Input interpretation:
Avatar (English word)

Noun:
Hindu deity | the manifestation of a Hindu deity (especially Vishnu) in human or superhuman or animal form (the Buddha is considered an avatar of the god Vishnu)
Personification | a new personification of a familiar idea (the very avatar of cunning)

Word origins:
Sanskrit (first recorded use: 1784 (226 years ago)

Synonyms:
Personification | embodiment | incarnation

Narrower terms:
Deification  |  Jagannath  |  Jagannatha  |  Jagganath  |  Juggernaut  |  Kalki  |  Krishna  |  Rama  |  reincarnation

Broader terms:
Hindu deity | personification

H1N1 (Influenza A) status around the world with October 2009 data.

Cases | deaths:

Latest reports for the world:
Date | reported cases | reported deaths:
Saturday, October 17, 2009 | 471254 | 4906
Saturday, October 10, 2009 | 458743 | 4754
Monday, October 5, 2009 | 458743 | 4754
Sunday, October 4, 2009 | 457303 | 4699
Saturday, October 3, 2009 | 358319 | 4480

Source: Wolfram Alpha

Input interpretation:
Security (English word)

Noun:
Assets | defense against financial failure; financial independence
Electrical device | an electrical device that sets off an alarm when someone tries to break in
Fearlessness | freedom from anxiety or fear
Official document | a formal declaration that documents a fact of relevance to finance and investment; the holder has a right to receive interest or dividends
Precaution | measures taken as a precaution against theft or espionage or sabotage etc
Safety | the state of being free from danger or injury
Section | a department responsible for the security of the institution’s property and workers
Transferred property | property that your creditor can claim in case you default on your obligation
Warrantee | a guarantee that an obligation will be met

Synonyms:
Precaution | security measures
Electrical device | security measure | security system
Warrantee | surety
Section | security department
Assets | protection
Transferred property | surety
Official document | certificate

Narrower terms:
Agency security  |  bond  |  bond certificate  |  confidence  |  convertible  |  convertible security  |  deposit  |  earnest  |  easy street  |  government security  |  hedge  |  hedging  |  insurance  |  letter security  |  listed security  |  mortgage-backed security  |  OTC security  |  over the counter security  |  partnership certificate  |  peace  |  proprietorship certificate  |  protection  |  public security  |  recognisance  |  recognizance  |  registered security  |  scrip  |  secureness  |  shelter  |  stock  |  stock certificate  |  stock-purchase warrant  |  stock warrant  |  tax-exempt  |  tax-exempt security  |  unlisted security  |  warrant

Broader terms:
Assets  |  bravery  |  department  |  electrical device  |  fearlessness  |  guarantee  |  guard  |  instrument  |  legal document  |  legal instrument  |  official document  |  precaution  |  safeguard  |  safety  |  section  |  transferred possession  |  transferred property  |  warrant  |  warrantee  |  warranty

Input interpretation:
Business (English word)

Definitions:
Noun:
Activity | the principal activity in your life that you do to earn money
Commerce | the activity of providing goods and services involving financial and commercial and industrial aspects
Commercial activity | the volume of commercial activity
Enterprise | a commercial or industrial enterprise and the people who constitute it
Object | an immediate objective
People | customers collectively
Playacting | incidental activity performed by an actor for dramatic effect
Sector | business concerns collectively
Vexation | a rightful concern or responsibility

Word origins:
Old English (first recorded use: 1387 (622 years ago))

Typical word frequency:
Written | 1/2700 (rank: 209th) 100% noun
Spoken | 1/4400 (rank: 354th) 100% noun
(Based on the 100-million-word British National Corpus)

Synonyms:
Playacting | byplay | stage business
Activity | job | line | line of work | occupation
Commerce | business enterprise | commercial enterprise
Sector | business sector
Enterprise | business concern | business organization | business organization | concern
People | clientele | patronage

Narrower terms:
Accountancy  |  accounting  |  advertising  |  agency  |  agribusiness  |  agriculture  |  appointment  |  berth  |  big business  |  billet  |  biz  |  brokerage  |  building  |  business firm  |  butchering  |  butchery  |  calling  |  career  |  carrier  |  catering  |  chain  |  common carrier  |  confectionery  |  construction  |  craft  |  dealership  |  discount business  |  employee-owned business  |  employee-owned enterprise  |  employment  |  factory farm  |  farming  |  field  |  field of operation  |  finance  |  firm  |  fishing  |  franchise  |  game  |  house  |  industry  |  land  |  land-office business  |  line of business  |  maker  |  manufacture  |  manufacturer  |  manufacturing business  |  medium  |  metier  |  occasions  |  office  |  packaging  |  partnership  |  patronage  |  photography  |  place  |  position  |  post  |  printing  |  processor  |  profession  |  publication  |  publicizing  |  publishing  |  real-estate business  |  salt mine  |  schtick   |  shipbuilder  |  shipping  |  shtik  |  situation  |  sport  |  spot  |  storage  |  tourism  |  touristry  |  trade  |  transport  |  transportation  |  treadmill  |  underperformer  |  venture  |  vocation  |  work

Broader terms:
Acting  |  activity  |  aim  |  business activity  |  commerce  |  commercial activity  |  commercialism  |  concern  |  enterprise  |  headache  |  mercantilism  |  object  |  objective  |  people  |  performing  |  playacting  |  playing  |  sector  |  target  |  vexation  |  worry

Input interpretation:
Serendipity (English word)

Noun:
Serendipity | good luck in making unexpected and fortunate discoveries

Word origins:
Sanskrit (first recorded use: 1754 (255 years ago))

Broader terms:
Serendipity | fluke | good fortune | good luck

Input interpretation:
Microsoft (MSFT) | Apple (AAPL)

Latest trades:
MSFT | $ 22.14 (lei 65.81) (MSFT | NASDAQ | Friday 8:10 pm EDT | 33 hours ago)
AAPL | $ 144.67 (lei 430.05) (AAPL | NASDAQ | Friday 8:10 pm EDT | 33 hours ago)

Fundamentals and financials:
| Microsoft | Apple
Market cap | $ 197 billion | $ 129.1 billion
Revenue | $ 61.17 billion | $ 33.69 billion
Employees | 91000 | 35100
Revenue / employee | $ 705 200 | $ 1.146 million
Net income | $ 15.82 billion | $ 5.018 billion
Shares outstanding | 8.9 billion | 892.1 million
Annual earnings / share | $ 1.75 | $ 5.30
P/E ratio | 12.65 | 27.3
Annual dividends / share | $ 0.48 |
Dividend yield | 2.37% |
(Based on trailing 12-month totals, last close price and annual employees)

Recent returns:
| Day | month | YTD | year | 5 year
MSFT | +1.42% | +11.87% | +13.89% | -21.77% | -16.23%
AAPL | +0.65% | +9.01% | +69.50% | -23.63% | +870.61%

Performance comparisons:
| Average daily return | daily volatility | annual return | annual volatility
MSFT | -0.060% | 3.38% | -13.92% | 53.60%
AAPL | -0.096% | 3.56% | -21.44% | 56.48%
SP500 | -0.137% | 2.88% | -29.07% | 45.62%
Bonds | +0.014% | 0.36% | +3.69% | 5.77%
T-bills | +0.003% | 0.00% | +0.63% | 0.00%

Mean-variance optimal portfolio:
| Weight | shares | cost
MSFT | 8.72% | 3939 | $ 87 210 (lei 259 200)
AAPL | 6.32% | 437 | $ 63 220 (lei 187 900)
SP500 | 16.17% | 1710 | $ 161 700 (lei 480 600)
Bonds | 34.21% | 342 | $ 342000 (lei 1.017 million)
T-bills | 34.58% | 346 | $ 346000 (lei 1.029 million)
(Amounts based on $1 million portfolio)
Optimal portfolio’s expected yearly return | 6.31%
Optimal portfolio’s yearly volatility | 8.45%

Definition:
Noun:
Exchange | the exchange of goods for an agreed sum of money
Promotion | the commercial processes involved in promoting and selling and distributing a product or service
Shopping | shopping at a market

Typical word frequency:
Written | 1/19000 (rank: 2007th) 100% noun
Spoken | 1/43000 (rank: 2193rd) 100% noun
(Based on the 100-million-word British National Corpus)

Synonyms:
Exchange | merchandising | selling

Narrower terms:
Bait and switch  |  bootlegging  |  capitalization  |  capitalization  |  channel  |  direct marketing  |  distribution channel  |  dumping  |  Dutch auction  |  hawking  |  peddling  |  private treaty  |  resale  |  retail  |  retailing  |  sale  |  syndication  |  telecommerce  |  telemarketing  |  teleselling  |  vending  |  vendition  |  wholesale

Broader terms:
Commerce | commercialism | mercantilism | shopping

Definitions:
Adjective:
Weather | towards the side exposed to wind
Noun:
Weather | the atmospheric conditions that comprise the state of the atmosphere in terms of temperature and wind and clouds and precipitation
Verb:
Angle | cause to slope
Crumble | change under the action or influence of the weather
Hold up | face and withstand with courage
Sail | sail to the windward of

Word origins:
Old English | Proto Germanic
(First recorded use: 1655 (354 years ago))

Typical word frequency:
Written | 1/18000 (rank: 1831st)
Spoken | 1/17000 (rank: 1089th)
(Based on the 100-million-word British National Corpus)

Synonyms:
Noun:
Weather | atmospheric condition | conditions | weather condition
Adjective:
Weather | upwind
Verb:
Hold up | brave | brave out | endure

Narrower terms:
Air current  |  atmosphere  |  atmospheric state  |  bad weather  |  cold weather  |  current of air  |  downfall  |  elements  |  fair weather  |  good weather  |  hot weather  |  inclemency  |  inclementness  |  precipitation  |  sunshine  |  temperateness  |  thaw  |  thawing  |  warming  |  wave  |  wind

Broader terms:
Angle  |  atmospheric phenomenon  |  crumble  |  decay  |  defy  |  dilapidate  |  hold  |  hold up  |  lean  |  sail  |  slant  |  tilt  |  tip  |  withstand

Input interpretation:
facebook.com (domain) | myspace.com (domain)

Registered hosts information:
| facebook.com | myspace.com

Organization:
| Facebook | Myspace.com
Location | San Jose, California, United States | Los Angeles, California, United States

Web statistics:
| facebook.com | myspace.com
Daily page views | ~~ 2.9 billion | ~~ 1.3 billion
Daily visitors | ~~ 270 million | ~~ 68 million
Site rank | 4th | 11th
Domain online | March 29, 1997 (12 years ago) | February 22, 1996 (13 years ago)
(Alexa estimates)

Mohamed Altoumaimi, a 16-year-old from Sweden, has found a solution to a 300-year-old mathematics formula. He explains and simplifies the so-called Bernoulli numbers, a sequence of calculations named after the 17th century Swiss mathematician Jacob Bernoulli.

Jacob is best known for the work Ars Conjectandi (1713). He describes the known results in probability theory and in enumeration, often providing alternative proofs of known results. This work also includes the application of probability theory to games of chance and his introduction of the theorem known as the law of large numbers.

In mathematics, the Bernoulli numbers are a sequence of rational numbers with deep connections to number theory.

According to WolframAlpha:
Bernoulli distribution | probability | p
Statistical properties:
Mean | p
Standard deviation | sqrt((1-p) p)
Variance | (1-p) p
Skewness | (1-2 p)/sqrt((1-p) p)
Kurtosis | (1-6 (1-p) p)/((1-p) p)+3