formulasearchengine - User contributions [en]

Low-energy electron diffraction

2014-02-09T09:16:10Z

218.186.15.10: /* Surface Sensitivity */

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Loss given default

2014-01-27T11:55:48Z

218.186.250.18:

'''Blue Monday''' is a name given to a date in January stated, as part of a publicity campaign by [[Sky Travel]], to be the most depressing day of the year. However, the whole concept is considered [[pseudoscience]],<ref name="burnett1">{{cite news | url=http://www.guardian.co.uk/science/blog/2012/jan/16/blue-monday-depressing-day-pseudoscience | title=Blue Monday: a depressing day of pseudoscience and humiliation | date=16 January 2012 | author=Dean Burnett | newspaper=[[The Guardian]] |accessdate=20 January 2014}}</ref> with its formula derided by scientists as nonsense.

== History ==
This date was published in a press release under the name of Cliff Arnall, at the time a tutor at the Centre for Lifelong Learning, a Further Education centre attached to [[Cardiff University]]. ''Guardian'' columnist Dr. [[Ben Goldacre]] reported that the press release was delivered substantially pre-written to a number of academics by [[public relations]] agency [[Porter Novelli]], who offered them money to put their names to it.<ref name="Guardian_1">{{cite news |url=http://www.guardian.co.uk/science/2006/dec/16/badscience.uknews |title=MS = media slut, but CW = corporate whore |newspaper=The Guardian |date=16 December 2006 |accessdate=21 January 2008 | location=London | first=Ben | last=Goldacre}}</ref> The Guardian later printed a statement from Cardiff University distancing themselves from Arnall: "Cardiff University has asked us to point out that Cliff Arnall... was a former part-time tutor at the university but left in February."<ref>{{cite news |url=http://www.guardian.co.uk/science/2006/nov/18/badscience.uknews |title=How GxPxIxC = selling out to your corporate sponsor |newspaper=The Guardian |date=18 November 2006 |accessdate=21 January 2008 | location=London | first=Ben | last=Goldacre |accessdate=20 January 2014}}</ref>

== Date ==

This date allegedly falls on the Monday of the last full week of January. The date was declared by Arnall to be 24 January in 2005,<ref>{{cite web |url=http://www.msnbc.msn.com/id/6847012/ |title=Jan. 24 called worst day of the year |publisher=MSNBC |date=24 January 2005 |accessdate=13 March 2007}}</ref> 23 January in 2006,<ref>{{cite web |url=http://www.ctv.ca/CTVNews/World/20060123/depressing_day_060123/ |title=Jan. 23 most depressing day of the year: report |publisher=CTV |date=24 January 2006 |accessdate=13 March 2007}}</ref> 22 January in 2007,<ref>{{cite news |url=http://www.dailymail.co.uk/news/article-430389/Blue-Monday-The-unhappiest-day-year.html |title=Blue Monday: The unhappiest day of the year |newspaper=Daily Mail |date=22 January 2007 |accessdate=13 March 2007 | location=London}}</ref> 21 January in 2008,<ref>{{cite news |url=http://www.telegraph.co.uk/news/features/3635353/Smile-Youre-not-the-only-one-in-a-bad-mood.html |title=Smile! You're not the only one in a bad mood |newspaper=Daily Telegraph |date=21 January 2008 |accessdate=21 January 2008 | location=London | first=Frances | last=Booth}}</ref> 19 January in 2009<ref name="mentalhealth1"/> and 18 January in 2010. In 2011 there was confusion about the correct date; some claimed it to be 17 January 2011<ref>{{cite web |url=http://www.beatbluemonday.org.uk/ |title=Beat Blue Monday 17th Jan 2011 |url=http://www.joe.ie/health-fitness/health-fitness-news/blue-monday-today-the-most-day-of-the-year-008758-1 |title='Blue Monday': Today the most depressing day of the year |publisher=www.joe.ie |date=17 January 2011 |accessdate=17 January 2011}}</ref> while others stated Blue Monday was on 24 January 2011.<ref>{{cite web |url=http://www.beatbluemonday.org.uk/?p=136 |title=2011 is so bad – we have two Blue Mondays! |publisher=beatbluemonday.org.uk |date=17 January 2011 |accessdate=18 January 2011}}</ref><ref name="bluemonday.org">{{cite web |url=http://www.bluemonday.org |title=Blue Monday |publisher=Canterbury College |date=17 January 2011 |accessdate=18 January 2011}}</ref><ref>{{cite web |url=http://www.guardian.co.uk/science/2011/jan/24/blue-monday-good-news |title=Today is the real Blue Monday |newspaper=The Guardian |date=24 January 2011 |accessdate=24 January 2011}}</ref> In 2012, the most depressing day of the year was said to be 23 January.<ref name="burnett1" /><ref>{{cite news|title=Is Blue Monday the most depressing day of the year... or was it all a marketing scam to make us book vacations? |url=http://www.dailymail.co.uk/news/article-2087553/Blue-Monday-Most-depressing-day-year-marketing-scam.html|accessdate=23 January 2012|date=16 January 2012 |newspaper=Daily Mail}}</ref><ref>{{cite news|title=Blue Monday is most depressing day of the year, research claims|url=http://www.telegraph.co.uk/finance/jobs/9017631/Blue-Monday-is-most-depressing-day-of-the-year-research-claims.html|accessdate=23 January 2012|newspaper=Daily Telegraph|date=16 January 2012}}</ref> In 2013, Blue Monday was reported to be on 21 January, <ref>{{cite web |url=http://www.dailymail.co.uk/news/article-2265639/Most-depressing-day-year-Feeling-Blame-Blue-Monday-2013.html |title=Feeling Down? |newspaper=The Daily Mail |date=20 January 2013 |accessdate=2 January 2014}}</ref> and 20 January in 2014.<ref>{{cite web |url=http://www.dailymail.co.uk/news/article-430389/Blue-Monday-The-unhappiest-day-year.html |title=Blue Monday: The unhappiest day of the yearRead more: http://www.dailymail.co.uk/news/article-430389/Blue-Monday-The-unhappiest-day-year|newspaper=Daily Mail |date=6 January 2014 |accessdate=6 January 2014}}</ref> <ref name="bluemonday.org" />

=== Calculation ===

According to a press release by a mental health charity,<ref name="mentalhealth1">{{cite web |url=http://www.mentalhealth.org.uk/media/news-releases/news-releases-2009/13-january-2009/ |title=Campaign aims to help ease January blues British public urged to ‘Beat Blue Monday’ |publisher=www.mentalhealth.org.uk |date=13 January 2009 |accessdate=13 January 2009}}</ref> the formula is:

:<math>\frac{[W + D-d] T^Q}{M N_a}</math>

where weather=W, debt=d, time since Christmas=T, time since failing our new year’s resolutions=Q, low motivational levels=M and the feeling of a need to take action=Na. 'D' is not defined in the release, nor are units.

Arnall says the date was calculated by using many factors, including: weather conditions, debt level (the difference between debt accumulated and our ability to pay), time since Christmas, time since failing our new year’s resolutions, low motivational levels and feeling of a need to take action.
Writing about the calculation, Ben Goldacre stated: "... the fact is that Cliff Arnall's equations ... fail even to make mathematical sense on their own terms."<ref name="Guardian_1"/> Dean Burnett, a neuroscientist who has worked in the psychology department of Cardiff University, has described the formula as "farcical", with "nonsensical measurements".<ref>{{cite news | url=http://www.guardian.co.uk/science/brain-flapping/2013/jan/21/blue-monday-depressing-day-nonsense-science | title=Blue Monday: a depressing day of nonsense science (again) | date=21 January 2013 | first=Dean |last=Burnett | newspaper=[[The Guardian]] |accessdate=20 January 2014}}</ref>

=== Happiest day ===

Mr Arnall also says, in a press release commissioned by [[Wall's (ice cream)|Wall's]],<ref>{{cite web |url=http://www.ctv.ca/CTVNews/TopStories/20060623/happiest_day_060623/ |title=It's the happiest day of the year, formula shows |publisher=CTV.ca |date=23 June 2006 |accessdate=13 July 2007}}</ref> that he has calculated the happiest day of the year—in 2005, 24 June,<ref>{{cite news |url=http://news.bbc.co.uk/2/hi/uk_news/wales/south_east/4618209.stm |title=Cheer up for year's happiest day |publisher=BBC |date=24 June 2005 |accessdate=13 March 2007}}</ref> in 2006, 23 June,<ref>{{cite news|url=http://www.chinadaily.com.cn/lifestyle/2006-06/23/content_624619.htm |title=Smile, it's the happiest day of the year |date=23 June 2006 |accessdate=13 March 2007 |newspaper=China Daily}}</ref> in 2008, 20 June<ref>{{cite news |url=http://www.telegraph.co.uk/news/newstopics/howaboutthat/2158104/Today-is-the-happiest-day-of-the-year-according-to-Cliff-Arnall's-maths-formula.html |title=Today is the happiest day of the year according to Cliff Arnall's maths formula |date=20 June 2008|accessdate=20 June 2008 | newspaper=The Daily Telegraph | location=London | first=Rebecca | last=Smith}}</ref> in 2009, 19 June, <ref>{{cite news |url=http://www.dailymail.co.uk/news/article-1194089/Why-June-19th-happiest-day-year.html|title=Here comes the sum... Algebra 'proves' how holiday hopes, heat and high spirits make today the year's happiest |date=19 June 2009 |accessdate=21 June 2009 | location=London | newspaper=Daily Mail}}</ref> and in 2010, 18 June.<ref>{{cite news |url=http://www.examiner.ie/ireland/happiness-is-today-claims-maths-equation-122804.html |title=Happiness is, today, claims maths equation |date=18 June 2010 |accessdate=18 June 2010 | newspaper=Irish Examiner | location=Cork | first=Alistair | last=Grant}}</ref> So far, this date has fallen close to [[Midsummer]] in the Northern Hemisphere (June 21 to 24).

== References ==
{{Reflist|2}}

== External links ==
* BBC pages referencing Blue Monday [http://news.bbc.co.uk/2/hi/uk_news/4187183.stm 2005] [http://news.bbc.co.uk/2/hi/uk_news/7836941.stm 2009] [http://www.bbc.co.uk/news/uk-scotland-16576438 2012]

[[Category:Monday]]
[[Category:January observances]]
[[Category:Unofficial observances]]
[[Category:Pseudoscience]]

Template:Userbox/UserLikesTaylorSwift

2013-12-05T05:58:00Z

218.186.153.21:

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Leibniz harmonic triangle

2013-08-09T06:29:44Z

218.186.90.251:

The '''layered [[hidden Markov model]] (LHMM)''' is a [[statistical model]] derived from the hidden Markov model (HMM).
A layered hidden Markov model (LHMM) consists of ''N'' levels of HMMs, where the HMMs on level ''i'' + 1 correspond to observation symbols or probability generators at level ''i''.
Every level ''i'' of the LHMM consists of ''K''''i'' HMMs running in parallel.

== Background ==

LHMMs are sometimes useful in specific structures because they can facilitate learning and generalization. For example, even though a fully connected HMM could always be used if enough training data were available, it is often useful to constrain the model by not allowing arbitrary state transitions. In the same way it can be beneficial to embed the HMM in a layered structure which, theoretically, may not be able to solve any problems the basic HMM cannot, but can solve some problems more efficiently because less training data is needed.

== The layered hidden Markov model ==

A layered hidden Markov model (LHMM) consists of <math>N</math> levels of HMMs where the HMMs on level <math>N+1</math> corresponds to observation symbols or probability generators at level <math>N</math>.
Every level <math>i</math> of the LHMM consists of <math>K_i</math> HMMs running in parallel.

[[Image:LHMM.png|thumbnail|400px|center|A layered hidden Markov model]]

At any given level <math>L</math> in the LHMM a sequence of <math>T_L</math> observation symbols
<math>\mathbf{o}_L=\{o_1, o_2, \dots, o_{T_L}\}</math> can be used to classify the input into one of <math>K_L</math> classes, where each class corresponds to each of the <math>K_L</math> HMMs at level <math>L</math>. This classification can then be used to generate a new observation for the level <math>L-1</math> HMMs. At the lowest layer, i.e. level <math>N</math>, primitive observation symbols <math>\mathbf{o}_p=\{o_1, o_2, \dots, o_{T_p}\}</math> would be generated directly from observations of the modeled process. For example in a trajectory tracking task the primitive observation symbols would originate from the quantized sensor values. Thus at each layer in the LHMM the observations originate from the classification of the underlying layer, except for the lowest layer where the observation symbols originate from measurements of the observed process.

It is not necessary to run all levels at the same time granularity. For example it is possible to use windowing at any level in the structure so that the classification takes the average of several classifications into consideration before passing the results up the layers of the LHMM.

Instead of simply using the winning HMM at level <math>L+1</math> as an input symbol for the HMM at level <math>L</math> it is possible to use it as a [[probability generator]] by passing the complete [[probability distribution]] up the layers of the LHMM. Thus instead of having a "winner takes all" strategy where the most probable HMM is selected as an observation symbol, the likelihood <math>L(i)</math> of observing the <math>i</math>th HMM can be used in the recursion formula of the level <math>L</math> HMM to account for the uncertainty in the classification of the HMMs at level <math>L+1</math>. Thus, if the classification of the HMMs at level <math>n+1</math> is uncertain, it is possible to pay more attention to the a-priori information encoded in the HMM at level <math>L</math>.

A LHMM could in practice be transformed into a single layered HMM where all the different models are concatenated together. Some of the advantages that may be expected from using the LHMM over a large single layer HMM is that the LHMM is less likely to suffer from [[overfitting]] since the individual sub-components are trained independently on smaller amounts of data. A consequence of this is that a significantly smaller amount of training data is required for the LHMM to achieve a performance comparable of the HMM. Another advantage is that the layers at the bottom of the LHMM, which are more sensitive to changes in the environment such as the type of sensors, sampling rate etc. can be retrained separately without altering the higher layers of the LHMM.

==See also==
*[[Hierarchical hidden Markov model]]

== References ==
*N. Oliver, A. Garg and E. Horvitz, "Layered Representations for Learning and Inferring Office Activity from Multiple Sensory Channels", Computer Vision and Image Understanding, vol. 96, p. 163–180, 2004.

[[Category:Hidden Markov models]]