arq - computer sciencerlaz/files/arqmath-poster-v4.pdf · asked 7 years, 3 months ago active 2...
TRANSCRIPT
ARQMath Answer Retrieval for Questions on Math
https://www.cs.rit.edu/~dprl/ARQMath
Richard Zanibbi Douglas W. Oard Anurag AgarwalRochester Institute of Technology University of Maryland Rochester Institute of [email protected] [email protected] [email protected]
— Goals — Advance techniques for math-aware search and semantic analysis of mathematical notation and texts
— Collection — Math Stack Exchange community QA forum(~1.1 million questions)
— Formula Representations — Appearance: the arrangement of symbols on writing lines.• LaTeX• Presentation MathML
Semantic: operators, arguments, order of operations • Content MathML
Task 1: Finding Answers to Math QuestionsGiven a posted question as a query, search all answer posts and
return relevant answers.
Topics and Runs • Goal: Create 100 topics using questions containing text and at least one formula • Queries may be processed using either text, math, or both text and math• Manual and automatic runs will be collected
Evaluation • Top-k hits (e.g., top-20) + additional manual runs by organizers will be pooled
• Most topics assessed once, some doubly-assessed to check agreement• Assessors will include volunteers from teams, along with hired assessors
•
•
During assessment, we propose organizing topics into three sets: (1) all topics, (2) topics where the text seems to characterize the topic on its own, and (3) topics where the formula(s) seem to characterize the topic on their own.We propose using extended inferred Average Precision (xinfAP) over the three topic sets as the primary measure to support comparison with future systems that do not contribute to the judgement pool
Task 2: Formula SearchGiven a formula query from a question, search formulas in question and answer posts and return relevant formulas.
Topics and Runs • Goal: Create 50 topics using formulas extracted from topics in Task 1
• Formulas provided in LaTeX, Presentation MathML, and Content MathML• Annotators create human-readable narratives to define relevant formulas, e.g.,
subexpressions, alternative notation, simplification, applications in specific fields, etc.• Manual and automatic runs will be collected
Evaluation • Top-k formulas from participants + additional manual runs by organizers will be pooled
• Assessors can use formula hits + pools from Task 1 to identify similar formulas• Most topics assessed once some doubly-assessed to check agreement• Assessors include volunteers from teams along with hired assessors
• We propose using extended inferred Average Precision (xinfAP) over formula topicsas the primary measure for comparing systems
Key Dates 2019
Nov 1 Release data, sample queriesNov 5 Registration opens
2020 Jan 15 Test queries released May 1 Submissions close Aug 14 Final lab reportSep 22-25 ARQMath@CLEF 2020
#ARQMathPlease join us! Feedback
also appreciated! Email: [email protected]
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How can I evaluate ?(! + 1)∑∞!= 0 "!
Asked 8 years, 5 months ago Active 4 months ago 34k timesViewed
384
146
How can I evaluate
I know the answer thanks to , but I'm more concerned with how I can derivethat answer. It cites tests to prove that it is convergent, but my class has never learned thesebefore so I feel that there must be a simpler method.
∑!= 1
∞ 2!3!+ 1
Wolfram Alpha
In general, how can I evaluate
(! + 1) ?∑!= 0
∞"!
sequences-and-series convergence power-series faq
edited Sep 24 '17 at 12:09
Parcly Taxel51.7k 13 80 120
asked Apr 3 '11 at 21:41
Backus2,072 3 12 8
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Query Search Results
How can I evaluate ?(! + 1)∑∞!= 0 "!
Asked 8 years, 5 months ago Active 4 months ago 34k timesViewed
384
146
How can I evaluate
I know the answer thanks to , but I'm more concerned with how I can derivethat answer. It cites tests to prove that it is convergent, but my class has never learned thesebefore so I feel that there must be a simpler method.
∑!= 1
∞ 2!3!+ 1
Wolfram Alpha
In general, how can I evaluate
(! + 1) ?∑!= 0
∞"!
sequences-and-series convergence power-series faq
edited Sep 24 '17 at 12:09
Parcly Taxel51.7k 13 80 120
asked Apr 3 '11 at 21:41
Backus2,072 3 12 8
2–
I believe this is an arithmo-geometric series. You can find information here:artofproblemsolving.com/wiki/… Jason Kim Jul 7 '18 at 19:11
19 Answers
338
+150
No need to use Taylor series, this can be derived in a similar way to the formula forgeometric series. Let's find a general formula for the following sum:
= ! .#$ ∑!= 1
$%!
Notice that
−%#$ #$ = −$ +%$+ 1 ∑$
%!
…
…
…
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1
2
3
Query Search Results
Mathematics Stack Exchange is a questionand answer site for people studying math atany level and professionals in related fields. Itonly takes a minute to sign up.
Sign up to join this community
Anybody can ask a question
Anybody can answer
The best answers are voted up andrise to the top
How can I evaluate ?(! + 1)∑∞!= 0 "!
Asked 8 years, 5 months ago Active 4 months ago 34k timesViewed
384
146
How can I evaluate
I know the answer thanks to , but I'm more concerned with how I can derivethat answer. It cites tests to prove that it is convergent, but my class has never learned thesebefore so I feel that there must be a simpler method.
∑!= 1
∞ 2!3!+ 1
Wolfram Alpha
In general, how can I evaluate
(! + 1) ?∑!= 0
∞"!
sequences-and-series convergence power-series faq
edited Sep 24 '17 at 12:09
Parcly Taxel51.7k 13 80 120
asked Apr 3 '11 at 21:41
Backus2,072 3 12 8
By using our site, you acknowledge that you have read and understand our , ,
and our .
Cookie Policy Privacy Policy
Terms of Service
.
.
.
1
2
3
Mathematics Stack Exchange is a questionand answer site for people studying math atany level and professionals in related fields. Itonly takes a minute to sign up.
Sign up to join this community
Anybody can ask a question
Anybody can answer
The best answers are voted up andrise to the top
How can I evaluate ?(! + 1)∑∞!= 0 "!
Asked 8 years, 5 months ago Active 4 months ago 34k timesViewed
384
146
How can I evaluate
I know the answer thanks to , but I'm more concerned with how I can derivethat answer. It cites tests to prove that it is convergent, but my class has never learned thesebefore so I feel that there must be a simpler method.
∑!= 1
∞ 2!3!+ 1
Wolfram Alpha
In general, how can I evaluate
(! + 1) ?∑!= 0
∞"!
sequences-and-series convergence power-series faq
edited Sep 24 '17 at 12:09
Parcly Taxel51.7k 13 80 120
asked Apr 3 '11 at 21:41
Backus2,072 3 12 8
By using our site, you acknowledge that you have read and understand our , ,
and our .
Cookie Policy Privacy Policy
Terms of Service
Mathematics Stack Exchange is a questionand answer site for people studying math atany level and professionals in related fields. Itonly takes a minute to sign up.
Sign up to join this community
Anybody can ask a question
Anybody can answer
The best answers are voted up andrise to the top
How can I evaluate ?(! + 1)∑∞!= 0 "!
Asked 8 years, 5 months ago Active 4 months ago 34k timesViewed
384
146
How can I evaluate
I know the answer thanks to , but I'm more concerned with how I can derivethat answer. It cites tests to prove that it is convergent, but my class has never learned thesebefore so I feel that there must be a simpler method.
∑!= 1
∞ 2!3!+ 1
Wolfram Alpha
In general, how can I evaluate
(! + 1) ?∑!= 0
∞"!
sequences-and-series convergence power-series faq
edited Sep 24 '17 at 12:09
Parcly Taxel51.7k 13 80 120
asked Apr 3 '11 at 21:41
Backus2,072 3 12 8
By using our site, you acknowledge that you have read and understand our , ,
and our .
Cookie Policy Privacy Policy
Terms of Service
Mathematics Stack Exchange is a questionand answer site for people studying math atany level and professionals in related fields. Itonly takes a minute to sign up.
Sign up to join this community
Anybody can ask a question
Anybody can answer
The best answers are voted up andrise to the top
Evaluate the integral: d!∫ 10
ln(!+ 1)+ 1!2
Asked 7 years, 3 months ago Active 2 years, 7 months ago 20k timesViewed
87
53
Compute
d!∫1
0
ln(! + 1)+ 1!2
calculus real-analysis integration definite-integrals
edited Aug 29 '14 at 22:39
Ali Caglayan3,793 8 32 64
asked Jun 9 '12 at 7:49
user 135711323k 9 80 230
– wolfram gives the answer as 0.272198 user9413 Jun 9 '12 at 7:57
– Mathematica gives the answer . But I do not know how it computed this number...log 2"8 Siminore
Jun 9 '12 at 8:25
– @Chris: Even, i thought of that only :) user9413 Jun 9 '12 at 8:26
7
–
Why dont you try and solve these Integrals yourself. Browsing through your most recent questions,you have had this type of question almost exclusively. Other users get downvoted for this. I see noreason not to hint the same to you and at least show some effort. -1 CBenni Mar 20 '13 at 17:01
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