text:
Advanced Emissions Solutions, Inc.'s (ADES) CEO Greg Marken on Q2 2020 Results – Earnings Call Transcript
Home Financial news Advanced Emissions Solutions, Inc.'s (ADES) CEO Greg Marken on Q2 2020 Results – Earnings Call Transcript
Advanced Emissions Solutions, Inc. (NASDAQ:ADES) Q2 2020 Results Earnings Conference Call August 11, 2020 9:00 AM ET
Ryan Coleman – Investor Relations
Greg Marken – Interim President and CEO and Treasurer
Chris Bellino – Chief Accounting Officer
Good morning, everyone. And thank you for joining us today for our Second Quarter 2020 Earnings Results Call. With me on the call today are Greg Marken, Interim President and Chief Executive Officer and Treasurer; and Chris Bellino, Chief Accounting Officer.
This conference call is being webcast live within the Investor section of the website and a downloadable version of today's presentation is available there as well. A webcast replay will also be available on the site and you can conduct — you can contact Alpha IR Group for Investor Relations support at 312-445-2870.
Let me remind you that the presentation and remarks made today include forward-looking statements as defined in Section 21E of the Securities and Exchange Act. These statements are based on information currently available to us and involve risks and uncertainties that could cause actual future results, performance, and business prospects and opportunities to differ materially from those expressed in or implied by these statements.
These risks and uncertainties include, but are not limited to those factors identified on slide two of today's slide presentation, in our Form 10-Q for the quarter ended June 30, 2020, and other filings with the Securities and Exchange Commission.
Except as expressly required by the securities laws, the company undertakes no obligation to update those factors or any forward-looking statements to reflect future events, developments, or changed circumstances or for any other reason.
In addition, it is very important to review the presentation and today's remarks in conjunction with the GAAP references in the financial statements.
So with that, I'd like to turn the call over to Greg.
Greg Marken
Thanks, Ryan, and thanks to everyone for joining us this morning. Before we begin, I'd like to introduce our Chief Accounting Officer, Chris Bellino, who is joining me on this morning's call. Chris has been with ADES for five years and has been invaluable to us serving in a variety of roles during that time. She will continue to join me on earnings conference calls as I serve in the Interim CEO role.
I'd also like to give a brief update on our mitigation efforts related to the pandemic. We are proud to continue to operate as an essential service provider and are focusing on things within our control to respond appropriately to the economic disruption resulting from the crisis.
Our number one priority will always be our employees' health and safety, and we have taken measures to protect our team. We have updated safe workplace protocols and are continuing to offer our employees the ability to work-from-home where it is possible.
When it became apparent to us that our operations could be interrupted, we sequestered certain operating plant personnel to build inventory balances in advance of any potential disruption. Our goal was to ensure that we would have sufficient inventory to properly serve our essential customers in the event that the plant were to experience a COVID outbreak and require a temporary pause in our operations, which has been seen throughout the country in certain manufacturing environments during this pandemic.
Thankfully, we have not experienced this type of event to-date. However, these actions have allowed us to continue to meet our customers' needs and we remain in frequent contact with these customers to ensure that they meet their emissions control and purification requirements.
We also took steps to protect our financial position. We evaluated our capital structure and all non-core capital spending. Our focus was to prioritize liquidity and organic investment to ensure manufacturing capabilities.
In accordance with that focus, we paused all share repurchases and suspended our dividend. We have also restricted corporate travel and limited backfilling open positions, in addition to other measures.
And as previously discussed, we applied for and were granted a $3.3 million loan through the SBA to ensure we were able to retain our workforce through the early stages of this crisis. The impact of that is recorded in our financial statements of debt, though we expect the loan to be forgiven and recorded as debt forgiveness in the income statement once the debt forgiveness process can be completed.
Let's turn to slide three for a high level review of our second quarter. We'll start with our Refine Coal or the RC segment. Tinuum distributions to ADES for the second quarter were $15.4 million, which is 17% lower than last year. The lower distributions were the result of renegotiated contracts for the third quarter of 2019 at Tinuum that resulted in lower net lease payments to the company.
Also contributing to the decline has been the decrease coal burn driven by cheap alternative energy sources, as well as by the lower aggregate energy demand in the U.S. from lower overall economic activity during the second quarter.
Our RC segment operating income in the second quarter was $10.8 million, compared to $24.6 million in the prior year, again driven by lower earnings from Tinuum, as well as point in time recognition during the second quarter of 2019 related to incremental RC facilities contracted during that period.
As we have discussed on past earnings calls, given the impacts of timing of revenue recognition and accelerated non-cash depreciation by Tinuum, our equity earnings are significantly reduced compared to the cash distributions we will receive.
READ ALSO Canada scrambles to save Keystone XL pipeline expansion before Biden administration scraps it
As a result of this, we believe adjusted Refined Coal segment, EBITDA helps to portray an additional year-over-year comparison of the earnings and associated cash flows of the segment. RC segment adjusted EBITDA in the second quarter was $18.1 million, compared to $22.6 million in the prior year.
In our PGI segment, our financial performance also remains challenged by lower aggregate power generation and coal dispatch, as well as changes in product mix. During the quarter, we took an impairment charge of roughly $26 million related to long-lived assets, of which $23 million was related to the PGI segment. Chris will cover the circumstances of that impairment in greater detail in a moment.
In the meantime, our focus here remains on areas where we have the right to win, building the plant's capacity and leveraging our holistic solutions package. Our execution has remained strong despite lower volumes and we expect to continue to maintain high renewal rates with our existing customers.
While the financial performance of the segment has been below our initial expectations, we remain confident in the quality of the asset and our position in the marketplace as a provider of choice. I'll talk more about this after the financial review.
From a consolidated perspective, our net loss in the second quarter was $23.8 million, primarily driven by the aforementioned impairment charge. Excluding this impairment charge, net income would have been $2.3 million for the second quarter and $0.4 million for the first half of the year. Our consolidated adjusted EBITDA was $12.3 million, compared to $15.1 million in the prior year.
Pertaining to our capital allocation, we are continuing to prioritize debt reduction and cash preservation during the pandemic. We remain focused on cost containment and have improve our overall liquidity position from last quarter.
Looking ahead, we are updating our projected after-tax cash flows from the IRC segment to be between $100 million and $125 million through the end of 2021. And remember that our financials are provided as of the close of the second quarter and thus this does not include the additional Refined Coal transactions we announced in July. We estimate that these two transactions will provide additional future cash flows to ADES of $5 million to $7 million due to additional rent payments and savings of Tinuum operating costs.
Although, we expect coal-fired power generation to remain down through the rest of 2020, driven by record low natural gas prices and increasing renewable energy generating capacity, we still see select opportunities for both of our segments.
In our RC segment, our primary goal is to protect our projected Refined Coal cash flow stream and to seek to add to those cash flows were able. These distributions will continue to facilitate our capital allocation plans, as we work to improve performance in our activated carbon assets.
In our PGI segment, we remain intently focused on finding ways to build a plant capacity and wind volumes where we are most competitive. Due to the challenging market conditions during the last 12 months, we have been working to strategically secure additional volumes to fill our Red River plant to better capture the low cost nature of the asset and improve its earnings profile.
We have spent considerable time and effort building out our product capabilities and internal sales infrastructure and we are beginning to have success on new contract awards for material supply agreements in markets outside of power generation.
So far this year, we are in line where we were expected to be with our growing Water business and we continue to see encouraging traction with industrial markets. We are remaining focused on identifying other non-power generation markets to diversify away from the power generation applications for activated carbon.
With that, I'd like to turn the call over to Chris who will review our second quarter and year-to-date financial performance.
Chris Bellino
Thank you, Greg. Let's turn to slide four for the financial review. Starting with earnings from equity method investments, the second quarter earnings from equity method investments totaled $8.2 million, compared to $20.9 million for the second quarter of 2019.
First half earnings from equity method investments were $16.4 million, compared to $42.6 million for the first half of 2019. The decreases during the second quarter and first half are mainly the result of lower earnings from Tinuum Group, resulting from decreased aggregate coal-fired power generation, higher depreciation on all Tinuum Group RC facilities as a result of a reduction in their estimated useful lives during the third quarter 2019. The decrease is also result of Tinuum Group previous restructuring of its RC facility leases with its largest customer.
This decreased net lease payments and equity earnings beginning in Q3 of 2019. Also contributing to the declines was the impact of point-in-time revenue recognition of certain RC contracts by two new in group during 2019 19 compared to the current year.
Moving on to revenues, net loss and net income, the second quarter consolidated revenue was $11.5 million, compared to $15.6 million in the second quarter of 2019. First half revenue was $23.7 million, compared to $34.9 million in the first half of 2019. The decreases in revenue were primary the result of lower consumable revenue and lower volumes that were negative impacted by low coal-fired power dispatch and overall decreases in power-generation driving reduced demand, as well as lower royalty income.
READ ALSO Oil Rallies Despite Growing Demand Concerns
Second quarter royalty earnings from Tinuum Group totaled $3.3 million, compared to $4.2 million for the second quarter of 2019. First half royalty earnings from Tinuum Group were $6.4 million, compared to $8.4 million for the first half of 2019. Royalty income is based upon a percentage of a per ton per tax margin, inclusive of impacts related to depreciation expense and other applicable expenses.
The lower royalty earnings in the first half were due to increased depreciation and lower rent payments to Tinuum which also impacted the company's equity earnings. Royalty earnings are expected to be negatively impacted due to these changes in both 2020 and in 2021. As of June 30, 2020, we had 20 RC facilities invested with 16 that are generating royalties, which does not include the previously announced transactions during the month of July.
During the quarter the company recorded consolidated pre-tax non-cash impairment charge of $26.1 million. The majority of this charge roughly $23 million was related to our PGI segments long-lived asset group such as certain plant and mind-related long-lived assets.
Our consolidated net loss during the second quarter was $23.8 million, compared to net profit of $8.1 million in 2019. First half net loss was $25.7 million, compared to net income is $22.5 million last year. Decreases in net income primarily driven by the aforementioned impairment charge and lower earnings from Tinuum. Excluding this impairment charge net income was $2.3 million for the second quarter of this year and $0.4 million for the first half of this year as well.
Consolidated adjusted EBITDA was $12.3 million for the second quarter, compared to $15.1 million in 2019. First half consolidated adjusted EBITDA was $23.1 million, compared to $33.1 million in 2019. The decreases in consolidated adjusted EBITDA were driven by lower earnings and distributions from equity method investments. This was partially offset by higher depreciation and amortization expense.
In terms of cash, we ended the second quarter with a cash balance, inclusive of restricted cash of $21.7 million, an increase of point — $4.7 million since year-end December 31, 2019. The $5 million in long-term restricted cash remains due to conditions related to the to the term loan. We will continue to focus on cash preservation and ensuring that we have properly — proper liquidity to serve our customers.
Wrapping up with an update on current and long-term debt of the company, during the second quarter, we made a $6 million principal payment on the term loan, reducing the principal balance including the current portion to $28 million as of June 30, 2020.
Total borrowings came in at $36 million, compared to $44 million at year-end 2019. The $36 million is comprised of the $28 million term loan and the $3.3 million of funds that we secured from the SBA potentially forgivable loan program, while the remainder is comprised of capital leases.
So for now, I'm going to turn it back over to Greg for his closing remarks.
Thank you, Chris. Turning to slide five, you can see our expected future Refined Coal cash flows. Based on the 20 invested facilities and cash distributions received during the second quarter, we are updating our expectation of after-tax cash flows to ADES to be between $100 million and $125 million to the end of 2021.
Tinuum continues to remain in active discussions with potential tax equity investors in our pipeline. As I mentioned, this total does not include two previously announced July transactions, which we expect to add between $5 million to $7 million of additional cash flows to this total.
Exclusive of a tax credit extension, we have just six quarters remaining with Refined Coal business. As such, Tinuum must taking appropriate steps to adjust its cost structure, while ensuring that their assets reliably produce Refined Coal. Naturally, we are also responding and we'll look to lower our cash cost dedicated to the Refined Coal segment.
Slide six reflects the opportunities we have identified and continue to execute against for our activated carbon assets. As we have discussed in prior calls, we had always underwritten declining coal dispatch in our assumptions when we acquire the activated carbon assets. However, the rate of decline in both 2019, and again, thus far in 2020 has been faster than our initial expectations. This declining aggregate coal-fired dispatch has prevented us from filling our Red River plant to greater capacity with power generation volume.
In response, we have proactively accelerated our focus on other adjacent market opportunities. We have done significant work since the acquisition of Carbon Solutions in December of 2018 to respond to this changing landscape.
We have talked about some of the non-power generation industrial applications for activated carbon, where we have gained traction with our products. This success we have seen here has continued and we remain on track with our forecasts and water market.
While the total volume we have won in these markets has been unable to fully offset the decline in power generation, we are seeing early signs of our competitive position in the marketplace and are encouraged by the trajectory of our role in these adjacent markets.
We are also seeing early successes in other growing market opportunities utilizing existing product technologies and capabilities that may provide additional volumes in areas where the historical Carbon Solutions business had not compete it. The effort by our team to continue to identify new areas to compete within our overall competitive market is key managing through this time period.
READ ALSO Stocks could 'explode' if Biden improves Covid vaccine rollout
Additionally, there remains potential for an improved environment from the first half of 2020 due to increased power generation demand, higher natural gas prices and impacts from the economy slowly opening, coupled with the work the team has done related to industrial and water applications.
We also expect supply and demand to ultimately rationalize in the industry in the coming years, which may include restructurings and M&A. Given today's imbalanced market, we're evaluating strategic opportunities to increase and diversify our addressable markets. We believe we'll be in position to capitalize on the opportunities given the premier, quality and cost advantageous nature of the assets we possess in this market, which has the potential to increase our earnings profile.
Slide seven shows the changing projections for coal-fired power in the U.S. The graph on the left side reflects the steep downward revisions to coal-fired power generation expectations from the EIA. In response, the figure on the right-hand side of the slide is our internal estimates around how we intend to diversify our products away from coal-fired power generation. As I said, these efforts are already well underway and we are encouraged by our early successes.
In spite of the decline in the power generation market, emissions control regulations, whether they are enforced at the state or federal level will continue to remain in place. As such, certain industries and power utilities will remain bound by emission caps and will need steady long-term providers of a full suite of emissions control solutions to serve as holistic partners to meet regulatory hurdles. We expect to be that provider given our quality asset base, existing customer relationships and technological expertise.
As we have mentioned, we are currently in ongoing negotiations with external parties that would allow us to leverage the new product and capabilities that we have built over the last year. If we're successful in closing some of the larger opportunities in our pipeline, this would greatly increase the current utilization rates for the asset, diversify the customer base, including decrease in exposure to power generation markets and more fully leverage the low cost nature of the plant.
We believe the fixed cost absorption that would result from these contracts would greatly improve the profitability and efficiency of the Red River plant. We feel as though we have made great progress since our last update in May and this work remains of the highest strategic importance for us.
Slide eight provides an update on our capital allocation program. We implemented our shareholder return initiatives during the second quarter of 2017, and since that time, we have returned $106.4 million to shareholders via dividends and share repurchases. We've also paid down $42 million of the $70 million term loan that funded the acquisition of Carbon Solutions in late 2018.
As we discussed last quarter, in order to improve our financial flexibility, we suspended our quarterly cash dividend and put a pause on share repurchases. These initiatives were important pillars of our capital allocation plan, so we did not make the decision lightly, but ultimately, it was important to preserve the roughly $5 million per quarter as we work our way through this crisis.
In the near-term debt reduction will remain a priority as the term loan is subject to mandatory quarterly principal payments of $6 million. We continue to expect to pay off the full balance of the loan prior to the end date of December 31, 2021.
And finally, slide nine outlines our priorities for the remainder of the year. Our first priority is to continue to maximize and protect our net Refined Coal cash flows. Although, Tinuum is marching towards the end of the tax credit generation period, there remain incremental opportunities for invested facilities, while simultaneously adjusting our cost structure.
We will also continue to leverage the best-in-class asset we have to win where our products and capabilities allow us to do so. This will entail filling the plant's capacity with incremental wins in the market opportunities we spoke about, as well as continuing to seek additional opportunities upon the expected market rationalization, while reducing cash costs.
As such, we're on track to our previously provided target of at least $5 million in reductions on an annualized basis, while optimizing our products and manufacturing processes. These cost mitigation actions were put into place before the current crisis. So they are exclusive of any cost changes related to the pandemic.
Lastly, we've shifted our near-term capital allocation focus to risk mitigation and cash preservation. We will continue to deleverage, but the shareholder return component of our capital allocation plan remains on hold to preserve liquidity.
With that, we will take your questions.
[Operator Instructions] And there are no questions at this time. I would like to turn the call back over to Greg for closing remarks.
Thanks again everyone for joining the call this morning and for your continued support. Stay healthy and we look forward to providing our next update.
This concludes today's conference call. You may now disconnect.
Previous PostU.S.-China trade deal is 'fine', China still buying U.S goods: KudlowNext PostSE: Why does the Turkish lira keep falling?


text:
Posted on April 3, 2017 by Times Gazette
Fairfield, McClain break school records
Schools excel in relays, hurdles, distance events
The Fairfield Lady Lions 4x800 relay team is shown, from left, Ciara Colwell, Grace Shope, Dakota Haynes and Chloe Barber.
The Fairfield Lions track team nailed down six school records at the Tippecanoe Invitational in Tipp City on Saturday.
Both the boys and girls teams came in 11th out of 16 teams at the meet.
Blake Adams was third in girls shot put with 35-11.25.
The 4×800 team of Chloe Barber, Ciara Colwell, Dakota Haynes, and Grace Shope placed fifth with a time of 11:28.65, breaking the school's 4×800 record.
Colwell was eighth in girls 1600-meter run with a school record 6:10.48. Colwell also set a school record in the girls 3200-meter with a time of 13:02.45, good enough for sixth place.
Ailean Duffie finished 14th in the girls 300-meter hurdles, setting a new school record with a time of 55.54.
Devon Haynes was ninth in the boys 200-meter dash, finishing at 24.77 to set a new school record.
McClain breaks three relay records
The McClain track team took second place at the Circleville Kiwanis Relay Invitational Saturday, breaking three McClain High School relay records.
The boys finished second out of seven teams with one record-breaking relay win.
The medley relay team of David Jett, Jensen Knaff, Johnny Free and Reece Schluep finished first at 3:54.
The girls team placed fourth out of eight teams with several first-place finishes.
The 4×100 relay team and the sprint medley relay team, both made up of Chayden Pitzer, Ashley Hardesty, Hunter Scott and Maddie Stegbauer, won in their respective events with times of 51.2 and 2:01.2, respectively.
Chayden Pitzer, Trish Poole, Allara Spurlock and Taylor Butterbaugh, McClain's shuttle hurdle crew, brought in a second-place finish with a final time of 1:16.2.
Owen O'Connor and Tristen Pitzer rounded out the meet for McClain with first-place honors in triple jump.
Jamie Discher, a McClain journalism student, contributed to this report.
The Fairfield Lady Lions 4×800 relay team is shown, from left, Ciara Colwell, Grace Shope, Dakota Haynes and Chloe Barber.
http://aimmedianetwork.com/wp-content/uploads/sites/33/2017/04/web1_girls4x800.jpgThe Fairfield Lady Lions 4×800 relay team is shown, from left, Ciara Colwell, Grace Shope, Dakota Haynes and Chloe Barber.
Hi! A visitor to our site felt the following article might be of interest to you: Fairfield, McClain break school records. Here is a link to that story: https://www.timesgazette.com/sports/14287/fairfield-mcclain-break-school-records

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: how to ignore jvm.config when running a mvn command? in the root there is a .mvn folder with jvm.config    with -XshowSettings:vm
if I run mvn -v
it outputs the VM Settings
I want to avoid it, but I cannot change the jvm.config
is there a way to override the jvm argument, how to unset XshowSettings:vm from command line?
Thanks

redpajama_set_name: RedPajamaStackExchange


text:
Marty Walsh beats John Connolly to become Boston's next mayor
Published: Nov. 06, 2013, 1:24 a.m.
Shira Schoenberg | sschoenberg@repub.com
By GARRETT QUINN and SHIRA SCHOENBERG
State Rep. Marty Walsh defeated City Councilor John Connolly on Tuesday to become the next mayor of Boston, winning the coveted job to replace 20-year Boston Mayor Thomas Menino.
Walsh beat Connolly in a close race, winning 52 percent of the vote to Connolly's 48 percent.
Walsh, in an interview Monday, said his first goal will be getting his transition team in place. Once he takes office, he said the big issues for him will be "education, economic development around public safety and creating more opportunities to making sure our seniors feel safe."
Asked Monday about his comeback, from trailing in the polls to a potential victory, Walsh said it was a combination of his own desire to be mayor and diehard support. "I have people who quit their job to support my candidacy," Walsh said.
Connolly conceded the race shortly after 9:30 p.m. and said he had spoken to Walsh. "Marty Walsh is a good man," Connolly said. "He wants to do good things for Boston, and he will do good things for Boston, and he has my full support."
Walsh, 46, of Dorchester is a former union laborer, who briefly worked in construction before taking a job with a local union. He ultimately became head of the Boston Building Trades, a position he left to run for mayor. He has served in the State House since 1997.
Connolly, 40, of West Roxbury, is an attorney and former teacher. He was elected to the Boston City Council in 2007 as an at-large councilor representing the entire city.
Doug Rubin, a political strategist working for Walsh, said Walsh was able to bring together a broad coalition. "It's all about Marty," Rubin said. "People had a chance after the primary...just to get to know him more. Because of who he is, what he's done in his career, and what kind of person he is they really warmed to that."
Walsh continued to hammer home the "common man" theme at his victory party at Boston's Park Plaza Hotel. "For this kid from Taft Street in Dorchester, you made Boston a place where dreams come true. Together we're gonna make Boston a place where dreams come true for every child, for every person," said Walsh.
"For this son of immigrants you've made Boston a place of comebacks and second chances and my life story is made possible by this city. Boston is tough and whip smart but we're caring, too. The city proved in the tragedy that happened on Marathon Monday, the Red Sox proved it last week; hard work, hope, and knowhow, these things make a real difference in people's lives and people all over this city prove it everyday," said Walsh.
In February, Connolly launched his mayoral campaign outside Brighton High School, even before the popular Menino decided whether or not to run for a sixth term.
The former teacher and education reform advocate declared himself the "education mayor" and built a campaign effort around that theme. Connolly was a rarity in the school reform movement, a champion of charter schools who has spent time teaching in urban classrooms.
When Menino announced in March that he would not seek a second term, additional candidates quickly assembled citywide campaigns to fill the impending vacancy at City Hall. A crowded field of 12 candidates battled through the Sept. 25 primary. The winners were Connolly and Walsh, a lifelong resident of Dorchester and the son of Irish immigrants.
Walsh, a son of labor and of the Dorchester Irish community, built his campaign around the theme of an everyman who understands the problems of everyday people in Boston. A survivor of childhood cancer, gun violence and a recovering alcoholic, Walsh crafted a populist image throughout his campaign. Walsh launched his campaign in May at Dorchester's Strand Theatre.
Both candidates tried to broaden their bases in the general election, with Walsh looking beyond labor and Connolly trying to expand his appeal on issues beyond school reform. But those constituencies still played a major role, particularly for Walsh. Outside labor groups poured $1 million into the race to support Walsh's campaign, including the labor union federation AFL-CIO-affiliated Working America, the Service Employees International Union and unions representing nurses, firefighters and others, according to reports with the Massachusetts Office of Campaign and Political Finance. The labor groups distributed literature portraying Connolly as elitist. (A political action committee called One Boston, chaired by Roslindale interior designer Jocelyn Hutt, also spent $480,000 supporting Walsh.) Walsh also got support from a number of minority and female politicians, including his former mayoral rivals, Charlotte Golar Richie, John Barros and Felix Arroyo.
Shannon O'Brien, the former Massachusetts treasurer and 2002 Democratic gubernatorial nominee, supported Connolly as someone who she believed would be independent and could reach out to all the different groups in the city. She said she thinks Connolly was hurt by the negative advertising of outside labor groups. O'Brien said some of Connolly's supporters urged him to hit back. "If he's not successful, it may be because he stuck to his guns and ran a positive campaign and that hurt him," O'Brien said.
Connolly said he had no regrets about how he ran his campaign. "We ran the race that we ran, and I would run it the same way," Connolly said. "The only change I heard pundits say was you should have gone negative and I was never going to do that. I wanted my campaign to be about ideas and vision, and I'm glad we ran it that way."
Education reform groups, including Stand for Children and Democrats for Education Reform, spent around $60,000 helping Connolly. Much of his support came from parents of school-age children.
There were few major differences between the candidates on the issues. In debates, many of the sharpest exchanges came over experience. Connolly argued that Walsh was beholden to organized labor while Walsh said his labor ties would make him better able to negotiate with unions on city issues. Walsh quizzed Connolly on his work as a corporate lawyer, a part of his resume that Connolly downplayed.


text:
Articles 2020 / August 2020 / New Products / by Terry Goble
1st Mate Is Ready To Assist For Boater-Overboard Scenarios
Mercury Marine today announced full compatibility of all Mercury SmartCraft-capable engines with the new 1st Mate Safety and Security System.
This technology comprises an intelligent hub, a set of wearable products and a mobile-device app that integrate with a boat's propulsion systems to provide potentially lifesaving safety features and to help secure property. Its three main features are: 1) a boater-overboard monitoring and alert system, 2) distress-messaging capability, and 3) deterrence against theft of the boat and/or its engine(s).
The 1st Mate mobile app is available now in the Apple Store for iOS® devices, with a version for Android™ devices coming soon.
Mercury SmartCraft-capable engines are the first to be compatible with this innovative new product.
The three main features of this product work in the following ways:
Boater-overboard monitoring and warning system
This system uses wearable fobs to protect a boat's captain and up to seven passengers.
These wearables connect to a mobile device and ensure that, if the captain falls overboard, the engine(s) will stop, an alarm will sound and alerts providing instructions to the passengers will be sent via the 1st Mate mobile app, thanks to direct integration with the vessel's propulsion system.
Similarly, if a passenger falls overboard, the app will sound an alarm, send alerts, and provide the captain with the overboard passenger's GPS location.
Distress messaging
If a boat captain (driver wearing the captain's fob) falls overboard and can't get back onboard, or passengers can't return the boat to the captain, 1st Mate can send a distress message to emergency contacts designated on the captain's mobile app.
Theft deterrence
This feature locks a boat's engine(s) to prevent unauthorized use. Once the boat captain is ready to get back behind the wheel, the engine(s) can easily be unlocked via the proximity of the captain's wearable or by use of the 1st Mate mobile app.
More information is available at mercurymarine.com
Breeze By Webasto 2.0 Is Smaller And More Powerful
On a hot, humid day, even the wind generated from running at wide-open throttle can feel warm. At idle speed or anchor, the heat on the water can be unbearable. Breeze by Webasto 2.0 is the revolutionary air conditioning system for open cockpit boats, blasting up to 30,000 BTU/h of refreshingly cold air, plus, when autumn comes and the weather changes, it'll generate heat with the flip of a switch.
Smaller and lighter than the original, Breeze by Webasto 2.0 runs on 12V DC but doesn't require a generator. It uses an engine-mounted and belt-driven compressor. The condenser and pump are easily installed in the engine compartment, and the compact evaporators are placed where access is available, such as inside the console or dash, or under gunwales.
Breeze by Webasto 2.0 works similar to an automotive air conditioner, but instead of using air to cool the condenser, it uses fresh or seawater like most traditional marine air conditioners.
Webasto Thermo & Comfort
North America, Inc.
15083 North Rd.,
Fenton, MI 48430.
www.webasto.com
4ocean, Seasucker And Boaters Band Together
Waterways around the world are increasingly becoming choked with plastic trash. To stem the tide of this environmental crisis, SeaSucker's partnership with 4ocean offers boaters a unique product that stores the trash they create and find.
Made in the USA from 50% recycled content by weight, the large SeaSucker Waste Band mounts to any smooth, non-porous surface with its two integrated 4.5-inch vacuum mounts. Far superior to a mere suction cup, each holds an astounding 120 lbs. so users can pile in the trash.
Built for a marine environment, the Blue Collection Waste Band is UV-stabilized and uses only stainless steel hardware. Its distinctive bright blue trim matches the 30-inch L x 18-inch W 4ocean Cleanup Tote. Made from 100% recycled plastic, the tote has built-in handles for combing the beach for trash or carrying waste for proper disposal.
Like all SeaSucker accessories, it doesn't require drilling, leaves no mark and can be moved where it's needed – even onto the side of the hull. 4ocean is a purpose-driven company whose mission is to end the ocean plastic crisis. Its website is www.4ocean.com
Captains for Clean Water is a nonprofit that works to restore the natural, unpolluted flow of rivers into the Everglades drainage basin. Its website is www.captains forcleanwater.org
The SeaSucker Blue Collection Waste Band 4ocean Edition with Cleanup Tote costs $149, with 15% going to Captains for Clean Water. The tote is also available separately for $15.
Contact SeaSucker, LLC,
1912 44th Ave E.,
Bradenton, FL 34203.
info@seasucker.com
Next story Lessons Learned – by Pat Carson


text:
Q: How would I go about predicting the survival probability or regress the survival date/time of an entity in a dataset? I have a longitudinal dataset comprising of physicians and their time independent covariates (age group, physician type, etc) and time dependent covariates (number of patients, hours worked, etc). I have several entries for each physician where the time-dependent covariates change from month to month (I have monthly intervals). This data is formatted in count process format.
I want to predict the risk/survival of a physician leaving. I am unsure how to do this because:
COXPH can handle the time-dependent covariates and does model the effect of the variables on the hazard but can't predict the survival out of the observation window.
Classical machine learning can predict/regress a physician leaving but may not model the time aspect very well (treats each sample as an independent sample, no relation to group of samples for a physician)
I am wondering if these approaches are correct?

*

*Would it be possible to extract the hazard from the coxph (or predict partial hazard) and keep this hazard constant until the survival probability reaches 0?

*Could I train a classical model such as xgboost or random forest to predict if a physician is going to leave before x months and include rolling averages on the time-dependent covariates to relate the different observation within a physicians group of observations?
EDIT: The input to this classical ML model would be my all my features (time-independent + time-dependent) and the output is physician did not leave/left ([0,1]). This Binary output is generated from doing term_date-study_start_date < num_days. This num of days could be 6 months. Meaning if at some point a person leaves we categorize this persons last 6 months as 1 (left) and this is what we are trying to predict. I am proposing to compute rolling averages for each of the time varying covariates and adding these averages as a new feature in the dataset.

*Another approach is to do the same as 2 but instead regress the term date. I can convert the term_date into days since beginning of study and regress this. I can then use this model to predict when they will leave and threshold on this. I think this would be a great feat but it may be difficult to do.
Essentially I would like to be able to predict either when a physician will leave (survival curve is ok here or a regressed value) or if they leave before a certain time interval for physicians that include time varying covariates. The above are some approaches I have thought about but I am not 100% sure if they are the correct way. How can I accomplish this?

A: As Therneau and Grambsch put it (page 272):

Survival curves based on a time-dependent covariate must be used with extreme caution.

My answer here covers many of the general problems in working with models based on time-varying covariates and making predictions from them. The warnings about potentially violating causality and modeling a covariate that changes suddenly and represents the "last straw" in a decision to leave seem particularly applicable here.
With respect to your questions:

Would it be possible to extract the hazard from the coxph (or predict partial hazard) and keep this hazard constant [beyond the observed survival window] until the survival probability is 0?

In a Cox model the hazard is identically 0 except at event times observed in the original data. So, no. You could consider extrapolation to later times with a parametric survival model, but predictions beyond the range of observations is always risky.

Could I train a classical model such as xgboost or random forest to predict if a physician is going to leave before x months ...

Old fogies like me don't think of xgboost or random forests as "classical" models, but this could be done with standard binomial regressions, too. The trick would be how to incorporate the time-varying covariates properly into a model that works with a fixed time window. I'm not sure how to do that.
You could, however, put a short time window together with a survival model incorporating time-varying covariates, as you seem to be interested in relatively short-term decisions to leave. That would move away from the individual-specific time origin, implicit in the survival modeling of your first question, and go to a panel-data approach with a fixed study start date as time = 0 for all individuals then employed, as in your second question. You then include things like prior length of service at study start as covariates in a survival model restricted to a reasonably short period (say, for just a few years) after the common study start date. That would avoid the difficulties of trying to extrapolate to long individual survival times that led in part to your question.
My answer here outlines such an approach, based on a thesis that modeled customer churn in the insurance industry (pretty similar in concept to your situation). The modeling in that thesis allowed for time-varying covariates. What you would be modeling is something different from the individual-survival analysis often done in clinical studies but might be more directly applicable to your business needs.

Another approach is to do the same as 2 but instead regress the term date.

The problem with this approach is that you omit the cases whose "term date" hasn't been reached. That introduces bias. Survival analysis is needed to help avoid that bias in regressions of times-to-events when some events, even if inevitable, haven't occurred during the study.
A final warning: using pre-Covid data on clinician turnover to model behavior either during the current pandemic or in a hoped-for thereafter seems to be pretty risky. Proceed "with extreme caution" on that account, too.


text:
Film about the lead up to the Polish uprising against German occupation at the end of the Second World War.
Genre: Drama, Thriller, War
Director: Wladyslaw Pasikowski
Actors: Grzegorz Małecki, Julie Engelbrecht, Michael Terry, Mirosław Baka, Patrycja Volny, Philippe Tłokiński, Rafał Królikowski
Watch The Messenger Online For Free 123Movies » Best site to watch movies free and TV shows online is CipFlix
Max Lowe is a Houston surgeon who has grown weary of the bureaucracy of American medicine. When he loses a patient on the operating table, Max impulsively decides to leave…
The Dustwalker
An alien spaceship crash-lands in an isolated town in the middle of the Australian desert, releasing an insidious parasite that attacks the brain of all creatures including humans, making them…
Country: Australia, United Arab Emirates
Genre: Drama, Science Fiction, Thriller
When a rare phenomenon gives police officer John Sullivan the chance to speak to his father, 30 years in the past, he takes the opportunity to prevent his dad's tragic…
Genre: Crime, Drama, Mystery, Science Fiction, Thriller
Ford Brody, a Navy bomb expert, has just reunited with his family in San Francisco when he is forced to go to Japan to help his estranged father, Joe. Soon,…
Fitzcarraldo
Fitzcarraldo is a dreamer who plans to build an opera house in Iquitos, in the Peruvian Amazon, so, in order to finance his project, he embarks on an epic adventure…
Country: Peru, West Germany
In the last days of a dying logging town, Christian returns to his family home for his father Henry's wedding. While home, Christian reconnects with his childhood friend Oliver, who…
Henry's Crime
An aimless man is sent to prison for a crime he did not commit.
Genre: Comedy, Crime, Drama, Romance
A look at the life of legendary American pilot Amelia Earhart, who disappeared while flying over the Pacific Ocean in 1937 in an attempt to make a flight around the…
Genre: Adventure, Biography, Drama, Romance
Sergeant Michael Dunne fights in the 10th Battalion, AKA The "Fighting Tenth" with the 1st Canadian Division and participated in all major Canadian battles of the war, and set the…
Genre: Drama, History, Romance, War
Carla's Song
A Glasgow man (Robert Carlyle) visits war-torn Nicaragua with a refugee (Oyanka Cabezas) tormented by her memories.
A hard-working small business owner and his two associates travel to Europe to close the most important deal of their lives. But what began as a routine business trip goes…
The story of a precocious six year-old and her ragtag group of friends whose summer break is filled with childhood wonder, possibility and a sense of adventure while the adults…
Trailer: The Messenger


EquuSpirit, a show for everyone!
We want to accomplish that by offering a show with non ASPC/AMHR classes, where horses from all breeds can participate, but also ASPC/AMHR approved classes. By offering non ASPC/AMHR classes a lot more people can participate at a good show and they have the chance to meet the ASPC/AMHR horses and ponies. This way everyone have the opportunity to take part in a multi-day show.
Our goal is to make our show as low budget as possible for the exhibitors. By offering low registration fees, low stables cost, … people with every budget can participate!
With all our ideas, we want to bring everybody together, the experienced exhibitors and the new ones, to enjoy their hobby on a show weekend full of fun.


text:
September 2022 by Lee Nichols
Soufiane El Bakkali made a familiar move off the final waterjump in kicking to the win. (VICTOR SAILER/PHOTO RUN)
NO, YOU'RE NOT having déjà vu – it really did happen all over again.
Just as in last year's Olympic final, Morocco's Soufiane El Bakkali surged past Ethiopia's Lamecha Girma at the final waterjump to win, with a Kenyan coming in 3rd. The only variations were a different time and different Kenyan.
El Bakkali crossed the line with the slowest winning time in meet history, 8:25.13 (his Olympic run was 16.23 faster). Girma followed in his wake at 8:26.01, followed by 2-time defending champion Conseslus Kipruto in 8:27.92.
One might think that Girma and the rest of the field would have chosen a faster pace to neutralize the favored El Bakkali's powerful kick. Instead, Girma led the field through a shockingly pedestrian first kilometer of 2:58.01.
He then surrendered the lead, but no one else really wanted it. Kipruto crawled through 2K at 5:52.44. At this point, first and last in the field of 15 were separated by only 1.33.
Girma's teammate Getnet Wale took a turn 200m later, and then Eritrea's Yemane Hailesilassie made a bid with half a K left. At the bell, Hailesilassie narrowly led Wale, Kipruto, Ethiopian Hailemariyam Amare, El Bakkali, American champion Hillary Bor and Girma.
The Ethiopian trio and Kipruto and El Bakkali swept past Hailesilassie on the backstretch, but then Amare tripped on the barrier. Wale had a stumble of his own as he exited the waterjump, leaving the other three to claim their medals.
El Bakkali's closing splits were 57.35, 28.02 and 13.68, compared to Girma's 58.09, 28.79 and 14.05.
El Bakkali now has a complete set of WC medals, adding to his London silver and Doha bronze.
Of the Americans, national recordholder Evan Jager capped off a 4-year comeback from injury by bolting into 6th (8:29.08) while Bor faded down the stretch to 8th (8:29.77).
Said the 26-year-old El Bakkali, "I am very happy to win my first World title after the Olympic gold. The race was very difficult; very tactical, slow. We had very good runners like defending champion Kipruto, the American Jager. I positioned well in the last lap. I am very strong in the 400m and it worked out for me."
Girma rued his improper strategy, saying, "I am happy but not satisfied with the silver. The pace was very slow today, my tactic did not work and that cost me the gold. I was trying to change tactics but the pace limited me very much. I will go for gold next year and my training is starting now. I am going to make my training special and then I will try for gold at the next championships."
"It was super messy," said Jager, who was only 10th with a half-lap to go and 9th with the straightaway left. "It was really windy. That's probably one of the slowest races I've been in. I thought the race would be fast, that Girma wanted a fast pace to try to shake Bakkali. We assumed it was going to get super-fast.
"The goal was to be as efficient as possible and that got in my head a little bit too much so I didn't run my style of race. I wish I could have positioned differently going with a lap to go, but everyone had so much energy left that it was hard to make those moves to get into those places and fight people off at the same time. I was able to pass a few people at the end, but I was already [too] far out of contention to do it."
The race's first lap featured an additional obstacle: an oblivious cameraman standing on the track with the field forced to run around him.
MEN'S STEEPLE RESULTS
FINAL (July 18; interior waterjump)
(temperature 79F/26C; humidity 43%)
1. Soufiane El Bakkali (Mor) 8:25.13
(13.68, 28.02, 57.35);
2. Lamecha Girma (Eth) 8:26.01 (2:58.01)
3. Conseslus Kipruto (Ken) 8:27.92 (5:52.44)
(15.81, 31.24);
4. Getnet Wale (Eth) 8:28.68
5. Abraham Kibiwot (Ken) 8:28.95
6. Evan Jager (US) 8:29.08
7. Yemane Hailesilassie (Eri) 8:29.40;
8. Hillary Bor (US) 8:29.77;
9. Daniel Arce (Spa) 8:30.05;
10. Hailemariyam Amare (Eth) 8:31.54;
11. Avinash Sable (Ind) 8:31.75;
12. Ahmed Abdelwahed (Ita) 8:33.43;
13. Mehdi Belhadj (Fra) 8:34.49;
14. Sebastián Martos (Spa) 8:36.66;
15. Leonard Bett (Ken) 8:36.74.
HEATS (July 16)
I–1. El Bakkali 8:16.65; 2. Bett 8:16.94; 3. Kibiwot 8:17.04; 4. Wale 8:17.49; 5. Martos 8:18.94; 6. Abdelwahed 8:21.04; 7. Benard Keter (US) 8:21.94; 8. John Gay (Can) 8:27.02; 9. Ben Buckingham (Aus) 8:29.15; 10. Kosei Yamaguchi (Jpn) 8:30.92; 11. Bilal Tabti (Alg) 8:38.45; 12. Frederik Ruppert (Ger) 8:45.55; 13. Tim Van De Velde (Bel) 9:03.11.
II–1. Girma 8:19.64; 2. Kipruto 8:20.12; 3. Bor 8:20.18; 4. Belhadj 8:20.47; 5. Ryuji Miura (Jpn) 8:21.80; 6. Edward Trippas (Aus) 8:23.83; 7. Mohamed Ismail Ibrahim (Dji) 8:25.85; 8. Tom Erling Kårbø (Nor) 8:26.12 PR; 9. Hichem Bouchicha (Alg) 8:27.39; 10. Ahmed Jaziri (Tun) 8:28.28; 11. Víctor Ruiz (Spa) 8:33.42; 12. Ryan Smeeton (Can) 8:33.51; 13. Salaheddine Ben Yazide (Mor) 8:38.46; 14. Carlos Andrés San Martín (Col) 8:48.66.
III–1. Amare 8:18.34; 2. Jager 8:18.44; 3. Sable 8:18.75; 4. Hailesilassie 8:18.75; 5. Arce 8:21.06; 6. Mohamed Amine Jihnaoui (Tun) 8:22.00; 7. Benjamin Kigen (Ken) 8:22.52; 8. Karl Bebendorf (Ger) 8:25.73; 9. Jacob Boutera (Nor) 8:31.47; 10. Vidar Johansson (Swe) 8:33.51; 11. Ryuma Aoki (Jpn) 8:33.89; 12. Jean-Simon Desgagnés (Can) 8:40.90; 13. Topi Raitanen (Fin) 8:43.01;… dnf—Mohammed Tindoufti (Mor).
Since 1986, Lee Nichols has been the Rockdale (Texas) High School record holder in the mile and 2-miles. He followed those feats with a brief and highly undistinguished tenure with the Texas Longhorns. He has been writing for Track & Field News since 2004. When he's not writing about track, he's either writing about or drinking craft beer and watching Tottenham Hotspur play soccer.
« World Champs Men's 5000 — Ingebrigtsen Bounces Back
World Champs Men's 1500 — Wightman's Upset »


text:
Q: jQuery - Check if a container div has a child with a specified attribute value I want to be able to check if a container div has a child in it with an attribute of a particular value and also how many instances exist.
For example, if I had the following HTML:

DIV CONTENTS

DIV CONTENTS

DIV CONTENTS

DIV CONTENTS

DIV CONTENTS

DIV CONTENTS

I would like  a jquery line that that would be able to find if any div with class "child" in $(".container") has an attr of "myattr" and a value of "myattrvalue3".  I would also like to be able to determine how many instances of such a child exists, which would be 3 instances of the child with myattr='myattrvalue3' in this example.

A: var $elems = $('.container .child[myattr=myattrvalue3]');
var length = $elems.length; // length of the selected elements

Note that myattr is not a valid attribute. You can use HTML5 data-* attributes instead.

A: How about the find() method?
var $children = $('.container').find('.child[myattr="myattrvalue3"]');

And to find the number of children:
$children.length


One of the great things about traveling abroad is trying the local cuisine and exposing oneself to different flavors and textures that come with it. Being in a place like Japan, you also can't help but try stuff that's local to you but exotic to the natives. To get their spin on it.
This brings me to Nestlé's Kit Kat bar.
Japanese Kit-Kat commercial from Oyastucafe's Youtube page.
During my first trip to Japan, I couldn't help but notice there were KitKat bars all over the place AND they were almost any flavor but traditional chocolate.
I'm not big on sweets but curiosity got the better of us and we tried the Apple, Green Tea, Blueberry, Sweet Potato, Cheesecake and braved the soy sauce flavored one. It's not what you think (wasn't salty at all) but not at the top of my list. We liked the Cheesecake and Green Tea flavors a lot, actually.
Nestlé will probably never actively market them in the US because of general American consumer conservatism. I mean corn flavor? Really? Compared to American cuisine, the Japanese live more on the edge with their ingredient selections; their food culture is awesomely insane!
Really not bad at all, actually.
…as well as the corn flavor.
Still, you can probably find some stuff on ebay if you look hard enough. These confections are great conversation starters and could give your taste buds a little adventure. You only live once right?
Maybe I should work for Nestlé…?
Flavors from a Kit-kat collector's (hungrycurioscat) blog.
I've seen people (online) collecting every flavor they can get their hands on, including special edition or limited runs. Again, I'm not really into desserts and sweets but the idea finding a new flavor when I return to Japan is kind of exciting.
Author hikikomori78Posted on June 30, 2013 June 13, 2013 Categories Japan, UncategorizedTags Cheesecake, Green Tea, Japan, Japanese Cuisine, Kit Kat, Nestlé11 Comments on Over 200 Flavors of Kit Kat in Japan. Who Knew?
I just watched a video documenting three gaijin bicyclist riding across Japan from the most southern point (Cape Sata) to the most northern point (Cape Soya). They also did this not long after 3/11.
However, watching it you wouldn't know it.
You can watch it here on Andrew Marston's website and can also get more info about the trip with additional media to help you plan your own journey.
Andrew, Scott, and Dylan's journey across Japan is beautifully recorded and edited in a way that this video comes across more as a friend's home video montage than a straight documentary and I'm good with that.
They hit some spots I've been to (in Kyoto) and others that are still on my list (Nagasaki/Hiroshima). I get excited when I see people in exact places I've visited and curious about others I may have missed or have yet to cross off my list.
It's a casual video and you can watch it for free. If it doesn't inspire you to visit another country, then I've wasted both of our time.
I found a short doc.
I found this, like everything else, during my attempts in researching my film. It has nothing to do with Hikikomori but does give some perspective (one man's perspective) on what it's like to live as a Japanese citizen. Parents, there is strong language.
This short doc is quirky but interesting in it's unbarred exposure of these people's lives in Yamagata. Speaking from experience, it can weeks if not months to gain this level of trust and brutal (when not belligerent) honesty. Also, nattō is fermented, not rotting.
Nattō: It's good for you but smells horrible. It's the one thing my wife and I don't eat. Her friends love it.
I think it's a great piece about small town life but not the only story.
Black in Japan: Not What You Assume.
Yes, I put a picture of my feet (in Japan) on this blog.
So as I continue on my journey to make an independent short film about a Hikikomori in the US, I find myself also becoming more like one in order to get these blogs out. My entry, "The 'D' Word" touched a soft spot but how about some personal accounts?
This video completely blew me away. If I can ever speak 日本語 half as skilled as Kemushichan, I would be a very happy man and so would my wife. (Conversations with the in-laws get frustrating for me real fast.) I'm re-inspired to improve my 日本語.
Ms. Scott's youtube page is all about helping you learn Japanese and her experiences in Japan. If her series is anything like this video, you're in for a good time. She's got great energy and you can tell she's passionate. For more about her and what she's really trying to do go to her website.
So after that I had to look up Rhyming Gaijin to see who Kemushichan was talking about. His video (below) wasn't so much a response but a pitch (similar to ABC's What would you do?) It should be also noted that both these videos were presented and showcased (in 2011) by Gimmeaflakeman. Victor and Tomoko Sensei do some fun and informative stuff.
I also agree with Victor that there will never be a satisfactory answer. (The question being: How do Japanese view "black" people?) And Rhymin Gaijin's attempt may fall on deaf ears but that's the purpose of vlogging. Whoever listens, great. Whoever doesn't, whatever. I believe Rhymin Gaijin believes (as I do, and my wife) that we should be proud of our culture and heritage BUT we have to look at ourselves as people, first. Not a color. If we continue to allow ourselves to be labeled as a color and not a person, how will we ever get past this whole race issue?
Before I met my in-laws, my wife told me that her family looks at my (American) nationality first, then my personality/intelligence. So far they're all on board but I had to earn it. Grandma and grandpa took a little longer but for obvious reasons (they come from a different generation of thinking).
I really appreciate Victor's attempt at going to the source and completely respect his effort in tackling this issue.
I do agree that if you want to know what Rhymin Gaijin's experiences are like check out his youtube page he put a lot of it there. People who are curious should check it out but you're not going to know for yourself until you go.
Everyone's experiences will be different, just as Victor and Sec1productions say… after Victor's bad hair day.
Out of the three, this video was my favorite.
For the record, I met and dated my wife in the states. The longest I've ever been in Japan (to date) has been a little less than a month. I work in the film / television industry, so Los Angeles is the best choice for me and my wife has chosen to stay with me. Our reasons for not living in Japan have more so to do with an individualistic society vs. a collectivistic society. Not race. As a matter of fact, her treatment as a foreigner by Americans is what inspired our film.
During a visit, when we've gone on roadtrips to more rural towns, people look. Some stare. A few try to strike up conversation but overall I haven't had any problems (as a visitor). What is a problem are the way some US enlisted men and other foreigners decide to commit crimes or a nuisance that gives every foreigner a bad rap. It's embarrassing as a visitor and insulting as an American when our own can't behave or are disrespectful.
Author hikikomori78Posted on June 9, 2013 June 9, 2013 Categories Film, Hikikomori, Japan, UncategorizedTags black in japan, hikikomori, Hollywood, Japan, life in japan, loneliness movie, racism1 Comment on Black in Japan: Not What You Assume.
During my first trip to Japan I went on a road-trip with my new in-laws and we wound up on the Northwest side of Honshu and I saw the Sea of Japan. For some reason I slowly gained a feeling of peace with an underlying sadness I couldn't shake.
For me, some places just have a an aura of sadness despite their beauty. It was the same for me when I visited New York's twin towers site, Gettysburg, Pennsylvania and Salem, Massachusetts. However I have no problems with hospitals, funeral homes, or most cemeteries.
When I stumbled on this video about a "Suicide Forest" in Japan, I wondered how overwhelming this place must be to visit. Just to be clear, I have no plans or intentions of going (if I want to make myself depressed, I only need to look at my bank account) and people (mainly foreigners) visiting in hopes of seeing dead bodies are ghouls.
So why did I show you this? I think the point the small sign is trying to make is spot on although people who've made up their mind aren't going to be that easily deterred.
For me, there is also a small degree of morbid curiosity but it only goes as far as Azusa Hayano's question: Why would someone want to commit suicide in a beautiful forest?
With all the chaos that can complicate our daily lives, maybe the question alone answers itself.


text:
\section{Introduction}
Among two-dimensional field theories, integrable field theories distinguish themselves by the existence of an infinite number of conserved
 charges.
In flat spacetime, two basic consequences of higher conservation laws are
 the absence of particle production and factorization of the higher-point S-matrix\cite{Zamolodchikov:1978xm,Dorey:1996gd,Shankar:1977cm,Parke:1980ki}.
Since  a Lax pair is in general hard to find,
no tree-level particle production is regarded as an important sign of classical integrability,
and it is a useful strategy for building classically integrable theories \cite{Arefeva:1974bk,Braden:1991vz,Dorey:1996gd,Gabai:2018tmm,Bercini:2018ysh}.

It is natural to wonder  what one can say about integrable field theories in other two-dimensional spacetimes. The $AdS_2$ case is of particular interest since it is maximally symmetric and has applications related to the AdS/CFT correspondence\cite{Maldacena:1997re,Witten:1998qj,Gubser:1998bc}.
S-matrix cannot be defined in AdS spacetime due to the periodicity of particle orbits and the timelike boundary.
The AdS analogs of the flat space S-matrix elements  are  boundary correlation functions which can be obtained as a limit of bulk correlation functions.
In the weak coupling regime, they can be computed by Witten diagrams. Such observables  in $AdS_2$ can be used to define a set of correlation functions in a one-dimensional conformal theory \cite{Paulos:2016fap}.
Due to the existence of infinitely many conservation laws, it is intuitive to expect  there should be something special about boundary correlation functions in integrable field theories.

Integrable field theories in $AdS_2$ are rare.
Toda field theories with simple Lie algebras provide an important class of such examples.
Toda field theories are conformal \cite{Gervais:1983am,Mansfield:1982sq,Braaten:1983pz} and  integrable\cite{Leznov:1979td,mikhailov1979integrability,Olive:1983mw,Olive:1984mb}.
It was shown in \cite{Bilal:1988ze,Bilal:1988jf,Bilal:1988jg,Bilal:1988nf} that they possess extended symmetries generated by  $\mathcal{W}$-algebras \cite{Zamolodchikov:1985wn} which are higher spin extensions of the Virasoro algebra (see \cite{Bouwknegt:1992wg} for a review of $\mathcal{W}$-algebras).

In this paper we focus on four-point functions of  boundary operators in Toda field theories in a classical $AdS_2$ background.
Unlike previous efforts devoted to the correlation functions of the vertex operators,
 we are interested in the boundary operators obtained by pushing bulk scalar fields to the conformal boundary.
 The conformal dimensions of the boundary operators are related to the masses of the bulk fields.
The potentials of Toda field theories in flat space  do not have a stable minimum.
When a Toda field theory is put in an arbitrary Riemann surface, the scalar fields need to couple to curvature  in order to preserve integrability.
Since the $AdS_2$ spacetime or its Euclidean version has a negative constant scalar curvature,
the potential acquires a  minimum and the scalar fields become massive. The spectrum of the theory is determined by the set of exponents of the associated Lie algebra.
We compute the tree-level four-point functions in  Toda field theories with the Lie algebras $a_1$, $a_2$ and $b_2$.
Adding up contributions from the exchange Witten diagrams and contact Witten diagrams, the final expressions are rather simple.
Indeed, they are related to the  four-point functions of generators in $\mathcal{W}$-algebra in the limit of large central charge.

This paper is organized as follows. In section \ref{s2} we briefly review Toda field theories in $AdS_2$.
In section \ref{s3}, we present in detail the calculation of four-point functions in the $a_1$, $a_2$ and $b_2$ Toda field theories.
Conclusions are given in section \ref{sc}.
Some reduced $\bar D$-functions used in the calculation are collected in appendix \ref{app1}.

\section{Toda field theories in $AdS_2$}\label{s2}
The action of a Toda field theory associated with a finite-dimensional simple Lie algebras $\mathfrak{g}$ of rank $r$ in an Euclidean $AdS_2$ (hyperbolic plane) is given by
\begin{equation}
S_{\mathfrak{g}}=\int d^2x  \sqrt{g}  \Big(
\frac{1}{2}g^{\mu \nu}\partial_\mu \phi \cdot \partial_\nu \phi+V_{\mathfrak{g}}(\phi)
\Big),
\end{equation}
with
\begin{equation}
V_{\mathfrak{g}}(\phi)= \frac{1}{\beta^2}\sum_i^r n_i e^{\beta \alpha_i \cdot \phi}+\frac{1}{2}R Q \cdot\phi,
\end{equation}
where $\alpha_i$ are simple roots of $\mathfrak{g}$ and  $\phi$ is an $r$-component scalar field.
We consider an $AdS_2$ with unit radius. The metric in Poincar\'e coordinates is
\begin{equation}
ds^2=\frac{dx^2+dz^2}{z^2}.
\end{equation}
Then the scalar curvature $R=-2$. In the classical theory if $Q=2\beta^{-1}\rho^{\vee}$
with the dual Weyl vector $\rho^{\vee}$ satisfying
\begin{equation}
\alpha_i \cdot \rho^{\vee}=1,~~~i=1,2,...,r,
\end{equation}
the equations of motion are invariant under the Weyl transformation
\begin{equation}
g_{ab}\rightarrow  e^{2\omega}g_{ab},~~~ \phi\rightarrow \phi-Q \omega.
\end{equation}
Therefore the theory is classically integrable because the flat space theory has a Lax pair.
The vector $Q$ needs to be modified at quantum level \cite{Mansfield:1982sq}.
In this paper we mainly focus on  classical aspects  of the theory so we simply set $Q=2\beta^{-1}\rho^{\vee}$.

The coefficients $n_i$ can be chosen arbitrarily through shifts in the scalar fields. If we require that the potential minimized at $\phi=0$, then
\begin{equation}
\sum_i n_i \alpha_i= 2\rho^{\vee},~~~ \Rightarrow \sum_i n_i \alpha_i\cdot \alpha_j=2,~~~j=1,2,...,r.
\end{equation}
The  mass spectrum can be obtained by calculating the eigenvalues of the matrix $\sum_i n_i\alpha_i^a  \alpha_i^b$.
In the standard holographic dictionary, the mass of a scalar field $\phi_a$ can be expressed as $m^2_a=\Delta_{a}(\Delta_a-1)$ where  $\Delta_{a}$ is the conformal dimension of the boundary operator dual to $\phi_a$.
The spectrum of conformal dimensions   coincides with the set of  exponents plus one or equivalently degrees of fundamental adjoint-invariant polynomials of the corresponding Lie algebra.
The sets of these values are given in Table \ref{dim2}.
\begin{table}[H]
	\begin{center}
\begin{tabular}{ll}
	\hline
Lie algebra	&  Conformal dimensions  \\
	\hline
$a_n$	&  2, 3, ..., $n+1$ \\
	\hline
$b_n$	&  2, 4, ..., $2n$ \\
	\hline
$c_n$ 	&  2, 4, ..., $2n$\\
	\hline
$d_n $	&  2, 4, ..., $2n-2$, $n$ \\
	\hline
$e_6$ 	& 2, 5, 6, 8, 9, 12\\
	\hline
$e_7$	& 2, 6, 8, 12, 14, 18 \\
	\hline
$e_8$ 	& 2, 8, 12, 14, 18, 20, 24, 30\\
	\hline
$f_4$	& 2, 6, 8, 12\\
\hline
$g_4$	& 2, 6 \\
\hline
\end{tabular}
\end{center}
\caption{Spectrums of conformal dimensions in Toda field theories\label{dim2}}
\end{table}

Interestingly, the spins of generators in the $\mathcal{W}$-algebras are also equal to the exponents of the Lie algebras plus one,
which implies that there is a one-to-one correspondence between the boundary operators and generators in the $\mathcal{W}$-algebras.
We will check this conjecture by computing the tree-level four-point correlation functions of boundary operators in the next section.

As some concrete examples, the potentials of Toda field theories with Lie algebras of rank 1 and 2  are given by
\begin{align}
V_{a_1}=&\frac{2}{\beta^2}(e^{\beta\phi}-\beta\phi-1)=\phi^2+\frac{1}{3}\beta\phi^3+\frac{1}{12}\beta^2\phi^4+O\left(\beta ^3\right),\label{va1}\\
V_{a_2}=&\frac{2 }{\beta ^2}(e^{\beta  \phi _1} \cosh (\sqrt{3} \beta  \phi _2)-\beta  \phi _1-1) \label{va2}\nn\\
=&\left(\phi _1^2+3 \phi _2^2\right)+\beta  \left(\frac{\phi _1^3}{3}+3 \phi _2^2 \phi _1\right)+\beta ^2
\left(\frac{\phi _1^4}{12}+\frac{3}{2} \phi _2^2 \phi _1^2+\frac{3 \phi _2^4}{4}\right)+O\left(\beta ^3\right),\\
V_{b_2}=&\frac{1}{5	\beta ^2}(4 e^{\beta  \left(\phi _1+3 \phi _2\right)}+6 e^{\beta  \left(\phi _1-2 \phi _2\right)}-10 \beta  \phi _1-10)\label{vb2}\nn\\
=&\left(\phi _1^2+6 \phi _2^2\right)+\beta  \left(\frac{\phi _1^3}{3}+6 \phi _2^2 \phi _1+2 \phi _2^3\right)+\beta ^2
\left(\frac{\phi _1^4}{12}+3 \phi _2^2 \phi _1^2+2 \phi _2^3 \phi _1+\frac{7 \phi _2^4}{2}\right)+O\left(\beta
^3\right),
\\
V_{g_2}=&\frac{1}{7 \beta ^2}(-14 \beta  \phi _1+9 e^{\beta  \left(\phi _1-5 \phi _2/\sqrt{3}\right)}+5 e^{\beta  \left(\phi _1+3 \sqrt{3} \phi _2\right)})\label{vg2}\nn\\
=&\left(\phi _1^2+15 \phi _2^2\right)+\beta  \left(\frac{\phi _1^3}{3}+15 \phi _2^2 \phi _1+\frac{20 \phi _2^3}{\sqrt{3}}\right)\nn\\&
+\frac{1}{12} \beta ^2 \left(\phi _1^4+90 \phi _2^2 \phi _1^2+80 \sqrt{3} \phi _2^3 \phi _1+305 \phi _2^4\right)+O\left(\beta ^3\right).
\end{align}

\section{Four-point functions in Toda field theories}\label{s3}

\subsection{Witten diagrams in $AdS_2$}
We now briefly review  some basic ingredients of Witten diagrams in $AdS_2$.
 Witten diagrams are Feynman diagrams built from
 bulk-to-bulk propagators and  bulk-to-boundary propagators.
 The  bulk-to-bulk propagator of a scalar with mass $m^2=\Delta(\Delta-1)$  is given by
\begin{equation}
G_\Delta(x_1,z_1,x_2,z_2)=C_{\Delta} u^{-\Delta} {}_2F_{1}(\Delta,\frac{2\Delta}{2},2\Delta ,-\frac{4}{u}),
\end{equation}
where
\begin{equation}
u=\frac{(x_1-x_2)^2+(z_1-z_2)^2}{z_1 z_2},~~~C_{\Delta}=\frac{\Gamma(\Delta)}{2 \sqrt{\pi} \Gamma(\Delta+1/2)}.
\end{equation}
The  bulk-to-boundary propagator is given by
\begin{equation}
K_\Delta(x,x_0,z_0)=C_{\Delta} \left(\frac{z_0}{z_0^2+(x-x_0)^2}\right)^\Delta.
\end{equation}
To get correlation functions for normalized operators whose  two-point functions have unit coefficient, every  external line has to be multiplied by a factor $C_\Delta^{-1/2}$. For instance, an $n$-point contact diagram takes the form
\begin{equation}
W^{\mathrm{contact}}_{\Delta_i}(x_i)=\int \frac{d x_0 d z_0}{z_0^2}  \prod_{i=1}^n  C_{\Delta_i}^{-1/2}  K_{\Delta_i}(x_i,x_1,z_1).
\end{equation}
where $\Delta_i$, $i=1,...,n$, are conformal dimensions of the external operators. The expression for $n=3$ can be found in \cite{Freedman:1998tz}
\begin{equation}\label{3pt}
\begin{split}
&W^{\mathrm{contact}}_{\Delta_1\Delta_2\Delta_3}(x_1,x_2,x_3)\\
=&\prod_{i=1}^3  C_{\Delta_i}^{1/2}
\frac{\sqrt{\pi } \Gamma (\frac{\Delta _1+\Delta _2-\Delta _3}{2})
	\Gamma (\frac{\Delta _1+\Delta _3-\Delta _2}{2})
	\Gamma (\frac{\Delta _2+\Delta _3-\Delta _1}{2})
	\Gamma (\frac{\Delta _1+\Delta _2+\Delta_3-1}{2})}{
	2 \Gamma \left(\Delta _1\right) \Gamma \left(\Delta _2\right) \Gamma \left(\Delta _3\right)
	|x_{12}|^{\Delta _1+\Delta _2-\Delta _3}
	|x_{23}|^{\Delta _2+\Delta _3-\Delta _1}
	|x_{13}|^{\Delta _1+\Delta _3-\Delta _2}},
\end{split}
\end{equation}
where $x_{ij}\equiv x_i-x_j$.

We shall concentrate on tree-level four-point functions in Toda field theories.
The contact Witten diagrams generated by quartic interactions
 can be written in terms of the $D$-functions \cite{Liu:1998ty,DHoker:1999kzh,Dolan:2003hv} defined as
\begin{equation}
D_{\Delta_1\Delta_2\Delta_3\Delta_4}(x_i)=\int \frac{d x_0 d z_0}{z_0^2}  \prod_{i=1}^4 \left(\frac{z_0}{z_0^2+(x_i-x_0)^2}\right)^{\Delta_i}.
\end{equation}
It is convenient to work with the reduced $\bar D$-functions which are functions of the cross-ratio  (not to confuse with the same symbol used for $AdS_2$ coordinate)
\begin{equation}
z=\frac{x_{12}x_{34}}{x_{13}x_{24}}.
\end{equation}
They are defined by extracting a kinematic factor
\begin{equation}
D_{\Delta_1\Delta_2\Delta_3\Delta_4}(x_i)= \frac{\sqrt{\pi} \Gamma(\Sigma -1/2)}{2 \prod_{i=1}^4 \Gamma(\Delta_i) }
\frac{x_{14}^{2(\Sigma-\Delta_1-\Delta_4)}x_{34}^{2(\Sigma-\Delta_3-\Delta_4)}}{x_{13}^{2(\Sigma-\Delta_2)}x_{24}^{2\Delta_2}}
\bar D_{\Delta_1\Delta_2\Delta_3\Delta_4}(z),
\end{equation}
with $\Sigma=\sum_{i=1}^4 \Delta_i/2$. $\bar D$-functions with integer indices can be evaluated recursively by using the identities in \cite{Arutyunov:2002fh}.
 We list some of the $\bar D$-functions in Appendix \ref{app1}.

We also need to consider exchange Witten diagrams mediated by the cubic interactions. An $s$-channel exchange Witten diagram can be written as
\begin{equation}
\begin{split}
W^{s}_{\Delta_1\Delta_2\Delta_3\Delta_4,\Delta_E} (x_i)=&\prod_{i=1}^4  C_{\Delta_i}^{-1/2}\int \frac{d y_1 d w_1}{w_1^2}\frac{d y_2 d w_2}{w_2^2}
 K_{\Delta_1}(x_1,y_1,z_1)K_{\Delta_2}(x_2,y_1,w_1)\\
 &\times G_{\Delta_E}(y_1,w_1,y_2,w_2)K_{\Delta_3}(x_3,y_2,w_2)K_{\Delta_4}(x_4,y_2,w_2).
\end{split}
\end{equation}
where $\Delta _E$ is the conformal dimension of the exchange operator.
In the special case when $k=(\Delta_1+\Delta_2-\Delta_E)/2$ is a positive integer, this diagram can be written as a sum of $D$-functions
\cite{DHoker:1999mqo}
\begin{equation}\label{wtod}
W^{s}_{\Delta_1\Delta_2\Delta_3\Delta_4,\Delta_E} (x_i)=\prod_{i=1}^4  C_{\Delta_i}^{1/2} \sum_{l=1}^{k}
\frac{(\Delta_1)_{-l} (\Delta_2)_{-l}D_{\Delta_1-l\,\Delta_2-l\,\Delta_3\Delta_4}(x_i)}{4(\frac{\Delta_1+\Delta_2-\Delta_E}{2})_{1-l} (\frac{\Delta_1+\Delta_2-1+\Delta_E}{2})_{1-l}x_{12}^{2l}  } .
\end{equation}
where the standard Pochhammer symbol $(a)_b=\Gamma(a+b)/\Gamma(a)$ is used.

\subsection{$a_1$ theory}

We start with the Liouville ($a_1$ Toda) field theory. The potential is given in (\ref{va2}).
The scalar field with $m^2=2$ corresponds to a boundary operator with conformal dimension $\Delta=2$.
The tree-level four-point function receives contributions from a quartic contact diagram and  exchange diagrams in $s$-, $t$- and $u$-channels.
We have
\begin{equation}
\begin{split}
\langle O(x_1)O(x_2)O(x_3)O(x_4)\rangle_{\mathrm{tree}}
=&\beta^2(4W^{s}_{2222,2}+4W^{t}_{2222,2}+4W_{2222,2}^{u}-2 W_{2222}^{\mathrm{contact}})\\
=&\frac{4\beta^2}{9\pi^2}(x_{34}^{-2} D_{2211}+x_{14}^{-2} D_{1221}+x_{24}^{-2} D_{2121}-2 D_{2222})\\
=&\frac{\beta^2}{6\pi x_{13}^{4}x_{24}^{4}}(\bar D_{2211}+\bar D_{1221}+\bar D_{2121}-5 \bar D_{2222}),
\end{split}
\end{equation}
where we have used (\ref{wtod}) to write exchange diagrams in terms of $D$-functions.
Using the explicit  expressions for the $\bar D$-functions  given in Appendix \ref{app1}, we get
\begin{equation}\label{c2222}
\begin{split}
&\bar D_{2211}+\bar D_{1221}+\bar D_{2121}-5 \bar D_{2222}\\
=&\frac{z^3 \log (\left| z\right| )+\left(-z^3+3 z-2\right) \log (\left| 1-z\right| )-z^2+z}{3 (z-1)^2 z^3}\\
&+\frac{(3-z) z^2 \log (\left| z\right| )+(z-1)^3 \log (\left| 1-z\right| )+z^2-z}{3 (z-1)^3 z^2}\\
&+\frac{z^2 (2 z-3) \log (\left| z\right| )-(2 z+1) (z-1)^2 \log (\left| 1-z\right| )+z^2-z}{3 (z-1)^2 z^2}\\
&+\frac{z^3 \left(-2 z^2+5 z-5\right) \log (\left| z\right| )+\left(2 z^2+z+2\right) (z-1)^3 \log (\left| 1-z\right| )+2 z \left(z^3-2 z^2+2 z-1\right)}{3 (z-1)^3 z^3}\\
=& \frac{z^2-z+1}{(z-1)^2 z^2}.
\end{split}
\end{equation}
and thus
\begin{equation}\label{c2222}
\langle O(x_1)O(x_2)O(x_3)O(x_4)\rangle_{\mathrm{tree}}=
\frac{\beta^2}{12\pi}\Big(
\frac{1}{x_{12}^2x_{23}^2x_{34}^2x_{14}^2}+
\frac{1}{x_{13}^2x_{23}^2x_{24}^2x_{14}^2}+
\frac{1}{x_{12}^2x_{24}^2x_{34}^2x_{13}^2}
\Big).
\end{equation}

 This looks like the connected part of a four-point function  of the stress-tensor operators $T$ in the Virasoro algebra up to an overall coefficient,
 although it is a one-dimensional correlation function. Furthermore, the disconnected parts of both four-point functions also take the same form.

Taking into account carefully the overall coefficient,
the central charge $c$ of  Virasoro algebra is related to the $\beta$ by $c = 48\pi \beta^{-2}$ and $O(x)$ corresponds to $-\sqrt{2/c}T(w)$.
This is consistent with tree-level three-point function computing by (\ref{3pt})
\begin{equation}
\langle O(x_1)O(x_2)O(x_3)\rangle_{\mathrm{tree}}
	=-\frac{\beta }{\sqrt{6 \pi }} \frac{1}{x_{12}^2x_{23}^2x_{13}^2}
\sim-\sqrt{\frac{8}{c^3}}\langle T(w_1)T(w_2)T(w_3)\rangle.
\end{equation}

The central charge of Liouville theory in our convention is
\begin{equation}
c_{a_1}=1+ 48 \pi  \left(\frac{\beta }{8 \pi }+\frac{1}{\beta }\right)^2
\end{equation}
In the classical limit $c_{a_1}\rightarrow  48\pi \beta^{-2}$.
One can expect that at the quantum level the central charge $c$ of  Virasoro algebra is equal to the central charge of Liouville theory.
If this conjecture is true,  $n$-point functions beyond tree-level can be obtained from correlation functions of the stress-tensor operators $T(w_i)$.

\subsection{$a_2$ theory}
We now  turn to the $a_2$ theory.
The boundary operators have conformal dimensions $\Delta_1=2$ and $\Delta_2=3$, which are equal to the spins of generators in the
 algebra $\mathcal{W}(2,3)$. The notation $\mathcal{W}(2,s_1,s_2,...)$ means that the algebra is generated by
primary currents $W^{(s_i)}$ of spins $s_i$ together with the Virasoro generator $T$ of spin 2.

The  four-point function of four $O_1$ is the same as (\ref{c2222}). The other independent four-point functions are
\begin{equation}
\begin{split}\label{c2233}
&\langle O_1(x_1)O_1(x_2)O_2(x_3)O_2(x_4)\rangle_{\mathrm{tree}}\\
=&\beta^2(12W^{s}_{2233,2}+36W^{t}_{2233,3}+36W_{2233,3}^{u}-6 W^{\mathrm{contact}}_{2233})\\
=&\frac{16\beta^2}{45\pi^2}(3x_{12}^{-2} D_{1133}+\frac{9}{2}x_{14}^{-2} D_{1232}+\frac{9}{2}x_{24}^{-2} D_{2132}-6 D_{2233})\\
=&\frac{\beta^2}{4 \pi  x_{13}^4 x_{24}^4 x_{34}^2}
(z^{-2}\bar D_{1133}+3\bar D_{1232}+3\bar D_{2132}-7 \bar D_{2222})\\
=&\frac{\beta^2}{8\pi {  x_{13}^4 x_{24}^4 x_{34}^2}} \frac{3 z^2-2 z+2}{  (z-1)^2 z^2}\\
=&\frac{\beta^2}{8\pi}\Big(
\frac{1}{x_{12}^2x_{23}^2x_{34}^4x_{14}^2}+\frac{1}{x_{12}^2x_{24}^2x_{34}^4x_{13}^2}+
\frac{2}{x_{13}^2x_{23}^2x_{24}^2x_{14}^2x_{34}^2}
\Big),
\end{split}
\end{equation}
and
\begin{equation}
\begin{split}\label{c3333}
&\langle O_2(x_1)O_2(x_2)O_2(x_3)O_2(x_4)\rangle_{\mathrm{tree}}\\
=&\beta^2(36W^{s}_{3333,2}+36W^{t}_{3333,2}+36W_{3333,2}^{u}-18 W^{\mathrm{contact}}_{3333})\\
=&\frac{64\beta^2}{225\pi^2}(\frac{45}{8}(x_{34}^{-4} D_{3311}+x_{14}^{-4} D_{1331}+x_{24}^{-4} D_{3131})
+\frac{9}{4}(x_{34}^{-2} D_{3322}+x_{14}^{-2} D_{2332}\\&+x_{24}^{-2} D_{3232})-18 D_{3333})\\
=&\frac{3\beta^2}{40\pi x_{13}^6 x_{24}^6}(5(\bar D_{3311}+\bar D_{1331}+\bar D_{3131})
+7(\bar D_{3322}+\bar D_{2332}+\bar D_{3232})-63 \bar D_{3333})\\
=&\frac{\beta^2}{x_{13}^6 x_{24}^6}\frac{3 \left(10 z^6-30 z^5+29 z^4-8 z^3+29 z^2-30 z+10\right)}{80 \pi  (z-1)^4 z^4}\\
=&\frac{3\beta^2}{80\pi}\Big(
\frac{5}{x_{12}^4x_{23}^2x_{34}^4x_{14}^2}+
\frac{5}{x_{13}^4x_{23}^2x_{24}^4x_{14}^2}+
\frac{5}{x_{12}^4x_{24}^2x_{34}^4x_{13}^2}+
\frac{5}{x_{12}^2x_{23}^4x_{34}^2x_{14}^4}\\&+
\frac{5}{x_{13}^2x_{23}^4x_{24}^2x_{14}^4}+
\frac{5}{x_{12}^2x_{24}^4x_{34}^2x_{13}^4}-\frac{16}{x_{12}^2x_{24}^2x_{34}^2x_{13}^2x_{14}^2x_{23}^2}
\Big).
\end{split}
\end{equation}

Comparing them to the four-point functions in the algebra $\mathcal{W}(2,3)$ \cite{Zamolodchikov:1985wn}
\begin{align}
&\langle T(w_1)T(w_2)W^{(3)}(w_3)W^{(3)}(w_4)\rangle\nn\\
=&{\frac{1} {w_{13}^4 w_{24}^4 w_{34}^2}}\left(\frac{ c^2}{6z^2}+c\left(\frac{2}{z^2}+\frac{3}{(1-z)^2}+\frac{2}{z}+\frac{2}{1-z}\right)\right),\label{w2233}\\[12pt]
&\langle W^{(3)}(w_1)W^{(3)}(w_2)W^{(3)}(w_3)W^{(3)}(w_4)\rangle\nn\\
=&\frac{1}{w_{13}^6 w_{24}^6}\bigg(  \frac{c^2}{9} \left(\frac{1}{z^6}+\frac{1}{(1-z)^6}+1\right)\nn\\&
 +c \left(\frac{2}{z^4}+\frac{2}{(1-z)^4}
 +\frac{2}{z^3}+\frac{2}{(1-z)^3}+\frac{9}{5 z^2}+\frac{9}{5 (1-z)^2}+\frac{8}{5 z}+\frac{8}{5 (1-z)}\right)\nn\\&
+\frac{32}{5} \frac{16 c}{5 c+22} \left(\frac{1}{z^2}+\frac{1}{(1-z)^2}+\frac{2}{z}+\frac{2}{1-z}\right) \bigg),\label{w3333}
\end{align}
one find the tree-level four-point functions (\ref{c2233}) and (\ref{c3333}) correspond to  the order $c$ contributions to (\ref{w2233}) and (\ref{w3333}) respectively.
The disconnected pieces of the four-point functions correspond to the order $c^2$ contributions.
Therefore, we get the expected correspondence.
This  correspondence provides a useful way to obtain higher-point functions, because correlation functions of $\mathcal{W}$-currents and stress-tensor $T$  can be computed by using recursion relations
derived  in \cite{Zamolodchikov:1985wn}.

\subsection{$b_2$ theory}
Finally we consider the $b_2$ theory. The conformal dimensions of the boundary operators are $\Delta_1=2$ and $\Delta_2=4$.
The  tree-level four-point functions are
\begin{align}
&\langle O_1(x_1)O_1(x_2)O_2(x_3)O_2(x_4)\rangle_{\mathrm{tree}}\nn\\
=&\beta^2(24W^{s}_{2244,2}+144W^{t}_{2244,4}+144W_{2244,4}^{u}-12 W^{\mathrm{contact}}_{2244})\nn\\
=&\frac{\beta^2}{6 \pi  x_{13}^4 x_{24}^4 x_{34}^4}
(z^{-2}\bar D_{1144}+6\bar D_{1243}+6\bar D_{1234}-3 \bar D_{2244})\nn\\
=&\frac{\beta^2}{3\pi {  x_{13}^4 x_{24}^4 x_{34}^4}}\frac{2 z^2-z+1}{ (z-1)^2 z^2},\\[12pt]
&\langle O_1(x_1)O_2(x_2)O_2(x_3)O_2(x_4)\rangle_{\mathrm{tree}}\nn\\
=&\beta^2(144W^{s}_{2444,4}+144W^{t}_{2444,4}+144W_{2444,4}^{u}-12 W^{\mathrm{contact}}_{2444})\nn\\
=&\sqrt{\frac{3}{70}} \frac{\beta^2 x_{14}^2}{\pi x_{13}^6 x_{24}^8 x_{34}^2}
\big(3(z^{-2}\bar D_{1344}+\bar D_{1443}+\bar D_{1434})
-\frac{11}{2} \bar D_{2444}\big)\nn\\
=&\sqrt{\frac{3}{70}} \frac{\beta^2 x_{14}^2}{\pi x_{13}^6 x_{24}^8 x_{34}^2} \frac{z^2-z+1}{(z-1)^4 z^2},\\[12pt]
&\langle O_2(x_1)O_2(x_2)O_2(x_3)O_2(x_4)\rangle_{\mathrm{tree}}\nn\\
=&\beta^2(144(W^{s}_{4444,4}+W^{t}_{4444,4}+W_{4444,4}^{u}
+W^{s}_{4444,2}+W^{t}_{4444,2}+W_{4444,2}^{u})
-84 W^{\mathrm{contact}}_{4444})\nn\\
=&
\frac{\beta^2}{\pi x_{13}^8 x_{24}^8}\big(\frac{1}{3}(\bar D_{4411}+\bar D_{1441}+\bar D_{4141})
+\frac{69}{70}(\bar D_{4422}+\bar D_{2442}+\bar D_{4242})\nn\\&
+\frac{33}{35}(\bar D_{4433}+\bar D_{3443}+\bar D_{4343})
-\frac{143}{20} \bar D_{4444}\big)\nn\\
=&\frac{\beta^2}{420 \pi x_{13}^8 x_{24}^8}
\frac{\left(z^2-z+1\right)^2 \left(280 z^6-840 z^5+279 z^4+842 z^3+279 z^2-840 z+280\right)}{  (z-1)^6 z^6},\label{c4444}
\end{align}
together with $\langle O_1(x_1)O_1(x_2)O_1(x_3)O_1(x_4)\rangle_{\mathrm{tree}}$ given by (\ref{c2222}).

As an application of the conjectured correspondence, we now demonstrate how to compute (\ref{c4444}) using recursion relations.
The operator product expansion of two spin-4 currents $W^{(4)}$ in the algebra $\mathcal{W}(2,4)$ can be found in
\cite{Bouwknegt:1988sv,Hamada:1988vw,Zhang:1989iz,Blumenhagen:1990jv,Kausch:1990bn}, and in the large central charge limit we have
\begin{equation}
\begin{split}
W^{(4)}(z)W^{(4)}(w)=&\frac{c/4}{(z-w)^8}+\sum_{k=0}^{5}\frac {12 (k + 1)} {\Gamma (k + 4)} \frac{\partial^k T(w)}{(z-w)^{6-k}}
\\
&+\sum_{k=0}^{3}\frac{72 \sqrt{105} (k+1)_3}{\Gamma (k+8)}\frac{\partial^k W^{(4)}(w)}{(z-w)^{4-k}}+O\left(c^{-1}\right).
\end{split}
\end{equation}
Following similar analysis in \cite{Zamolodchikov:1985wn}, we have the recursion relation
\begin{equation}
\begin{split}
&\langle W^{(4)}(w_1)W^{(4)}(w_2)...W^{(4)}(w_n)\rangle\\
=&
\sum_{i=2}^{n}\frac{c/4}{(w_1-w_2)^8}\langle W^{(4)}(w_2)...W^{(4)}(w_{i-1})W^{(4)}(w_{i+1})...W^{(4)}(w_n)\rangle\\
&
+\sum_{i=2}^{n}\sum_{k=0}^{5}\frac {12 (k + 1)} {\Gamma (k + 4)} \frac{\partial^k_{w_i} }{(w_1-w_i)^{6-k}}
\langle W^{(4)}(w_2)...W^{(4)}(w_{i-1})T(w_i)W^{(4)}(w_{i+1})...W^{(4)}(w_n)\rangle
\\
&+\sum_{i=2}^{n}\sum_{k=0}^{3}\frac{72 \sqrt{105} (k+1)_3}{\Gamma (k+8)}\frac{\partial^k_{w_i}}{(w_1-w_i)^{4-k}}\langle W^{(4)}(w_2)...W^{(4)}(w_n)\rangle
+O\left(c^{n/2-2}\right).
\end{split}
\end{equation}
Using the correspondence $O_1\sim -\sqrt{2/c}T$ and $O_2\sim -\sqrt{4/c}W^{(4)}$, we get
\begin{equation}
\begin{split}\label{r4444}
&\langle O_2(x_1)O_2(x_2)O_2(x_3)O_2(x_4)\rangle_{\mathrm{tree}}\\
=
&
-\sum_{k=0}^{5}\frac{\beta }{\sqrt{6 \pi }}\frac {12 (k + 1)} {\Gamma (k + 4)}
\Big( \frac{\partial^k_{w_2} }{(w_1-w_2)^{6-k}}
\langle O_1(x_2)O_2(x_3)O_2(x_4)\rangle_{\mathrm{tree}}
\\
&+\frac{\partial^k_{w_3} }{(w_1-w_3)^{6-k}}
\langle O_2(x_2)O_1(x_3)O_2(x_4)\rangle_{\mathrm{tree}}+\frac{\partial^k_{w_4} }{(w_1-w_4)^{6-k}}
\langle O_2(x_2)O_2(x_3)O_1(x_4)\rangle_{\mathrm{tree}}\Big)
\\
&-\sum_{i=2}^{4}\sum_{k=0}^{3} \frac{36 \sqrt{35}\beta}{ \sqrt{ \pi }}\frac{ (k+1)_3}{\Gamma (k+8)}\frac{\partial^k_{w_i}}{(w_1-w_i)^{4-k}}
\langle O_2(x_2)O_2(x_3)O_2(x_4)\rangle_{\mathrm{tree}}.
\end{split}
\end{equation}
The three-point functions can be obtained by use of (\ref{3pt})
\begin{align}
&\langle O_1(x_2)O_2(x_3)O_2(x_4)\rangle_{\mathrm{tree}}=-\frac{2\beta}{\sqrt{6 \pi }} \frac{1}{ {  x_{23}^2 x_{24}^2 x_{34}^6}},\\
&\langle O_2(x_2)O_2(x_3)O_2(x_4)\rangle_{\mathrm{tree}}=-\frac{3 \beta }{2 \sqrt{35 \pi }}\frac{1}{ {  x_{23}^4 x_{24}^4 x_{34}^4}}.
\end{align}
Plugging them into (\ref{r4444}) one immediately obtain the expected result (\ref{c4444}).
It is reasonable to expect that higher-point functions can be obtained in the same way.

\section{Conclusions}\label{sc}
In this paper, we have studied the	boundary correlation functions in Toda field theories in $AdS_2$.
We have found a relation between boundary operators and generators  in the $\mathcal{W}$-algebra
 by computing  tree-level four-point functions in some simple Toda field theories.
The  conformal dimensions of boundary operators are equal to the spins of generators in the $\mathcal{W}$-algebra,
and the tree-level four-point functions correspond to the
 connected four-point functions of the $\mathcal{W}$-currents or the stress-tensor in the large central charge.
We  conjecture the correspondence holds at the quantum level.
If rigorously proved, this conjecture will provide useful information about higher-loop and higher-point Witten diagrams in
$AdS_2$.
It would be interesting to extend our study to the supersymmetric  Toda field theories.

\section*{Acknowledgments}
I would like to thank Konstantin Zarembo for motivating me to  work on the topic of this paper and making valuable suggestions.
I also thank Zhibin Li and Jun-Bao Wu for helpful discussions.
This work was supported by the grant ``Exact Results in Gauge and String Theories'' from the Knut and Alice Wallenberg foundation.

redpajama_set_name: RedPajamaArXiv