text:
It's time to rock: bridge embankment work to begin again on John Counter
November 14, 2017 -
The work to build up the embankments to the bridge across the rail tracks on John Counter Boulevard is set to begin again on Monday, Nov. 20. Motorists and cyclists should expect occasional delays over the course of this work which will continue until mid-December.
"This is the final layer of rock we are adding to the embankment that will eventually support the bridge over the tracks. There will be heavy truck traffic in this area as we complete this work," says Mark Campbell, acting director of engineering for the City of Kingston.
Building the bridge embankment is Phase 3 of the five phase project to widen John Counter Boulevard. Phase 4 work – widening John Counter to four lanes between Sir John A. Macdonald and Indian Road – will be complete by the end of this construction season. The final phase will involve realigning Portsmouth Avenue and building the bridge over the rail line. That work is tentatively scheduled for 2018-19.
Truck Routes
Trucking activity at the entrances to the embankments – just east of Portsmouth Avenue on John Counter Boulevard and at the intersection of Old Mill Road and John Counter Boulevard – may result in minor traffic delays along John Counter Boulevard.
Here are the hauling routes:
East embankment (east of CN tracks): Trucks will travel from McAdoos Lane to Division Street, then along the 401 to Sir John A. Macdonald Boulevard then to John Counter Boulevard and on to the site.
West embankment (west of CN tracks): Trucks will travel from McAdoos Lane to Division Street, then along Highway 401 to Sydenham Road and onto Princess Street to John Counter Boulevard and on to the site.
For more on this project, go to www.CityofKingston.ca/JCB.
About the City of Kingston
The City of Kingston provides municipal services to 125,000 residents living in this visually stunning, historic city, often ranked one of the best places to live in Canada. Kingston is focusing on being smart and livable as it pursues its vision to become Canada's most sustainable city. We focus on environmental responsibility, social equity, economic health and cultural vitality –ensuring that today's decisions don't compromise our future.
Please visit www.CityofKingston.ca and join the conversation on social media.
Twitter: @CityofKingston
Facebook: www.facebook.com/TheCityofKingston
Media contact: For more information call the communications and customer experience department at 613-546-4291, ext. 2300.


An old controversy is that EuroModel sells a ship model of la Renommée that is not la Renommée. EuroModel is a model kit and accessories company operating in Como, Italy. For many years it has offered to model builders a kit labeled La Renommée, 18th Century French Frigate. The standard cost is around 688,00 € ($848.07 US) which includes numerous downloadable and printed instruction booklets, bags of wood, rigging, and hardware parts to construct the ship model at a 1:70 scale.
There were two Renommee's built in France, one in the 17 Century and this one in the 18 Century. Launched in 1744 at either Byrone or Brest, La Renommee was a one-off 40-gun ship designed by Antoine Groignard with 30 12-pounders and 10 8-pounder guns. She was captured by the British Navy (HMS Dover) 27 September 1747 and converted into a 30-gun fifth-rate frigate as the HMS Renown and served until she was broken up in 1771.
However, this type of frigate is very important in the evolution of ships of the British Navy because it inspired the development of a series of fifth-rate frigates equipped with only thirty guns of large caliber, all placed on the second deck.
Although this is a well-known issue to ship modelers, it bears repeating for those who have never been made aware of the dispute. For all that the company has put into creating the product, we must commend their efforts. Yet over ten years ago their attention was drawn to the fact that their advertising copy was in error. Let us begin by diagnosing the lines, point-by-point, from their ad copy.
*See my post of June 15, 2018, "The Other French La Renommée Ships", in the Nautical Thoughts section for a more complete list with references and histories.
• La Renommée of 1744 was launched at Brest.
• La Renommée of 1744 was a 30-gun ship.
• La Renommée of 1744 was designed by François-Guillaume Clairin Deslauriers. The later la Renommée of 1767 was designed by Antoine Groignard.
• La Renommée of 1744 carried at launch 26 8-pounders and 4 4-pounders. Later after capture, the British armed her with 24 9-pounders and 6 4-pounders.
• Mostly correct but to be picky, only the heavier guns were on the second deck, lighter guns were on the quarterdeck and forecastle.
• And herein lies the error that created the wrong identity for the ship being sold. Differences became obvious between EuroModel's version and other historic records referencing la Renommée. According to the posts on the Shipmodeling website, sometime before 2005, Dmitry Sidorov discovered that a French book, "Souvenirs de la Marine" (Memories of the Navy) by Admiral Paris published in 1879 refers to an anchor similarity between la Renommée and another ship. Admiral Paris used the plan of the other ship to illustrate the similarity. The plan he used, Plates XXXI and XXXII, were taken from Chapman's "Architectura Navalis Mercatoria" (Merchant Naval Architecture) published in 1768. Plate XXXI came from the section listing privateers, not naval vessels and nowhere on the plate or in the index does it state that the plans are of la Renommée or even French but only "frigate." In the next book by Paris, he repeated the section by just copying the plans and labeling them either erroneously or generically "la Renommée." According to Dmitry, EuroModel must have used that second book as its source for plans of la Renommée which were in fact not la Renommée but the ship Paris was drawing a comparison to. Dmitry also believed that the plans are actually of the Swedish ship Jupiter of 1760. The plans shown on the forum page do indeed look unlike the French frigate and more like the Swedish one.
An additional discussion in 2016 was also carried on the Nautical Research Guild's Model Ship World posts. A number of discrepancies were pointed out about EuroModel's ship and the construction methods of the 1740s. The writer stated that the model's waist is too closed and the stern and gunport rows match later ship design, along with other inconsistencies.
In overlaying the National Maritime Museum plans of la Renommée taken immediately after the ship's capture onto the EuroModel's, it becomes apparent that EuroModel's ship is not, nor could be unless massively reconstructed, the same ship. The 42 guns of EuroModel's ship versus those on the NMM plans pierced for 30 guns, are in itself telling. No historical or biographical references were made to either la Renommée or the Renown as having 42 or even 40 guns. And as an artistic side note, the figurehead on Plate XXXI is the sculpture of a man. Renommée, or Fame in English, was traditionally depicted as a female figure carrying a trumpet and/or victory wreath, at least throughout the 18th century. Other artistic incompatibilities between the 1740s and later years are also easy to pick out on the model, such as the oval-shaped taffrail without side pillars and the use of more modest embellishments as opposed to the earlier, grandly-ornate baroque or Master Sculptor Caffieri's post-baroque period styling. Also, the original drawings of the master sculptor are still in existence and do not match in any manner the quarter gallery, taffrail bas-relief, or figurehead that is on the EuroModel ship.
So, if the model is not the la Renommée of 1744, could it be one of a later year? Apparently not. None of the later la Renommée plans available match the size, cannons carried, or length of the model. It appears their model is the Jupiter or some other ship as yet unidentified.
One other slight but disturbing error is the ensign that EuroModel decided to use for the ship. It shows the French Republic Tricolor flag of red, white, and blue instead of the all-white one of the Bourbon era. The Tricolor was not used until after the beginning of the French Revolution, adopted in 1794. This is akin to portraying a colonial New England regiment during the French and Indian War carrying the Stars and Stripes into battle while Betsy Ross was only two years old. In EuroModel's own ad copy they note la Renommée was broken up in 1771, twenty-three years before the Tricolor was used. How do they justify such obvious negligence in accurate detailing?
There is no doubt that EuroModel did a reasonable amount of research before producing the model. But when the discrepancies were revealed, EuroModel should have dug further to discover the actual name of the ship they were selling, corrected the errors, and settled the issue. As it stands now there are a lot of scale model ship builders out there rightfully proud of their model, but it's not really la Renommée.


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Q: Solving bernoulli differential equation How to solve $$t \frac{dy}{dt} + y = t^4 y^3$$
First I divided by $t$ to get $$\frac{dy}{dt} + \frac{y}{t} = t^3 y^3$$
Then I multiplied through by $y^{-3}$ to get $$y^{-3} \frac{dy}{dt} + \frac1{ty^2} = t^3$$
Then I used the subsitution $w = y^{-2}$ and $w'=-2y^{-3}\frac{dy}{dt}$
Subbing that in the equation becomes $$\frac1{y^3} \frac{dy}{dt} + \frac1{ty^2} = t^3$$
How do I solve it from here as I still have a $\frac1{ty^2}$ instead of just $y$ making it linear?
Also are all the rest of my workings correct?

A: You didn't do the substitution.  With $w = y^{-2}$, $y^{-3}\; dy/dt = -\dfrac{1}{2} dw/dt$ and $1/(t y^2) = w/t$, so you should get $-w'/2 + w/t = t^3$.

A: You almost find the solution. You've made a good substitution by letting $w=\frac{1}{y^2}$ and $w'=-\frac{2y'}{y^3}$, then
\begin{align}
\frac{1}{y^3}\frac{dy}{dt}+\frac{1}{ty^2}&=t^3\qquad\rightarrow\qquad-\frac{1}{2}w'+\frac{w}{t}=t^3\qquad\rightarrow\qquad w'-\frac{2}{t}w=-2t^3
\end{align}
The first-order nonlinear ODE becomes a first-order linear ODE. Take the integrating factor
\begin{align}
e^{-\Large\int\;\frac{2}{t}\,dt}=e^{-2\ln t+C}=e^{\ln t^{-2}}e^C=At^{-2}
\end{align}
then multiply both sides of the first-order linear ODE by $At^{-2}$.
\begin{align}
At^{-2}w'-At^{-2}\frac{2}{t}w&=-2t^3At^{-2}\\
At^{-2}w'-2At^{-3}w&=-2At\\
\frac{d}{dt}\left(At^{-2}w\right)&=-2At\\
d\left(At^{-2}w\right)&=-2At\;dt
\end{align}
The last step is integrating both sides.

redpajama_set_name: RedPajamaStackExchange


These quirky vases are the perfect talking point on any mantlepiece. You can leave them empty and let them speak for themselves or fill them up with flowers or mossy balls and give them some hair! Bring some fun into your home with these unique ceramic vases. The neutral tones allow them to complement any interior, buy just one or the whole set for a little family on your shelf.


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text:
Ölfusárbrú är en hängbro över älven Ölfusá i Selfoss på Island.

Den första bron på platsen var Islands längsta när den byggdes år 1891. Den förstördes i september 1944 när en av bärkablarna brast på grund av överbelastning när två lastbilar körde över bron samtidigt.
Den förstörda hängbron ersattes av en ny, 84 meter lång bro av samma typ, som byggdes på bara fem och en halv månad. Den gamla bron reparerades provisoriskt så att den kunde användas under byggnadstiden.

En ny snedkabelbro med två 56 meter höga pyloner är under byggnad. Den kommer att bli 305 meter lång med ett längsta spann på 150 meter och beräknas vara klar år 2026.

Bron, som beräknas kosta 6 miljarder isländska kronor att bygga, kommer att beläggas med
vägtullar medan det blir gratis att köra över den befintliga bron.

Källor

Hängbroar
Broar invigda 1945
Broar i Island
1945 på Island
Suðurland

redpajama_set_name: RedPajamaWikipedia


Care for the earth, care for the people, and return the surplus!
Permaculture works with nature instead of against it—saving energy, minimizing waste, and lowering environmental impact. Local permaculture expert Nicholas Hardy will discuss how to holistically restore and regenerate the degraded ecology of our local landscapes and watersheds and will talk about soil, vegetation and water harvesting strategies. You'll have a better understanding of a diversified and balanced garden design and management practices to apply to your own garden!
Nicholas Hardy has spent the last 10 plus years developing his Permaculture/Regenerative Agriculture tool kit. Immersing himself in nature & observing the patterns have informed his approach to designs. His expertise is in water system designs (passive & active water harvesting), unusual edible plants in food forest design, livestock integration to create a more holistic system & the soil food web. He is the Project Manager of Circlefoot Permaculture, a local design & install company, and is also is experienced in solar system designs.


"Florida's U.S. Representatives who voted to repeal critical patient and consumer protections in the Affordable Care Act and replace it with Trumpcare have ignored condemnation by health professionals and turned their backs on Florida families. In doing so, they're shamelessly doling out $600 billion in tax cuts for the very wealthy and big insurance and drug companies.
"Trumpcare will increase health care costs, reduce quality of care, strip coverage from an estimated 24 million Americans and gut protections for people with pre-existing conditions. Adding insult to injury, Trumpcare would exempt Members of Congress from the law.


SharePoint Calculated Columns or fields can be used to create clickable links, these links can also be configured to open in a new tab. To make the URLs clickable, you have to save the Calculated Column as a Number data type. I know this is totally crazy, but the number field type will for some reason render html in calculated fields.
In this example our list has a single line of text field called 'Search Topic', this is the topic you should search for if you want to find more related information about the list item. What we want to do is display that Search Topic as a clickable link that does a google search for that topic when someone clicks on it.
1. Click on the List/Library tab, click on the List/Library Settings option.
2. On the Settings page, click on the Create Column option.
3. Enter a name for the Column, choose the Calculated type.
If you are using a column in your URL and if this column is not required, this could create a URL that doesn't work. Because your URL will only be partially completed as the inserted column reference will be blank.
Since both of these examples use static text for their links, we will need to edit the formula to ensure that the link text is only displayed if the column (Search Topic) actually has a value entered.
On our calculated column formula, we will need to a add an IF ISBLANK operator.
Visit the SharePoint Calculated Column Overview for a full list of calculated column tutorials.
Thanks so much for this tutorial. It really helped me.
Got any ideas for a work-around?


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JOHN WOODLAND
Overview and Research Interests
Science Engagement
VOX Cape Town
Talks and Broadcasts
UCT Choir
Musical Background
I am passionate about bridging the gap between science and the South African public.
Chemistry-inspired plays for schoolchildren (and adults!)
In 2018, I was fortunate to receive a Royal Society of Chemistry Inspirational Member Award. The citation read: "For his positive impact through his plays promoting the chemical sciences, and ensuring that the performances were accessible to children from all parts of the local community." These plays, co-written and co-directed with Kathryn Wicht, were performed for the UCT Department of Chemistry's annual Jack Elsworth lecture-demonstrations. The plots were based on popular movies, viz. The Wizard of O2 (2012), Harry Potter and the Molecule of Doom (2013) and How To Train Your Molecule (2014). Please get in touch if you would like to find out more or stage any of these demonstrations.
Public talks
In 2018 and 2019, I participated in the global Pint of Science initiative ("Quench your thirst for knowledge") with the following talks at the Cause Effect Cocktail Kitchen in Cape Town:
From the bench to the bedside: How difficult is it to make new medicines? (2019)
Small-molecule medicines have changed our society, permitting the successful treatment of infectious pathogens, "diseases of affluence" and mental illnesses. But what does it take to advance a new drug from the bench to the bedside? Historically, drugs were discovered serendipitously and were usually isolated from natural sources. Today, drug discovery efforts take many years and cost hundreds of millions of dollars. They also require the input of dozens of specialists from a multitude of backgrounds to ensure that therapeutic compounds are effective and safe. Given these challenges, and the reality that most drug development efforts fail, you may be surprised to learn that we have any new medicines at all!
See: "Suspense and discovery with Pint of Science" (South African Journal of Science, November 2019)
Quinine: Shining new light on an ancient molecule (2018)
From human health to new materials, chemistry has transformed society. The capacity of chemists to manipulate useful molecules has given us exceptional control over the world. Quinine is a compound that was first isolated from the bark of the Cinchona tree hundreds of years ago. Possessing a host of therapeutic properties, it was the first effective treatment for malaria and has been described as "a drug that has probably benefited more people than any other in the combat of infectious disease". What is so special about quinine, and why does it continue to beguile us after centuries of study?
See: "Four awesome scientific ideas you should know about" (City Press, June 2018)
DAY 3 of Global Festival of Science @pintofscienceZA in #CapeTown #SouthAfrica !! @pintsworld #pintsa19 #pint19 #PintOfScience @michefrvntz @chantallailvaux #sciencetwitter pic.twitter.com/OM7kSrLsNd
— Sonny Patel (@sonnypatel) May 22, 2019
I have twice addressed the Waterfront Rotary Club on topics of interest. These presentations were entitled "Teaching old drugs new tricks: Using ancient compounds to develop new drugs" (2015) and "Treatments and vaccines for Covid-19 (in March 2021): A scientist's perspective" (2021).
Science communication and innovation competitions
In 2013, I participated in the inaugural FameLab South Africa ("Pop idols for scientists") event in Grahamstown, South Africa, for which my talk ("The Human Element") was awarded Second Prize.
That same year, I participated in the Falling Walls Lab in Johannesburg for which I was awarded First Prize. This allowed me to participate in the Falling Walls Lab in Berlin, Germany, for which I was awarded Third Prize in the Young Innovator of the Year Competition. This resulted in an invitation to deliver an oral presentation at the Falling Walls Conference in Berlin the following day, billed as "The International Conference on Future Breakthroughs in Science and Society".
Finally, I participated in the inaugural Science Slam at the Sci-Bono Discovery Centre in Johannesburg, also in 2013.
FM #Steinmeier enjoys a Science Slam w/ SA slammers Hope Serepa, @Vinu_Nair_ Nair, John Woodland @GermanyDiplo pic.twitter.com/Iafzt1Z7eD
— Germany in SA (@GermanEmbassySA) November 20, 2014
The "science" of science communication
Occasionally, I am invited to deliver presentations on science communication itself. Previous engagements have included the "Write Science" writing courses at UCT (June 2015, February 2016 and November 2017), the Royal Society of Chemistry Local Section AGM (May 2014) and a meeting of the South African Society for Cardiovascular Research (February 2014).
Making the Difference
In late 2020, I participated in a Royal Society of Chemistry outreach programme to inspire the next generation of chemical scientists. The Making the Difference campaign aims to inspire school-aged children to study chemistry and go on to pursue careers in the chemical sciences. Recent research from ASPIRES2, a longitudinal research project studying young people's science and career aspirations, showed that young people don't know what careers in chemistry look like. Diversity amongst those who are interested in becoming a scientist also decreases over time. I was featured as a medicinal chemist working to change lives by researching safe and affordable treatment options for malaria and tuberculosis.
www.johnwoodland.net

redpajama_set_name: RedPajamaCommonCrawl


There are a couple of fairs coming up at the end of the month, so work is in full swing to make some new additions to the folio. I finished this one today, it should be on the website in the next few days.
I have some two for one tickets and invites to the private view on Friday 23rd April (the event continues on Sat 24th and Sun 25th) email me if you are in the market for a ticket- don't forget to include your postal address.


For many Americans, 2015 is finally the year that the economy is starting to look strong. Employment is up and economic growth in the U.S. is increasing. Many people who would have liked to buy a home in recent years but were unable to are now wondering whether they should buy. Homebuyers have a lot of considerations to make, including the effects of the recent subprime mortgage crisis, current affordability factors, and if mortgage rates will go up this year.
This infographic by Pearl Insurance guides real estate agents and buyers alike through all the good, bad, and wobbly intricacies of the housing market in 2015.


text:
ZEDXION
Centralized
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Zedxion offers a comprehensive solution to the major problems faced by the traditional, fiat-driven monetary system. Building a crypto powered ecosystem comprising Zedxion Token.
Review: Beginner's Guide to ZEDXION
ZEDXION's Dashboards
Developer ZEDXION
Thank you for our listing Name Token: Zedxion BEP-20 and Zedxion ERC-20 Supply: 4,746,558,037 Website: www.zedxion.io https://etherscan.io/token/0xfbc4f3f645c4003a2e4f4e9b51077d2daa9a9341 https://bscscan.com/token/0xfbc4f3f645c4003a2e4f4e9b51077d2daa9a9341 https://github.com/zedxioncryptocurrency OUR ZEDXION ZEDXION- powered digital currencies, or cryptocurrencies, hold the massive potential to disrupt the financial market they can be issued and used without the involvement of a central bank of other traditional financial institution. All fiat money in circulation today is owned by the central and commercials banks of the underlying currency's legal jurisdiction, except for cash that is in the hand of individuals. The bank holds liability to the depositor but can utilize the depositor's money to give to another individual as a loan. PROBLEM STATEMENT The current monetary system, driven by fiat currency, is plagued by serious problems like time-consuming and expensive transactions, limited accessibility to the national currency, money-laundering, and more. The following points elaborate on the problems with fiat currency. High Transaction Settlement Time As with fiat currency, domestic and international money transfer takes days or even weeks to go through. Specifically for international transactions, every cross-border transaction but to traverse through correspondent banks responsible for managing activities like receiving and collating payment messages before retransmitting confirmation or denial to respective banks. This increases the settlement time of transactions. Today, many businesses rely on timely deliveries which are shipped when the transactions are processed. A delay in transactions means a delay in the shipping of orders that can cost companies millions in lost revenue and productivity. High Transaction Fees Conventional banks charge somewhere between 0.5 percent and 5 percent to transfer money. Apart from this, banks also charge an additional one-off fee for the transaction and offer worse than the market exchange rate for cross-border transactions. This can result in businesses losing between 1 percent and 5 percent of potential earnings on transfer fees alone. This elevates the prices of products for consumers and reduces wages as businesses try hard to cut cost to make a profit. Political Risk A major problem with fiat currencies is hyperinflation. Hyperinflation occurs when the price of goods and services increases by over 50 percent a month. As the governments control fiat currency, they can print as much new money as the like which devalues the money in circulation. Wealth Redistribution Arbitrarily increasing the quantity of currency in an economy has an adverse effect on the distribution of money and, thus, redistributes purchasing power, stealing wealth from majority, such as wage workers and savers, to serve the interest of a privileged minority. Redistribution of wealth leads to a net loss of wealth to society. Government deficit spending, which should otherwise be motivated by good intentions, alters the quantity of currency in circulation and result in currency debasement. THE SOLUTION Zedxion offers a comprehensive solution to the major problems faced by the traditional, fiat-driven monetary system. Zedxion envisions building a crypto- powered ecosystem comprising Zedxion Token, Wallet, Trading platform, Point of sale Platform and more to effectively replace fiat currency while empowering users to harness the power of crypto in all types of transactions- from trade finance to international payment remittance to trading. ZEDXION TOKEN: Zedxion Token will be an TRC20 and BEP20 and TRC10 Token that can be bought in exchange for BitToken (BTC), Ethereum (ETH), (LTC), Tron (TRX) and Doge. The sale of Zedxion Token will be carried out in two phases- Public Sale and Private Sale. While Private sale will be for the team and Advisors, The Public Sale will allow anyone across the globe to participate in the sale and buy Zedxion Token. Designed on Tron ZEDXION, Zedxion Token will allow for accelerated transactions and lower transaction fees, Zedxion will play a chief role in driving transactions on all Zedxion platform, such as Zedxion Trading Platform, Zedxion Point of Sale System, Zedxion trade finance. Zedxion Token will also be the backbone of the Zedxion referral and reward program. Kind Regards, Elizabeth Newman Zedxion Team


Look on-trend with these unlined corduroy trousers with button fastening. Mustard is the perfect colour to transition your wardrobe into the new season. We love it so much we are embracing the shade head to toe. 84% Cotton, 15% Viscose, 1% Polyester. Dry clean only.


Here we are showing our colors in order by wood species. This way you can pick what color and wood type you like. Can't make up your mind from our picture gallery then stop by and check them out for yourself. We have all samples on hand so you can feel and take them home and look at them with your lights and room. This shows samples of all of our available colors. They are simple swatches to view our colors. Besides being split into wood species these are also separated by tones of color.


In their approach to business development, manufacturers either have a strong understanding of who they are and their value to customers and prospects, or they understand what they make, but lack the full understanding of their value proposition. Those in the latter category can struggle to understand who their best sales targets are and how to communicate their products and services to them.
Smart Business spoke with Nadine Nocero, senior account manager at SyncShow, about how manufacturers can discover and promote their value proposition to increase sales opportunities.
How can manufacturers determine what their value proposition is?
Understanding value proposition means looking at the whole business to understand how it's better than the competition. Companies that aren't sure of their value proposition may rely on longevity, for example, as a differentiator. But being in business for 100 years doesn't prove enough to get a buyer to make a purchase. Look closer at what that longevity means to find the true differentiator.
Price can be a differentiator, but it's a dangerous approach because it drives a business to constantly reduce costs and doesn't facilitate relationship building. An alternative approach is to focus on developing products or services that are proprietarily better, which can be done through patents, shorter lead times, services with specific processes or strategies that competitors aren't offering, or improvements that save customers time.
How has the buying process changed in recent years?
The buyers' journey on the front end, which includes research and information gathering, now takes place online. The internet has brought transparency to the forefront. When the buying process goes well, people share the experience. That has led customers to learn from other customers, getting validation from other buyers that they're making the right choices. But customers also share negative experiences.
People want information on demand. Be sure to make whatever information customers might need available so they can access it whenever they decide to start their buying process.
How well would you say manufacturers have adapted to buyers' new methods?
Manufacturers have mostly been slow to respond to the way the buying cycle has changed. Multigenerational companies have experienced success by doing things a certain way and they're hesitant to change.
Manufacturers that have adapted are seeing strong gains. Customers are engaging with them online and are moving through the buying process easier and faster. This, in part, requires an updated website. Customers should be able to access a manufacturer's site and learn what the company does, how it can solve their problems and how they can connect with the company.
What should manufacturers do to align their value proposition with the buyers' journey?
Manufacturers should put themselves in their buyers' shoes and construct a communication platform that addresses all stages of the buying cycle. The company's value proposition should be integrated into every aspect of the cycle.
During the research phase, the company's value proposition should be presented in a general way so buyers can see the company as a solution. Provide white papers and tip sheets that speak generally to the industry.
As buyers move down funnel, the company's specific value proposition should become much clearer. This can be done through case studies, case histories and client testimonials that show how the company has solved specific client problems.
During the sales phase, content should be centered on what that client needs and how the company is the best solution. It should feel organic to the buyer because the value proposition has been seeded all through the sales funnel.
Fundamentally, manufacturers should step back and look at their overall business goals to determine what gives their company the greatest value. Once it's discovered, incorporate it into all internal and external communications, including the company's website, email marketing, data sheets, proposals, contracts, etc.
Manufacturers, get more marketing insights from SyncShow.


Seydel Blues FAVORITE Standard Harmonica Discounts Apply !
Blues Favorite Standard Harmonicas - The Seydel Premium Model – available in countless variations.
If you start as a beginner, then you should be aware, that this is the mother of all tunings, the so called 'Richter-Tuning'. The ingenious finding of the 'Diatonic Harmonica' is the work of this man.
Richter is said to be descent from the Bohemian area east of Klingenthal from a town called 'Haida'.
It's not really proven, however it's fact, that the 'Richter Harmonica' is only called 'Haidaer' by Seydel employees since the beginning of the production more than hundred years ago.
All this shouldn't bother you when starting to play harmonica. The only important thing is, that you cannot fail completely when you start the adventure playing harmonica with this tuning.
Almost every great player has begun with it.
With the emphasis on blow notes you start to play folk music within five minutes, if you take the draw you start to dive into the magic of Blues and Rock'n Roll, the musical style this product line is named after.


There are a variety of sources of money for research and treatment programs. There are a number of government funding agencies and private funding organizations. Although this is not a comprehensive list, the links will help you to get started. If you have a lead, please contact us, so that we can include the information in this website.


text:
package container // import "github.com/docker/docker/integration/container"

import (
	"context"
	"encoding/json"
	"testing"
	"time"

	"github.com/docker/docker/api/types"
	"github.com/docker/docker/api/types/filters"
	"github.com/docker/docker/integration/internal/container"
	"github.com/docker/docker/internal/test/daemon"
	"github.com/docker/docker/internal/test/request"
	"github.com/docker/docker/pkg/jsonmessage"
	"gotest.tools/assert"
	is "gotest.tools/assert/cmp"
	"gotest.tools/poll"
	"gotest.tools/skip"
)

// export an image and try to import it into a new one
func TestExportContainerAndImportImage(t *testing.T) {
	skip.If(t, testEnv.DaemonInfo.OSType != "linux")

	defer setupTest(t)()
	client := request.NewAPIClient(t)
	ctx := context.Background()

	cID := container.Run(t, ctx, client, container.WithCmd("true"))
	poll.WaitOn(t, container.IsStopped(ctx, client, cID), poll.WithDelay(100*time.Millisecond))

	reference := "repo/testexp:v1"
	exportResp, err := client.ContainerExport(ctx, cID)
	assert.NilError(t, err)
	importResp, err := client.ImageImport(ctx, types.ImageImportSource{
		Source:     exportResp,
		SourceName: "-",
	}, reference, types.ImageImportOptions{})
	assert.NilError(t, err)

	// If the import is successfully, then the message output should contain
	// the image ID and match with the output from `docker images`.

	dec := json.NewDecoder(importResp)
	var jm jsonmessage.JSONMessage
	err = dec.Decode(&jm)
	assert.NilError(t, err)

	images, err := client.ImageList(ctx, types.ImageListOptions{
		Filters: filters.NewArgs(filters.Arg("reference", reference)),
	})
	assert.NilError(t, err)
	assert.Check(t, is.Equal(jm.Status, images[0].ID))
}

// TestExportContainerAfterDaemonRestart checks that a container
// created before start of the currently running dockerd
// can be exported (as reported in #36561). To satisfy this
// condition, daemon restart is needed after container creation.
func TestExportContainerAfterDaemonRestart(t *testing.T) {
	skip.If(t, testEnv.DaemonInfo.OSType != "linux")
	skip.If(t, testEnv.IsRemoteDaemon())

	d := daemon.New(t)
	client, err := d.NewClient()
	assert.NilError(t, err)

	d.StartWithBusybox(t)
	defer d.Stop(t)

	ctx := context.Background()
	ctrID := container.Create(t, ctx, client)

	d.Restart(t)

	_, err = client.ContainerExport(ctx, ctrID)
	assert.NilError(t, err)
}

redpajama_set_name: RedPajamaGithub


Duane Andrews' music is the product of a great ear, an adventurous spirit and a love of music that is beyond category. Uniting what would seem to be impossible – traditional Newfoundland music with the swing jazz of the legendary Django Reinhardt, Andrews makes it not just work – he makes it soar.
Juno winning producer, composer, guitarist and international performer, Duane Andrews, brings his famous Conception Bay record to Revival House, featuring Stratford Summer Music's Artistic Director, Mark Fewer, and members of Stratford's own, INNERchamber, playing a potent combination of swing jazz and Jigs and Reels to boot! Together, they will bring it all back home.
Dinner & Show packages include one show and a 3-course dinner, HST, beverages and gratuities are extra. Dinner reservations are to be made between 7:30pm and 8pm and are only available by calling the Stratford Summer Music office. Show-only tickets are available online. À la carte menu available late night.


Running a business isn't easy. We can evaluate and implement strategies designed to protect your business and take advantage of opportunities to improve cash flow, tax situation, benefits and the bottom line of your business.
We can assist businesses with financial statement preparation, bookkeeping, accounting, payroll services, and tax research, planning, and preparation.
Offering a retirement package is a great way for employers to retain key employees. However, some business owners haven't done so because they aren't sure how to start or what to look for. We can assist small business owners in determining the appropriate retirement plan that benefits both the employer and employees and answer common questions employers and employees may have.
Whether a client wishes to sell their interest or is leaving the business to a family member upon retirement, it's critical that the business owner has a succession plan and exit strategy in place ahead of time. We assist clients with formalizing their goals and objectives, including when they want to transfer their business and how they intend to do so. We strive to help clients determine a tax-efficient method of business succession and can work with clients' tax and legal advisors throughout the succession planning process.
All business owners, whether they own or co-own their business, should have a plan in the case of an unexpected death. Buy-sell agreements can help protect a business owner and his business from unintended ownership transfers and protect the heirs by offering them the chance to turn shares into cash. We can offer advice on buy-sell agreements and can provide referrals to attorneys who can help determine the right type and draft the agreement.
*These services are offered by Charlene Wehring through her affiliation with H.D. Vest Investment Services SM and H.D. Vest Advisory ServicesSM.


Ohio Dreams Action Sports Camp is excited to announce our sponsorship of the 2012 Mad River Mountain / Capital Park Big Air and Slope Style Contests. At each contest participants will have the opportunity to win a free session at Ohio Dreams this summer to learn some big tricks on our trampolines and then take them to the water ramps.
In addition to sponsoring the events Ohio Dreams will be hosting Big Air Camps on the Friday evening before each contest, this is a perfect time to work with Ohio Dreams Head Ski Coach and Dew Tour Coach Chris Ashcraft. Chris was the on-hill coach for Nick Goepper at the 2011 Killington Winter Dew Tour where Nick took a third.


text:
A selection of images from many different areas. Also see Scotland and Iceland.
Sunset over Durdle Door, Dorset | Andrew Sproule Travel Photography
A stunning sunset over Durdle Door on the Jurassic Coast, UNESCO World Heritage Site, Dorset, England, United Kingdom, Europe
The Ouse Valley Viaduct | Andrew Sproule Travel Photography
The Ouse Valley Viaduct (also known a Balcombe Viaduct) carries the London-Brighton Railway Line over the River Ouse in West Sussex.
Golden sunrise over Corfe Castle, Dorset | Andrew Sproule Travel Photography
Golden sunrise over the village and castle at Corfe, Dorset, United Kingdom, Europe
Portland Bill Lighthouse | Andrew Sproule Travel Photography
Portland Bill Lighthouse at dusk, Isle of Portland, Jurassic Coast, UNESCO World Heritage Site, Dorset, England, United Kingdom, Europe
A stunning sunset over Durdle Door on the Jurassic Coast, UNESCO World Heritage Site, Dorset, England, United Kingdom, Europe.
Fairfield Church, Romney Marsh | Andrew Sproule Travel Photography
St Thomas a Becket Church (also known as Fairfield Church) is the most iconic of all the churches on Romney Marsh. The tiny building that dates back to the late 12th century sits isolated in a field cut through with dykes and grazed by sheep
Southwold Pier, Suffolk, UK, Europe | Andrew Sproule Travel Photography
Southwold Pier in Suffolk at first light
Herne Bay Pier, Kent, UK, Europe | Andrew Sproule Travel Photography
Stormy skies and dramatic lighting over Herne Bay pier on the north coast of Kent, United Kingdom, Europe
Hastings Pier, East Sussex, UK, Europe | Andrew Sproule Travel Photography
Hastings Pier was named the best new building in the UK in the prestigious annual architectural awards. It was awarded the Royal Institute of British Architects 2017 RIBA Stirling Prize by a panel of industry experts.
Limestone, Yorkshire Dales National Park, United Kingdom | Andrew Sproule Travel Photography
Windblown twisted hawthorn tree growing through the limestone pavement at Twistleton Scar in the Yorkshire Dales National Park, United Kingdom
London's South bank on the River Thames at dusk | Andrew Sproule Travel Photography
The River Thames in London at dawn with the Coca Cola London Eye
Sunrise and low tide at Eastbourne Pier in Sussex, UK | Andrew Sproule Travel Photography
Fishing boat on the pebble beach at Branscombe in Devon at sunset
Winnats Pass near Castleton in the Peak District National Park, Derbyshire, England, United Kingdom, Europe
Southwold Pier in Suffolk at sunrise
Twilight over Tower Bridge and The River Thames in London, United Kingdom
The River Thames in London at dusk with the Coca Cola London Eye
Brighton seafront at dawn | Andrew Sproule Travel Photography
A fisherman takes advantage of a quiet morning on Brighton seafront
Tower Bridge, The River Thames and City Hall on London's South Bank, United Kingdom
Sunrise at Brighton Pier in Sussex in the UK
Sunrise and low tide at Eastbourne Pier in Sussex, UK


Intrepid Industries was founded in Lethbridge, Alberta in 1999 by Darcy Berent. Its headquarters are located in Lethbridge at 2525 36 St. N, where it has several professional office areas, a spacious meeting room, and a large, well organized shop. It has a small fleet of clean vehicles in Company colours, decaled with the Company logo. And it has an array of equipment to perform its various maintenance services.
Intrepid Industries specializes in property maintenance services for various sectors of the economy in Lethbridge and the Greater Surrounding Area, these being: Retail, Commercial, Industrial, and Institutional. Intrepid Industries has five (5) divisions: Industrial Rope Access, High & Low Rise Window Washing, Lawn Care, Snow Removal, and Janitorial; and it has more than thirty (30) employees.
Intrepid Industries has more than sixty years of combined management experience in: administration, human resources, marketing and sales, customer service, and operations. Two of its Team Members have had oversight of multiple business locations across Western Canada. And the Executive Officer of the Company is active in the general management of the day-to-day business, believing that it is important to keep hands-on also in the operational matters of the Company, to the extent that his management responsibilities permit.
Intrepid Industries strives to provide its customers with the highest quality products, superior workmanship, and outstanding service at a price that provides good value to the consumer. And this is delivered with the oldest standards of good business conduct: Truthfulness, Honesty, Integrity, and Hard Work. The four pillars upon which Intrepid Industries is founded!
To that end, our Company has incorporated these high standards into our Mission Statement and endeavors to foster these ideals throughout the Company by means of the example of management, Company Policy, and regular employee meetings.
Intrepid Industries holds to the concepts that employees: are to be treated with dignity; have the right to expect a safe workplace; deserve adequate training for their job duties; are to be fairly compensated for their contribution to Company objectives.
To that end, our Company affords its employees a respectful, calm, friendly work environment that focuses on safe operating procedures. Employees are provided a variety of on-going instruction, training, and certification, thus enabling them to perform their duties proficiently, and are handsomely remunerated for their efforts through wages, bonuses, and benefits.
Intrepid Industries is keenly interested in the growth of the local economy and the welfare of the Lethbridge Area community.
To that end, our Company endeavours to recruit personnel from the local area and to support local businesses by purchasing within our trading area. Additionally, Company employees, at all levels, volunteer their time on a regular basis to assist others in the local area, thus reaching out to aid fellow community members personally, as well as helping to enhance the overall quality of the community in Lethbridge and Area.
For the last fifteen years our Company has helped to maintain the cleanliness, beauty, and safety of properties in Lethbridge and the Greater Surrounding Area. For over ten years of that, by dropping down on ropes from the top of the 'big-and-tall' buildings in the Area to wash the exterior of windows, ledges, and frames on high-rises — now that takes an "intrepid" spirit!
From exterior window washing on high and low rise buildings – to interior washing of full-height interior glass walls, partition glass walls, and window panes.
From cleaning in grocery stores, restaurants, entertainment venues, offices, and clinics – to lobbies, entrances, common areas, employee rest areas, and warehouses.
From manicuring the lawns at strip malls, business parks, condominium and retirement complexes – to grooming city boulevards and city parks.
From keeping surfaces safe by removing snow off retail and commercial parking lots and sidewalks – to that of industrial and institutional properties.
From local and national companies – to City, County, Provincial, and Federal Governments.
From Lethbridge, Coalhurst, Coaldale, Taber, Medicine Hat – to the Crowsnest Pass and other towns.
Intrepid Industries is confident that we can deliver to YOU the quality service you need, with the peace of mind that you deserve.
Get in touch and get us working for YOU!


text:
\section{Introduction}

In the 1980s, at the Hong Kong Jockey Club, Bill Benter gathered data to create a statistical prediction model for horse-racing, which made him one of the most profitable gamblers of all time \cite{Bloomberg2018}. Data became essential in most sports, impacting all aspects of their ecosystem: performance, strategy, and transfers. Advanced Sports Analytics started in the United States; franchises in Baseball, American Football, and Basketball being the first to consider data as a key for improvement and success. In charge of scouting in Baseball minor leagues for Oakland Athletics in the 1990s, Billy Beane proved that it was possible to create a cost-efficient team by finding undervalued players \cite{Lewis2003}. Using sabermetrics to value players, his 2006 Athletics team ranked 5th best of the regular season while being 24th of 30 major league teams in player salaries. Most of the popular European sports are now beginning to follow the trend, and data departments hold a more and more significant position in major clubs. Ten years after Beane's success story, in 2016 and 2017, Liverpool FC respectively acquired Sadio Mané for £34 million and Mohamed Salah for £39 million thanks to a significant push from their director of research Ian Graham, Cambridge Ph.D. \cite{NYT2019}. These two key players led Liverpool FC to a historical 2019 Champions League victory in Madrid. Today, Sadio Mane's and Mohamed Salah's contracts are worth more than £100 million each.

One way of finding such an undervalued soccer player is to find alternative metrics to the traditional ones such as number of goals or passes accuracy. Here, we will present a general framework for soccer player evaluation from live camera: a tracking model processing camera's input into players' coordinates, and an \textit{Expected Discounted Goal} (EDG) model evaluating an action based on each player tracking data. The particularity of our approach comes from the idea that our EDG model is trained purely on simulation, and never on real soccer data. This makes it much easier to train, and utterly independent from large soccer datasets that are either too complicated to produce, or too expensive to acquire.

Our EDG model generalizes well to many playstyles and many teams. It also produces similar or even more accurate results than existing models.

Our tracking model predicts the player's coordinates and computes precise results even on difficult scenes such as sunny or covered with shadow ones. This is also the first end-to-end open-source framework for soccer player tracking, and could easily be extended to other team sports.

\section{Related Work}
\label{sec:related}

\subsection{Tracking players on a sport field}

\xhdr{Player detection} Detecting soccer players can be a complicated task, especially in a multi-actors situation. There are multiple ways of doing this detection, \citet{Kaarthick2019} explored the usage of a HOG color based detector that gives each image a detection of the players. \citet{Neil2020} worked on a deeper model: an open-source multiperson pose estimator named \href{https://github.com/MVIG-SJTU/AlphaPose}{AlphaPose}, based on the COCO dataset. Another approach is to consider players as objects and use \emph{Object Detection Models}. \citet{Ramanathan2015} used such a model, a CNN-based multibox detector for the player detection.

\xhdr{Field registration} One key element of any sports tracking model is how players coordinates can be represented in two dimensions. One way to do so is \emph{Sport Field Registration}, the act of finding the homography placing a camera view into a two-dimensional view, fixed across the entire game. More about Field Registration can be found in the Supplementary Materials-\ref{supp:sec:model-homography}. \citet{sharma2017} formulated the registration problem as a nearest neighbor search over a generated dictionary of edge maps and homography pairs that they made synthetically. To extract the edge data from their images, they compared 3 different approaches: Histogram of oriented gradients (HOG) features, chamfer matching, and convolution neural networks (CNN). Finally, they enhanced their findings using Markov Random Field (MRF). \citet{homayounfar2017} figured out the homography's attributes by parametrizing the problem as one of inference in an MRV which features they determine using structured SVMs. The use of synthetic data is also explored by \citet{chen2018}, which takes \citet{homayounfar2017} and \citet{sharma2017}'s work one step further by building a generative adversarial network (GAN) model. Finally, \citet{jiang2019} used a ResNet to directly predict the homography parameters iteratively, while \citet{Citraro_2020} used particular keypoints detected with a Unet from the field to achieve the same goal.

\xhdr{Entities tracking in Video}

\citet{Ramanathan2015} used a Kanade–Lucas–Tomasi feature tracker for player tracking across a game. Recent ReIdentification models go a step further: \citet{zheng2019joint} used an embedding model to extract player features, and a mixture of IoU and embedding similarities to track persons. Another approach was used by \citet{Liang2020}, with a \emph{k}-Shortest Path algorithm and an embedding model to extract players' numbers and colors.

\subsection{Valuing player actions}

Before the revolution brought by data analysis in football, valuing players was mostly based on traditional statistics such as the number of goals, the number of assists, passes accuracy, or the number of steals. These post-game statistics can be relevant as an overview of a player's quality, but it does not reflect how a player can impact a game thanks to his vision or his moves. Furthermore, focusing on general statistics also means ignoring the entire universe of actions in which a player took part. Thanks to the growing availability of event and tracking data, researchers started to create models using all game events and tracking data to evaluate players' actions on and off-ball. In 2018, \citet{Spearman2018} suggested an indicator to evaluate off-ball positioning called \emph{Off-Ball Scoring Opportunities} (OBSO). Thanks to his previous fundamental works on \emph{Pitch Control} (PC), he was able to measure the positioning quality of attacking players by evaluating the danger of their position if they would receive the ball.

The same year, using tracking data, \citet{Fernandez2018} presented two main indicators to measure the use of space and its creation during a game: \emph{Space Occupation Gain} (SOG), and \emph{Space Generation Gain} (SGG). Later on, in 2019, \citet{Fernandez2019} adapted \emph{Expected Possession Value} (EPV), a deep learning based method, from basketball to football enabling analysts to reach a goal probability estimator at each instant of a possession. By discounting EPV, researchers were able to access the impact of a single event like a key pass which would increase significantly EPV. Similarly, \citet{Decroos2019} presented their VAEP model for which they developed an entire language around event data called \emph{Soccer Player Action Description Language} (SPADL). Thanks to supervised learning, their model was trained to evaluate the impact an event could have on the scoring or conceding probability. Therefore, this model enables analysts to estimate the effect of each action from a player and then evaluate his global performance.

We start by going into the \textbf{Theoretical framework} of both our tracking model and our EDG model. In \textbf{Experimental methods}, we review the implementations and learning procedures of our models. Finally, in \textbf{Results}, we quickly present the tracking results to focus more on the insights given by our EDG model.

\section{Theoretical framework}
\label{sec:model}
\subsection{Tracking model}
\label{sec:model:tracking}
 Our EDG model needs to know the state of the game at any time $t$: we chose to do so by representing a Soccer game with a list of entities coordinates. Given a list of images, our tracking model computes the 2-dimensional trajectories of both the ball and each player. The model adopts a 3-steps method: \textsc{Entity Tracking}, \textsc{Homography Estimation}, \textsc{ReIdentification} (see Figure \ref{fig:schematic}) (ET,HE,REID). Each of these steps is represented by one or several models, and more theoretical background on the homography estimation can be found in the Supplementary Materials-\ref{supp:sec:model-homography}. The first 2 steps do not consider any temporal information as they approximate results for each image separately.  However, the last step compares each new image to the list of images that have already been processed. Doing so allows us to take into consideration each entity's movement over time and counters the mistakes the previous models might do. We quickly review here each of the 3 steps: ET, HE, REID.

\xhdr{\textsc{Entity Tracking} definition} The ET : $\mathbb{R} ^ {n \times n \times 3} \to \mathbb{R} ^ {m \times 4} \times \left[0,1\right] ^ {m} \times \left[0,1\right] ^ {m}$, takes an image as input, and predicts a list of bounding boxes associated with a class prediction (Player or Ball) and a confidence value\footnote{$m$ is defined as the number of predictions we make and is usually fixed at $100$}.

\xhdr{\textsc{Homography Estimation} definition} The HE is made of 2 separate models. The first one : $\mathbb{R} ^ {n \times n \times 3} \to \mathbb{R} ^ {3 \times 3}$ takes an image as input, and predicts the homography directly. The second one : $\mathbb{R} ^ {n \times n \times 3} \to \mathbb{R} ^ {p \times n \times n}$ also takes an image as input, but predicts $p$ masks, each mask representing a particular keypoint on the field (see Figure \ref{fig:field-keypoints}). The homography is computed knowing the coordinates of available keypoints on the image, by mapping them to the keypoints coordinates on a 2-dimensional field (see Supplementary Materials-\ref{supp:sec:model-homography} for more details). Using both models allows us to have better result stability, and to use one model or the other when outliers are detected.

\xhdr{\textsc{ReIdentification} definition} The REID model gathers all information from the ET model and builds the embedding model as well. The embedding model : $\mathbb{R} ^ {n \times n \times 3} \to \mathbb{R} ^ {751}$ takes the image of a detected player, and gives a meaningful embedding\footnote{751 was the initial number of classes in the Market-1501 Dataset. We kept the same number for the size of our embedding, although a smaller embedding size might lead to better results according to recent papers \cite{zheng2019joint}}. The model initializes several tracklets based on the boxes from ET in the first image. In the following ones, the model links the boxes to the existing tracklets according to: (1): their distance measured by the embedding model, (2): their distance measured by boxes IoU's. A Kalman Filter \cite{Kalman1960ANA} is also applied to predict the location of the tracklets in the current image and removes the ones that are too far from the linked detection. The model also updates the embedding of each player over time with another Kalman Filter.

\begin{figure}[t]
  \centering
  \includegraphics[width=0.48\textwidth]{figs/footballField_with_keypoints.png}
  %
  %
\caption{Positions of the $28$ keypoints the HE model predicts. During training and inference, each keypoint is associated with a different mask. Such a mask is a binary matrix, with $1$s at the position of the keypoint, and $0$s elsewhere. We have $28$ masks, one per keypoint.}
  \label{fig:field-keypoints}
\end{figure}

\subsection{EDG model}
\label{sec:model:theory}

We assume $s_t \in \mathcal{S}$ is the state of the game at time $t$. It may be the positions of each player and the ball for example. Given an action $a \in \mathcal{A}$ (\emph{e.g.} a pass, a shot, more details in the Supplementary Materials-\ref{supp:sec:datasets}), and a state $s' \in \mathcal{S}$, we note $\mathbb{P} \colon \mathcal{S} \times \mathcal{A} \times \mathcal{S} \to [0,1]$ the probability $\mathbb{P} (s' \vert s, a)$ of getting to state $s'$ from $s$ following action $a$.
Applying actions over $K$ time steps yields a trajectory of states and actions, $\tau ^{t_{0:K}} = \big(s_{t_0},a_{t_0}, ... ,s_{t_K},a_{t_K} \big)$. We denote $r_t$ the reward given going from $s_t$ to $s_{t+1}$ (\emph{e.g.} $+1$ if the team scores a goal). More importantly, the cumulative discounted reward along $\tau ^{t_{0:K}}$ is defined as:

$$R(\tau ^{t_{0:K}}) = \sum_{n=0}^{K} \gamma^{n} r_{t_n}$$

where $\gamma \in \left[0,1\right]$ is a discount factor, smoothing the impact of temporally distant rewards.

A policy, $\pi _{\theta}$, chooses the action at any given state, whose parameters, $\theta$, can be optimized for some training objectives (such as maximizing $R$). Here, a good policy would be a policy representing the team we want to analyze in the right manner. The \textit{Expected Discounted Goal} (EDG), or more generally, the state value function, is defined as:

$$V^\pi (s) = \underset{\tau \sim \pi}{\mathbb{E}} \big[ R(\tau) \vert s \big]$$

It represents the discounted expected number of goals the team will score (or concede) from a particular state. To build such a good policy, one can define an objective function based on the cumulative discounted reward:

$$J(\theta) = \underset{\tau \sim \pi_\theta}{\mathbb{E}} \big[ R(\tau) \big]$$

and seek the optimal parametrization $\theta ^*$ that maximize $J(\theta)$:

$$\theta^* = \arg \max_\theta \mathbb{E} \big[ R(\tau) \big]$$

To that end, we can compute the gradient of such cost function\footnote{Using a log probability trick, we can show that we have the following equality: $\nabla_\theta J(\theta) = \underset{\tau \sim \pi_\theta}{\mathbb{E}} \left[ \sum_{t=0}^T \nabla_\theta \log \left( \pi_\theta (a_t \vert s_t) \right) R(\tau) \right]$} $\nabla_\theta J(\theta)$ to update our parameters with $\theta \leftarrow \theta + \lambda \nabla_\theta J(\theta)$. In our case, the evaluation of $V^\pi$ and $\pi_\theta$ is done using Neural Networks, and $\theta$ represents the weights of such networks (more details on Neural Networks can be found in \citet{Goodfellow2017}). At inference, our model will take the state of the game as input, and will output the estimation of the EDG. A more advanced view of Reinforcement Learning can be found in \citet{SuttonDRL}

\section{Experimental methods}
\label{sec:experiments}

All of the models were implemented using standard deep learning libraries and the usual image processing library. Models, code, and datasets will be released at \href{https://github.com/DonsetPG/narya}{https://github.com/DonsetPG/narya}.

\subsection{Tracking implementation details}
\label{sec:experiment:tracking}

\xhdr{\textsc{Entity Tracking} details} The ET model is based on a Single Shot MultiBox Detector (SSD) \cite{Liu_2016}. The model takes images of shape $(512,512)$, and makes prediction for 2 classes: players (including referees) and the ball. We used an implementation from GluonCV \cite{gluoncvnlp2020}.

\xhdr{\textsc{Homography Estimation} details} The first model (direct estimation) is based on a Resnet-18 architecture \cite{he2015deep}. It takes images of shape $(280,280)$ and randomly crops images of shape $(256,256)$ during training. The model doesn't directly estimate the homography, but rather the coordinates of 4 control points, in the same manner as \cite{jiang2019}. More details can be found in Supplementary Materials-\ref{supp:sec:model-homography}. The model is implemented with Keras \cite{chollet2015keras}. The second model is based on an EfficientNetb-3 backbone \cite{tan2019efficientnet} on top of a Feature Pyramid Networks (FPN) \cite{lin2016feature} architecture to predict the mask of each keypoint. We implemented our model using Segmentation Models \cite{Yakubovskiy:2019}.

\xhdr{\textsc{ReIdentification} details} The embedding model is based on a Resnet-50 architecture \cite{he2015deep} to produce embeddings of size $751$. The model was produced for supervised Re-Identification \cite{zheng2019joint} and implemented on Torch \cite{paszke2017automatic}.

\subsection{DRL implementations details}
\label{sec:experiment:drl}

The EDG model is based on a Deep Reinforcement Learning environment \cite{kurach2019} built by the Google Brain Team and based on a gym environment \cite{openai}.

\xhdr{States, actions, and reward representations} Each state $s$ is represented by a \textit{Super Mini Map} (SMM), stacked 4 times to represent the last 4 positions of each entity. More precisely, $s \in \mathbb{R} ^ {72 \times 96 \times 16}$, where each consecutive 4 matrices encode the positions of the home team, the away team, the ball, and the active player (leading to $ 4 \times 4 = 16 $ for third dimension). The encoding is binary in $\{0,255\}$, representing whether an entity is at the given coordinates or not.

The actions $a$ include movements in 8 directions, different kicks (\emph{e.g.} \; short and long passes, shooting), and high passes. Each action is sticky, meaning that once executed, a moving or sprinting action will not stop until explicitly told to do so. The reward $r \in \{-1,0,1\}$ represents if a goal is conceded, not happening or scored.

\xhdr{EDG model details} The DRL agent, capturing the policy and the EDG is represented by a PPO \cite{schulman2017proximal} algorithm, with an Impala policy \cite{espeholt2018impala}. The architecture is available Figure-\ref{fig:agent-archi}.

\begin{figure}[t]
  \centering
  \includegraphics[width=0.48\textwidth]{figs/agent-archi.png}
  %
  %
\caption{Architecture used for our agent.}
  \label{fig:agent-archi}
\end{figure}

\subsection{Training}
\label{sec:experiment:training}

\subsubsection{Tracking models}

\xhdr{Datasets} We built 3 datasets: a tracking dataset, a homography dataset, and a keypoint dataset. They all consist of the same images from the 2014 World Cup, the Premier League, the Ligue 1, and the Liga. They typically contain $450$ train images, $50$ validation images, and $50$ test images. The homography dataset was based on an existing 2014 World Cup dataset \cite{homayounfar2017}. We extended it to the rest of our images. More details on the datasets can be found in the Supplementary Materials-\ref{supp:sec:datasets}.

\xhdr{Data augmentation} The models were trained on a Tesla-P100 GPU, and each model takes a few hours to train. In each training we used data augmentation : (1): Use the entire original input image, (2): Randomly flip the image horizontally, (3): Randomly add Gaussian Noise and shadows on the field, (4): Randomly change the brightness, the contrast, and the saturation, (5): Add motion blur.

\xhdr{Optimization procedures} Both of the homography models were trained for $200$ epochs, with a batch size of $32$ and a learning rate of $10^{-4}$. We used an exponential learning rate decay down to $10^{-8}$. The tracking model was trained for $100$ epochs, with a batch size of $2$ and a learning rate of $10^{-3}$. The embedding model was pretrained on the Market-1501 dataset \cite{zheng2015scalable}. Each model was evaluated each $5$ training epochs, and we stopped training when we observed a negligible decrease in the loss function. Each model was trained using an Adam optimizer \cite{kingma2014adam}.

\subsubsection{DRL Agent}

\xhdr{Selfplay} We started with a pretrained Agent from Google, trained from 50M steps against an easy bot. We then kept training it for 50M steps against a medium bot. Finally, we trained the agent another 50M against the last version of itself twice. While previous results \cite{kurach2019} were mitigated about self-play, we believe that given the significant advantage our agent had against a medium bot, it was the right decision to improve its capability to find actions with potentials. We compare the results of agents with and without selfplay Figure \ref{fig:res-value} \textbf{(right)} and in the Supplementary Materials-\ref{supp:sec:drl-supp-results}.

\xhdr{Optimization procedures} The agent was trained on $8$ parallel environments with a learning rate of $.000343$ and a discount factor $\gamma$ of $0.993$. We use $8$ minibatches per epoch and update our agent $4$ times per epoch. Finally, the agent is updated with a batch size of $1024$, using an Adam optimizer again. More details on the hyperparameters can be found in the Supplementary Materials-\ref{supp:sec:drl-hyp} Figure \ref{supp:fig:us-vs-easy}.

\subsection{Evaluation}
\label{sec:experiment:evaluation}

The homography estimation models use the IoU between the warped field with our estimation and ground truth homography as the primary metric. We used the mean Average Precision (mAP) for the tracking model for bounding boxes with an IoU greater than $0.5$. Finally, we did not use any metric for the ReIdentification model, as the model we used was not finetuned on a Soccer player dataset. Mode details on the metrics, results, and hyperparameters can be found in the Supplementary Materials-\ref{supp:sec:results}.

We report the result of our DRL agent both with the Average Goal Difference against its opponent and by comparing the EDG to existing frameworks on the same actions. This allows both to grasp the policy's level and how close it reacts to policy based on real players.

\section{Results}
\label{sec:results}

Our main findings are that the EDG model can have a relevant representation of the potential of an action. It can even detect events that previous frameworks could not, even though the agent never trained on real game data. Furthermore, the tracking model can produce reliable coordinates for short plays from only one camera. This model allows us to produce the EDG of any given action quickly. We start by quickly reviewing the results of our Tracking model in Section \ref{sec:results:tracking}. In Section \ref{sec:results:edg} and \ref{sec:results:comparison}, we present the results of the EDG model and compare it to existing value frameworks.

We kept the same agent and the same tracking models throughout the results to challenge their robustness to different scenarios or teams.

\subsection{Generating players' coordinates}
\label{sec:results:tracking}

\begin{figure*}[t!]
  \centering
  \includegraphics[width=\textwidth]{figs/res-tracking.png}
  \caption{We can track almost every player and the ball, even in very different settings. We present here some examples of tracking failures and success. In sequence (a), the REID model fails to identify player 19 between frame 1. and 2., letting the same player having a new id (15). Between frames 3., 4. and 5., the boxes of players 4 and 5 merge into id 20. When the merge is undone, the model can retrieve the right id for each player \newline
  In sequence (b), the same phenomenon appears frame 2., 3. and 4. but the model fails to recognize player 8 and gives him a new id (16). Another issue with our model is when a player runs out of the camera's range and returns later. This almost always leads to a change of id, as seen in frame 5. with player 17. However, this can easily be managed by merging the two ids trajectories.}
  \label{fig:res-tracking}
\end{figure*}

We found that each component of the Tracking Model generalizes well to many scenarios. We start by reviewing the results for each component and leave discussion about some architectural choices to the Supplementary Materials.

\begin{table}[t!]
\begin{center}
\begin{tabular}[p]{lcc}

\toprule

            \textbf{Method} & \textbf{IoU - Mean} & \textbf{IoU - median} \\

\hline

OURS & 0.908 & 0.921   \\
OURS, keypoints & 0.892 & 0.923   \\
OURS, direct estimation & 0.891 & 0.906   \\

\hline

Keypoints, with Players$^a$ & 0.939 & 0.955   \\
Keypoints, w/o Players$^a$ & 0.905 & 0.918   \\

\hline

Synthetic Dictionary$^b$ & 0.914 & 0.927   \\

\hline

Learned Errors$^c$ & 0.898 & 0.929   \\

\hline

Branch and Bound$^d$ & 0.83 & -   \\

\hline

PoseNet$^e$ & 0.528 & 0.559   \\

\hline

SIFT$^f$ & 0.170 & 0.011   \\

\hline

\bottomrule
\end{tabular}
\caption{\label{tab:res-homo}Quantitative results of the Homography estimator models on the 2014 World Cup dataset. Even though \cite{Citraro_2020} obtain better results with their method when using the positions of players as well, we believe that our results where good enough for our purpose, which was to provide reliable tracking data to our EDG model. \newline
\footnotesize{$^a$ \cite{Citraro_2020}, $^b$ \cite{sharma2017}, $^c$ \cite{jiang2019},  $^d$ \cite{homayounfar2017},  $^e$ \cite{kendall2015},  $^f$ \cite{Lowe2004}}}
\end{center}
\end{table}

\begin{table}[t!]
\begin{center}
\begin{tabular}[p]{l|cc|c}

\toprule

\textbf{Backbone} & \textbf{Player - AP} & \textbf{Ball - AP} & \textbf{mAP} \\

\hline

VGG16 & 89.3 & 39.5 & 64.4   \\
Resnet50 & 89.9 & 59.3 & 74.6  \\

\bottomrule
\end{tabular}
\caption{\label{tab:res-tracking-gluon}Quantitative results of the player Tracking model, with a SSD model. More details about the results for less impactfull choices can be found in the Supplementary Materials-\ref{supp:sec:results}}
\end{center}
\end{table}

\begin{table}[t!]
\begin{center}
\begin{tabular}[p]{l|c|cc}

\toprule

\textbf{Architecture} & \textbf{Backbone} & \textbf{IoU} & \textbf{F1-Score} \\

\hline

Unet & EfficientNetb-3 & 0.817 & 0.831\\

\hline

LinkNet & EfficientNetb-3 & 0.813 & 0.828\\

\hline

FPN & EfficientNetb-3 & 0.882 & 0.91 \\
    & Resnet18 & 0.862 & 0.885 \\
    & Resnet50 & 0.841 & 0.863 \\

\bottomrule
\end{tabular}
\caption{\label{tab:res-masks}Quantitative results for the keypoints masks generations. More details about the results for other backbones can be found Figure \ref{supp:fig:keypoints-ablation}}
\end{center}
\end{table}

\xhdr{\textsc{Entity Tracking} results} The main results are available in Table \ref{tab:res-tracking-gluon}. Overall, the Resnet50 backbone yields much better results than the VGG16. The Average Precision for the player class is about $90\%$, where the mistakes often come from stacks of players that are hard to distinguish even for the human eye. Because of its relatively small size and its frequent occlusion by players, the ball Average Precision does not get higher than $60\%$.

\xhdr{\textsc{Homography Estimation} results} The results and comparison against existing methods are available Table \ref{tab:res-homo}. We find similar results to \cite{Citraro_2020} for our Keypoints based method and slightly better results than the direct estimation implementation from \cite{jiang2019}. This can be explained by the higher number of dense layers added at the end of our Resnet18 architecture. Our combination of 2 very different strategies allows the complete model to react better to outliers and bypass the condition of 4 non-collinear points needed by the keypoints based model. Producing high-quality estimations of the homography is a hard task with many consequences. If an estimation is incorrect, players' coordinates will be as bad and produce noisy or false trajectories. For this reason, it is useful to manually check some estimations by hand during the tracking process, and remove them if they are too far from the truth. The more detailed results of the keypoints mask prediction are available in Table \ref{tab:res-masks}.

\xhdr{\textsc{ReIdentification} results} Since we have no dataset of soccer player re-Identification, it is impossible to evaluate our embedding model. However, we can denote the number of operations we had to do manually after a tracking is produced. On average, we had to delete $3.5$ trajectories per action (one trajectory to remove every $60.57$ frame, or $3$ seconds, on average). This number includes the referees that we also detect in our dataset and model. We merge $5$ trajectories per action on average (\emph{e.g.} when a player is not recognized and gets a new id). Finally, we manually add $3.75$ missing coordinates on average, mostly when we do not find the ball at a critical moment (\emph{e.g.} \; the beginning of a pass or a shot).

We present the results of our entire model Figure \ref{fig:res-tracking} for $2$ different actions, and give a more in-depth analysis of when our model successfully tracks each player even when the tracking model fails to detect them, but also highlight particular cases of Re-Identification failure. We discuss in the Supplementary Materials-\ref{supp:sec:results} the rest of architectural choices. We also display more results for each model in Figure \ref{fig:full-results}.

\subsection{Valuing expected discounted goals}
\label{sec:results:edg}

\begin{figure*}[!t]
  \centering
  \includegraphics[width=\textwidth]{figs/rse-edg-map-full.png}
  \caption{EDG mapping based on the position of the ball. In (1), passing the ball to the midfield would release pressure and increase the EDG, but lose momentum. A forward pass inside the box or to the right-wing would also increase the EDG and keep the current momentum. In (2), a forward pass to the right-wing would have less impact as one inside the box, given the current players' velocities. We present in (3) an evolution of the EDG overtime. In the first frame, a pass to the middle would help release the high pressure. The team prefers to stay on the right side and to create a momentum towards the goal. The EDG evolves then to increase on the wing. The EDG does not take into account the different physical capabilities of each player, thus underestimate the potential the team attack's speed.}
  \label{fig:res-edg}
\end{figure*}

\begin{figure*}[!t]
  %
  \begin{tabular}[p]{l|r}
  \begin{minipage}{4.04in}
  \includegraphics[trim=2.5mm 0 0 0,width=\textwidth]{figs/res-value.png}%
  \end{minipage}
& {\begin{minipage}{2.49in}
  %
  \includegraphics[width=1.\textwidth]{figs/us-vs-easy-res.png} \\
  \end{minipage}}
\end{tabular}

  %
  \caption{\textbf{(left)} We present here the EDG over time alongside the tracking of players. The green arrows represent the action taken in the next frame by the player. Between frame (1) and (2), the EDG increases with the long forward pass to the right-wing. It keeps increasing frame (2) to (3) with a decisive pass inside the box, before decreasing due to the very high pressure. It increases again with a shot. \\
  \textbf{(right)} Comparison between our agent EDG map and an agent trained for 50M steps against an easy bot. The easy agent attribute on average the same potential to every location on the field. It shows how training against a more difficult agent and self-play helped our agent learn real soccer players' behavior.}
  \label{fig:res-value}%
\end{figure*}

Our Agent imparts a satisfactory understanding of soccer and soccer dynamics, even while training on simulations. First, Table \ref{res:table:rewards} shows the Average Goal Difference between our Agent and its opponent at the end of each training step ($50$M updates): not only does the Agent learn to beat easy and medium bots, but it also learns more complex dynamics while training against itself. The major impact of this selfplay component can be seen Figure \ref{fig:res-value} \textbf{(right)}, and in the Supplementary Materials Figure \ref{supp:fig:us-vs-easy}. We displayed on these maps the EDG estimated by our Agent if the ball was located at this location. After the first 2 steps of training, the Agent attributes on average the same EDG to each location of the field. After selfplay, a more realistic and insightful potential is discovered.

This potential can be seen Figure \ref{fig:res-edg} for 4 different games. While the front of the center circle and penalty sport both get a high EDG (for releasing the pressure and a high probability of goal respectively), the Agent also accurately captures the most dangerous zones. For example, in both Figure \ref{fig:res-edg} (1) and (2), a forward pass to the right-wing would bring a lot of value to the action. Since the Agent inputs take into consideration the four last frames, it can consider each entity's velocity.

Our model can also estimate the EDG of an action over time. We present  \ref{fig:res-value} \textbf{(left)} the evolution of the EDG during an action, with the player tracking as well. While our Agent can capture the potential of an action, we believe that 2 components make the EDG extremely valuable for soccer analysis:

\xhdr{The discount factor, $\gamma$} We chose a discount factor of $0.993$, meaning that if a goal takes place 100 frames later, it brings a value of $0.993^{100} \approx 0.5$. It reduces the bias from which a single goal would bring immense value to each previous action, even ones that are far away. This allows linking each action to the goal they might lead to realistically, without any arbitrary tricks\footnote{Such as completely splitting the relations between passes and shots, for example, or attributing the same reward to each action that led to a goal, or only to the last 10.}. The value of a goal is, therefore, more uniformly distributed over actions.

\xhdr{The expected value, $\underset{\tau \sim \pi_\theta}{\mathbb{E}}$} First, the Expected Value allows the EDG to get closer to the concept of \emph{almost-goal}, which means that we want to remove any randomness in soccer and consider equal a goal or a shot striking the goalposts for example. Equivalently, we don't want to consider too many outliers, such as lucky goals. This has two effects: a better estimation of the real potential of an action, and better detection of undervalued (resp. overvalued) actions and players. Most importantly, it forces analysis to focus on what leads to a goal, not on the shot itself.

\begin{table}[h]
\begin{center}
\begin{tabular}[p]{l|c|c}

\toprule

\textbf{Training Step} & \textbf{Opponent} & \multiline{25mm}{\centering\textbf{Average \\ Goal Difference}} \\
\hline

Step 1 & Easy Bot & 8.14  \\
Step 2 & Medium Bot & 4.7 \\
Step 3 & end of Step 2 & 5.3\\
Step 4 & end of Step 3 & 4.8\\

\bottomrule
\end{tabular}
\caption{\label{res:table:rewards}Average Goal Differences at the end of the training between our Agent and the opponent.}
\end{center}
\end{table}

\subsection{Comparison with existing framework}
\label{sec:results:comparison}

\begin{figure}[!t]
  \centering
  \includegraphics[width=0.48\textwidth]{figs/comparaison-vaep.png}
  %
  %
\caption{We compare here on the same scenario, VAEP \cite{Decroos2019} (a) and our EDG (b). Our EDG is negative on pass (1), as we take into account the 2 close surrounding opponents to the receiver. The next 2 passes are highly important, and get more values in our framework as they allow to: (2) release pressure, (3) add momentum and danger close to the goal. The next two actions get overall the same value as the VAEP. However, the shot gets a much smaller value within our framework, as our model discounts the goal and attributes more uniformly the potential of an action.}
  \label{fig:comp-vaep}
\end{figure}

\begin{figure*}[!t]
  \centering
  \includegraphics[width=\textwidth]{figs/comparaison-fernandez.png}
  \caption{We compare here in the same scenario the EPV \cite{Fernandez2019} and our EDG. We pick up the same increase in value for action A and B, while our model doesn't value as much action C. On the other hand, our model values a lot action a, which is a long forward pass to the left-wing, and a strong situation that could lead crossing the ball to a teammate. We also kept track of the end of the action (situation b) with a great pass followed by a caught header.}
  \label{fig:comp-VAEP}
\end{figure*}

One way to ensure our Agent produces good analysis is to compare it to other algorithms whose purpose is to evaluate soccer players. We focus on 2 different models: the Expected Possession Value (EPV) from \citet{Fernandez2019}, and Valuing Actions by Estimating
Probabilities (VAEP) from \citet{Decroos2019}. We compare the three approaches to the scenario they used on their paper, as we do not have access to their training procedures or their data.

Overall, we find that our approach, while never trained on data extracted from a real game, find on average the same value as the other 2 approaches. The EPV and our Agent always agree on the positive or negative impact of an action, and when the surrounding is not too impactful, the VAEP and our Agent also agree on the value of an action\footnote{Since the VAEP doesn't take into consideration if opponents are close to a player for example}.

It does, however, find more precise and meaningful values for more subtle actions. This is a powerful result and proof that our Agent learnt realistic soccer behaviors in a simulation, and can understand and process information at various levels: \emph{e.g.} action a player can perform, pressing on a player, players' velocities. For example, a forward pass would get a good value from the VAEP algorithm, while our Agent could give him a weak value because opponents are close, or if a pass is risky because of the field limits. Overall, we find that the value of a goal is much more uniformly distributed in the previous actions with our framework. For example, an assist and its related goal would get values distribution of 10\% and 90\% in the other frameworks, while our Agent would give a distribution of 35\% and 65\%.

\section{Conclusion}
\label{sec:conclusion}

We presented a generic framework for soccer player tracking and evaluation based on machine learning and Deep Reinforcement Learning. Our experiments show that we can produce trajectories of players only from a single camera and that our EDG framework captures more insightful potential than previous models, while being based on simulations. We find that both the tracking model and EDG agent are the first open-sourced one while being more accurate than previous approaches.

Regarding the tracking models, our model could easily be extended to other sports, with appropriate datasets. Some improvements may be obtained by building a soccer ReIdentification datasets or building Unsupervised Approach.

Our DRL Agent would benefit a lot from being replaced by a multi-agent algorithm, where more than one player are being controlled at once. Improvements over the soccer environment would also help a lot: bringing more physical statistics for players or particular teams, for example. While we focus on pure simulation-based training, finetuning the Agent on Expert Data from real games could help to bridge the gap with a more realistic playstyle.

Finally, this work aims to give a broader audience access to soccer tracking data and analysis tools. We also hope that our datasets will help to build more performant models over time.

\section*{Acknowledgements}

We thank Arthur Verrez and Gauthier Guinet for valuable feedback on the work and manuscript, and we thank Matthias Cremieux for advice on object detection models. We also thank \href{https://twitter.com/lastrowview}{Last Row} for the first tracking data we used to test our agent.

redpajama_set_name: RedPajamaArXiv


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