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Celebrity Wiki
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Rebekah Vardy Wiki, Age, Husband Jamie Vardy, Kids, Net Worth, Bio
On October 11, 2019 Celebrity spouse No Comments
Rebekah Vardy Wiki
Rebekah Vardy is an English Model, Television personality and former Nightclub partner, who is best known for being the Spouse of Jamie Vardy. He is a professional football player currently playing for the England National team and Leicester City as a striker.
Furthermore, the football player began his career in 2007 by playing for Stocksbridge Park Steels and by 2010 he later joined Northern Premier League club F.C. Halifax Town. In 2012, Vardy signed a contract with Leicester City and also helped the team win the championship in 2014.
Moreover, Jamie also made his international debut in 2015 and was selected for the 2018 FIFA World cup.
Recently, Wayne Rooney's wife, Coleen Rooney has claimed that her private data was leaked from Rebekah's Instagram account and she further accused Jamie's wife of passing her personal information to a tabloid newspaper, The Sun. However, Rebekah has denied all the allegations against her.
Rebekah Vardy Family
Jamie Vardy's wife, Rebekah Vardy was born on February 17, 1982, in England, United Kingdom. She is currently 37 years old and belongs to a white Caucasian ethnicity. She is the daughter of Carlos Miranda (Father) but we do not have any details about her mother.
As of education, the former Nightclub partner completed her schooling from a local school in her native and later got graduated with a bachelor's degree.
Rebekah Vardy Husband
The 37-year-old Television personality, Rebekah initially met her then-boyfriend, Jamie Richard Vardy in 2014, while she was working as a nightclub promoter. Eventually, this loving pair started dating and later got married on May 25, 2019, in a lavish wedding ceremony that took place at Peckforton Castle in Cheshire. The couple also welcomed two kids including a daughter named Sofia Vardy and Finley Jaiden Vardy born in 2017.
Rebekah Vardy Career
Jamie Vardy's partner was initially working as a promoter in 2014 before she got married to the footballer. Later she launched V9 Academy in 2015 along with a partner, and it was an annual week-long camp. In 2017, Mrs. Vardy was announced as the Brand Ambassador for Barnardos Campmate IAC.
Rebekah Vardy Net worth
The estimated net income of the reality star is currently under review and will be updated shortly.
Full Name: Rebekah Vardy
Nick Name: Rebekah
DOB: February 17, 1982
Born: England, United Kingdom
Famous for: Former Nightclub Partner, Model, Television star
Education Details
College: Will be updated
School: High School
Physical Statics
Height: 5 feet 7 Inch Tall
Favorites and hobbies
Hobbies: Travelling, Cooking
Favorite Actor: Tom Cruise
Favorite Actress: Jennifer Lawrence
Favorite Destination: Miami
Favorite Food: Italian
Father: Carlos Miranda
Mother: Name not known
Brother: No
Sister: NA
Relatives: NA
Relationships, Affairs, Dating, Husband
Boyfriend: NA
Dating history: Jamie Vardy & Luke Foster (Ex-Spouse)
Husband: Jamie Richard Vardy
Sons: Finlay Jaiden Vardy
Daughters: Sophie Vardy
Net worth: Under review
Twitter Account: Yes
Facebook Account: Yes
Instagram Account: Yes
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Sent my gf a surprise but she's moving. HELP!
I'm having a huge problem right now guys. A few months ago, I pre-ordered a package to be delivered to my girlfriend overseas in Thailand. We met each other through a romance tour service more than a year ago and I've been planning this surprise since then.
After we got together in a relationship, I bought her this awesome statue of a pink elephant which she's been wanting since she was little. I was able to find one online with a very intricate design attached with some precious jewels.
Since the statue was a bit expensive for my budget, I reserved and pre-ordered it until I was able to pay everything off. So, here's my problem now, it's turns out that she's moving to another apartment in a couple of days and the package might arrive a few days afterwards.
The timing could not have been more inappropriate! What do I do guys?? She doesn't know yet where she's moving to exactly since she's still deciding which apartment to choose from so, I'm like a sitting duck here. Guys I really need some advice! I need help! What should I do?
Re: Sent my gf a surprise but she's moving. HELP!
Looks like you are going to have to tell her its on its way.
Sunnysam43 - you have got to be trying a wind-up! Pink elephant!!!
"this weirdo forum troll farang with only 1 post who sends me strange gifts, like a pink elephant which no lady would ever want ever, is actually coming here to visit me, which I never planned for or wanted or thought he could ever afford after sending me all his cash on-line, -how do I move out of my Thai boyfriend's Mom's sister's uncle's tin and aluminum and tarp house real quick, and set up a second apartment, while this ting tong man visit me so I can figure out if I can stand him enough to get some money out of it to pay for my kid by my another husband? Can I harvest his organs or what? help I need help liew liew maak. uhhhhh uhhhhh aiiii ohhh oyyyyyy"


An immersive journey into the New York Public Library with great documentarian Frederick Wiseman.
In his latest captivating endeavour to explore the great American institutions, legendary documentary filmmaker Frederick Wiseman turns his inquisitive eye to the New York Public Library. It encompasses 92 branches throughout Manhattan, the Bronx and Staten Island, and receives 32 million online visitors annually. NYC's beloved institution is an incredible resource of knowledge as well as community support for all the city's inhabitants, no matter their social status or ethnicity.
Wiseman goes behind the scenes to record animated board meetings, talks with guest speakers such as Patti Smith and Elvis Costello, book club events and donors' dinners, as well as the day-to-day activity of lending books. Wiseman's patient, observational style, combined with his deft editing, draws you into this fascinating world. The result is a thought-provoking love letter to a model of inclusion and knowledge sharing, and a topical reminder of the preciousness of libraries everywhere.
Casey Affleck and Michelle Williams shine in this devastating, Oscar-winning drama from Kenneth Lonergan about a man's painful hometown return.
Hope Dickson Leach's hugely impressive first feature about a middle class farming family's crisis, set against the backdrop of the Somerset floods.
Ben Wheatley's (High-Rise, Sightseers) all-guns-blazing bullet opera, starring Brie Larson, Cillian Murphy and Armie Hammer.
Isabelle Huppert gives an unforgettable performance in Paul Verhoeven's provocative thriller about one woman's response to a violent attack.
The inner workings of London's National Gallery are laid bare in this absorbing, forensic examination by revered filmmaker Frederick Wiseman.


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MANCHESTER BASED PARTNER ALEXANDER & CO SCOOPS NATIONAL AWARD
The award celebrates firms that have really helped and stepped up to make a difference to clients and their businesses.
Manchester Based chartered accountants and tax advisors Alexander & Co has been recognised in the work it has undertook this year by being crowned the best tax advisory firm in the UK in the Accountancy Age Resilience Awards.
The national awards, which were open to all UK firms, aims to celebrate those organisations that have genuinely helped to make things easier for clients and businesses during 2020. It recognises those teams and individuals that have gone above and beyond to help with the many challenges clients and co-workers have faced.
Michael McCaw, Editor of Accountancy Age said:
"Given the difficulties faced by businesses and practices throughout the course of this year, new approaches and standards have been placed on accountancy. Leaders have been forced to show their true qualities while teams have needed to collaborate in the most strenuous circumstances.
"In judging the Resilience Awards, the Accountancy Age judging team looked for those individuals and teams that have really helped bring stability and clarity for those they work with in these uncertain times. This year's awards were incredibly competitive, making the judging process arduous – and reflecting an industry that has raised the standards across the board."
John McCaffery, Tax Partner at Alexander & Co said:
"Naturally, we are delighted to win. 2020 has been a tough year for many businesses and this award recognises the lengths the team at Alexander & Co goes to in helping its clients. It is a result of all the hard work the entire team at Alexander & Co has put in this year.
"As we approach 2021, we look forward to assisting clients both new and existing, as Alexander & Co continues to steadily expand our teams across the board"
Over the past five decades, Alexander & Co has earned its reputation as one of the most trusted and dependable business advisors in the region. It provides a wide range of expert services in the fields of accountancy, taxation, corporate finance and business advisory, specialising in helping owner managed businesses.

redpajama_set_name: RedPajamaCommonCrawl


If you are like me I look at the Lactic Acid Face Peel, and really do not want to put that on my face. Well because of that I have put this review off for as long as I could. I committed and I will do it. Ok now the pep talk is over!
The exfoliating properties of lactic acid peel works like magic on your skin, causing your skin to generate new cells faster. This causes the signs of aging, such as wrinkles, crow's feet, fine lines and dark patches, to disappear, and makes you look youthful and attractive!
As we grow older, our skin grows old too and this is evident in the rough texture of the skin. To "bring back" the skin you once had, you can try a lactic acid peel. It exfoliates the skin and helps it regain its smooth and flawless texture!
also says to start with 1 minute to leave it on for the first time, no problem I washed it off.
I immediately checked a dark spot on my face that has been growing. I was told by my mean brothers when I was young to go out in the sun and all my freckles will blend together and I will look tan. No, I did not believe them, but the spot on my face was something that almost looked like it happened. Since my skin is fair, with freckles I burn easy, so I do not spend time in the sun very often. Anyways this spot seemed a lot lighter. My face felt a little strange but I did not have any redness. I believe it works really well.
I cannot use this again for 7 days, so I will keep you updated the next time I use it.
Dr Song Medical is a medical cosmetic laboratory that originally manufactured natural based products for professionals, doctors, and medical facilities. Dr Song Medical products are made in the USA and is FDA compliant and a provider of professional products that focus on natural ingredients.


Enjoy the inspirational words to the A Christmas Creed. These online, free words can be printed and used to create a personalised Christmas Prayer book. Add to your collection of printable prayers which are suitable for different occasions. You will find the words are inspirational, spiritual and joyful which celebrate the Nativity especially for the festive season.
God, born in Bethlehem this night, for me and for the world.


Six to ten seconds. That's the typical amount of time a recruiter spends reviewing a resume. What can you do to make sure your resume stands out in the crowd?
Military resumes offer a unique challenge – generally, they're broad in scope. That's why it's important to tailor your resume to each job. Focus on the future – what job do you want? What skills and experiences are most relevant to that career path? Keep those on the resume and leave off extraneous details. And keep it brief: most resumes should not exceed two pages.
Are you exceptionally detail oriented and work well under pressure? Or maybe you're a big thinker who loves coming up with game-changing ideas. Each of these traits would be part of your personal brand – the way your unique personality and skillset combines to make you a great candidate. If you're struggling to figure out your personal brand, ask a trusted peer or mentor to describe you in three words. You may begin to see similar themes in their responses; you can craft your personal brand from these common ideas!
Example: Delivering project management expertise, along with business analysis and application design, development, and implementation proficiencies to organizations seeking a dynamic, self-motivated professional.
A recruiter or interviewer may not be familiar with military acronyms or phrases.
Instead of this: Deployed in support of OFI as a M249 gunner in a 20-man recon platoon.
Try this: Served in support of Operation Iraqi Freedom as part of a 20-person team tasked with intelligence gathering missions.
When a reviewer skims a resume, hard numbers will always tend to jump out. Use percentages, dollar values, and actual numbers to support your accomplishments.
Instead of this: In charge of operations training across many locations.
Try this: Led 8 team members to develop operations training for 2,000 personnel in 35 separate groups and 3 different locations, increasing operational readiness by 15%.
You can highlight recent and relevant degrees by putting them towards the top of your resume.
Certain citations and awards can help you stand out from other candidates, but a recruiter may not understand their significance without context. Consider tying them to an action.
If a clearance is required for the position, consider highlighting it towards the top of your resume.
Spend time crafting your resume and looking it over. Proofread for spelling or grammatical errors, use consistent grammatical tense (past tense vs. present tense), and use a readable font size that's at least 11 points. Make sure all the different versions of your resume have a consistent timeline of work experiences. Finally, ask a few non-military friends to look over your resume and point out areas they don't quite understand.


Who hasn't secretly wanted to don a cheerleading costume at some point in their life? To do those high kicks, shake those pom poms and attempt to do the splits! You can be a Stag do, a Hen Party or an individual who rocks up to the P.A.R.T.Y, one thing is for sure, this Classic Cheerleader is the way to go to support your dream! Go team!


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Missouri legislature gives bill legalizing industrial hemp final approval
Conservation and Agriculture House Legislature motimesblog.com Policy
JEFFERSON CITY, Mo. — The Missouri General Assembly has voted to give farmers the option of growing another crop.
On Wednesday, the Senate made some technical changes to Rep. Paul Curtman's bill legalizing industrial hemp and passed HB 2034 in a 29-3 vote. Coming back to the lower chamber on Thursday, the House adopted the changes and voted 133-6 in favor of the bill.
"This bill has been four years in the making," said Curtman. "I'm looking forward to getting this out of both chambers and signed by the governor."
Currently 34 states, including Nebraska, Illinois, Kentucky, Tennessee, and Arkansas — five of the eight states that border Missouri — allow the cultivation of hemp for commercial, research, or pilot programs.
The bill authorizes a pilot program in Missouri for hemp — as outlined in the 2014 U.S. Farm Bill. Farmers would be required to undergo a background check, obtain a permit from the Department of Agriculture, and submit to random testing of the crop.
Hemp production would be limited to 2,000 acres statewide and to 10 acres to 40 acres per farmer — unless for research purposes.
"I think it's a shame to pass it, [we] needed to put in so many limiting restrictions," said Rep. Deb Lavender. "I'm concerned about who gets to have a license, where they get to plant…who is going to get the opportunity. I'm just concerned with licenses fees, backgrounds check, we are already selecting who gets to win at this game."
Hemp and marijuana come from the same cannabis species, Cannabis sativa, but are from different subspecies making them scientifically and genetically different. Industrial hemp — which has less than .3 percent THC — is non-psychoactive, which means it is unable to intoxicate the user, and specially bred for fiber and oil use.
The close relationship between hemp and marijuana has resulted in some pushback previously. During a Senate hearing, a retired state trooper argued the bill would legalize marijuana because law enforcement wouldn't be able to tell the plants apart.
Backers of the bill argue that the cultivation of hemp will keep Missouri's economic dollars in the state and be a boon for farmers.
The product can be used in an estimated 25,000 products, according to the Congressional Research Service, including rope, clothes, food, paper, textiles, plastics, insulation, biofuel, and concrete.
"Right now, we have manufacturers who currently have to import industrial hemp from out of the state, sometimes from out of the country," Curtman said.
"There is a paper manufacturer in west central Missouri who uses hemp in the manufacturing of their paper," said Curtman. "There are restaurants around the state that use byproducts of industrial hemp."
This legislation will enable those businesses to purchase the product from Missouri farmers instead of importing hemp, in turning keeping economic dollars in the state, according to supporters.
Tagged in : industrial hemp Rep. Paul Curtman
Vote pushed back on SJR 39, support not there yet
Casas retains passion for policy
Dairy industry hopes to see growth after bill sent to governor
Previous Previous post: Clean Missouri submits 346K signatures for initiative petition dealing with ethical issues in legislature
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Vespa alsatica är en getingart som beskrevs av Erber 1867. Vespa alsatica ingår i släktet bålgetingar, och familjen getingar. Inga underarter finns listade i Catalogue of Life.

Källor

Bålgetingar
alsatica

redpajama_set_name: RedPajamaWikipedia


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The Eagle's 2010 All-Metro baseball team | The Wichita Eagle
Eagle+ Sign In
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The Eagle's 2010 All-Metro baseball team
This is the sixth year for All-Metro teams selected by The Eagle, recognizing the best high school athletes in team sports throughout Sedgwick, Butler and Harvey counties.
The selection process
In May, Eagle high school beat writers Joanna Chadwick and Chris Elliott sent nomination ballots to all baseball coaches at the 38 high schools in Sedgwick, Butler and Harvey counties.
Coaches were asked to return the ballots with nominations of the best players within those counties that they saw this season, including their own players.
Bob Arens
Senior catcher
Arens, a Wichita State signee, led Northwest in hits (34), doubles (10), and homers (4). His .472 batting average was also a team-high for a squad that always seemed to be in the position to drive runs in.
Jason Axtell
Andover Central
Senior outfielder
Axtell seemed to want to be a prime-time performer for Andover Central. He entered the team's regional hitting .485 and came out of with a .514 batting average and a Class 5A tournament appearance. He went into the state tournament with 30 runs and 16 RBIs.
Nolan Barrientos
Bishop Carroll
Sophomore third baseman
It would be hard for anyone to stand out on a squad that hit .399, but Barrientos did. He hit .514 for the Eagles and scored 36 runs. He was second on the team with 29 RBIs and showed discipline at the plate by drawing 14 walks and striking out seven times in 70 plate appearances.
Gage Byers
Junior pitcher
Maize's junior ace combined power and command to put together a dominant season (0.95 ERA, 8-0 record). Byers kept batters off-balance all year with a fastball with movement and changeup that he liked to work on the outside corners. He led a deep Maize pitching staff to the Class 6A championship game.
Timmy Chadd
Senior first baseman
Chadd was a staple in the lineup for a bat-heavy Carroll squad that had a reputation for scoring. Chadd drove in 24 runs for the Golden Eagles and was a key cog in the team's 22-win season and appearance in the Class 5A title game. He had a .384 batting average and showed the ability to dig balls out of the dirt at first.
Ethan Chadick
Senior pitcher
The Grizzlies got off to the hottest start in the area as they were 11-0 heading into their City League showdown against Carroll. Chadick was a huge part of that success. He had an ERA under 1.00 at the halfway point . He remained a constant, and finished 7-1 record as a starter with a 2.04 ERA.
Tyler Coughenour
Senior shortstop
Coughenour had a monster offensive season. The senior slugger had a .695 batting average, got on base 77 percent of the time and had a 1.390 slugging percentage. The Wichita State signee blasted eight homers and 13 doubles as Collegiate finished 19-2.
Johnston helped Andover Central reach the Class 5A tournament with a good bat (.545 average, .864 slugging percentage). Johnston's 36 RBIs and 10 stolen bases for the Jaguars didn't hurt, either. The senior outfielder was also able to cover plenty of territory.
Conner Knight
Junior utility player
Knight hit .424 with 24 RBIs. He ran down balls in the outfield, and on the mound he doubled up on starting and relief duties. Knight had five wins and led the team with three saves.
Storm Marlar
Marlar hit .514 for the Railroaders with 29 RBIs, four triples and nine stolen bases. His team also benefited from his contributions on the mound. Marlar was 6-1 as a starter and had a 1.50 ERA.
Alec Meier
Alec Meier blossomed during his junior season on the mound for Campus. Playing for a young team that fluctuated around the .500 mark for most of the season, Meier was a constant. He was 9-1 with a 3.43 ERA for an 11-win team with 53 strikeouts in 57 innings of work.
Zach Nielsen
Senior designated hitter
The Golden Eagles power hitter had 19 RBIs, two home runs and two doubles even after starting the first half of the season limping around the bases. He was also the team's No. 1 pitcher, going 6-1 with a 2.94 ERA.
Austin White
Sophomore second baseman
His .395 batting average was second on the team and at the top of the lineup he always seemed to get in position to score. He led the team with 29 runs. White had a team-leading nine stolen bases.
Charlie Ebright
Losing nine seniors from his successful 2009 team didn't seem to affect the Eagles' success. He led a sophomore- and junior-heavy team to win the City League Championship and earn a No. 1 seed in its regional. Carroll cruised all the way to the Class 5A title game, where it lost 4-3 to Topeka Seaman.
All Metro Baseball Team
See the moment a Kansas coach loses his cool over ice bath
Campus holds off Newton's late comeback and picks up road victory
MLB's top draft pick Adley Rutschman will be in Wichita as finalist for catcher award
By Taylor Eldridge
The Greater Wichita Sports Banquet is Thursday, June 27 and will award the Buster Posey Award to the nation's top college baseball catcher with 2019 MLB No. 1 pick Adley Rutschman (Orioles) as the favorite.
Wichita's Trinity Academy soars to 4A title at rain-delayed boys state golf tourney
Varsity Soccer
Blue Valley West wins third straight Class 6A state soccer championship
Bishop Carroll loses in state softball title game to Shawnee Heights
Campus High baseball tops Lawrence Free State for state crown
Bishop Carroll claims its first-ever girls swimming state championship
Shockers make good show of it at KU Relays, Wichita high schools have a quiet meet


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Negative Effect of Immediate Sunitinib Interruption on Survival in Patients With Metastatic Renal Cell Carcinoma.
Treatment modification due to adverse events reduces the dose intensity in cancer treatment. The prognostic impact of sunitinib treatment interruption within the initial period of therapy for metastatic renal cell carcinoma (mRCC) remains unknown.
We retrospectively evaluated 97 patients with mRCC treated with first-line sunitinib treatment. The patients were classified into two groups according to the presence of treatment interruption (TI) within the initial two cycles. The prognostic impact of TI was analyzed using the Kaplan-Meier method and log-rank test, and multivariate analyses using the Cox proportional hazard model.
Thirty-eight patients (39.2%) experienced an immediate TI. The median progression-free (PFS) and overall (OS) survival were significantly shorter in patients with a TI than in those without (PFS= 6.54 vs. 11.3 months, p=0.0246; OS=16.9 vs. 30.0 months, p=0.0420). Multivariate analyses for PFS and OS showed that TI was an independent factor predicting poorer PFS (hazard ratio(HR)=1.93, p=0.0141) and OS (HR=2.09, p=0.0102). In addition, the relative dose intensity within the initial two cycles was significantly lower in patients with a TI than in those without (52.7% vs. 75.0%, p<0.0001).
This study showed the significantly negative effect of immediate TI on survival of patients under sunitinib treatment for mRCC. Therefore, the careful monitoring of patient tolerability is required in order to maintain therapeutic efficacy in the early phase of sunitinib treatment.
In vivo (Athens, Greece). 0000 Jan [Epub]
Ryo Ishiyama, Hiroki Ishihara, Tsunenori Kondo, Toshio Takagi, Kazuhiko Yoshida, Junpei Iizuka, Hirohito Kobayashi, Masayoshi Okumi, Hideki Ishida, Kazunari Tanabe
Department of Urology, Tokyo Women's Medical University, Tokyo, Japan., Department of Urology, Tokyo Women's Medical University, Tokyo, Japan ., Department of Urology, Tokyo Women's Medical University Medical Center East, Tokyo, Japan.
PubMed http://www.ncbi.nlm.nih.gov/pubmed/31662551


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Home » Interview List
Brenda Safford
College Administrator, Director of Multicultural Affairs
They told me, 'You should go to college,' and at that point I was 38. So thought, 'It is over for me, I can't, are you crazy? I can't go to school now.' And they said, 'Why not?' And that is how I began my educational journey as a late learner, an adult learner.
Brenda Safford was born on August 5, 1956 in Lubbock, Texas. Moving to Worcester with her second husband, Brenda worked within the community and became an adult learner at the age of 38, receiving both her Bachelor's Degree and Master's Degree in Human Services. Brenda is currently the director of Multicultural Affairs at Assumption College. In this interview, Brenda speaks about her days growing up in Lubbock, Texas, and her experiences with both racial segregation and integration in her school system. She speaks of the personal challenges she faced becoming an adult learner, and going to college at a time when she felt her opportunity to do so had been missed. Brenda also reflects life lessons that she has collected along the way from influential women in her life and from times of celebration, grief, revelation, and defining moments of spirituality. Brenda offers advice to future generations of women and emphasizes the true importance of knowing and believing in one's self.
Hannah Brencher
Safford_Brenda_wwohp1edit.pdf
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\section*{Introduction}
The cryptocurrency market has grown rapidly since the creation of bitcoin in 2008.  From initially being comprised of a single cryptocurrency, by 2022 there were over 10,000 active cryptocurrencies with a combined market capitalization near 2 trillion USD \cite{explodingtopics}.  Cryptocurrencies have become a popular speculative investment, leading to a proliferation of exchanges where cryptocurrencies are actively traded 24 hours a day, seven days a week \cite{exchanges}.  Unlike more traditional asset classes such as stocks, the value of cryptocurrencies are not primarily driven by concrete measures such as earnings.  Instead, their value is driven mainly by public sentiment and the perception of future price movements.  This leads one to ask to what extent can  future cryptocurrency returns be predicted and what type of data is suitable for such predictions.

Cryptocurrency markets are highly volatile and can have extreme reactions to external events.  This is especially true of cryptocurrencies with small market capitalizations, commonly referred to as \emph{alt-coins}.  One famous example of an alt-coin reacting to external events is dogecoin.  This is an alt-coin initially created as a way to mock the speculative nature of cryptocurrenices.  Nevertheless, it was able to reach a market capitalization of 50 billion USD in 2021 \cite{doge}.  Elon Musk, the founder of Tesla Motors, took an interest in dogecoin and on Twitter he would often post humorous messages, known as tweets, about it.  The price of dogecoin would often fluctuate wildly in response to Musk's tweets \cite{ante2021elon}.

While dogecoin is an extreme case, it does illustrate the potential for social media to predict the future performance of cryptocurrencies, especially alt-coins.  Social media can capture the sentiment and general level of engagement of a population towards a variety of topics.  Cryptocurrencies are no exception to this, and in principle a positive sentiment or high level of engagement can lead to positive future returns.  This was demonstrated in \cite{steinert2018predicting} where it was found that short-term returns of alt-coins could be predicted using activity and sentiment from Twitter.  A relationship between social media sentiment and short-term bitcoin returns was found in \cite{garcia2015social}.   In the context of social media manipulation, \cite{nghiem2021detecting} found that alt-coins were often exploited by coordinated ``pump and dump'' schemes orchestrated by fraudulent groups.  These are schemes where artificial social media activity is used to created excitement for an alt-coin and pump up the price, after which the perpetrators of the scheme sell the alt-coin before the price dumps down to extremely low levels.  Whether genuine or artificial, it does appear that social media activity can tell us something about the future performance of a cryptocurrency.

The power of social media to predict financial performance has been demonstrated outside of cryptocurrencies.  It has been shown that the volume of social media posts about a film are predictive of its ticket sales \cite{asur2010predicting}.  In traditional finance, there are many works that use social media data to predict the prices of stocks \cite{bollen2011twitter,zhang2011predicting,sprenger2014tweets,mittal2012stock,rao2012analyzing,si2013exploiting, sul2017trading, bartov2018can, oliveira2017impact }.   These works often utilize the sentiment of social media posts in addition to their volume.

Many approaches attempting to predict financial performance using social media rely upon the volume as a predictive feature.  This reasonable  if one has access to all relevant social media posts.  However, many times one faces data limitations and only has access to a sample of the posts.  In this case the volume feature will be censored and one cannot gauge its true value.  Even if one has access to all posts, the data demands of the volume feature can be high.  Consider the daily tweet volume on Twitter for different cryptocurrenices in Figure \ref{fig:tweets}.  The daily number of tweets varies from  10  to 100,000.  To construct the volume feature, an excessive number of posts must be collected for popular cryptocurrencies.  If one reached a data collection limit, one might mistakenly conclude that the volume was equivalent for extremely popular and less popular cryptocurrencies.

\begin{figure}[h]

			\centering
		\includegraphics[scale = 0.25]{figures/tweets_time2.pdf}
		\caption{Daily tweet volume for select cryptocurrencies over time. }
		\label{fig:tweets}

\end{figure}

Sentiment is another dimension of social media data used to predict financial performance.  Conventional approaches analyze the text to measure the sentiment of a social media post.  However,the  language used on social media can evolve rapidly and may not be understood by sentiment analysis tools.  This can include hashtags created by users in the online cryptocurrency community, such as \#buythedip or \#hodl, both of which express positive sentiment, but may not be comprehensible to sentiment analysis tools which are not trained on cryptocurrency social media data. Other times, social media posts contain no text at all and instead are just images.  These ``memes'' as they are commonly known, contain strong sentiment signals which cannot be extracted by text analysis.

Instead of volume or text based sentiment, a more useful social media signal can be obtained from the level of engagement from the followers of social media users.  Many social media platforms have network structures, where users have followers who are able to see their posts.  These followers can then show their engagement with the topic of the post by interacting with it in different ways.  For instance, in Twitter, one interaction is called liking, where a user clicks on a post to signal that they like it.  Interaction counts are a good way to gauge the engagement of users with a topic on social media.  First, they are language agnostic.  If a post is simply an image, or a cryptic hashtag, the interaction count can be measured.  Second, they are not subject to data limitations.  If a post receives an incredibly large number of interactions, this value can be easily measured, no matter how large.  This is in contrast to social media volume, where one must collect all posts about a topic.

\subsection*{Our Contributions}

In this work we propose a generative model for social media engagement for different topics based on the  interaction counts of relevant social media posts.  A key element of this model is the \emph{engagement coefficient} for a topic, which measures how engaged social media users are with posts about the topic. This model is language agnostic and not vulnerable to data collection limitations.  We derive closed form expressions for the engagement parameter maximum likelihood estimates.  We then apply this model to cryptocurrencies.  We collect price histories and social media posts for all alt-coins created between 2019 and 2022 with sufficiently high fund-raising goals.  In total our dataset contains over 1.36 million tweets for 48 different alt-coins.  We estimate the engagement coefficient for these alt-coins and analyze their relationship with future returns.  We find that returns are low if the engagement coefficient is too low or too high.  Too low indicates lack of engagement, while too high suggests artificial engagement from artificial accounts, known as bots.  We analyze the prevalence of bot posts for each cryptocurrency and find that a higher prevalence is associated with lower future returns.  We find that investment strategies based on the engagement coefficients can achieve significant short-term returns (one month), but are less effective for long-term returns (one year).  {We provide the dataset used in this study in the Supporting Information (S1 Data)}.

\section*{Materials and Methods}

\subsection*{Social Media Engagement Model}\label{sec:model}
We consider a topic or item $c$ that has some quantifiable performance metric.  For instance, $c$ could be a movie and the metric is ticket sales, or $c$ could be a politician and the metric is votes received in an election.  In this work we will assume $c$ is a cryptocurrency and the performance metric is future returns.  We assume that if there is a great deal of excitement and enthusiasm for the topic, then in the future its performance metric will increase.  For instance, if people are excited about a new cryptocurrency, this will lead them purchase it, which will increase its price and future returns. We capture this excitement for the topic with a latent engagement coefficient $\alpha_c$.
If the current excitement for the topic affects the performance metric in the future, then one can in principle use the engagement coefficient to predict these future values.

To predict future performance using the engagement coefficient, we need data  where people manifest their excitement for a topic in some measurable manner before the future performance metrics are realized.  We can then use this data to estimate $\alpha_c$, and in turn use $\alpha_c$ to predict future performance.  Social media platforms allow individuals to show such excitement.  For instance, consider Twitter, a large social media platform.  A Twitter user can post a tweet discussing a topic.  Once this tweet is posted, it becomes visible to the {followers} of this user. The followers can show their excitement for the topic by interacting with the tweet.  There are three different ways Twitter users can interact with a tweet.  First, they can \emph{like} the tweet by clicking the like button on the tweet.  Second, they can \emph{retweet} the tweet by clicking the retweet button on the retweet.  Third, they can post a \emph{reply} to the original tweet.  Liking will only change the like count visible on the tweet.  Retweeting will post the original tweet on the retweeting user's Twitter timeline, making it visible to their own followers.  Replies are tweets, and so will also be visible to the replying user's followers.

One important factor to consider with interaction counts is the follower count of the posting users.  Generally, users with more followers will receive more interactions, as the bulk of these come from followers.  Therefore, interaction counts are more useful if they are normalized by the follower count of the posting user.  Then one can view engagement with a topic as the fraction of followers who interact with posts about it.  This way we can define a uniform measure of engagement which is not sensitive to follower count.  Normalizing by follower count has been used in previous works trying to forecast the reach of social media posts on Twitter \cite{zaman2014bayesian}.

We assume that the number of interactions a tweet receives will be higher if the tweet is about a topic with a larger engagement coefficient.  Naturally, if people are more excited about a topic, this should increase the probability that they will interact with a tweet about the topic.  Therefore, we can use social media data on interactions with tweets to estimate engagement coefficients for different topics.

\subsection*{Model Specification}
We now present a generative model for social media interactions about a topic based on its latent engagement coefficient.  For simplicity, we assume the social media platform is Twitter.  However, the model can easily be generalized to other social media platforms with different interaction types.

We consider a set $\mathcal C$ of topics.  For each topic $c\in\mathcal C$, we associate an engagement coefficient $\alpha_c\geq 0$.  We observe a set $\mathcal U$ of social media users .  Each user $u\in\mathcal U$ has a follower count $f_u\geq 0$.  These followers are able to see tweets posted by $u$ and interact with them.  We assume there is a discrete set $\mathcal I$ of interactions that can be performed on a tweet.  For each interaction $i\in\mathcal I$ we associate an interaction coefficient $\beta_i\geq 0$ which quantifies the effort needed to perform the interaction.  For instance, in Twitter, liking has a relatively low effort, as it only requires clicking a button.

Each user $u$ has $m_{cu}$ tweets about topic $c$.  Tweet $k$ by user $u$ for topic $c$ has $n_{cuik}$ type $i$ interactions.  We assume that $n_{cuik}$ is a Poisson random variable with mean $\mu_{cui}$ given by
\[
\mu_{cui} = \beta_i\alpha_cf_u
\]
Our specification assumes the mean number of interactions scales linearly with the follower count of the user.  Generally, the interactions on a user's tweet come from their followers, and users with more followers have higher mean interaction counts.  From our specification we also see that a higher engagement coefficient and a higher interaction coefficient  will lead to a higher mean interaction count.

Our dataset consists of interaction counts for a set of tweets from multiple users about multiple topics.  We denote this dataset as $\mathbf n =\curly{n_{cuik}}_{k = 1,c\in\mathcal C,u\in\mathcal U, i \in\mathcal I}^{m_{cu}}$.  We define the set of engagement coefficients as $\alpha = \curly{\alpha_c}_{c\in\mathcal C}$ and the set of interaction coefficients as $\beta = \curly{\beta_i}_{i\in\mathcal I}$.  With this notation,  the log-likelihood of the dataset is
\[
L(\alpha,\beta|\mathbf n) = \sum_{c\in\mathcal C}\sum_{u\in\mathcal U}\sum_{i\in\mathcal I}\sum_{k=1}^{m_{cu}}\paranth{-\mu_{cui} + n_{cuik}\log(\mu_{cui}) - \log(n_{cuik}!)}.
\]
To simplify notation, we make the following definitions for the total interactions and the total interactions for a topic, a (user, topic) pair, a (user,topic,interaction) triplet, and a single interaction:
\begin{align*}
	n &=\sum_{c\in\mathcal C}\sum_{i\in\mathcal I}\sum_{u\in\mathcal U} \sum_{k=1}^{m_{cu}}n_{cuik}\\
	n_{c} &=\sum_{i\in\mathcal I}\sum_{u\in\mathcal U} \sum_{k=1}^{m_{cu}}n_{cuik}\\
	n_{cu} &= \sum_{i\in\mathcal I}\sum_{k=1}^{m_{cu}}n_{cuik}\\
	n_{cui} &= \sum_{k=1}^{m_{cu}}n_{cuik}\\
	l_{i} &=\sum_{c\in\mathcal C}\sum_{u\in\mathcal U} \sum_{k=1}^{m_{cu}}n_{cuik}.
\end{align*}
We also define the maximum number of follower interactions for a single interaction type for the tweets posted about a topic $c$ as
\begin{align*}
	v_{c} & = \sum_{u\in\mathcal U}m_{cu}f_u.
\end{align*}
For a single interaction type, if all followers of the users in $\mathcal U$ performed this interaction with all of their tweets about topic $c$, the total number of interactions would be $v_c$.

With this notation we can rewrite the log-likelihood as
\[
L(\alpha,\beta|\mathbf n) = -\sum_{c\in\mathcal C}\alpha_cv_c\paranth{\sum_{i\in\mathcal I}\beta_i} +
\sum_{c\in\mathcal C}n_{c}\log(\alpha_c) +
\sum_{i\in\mathcal I}l_{i}\log(\beta_i) +C.
\]
Above, we put all terms not dependent on the model parameters into the constant $C$.

To fit the model we use maximum likelihood (ML) estimation.  The gradients of the log-likelihood for each parameter are set to zero and then this system of equations is solved to obtain the model parameters.  However, in the model's current form, there are multiple solutions.  For instance, we can multiply the $\alpha_c$'s by a positive constant and divide the $\beta_i$'s by the same constant, and have an equivalent model.  To obtain a unique solution, we fix the value of one of the interaction coefficients.  Without loss of generality, we set $\beta_1=1$ for interaction type one.  Then, we obtain the following closed form solutions for the parameter ML estimates, with a detailed derivation provided in the Supporting Information (S2 Appendix):
\begin{align}
	\widehat{\alpha}_c &= \frac{n_cn}{v_cl_1}, ~c\in \mathcal C\label{eq:alpha}\\
	\widehat{\beta_i} &= \frac{l_i}{l_1}, ~i\in \mathcal I.\label{eq:beta}
\end{align}
If we consider the case of a single interaction type, the ML solution becomes very easy to interpret.  To obtain a unique solution, we do not include any interaction coefficients and set $\mu_{cu} = \alpha_cf_u$.   The ML solution is
\begin{align*}
	\widehat{\alpha}_c &= \frac{n_c}{v_c},~ c\in \mathcal C.\label{eq:alpha_1}
\end{align*}
We see from this solution that the engagement coefficient is simply the ratio of the number of interactions divided by the maximum possible follower interactions for the topic.  Essentially, it captures the fraction of followers that interact with posts about the topic.  If all interactions only came from followers, the engagement coefficient would have a maximum value of one.  In reality, non-followers can also interact with the posts, so the value can exceed one.  However, we will see that typically the value is much less than one.

\subsection*{Performance Data}
In this study we consider cryptocurrencies created between 2019 and 2021.  There are different ways that cryptocurrencies are created and initially offered for sale.   An initial coin offering (ICO) involves a company's sale of a coin, app, or service in order to raise funds for the continuation of the underlying project. In most cases, the company sets a fixed fundraising goal and a fixed supply of the coin. More recent variations include a dynamic price and supply based on the public's interest. An initial exchange offering (IEO), on the other hand, involves launching the coin directly on a centralized exchange. The projects are carefully examined and vetted before the launch, reducing the risk of scam and fraud often found in ICOs. Finally, an initial decentralized exchange offering (IDO) involves the listing on a decentralized exchange instead of a centralized one. IDOs also differ from IEOs since they tend to have a lower review time as well as lower listing costs.

For this study we considered  cryptocurrencies created between 2019 and 2021.  The creation date of a cryptocurrency will refer to its initial offering date.  We only considered cryptocurrencies with an ICO, IEO, or IDO whose fundraising goal was 1 million USD or higher.  We used this fundraising threshold in order to focus on coins which could potentially have large market capitalizations.  We fetched the initial offering data from the website CoinMarketCap \cite{coinmarketcap}. Figure \ref{fig:offerings} shows the number of coins created each month.  We see that the majority of the coins were created in 2021.  In total we have 48 coins in the 2019-2021 time period.   We provide the complete list of the cryptocurrencies and their initial offering dates in the Supporting Information (S3 Table).  For each of the cryptocurrencies meeting our fundraising threshold, we also collected the daily price data between the initial offering date to one year after from CoinGecko \cite{coingecko}. The performance metric for the cryptocurrencies that we consider is their price returns.

\begin{figure}[h]
	\centering
		\includegraphics[scale = 0.5]{figures/figure_creation_dates.pdf}
		\caption{The number of cryptocurrencies in our dataset created each month between 2019 and 2021. }
		\label{fig:offerings}
\end{figure}

\subsection*{Social Media Data}
We collected social media data about the cryptocurrencies from  Twitter.  For each cryptocurrency, we used a historical search via the Twitter API \cite{twitterapi} to collect all tweets containing the \emph{powertag} of the cryptocurrency that were posted between its creation date to one month after.  A powertag is a dollar sign followed by the ticker symbol for the cryptocurrency.  Powertags are a common way people mention cryptocurrencies on Twitter. Examples of powertags include \$BTC for bitcoin, \$ETH for ethereum, and \$CAKE for cake.   We chose one month as the time period for which we collect social media data because this is a reasonable amount of time to gauge the engagement of users with the cryptocurrency.  In practice, one would estimate the engagement parameter with this one month of data, and then make an investment decision about the cryptocurrency.

In addition to tweets,  we also collected  the Twitter profiles for each user in our dataset.  From the profiles we were able to obtain the follower count of the users, which is necessary to fit our model for the engagement coefficient.  In total, our dataset contained 1.36 million tweets from {129,071} unique users.    Detailed statistics of the social media dataset are provided in the Supporting Information (S3 Table).

\section*{Results}
For each cryptocurrency, we have social media posts from the first month of its existence. The cryptocurrencies were created at different points in time, which allows for different ways to estimate the engagement model.  First, we do a completely in-sample estimation using all of the social media data.  This means that engagement coefficients for some cryptocurrencies will be estimated using future data.  Second, we estimate  the model separately for each cryptocurrency using only data available when it has existed for one month.  Estimating the model in this manner, which we refer to as prior data estimation, avoids any look-ahead bias.  In practice, an investor would estimate the model in this manner.  After estimating the model, we  analyze the relationship between the engagement coefficients of the cryptocurrencies and their  future returns.

\subsection*{Model Estimation}
We apply equation \eqref{eq:alpha} to all the Twitter data collected for the cryptocurrencies to obtain the in-sample model parameter ML estimates.  The resulting engagement coefficients are shown in Figure \ref{fig:alphas} and the interaction coefficients are listed in Table \ref{table:interaction_parameter}. From the figure we that see the engagement coefficients span several orders of magnitude, ranging from $5\times10^{-6}$ up to $1.7\times10^{-2}$, and 43 of the 48  cryptocurrencies have engagement parameters in the narrower $10^{-3}$ to $10^{-5}$ range.  There are two cryptocurrencies with engagement parameters greater than $10^{-3}$: krypto, and  safebtc. The lower range has mpt, palg, and cspr with engagement coefficients less than $10^{-5}$.

We plot the engagement coefficients of the cryptocurrencies versus their creation date in Figure \ref{fig:alphas_date} to show an interesting temporal relationship.  Cryptocurrencies created prior to 2021 have engagement coefficients almost entirely in the  $10^{-4}$ to $10^{-3}$ range.  In contrast, after 2021, the engagement coefficients shows a larger variation, with many cryptocurrencies in the lower range of $10^{-5}$ to  $10^{-4}$.  The majority of the cryptocurrencies were created in 2021, and from this we see that many of them had low engagement.   Also, in 2021 we see two cryptocurrencies (krypto and safebtc) with engagement coefficients greater than $10^{-3}$, and three below $10^{-5}$ (mpt, palg, and cspr).

The estimated interaction coefficients are shown in Table \ref{table:interaction_parameter}.  Our model specification fixes the liking coefficient to one.  The retweet coefficient is 0.31, indicating that retweets are one third as common as likes.  Replying has an interaction coefficient of 0.19, making it the least common interaction.  These values align with what is expected, as retweeting and replying require more effort than liking, an liking requires the most effort because one must write a reply tweet.

\begin{figure}[h]

			\centering
		\includegraphics[scale=0.44]{figures/figure_1_alpha.pdf}
		\caption{Plot of the in-sample estimated engagement coefficients.}

\label{fig:alphas}
\end{figure}

\begin{figure}[h]
		\centering
		\includegraphics[scale=0.44]{figures/figure_alpha_date.pdf}
		\caption{Plot of the cryptocurrency engagement coefficients versus creation date.}
\label{fig:alphas_date}
\end{figure}

\begin{table}[ht]
	\centering
	{%
		\begin{tabular}{|l|c|}
			\hline
			Interaction     & Interaction coefficient\\ \hline
			Liking & 1.00\\\hline
			Retweeting & 0.31\\\hline
			Replying & 0.19\\\hline
			\hline
		\end{tabular}%
	}
	\caption{Interaction coefficients estimated using all data.  Note that the interaction coefficient for liking is set equal to one.}
\label{table:interaction_parameter}
\end{table}

If one were to use the engagement coefficients to make investment decisions for cryptocurrencies, then data from the future could not be used to estimate the coefficients.   To simulate this scenario, we estimate the engagement coefficients for each cryptocurrency using only data available one month after the creation date.  This includes data for the cryptocurrency in question along with any other cryptocurrencies created before it.  In this way, the estimated engagement coefficients can be used for investment decisions.  This approach has a separate estimation performed for each cryptocurrency.  We find that the engagement coefficients for each method are nearly equal.  The mean absolute percent error  between the engagement coefficients estimated using both methods is 1.3\%, with a maximum absolute percent error of 3.4\%.  Therefore, we see that the model estimates for the engagement coefficients are robust to the data used.

\subsection*{Engagement Coefficient and Returns}
Now that we have estimated the engagement coefficients using prior social media data, we can investigate their relationship to the future returns of the cryptocurrencies.  We consider returns measured with respect to one month after the cryptocurrencies were created because the first month is an observation period during which we collect social media data to estimate the engagement coefficient.

We begin by looking at the cryptocurrencies with the top returns in for different holding times in Table \ref{table:alpha_returns}.  We see that the returns become quite large, and the maximum return increases with time.  After 12 months, there are cryptocurrencies with returns above 2,000\%. The highest return is 24,985\% for axs.  This cryptocurrency is the governance token for the online video game Axie Infinity which experienced an incredible increase in popularity during that time period \cite{axie}.   We note that for these top performing cryptocurrencies, the engagement coefficient has an order of magnitude of $10^{-4}$, with the exception of inj which has a value of  $0.77\times10^{-5}$.

To further visualize the relationship between the engagement coefficient and returns, we plot the evolution of the cryptocurrency returns over time as a function of the engagement coefficient in Figure \ref{fig:alphas_returns_3d}.  We see that the cryptocurrencies with the highest returns have engagement coefficients  between $10^{-4}$ and $10^{-3}$.  The returns are very low for cryptocurrencies with engagement coefficients outside of this range.

Very low engagement coefficients are due to the followers not interacting with posts about the cryptocurrency.  This signals a lack of interest, which we expect leads to low returns.  The surprising aspect is that extremely high engagement coefficients also have low returns.  We would expect that if the followers are likely to interact with posts about a cryptocurrency, then there is strong interest in it, leading to a price increase.  However, we find this is not the case.  We suspect that the reason we do not see this monotonic type of behavior is due to artificial Twitter accounts, known as bots.  Studies have suggested that between 9\% and 15\% of active Twitter accounts are bots \cite{varol2017online}.   One can create a large number of bots and have them interact with posts about a cryptocurrency to create the impression that there is excitement for it, which is typical of pump and dump schemes \cite{nghiem2021detecting}.  This can lead to engagement coefficients being unusually high.  From Figure \ref{fig:alphas} we see that the cryptocurrency with the highest engagement coefficient is  krypto, which is used for in-game purchases in the online game Kryptobellion.  The returns for krypto were as high as 49\% after two months, but then dropped to negative values thereafter.  The engagement coefficient for krypto is $1.67\times 10^{-2}$, which is nearly an order of magnitude larger than the next highest value.  This is likely due to bots programmed to like and retweet any tweets about krypto. However, with the data we have available, we cannot make this claim with certainty.  Nonetheless, the engagement coefficient can still provide some indication that there is  artificial manipulation of social media activity.  Given our analysis here, we would suggest $10^{-3}$ as a threshold for when there is possible manipulation.

\begin{table}[ht]
	\centering
	{%
		\begin{tabular}{|l|l|l|l|}
			\hline
			Cryptocurrency &  Creation Date& Engagement Coeff. & 1 Month Return [\%]\\\hline
			safemoon   & 3/6/2021   &  8.58 $\times 10^{-4}$& 1,182\\\hline
			safemars &  3/19/2021   &  8.48$\times 10^{-4}$ &  545\\\hline
			alpha &  10/2/2020  &   1.07 $\times 10^{-4}$&  361\\\hline\hline

			Cryptocurrency &  Creation Date& Engagement Coeff. & 3 Month Return [\%]\\\hline
			alpha&   10/2/2020&     1.07 $\times 10^{-4}$ & 4,312\\\hline
			inj & 10/10/2020 &    7.7$\times 10^{-5}$  & 952\\\hline
			axs  &10/25/2020  &   1.52$\times 10^{-4}$   &328\\\hline\hline

			Cryptocurrency &  Creation Date& Engagement Coeff. & 6 Month Return [\%]\\\hline
			cake&   9/28/2020&     2.14$\times 10^{-4}$&  8,829\\\hline
			alpha &  10/2/2020 &    1.07$\times 10^{-4}$ & 3,843\\\hline
			sushi  & 8/28/2020  &   3.87$\times 10^{-4}$  &1,078\\\hline\hline

			Cryptocurrency &  Creation Date& Engagement Coeff. & 9 Month Return [\%]\\\hline
			axs&  10/25/2020&     1.52$\times 10^{-4}$&  14,329\\\hline
			cake &  9/28/2020 &    2.14$\times 10^{-4}$&   3,587\\\hline
			alpha &  10/2/2020 &    1.07$\times 10^{-4}$ &  1,902\\\hline\hline

			Cryptocurrency &  Creation Date& Engagement Coeff. & 12 Month Return [\%]\\\hline
			axs&  10/25/2020& 1.52$\times 10^{-4}$&  24,985\\\hline
			cake &  9/28/2020 & 2.14$\times 10^{-4}$ &  4,409\\\hline
			alpha &  10/2/2020 & 1.07$\times 10^{-4}$ &  2,416\\\hline

		\end{tabular}%
	}
	\caption{Engagement coefficients and returns for cryptocurrencies with top returns in different time periods.}
 \label{table:alpha_returns}
\end{table}

\begin{figure}

			\centering
		\includegraphics[scale = 0.5]{figures/figure_alpha_prior_returns_3d.pdf}
		\caption{Plot of the evolution of the returns of different cryptocurrencies as a function of the logarithm of their engagement coefficient (estimated using prior data).  The returns are measured relative to one month after the cryptocurrency was created.}

	\label{fig:alphas_returns_3d}
\end{figure}

\subsection*{Bot Tweets and Returns}
Our analysis of the engagement coefficients suggested that there may be bots artificially increasing engagement for different cryptocurrencies by interacting with tweets.  The presence of bots tweeting about a cryptocurrency may be indicative of future performance.  For instance, a cryptocurrency whose social media discussion contains a large fraction of bots may be a pump and dump scheme.

Unfortunately, we are not able to determine which tweet interactions come from bots.  However, in addition to interacting with tweets, bots can also post tweets about cryptocurrencies, and unlike interactions, it is possible to identify which tweets come from bots.  To do this, we used the Botometer, a machine learning algorithm that calculates the probability that a Twitter account is a bot based on its posted tweets, profile information, and local follower network \cite{yang2022botometer}.   The Botometer has been used in other studies to identify  bot accounts in Twitter \cite{vosoughi2018spread}. Although it is imperfect, as discussed in \cite{torusdaug2020we}, its use is widely accepted in the academic community.

We used the Botometer  API \cite{botometer_api} to obtain the bot probability for each user in our dataset. The Botometer bot probabilities can be used to quantify the amount of bot discussion for a cryptocurrency.  One measure of bot prevalence is the mean bot probability for all users discussing the cryptocurrency. We calculate this quantity for each cryptocurrency and show a histogram of the resulting values in Figure \ref{fig:bot_prob}.  The lowest mean bot probabilities are for sushi (0.25) and cake (0.31).  Both of these are decentralized finance (DeFi) cryptocurrencies which achieved some success.  The 12 month returns were 630\% for sushi and 4,400\% for cake.   The highest mean bot probability belonged to latte (0.49), another DeFi cryptocurrency, but which did not achieve any success. The latte price decreased by 95\% in three months and did not recover by the 12th month.

From visual inspection we find three clusters of mean bot probabilities.  We apply k-means with three clusters to the mean  bot probabilities and find clusters centered at 0.30, 0.40, and 0.44.  The cluster at 0.30 has  three cryptocurrencies, the cluster at 0.40 has 16 cryptocurrencies, and the cluster at 0.44 has 29 cryptocurrencies.  To understand the relationship between the mean bot probability and performance, we plot the median returns of cryptocurrencies in the three different bot probability clusters versus time in Figure \ref{fig:bot_prob}.  We see that the later returns are highest for the cluster with the lowest mean bot probability.   The two clusters with the highest bot probabilities show similar returns which are quite low.

\subsection*{Comparing the Dependence of Returns on Social Media Features}
We now have multiple social media features for cryptocurrencies.  There is the engagement coefficient, which captures user enthusiasm.  There is the mean user bot probability, which captures the prevalence of bots in the social media activity of a cryptocurrency.  Finally, as a baseline feature, there is the total number, or volume, of tweets posted about a cryptocurrency in its first month.  The tweet volume is related to the engagement coefficient because it attempts to measure enthusiasm.  However, unlike the engagement coefficient, tweet volume is unbounded and does not take into account the follower counts of users.

Previous studies have used tweet volume to predict short-term future returns of cryptocurrencies \cite{steinert2018predicting}.  We wish to see if our new social media features have any advantage over the volume feature.   To compare the effectiveness in predicting returns, we use two different approaches.  First, we calculate the absolute value of the Spearman correlation coefficient between the feature and the monthly returns.  We use the absolute value because the correlation is negative for the mean user bot probability (higher bot probability leads to lower returns, as we saw earlier).  Second, we try to predict the sign of the returns using the feature.  To do this we construct receiver operating characteristic (ROC) curves for each feature and then calculate the corresponding area under the curve (AUC) metric.  The AUC is a common metric used to evaluate the predictive power of a binary classifier.  In our case, the binary label for each cryptocurrency is the sign of its returns in each month, and the classifier is the feature value.  The AUC is one for a perfect classifier and 0.5 for random guessing.

Figure \ref{fig:bot_auc_corr} shows the absolute value of the Spearman correlation coefficient and the AUC versus time  for each feature.  We see that in the early stages the engagement coefficient and tweet volume have a much higher correlation coefficient and  AUC than the bot probability.  This suggests that the engagement coefficient and tweet volume are better at predicting initial performance.   The AUC and absolute correlation coefficient for the one month returns are nearly equivalent for the engagement coefficient and tweet volume.   However, in the later months, the engagement coefficient and mean user bot probability have similar AUC values around 0.7.  In contrast, the tweet volume AUCs for returns after six months are below 0.65.

The absolute correlation coefficient of the engagement coefficient and tweet volume are much greater than the mean user bot probability up to six month returns.  After six months, tweet volume and mean user bot probability have similar values.  However, the engagement coefficient correlation is much great in this period.  For returns up to six months, tweet volume and engagement coefficient have similar correlation coefficients.

Both measures show that the dependence of the one month returns is  higher for the engagement coefficient and tweet volume than the mean user bot probability.  The tweet volume and engagement coefficient are directly measuring initial social media activity. High enthusiasm for the cryptocurrency on social media early will result in people buying the cryptocurrency, leading to higher early returns.  This may be why  in the early stages of a cryptocurrency, the enthusiasm of social media users appears to be a better predictor of performance than the presence (or absence) of bots posting content.  Of the two social media enthusiasm features, the engagement coefficient seems to have a stronger dependence with the returns than the tweet volume.  This suggests that for investment strategies, it may be better to use the engagement coefficient.  We explore this in the next section.

\begin{figure}

			\centering
		\includegraphics[scale = 0.4]{figures/figure_botprob_returns.pdf}
		\caption{(left) Histogram of the cryptocurrency mean bot probabilities. (right) Plot of the median returns in each bot probability cluster versus time (relative to one month after the cryptocurrency's creation).}

	\label{fig:bot_prob}
\end{figure}

\begin{figure}

		\centering
		\includegraphics[scale = 0.4]{figures/figure_auc_corr.pdf}
		\caption{Plot of the (left) AUC  and (right) absolute value of the Spearman correlation coefficient for predicting returns  versus time (relative to one month after the cryptocurrency's creation) for the social media features.}

	\label{fig:bot_auc_corr}
\end{figure}

\subsection*{Investment Strategies}
We now consider investment strategies based on social media features.  The strategies we consider utilize thresholds for the features.  We set a minimum threshold for a feature, and then purchase a fixed dollar amount of any cryptocurrency whose feature value exceeds the threshold.  Each cryptocurrency that is purchased is held for a fixed amount of time, after which it is sold.   With this approach, the cryptocurrencies are purchased and sold at different times, but held for an equal amount of time.  Throughout our analysis, we consider a baseline portfolio that invests in all of the cryptocurrencies.
 This portfolio has a feature threshold equal to zero since all features are positive.

In calculating the feature values, we only use data available during the first month of each cryptocurrency's existence, as a real investor would do.  This is straightforward for the tweet volume and mean user bot probability.  However, to calculate the engagement coefficient, we use the approach where the model is estimated only using prior social media data.

In our first analysis we choose the thresholds  to be quartiles of the respective feature distribution for all cryptocurrencies in our dataset.  This way, each higher threshold removes a fixed number of cryptocurrencies from the portfolio.  We note that this approach could not be used in practice, as the thresholds can depend on data created after the purchase date of a cryptocurrency.   Therefore, this analysis does not tell us what feature performs the best in actual portfolios.  Rather, we use this approach to understand the properties of the different social media features with respect to the returns.

We construct a portfolio for each feature and quartile threshold.  For three social media features and five thresholds (four quartiles plus the baseline portfolio) this gives 15 different portfolios.  We can then look at the returns of these portfolios for different holding times.  Figure \ref{fig:portfolio_threshold} shows the returns versus the cryptocurrency holding time for each portfolio, grouped by the feature.  Each curve corresponds to a threshold for the feature.

The returns for each feature exhibit different behaviors with respect to the thresholds.  For the tweet volume, the highest post-six month return  is achieved for a threshold of 35,800 tweets, which is the 75th quantile.  In contrast, the engagement coefficient achieves the highest post-six month return at a threshold of $1.01 \times 10^{-4}$, which is the median.  The 75th quantile does the worst for returns with holding times greater than two months.  The mean user bot probability portfolios all perform equal to or worse than the baseline portfolio.  This analysis suggests that the bot probability is not as useful for investment strategies compared to the other features.

\begin{figure}

		\centering
		\includegraphics[scale = 0.38]{figures/figure_returns_vs_time_threshold.pdf}
		\caption{Plots of returns of investment strategies versus holding time for different social media features.  The investment strategies are based on fixed cryptocurrency holding times and minimum feature thresholds. Each plot is titled with the feature considered.}

	\label{fig:portfolio_threshold}
\end{figure}
To further study the effect of the threshold choice, we plot the returns versus the feature threshold in Figure \ref{fig:portfolio_threshold}. The tweet volume and bot probability show clusters in their respective feature values.  There is no clear pattern for these two features in their returns.  As the threshold increases, the returns can increase or decrease.  In contrast, the engagement coefficient shows much clearer patterns. The feature values are not clustered, unlike the tweet volume and bot probability.  We see that for a one month holding time, the returns increase monotonically in the threshold.  For other holding times, the returns show a monotonic increase up to a threshold of $10^{-4}$, after which the returns decrease. Cryptocurrencies with engagement coefficients above this threshold appear to have low long-term returns, but high short-term (one month) returns.  This supports our earlier observations in Figure \ref{fig:bot_auc_corr} that the engagement coefficient may be a useful feature for selecting cryptocurrencies which perform well over short time horizons.

\begin{figure}

		\centering
		\includegraphics[scale = 0.38]{figures/figure_returns_vs_threshold_time.pdf}
		\caption{Plots of returns of investment strategies versus feature threshold for different social media features.  The investment strategies are based on fixed cryptocurrency holding times and minimum feature thresholds. }

	\label{fig:portfolio_threshold}
\end{figure}

We now try to recreate the scenario faced by an investor and  determine the threshold using historical data.  We first select an  investment date.  Then, we use quartiles of the feature distribution for all cryptocurrencies created before this date as threshold values.  We use the same investment strategy as before, but now only consider cryptocurrencies created after the investment date.  We consider returns for short-term holding times (one month) and long-term holding times (one year).

The resulting returns for different features, thresholds, and investment dates  are shown in Figures \ref{fig:portfolio_historic_1m} and \ref{fig:portfolio_historic_12m}. For the tweet volume and engagement coefficient, the one month returns are positive for all investment dates and thresholds. In contrast, the bot probability  has negative returns for different thresholds and investment dates.  The highest returns for each investment date are achieved by the engagement coefficient using the 75th quantile as the threshold.  The corresponding threshold values ranged from $2.13\times10^{-4}$ to $2.89\times10^{-4}$.  On the upper end, the returns for the engagement coefficient portfolios  are nearly 200\%.  In contrast, the maximum return  for the tweet volume is below 150\%, and for the bot probability it below 120\%.  These results show that the engagement coefficient is the best social media feature for maximizing short-term returns.

\begin{figure}

			\centering
		\includegraphics[scale = 0.25]{figures/figure_portfolio_1m.pdf}
		\caption{Plots of one month returns of investment strategies for different investment dates based on thresholds for different social media features.  The thresholds are quartiles of the relevant feature for cryptocurrencies created before the investment date.}
	\label{fig:portfolio_historic_1m}
\end{figure}

The one year returns are negative for investments made  in 2021.  There is not a substantial difference in returns with respect to the feature threshold when the returns are negative. For earlier investment dates, no feature or threshold shows clear dominance.  These findings suggest that long-term returns are less dependent on social media features than short-term returns.

\begin{figure}

			\centering
		\includegraphics[scale = 0.25]{figures/figure_portfolio_12m.pdf}
		\caption{Plots of 12 month returns of investment strategies for different investment dates based on thresholds for different social media features.  The thresholds are quartiles of the relevant feature for cryptocurrencies created before the investment date.}
	\label{fig:portfolio_historic_12m}
\end{figure}
\section*{Discussion}

The social media activity surrounding certain topics can be predictive of their future performance.  Here we found such a relationship for cryptocurrencies.  We presented a Poisson model for social media engagement that is simple to estimate, does not require a large amount of data,  and can be applied to any topic, not just cryptocurrencies.  The model produced a numerical value for each cryptocurrency called the engagement coefficient.  We found that this value was correlated with the future returns of the cryptocurrencies, and was most predictive of short-term returns.  We also found that excessive bot activity surrounding a cryptocurrency was correlated with lower future returns, though the bot activity was less predictive than the engagement coefficient.  We developed a simple investment strategy utilizing different social media features, investing only in cryptocurrencies whose feature value exceeded a fixed threshold.  We found that if the feature was the engagement coefficient, then this strategy was effective for increasing short-term returns, but not as much for long-term returns.  Overall, our results show that one can use social media activity to predict the future performance of cryptocurrencies over longer time horizons than previously known (months versus hours or days) \cite{steinert2018predicting}.

\section*{Conclusion}
The generality of our social media engagement model makes it applicable in diverse settings.  Future studies can investigate the predictive power of the model for other topics, such as movies and television shows (ratings, ticket sales), fashion items (sales), political campaigns (votes), or even cryptocurrencies with larger market capitalizations.  Indeed, such studies can establish if the range of engagement coefficients we saw here that correlated with positive future returns are similar in other fields and social media platforms.
 In addition, one can use our model to estimate time varying engagement coefficients using temporally segmented data to track the evolution of engagement over longer time horizons.  The simplicity of our model allows it to be easily be applied in this dynamic setting.  Finally, we note that our model can be also used to detect artificial manipulation of social media in the context of pump and dump schemes.  In this way, our work naturally complements that of \cite{nghiem2021detecting} and can become another tool to protect investors in the cryptocurrency space.

\section*{Supporting information}

\paragraph*{S1 Data.}
\label{S1_Fig}

The data used in this study along with various code for analysis can be found at \url{https://github.com/kai-trading-bot/crypto_engagement}.

\paragraph*{S2 Appendix.}
\label{S2_Appendix}
\textbf{Derivation of Maximum Likelihood Estimates.} \\
The log-likelihood of the dataset is
\[
L(\alpha,\beta|\mathbf n) = -\sum_{c\in\mathcal C}\alpha_cv_c\paranth{\sum_{i\in\mathcal I}\beta_i} +
\sum_{c\in\mathcal C}n_{c}\log(\alpha_c) +
\sum_{i\in\mathcal I}l_{i}\log(\beta_i) +C.
\]
To obtain the ML solution with set the gradient of the log-likelihood to zero, giving
\begin{equation}
	\frac{\partial L}{\partial \beta_i} = -\sum_{c\in \mathcal{C}} \alpha_c v_c + \frac{l_i}{\beta_i} = 0\label{eq:dbeta}
\end{equation}
and
\begin{equation}
	\frac{\partial L}{\partial \alpha_c} =
	-v_c \beta + \frac{n_c}{\alpha_c} = 0,\label{eq:dalpha}
\end{equation}
where we have defined $\beta = \sum_{i\in\mathcal I}\beta_i$.  We fix $\beta_1=1$, which from equation \eqref{eq:dbeta} gives
\begin{align*}
		\sum_{c\in \mathcal{C}} \alpha_c v_c & = l_1
\end{align*}
Substituting this again into equation \eqref{eq:dbeta} gives
\begin{align*}
	\beta_i & = \frac{l_i}{l_1}, ~~ i\in \mathcal I.
\end{align*}
Substituting this into equation \eqref{eq:dalpha} gives
\begin{align*}
	\alpha_c & = \frac{n_c\sum_{i\in \mathcal I}l_i}{v_cl_1}\\
	& = \frac{n_cn}{v_cl_1},\\
\end{align*}
where we have used the definition $n = \sum_{i\in\mathcal I}l_i$.

\paragraph*{S3 Table.}
\label{S1_Table_finance}
\textbf{Cryptocurrency Data.}   \\
The following tables provide more details about the cryptocurrencies used in our study, including their ticker, type of initial offering,  fundraising goals, and dates of the initial offering.  We also provide the number of tweets collected for each cryptocurrency and the collection dates.  The tweets are collected from the beginning of the initial offering up to 30 days later.

\begin{table}[]
	\label{tab:ico_dates_1}
	\centering

		\begin{tabular}{|l|l|l|l|l|}
\hline
\textbf{Ticker} & \textbf{Initial Offering} & \textbf{Goal } & \textbf{Initial Offering} & \textbf{Tweet} \\
 & \textbf{Type} & \textbf{(USD)} & \textbf{Dates} &  \textbf{Count} \\ \hline
{MATIC} & IEO & 5,000,000 & 2019-04-18 to 2019-04-25 & 9,487  \\ \hline
{PERL}  & IEO & 6,700,000 & 2019-08-18 to 2019-08-25 & 9,541  \\ \hline
{BAND}  & IEO & 5,850,000 & 2019-09-10 to 2019-09-17 & 35,813 \\ \hline
{TROY}  & IEO & 4,000,000 & 2019-11-27 to 2019-12-04 & 9,538  \\ \hline
{WRX}   & IEO & 2,000,000 & 2020-01-27 to 2020-02-04 & 35,784 \\ \hline
{CTSI}  & IEO & 1,500,000 & 2020-04-16 to 2020-04-22 & 35,689 \\ \hline
{ALPHA} & IEO & 2,000,000 & 2020-10-02 to 2020-10-10 & 9,621  \\ \hline
{INJ}   & IEO & 3,600,000 & 2020-10-10 to 2020-10-20 & 36,127 \\ \hline
{AXS}   & IEO & 2,970,000 & 2020-10-25 to 2020-11-04 & 35,829 \\ \hline
\end{tabular}%

\caption{Cryptocurrencies created before 2021 in our dataset, their initial offering type, target fund-raising goal, initial offering  dates, and total tweets collected.}
\end{table}
\begin{table}[]
	\label{tab:ico_dates_2}
	\centering

		\begin{tabular}{|l|l|l|l|l|}
\hline
\textbf{Ticker} & \textbf{Initial Offering} & \textbf{Goal } & \textbf{Initial Offering} & \textbf{Tweet} \\
 & \textbf{Type} & \textbf{(USD)} & \textbf{Dates} &  \textbf{Count} \\ \hline
{STC}    & ICO & 21,000,000  & 2021-02-01 to 2021-04-30 & 35,689 \\ \hline
{SFP}    & IEO & 5,000,000   & 2021-02-02 to 2021-02-08 & 35,782 \\ \hline
{ACM}    & IEO & 1,000,000   & 2021-02-17 to 2021-02-24 & 9,539  \\ \hline
{RAMEN}  & ICO   & 1,250,000 & 2021-02-19 to 2021-02-19 & 420 \\ \hline
{MASK}   & ITO & 2,700,000   & 2021-02-22 to 2021-02-24 & 35,669 \\ \hline
{ARC}    & ICO & 7,800,000   & 2021-03-03 to 2021-03-09 & 9,452  \\ \hline
{SAFEMOON} & ICO  & 10,000,000 & 2021-03-06 to 2021-03-06 & 58,411 \\ \hline
{ETHA}   & IDO & 10,000,000  & 2021-03-04 to 2021-03-04 & 9,441  \\ \hline
{BELT}   & IDO & 3,000,000   & 2021-03-10 to 2021-03-10 & 9,468  \\ \hline
{TARA}   & ICO & 3,000,000   & 2021-03-11 to 2021-03-11 & 9,486  \\ \hline
{DEFIT}  & IDO & 1,111,000   & 2021-03-14 to 2021-03-30 & 35,729 \\ \hline
{SAFEMARS} & ICO   & 2,500,000  & 2021-03-19 to 2021-03-19 & 16,935 \\ \hline
{ORAO}   & IDO & 1,000,000   & 2021-03-21 to 2021-03-24 & 9,445  \\ \hline
{VEN}    & IDO & 7,500,000   & 2021-03-22 to 2021-03-24 & 35,773 \\ \hline
{CSPR}   & IEO & 12,000,000  & 2021-03-22 to 2021-03-22 & 9,459  \\ \hline
{COOK}   & IDO & 300,000,000 & 2021-03-30 to 2021-03-31 & 35,931 \\ \hline
{BOSON}  & IDO & 4,500,000   & 2021-04-06 to 2021-04-07 & 35,808 \\ \hline
{CERE}   & ICO & 27,800,000  & 2021-04-07 to 2021-04-15 & 35,797 \\ \hline
{XNL}  & Private Sale   & 2,300,000  & 2021-04-09 to 2021-04-22 & 35,602  \\ \hline
{FINE}   & IDO & 3,090,000   & 2021-04-26 to 2021-04-27 & 9,612  \\ \hline
{KRYPTO} & IDO & 1,500,000   & 2021-04-30 to 2021-04-30 & 35,895 \\ \hline
{WEC}    & IEO & 2,300,000   & 2021-05-13 to 2021-05-19 & 35,646 \\ \hline
{LATTE}  & ICO& 1,000,000    & 2021-05-19 to 2021-05-19 & 207\\ \hline
{NFT}    & IEO & 2,399,976   & 2021-05-20 to 2021-05-20 & 36,080 \\ \hline
{HOTCROSS} & IFO  & 2,500,000  & 2021-05-20 to 2021-05-20 & 35,696 \\ \hline
{COW}    & ICO & 1,500,000   & 2021-05-25 to 2021-05-25 & 9,470  \\ \hline
{CFG}     & IEO       & 3,506,250  & 2021-05-26 to 2021-05-31 & 9,496  \\ \hline
{LESS}    & Presale   & 1,650,000  & 2021-05-27 to 2021-06-01 & 35,701 \\ \hline
\end{tabular}%

\caption{Cryptocurrencies created during the first half of 2021 in our dataset, their initial offering type, target fund-raising goal, initial offering  dates, and total tweets collected.}
\end{table}

\begin{table}[]
	\label{tab:ico_dates_3}
	\centering

		\begin{tabular}{|l|l|l|l|l|}
\hline
\textbf{Ticker} & \textbf{Initial Offering} & \textbf{Goal } & \textbf{Initial Offering} & \textbf{Tweet} \\
 & \textbf{Type} & \textbf{(USD)} & \textbf{Dates} &  \textbf{Count} \\ \hline
{SAFEBTC} & ICO       & 2,000,000  & 2021-06-02 to 2021-06-05 & 35,882 \\ \hline
{ITGR}    & ICO       & 4,410,000  & 2021-06-10 to 2021-06-13 & 35,628 \\ \hline
{BZZ}     & ICO       & 9,933,953  & 2021-06-13 to 2021-06-14 & 35,658 \\ \hline
{HMT}     & IEO       & 50,000,000 & 2021-06-17 to 2021-06-22 & 35,619 \\ \hline
{PALG}    & ICO       & 8,000,000  & 2021-08-05 to 2021-09-05 & 35,600 \\ \hline
{TUP}     & ICO       & 8,000,000  & 2021-08-21 to 2021-09-05 & 35,712 \\ \hline
{MPT}     & IDO       & 1,000,000  & 2021-08-29 to 2021-08-30 & 35,604 \\ \hline
{DMZ}     & Seed Sale & 1,200,000  & 2021-09-06 to 2021-09-07 & 35,723 \\ \hline
{FOREX}   & ICO       & 4,410,000  & 2021-09-20 to 2021-09-22 & 35,653 \\ \hline
{DANA}    & ICO       & 1,000,000  & 2021-10-28 to 2021-10-28 & 35,991 \\ \hline
{TEX}     & IDO       & 1,980,000  & 2021-11-03 to 2021-11-04 & 35,732 \\ \hline
{YIN}     & IDO       & 4,500,000  & 2021-11-03 to 2021-11-05 & 35,636 \\ \hline
{GOG}     & ICO       & 5,500,000  & 2021-11-10 to 2021-11-10 & 9,438  \\ \hline
\end{tabular}%

\caption{Cryptocurrencies created during the second half of 2021 in our dataset, their initial offering type, target fund-raising goal, initial offering  dates, and total tweets collected.}
\end{table}

\bibliographystyle{unsrt}

\section{Introduction}
\lipsum[2]
\lipsum[3]

\section{Headings: first level}
\label{sec:headings}

\lipsum[4] See Section \ref{sec:headings}.

\subsection{Headings: second level}
\lipsum[5]
\begin{equation}
\xi _{ij}(t)=P(x_{t}=i,x_{t+1}=j|y,v,w;\theta)= {\frac {\alpha _{i}(t)a^{w_t}_{ij}\beta _{j}(t+1)b^{v_{t+1}}_{j}(y_{t+1})}{\sum _{i=1}^{N} \sum _{j=1}^{N} \alpha _{i}(t)a^{w_t}_{ij}\beta _{j}(t+1)b^{v_{t+1}}_{j}(y_{t+1})}}
\end{equation}

\subsubsection{Headings: third level}
\lipsum[6]

\paragraph{Paragraph}
\lipsum[7]

\section{Examples of citations, figures, tables, references}
\label{sec:others}
\lipsum[8] \cite{kour2014real,kour2014fast} and see \cite{hadash2018estimate}.

The documentation for \verb+natbib+ may be found at
\begin{center}
  \url{http://mirrors.ctan.org/macros/latex/contrib/natbib/natnotes.pdf}
\end{center}
Of note is the command \verb+\citet+, which produces citations
appropriate for use in inline text.  For example,
\begin{verbatim}
   \citet{hasselmo} investigated\dots
\end{verbatim}
produces
\begin{quote}
  Hasselmo, et al.\ (1995) investigated\dots
\end{quote}

\begin{center}
  \url{https://www.ctan.org/pkg/booktabs}
\end{center}

\subsection{Figures}
\lipsum[10]
See Figure \ref{fig:fig1}. Here is how you add footnotes. \footnote{Sample of the first footnote.}
\lipsum[11]

\begin{figure}
  \centering
  \fbox{\rule[-.5cm]{4cm}{4cm} \rule[-.5cm]{4cm}{0cm}}
  \caption{Sample figure caption.}
  \label{fig:fig1}
\end{figure}

\subsection{Tables}
\lipsum[12]
See awesome Table~\ref{tab:table}.

\begin{table}
 \caption{Sample table title}
  \centering
  \begin{tabular}{lll}
    \toprule
    \multicolumn{2}{c}{Part}                   \\
    \cmidrule(r){1-2}
    Name     & Description     & Size ($\mu$m) \\
    \midrule
    Dendrite & Input terminal  & $\sim$100     \\
    Axon     & Output terminal & $\sim$10      \\
    Soma     & Cell body       & up to $10^6$  \\
    \bottomrule
  \end{tabular}
  \label{tab:table}
\end{table}

\subsection{Lists}
\begin{itemize}
\item Lorem ipsum dolor sit amet
\item consectetur adipiscing elit.
\item Aliquam dignissim blandit est, in dictum tortor gravida eget. In ac rutrum magna.
\end{itemize}

\section{Conclusion}
Your conclusion here

\section*{Acknowledgments}
This was was supported in part by......

\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


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The permit is only available for private passenger vehicles and is valid for a period of one (1) year.
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How great would it be if customers showed up in your store or on your website with a sandwich board on their shoulders, advertising their level of interest in what you have to offer.
Well it might not be a sandwich board, but there are some ways get a good sense for this buyer intent.
Today's marketing specialists have a great grasp on sales funnels, the way that customers move from awareness to purchase (and beyond). These funnels cover all the different touch points, marketing channels, and key metrics that go into a buying decision and help you have a better sense for what messaging and content makes the most sense at different points of the customer's journey.
And the big question on our minds at Buffer: Where does social media fit within this sales funnel?
We've got some thoughts on this, as well as some examples and steps to help you build your own sales funnel, with a clear social media focus.
So where does social media fit in these funnels?
In my experience, social media has typically appeared at the top, at the exact polar opposite from the sale. Maybe it's no wonder then that bosses, clients, and teams have a difficult time being fully on board with prioritizing social as a channel. According to the funnel, you don't make your money from social — at least, not directly.
Maybe it's not as cut-and-dry that social is always top-of-funnel?
Maybe it's not as cut-and-dry that there even is a funnel!
Some of these thoughts have a bit of data behind them, thanks to an exploration from McKinsey & Company where they analyzed more than 20,000 customers and how they experienced the sales funnel. McKinsey & Company found that the funnel might be more of a circle.
The funnel concept fails to capture all the touch points and key buying factors resulting from the explosion of product choices and digital channels, coupled with the emergence of an increasingly discerning, well-informed consumer.
Even here, while there is less of a top-down approach in this model, still social media primarily appears only at the beginning, in the Initial Consideration phase.
How does this jive with your experience with social?
For us, we've observed a slightly different take on things, both with where social media fits within the funnel and possibly with social media having a funnel of its very own. I'd love to share more.
We believe that social media doesn't always have to be top of funnel. Or that there even is a funnel!
… and even some that fit at the bottom (things like the Pinterest Buy button, for instance).
From what we've seen, there are just so many different types of interactions on social media that it's hard to pigeonhole social into any particular element of the funnel.
Social media covers the full spectrum of the buying process, everything from awareness all the way through to advocacy.
And what's more, we've seen that social media has its very own funnel.
Everything on this spectrum from viewing a profile to selling a product can happen with social media. Just as a user moves through from awareness to interest to engagement and beyond, so too does a social media lead go from viewing to following to interacting to buying.
What does this mean for the traditional funnel?
Well it's certainly still a valuable exercise to think through the buyer's journey (more on those exercises below). At the same time, it might feel great to recognize that your customers — especially those from social media — are taking a less-and-less linear journey toward closing the deal.
We feel there is no one right way to make a funnel. Every brand is different, and every potential buyer's journey is unique.
How do customers at this stage find me?
Answering these questions will go a long way toward settling in with a uniquely "you" sales funnel. Here are a few options for getting a very official or unofficial funnel in place.
The above graphic from Visual Website Optimizer makes for a pretty standard-looking sales funnel.
It's been said any number of additional ways, too: Awareness → Consideration → Decision; Acquisition → Activation → Absorption; TOFU→ MOFU→ BOFU; etc. And it turns out that different customers progress through these stages in different ways, perhaps starting at the top and working down (classic) or jumping back and forth between stages (unorthodox).
The traditional sales funnel process starts with an understanding of your buyers.
Then it transitions into choosing the different parts of your funnel (the TOFU, MOFU, BOFU parts above).
Analytical thinkers appreciate having all the facts, and will read thoroughly to get them. Whitepapers, use cases and case studies are great for these buyers.
Impulsive buyers don't want to read everything – they just need the gist, preferably in bullet-points.
… and the location in the funnel.
And when it comes to analyzing this data to see what works, one great way to further evaluate is with a matrix of the types of visitors, leads, and customers you've been able to pull in.
Low interest and low fit – The leads don't meet your company's target criteria and are unlikely to make a move soon. A common example of these types of leads is the low level employee who's browsing solutions out of curiosity, not an immediate need.
We take a lot of inspiration from our friends at MailChimp, who came up with the idea of an upside down funnel.
I could also see it being the case that some companies might not want to have any funnel whatsoever.
A couple years ago, there was an interesting article on Harvard Business Review talking about how the funnel is no longer an accurate way to describe a buyer's journey. And I have the sense that things have only become more muddied with online marketing in the two years since!
Consider items that come recommended on an e-commerce site. With a click you can add them to your cart, moving straight from awareness through consideration to purchase in only a few seconds. The same holds true on items discovered in a Tweet, Facebook post, or Pinterest board.
In this way, there really is no traditional funnel. Everyone's journey is unique.
And the takeaway for marketers is to simply keep on doing what you're doing. Find what's working well and double down, without thinking too much about how the funnel is supposed to look.
Many thanks to Social Media Examiner for this idea; I found their guide on the social media sales funnel to be wonderfully concise and easy to follow, like a minimalist's version of a funnel.
Start by making a list of all the different social media marketing channels you've currently got going on.
Then figure out what one goal each of these have, relative to some of the aspects of a buyer's journey. I'll use the "Acquisition > Activation > Absorption" method.
Once these categories are in place, you then add your key stats to each area so that you can monitor the success and performance of each. This'll be critical later on when you come back to analyze your tests and experiments.
Interested in making your own? You can grab a free Canva template here.
Once the sales funnel is in place (or, never mind if you're working from the contrarian model), now comes my favorite part: Testing!
Knowing the KPIs for each channel and section of your funnel makes it super simple to run experiments and see what works. We're big fans of the Brian Balfour growth machine here at Buffer. There're a ton of other frameworks that might be helpful, too.
Some of my favorite tips on what to try come down to the different types of materials to test at different stages of the funnel.
Increasing conversion rates from 0.9% to 1.1% doesn't matter if only 100 people come to ur site every day.
Much more important is getting 1,000 people (OR TEN THOUSAND PEOPLE) in the top of ur funnel every day.
If ur early, aim to 3X ur One Metric That Matters. U can always micro-optimize later.
Use lead magnets (special offer in exchange for email, more info or addnl engagement) that are tailored to each stage of your conversion funnel.
1. TOFU (top of funnel) – convert visitors into leads.
3. BOFU (bottom of funnel) – CONVERT.
Final thoughts and your thoughts!
As you can see, there are huge number of ways to think about sales funnels — if you want to think about them at all!
I'm excited to say that you can pursue any of these paths you want, whatever makes the most sense for you and your brand.
What do you currently have in place? What might you try out?
I'd love the chance to learn a bit more from you. Feel free to leave a comment below or drop me a note on Twitter. Thanks a million for reading!
The post How to Build Social Media Into Your Sales Funnel appeared first on Social.


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Mold, Micotoxins, and Lyme
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Michelle McKeon, of Ridgewood, went to Germany to seek treatment for the illness, which remains a disputed condition in the medical community By Laura Bertocci, Neighbor Feb 28, 2012 9:09 pm ET | Updated Mar 8, 2012 10:51 pm ET On a summer day in July 2006, Michelle...


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