://www.linkedin.com/company/bitfarms/
Trading in the securities of the Company should be considered highly speculative. No stock exchange, securities commission or other regulatory authority has approved or disapproved the information contained herein. Neither the Toronto Stock Exchange, Nasdaq, or any other securities exchange or regulatory authority accepts responsibility for the adequacy or accuracy of this release.
This news release contains certain "forward-looking information" and "forward-looking statements" (collectively, "forward-looking information") that are based on expectations, estimates and projections as at the date of this news release and are covered by safe harbors under Canadian and United States securities laws. The statements and information in this release regarding expansion plans, including construction in Argentina and Québec , expectations for monthly growth, targets, and goals for productive capacity and hashrates and other future plans and objectives of the Company are forward-looking information. Other forward-looking information includes, but is not limited to, information concerning: the intentions, plans and future actions of the Company, as well as Bitfarms' ability to successfully mine digital currency, revenue increasing as currently anticipated, the ability to profitably liquidate current and future digital currency inventory, volatility of network difficulty and digital currency prices and the potential resulting significant negative impact on the Company's operations, the construction and operation of expanded blockchain infrastructure as currently planned, and the regulatory environment for cryptocurrency in the applicable jurisdictions.
Any statements that involve discussions with respect to predictions, expectations, beliefs, plans, projections, objectives, assumptions, future events or performance (often but not always using phrases such as "expects", or "does not expect", "is expected", "anticipates" or "does not anticipate", "plans", "budget", "scheduled", "forecasts", "estimates", "believes" or "intends" or variations of such words and phrases or stating that certain actions, events or results "may" or "could", "would", "might" or "will" be taken to occur or be achieved) are not statements of historical fact and may be forward-looking information and are intended to identify forward-looking information.
This forward-looking information is based on assumptions and estimates of management of the Company at the time they were made, and involves known and unknown risks, uncertainties and other factors which may cause the actual results, performance, or achievements of the Company to be materially different from any future results, performance or achievements expressed or implied by such forward-looking information. Such factors include, among others, risks relating to: the global economic climate; dilution; the Company's limited operating history; future capital needs and uncertainty of additional financing, including the Company's ability to utilize the Company's at-the-market offering (the "ATM Program") and the prices at which the Company may sell Common Shares in the ATM Program, as well as capital market conditions in general; risks relating to the strategy of maintaining and increasing Bitcoin holdings and the impact of depreciating Bitcoin prices on working capital; the competitive nature of the industry; currency exchange risks; the need for the Company to manage its planned growth and expansion; the effects of product development and need for continued technology change; the ability to maintain reliable and economical sources of power to run its cryptocurrency mining assets; the impact of energy curtailment or regulatory changes in the energy regimes in the jurisdictions in which the Company operates; protection of proprietary rights; the effect of government regulation and compliance on the Company and the industry; network security risks; the ability of the Company to maintain properly working systems; reliance on key personnel; global economic and financial market deterioration impeding access to capital or increasing the cost of capital; share dilution resulting from the ATM Program and from other equity issuances; and volatile securities markets impacting security pricing unrelated to operating performance. In addition, particular factors that could impact future results of the business of Bitfarms include, but are not limited to: the construction and operation of facilities may not occur as currently planned, or at all; expansion may not materialize as currently anticipated, or at all; the digital currency market; the ability to successfully mine digital currency; revenue may not increase as currently anticipated, or at all; it may not be possible to profitably liquidate the current digital currency inventory, or at all; a decline in digital currency prices may have a significant negative impact on operations; an increase in network difficulty may have a significant negative impact on operations; the volatility of digital currency prices; the anticipated growth and sustainability of hydroelectricity for the purposes of cryptocurrency mining in the applicable jurisdictions; the inability to maintain reliable and economical sources of power for the Company to operate cryptocurrency mining assets; the risks of an increase in the Company's electricity costs, cost of natural gas, changes in currency exchange rates, energy curtailment or regulatory changes in the energy regimes in the jurisdictions in which the Company operates and the adverse impact on the Company's profitability; the ability to complete current and future financings, any regulations or laws that will prevent Bitfarms from operating its business; historical prices of digital currencies and the ability to mine digital currencies that will be consistent with historical prices; an inability to predict and counteract the effects of COVID-19 on the business of the Company, including but not limited to the effects of COVID-19 on the price of digital currencies, capital market conditions, restriction on labour and international travel and supply chains; and, the adoption or expansion of any regulation or law that will prevent Bitfarms from operating its business, or make it more costly to do so. For further information concerning these and other risks and uncertainties, refer to the Company's filings on www.SEDAR.com (which are also available on the website of the U.S. Securities and Exchange Commission at www.sec.gov), including the annual information form for the year-ended December 31, 2021, filed on March 28, 2022. The Company has also assumed that no significant events occur outside of Bitfarms' normal course of business. Although the Company has attempted to identify important factors that could cause actual results to differ materially from those expressed in forward-looking statements, there may be other factors that cause results not to be as anticipated, estimated or intended. There can be no assurance that such statements will prove to be accurate as actual results and future events could differ materially from those anticipated in such statements. Accordingly, readers should not place undue reliance on any forward-looking information. The Company undertakes no obligation to revise or update any forward-looking information other than as required by law .
LHA Investor Relations
Investors@bitfarms.com
Actual Agency
Matt Weaver
mediarelations@bitfarms.com
Québec Media: Ryan Affaires Publiques
Valérie Pomerleau, Public Affairs and Communications
valerie@ryanap.com
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The SP PNG Hunters suffered 30 - 12 defeat from the defending Champions Ipswich Jets in this afternoon's round 12 match at the Ipswich Reserves. The Hunters have registered more loses in Australian than at home soil and this loss adds to the tally.
The defending champions were first to score at the 12 minute and took the early lead 6 - 0. A penalty was awarded to the Hunters close to the Jets try line, however, captain Zeming resorted to shoot a penalty goal and trailed 6- 2.
On the 29th minute, Hunter's fullback Stagroth Amean was injured and was taken out of the field that affected the Hunters attack and deference.
The Jets scored again to extend their lead to 12 - 2 at half time.
In the second half, the Hunters put themselves right back into the game when Thompson Teteh scored out wide on the 52nd minute.
Captain Noel Zeming missed the uprights and the Hunters trailed 12-6.
The Jets responded straight away through PNG boy Richard Pandia, who proved too much to handle on the wing and scored for Jets. The conversion was successful and the Jets led 18 - 6 .
The Hunters replied with a try on the 60 minute after a nice foot race from Thomson Teteh who set up Watson Boas to score. Zeming converted the try and reduced the margin to 18 - 12.
The spirited Hunters fight back was short lived after stand-in fullback Adex Wera dropped the ball in the Hunters in goal that saw Jets forward Nat Neale recouped the lost ball and scored. The conversion was successful and the home team led 24 - 12.
The Hunters threw everything at the Jets in the last ten minutes but the Jets repelled them.
The icing on the cake came a minute out from full time when Nemani Velekapa crossed over.
Kicker and fullback Carlin Anderson was impressive , kicking 5 from 5 conversions.


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If you're unsure if that option was turned on or off, you can double check and change the renewal setting for your subscription at any time through your Avira account.
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In this episode I am talking with Pamela Morgan. She is the author of "Crypto-Asset Inheritance Planning: A Simple Guide for Owners" a book about strategies to store your private keys for bitcoin and other digital assets safely for your heirs. Pamela is an educator, attorney and entrepreneur. She has studied Business and Computer Programming before pursuing a Juris Doctors degree. In early 2015 Pamela has founded Thirdkey solutions (with Andreas M. Antonopoulos as CTO), a key consulting firm that works with individuals and organizations to improve the security of their crypto-holdings and ensure these assets are accessible in the event of crisis, death, or disaster.
*Affiliate Links: if you buy a wallet after clicking these links I'll earn a small commission.
The post Pamela Morgan on Inheritance Planning for Crypto-Assets appeared first on BITCOIN & CO. Podcast.


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DSHEA In Action
Chester J. Zelasko, Ph.D. | July 8, 2003
How many times have you read that there are no regulations of the dietary supplement industry? I've discussed this before in a previous issue of the Newsletter (1). Recent events have shown how laws regulating dietary supplements are supposed to work. Here are two specific examples.
Coral calcium has been the focus of at least two infomercials over the past two years. Whether this product works as advertised has been one of the most frequent questions coming in to Better Life Unlimited. It usually goes something like this: "Does coral calcium do everything that they say in the infomercial?" The answer is no--not that we could find in any of the scientific literature.
It looks like the U.S. Federal Trade Commission agrees--they've launched an investigation into the claims made for coral calcium regarding cancer, heart disease, and other diseases (2). Compounding the trouble for the distributors of coral calcium was the finding by consumerlab.com of excessive lead levels in batches of coral calcium, and I don't need to tell you how toxic lead is.
SeaSilver has also made fantastic claims about the effectiveness of its products. One of the claims is that liquid vitamins and minerals are better absorbed than tablets. Research to back that statement simply doesn't exist in the published scientific literature. That claim is minor compared to the claims of disease cures. The FTC seized the inventory of the manufacturers of SeaSilver because of false advertising (3).
These are two examples of the Dietary Supplement Health Education Act (DSHEA, pronounced de-SHAY) in action. DSHEA prohibits unproven claims on the labels or in advertising of dietary products. These companies violated the law and are the subject of scrutiny by both federal agencies. But that's not all that's happening when it comes to regulating the supplement industry.
The FDA recently called for the establishment of a policy requiring companies to use Good Manufacturing Practices (GMP) in the manufacture of the dietary supplement and to test and verify for accuracy (4) the information on nutrition labels. Reputable manufacturers already subject themselves to these high standards. The problem is that not all manufacturers do, and that's why the government is calling for a more comprehensive law to be enacted.
Critics say that's not enough. They say that dietary supplement manufacturers should be subjected to the same laws as the pharmaceutical industry. But let's be realistic--it doesn't matter how many laws are enacted, people will still make unsubstantiated claims for products. That's happened in television advertising for pharmaceutical products as well. We don't really need more laws--GMPs and accuracy in labeling for the dietary supplement industry are enough if they're enforced.
What's more important is common sense. Consumers should always use two criteria when deciding whether or not to use a dietary supplement. First, remember that if it sounds too good to be true, it probably is. There are no miracle cures that the government and the pharmaceutical industry don't want you to know about. It may sound intriguing, but it should also set off your radar. Second, know your manufacturer. If you don't know anything about the manufacturer, find out before you buy. Often the price of a supplement is low enough that you don't do the checking you would do when buying a toaster or a television.
Keep this in mind: you are taking those pills, powders, or liquids into your body and your family's bodies. Don't you want to know as much about them as you can before you take them? Do your homework before you buy. That's the best form of regulation any industry can have: an informed consumer.
Regulating Food Supplements. The Newsletter. March 5, 2002.
FTC and FDA Take New Actions in Fight Against Deceptive Marketing: FTC Charges Marketers of Coral calcium Supreme Dietary Supplement. Federal Trade Commission for the Consumer. June 10, 2003.
No Silver Lining for Marketers of Bogus Supplement; Federal Agencies Crack Down on Health Fraud. Federal Trade Commission for the Consumer. June 19, 2003.
FDA Proposes Labeling and Manufacturing Standards For All Dietary Supplements. FDA News. March 7, 2003.
© 2011 Better Life Unlimited™
A division of Better Life Institute © (BLI, Inc.)

redpajama_set_name: RedPajamaCommonCrawl


So, My name is Ashley (as if that wasn't totally obvious…). I'm 16 years old, and currently attending grade 11 in a tiny high school in Canada. (Ay? ;] ) As of today, my monthly "blessing" was supposed to visit me about a week ago. Yesterday, I woke up feeling extremely sick and dizzy. So today, I made the distant drive to Rocky Mountain House, Alberta and bought myself a couple pregnancy tests. Well! As if the obvious wasn't happening, 2 tests, and 4 pink lines later, I was making the phone call to my best friend Jordan in a complete panic. She met me at the hospital (all of the clinics were closed by this time) and we made an appointment to see a doctor! Yay? Two hours, one cup of pee and a nurse stabbing me in the arm to steal my blood later, the doctor knocked on my door. He came in, and immediately handed me a booklet explaining about abortion. He basically explained to Jord and I, that abortion is the answer, and it will solve all of our problems. We live in a tiny town, in southern Alberta. There's seriously like 200 kids in our school. My pregnancy would be the first in like the last… Gazillion years. Being a small school, everyone would know, and everyone would judge me. We all know this too well. I've dreamed of being a teacher since I was like… Little. If I have this baby, it's going to change everything, and make pursuing my dreams a lot more difficult. So of course, abortion is at the top of my list at the moment. My doctor directed me to StandUpGirl to read testimonials from other teenage girls and how they dealt with their abortions. After reading them, I'm finding myself quite scared. I really don't want to go ahead with this if it's going to make me depressed for the rest of my life… But I really have to think about my future, and how it's going to effect me. Right now, 5 weeks in, I'm feeling nauseated all the time, I'm eating a ton and I'm constantly tired. I can imagine in like 6 months, when finals are about to roll around the corner, it'll probably be like 50 times worse. I'm honestly at a loss of what to do. Abortion is seeming like the right decision, but so many people seem so depressed after the initial procedure, and regret it for such a long time. Plus at 5 weeks, I know that my baby is already developing it's eyes, it's ears, and it's respiratory system… I feel like if I go through with this, I'm going to be murdering an innocent human being.


Home→Blog→Uncategorized→Gary Mckinstry Second Psychic Show Tickets Selling Fast!
Gary Mckinstry Second Psychic Show Tickets Selling Fast!
Yes, after an unprecedented sellout of Gary's first show, we added a second to accommodate everyone and anyone that missed out on our sold out show of May 5th.
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* Israel holds major drill to practice fighting Hamas and Hezbollah simultaneously Ongoing 10-day exercise by Commando Brigade tackles battling Hamas in Gaza, Hezbollah in north at the same time, a prospect military fears is liable to occur.
* Czech President Proclaims Himself to be 'Israel's Best Friend' Zeman expressed interest in one-state solution in meeting with Rivlin.
* Chad's President Arrives in Israel, Asks for Help Fighting Al-Qaeda, ISIS In further evidence that Israel's charm offensive with Gulf States and majority-Muslim African states may be bearing fruit, Chad's President Idriss Deby is currently visiting the country - the first such visit since the establishment of the state.
* U.S. ambassador to Israel says peace plan will come at "appropriate time" U.S. Ambassador to Israel David Friedman said in a rare statement today that President Trump will release his Israeli-Palestinian peace plan at a time that will allow its best chance for success.
* Ukraine Considers Martial Law Amid Tensions with Russia Ukraine's parliament is considering President Petro Poroshenko's call to impose martial law in the country, in the wake of Russia seizing three of its ships and their crews.
* Tony Blair says May's deal is hated by both Leavers and Remainers because it is 'painful and pointless' as he calls for a new referendum Tony Blair said the terms of May's deal boosted case for a second referendum.
* Iran nuclear chief warns of unpredictable consequences if deal breaks down Iran's nuclear chief warned the European Union on Monday of "ominous" consequences if it did not follow through with action to keep the economic benefits of the 2015 nuclear agreement alive.
* "We Will Displace You": Extremist Persecution of Christians, July 2018 There were 128 incidents of church vandalism or other anti-Christian attacks in France during the first five months of 2018, according to a Paris-based Roman Catholic non-profit organization that tracks attacks against Christians.
* Turkey Stabilizing Libya? Think Again. "The chaotic situation enables the emergence of enclaves of terror, inspired by the ideology of ISIS and al-Qaeda. The world should make sure that Libya does not turn into another pre-2001 Afghanistan-like state on the doorstep of Europe." - Dr. Mordechai Kedar and Dr. Dan Gottlieb.
* 'Trump's Mideast team in agreement on Deal of the Century' US Ambassador to Israel David Friedman rejects reports of dissension among Trump's Mideast advisors regarding peace plan.


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Our collection also contains organic cotton sheets, crafted of cotton farmed without harmful chemicals and refined using eco- friendly processes.


Cabaré is a combination series with Continental design. The series consists of a sofa and canapé section in several sizes allowing the freedom to create your own style. You can choose among several types of legs, as well as all of our fabrics. Cabaré always comes with removable upholstery.
"I've always focused on designing products that create a relationship with the user."
Quite a few of the best-selling classics in our collection were designed by multiple award winner Carl-Henrik Spak. Spak's design is characterised by purity and timelessness, as well as Swedish design tradition — but also by an international feeling, finish and elegance. These are qualities that also distinguish Ire as a furniture manufacturer and a brand. Carl-Henrik was trained at HDK in Gothenburg and the Royal College of Art in London. For many years Carl-Henrik Spak was a partner and creative design advisor at Ire.


Warnings often appear as mere suggestions until it's too late.
Psalm 119: 149 In your faithful love, O LORD, hear my cry; let me be revived by following your regulations. 150 Lawless people are coming to attack me; they live far from your instructions. 151 But you are near, O LORD, and all your commands are true. 152 I have known from my earliest days that your laws will last forever.
Chapter 27 & the end of 28 has a litany of curses that the people listened to and agreed to by saying Amen. This was a caring remembrance of the abominable sins that separated the people from their God and thus 'cursed' them. The end of Chapter 28 (starting in verse 36) is a prophetic glimpse of the ultimate cost of Israel's future disobedience…they will be given unto another nation. This will be fulfilled in future generations and we will study it later in this year.
The first half of Chapter 28 is the opposite in that it gives the blessings of Obedience. This can be seen as the promises of God for those who walk in His way. With these promises God casts a vision for a people who would lend but not borrow (have plenty), be the head and not the tail (leaders).
Lord, help me to heed the commands of your gracious Word.
Chapter 28:65-68 shows a picture of what we would call modern-day depression or even mental illness. These are very real things that have their root in sin (as do all problems we find).
Often times we become stuck in a rut. God's Word will keep us out of the rut if we Know it and Obey it.


Ah, this spring weather gets me going. I can't wait to start planting the garden. Daniel plowed our garden plot a couple days ago in hopes to have it dry out faster. Digging deeper by plowing also helps some of those buried nutrients to get closer to the surface where the plants will be taking root. The way it sounds, we have more rain coming the next couple of days, so we'll try to stay patient. There's just nothing like fresh goodies from the garden. Equally fulfilling is watching the children's eyes widen with delight as they help harvest veggies straight from plants they had started from seed, weeded and helped keep watered.
A couple girls from our church own a greenhouse, and they have been experimenting with growing greens all winter long. Now that is quite impressive, if you ask me. Fresh, nutritious salad greens in December surely is an amazing experience. Even children will eat salads more if they're made up of tender young greens fresh from the patch. We have found, too, that having a good dressing to go over the salad does go a long way, whether you're feeding youngsters or even Daddy! Daniel is just like my dad has been as long as I can remember: to them, it's not worth even eating a salad if you don't have some good old-fashioned, homemade dressing to go with it.
Another alternative I've found, when it comes to salad in the dead of winter or when you run out of patience while waiting in the springtime, is sprouting your own seeds. It doesn't take nearly as long as planting and waiting till your lettuce is ready to harvest, and not only that, you can keep growing it on your countertop through every inch of rain that falls relentlessly on the outdoors.
Talking about rain, yesterday when Julia stepped inside after her walk home from school, she said, "Mom, I know what we could do to help the garden dry off faster. We could use buckets and dip the water out of those furrows." Bless her heart. Obviously, she heard Daniel and me discussing the matter the day before and noticed all the water that still needed to dry out as she walked past the garden.
I went with her to investigate. Yes she was correct, gardening does look like it could be a little way off yet, but then this really can be an opportunity to be an example to the children of being thankful for the weather God sends us and not spend time pining over it.
Flowers are another thing I enjoy, but I need or want to keep things basic this year. Never again will I have this summer with two 1-year-old boys and a 2-year-old girl. As my aunt would say, "Your flowers run around." Yes, I wouldn't trade my darlings for the world's most stunning flowers. Neither do I want my little ones to grow up with the memory that Mom was constantly saying, "No, no, don't pick Mommy's flowers!" So one lofty goal that I do have is having a few nice long rows of flowers in the garden, solely for the children to be able to go out and pick bouquets. I'm not sure what kind it'll be yet, perhaps some gladiolus and freesias that cousin Owen gave. Since Owen is staying at our house, we also get to have his blueberry plants which he planted in large totes a year ago. A brainy idea, now he could just move it with him. I can just see the little boys' hands reach up and pick fresh berries, that is if we can keep their hands off long enough to allow the berries to ripen.
Now as we think of springtime salads, how about trying our family favorite dressing to go with tossed salad?
Mix and drizzle over your choice of tossed salad goodies. Extra dressing will store refrigerated for months. I like making up to eight batches of this at a time and using it for tossed salads, or Daniel even likes drizzling it over some types of casseroles.


text:
\section{Introduction}
The \emph{matroid secretary problem} was introduced by Babaioff, Immorlica, and Kleinberg \cite{BIK07} as a generalization of the classical secretary problem.  The setup is as follows.  We are given a matroid $M$ whose elements are `secretaries' with an (unknown) weight function $w\colon E(M) \to \mathbb{R}_{\ge 0}$. The secretaries are presented to us online in a random order.  When a secretary $e$ is presented to us, we learn its weight $w(e)$.  At this point, we must make an irrevocable decision to either hire $e$ or not.  The \emph{weight} of a set of secretaries is the sum of their weights.  Our goal is to design an algorithm that hires a set of secretaries with large weight, subject to the constraint that the hired set of secretaries are an independent set in $M$. The \emph{value} of an algorithm on $(M, w)$ is the average weight of an independent set it produces, taken over all orderings of $E(M)$.  We write $\opt(M,w)$ for the maximum weight of an independent set of $M$.  For $c \ge 1$, an algorithm is \emph{$c$-competitive} for $M$ if the value it outputs for $(M,w)$ is at least $\frac{1}{c}\opt(M,w)$ for all weight functions $w\colon E(M) \to \mathbb{R}_{\ge 0}$.  The following deep conjecture remains open.

\begin{conjecture}[Babaioff, Immorlica, and Kleinberg \cite{BIK07}] \label{mainconjecture}
For all matroids $M$, there is a $O(1)$-competitive matroid secretary algorithm for $M$.
\end{conjecture}

Babaioff, Immorlica, and Kleinberg \cite{BIK07} gave a $O(\log r)$-competitive algorithm for all matroids $M$, where $r$ is the rank of $M$.  This was improved to a $O(\sqrt{\log r})$-competitive algorithm by Chakraborty and Lachish \cite{CL2012}.  The state-of-the-art is a $O(\log \log r)$-competitive algorithm, first obtained by Lachish \cite{Lachish14}.  Using different tools, Feldman, Svensson, and Zenklusen \cite{FMZ15} give a simpler $O(\log \log r)$-competitive algorithm for all matroids.

On the other hand, there are constant-competitive algorithms for restricted classes of matroids. Graphic matroids have a $2e$-competitive algorithm due to Korula and Pál \cite{KP09}.  Cographic matroids have a $3e$-competitive algorithm due to Soto \cite{Soto13}.  Regular matroids and max-flow min-cut matroids both have $9e$-competitive algorithms due to Dinitz and Kortsarz \cite{DK14}.

Our first result is a vast generalization of all the aforementioned constant-competitive algorithms.  To be forthright with the reader, we stress that this result relies on a deep structure theorem communicated to us by Geelen, Gerards and Whittle, which has not yet appeared in print.  Therefore, we state this structure theorem as Hypothesis~\ref{structure}.  Roughly,  Hypothesis~\ref{structure} asserts that every matroid in a proper minor-closed class of $\mathbb{F}_p$-representable matroids admits a tree-like decomposition into sparse or graph-like pieces. The proof of (a stronger version of) Hypothesis~\ref{structure} will stretch to hundreds of pages and will be a consequence of their decade-plus `matroid minors project'. This is a body of work generalising Robertson and Seymour's graph minors structure theorem \cite{rs03} to matroids representable over a fixed finite field, leading to a solution of Rota's Conjecture~\cite{GGW14}. See \cite{Geelen2015} for a discussion of the project.

A class of matroids $\mathcal{M}$ is \emph{minor-closed} if $M \in \mathcal{M}$ and $N$ a minor of $M$ implies that $N$ is also in $\mathcal{M}$.  A \emph{proper minor-closed} class of $\mathbb{F}_p$-representable matroids is a minor-closed class of $\mathbb{F}_p$-representable matroids that is not equal to the class of all $\mathbb{F}_p$-representable matroids.

\begin{theorem}\label{main}
    Suppose that Hypothesis~\ref{structure} holds. Let $p$ be a prime and $\mathcal{M}$ be a proper minor-closed class of the $\mathbb{F}_p$-representable matroids. Every matroid in $\mathcal{M}$ has an $O(1)$-competitive matroid secretary algorithm.
\end{theorem}

Note that the existence of constant-competitive algorithms for transversal matroids~\cite{DP12} and laminar matroids~\cite{IW11, HP13, JSZ13} is not implied by Theorem \ref{main}.  In addition, the matroid secretary algorithm in Theorem~\ref{main} requires knowledge of the entire matroid upfront.  This is the same model as originally introduced by Babaioff, Immorlica, and Kleinberg \cite{BIK07}, but many of the known matroid secretary algorithms also work in the online setting, see \cite{HKC04}.  We do not know if Theorem~\ref{main} holds in the online setting.

Our proof of Theorem~\ref{main} extends the nice framework of Dinitz and Kortsarz \cite{DK14} for obtaining constant-competitive algorithms for `decomposable' matroids.  In Theorem \ref{treealgorithm}, we prove that if $M$ admits a certain type of `tree-decomposition' into matroids for which we already have constant-competitive algorithms, then there is a constant-competitive algorithm for $M$ itself.  Note that the proof of Theorem \ref{treealgorithm} is independent of any matroid structure theory results.   For example, plugging in the regular matroid decomposition theorem of Seymour \cite{Seymour80} into Theorem \ref{treealgorithm}, we recover the constant competitive algorithm for regular matroids.   Our framework is slightly more general than \cite{DK14}, where only $1$-, $2$-, and $3$-sums of matroids are considered, while we allow tree-decompositions of any fixed `thickness'.  Plugging in the matroid structure machinery into Theorem \ref{treealgorithm} gives Theorem \ref{main}.

Our second result shows that Conjecture \ref{mainconjecture} holds for almost all matroids.  For each $M$, let $\mathsf{RB}$ denote the matroid secretary algorithm that chooses a uniformly random basis $B$ of $M$, and selects precisely the elements of $B$, ignoring weights.

\begin{theorem}\label{main2}
    For asymptotically almost all matroids on $n$ elements, the algorithm $\mathsf{RB}$ is $(2+\tfrac{3}{\sqrt{n}})$-competitive.
\end{theorem}

The veracity of Theorem~\ref{main2} is not terribly surprising, although given the limited tools in asymptotic matroid theory, it is a bit surprising that we can prove it.  Indeed, the proof of Theorem~\ref{main2} relies on recent breakthrough results of Pendavingh and van der Pol \cite{PP15, PP16}.

One can think of Theorem~\ref{main} and Theorem~\ref{main2} as complementary results.  Theorem~\ref{main2} asserts that the `typical' matroid has a constant-competitive algorithm, so we expect counterexamples to Conjecture \ref{mainconjecture} to come from structured classes of matroids.  On the other hand, Theorem~\ref{main} says that restricting to proper-minor closed classes of $\mathbb{F}_p$-representable matroids also cannot produce counterexamples to Conjecture \ref{mainconjecture}.

Recall that for the classical secretary problem, the algorithm that samples and rejects the first $\frac{1}{e}$ of the secretaries and then hires the first secretary that is better than all secretaries in the sample is $e$-competitive.  Dynkin \cite{Dynkin63} showed that this algorithm is best possible.  Thus, interestingly, for almost all matroids the algorithm $\mathsf{RB}$ has a better competitive ratio than the best classical secretary algorithm.  Indeed, under a widely believed conjecture in asympotic matroid theory, we note that there is in fact a $(1+o(1))$-competitive algorithm for almost all matroids.

\begin{theorem} \label{main3}
If asymptotically almost all matroids are paving, then there is a $(1+o(1))$-competitive matroid secretary algorithm for asymptotically almost all matroids.
\end{theorem}

We will discuss and prove Theorem \ref{main2} and \ref{main3} in the last section of the paper.

\section{Preliminaries}
In this section, we review some results that we will require later.  We assume basic knowledge of matroid theory and follow the notation of Oxley \cite{Oxley11}.

We begin by quickly defining the matroids that appear in this paper.  A matroid is \emph{graphic} if it is isomorphic to the cycle matroid of a graph.  It is \emph{cographic} if it is the dual of a graphic matroid.  Let $\mathbb{F}$ be a field.  A matroid is \emph{$\mathbb{F}$-representable} if it is isomorphic to the column matroid of a matrix with entries in $\mathbb{F}$, and it is \emph{regular} if it is $\mathbb{F}$-representable for every field $\mathbb{F}$.  A \emph{represented frame matroid} is a matroid that has a matrix representation in which each column has at most two nonzero entries.  Finally, we let $M(K_n)$ denote the cycle matroid of the complete graph $K_n$ and $U_{r,n}$ denote the matroid on $\{1, \dots, n\}$ where all $r$-subsets are bases.  The latter matroids are called \emph{uniform matroids}.

Let $M$ be a matroid with ground set $E$ and let $C$ and $D$ be disjoint subsets of $E$.  We let $M / C \setminus D$ denote the matroid obtained from $M$ by contracting the elements in $C$ and deleting the elements in $D$.  A matroid $N$ is a \emph{minor} of a matroid $M$ if $N$ is isomorphic to $M / C \setminus D$ for some choice of $C$ and $D$.  We let $\si(M)$ be the matroid obtained from $M$ by suppressing loops and parallel elements.

We will use two theorems of Soto. The first (\cite{Soto13}, Theorem 5.2) gives a constant-competitive algorithm for `sparse' matroids.

\begin{theorem}\label{sparse}
    Let $\gamma \in \mathbb{R}$. If $M$ is a matroid so that $N = \si(M)$ satisfies $|X| \le \gamma r_N(X)$ for all $X \subseteq E(N)$, then there is a $\gamma e$-competitive matroid secretary algorithm for $M$.
\end{theorem}

The next (\cite{Soto13}, Theorem 5.4) gives a constant-competitive algorithm for representable frame matroids.

\begin{theorem}\label{frame}
    If $M$ is a represented frame matroid, then there is a $2e$-competitive matroid secretary algorithm for $M$.
\end{theorem}

Finally, we use a trivial lemma that is proved by setting elements to have zero weight appropriately.
\begin{lemma}\label{deletion}
    If there is a $c$-competitive matroid secretary algorithm for $M$, then there is a $c$-competitive algorithm for every restriction of $M$.
\end{lemma}

\section{Lifting and Projection}

Let $M_1$ and $M_2$ be matroids on a common ground set $E$. We say that $M_1$ is a \emph{distance-$1$ perturbation} of $M_2$ if there is a matroid $M$ and a nonloop element $x$ of $M$ such that $\{M / x, M \backslash x\} = \{M_1,M_2\}$. We say that  $M / x$ is a \emph{projection} of $M \backslash x$ and $M \backslash x$ is a \emph{lift} of $M / x$ (many authors call these \emph{elementary} projections/lifts). The \emph{perturbation distance} between two matroids $M,M'$ on a common ground set is the minimum $t$ for which there exists a sequence $M = M_0, M_1, \dotsc, M_t = M'$ where each $M_i$ is a distance-$1$ perturbation of $M_{i-1}$. We write $\dist(M,M')$ for this quantity. Note that if $M$ and $M'$ are representable (say by matrices $A$ and $A'$), then $\dist(M,M')$ is small if and only if $A'=A+P$ for some low-rank matrix $P$.

In this section, we show that the existence of constant-competitive algorithms is robust under a bounded number of lifts/projections.

\begin{lemma}\label{lift}
    Let $N$ be a lift of a matroid $M$. If there is a $c$-competitive algorithm for $M$ then there is a $\max(e,2c)$-competitive algorithm for $N$.
\end{lemma}
\begin{proof}
    Let ${\mathsf{ALG}}_M$ be a $c$-competitive algorithm for $M$. Let $L$ be a matroid and $x$ be a nonloop of $L$ such that $L / x = M$ and $L \backslash x = N$. Let $P$ be the parallel class of $L$ containing $x$. Note that each element in $P - \{x\}$ is a loop in $M$, and hence will never be selected by ${\mathsf{ALG}}_M$.  We specify an algorithm ${\mathsf{ALG}}_N$ for $N$ as follows:
    \begin{itemize}
        \item as the elements of $P - \{x\}$ are received, ${\mathsf{ALG}}_N$ runs the classical secretary algorithm to select one. If $P = \{x\}$, then no element is chosen in this way.
        \item as the elements of $E(M) - P$ are received, ${\mathsf{ALG}}_N$ passes them to ${\mathsf{ALG}}_M$ and selects them as ${\mathsf{ALG}}_M$ does.
    \end{itemize}

    Let $I$ be the set of elements chosen in the first way (so $|I| \le 1$) and $J$ be the set of elements chosen in the second way. Clearly $J$ is independent in $N / I$ and so $I \cup J$ is independent in $N$. It remains to show that $\mathbf{E}(w(I \cup J)) \ge \tfrac{1}{\max(e,2c)}\opt(N,w)$. Let $B$ be a max-weight basis of $(N,w)$ and let $C$ be the unique circuit of $L$ with $\{x\} \subseteq C \subseteq B \cup \{x\}$. To analyse ${\mathsf{ALG}}_N$ we distinguish two cases.

    If $|C| \ge 3$, then let $C' = C-\{x\}$ and let $y$ be a minimum-weight element of $C'$. Now $w(C'-\{y\}) \ge \tfrac{1}{2}w(C')$ and $B - \{y\}$ is a basis of $M$ satisfying $w(B-\{y\}) = w(B-C') + w(C'-\{y\}) \ge w(B-C') + \tfrac{1}{2}w(C') \ge \tfrac{1}{2}w(B)$. Therefore $\opt(M,w) \ge \tfrac{1}{2}\opt(N,w)$ and so $\mathbf{E}(w(J)) \ge \tfrac{1}{c} \opt(M,w) \ge \tfrac{1}{2c}\opt(N,w)$.

    If $|C| < 3$, then (since $x$ is a nonloop of $L$) we have $C = \{x,x'\}$ for some $x' \in P-\{x\}$. In this case $B = \{x'\} \cup J'$ for some independent set $J'$ of $M$. Now $I$ is chosen by an $e$-competitive secretary algorithm on $P-\{x\}$, so $\mathbf{E}(w(I)) \ge \tfrac{1}{e}w(x')$. Moreover, since $B$ is optimal and $\{x'\} \cup B_0$ is independent in $N$ for every basis $B_0$ of $M$, we have $w(B - \{x'\}) = \opt(M,w)$. Therefore
    \begin{align*} \mathbf{E}(w(I \cup J)) &\ge \tfrac{1}{e}w(x') + \tfrac{1}{c}\opt(M,w) \\
    &= \tfrac{1}{e}w(x') + \tfrac{1}{c}w(B- \{x'\}) \\
    &\ge \tfrac{1}{\max(e,c)}\opt(N,w).
    \end{align*}

    It follows from these two cases that ${\mathsf{ALG}}_N$ is $\max(e,2c)$-competitive for $N$.
\end{proof}

\begin{lemma}\label{projection}
    Let $N$ be a projection of a matroid $M$. Let $L$ be the set of loops of $N$. If there is a $c$-competitive algorithm for $M$ then there is an $(e+1)c$-competitive algorithm for $M \backslash L$ whose output is always independent in $N$.
\end{lemma}
\begin{proof}
    By Lemma~\ref{deletion}, there is a $c$-competitive algorithm ${\mathsf{ALG}}_{M \backslash L}$ for $M \backslash L$. Let $P$ be a matroid and $x$ be a nonloop of $P$ so that $P / x = N$ and $P \backslash x = M$. Let $X$ be the random variable taking the value $\mathsf{heads}$ with probability $\tfrac{e}{e+1}$ and $\mathsf{tails}$ with probability $\tfrac{1}{e+1}$. We define another matroid secretary algorithm ${\mathsf{ALG}}_N$ for $M \backslash L$ as follows:
    \begin{itemize}
        \item if $X = \mathsf{heads}$, then we run a classical secretary algorithm on $N \backslash L$ to select just one element.
        \item if $X = \mathsf{tails}$, then we run ${\mathsf{ALG}}_{M \backslash L}$, except we only pretend to hire any element whose selection would create a dependency in $N$ with the elements already chosen.
    \end{itemize}

    Fix a weighting $w$ of $M \backslash L$. Let $x_0 \in E(M \backslash L)$ have maximum weight, and let $I$ be the set selected by ${\mathsf{ALG}}_N$. Clearly if $X = \mathsf{heads}$ then $I$ is independent in $N$, and we have $\mathbf{E}(w(I) | X = \mathsf{heads}) \ge \tfrac{1}{e}w(x_0)$. Moreover, if $J$ is the set output by ${\mathsf{ALG}}_{M \backslash L}$, then $J \cup \{x\}$ contains at most one circuit of $P$.  It follows that if $X = \mathsf{tails}$ then $I$ is obtained from $J$ by removing at most one element, so $w(I) \ge w(J) - w(x_0)$. Thus
    \begin{align*}
        \mathbf{E}(w(I)) &= \tfrac{e}{e+1} \mathbf{E}(w(I)|X = \mathsf{heads}) + \tfrac{1}{e+1}\mathbf{E}(w(I)| X = \mathsf{tails}) \\
        & \ge \tfrac{1}{e+1}w(x_0)  + \tfrac{1}{e+1}(\mathbf{E}(w(J) - w(x_0)) | X = \mathsf{tails})\\
        & = \tfrac{1}{e+1}\mathbf{E}(w(J) | X = \mathsf{tails})\\
        & \ge \tfrac{1}{c(e+1)}\opt(M \backslash L,w).
    \end{align*}
    It follows that ${\mathsf{ALG}}_N$ is $(e+1)c$-competitive for $M \backslash L$.
\end{proof}

In particular, since every independent set in $N$ is an independent set of $M \backslash L$, the algorithm ${\mathsf{ALG}}_N$ is $(e+1)c$-competitive for $N$. Since $(e+1)c > \max(e,2c)$ for $c \ge 1$, we can thus combine Lemmas~\ref{lift} and~\ref{projection} with an inductive argument to yield the following.

\begin{lemma}\label{perturb}
Let $t \in \mathbb{N}$ and let $M$ and $N$ be matroids with $\dist(M,N) \le t$. If there is a $c$-competitive algorithm for $M$, then there is a $(e+1)^tc$-competitive algorithm for $N$.
\end{lemma}

Similarly, iterating Lemma~\ref{projection} yields the following:
\begin{lemma}\label{multprojection}
    Let $N$ be a matroid obtained from a matroid $M$ by a sequence of $t$ projections. Let $L$ be the set of loops of $N$. If there is a $c$-competitive algorithm for $M$, then there is a $c(e+1)^t
    $-competitive algorithm for $M \backslash L$ whose output is always independent in $N$.
\end{lemma}

\section{Tree-decompositions}
In this section, we introduce a notion of tree-decompositions of matroids, and give a constant-competitive matroid secretary algorithm for matroids having a `bounded-thickness' tree-decomposition into pieces for which constant-competitive algorithms are known.  We use the term \emph{thickness}, to distinguish our notion from other well-known width parameters for matroids such as
\emph{branch-width} \cite{GGW02}.

 For a matroid $M = (E,r)$ and disjoint sets $X,Y \subseteq E$, we write $\sqcap_M(X,Y) = r_M(X) + r_M(Y) - r_M(X \cup Y)$. The \emph{connectivity function} $\lambda_M$ of a matroid $M$ is the function $\lambda_M\colon 2^{E} \to \mathbb{Z}_{\geq 0}$ defined by $\lambda_M(X)= \sqcap_M(X,E-X)$. Note that if $M$ is graphic, then $\lambda_M$ (essentially) encodes graph connectivity (see Oxley \cite{Oxley11}).  It is also easy to check that $\lambda_M$ is a symmetric and submodular function.  We use the following easy lemma:

 \begin{lemma}\label{lambda}
     Let $M = (E,r)$ be a matroid and let $X \subseteq E$. Then $M / (E-X)$ is obtained from $M|X$ by a sequence of $\lambda_M(X)$ projections.
 \end{lemma}
 \begin{proof}
   Let $I_1 \subseteq X$ and $I_2,I_3 \subseteq E-X$ be disjoint independent sets of $M$ so that $I_1$ is a basis for $M|X$, $I_1 \cup I_2$ is a basis for $M$, and $I_2 \cup I_3$ is a basis for $M \backslash X$. We have $|I_3| = r_M(E-X) - (r_M(E) - r_M(X)) = \lambda_M(X)$. Now the matroid $N = (M / I_2)|(X \cup I_3)$ satisfies $N / I_3 = M / (E-X)$ and $N \backslash I_3 = M|X$. The lemma follows.
 \end{proof}

 A \emph{tree-decomposition} of a matroid $M$ is a pair $(T, \mathcal{X})$ where $T$ is a tree and $\mathcal{X}:=\{X_v : v \in V(T)\}$ is a  partition of $E(M)$ indexed by $V(T)$.
Let $e = v_1v_2 \in E(T)$ and $T_1$ and $T_2$ be the components of $T \setminus e$ where $v_i \in V(T_i)$.  Let $X_1:=\bigcup_{v \in V(T_1)} X_v$.  We define the \emph{thickness} of $e$, $\lambda(e)$, to be $\lambda_M(X_1)$.  The \emph{thickness} of $(T, \mathcal{X})$ is $\max_{e \in E(T)} \lambda(e)$.   Given $v \in V(T)$, we write $M(v)$ for $M|X_v$; this is a restriction of $M$. If, for all $e = uv \in E(T)$, we have $\sqcap_M(X_u,X_v) = \lambda(e)$, then we say $(T,\mathcal{X})$ is a \emph{full tree-decomposition} of $M$.

\begin{theorem} \label{treealgorithm}
Let $\mathcal{M}$ be a class of matroids for which there exists a $c$-competitive matroid secretary algorithm. Let $k \in \mathbb{N}$ and let $t_k(\mathcal{M})$ be the set of all matroids $M$ with a full tree-decomposition $(T, \mathcal{X})$ of thickness at most $k$ such that  $M| \cl_M(X_v) \in \mathcal{M}$ for each $v \in V(T)$.  Then there is an $c(e+1)^k$-competitive matroid secretary algorithm for $t_k(\mathcal{M})$.
\end{theorem}
\begin{proof}
    We say a tree-decomposition $(T,\mathcal{X})$ of a matroid $M$ is an \emph{$\mathcal{M}$-tree decomposition} if $M|\cl_M(X_v) \in \mathcal{M}$ for all $v \in V(T)$. For each $m \ge 1$, let $t_{k,m}(\mathcal{M})$ denote the class of matroids in $t_k(\mathcal{M})$ having a full $\mathcal{M}$-tree-decomposition $(T,\mathcal{X})$ of thickness at most $k$ with $|V(T)| \le m$.  There is clearly a $c(e+1)^k$-competitive matroid secretary algorithm for every matroid in $t_{k,1}(\mathcal{M}) = \mathcal{M}$. Let $m > 1$ and suppose inductively that every matroid in $t_{k,m-1}(\mathcal{M})$ has a $c(e+1)^k$-competitive matroid secretary algorithm.

    Let $M \in t_{k,m}(\mathcal{M})$, let $E = E(M)$, and let $(T,\mathcal{X})$ be a full $\mathcal{M}$-tree-decomposition of $M$ of thickness at most $k$ with $1 < |V(T)| \le m$. Let $\ell$ be a leaf of $T$ and let $e = \ell u$ be the edge of $T$ incident with $\ell$. Let $X_\ell'$ and $X_u'$ be obtained from $X_\ell$ and $X_u$ by moving all elements from $X_\ell \cap \cl_M(X_u)$ into $X_u$.  It is easy to check that $\lambda_M(X_\ell') \leq \lambda_M(X_\ell)$ and that $\lambda_M(X_\ell')=\sqcap_M(X_\ell', X_u')$.  Futhermore, since $\cl_M(X_u')=\cl_M(X_u)$, it follows that $\sqcap_M(X_u',X_v)=\sqcap_M(X_u,X_v)$ for all $v \notin \{u,\ell\}$. Therefore, this move preserves the property of being a full $\mathcal{M}$-tree-decomposition of thickness at most $k$; and so we may assume that $X_\ell \cap \cl_M(X_u) = \varnothing$.

    Let $M(\ell) = M|X_\ell$ and let $M'(\ell) = M / (E-X_{\ell})$. By Lemma~\ref{lambda}, the latter is obtained from the former by at most $\lambda_M(X_\ell) \le k$ projections. Moreover, since $\sqcap_M(X_\ell,X_u) = \lambda_M(X_\ell)$, we have $\lambda_{M / X_u}(X_\ell) = 0$ and so $M'(\ell) = (M / X_u)|X_\ell$; since $X_\ell \cap \cl_M(X_u) = \varnothing$ it follows that $M'(\ell)$ has no loops.

     By Lemmas~\ref{deletion} and~\ref{multprojection}, there is a $c(e+1)^k$-competitive algorithm ${\mathsf{ALG}}_{\ell}$ for $M(\ell)$ whose output is always independent in $M'(\ell)$. Moreover, we see that $(T \backslash \ell,\{X_w\colon w \in V(T \backslash \ell)\})$ is a full $\mathcal{M}$-tree-decomposition of $M \backslash X_\ell$ with thickness at most $k$, so $M \backslash X_\ell \in t_{k,m-1}(\mathcal{M})$ and there is thus a $c(e+1)^k$-competitive algorithm ${\mathsf{ALG}}'$ for $M \backslash X_\ell$. Define an algorithm ${\mathsf{ALG}}$ for $M$ by running ${\mathsf{ALG}}'$ and ${\mathsf{ALG}}_\ell$ on the elements of $E-X_\ell$ and $X_\ell$ respectively as they are received, choosing all elements chosen by either.

     Let $I_\ell$ and $I'$ be the sets chosen by ${\mathsf{ALG}}_\ell$ and ${\mathsf{ALG}}'$ respectively. Since $I'$ is independent in $M$ and $I_{\ell}$ is independent in $M'(\ell)$, the set $I = I_{\ell} \cup I'$ chosen by ${\mathsf{ALG}}$ is independent in $M$. Moreover, for each weighting $w$ of $M$ we have

     \begin{align*}
         \mathbf{E}(w(I)) &= \mathbf{E}(w(I')) + \mathbf{E}(w(I_\ell)) \\
         &\ge \tfrac{1}{c(e+1)^k}(\opt(M(\ell),w|X_\ell) + \opt(M \backslash X_\ell,w|(E - X_\ell)) \\
         &\ge \tfrac{1}{c(e+1)^k}\opt(M,w),
     \end{align*}
     since each independent set of $M$ is the union of an independent set of $M(\ell)$ and one of $M \backslash X_\ell$. The theorem follows.
    \end{proof}

As an easy corollary of Theorem \ref{treealgorithm}, we obtain a short proof that there is an $O(1)$-competitive algorithm for regular matroids, a result first proved by  Dinitz and Kortsarz \cite{DK14}. The constant $9e$ that they obtain is better than ours by a factor of $\tfrac{1}{3}(e+1)^2 \approx 4.6$.

\begin{corollary} \label{regular}
There is a $3e(e+1)^2$-competitive matroid secretary algorithm for each regular matroid.
\end{corollary}

\begin{proof}
By Seymour's regular matroid decomposition theorem \cite{Seymour80}, every regular matroid $M$ is obtained from pieces that are either graphic, cographic or $R_{10}$ by $1$-, $2$- or $3$-sums. This gives a tree-decomposition $(T,\mathcal{X})$ of thickness at most $2$ in $M$ so that each $M|X_v$ is either graphic, cographic or $R_{10}$. Moreover, by performing parallel extensions of the elements to be deleted before each $2$-sum and $3$-sum, one can construct a matroid $M'$ having $M$ as a restriction and a \emph{full} tree-decomposition $(T,\mathcal{X}')$ of $M'$ so that each $M'|\cl_{M'}(X'_v)$ is either graphic, cographic or a parallel extension of $R_{10}$.

Korula and P{\'a}l \cite{KP09} proved that there is a $2e$-competitive matroid secretary algorithm for graphic matroids.  Soto \cite{Soto13} proved that there is a $3e$-competitive matroid secretary algorithm for cographic matroids. Since $R_{10}$ is the union of two bases, Theorem~\ref{sparse} implies that each of its parallel extensions has a $2e$-competitive algorithm. It follows from Theorem~\ref{treealgorithm} that there is a $3e(e+1)^2$-competitive algorithm for $M'$; by Lemma~\ref{deletion} there is also one for $M$.
\end{proof}

\section{Proper Minor-Closed Classes}

In this section we show that, contingent on a certain deep structure theorem, there is a constant-competitive algorithm for every proper minor-closed subclass of the matroids representable over a fixed prime field. As well as this structure theorem, we require one other result, due to Geelen (\cite{Geelen2011}, Theorem 4.3).

\begin{theorem}\label{excludeclique}
    Let $q ,n \in \mathbb{N}$. If $M$ is a simple matroid with no $U_{2,q+2}$-minor and no $M(K_n)$-minor, then $|M| \le q^{q^{3n}}r(M).$
\end{theorem}

Since no restriction of such an $M$ has either of the forbidden minors, for such an $M$ we also have $|X| \le q^{q^{3n}}r_M(X)$ for each $X \subseteq E(M)$. Combining this theorem with Theorem~\ref{frame}, we thus have the following.

\begin{corollary}\label{secexcludeclique}
    Let $q,n \in \mathbb{N}$. If $M$ is a matroid with no $U_{2,q+2}$-minor and no $M(K_n)$-minor, then there is a $eq^{q^{3n}}$-competitive matroid secretary algorithm for $M$.
\end{corollary}

We now state the structure theorem we will use to prove Theorem~\ref{main}.

\begin{hypothesis}\label{structure}
Let $p$ be a prime. For every proper minor-closed class $\mathcal{M}$ of $\mathbb{F}_p$-representable matroids, there exist $k,n$ and $t$ for which every $M \in \mathcal{M}$ is a restriction of a matroid $M'$ having a full tree-decomposition $(T, \mathcal{X})$ of thickness at most $k$ such that for all $v \in V(T)$, if $M'|\cl_{M'}(X_v)$ has an $M(K_n)$-minor, then there is a represented frame matroid $N$ with $\dist(M'|\cl_{M'}(X_v),N) \le t$.
\end{hypothesis}

We can now prove Theorem~\ref{main}, which we restate here.
\begin{reptheorem}{main}
    Suppose that Hypothesis~\ref{structure} holds. If $p$ is prime and $\mathcal{M}$ is a proper minor-closed subclass of the $\mathbb{F}_p$-representable matroids, then there exists $c = c(\mathcal{M})$ so that every $M \in \mathcal{M}$ has a $c$-competitive matroid secretary algorithm.
\end{reptheorem}
\begin{proof}
Let $k,n$ and $t$ be the integers given for $\mathcal{M}$ by Hypothesis~\ref{structure}. Let  $\mathcal{M}_1$ denote the class of matroids having perturbation distance at most $t$ from some represented frame matroid. Let $\mathcal{M}_2$ denote the class of matroids with no $U_{2,p+2}$-minor or $M(K_n)$-minor. By Theorem~\ref{frame} and Lemma~\ref{perturb}, every matroid in $\mathcal{M}_1$ has a $2e(e+1)^t$-competitive matroid secretary algorithm. Corollary~\ref{secexcludeclique} gives a $ep^{p^{3n}}$-competitive matroid secretary algorithm for each matroid in $\mathcal{M}_2$. It is also easy to show that $U_{2,p+2}$ is not $\mathbb{F}_p$-representable. Thus, by Hypothesis~\ref{structure}  every $M \in \mathcal{M}$ is a restriction of a matroid $M'$ having a proper tree-decomposition $(T,\mathcal{X})$ of thickness at most $k$ so that $M|\cl_{M'}(X_v)  \in \mathcal{M}_1 \cup \mathcal{M}_2$ for each $v \in V(T)$. By Theorem~\ref{treealgorithm}, every such $M'$ has a $c$-competitive matroid secretary algorithm, where $c = (e+1)^k\max\left(2e(e+1)^t,ep^{p^{3n}}\right)$. By Lemma~\ref{deletion}, the same is true for every $M \in \mathcal{M}$.
\end{proof}

\section{Asymptotic Results}

    We say \emph{asymptotically almost all matroids} have a property if the proportion of matroids with ground set $\{1, \dotsc, n\}$ having the property tends to $1$ as $n$ approaches infinity.  We finish our paper by showing that asymptotically almost all matroids have a constant-competitive matroid secretary algorithm.  We require two recent results of Pendavingh and van der Pol \cite{PP15, PP16}.

\begin{theorem}\label{manybases}
    There exists $\alpha > 0$ so that asymptotically almost all matroids on $n$ elements have at least $\left(1 - \tfrac{\alpha (\log n)^3}{n}\right)\binom{n}{r}$ bases.
\end{theorem}
\begin{theorem}\label{rankbounds}
    If $\beta > \sqrt{\tfrac{1}{2}\ln(2)}$, then asymptotically almost all matroids on $n$ elements have rank between $\tfrac{n}{2} - \beta \sqrt{n}$ and $\tfrac{n}{2} + \beta \sqrt{n}$.
\end{theorem}

    Recall that $\mathsf{RB}$ denotes the algorithm that selects a basis $B$ uniformly at random from the set of all bases of $M$, and chooses the elements of $B$ as secretaries regardless of the weights. By Theorem~\ref{manybases}, nearly every $r$-set in a typical matroid is a basis, so a uniformly random basis can be sampled in probabilistic polynomial time in almost all matroids by repeatedly choosing a uniformly random $r$-set until a basis is chosen.

    We now state and prove a stronger version of Theorem~\ref{main2}.

\begin{reptheorem}{main2}
    Let $\gamma > \sqrt{8 \ln(2)}$. For asymptotically almost all matroids $M$ on $n$ elements, the algorithm $\mathsf{RB}$ is $(2+ \tfrac{\gamma}{\sqrt{n}})$-competitive for $M$.
\end{reptheorem}
\begin{proof}
    Let $\gamma' \in (\sqrt{8 \ln (2)},\gamma)$. Note that for each $\alpha \in \mathbb{R}$ we have $\tfrac{1}{2} - \tfrac{\gamma'}{4 \sqrt{n}} - \tfrac{\alpha (\log n)^3}{n} > (2 + \tfrac{\gamma}{\sqrt{n}})^{-1}$ for all sufficiently large $n$. Let $n$ be a positive integer and let $M$ be a matroid on $n$ elements with ground set $E = \{1,\dotsc, n\}$ and rank $r$. Let $\mathcal{B} \subseteq \binom{E}{r}$ denote the set of bases of $M$. For each $e \in E$ let $\mathcal{B}_e = \{B \in \mathcal{B}: e \in B\}$. By Theorems~\ref{manybases} and~\ref{rankbounds}, there exists $\alpha \in \mathbb{R}$ so that, asymptotically almost surely, $|\mathcal{B}| \ge (1 - \tfrac{\alpha (\log n)^3}{n})\binom{n}{r}$ and $r \ge (\tfrac{1}{2} - \tfrac{\gamma'}{4\sqrt{n}})n$. Thus, almost surely,
    \begin{align*}
        |\mathcal{B}_e| &\ge |\{B \in \binom{E}{r}: e \in B\}| - \left(\binom{n}{r}-|\mathcal{B}|\right) \\
        &= \frac{r}{n}\binom{n}{r} - \binom{n}{r} + |\mathcal{B}| \\
        &= \binom{n}{r}\left(\frac{|\mathcal{B}|}{\binom{n}{r}} + \frac{r}{n} - 1\right).\\
        &\ge |\mathcal{B}|\left(1 - \tfrac{\alpha (\log n)^3}{n} + \tfrac{1}{2} - \tfrac{\gamma'}{4\sqrt{n}} - 1 \right)\\
        &\ge |\mathcal{B}|(2 + \tfrac{\gamma}{\sqrt{n}})^{-1}.
    \end{align*}
    Let $B_0$ be a basis chosen uniformly at random from $\mathcal{B}$, as per $\mathsf{RB}$. For each $e \in E$, we have $\mathbf{P}(e \in B_0) = |\mathcal{B}_e|/|\mathcal{B}| \ge (2 + \tfrac{\gamma}{\sqrt{n}})^{-1} $. Given a weighting $w$ of $M$, we therefore have \[\mathbf{E}(w(B_0)) = \sum_{e \in E}w(e) \mathbf{P}(e \in B_0) \ge (2 + \tfrac{\gamma}{\sqrt{n}})^{-1} w(E)\ge (2 + \tfrac{\gamma}{\sqrt{n}})^{-1}\opt(M,w).\]  $\mathsf{RB}$ is thus $(2 + \tfrac{\gamma}{\sqrt{n}})$-competitive.
\end{proof}

A rank-$r$ matroid is $\emph{paving}$ if all its circuits have cardinality at least $r$. Although few well-known constructions of matroids have this property, it is believed to almost always hold.  The following conjecture due to Mayhew, Newman, Welsh, and Whittle \cite{MNWW11} is central in asymptotic matroid theory.

\begin{conjecture}\label{pavingconjecture}
    Asymptotically almost all matroids on $n$ elements are paving.
\end{conjecture}

An alternative characterisation is that a matroid $M$ is paving if and only if its truncation to rank $r(M)-1$ (which we denote as $T(M)$) is a uniform matroid. The matroid secretary problem for uniform matroids is known as the \emph{multiple-choice secretary problem}, and has been essentially completely solved by Kleinberg \cite{Kleinberg05}. In the language of matroids, his result is the following.

\begin{theorem}
    Let $r > 25$. There is an algorithm $\mathsf{UNI}$ that is  $(1 - \tfrac{5}{\sqrt{r}})^{-1}$-competitive  for each uniform matroid $U_{r,n}$.
\end{theorem}

We slightly modify $\mathsf{UNI}$ to deal with paving matroids. Let $\mathsf{PAV}$ be the algorithm that, given a rank-$(r > 26)$ weighted paving matroid $(M,w)$, returns the output of $\mathsf{UNI}$ on the rank-$(r-1)$ weighted uniform matroid $(T(M),w)$. Note that, since every independent set in $T(M)$ is independent in $M$, this output is always legal.

\begin{theorem} \label{paving}
    The algorithm $\mathsf{PAV}$ is $(1 - \tfrac{6}{\sqrt{r}})^{-1} $-competitive for every paving matroid of rank at least $37$.
\end{theorem}
\begin{proof}
    Let $B$ be a maximum-weight basis of a rank-$r$ paving matroid $M$ with weights $w$, and let $x \in B$ have minimum weight. Now $B-\{x\}$ is a basis of $T(M)$ and has weight at least $\tfrac{r-1}{r}w(B)$, so $\opt(T(M),w) \ge (1 - \tfrac{1}{r})\opt(M,w)$. Let $I$ be the independent set output by $\mathsf{UNI}$ on $T(M)$. Now
    \[\mathbf{E}(w(I)) \ge (1 - \tfrac{5}{\sqrt{r-1}})\opt(T(M),w) \ge (1-\tfrac{5}{\sqrt{r-1}})(1-\tfrac{1}{r})\opt(M,w).\]
    Since $(1- \tfrac{5}{\sqrt{r-1}})(1-\tfrac{1}{r}) \ge 1 - \tfrac{6}{\sqrt{r}}$ for all $r \ge 37$,  $\mathsf{PAV}$ is thus $(1 - \tfrac{6}{\sqrt{r}})^{-1}$-competitive.
\end{proof}

As promised, we finish with a proof of Theorem \ref{main3}, which we restate for convenience.

\begin{reptheorem}{main3}
If asymptotically almost all matroids are paving, then there is a $(1+o(1))$-competitive matroid secretary algorithm for asymptotically almost all matroids.
\end{reptheorem}

\begin{proof}
By Theorem~\ref{rankbounds}, almost all matroids have $37 < r \approx \tfrac{n}{2}$ and so, conditional on Conjecture~\ref{pavingconjecture}, Theorem \ref{paving} implies that $\mathsf{PAV}$ is $(1+ \epsilon(n))$-competitive for asymptotically almost all matroids on $n$ elements, where $\epsilon(n) \approx \tfrac{6\sqrt{2}}{\sqrt{n}}$.
\end{proof}

redpajama_set_name: RedPajamaArXiv


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text:
The lead singer of Wye Oak showed us her camera roll
By Will Schube
Photographed by Shervin Lainez
Jenn Wasner, the North Carolina-based singer of Wye Oak, documents her life avidly, but keeps the results to herself. Her phone is full of snapshots, many of which she deemed too private for public viewing. When we asked her to share some photos from her life on tour, in the studio, and those increasingly few hours in-between, she was skeptical: "This was kind of surprisingly hard for me. I have a phone full of dumb shit, but as I realized as I was going through my photos, I'm kind of weirdly private about a lot of things in my life," she explains from a van en route to South By Southwest last month, where her band—along with Andy Stack—will be playing in order to promote their new LP, The Louder I Call, The Faster It Runs. "I like to keep my personal life to myself. There were a lot of photos I didn't want to talk about, but I tried to find ones that gave me something to say. I tried to push myself to let some things out into the world that I wasn't super comfortable with," she adds.
Wasner's collection consists of personal reminders to be a better person, exotic tour locales, and a strangely erotic book about ghosts. When Wasner discusses these pictures, she has a relentless energy and infectious excitement, the same sort of qualities that infuse her body of work in Wye Oak. The first photo in this collection is a phrase which Wasner has chosen as a mantra for her band: "It takes courage to believe in chaos."
JENN WASNER: I tend to be really attracted to real world mantras I find scattered around. This particular photo is from a place called Meow Wolf in Santa Fe. I remember taking that picture specifically because I spent a good portion of that day…It's very easy to fall into a deep existential pit while driving through the desert. I'm particularly susceptible to that kind of thinking, but especially when on tour and you're cut off from routine, stability, your family, and friends; all the things you use to anchor your life. I had been thinking about that all day on the way to Meow Wolf, and when I saw that it just instantly struck me.
WASNER: That is from one of the more magical day-offs we've ever had on tour as a band. I think we had played in Milwaukee or something. We had a day off in Wisconsin and I had heard from friends over the years about this place called House on the Rock. The hotel we stayed out was directly across the street from this crazy motel called The Don Q Inn. They parked this airplane in the front yard of the hotel in the middle-of- nowhere-Wisconsin and it was just sitting there. You could go in and explore. It felt like a magical discovery we stumbled across.
WASNER: That's another real-world mantra I discovered at another really opportune moment. That was taken not long after the great election of 2016 disaster took place. We were on tour at the time. I was one of those deluded people who just didn't see it coming. We played a show that night and it was one of the more miserable tour times I can think of. It was sinking into this feeling of, 'Why am I doing this incredibly selfish and self-serving thing when there are so many bigger problems to deal with.' I was really beating up on myself for not having done more. I was feeling incredibly bleak. I got that fortune and it was so direct and abrupt. It's so easy and tempting to fall into that mindset of 'Why bother? Everything's fucked.' But that's how things fall into disrepair. It's so much more valuable to have some sort of hope in the face of those circumstances. It's a reminder I really needed and a reminder I still need.
WASNER: They had an Arthur Russell exhibit at BAM in Brooklyn. It was sheet music, personal affects, and unreleased music. I traveled to New York specifically to see that show because I'm a superfan. It was 1,000% worth it. There are few artists in history who have been more moving and important to me than Arthur Russell.
WASNER: The man in that picture is Jonathan Meiburg from Shearwater. I chose this photo because I get to brag about the one time I was legitimately psychic in my life. During the recording of The Louder I Call… I was in Marfa. We finished up a week of recording and I was flying back to North Carolina but I had a layover in Austin. Jonathan's from Austin but he's lived in New York for a long time. As I was on the plane flying to Austin I had this deep, weird, heart-cracking open creative flow moment and I started writing furiously. I ended up writing words that were added to "Say Hello." I landed in Austin with some time to kill and off the cuff for no particular reason texted Jonathan like, "Any chance you're in the Austin airport right now?" And he fucking was! It was really weird and we were both really freaked out.
WASNER: That's me and Andy [Stack] and John Congleton. He mixed Civilian and The Louder I Call…He's a really great guy and a really great friend and a really talented and inventive person. He got a package in the mail and he was like, 'Oh, someone sent me a book!' And it was a copy of The Pregnant Ghost and Other Sexual Hauntings, which, I can say from the little bit of time I spent reading it during mixing, really lives up to its title.
WASNER: This is actually from pretty recently. I was sick and exhausted and really leaning into the sloth. I made my boyfriend get me jelly donuts so I could eat them in bed. I included this photo because I'd like to put it out in the universe: If someone reads this, I would really love a realistic oil painting of me in bed with a dozen jelly donuts.
WASNER: This is from White Sands in New Mexico. This is where our album art, video, and a bunch of our photos were shot. White Sands is an absolutely gorgeous place. It's an invert, a void of a place. There's nowhere else I've ever been that plays with your perception of distance and space the way it does. As we were shooting these things we were wandering deeper and deeper into the dunes and we had to make these arrows for us to find our way back. It's so easy to get totally swept up in it.
WASNER: This is at Marfa Recording Company. That was with our engineer and front-of- house person extraordinaire Brandon Eggleston. He flew down to Marfa to help Andy and I get our initial tracks and not go totally insane during this recording process. I do a lot of goofy stretches. That's pretty typical. I think that's the first day we got sounds for this record.
WASNER: This was in LA. I immediately knew I fucking loved it. There's something about the phrase 'emotional intelligence' being spray painted on a literal can of garbage was just a perfect representation of how much value a sense of emotional intelligence has in our shitty culture. Someone's just throwing it out with the trash. It also felt like this secret, weird Jenny Holzer piece. I just thought the juxtaposition of that phrase on an actual pile of garbage was just too good to me.
WASNER: I think this is the funniest thing in the world. The absolute pinnacle of my sense of humor: the fact that Faulkner's grave has a Yelp page and it has 3 and ½ stars. It's the kind of funny that you almost can't even laugh at. You curl up in a ball and your eyes tear up. It's so insane to me. We discovered that when we were in Oxford, Mississippi. I'm a huge Faulkner fan so we went to go find it. It was after a show and we were all a little drunk, so it was really hard to find the grave, which we eventually did. I was very happy to have found the grave, but even happier to have found the Yelp review. Our world is trash. If you die and write some of the best books in history, you can be rewarded with a mediocre Yelp review.
WYE OAK'S LATEST RECORD THE LOUDER I CALL, THE FASTER IT RUNS IS OUT NOW ON MERGE.
Sofi Tukker's Camera Roll is A Dance Party, Ice Buckets Included
Cottweiler Goes to Cairo
Abdu Ali, a Musician with Restless Charisma, Shares Their Camera Roll With Us
Dreezy, the Chanel-Obsessed Chicago Rapper, Shows Us Her Camera Roll
Budding Pop Star Emily Vaughn Shows Us Her Camera Roll
Rap Wunderkind Gunna Shows Us His Camera Roll


text:
Die deutsche B-Jugendmeisterschaft 2000 war die 24. Auflage dieses Wettbewerbes. Meister wurde Hertha BSC, das im Finale den FC Bayern München mit 1:0 besiegte.

Teilnehmende Mannschaften
An der B-Jugendmeisterschaft nahmen die Meister der Regionalligen Nord (2 Gruppe Nord + Süd), Nordost, West, Südwest sowie die Sieger nach Qualifikationsturnier (2 Gruppen) der Verbände Baden, Südbaden, Bayern (Nord + Süd), Hessen und Württemberg.

Viertelfinale

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Halbfinale

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Finale

Einzelnachweise

Weblinks
 B-Juniorenmeisterschaft Endrunde 2000

2000
Fußballsaison 1999/2000

redpajama_set_name: RedPajamaWikipedia


On Easter Sunday we went to a new Church.
The church that Alex will go to preschool at next year.
see what a service is like that is not Easter Sunday.
After church we headed right to Olympic Hills and met some of my family for brunch.
the sun was actually shinning.
Olympic Hills is the Golf Club that Chad and I got married at.
Actually my mom and step dad got married there.
My step brother and his wife had a reception there and so did my step sister and her husband.
Did I mention the sun was shinning that day.
Sorry these pictures are a little bright.
We had a great brunch and there was a ton of food.
It was nice to be with family and talk and just hang out.
This is Alex new pose. ALL THE TIME!
Umm I love this picture of my brother with my girls.
I am so excited that my brother and his wife are going to have a baby in a few months.
My mom and step dad with my girls, then we added my grandparents in.
See Alex is always making such a crazy face.
My sister in law was out of town visiting her grandma.
The husbands family ( missing his brother and wife ).
Grandma and Grandpa Schuler with the girls.
I will end with that. The Easter Bunny did come back again while Alex was at the park and she was super excited. So I will save those pictures for another post.
Alex knows she is special and the Easter Bunny made her feel extra special on Easter.
beautiful pics of your beautiful family!!
I'm so glad you had a nice Easter! Beautiful family pictures. The girls looked so pretty in their dresses!
Avin looks so cute in Abby's dress. :) LOVE the pictures!!


text:
Taxandria (1994), een bekroonde langspeelfilm van Raoul Servais, 1994.
 Taxandria (2008), een film uit 2008 van Mark Weistra.


The CH337 is an extendable dining table designed in 1962 by Hans J. Wegner. Timeless, elegant as well as practical, the oval table made of oak is the perfect focal point in the dining room.
The CH337 measures 140 x 115 cm and offers space for 6-8 people. This makes it possible to organise cosy dinner parties and big breakfasts with friends and family. Up to 4 unexpected guests can also be welcomed to the dinner table thanks to the additional leaves measuring 60 cm in width each (sold separately).
The dining table is made of solid oak and is available in an oiled or soaped version. The tapering legs give the charming Nordic style table an elegant touch that can be introduced into any environment.
The Carl Hansen - CH337 extendable dining table in single view. The dining table is made of solid oak, in oiled or soaped variants. The narrow legs give it an elegant touch, so that the table blends perfectly into any ambience and spreads Nordic charm.
Isolated product image of the Carl Hansen - CH337 extendable dining table. The CH337 is an extendable dining table, designed in 1962 by Hans J. Wegner.
Carl Hansen - CH337 Extendable Dining Table with CH24 Wishbone Chair.
Lifestyle product image of the Carl Hansen - CH337 extendable dining table and CH24 Wishbone chair. Together, these two pieces help to create a stylish dining area, perfect for eating, playing or relaxing.


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Film FestivalsMovie ReviewsTIFF 2017: Downsizing Review
Keith NoakesSeptember 16, 2017
This will be one of many reviews during this year's Toronto International Film Festival. If you would like to keep up with our content, click here.
Synopsis: A social satire in which a guy realizes he would have a better life if he were to shrink himself. (IMDB)
Starring: Matt Damon, Christoph Waltz, and Hong Chau
Writers: Alexander Payne, Jim Taylor
Director: Alexander Payne
Rating: n/a
For those complaining about films not being original, take a look at this one. Most science-fiction is somewhat rooted in reality and this was the case here. With overpopulation contributing to global warming and other ecological problems, scientists have come up with a solution. What if we shrink ourselves so small to reduce our consumption? It's a silly premise but the film knows that and doesn't play it too seriously and was better for it. The film follows a middle-class couple named Paul (Damon) and Audrey Safranek (Kristen Wiig) who, looking for a fresh start, decide to undergo the procedure to shrink themselves, also called downsizing.
Abandoned by his wife, Paul is forced to fend for himself in this new miniaturized world. This new miniaturized world may seem like a perfect world but it has the same problems as our regular-sized world. Things change for Paul once he meets a cleaner named Gong Jiang (Chau), a one-legged Vietnamese dissident, who offered Paul a new perspective on life. Chau was the best part of the film with Jiang acting as its heart. Her energy and personality led her to steal almost every scene she was in. She has gotten a lot of buzz for her performance and it is deserved. Damon and Christoph Waltz were great as the lovable loser Paul and Paul's shady neighbor Dusan respectively.
Overall, this was an original, fun to watch sci-fi dramedy that never took itself too seriously and features great performances all around.
If you liked this, please read my other reviews here and don't forget to follow me on Twitter, follow me on Instagram, and also like me on Facebook.
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